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Enhancement of the Performance and Data Processing Rate of an Optical Frequency Domain Reflectometer Distributed Sensing System Using A Limited Swept Wavelength Range Kunpeng Feng 1,2, *,† , Jiwen Cui 1, *,† , Yihua Jin 1,† , Xun Sun 1 , Dong Jiang 1,3 , Hong Dang 1 , Yizhao Niu 1 and Jiubin Tan 1 1

2 3

* †

Institute of Ultra-precision Optoelectronic Instrument Engineering, Science Park, Harbin Institute of Technology, Harbin 150080, China; [email protected] (Y.J.); [email protected] (X.S.); [email protected] (D.J.); [email protected] (H.D.); [email protected] (Y.N.); [email protected] (J.T.) Department of Automation, Harbin Engineering University, Harbin 150001, China Huawei Technologies Limited Company, Huawei Building, Beijing 100085, China Correspondence: [email protected] (K.F.); [email protected] (J.C.); Tel.: +86-451-8641-2041 (J.C.) These authors contributed equally to this work.

Received: 25 August 2018; Accepted: 11 October 2018; Published: 16 October 2018







Abstract: A novel optical frequency domain reflectometer (OFDR) processing algorithm is proposed to enhance the measurable range and data processing rate using a narrow swept spectrum range and reducing the time consuming of the process distributed sensing results. To reduce the swept wavelength range and simultaneously enhance strain measurable range, the local similarity characteristics of Rayleigh scattering fingerprint spectrum is discovered and a new similarity evaluation function based on least-square method is built to improve the data processing rate and sensing performance. By this method, the strain measurable range is raised to 3000 µε under a highest spatial resolution of 3 mm when the swept spectrum range is only 10 nm and the data processing rate is improved by at least 10 times. Experimental results indicate that a nonlinearity of less than 0.5%, a strain resolution of better than 10 µε, a repeatability at zero strain of below ±0.4 GHz and a full-scale accuracy is lower than 0.85 GHz under a highest spatial resolution of 3 mm can be achieved. Advantages of this method are fast processing rate, large strain measurable range, high SNR, and applicability with current OFDR systems. Keywords: distributed sensing; Rayleigh scattering; optical fiber; least-squares method

1. Introduction In the areas of non-destructive measurement and structural health monitor, optical frequency domain reflectometers (OFDRs) have been widely utilized for many years because of their excellent spatial resolution and high strain accuracy [1,2]. Over these years, OFDRs based on the Rayleigh scattering (RS) spectrum gave gradually received increasing attention with the progress of the investigation of Rayleigh backscatter spectra in optical fibers. Rayleigh backscatter in optical fibers is induced by the fluctuations of the index of refraction profile along the fiber. The RS spectrum, just like a “fingerprint”, is stable and unique once the fiber is manufactured [3]. Also, a relation between the measurable strain of the fiber gauge and the inerratic fingerprint spectrum shift has been established for distributed strain sensing [4]. The spectrum shift is usually achieved by combining OFDR with cross-correlation of the RS fingerprint spectra. Thus, even a common single mode fiber (SMF) without FBGs can be employed as a distributed sensor [3,5].

Sensors 2018, 18, 3480; doi:10.3390/s18103480

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However, in practice, the sensing accuracy of distributed strain, even the feasibility of this method is based on the similarity between RS reference spectrum (ReS, with known distributed strain) and RS measurement spectrum (MeS, with unknown distributed strain). Furthermore, the swept spectrum range should be expanded to enhance the measurable strain range. The data processing rate is thus limited by the sweep time and large amount of data. Otherwise, the similarity will significantly degenerate when the loaded strain is over 1000 µε and swept wavelength range is 10 nm once the spatial resolution is downwards to several mm and spectrum resolution is downwards to several pm. With the degeneration of the similarity, fake peaks or multi-peaks start to appear in the cross-correlation results, which would yield mistakes in calculating spectrum shifts. OFDR based on RS fingerprint spectrum which can measure a distributed strain larger than 1000 µε and the swept range is less than 20 nm was rarely reported, especially under a high spatial resolution downwards to mm-level [6]. On the other hand, the Pearson correlation coefficient should be employed to evaluate the similarity between ReS and MeS. In this process, the conventional evaluation function is performed and it is very time-consuming when processing distributed sensing data of high spatial resolution and a long measurable range. The real-time performance needs to be improved. In this paper, a novel OFDR processing algorithm is proposed to enhance the measurable strain range and data processing rate with a limited swept wavelength range of 10 nm. The strain is related to the spectrum shift. The motivation of this work is to solve the problem of invalidation of the conventional method when measuring a large strain and the failure to find the true cross-correlation peak when the sweep is insufficient. First, the degeneration mechanism of RS spectrum similarity is investigated and the local similarity characteristics of the RS fingerprint spectrum are discovered to improve the similarity between ReS and MeS under a large strain. Then, a new similarity evaluating function based on the least-squares method is built to replace the Pearson correlation coefficient and the calculation amount is significantly decreased. By combining these two variations, the proposed OFDR method matches the local ReS on the MeS to find the most similar MeS segment wherein the least-square method is employed to evaluate similarity. Therefore, a higher SNR during the determination of the spectrum shift and a faster data processing rate can be achieved. Experimental results indicate that SNR is improved from 1~2 to 2~12 and the data processing rate is 10 times faster than with the current method. The measurable strain range of the proposed method is improved up to 3000 µε (limited by maximum stretch of optical fiber) and the nonlinearity is less than 0.5% under a highest spatial resolution downwards to 3 mm. The strain resolution is better than 10 µε, the repeatability at zero strain is below ±0.4 GHz and the full-scale accuracy is less than 0.85 GHz under a highest spatial resolution of 3 mm, which is better than that of LUNA ODiSI-B representing the leading level of OFDR. 2. Sensing Principle 2.1. The Degeneration Mechanism of the RS Spectrum Similarity and the Local Similarity Characteristics Monitoring the RS spectrum of the sensing fiber is commonly utilized to sense variations of the distributed strain along the sensing fiber in conventional OFDR methods. That is based on the characteristics of the sensing fiber that RS spectrum remains stable and unique once the fiber was manufactured and is only influenced by variations of the temperature or strain [7]. RS spectrum is induced by random fluctuation of the refractive index in the fiber, and its properties are similar to the fiber Bragg grating (FBG). Therefore, the RS can be considered as the weak random Bragg grating [3]. As the FBG’s spectrum varies with the loaded strain, the external strain also causes a shift of the RS spectrum. The ratio of spectrum shifts to strain variations is usually constant for a specific fiber. Thus, distributed strain sensing can be accomplished by monitoring the RS spectrum shift of the measured gauge. In the OFDR system, a tunable laser source working in linear-frequency-sweeping mode is utilized to demodulate the position information and distributed strain of every gauge. The beat signal

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In the OFDR system, a tunable laser source working in linear-frequency-sweeping mode is utilized to the demodulate the local position information and distributed strain of linear every frequency gauge. Theswept beat consists of RS light and oscillator light. Based on properties of the signal consists ofrelationship the RS light between and localthe oscillator onfrequency propertiesisofdirectly the linear frequency light source, the positionlight. and Based the beat proportional. swept light source,information the relationship betweenthrough the position and the beat from frequency is directly Therefore, position can be achieved transforming signals time-domain into proportional. Therefore, position information can beAccordingly, achieved through transforming signals from frequency-domain using fast Fourier transform (FFT). the RS spectrum located at different time-domain into frequency-domain using fast transform Fourier transform (FFT). Accordingly, the the RS positions can be extracted by a short-time Fourier (STFT). The spatial resolution and spectrum located at different positions can be extracted by a short-time Fourier transform (STFT). measured gauge position are controlled by setting the length and center position of the window of The and the measured position are shift controlled bythe setting the length and STFT.spatial Then, resolution the cross-correlation is used to gauge calculate spectrum between MeS (with unknown center position of the window of STFT. Then, the cross-correlation is used to calculate spectrum distributed strain) and the ReS (with known distributed strain). The achieved corresponding spectrum shift between the MeS (with unknown distributed strain) the ReSstrain (withofknown distributed shift is proportional to the distributed strain. Theoretically, theand distributed the whole sensing strain). achieved corresponding spectrum shift is proportional to the distributed fiber canThe be obtained by performing the STFT and the cross-correlation on every measured gaugestrain. along Theoretically, the distributed strain of the whole sensing fiber can be obtained by performing the the fiber. The conventional OFDR method is illustrated in Figure 1. The cross-correlation between STFTi and the cross-correlation onas: every measured gauge along the fiber. The conventional OFDR WRS and WMS i can be expressed method is illustrated in Figure 1. The cross-correlation between WRSi and WMSi can be expressed as: 2N −1

R(n) =2 N -1 WRSi (m)·WMSi (m + n) R (n) = å∑ WRSi ( m) ⋅ WMSi (m + n) m =0

(1) (1)

m =0

where, N, −N −N++1,1,…, . . . N, N− − 1, N the lengthofofthe theWRS WRSi and WMSi isequences, sequences,and and the the elements elements i andWMS where, nn == − −N, 1, N is is the length WRS and WMS sequences are zeros when the index is not within [0, N]. WRS and WMS sequences are zeros when the index is not within [0, N].

Figure 1. 1. The conventional OFDR OFDR method. method. OFDR: optical frequency-domain frequency-domain The flow flow diagram of conventional reflectometry; Sr(t):the thereference referenceOFDR OFDR signal; Rr(l) reference OFDR reflectivity reflectometry; Sr(t): signal; Rr(l) the the reference OFDR reflectivity signal;signal; WRSi: WRSi: whole whole reference spectrum of i-th fiber gauge; Sm(t): the measurement OFDR Rm(l) the reference spectrum of i-th fiber gauge; Sm(t): the measurement OFDR signal; Rm(l)signal; the meaurement OFDR reflectivity signal; WMSi:signal; wholeWMSi: measurement spectrum of i-th fiber gauge. meaurement OFDR reflectivity whole measurement spectrum of i-th fiber gauge.

The swept The swept spectrum spectrum range range should should be be expanded expanded to to enhance enhance the the strain strain measurable measurable range range which which would induce a long sweep time and large amount of data. However, a broad swept spectrum range would induce a long sweep time and large amount of data. However, a broad swept spectrum would limit the data processing and occupy a big memory when a high spectrum or strain/temperature range would limit the data processing and occupy a big memory when a high spectrum or resolution is required. When theisswept spectrum is B1 and the spectrum suffered strain/temperature resolution required. Whenrange the swept spectrum rangeshift is B1induced and thebyspectrum strain is S , the different spectrum percentage between ReS and MeS is written as: 1 shift induced by suffered strain is S1, the different spectrum percentage between ReS and MeS is

written as:

B − S1 p= 1 × 100% (2) B1 - B S11 ´100% p= (2) B1 The positive and negative shift of the reference spectrum is equivalent. So the positive is taken as an example to investigate the influence new segments. The spectrum is R(n) (wherein, The positive and negative shift of of thethe reference spectrum is reference equivalent. So the positive is taken n =an 1, 2, 3, . . . , K) the measurement spectrum can be expressed as: as example toand investigate the influence of theMnew segments. The reference spectrum is R(n) i (wherein, n = 1, 2, 3, …, K) and the measurement spectrum Mi can be expressed as: Mi = [ Ni (m), R(n + m)] (3) M i = [ N i (m), R(n + m)] (3)

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where, Ni(n) is the new spectrum segment, n = 1, 2, 3, …, K − m, m is the spectrum shift, and m ≤ where, Ni(n) is the new spectrum segment, n = 1, 2, 3, …, K − m, m is the spectrum shift, and m ≤ 0.5K. where, 0.5K. Ni (n) is the new spectrum segment, n = 1, 2, 3, . . . , K − m, m is the spectrum shift, and m ≤ 0.5K. Then, simulation simulation is is run run to to investigate investigate the the influence influence of of the the parameter parameter pp on on finding finding the the true true peak peak Then, representing the the spectrum spectrum shift. shift. In the the simulation, simulation, experimental experimental results of 180 180 reference reference spectra spectra are are representing In results of statistically analyzed and new spectrum segments is randomly selected in the reference spectra statistically spectrum segments is randomly selected in the in reference spectra spectra (except statistically analyzed analyzedand andnew new spectrum segments is randomly selected the reference (except thereference current spectrum). reference Figure spectrum). Figure 2 the demonstrates the statistical results ratio of the the current 2 demonstrates statistical results of the amplitude of (except the current reference spectrum). Figure 2 demonstrates the statistical results of the amplitude ratio of the peak to highest peak when the parameter p varies from 0 to 50% with a 10% the peak to ratio highest when parameter variesthe from 0 to 50% pwith a 10% step and thewith simulation amplitude of peak the peak tothe highest peak pwhen parameter varies from 0 to 50% a 10% step and the simulation issame run 180 times under same condition. Figure 2 demonstrates the results is runand 180the times under ais condition. Figureaa 2same demonstrates results of 180 times the andresults every step simulation run 180 times under condition.the Figure 2 demonstrates of 180 times and every curve represents an experiment. It can be concluded that the curve an experiment. It can be concluded the cross-correlation is valid of 180represents times and every curve represents an that experiment. It can be method concluded thatwhen the cross-correlation method is valid when the ratio ishighest greater than 1 because the true peak is the the ratio is greatermethod than 1 because true peak is theis and it can be determined by this cross-correlation is validthewhen the ratio greater than 1 because the true peakmethod. is the highest and it can be determined by this method. Figure 2 indicates that the cross-correlation Figure 2 indicates that the cross-correlation method is invalid when the different spectrum percentage highest and it can be determined by this method. Figure 2 indicates that the cross-correlation method is invalid when the different spectrum percentage between ReS and MeS is over ~13%. So between and MeS is the overdifferent ~13%. So the measurable strain is less than ~1100 µε is when swept method isReS invalid when spectrum percentage between ReS and MeS overthe ~13%. So the measurable strain is less than ~1100 µε when the swept spectrum range is 10 nm. spectrum range strain is 10 nm. the measurable is less than ~1100 µε when the swept spectrum range is 10 nm.

Figure 2. Statistical results of the influence of the parameter p on finding the true peak representing Figure 2. Statistical results of the influence of the parameter p on finding the true peak peak representing representing the spectrum shift. the spectrum shift.

This physical description is demonstrated in Figure and ititindicates that the MeS (0(0µε) has This description is is demonstrated demonstratedin inFigure Figure333and andit indicatesthat thatthe theMeS MeS(0 µε)has hasaa This physical physical description indicates µε) high similarity with the ReS (0 µε), however, the original MeS shifts relative to the ReS when the ahigh highsimilarity similaritywith withthe theReS ReS(0(0µε), µε),however, however,the theoriginal originalMeS MeS shifts shifts relative relative to to the the ReS ReS when when the the strain is loaded on the sensing fiber. New spectrum segment appears in the MeS spectrum and it strain spectrum segment appears in the MeSMeS spectrum andand it has strain is is loaded loadedon onthe thesensing sensingfiber. fiber.New New spectrum segment appears in the spectrum it has no corresponding similar spectrum segment in the ReS. The spectrum shift under a small strain no similar spectrum segment in the The spectrum shift shift under a small strainstrain load hascorresponding no corresponding similar spectrum segment inReS. the ReS. The spectrum under a small load is relatively small, so that the proportion of new spectrum is not large enough to cause is relatively small, small, so thatso thethat proportion of new spectrum is not large to enough cause significant load is relatively the proportion of new spectrum is enough not large to cause significantdegeneration. similarity degeneration. Therefore, it can that be deduced that the low similarity between the similarity Therefore, it can be deduced the low similarity between the MeS and the significant similarity degeneration. Therefore, it can be deduced that the low similarity between the MeS and the ReS is owingspectrum to the large spectrum shift induced by the large strain. ReS owing to the shiftspectrum induced shift by the large strain. MeSisand the ReS is large owing to the large induced by the large strain.

Figure Figure 3. 3. Schematic of the reason for the degeneration of similarity between MeS and ReS caused by Figure 3. Schematic of the reason for the degeneration of similarity between MeS and ReS caused by the the distributed distributed strain. strain. the distributed strain.

The experimental data datain inFigure Figure4 4are arederived derived from distributed strain experiments in which The experimental from distributed strain experiments in which the The experimental data in Figure 4 areµε derived from distributed strain spectrum experiments in which the the strain loads are 700 µε, 1300 µε, 2100 and 2300 µε when the swept range is nm. 10 nm. strain loads are 700 µε, 1300 µε, 2100 µε and 2300 µε when the swept spectrum range is 10 In strain loadshowever, are 700 µε, 1300 µε, 2100 µε andwell 2300when µε when the swept strain spectrum rangeExperimental is 10 nm. In In practice, this method onlyworks works thedistributed distributed is small. small. practice, however, this method only well when the strain is Experimental practice, however, this method only works well when the distributed strain is small. Experimental results results indicate indicate that that SNR SNR of of the the cross-correlation cross-correlation result result degenerates degenerates significantly significantly and and multi multi or or fake fake results indicate that SNR of the cross-correlation result degenerates significantly andstrain multiexceeds or fake peaks begin to appear in the cross-correlation results when the loaded distributed peaks begin to appear in the cross-correlation results when the loaded distributed strain exceeds peaksµε. begin to appear in the cross-correlation results when the loaded distributed strain exceeds 1000 1000 µε. 1000 µε. In conventional OFDR methods, spectrum shifts are calculated by true peaks’ position in In conventional OFDR methods, spectrum shifts are calculated by true peaks’ position in cross-correlation results. Under a small strain load, the true peak is usually unique and keeps cross-correlation results. Under a small strain load, the true peak is usually unique and keeps highest amplitude. Figure 4a shows the ideal cross-correlation result and the true peak is unique highest amplitude. Figure 4a shows the ideal cross-correlation result and the true peak is unique

ideal cross-correlation results exceeds 0.8, while the highest peaks of multi and fake peaks are lower than 0.2. Therefore, it can be concluded that the appearance of multi and fake peaks is mainly caused by the degeneration of similarity between the MeS and ReS. With the increase of the loaded strain, the similarity between the MeS and ReS decreases significantly, and multi and fake peaks begin to appear Sensors 2018, 18, 3480in cross-correlation results. Finally, the determination of the spectrum shift is 5 ofno 17 more robust and becomes inaccurate. The strain measurable range of OFDR is thus limited.

(a)

(b)

(c)

(d)

Figure Figure 4. 4. Cross-correlation Cross-correlation results results between between ReS ReS and and MeS MeS under under different different strain strain load. load. (a) (a) the the single single peak peak under under aa strain strain of of 700 700 µε. µε. (b) (b)multi-peaks multi-peaks under under aa strain strain of of 1300 1300 µε. µε. (c) (c)multi-peaks multi-peaks under under aastrain strain of 2100 2100 µε. µε. (d) (d) the the fake fake peak peak under under aa strain strain of of 2300 2300 µε. µε. of

In conventional OFDR methods, shifts areis calculated by GHz) true peaks’ in During the experiments, the sweep spectrum wavelength range 10 nm (~1200 and theposition spectrum cross-correlation results. a small load,spectrum the true peak is usually unique and keeps highest shift caused by 3000 µε isUnder ~3.8nm. Thus,strain the new without similarity accounts for ~38% of amplitude. Figure 4a shows the ideal cross-correlation result and the true peak is unique and highest. the ReS under a strain of 3000 µε, which will result in a significant decrease of similarity between Figure shows that and therethe areappearance multiple peaks in the cross-correlation and this will make the the the MeS4b,c and the ReS of multiple or fake peaks.result In summary, avoiding determination the trueand peak difficult. 4d shows refer of to that therespectrum are some appearance of of multiple fake peaks Figure is mainly to rulethat outfake thepeaks influence the new peaks which are higher than the true peak and will lead to wrong determination of the spectrum shifts. segment. On the other hand, there exists a section of MeS spectrum always located in the ReS. As Based on the experimental data,spectrum peaks in cross-correlation results areoriginal relatively lower when or illustrated in Figure 3, the local is defined as a part of the ReS, which willmulti remain fake appear. As illustrated in have Figurehigh 3, the highest peak in the ideal in thepeaks latterbegin MeS to (after loading strain) and similarity to a segment of cross-correlation the MeS. So the results exceedsof0.8, the highest of multi and fake are lower 0.2. Therefore, can improvement thewhile similarity can bepeaks achieved through the peaks utilization of thethan local spectrum of ithigh be concluded the appearance of multi fake peaks is mainly causedavoided by the degeneration of similarity. Thethat appearance of multiple andand fake peaks can be effectively under a large similarity between the MeS and ReS. With the increase of the loaded strain, the similarity between the strain load. MeSFigure and ReS decreases significantly, and fake peaks begin to appear in cross-correlation 5 illustrates the MeS and and ReS multi of a distributed sensing gauge in 3 mm length under a results. of the spectrum is no(marked more robust andpurple becomes strain of Finally, 1000 µεthe anddetermination it indicates that a segment of shift the MeS in solid line)inaccurate. has high The strain measurable range of OFDR is thus limited. similarity with the shifted ReS segment (marked in solid blue line), even though it is hard to During the experiments, the sweep range is 10 nm(marked (~1200 GHz) and the spectrum identify the similarity and spectrum shiftwavelength between the whole MeS in dotted purple line) shift caused by 3000 µε is ~3.8nm. Thus, the new spectrum without similarity accounts for ~38% of the ReS under a strain of 3000 µε, which will result in a significant decrease of similarity between the MeS and the ReS and the appearance of multiple or fake peaks. In summary, avoiding the appearance of multiple and fake peaks is mainly to rule out the influence of the new spectrum segment. On the other hand, there exists a section of MeS spectrum always located in the ReS. As illustrated in Figure 3, the local spectrum is defined as a part of the original ReS, which will remain in the latter MeS (after loading strain) and have high similarity to a segment of the MeS. So the improvement of the similarity can be achieved through the utilization of the local spectrum of high similarity. The appearance of multiple and fake peaks can be effectively avoided under a large strain load.

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Figure 5 illustrates MeS and ReS of a distributed sensing gauge in 3 mm length under a strain Sensors 2018, 18, x FOR PEERthe REVIEW 6 of 17 of 1000 µε and it indicates that Sensors 2018, 18, x FOR PEER REVIEWa segment of the MeS (marked in solid purple line) has high similarity 6 of 17 with ReSinsegment (marked in solid blue line), it is hard similarity to identifycharacteristics the similarity and the ReSshifted (marked dotted purple line). Therefore, theeven highthough local spectrum and spectrum shiftinbetween the whole MeS (marked the in dotted purple line) and ReS (marked in dotted ReS (marked dotted purple line). Therefore, high local spectrum similarity characteristics are experimentally verified. purple line). Therefore, the high local spectrum similarity characteristics are experimentally verified. are experimentally verified.

Figure 5. Schematic of local spectrum similarity characteristics. WRS: whole reference spectrum; WMS: 5. measurement spectrum; LRS: local reference WRS: spectrum; matched local 5.whole Schematic of local spectrum similarity characteristics. whole reference spectrum; Figure similarity characteristics. WRS: wholeLMS: reference measurement spectrum; ∆λ: thespectrum; corresponding spectrum shift. WMS: wholemeasurement measurement LRS:reference local reference spectrum; LMS: local WMS: whole spectrum; LRS: local spectrum; LMS: matched localmatched measurement spectrum; ∆λ: spectrum; the corresponding spectrum shift.spectrum shift. measurement ∆λ: the corresponding

During this experiment, a segment of ReS is selected as the local ReS (LRS) and the During experiment, a segment of selected as the is local (LRS) and corresponding During this thislocal experiment, a with segment ofis ReS is selected as ReS theby local ReSthe(LRS) and the corresponding MeS (LMS) theReS highest similarity found comparing the similarity local MeS (LMS) with the highest similarity is found by comparing the LRS corresponding local (LMS) highest similarity is foundthe byissimilarity comparing similarity among the LRS andMeS each LMS.with Thethe Pearson correlation coefficient utilized among tothe evaluate the and each LMS. The Pearson correlation coefficient is utilized to evaluate the similarity. Then, among the Then, LRS and each LMS. Thespectrum Pearson shift correlation coefficientbyisthe utilized to evaluate the similarity. the corresponding can be achieved wavelength difference the corresponding spectrum shift can be achieved by wavelength between thewhole LRS similarity. Then, corresponding spectrum shift canthe bethe achieved bydifference the wavelength between the LRSthe and the matched LMS. Figure 6 shows cross-correlation results of difference the and the and matched Figure 6 shows cross-correlation results of the whole spectra and local between the local LRS LMS. and the matched LMS.the Figure 6 indicate shows the cross-correlation results of the spectra spectra. The comparison results that the cross-correlation result of whole whole spectra. The comparison results indicate that the cross-correlation result of whole spectra has fakeis spectra localpeaks spectra. indicate the cross-correlation result of whole spectra and has fake andThe thecomparison similarity isresults lower than 0.25.that However, a single peak of a high SNR peaks and the similarity is lower than 0.25. However, a single peak of a high SNR is achieved through spectra hasthrough fake peaks and the similarityofisthe lower than 0.25. and However, a single is peak a highisSNR is achieved the cross-correlation local spectra the similarity ~0.8ofwhich raised the cross-correlation of the local spectra and the similarity is ~0.8 which is raised by 4-fold. It is achieved the cross-correlation of the local spectra thespectrum similaritysimilarity is ~0.8 which is raised by 4-fold.through It is experimentally verified that utilization of theand local characteristics experimentally verified that ofofthe localand spectrum similarity characteristics can effectively by It is experimentally verified that utilization of thepeaks, local spectrum similarity characteristics can4-fold. effectively suppress the utilization appearance multi fake and improve the similarity and the suppress thecross-correlation appearance of appearance multi andsofake peaks, improve the similarity and the SNRand of the can suppress the of multi andand fake peaks, improve the similarity the SNReffectively of the results, this method can achieveand a higher strain measurable range cross-correlation results, so this method can achieve a higher strain measurable range using a narrow SNR cross-correlation results, so this method can achieve a higher strain measurable range usingofa the narrow swept spectrum range. swept range.spectrum range. using aspectrum narrow swept

(a) (a)

(b) (b)

Figure6.6.Comparison Comparison between cross-correlation using different algorithms. Whole Figure between cross-correlation resultsresults using different algorithms. (a) Whole(a) spectrum spectrum algorithm. (b) Local spectrum (LS) algorithm. Figure 6. (WS) Comparison cross-correlation results using different algorithms. (a) Whole (WS) algorithm. (b) Localbetween spectrum (LS) algorithm. spectrum (WS) algorithm. (b) Local spectrum (LS) algorithm.

2.2. 2.2. The T.heSimilarity SimilarityEvaluation EvaluationFunction FunctionBased Basedononthe theLeast-Square Least-SquareMethod Method 2.2. T.he Similarity Evaluation Function Based on the Least-Square Method Based local similarity similarity characteristics characteristicsofofthe theRSRSspectrum, spectrum, spectrum shift between Based on on the the local thethe spectrum shift between the the LRS and LMS can be achieved through matching the LRS of the highest similarity in on the local characteristics of thethe RSLRS spectrum, spectrum shift between the LRS Based and LMS can be similarity achieved through matching of the the highest similarity in the the MeS. MeS. Therefore, similarity evaluating determines the accuracy of the achieved spectrum shiftMeS. and LRS and LMS can be achievedfunction through matching thethe LRS of the highest similarity in the Therefore, similarity evaluating function determines accuracy of the achieved spectrum shift data rate. rate. In conventional OFDR methods, the of similarity is onshift Therefore, similarity evaluating function determines the evaluation accuracy ofcriterion thecriterion achieved and processing data processing In conventional OFDR methods, the evaluation of spectrum similarity isthe on

and rate. Incorrelation conventional OFDR methods, the evaluation criterion of similarity on the data basisprocessing of the Pearson coefficient. The Pearson correlation coefficient cannot isfully the basisthe oftrend the Pearson Theit Pearson cannot fully express betweencorrelation the LRS andcoefficient. LMS because is only a correlation measure of coefficient the linear correlation [8]. express trend between the LRS and LMS because it is maintain only a measure of the linear correlation Besides,thethe Pearson correlation coefficient cannot a high performance when [8]. the Besides, the Pearson correlation coefficient cannot maintain a high performance when the

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basis of the Pearson correlation coefficient. The Pearson correlation coefficient cannot fully express the trend between the LRS and LMS because it is only a measure of the linear correlation [8]. Besides, the Pearson correlation coefficient cannot maintain a high performance when the distributed strain is over 2000 µε, even if the similarity is improved by local spectrum characteristics. Multiple and fake peaks will appear in the similarity evaluation results and affect matching the LRS on the MeS, so the similarity evaluating function must be researched and improved. The cross-correlation is invalid in measuring a larger strain, so similarity between reference and measurement spectra is used to find their shift. In the conventional method, the Pearson correlation coefficient can reflect the correlation or similarity between two signals. The sequence shift represents spectrum shift. The Pearson correlation coefficient is written as: cov(yLRSi , yLMSj ) (4) r (yLRSi , yLMSj ) = r i   h var yLRSi var yLMSj   where, cov(yLRSi , yLMSj ) is the covariance of spectra sequences yLRSi and yLMSj ; var yLRSi and h i var yLMSj are the variance of spectra sequences yLRSi and yLMSj . The least squares function is usually utilized to evaluate the approximating degree of two curves and achieve the fitting function [9,10]. On the other hand, the least squares function can also represent the Euclidean distance between two curves. In the match of the LRS in the LMS, the trend of these two spectra is more considerable and the least squares function is therefore more suitable for evaluating the spectrum similarity. It can be concluded that when the residual sum of squares reaches the lowest, the trend bias between spectra is smallest. A similarity evaluation function based on the least-square method is thus proposed. Furthermore, there are two factors need to be taken into consideration for the practical application: (1) the similarity between each LMS and a fixed LRS is needed to be evaluated and compared; (2) two local spectrum segments with a large amplitude difference may influence similarity evaluation badly. Therefore, normalization operation is needed before each evaluation function. The similarity evaluation function is constructed by residual sum of squares between normalized LMS and LRS: n− j

v( j) =

∑ [y LRS (i) − y LMS (i + j)]2

(5)

i =1

wherein, yLRS (i ) and yLMS (i ) are the local spectrum sequences and the sequence length is n (note: the data is discrete and variables of the above function are also discrete). The sum of the squares of the residuals v between the fixed LRS and each LMS can be considered as a similarity index in the matching procedure. The value of v reaches its minimum when the most similar spectrum is matched. Next, the performances of the similarity evaluation function based on the Pearson correlation coefficient and the least squares function are compared experimentally. Experiments on processing rate are conducted firstly. The time consumption of the two evaluation functions in MATLAB is compared when processing the data amount ranges from 1000 to 10,000. Figure 7 shows the comparison results and it indicates that the processing rate of the similarity evaluation function based on the least squares is at least 10 times faster. Furthermore, the evaluation method based on the least squares takes more advantage in terms of the growth rate of time consumption to data amount, which has benefits on processing the distributed sensing of a high density and resolution. Subsequently, the performance of the two evaluation functions on improving the similarity is compared experimentally. SNR is taken as the index for comparing the similarity improvement achieved by the different methods. The definition of SNR for the conventional evaluation function is the amplitude ratio of the highest peak to the secondary peak in the cross-correlation results wherein the highest peak represents the available spectrum shift signal and the secondary peak represents the noise signal. According to this definition, SNR of the whole and local spectrum cross-correlation result in Figure 6 is respectively ~1.1 and ~3.1. By employing the local spectrum similarity characteristics,

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the SNR raised by 3-fold. Sensors 2018,is18, x FOR PEER REVIEWConsidering Sensors 2018, 18, x FOR PEER REVIEW

the true peak value is the minimum sum of squares 8 of of 17 8 of 17 residuals, the definition of SNR of the latter method is the ratio of the secondary lowest peak amplitude to the lowest amplitude. Figurefunction 8 illustrates on the least method basedpeak on the least squares andthe theresult SNR of is the overmethod than 7.based The similarity is squares further method based on the least squares function and the SNR is over than 7. The similarity is further function and SNR is over than 7. The similarity is further improved by 2-fold through combining improved bythe 2-fold through combining the local spectrum similarity characteristics with the improved by 2-fold through combining the local spectrum similarity characteristics with the evaluation methodsimilarity based oncharacteristics the least squares function, so the improvement proposed the local spectrum with the evaluation method based on of thethe least squares evaluation method based on the least squares function, so the improvement of the proposed method can be experimentally verified. function,on sothe thesimilarity improvement of the proposed method on the similarity can be experimentally verified. method on the similarity can be experimentally verified.

Figure 7.7. Comparison time consumption between evaluation function based on least-squares method Figure Comparisonofof time consumption between evaluation function based on least-squares Figure 7. Comparison of timeonconsumption between evaluation function based on least-squares and evaluation function based Pearson correlation coefficients. method and evaluation function based on Pearson correlation coefficients. method and evaluation function based on Pearson correlation coefficients.

Figure 8. The diagram of the residual sum of squares between the fixed local ReS and each local MeS. Figure 8. The The diagram diagramof ofthe theresidual residualsum sumofofsquares squaresbetween betweenthe thefixed fixedlocal localReS ReSand andeach eachlocal local MeS. MeS.

2.3. The 2.3. The Proposed Proposed OFDR OFDR Method Method 2.3. The Proposed OFDR Method The combinationbetween between local spectrum similarity characteristics with the evaluation The combination thethe local spectrum similarity characteristics with the evaluation method The combination between the local spectrum similarity characteristics with the evaluation method based on the least squares function would enhance the similarity under a large distributed based onbased the least squares enhance similarity under a large distributed strain and method on the leastfunction squares would function wouldthe enhance the similarity under a large distributed strain and the rate. processing rate.processing An OFDRalgorithm processing algorithm is thus proposeda for achieving a the processing An OFDR is thus proposed for achieving high speed and strain and the processing rate. An OFDR processing algorithm is thus proposed for achieving a high speed and arange largeofmeasurable range of sensing. the distributed strain procedures sensing. The algorithm a large measurable the distributed strain The algorithm are illustrated high speed and a large measurable range of the distributed strain sensing. The algorithm procedures are illustrated in Figure 9 and the processing as followsand (note: the dataofisthe discrete and in Figure 9 and the processing is as follows (note: the datais variables following procedures are illustrated in Figure 9 and the processing isisasdiscrete follows (note: the data is discrete and variables of the are also discrete): function alsofollowing discrete):function variablesare of the following function are also discrete): (1) Sample OFDR signal Sr (t ) in a SMF in unstressed status or under a known distributed strain (1) Sample Sample OFDR signal a SMF in in unstressed status or under a known distributed strain and a SMF unstressed status or under a known distributed strain signal SS r (r t()t )inin and save itthe as reference the reference OFDR signal. save it as OFDR signal. and save it as the reference OFDR signal. S (t ) into distance domain and achieve the reflectivity (2) Transform the reference OFDR signal (2) Transform Transform the the reference reference OFDR OFDR signal signal SSrrr (t )) into into distance distance domain domain and achieve the reflectivity R ( l ) along the SMF via FFT. signal r( l ) along signal R the SMF via FFT. signal Rrr ( ) along the SMF via FFT. (l ) located a certain position wherein data length determines (3) Extract signal data data R (3) Extract the the i-th i-th signal at at a certain position wherein data length determines the ririri( l()l )located located at a certain position wherein data length determines (3) Extract the i-th signal data RR the spatial resolution of the fiber gauge. spatial resolution of the fiber gauge. the spatial resolution of the fiber gauge. (l ) to (l ) offsetting (4) Add to RR achieve for offsetting theofloss of spectral resolution which is (4) Add zeros zeros achieve Zri (Z the loss spectral resolution which is caused riri( l()l )toto Zl )riri for (l ) for offsetting (4) Add zeros to to R achieve the loss of spectral resolution which is ri caused by the data extraction. zero is number is determined byspectrum selected or spectrum or strain by the data extraction. The zeroThe number determined by selected strain resolution. caused by the data extraction. The zero number is determined by selected spectrum or strain resolution. Theresolution spectrumisresolution calculated dividing experimental spectrum The spectrum calculatedisby dividing by experimental spectrum range by the range lengthby of resolution. The spectrum resolution is calculated by dividing experimental spectrum range by the of Z ri (l ) . Zri (length l ). the length of Z ri (l ) . into spectrum domain and achieve the of WRSi of fiber the gauge i-th fiber gauge (5) Transform Transform ZZ ri((ll)) into spectrum domain and achieve the WRSi the i-th via STFT. (5) Transform Zriri (l ) into spectrum domain and achieve the WRSi of the i-th fiber gauge via STFT. via STFT. (6) Save a segment located at a certain position of each WRSi as LRSi and the length of the (6) Save a segment located at a certain position of each WRSi as LRSi and the length of the segment is N. segment is N.

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(7) Sample OFDR signal Sm (t ) under with unknown distributed strain as the measurement 9 of 17 OFDR signal. (8) Transform measurement OFDR signal Sm(t) into the distance domain and achieve the reflectivity signal Rm(l) along the SMF via FFT. (6) Save a segment located at a certain position of each WRSi as LRSi and the length of the segment R ( l ) (9) is Extract located at a certain position wherein data length determines N. the i-th signal data mi the spatial resolution fiber gauge. (7) Sample OFDR signalofSthe m ( t ) under with unknown distributed strain as the measurement (10) OFDR Add zeros to Rmi (l ) to achieve Z mi (l ) . signal. Z mi (l ) into the spectrum and WMSiand of the i-th fiber gauge via (11) Transform Transform measurement (8) OFDR signal domain Sm (t) into theachieve distancethe domain achieve the reflectivity Sensors 2018, 18, 3480

STFT. Rm (l) along the SMF via FFT. signal (12) Extract Match the i-th LRSisignal withdata the Rmost similar at spectrum of the WMSi by searching the (9) a certainsegment position wherein data length determines mi ( l ) located minimum sum of squares: the spatial residual resolution of the fiber gauge. (10) Add zeros to Rmi (l ) to achieveN Zmi (l ). 2 L(nspectrum ) = å [ yLRdomain m + n) ] ,the n =WMSi 0, 1 M - Ni-th fiber gauge via STFT. S ( m) - yand WMS (achieve (11) Transform Zmi (l ) into the of the (6) m =1 (12) Match the LRSi with the most spectrum segment of the WMSi by searching the minimum min L(nmsimilar ) residual sum of squares: where, yLRS ( m) and yWMS (m) are the local reference spectrum and measurement spectrum, N is N the length of local reference and length of 2measurement spectrum. L(n) spectrum = ∑ [y LRS (mM ) −isythe W MS ( m + n )] , n = 0, 1 · · · M − N (6) m = 1 (13) Calculate the spectrum shift Δλ by comparing the wavelength shift between the matched LMSi min L ( n ) m and LRSi:

M spectrum and measurement spectrum, N is where, yLRS (m) and yWMS (m) are the local reference Dl = n - + Dn (7) the length of local reference spectrum and Mmis the 2 length of measurement spectrum. (13) Calculate the spectrum shift ∆λ by comparing the wavelength shift between the matched LMSi where, nm is the index of the best match local spectrum, M is the length of measurement spectrum and LRSi: and Dn is the internal shift between the local reference M and measurement spectra. ∆λthe = linear nm − relationship + ∆n (7) (14) Calculate the corresponding Δε using between the spectrum shift and 2 distributed where, nm isstrain. the index of the best match local spectrum, M is the length of measurement spectrum (15) and Repeat process form (9)between to (14) and the full and distributed strain along the SMF. ∆n the is the internal shift theachieve local reference measurement spectra. (14) Calculate the corresponding ∆ε positive using theand linear relationship the spectrum shift and In the proposed method, both negative strain between can be demodulated. The local distributed strain. reference spectrum segment is matched from the start to the end of the measurement spectrum. So (15) Repeat the form (9)of tothe (14)matched and achieve full distributed strain along the respecting SMF. the positive andprocess negative shift localthe measurement spectrum segment to the local reference spectrum can be achieved.

Figure Figure 9.9. The flow diagram diagram of of OFDR OFDR strain strain discrimination discrimination processing processing algorithm algorithm based based on on high high similarity similarity local local spectra. spectra. OFDR: OFDR: optical optical frequency-domain frequency-domain reflectometry; reflectometry; Sr(t): Sr(t): the the reference reference OFDR OFDR signal; signal; Rr(l) Rr(l) the the reference reference OFDR OFDR reflectivity reflectivity signal; signal; WRSi: WRSi: whole reference spectrum spectrum of of i-th i-th fiber fiber gauge; LRSi: a segment of WRSi; Sm(t): the measurement OFDR signal; Rm(l) the meaurement OFDR gauge; LRSi: a segment of WRSi; Sm(t): the measurement OFDR signal; Rm(l) the meaurement reflectivity signal; WMSi: whole measurement spectrum of i-th fiber gauge; LMSi: a segment of WMSi which has the minimum residual sum of squares.

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In the proposed method, both positive and negative strain can be demodulated. The local OFDR reflectivity signal;isWMSi: whole measurement of the i-th measurement fiber gauge; LMSi: a segment reference spectrum segment matched from the start tospectrum the end of spectrum. So the of WMSi which has the minimum residual sum of squares. positive and negative shift of the matched local measurement spectrum segment respecting to the local reference spectrum can be achieved. 3. Experiments and Discussion 3. Experiments and Discussion In this section, experimental configuration and experiments are demonstrated. First, the OFDR distributed sensingexperimental system is introduced in detailed. Then, investigations on the influences of local In this section, configuration and experiments are demonstrated. First, the OFDR spectrum setup aresystem performed for optimizing the match. performance of the proposed distributed sensing is introduced in detailed. Then,Finally, investigations on thetests influences of local OFDR methods areperformed performed. spectrum setup are for optimizing the match. Finally, performance tests of the proposed OFDR methods are performed. 3.1. Experimental Setups 3.1. Experimental Setups Figure 10a illustrates the experimental setups of the OFDR distributed sensing system [11]. The 10a illustrates the is experimental setups ofbythe OFDR distributed sensing The system [11]. dataFigure acquisition (DAQ) card PCI-1714 produced Advantech (Taibei, Taiwan). balanced The data acquisition (DAQ) is PCI-1714 producedbalanced by Advantech (Taibei, Taiwan). The balancedby photodetector (BPD) is a card polarization dependent detector INT-POL-1550 produced photodetector (BPD)NJ, is USA). a polarization dependent balanced detector produced Thorlabs (Newton, The external cavity tunable laser source INT-POL-1550 (TLS) is a T100R producedby by Thorlabs USA). Canada). The external laser (TLS) is a T100Rbyproduced by Yenista (Newton, (Quebec, NJ, Quebec, Thecavity HCNtunable gas cell is source H13C14N produced Wavelength Yenista (Quebec, QC, Canada). HCN cell is H13C14N produced by Wavelength Reference Reference (Corvallis, OR, USA)The which is gas equivalent of the NIST SRM 2519. The other optical fiber (Corvallis, OR, USA) which is equivalent of the NIST SRM 2519. The other optical fiber devices are all devices are all produced by Advance Fiber Resources (Zhuhai, Guangdong, China). produced by Advance Fiber Resources (Zhuhai, Guangdong, China).

①

50

HCN 50

Isolator OC6

TLS OC1

50

10

90 ③

BPD

FR

50

DAQ

② 10

OC3

Attenuator

OC4

OC2 90 FUT

OC5 Circulator

PBS

BPD

(a) A cantilever beam

A Fixed stage

FUT

A stepper motorized stage FUT (back)

(b)

(c)

Figure10. 10.Schematic SchematicofofOFDR OFDRdistributed distributedsensing sensingsystem systemand andexperimental experimentalsetups. setups.(a) (a)Configuration Configuration Figure OFDR distributed sensing system. (b) Experimental of stretching device for ofofOFDR distributed sensing system. (b) Experimental setups ofsetups stretching fiber devicefiber for generating large distributed (c) Experimental setups of cantilever for generating micro distributed generating largestrain. distributed strain. (c) Experimental setups device of cantilever device for generating micro strain. TLS: tunable optical coupler; Faraday reflector; polarization beam distributed strain. laser TLS:source; tunableOC: laser source; OC: FR: optical coupler; FR: PBS: Faraday reflector; PBS: splitter; BPD: balanced photodetector; FUT:photodetector; fiber under test; DAQ: acquisition. polarization beam splitter; BPD: balanced FUT: fiberdata under test; DAQ: data acquisition.

Figure Figure10b,c 10b,cshow showthe thedevices devicesfor forgenerating generatingcontrollable controllabledistributed distributedstrain. strain.AAstretching stretchingfiber fiber device and a cantilever device are respectively for testing large and small distributed strain. A stepper device and a cantilever device are respectively for testing large and small distributed strain. A motorized stage KXC06 by Suruga (Shizuoka, Shizuoka, Japan) is employed to generate microto stepper motorized stage KXC06 Seiki by Suruga Seiki (Shizuoka, Shizuoka, Japan) is employed

generate micro displacements downwards to 50 nm. In Figure 10b, the fiber under test (FUT) is a section of sensing fiber between 1.3 m to 1.6 m and it is glued on the stepper motorized stage and a fixed stage. A maximum distributed strain up to 3000 µε can be achieved. Besides, the computing

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Sensors 2018, 18, xdownwards FOR PEER REVIEW 11 fiber of 17 displacements to 50 nm. In Figure 10b, the fiber under test (FUT) is a section of sensing between 1.3 m to 1.6 m and it is glued on the stepper motorized stage and a fixed stage. A maximum time based on Pearson andbeproposed processing 200 distributed sensing gauges distributed strain up tocoefficient 3000 µε can achieved.method Besides, the computing time based on Pearson is ~240 ms and ~25 ms, respectively. The sweep time for conventional method with a sweep range coefficient and proposed method processing 200 distributed sensing gauges is ~240 ms and ~25 ms, of 30 nm is 750 ms. By this method, a sweep range of 10 nm would save 500 ms based on respectively. The sweep time for conventional method with a sweep range of 30 nm is 750 ms. the By configuration of the personal computer used to run the program which is as follows: the processor this method, a sweep range of 10 nm would save 500 ms based on the configuration of the personal frequencyused is 3.2to GHz core number is four. is 16 computer runand the program which is as RAM follows: theGHz. processor frequency is 3.2 GHz and core In Figure 10c, the fiber under test (FUT) is a section of sensing fiber between 0.85 m to 0.9 m number is four. RAM is 16 GHz. and In it is glued10c, on the a silico-manganese bronze accuracy of the generated strain Figure fiber under test (FUT) is acantilever. section of The sensing fiber between 0.85 m to micro 0.9 m and it is higher than 10 µε. The wavelength repeatability of TLS is ~25 pm and is much worse than the is glued on a silico-manganese bronze cantilever. The accuracy of the generated micro strain is higher requirement of strain resolution. On the other resolution related to the the requirement nonlinearity than 10 µε. The wavelength repeatability of TLShand, is ~25spatial pm and is much is worse than of frequency sweeping and equal-wavelength-sampling or equal-spectrum-sampling are thus of strain resolution. On the other hand, spatial resolution is related to the nonlinearity of frequency highly required. The equal-wavelength-sampling interval is determined by the length difference of sweeping and equal-wavelength-sampling or equal-spectrum-sampling are thus highly required. the auxiliary interference arms which cannot be precisely a wavelength The equal-wavelength-sampling interval is determined bymeasured, the lengthsodifference of thecalibration auxiliary configuration consisting of the auxiliary interferometer and HCN gas cell is designed to improve interference arms which cannot be precisely measured, so a wavelength calibration configuration the absolute accuracy to sub pm calibration wavelength-sampling interval [12]. consisting of wavelength the auxiliary interferometer andand HCN gas cellthe is designed to improve the absolute During the experiments, the tunable of the the TLSwavelength-sampling is from 1540 to 1550 nm and the sweep velocity wavelength accuracy to sub pm andrange calibration interval [12]. During the is ~40 nm/s. The normalized absorption curve of the HCN gas cell between 1549 nm and 1551 nm experiments, the tunable range of the TLS is from 1540 to 1550 nm and the sweep velocity is ~40 nm/s. are illustrated Figure 11a.curve The absorption indexes (P11, 1549.7302 1550.5149 nm) The normalizedinabsorption of the HCNcentral gas cell between 1549 nm and nm; 1551P12, nm are illustrated are achieved through fitting the curve into a Vogt function and the equal-wavelength-sampling in Figure 11a. The absorption central indexes (P11, 1549.7302 nm; P12, 1550.5149 nm) are achieved interval can be derived as:into a Vogt function and the equal-wavelength-sampling interval can be through fitting the curve derived as: λ −λ Δλ Δλλ=2 −2 λ1 1 =∆λ22−−11 (8) N − N= ΔN ∆λ = (8) N2 −2 N1 1 ∆N22−−11 N i index where,λ1λ1isisthe theith iabsolute absorption peak wavelength of HCN the HCN gas cell, is the of index of th absolute where, absorption peak wavelength of the gas cell, Ni is the the ith λ is thewavelength and derived wavelength the iand peak ∆λ is the Δderived interval. interval. th peak

(a)

(b)

Figure experimental on the calibration configuration. (a) The absorption spectrum Figure 11. 11.The The experimental on wavelength the wavelength calibration configuration. (a) The absorption between and P12P11 peakand of the HCN gas cell and HCN the Vogt fitting (b) Vogt Experimental results spectrumP11 between P12 peak of the gas cell results. and the fitting results. of equal-wavelength-sampling interval. P11: the 11-th absorption peak of the HCN; P12: the 12th (b) Experimental results of equal-wavelength-sampling interval. P11: the 11-th absorption peak of absorption peakthe of 12th the HCN. the HCN; P12: absorption peak of the HCN.

The The length length difference difference of of the the auxiliary auxiliary interference interference arms arms is is affected affected by by slow slow temperature temperature drifts. drifts. The is performed twice every minute. Figure 11b shows the calibration results The wavelength wavelengthcalibration calibration is performed twice every minute. Figure 11b shows the calibration of 30 times. Based on Based the experimental results, the equal-wavelength-sampling interval is 42.012 fm and results of 30 times. on the experimental results, the equal-wavelength-sampling interval is the calibration is 0.041 fm. It can beisinferred thatItthe wavelength calibration 42.012 fm andrepeatability the calibration repeatability 0.041 fm. can be inferred that theconfiguration wavelength is stable andconfiguration robust. calibration is stable and robust.

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3.2. Optimization Optimization ofofthe theProposed ProposedOFDR OFDRDistributed DistributedSensing SensingMethod Method 3.2. Although itithas hasbeen beenverified verifiedthat thatusing usingthe thelocal localspectrum spectrumcan cansignificantly significantlyimprove improveSNR SNRand and Although similarity,ititisisnecessary necessarytoto investigate influence of the local spectrum length position on similarity, investigate thethe influence of the local spectrum length andand position on the the performance the distributed strain sensing. Theoflength ofspectrum the localrefers spectrum to the performance of theof distributed strain sensing. The length the local to therefers wavelength wavelength rangespectrum. of the local of the refers local spectrum to thecenter local range of the local Thespectrum. position ofThe the position local spectrum to the localrefers spectrum spectrum centerto position relative to the whole spectrum. position relative the whole spectrum. The experiments experiments are are conducted conducted 30 30 times times under under aasame sameconditions conditions and and the the SNR SNRisisan anaveraged averaged The resultofofthe thedistributed distributed sensing region of m 0.2subjected m subjected to a strain. The statistical results are result sensing region of 0.2 to a strain. The statistical results are shown shown Figure 12.12a Figure 12athe shows the influences of the local spectrum on when the SNR in Figurein12. Figure shows influences of the local spectrum length onlength the SNR the when local the local position spectrumis position set atofthe of the whole defined asratio the spectrum set at the is middle themiddle whole spectrum. SNRspectrum. is definedSNR as theisamplitude amplitude ratio of the secondary lowest to peak to amplitude the lowestwhen peak the amplitude when are the of the secondary lowest peak amplitude the amplitude lowest peak local spectra local spectramatched. are all correctly matched. However, is defined once there is Figure a mistaken all correctly However, SNR is defined as SNR zero once there as is azero mistaken match. 12a match.that Figure shows thatthe SNR is spectrum zero when the local spectrum is less the thanspectrum ~0.5 nm shows SNR12a is zero when local length is less than ~0.5length nm because because the spectrum characteristics are not sufficient. SNRspectrum increaseslength with under the local spectrum characteristics are not sufficient. SNR increases with the local a distributed lengthofunder a distributed strain of less 1600 µε as It a result of athat higher It suggests that strain less than 1600 µε as a result of athan higher match. suggests the match. longer local spectrum the longer local spectrum contains more characteristics improve the accuracy of influence spectra matching contains more characteristics to improve the accuracy oftospectra matching and the of new and the influence new spectrum segment is relatively weak. However, SNR begins to decrease spectrum segment isofrelatively weak. However, SNR begins to decrease with the local spectrum length with the spectrum length 2100 whenµε. theBesides, loaded as strain exceedsin2100 µε.4,Besides, illustrated in when the local loaded strain exceeds illustrated Figure a red oras blue spectrum Figure 4, a nm red induced or blue by spectrum shift of ~3.8 nm induced by tensile or compressive distributed shift of ~3.8 tensile or compressive distributed strain of 3000 µε and the length of the strain of LMS 3000 spectrum µε and thesegments length ofkeeping the LRSaand spectrum segments keeping high similarity LRS and highLMS similarity is ~1.0 nm. Finally, the alength of the localis ~1.0 nm. Finally, spectrum is set as the 1.0 length nm. of the local spectrum is set as 1.0 nm.

(a)

(b)

Figure Figure 12. 12. Experiments Experiments on on the the optimizing optimizing the the local localspectrum spectrum(LS) (LS)parameters. parameters. (a) (a) Experimental Experimental results results of of optimizing optimizing the the local localspectrum spectrumlength. length. (b) (b) Experimental Experimental results results of of optimizing optimizing the the local local spectrum spectrumcenter. center.

Then, Then, the the influence influence of ofthe thelocal localspectrum spectrumposition positionisisexperimentally experimentally investigated investigated and and the the local local spectrum length is 1.0 nm. Figure 12b illustrates the experimental results and it indicates that SNR is spectrum length is 1.0 nm. Figure 12b illustrates the experimental results and it indicates that SNR hardly influenced by the position. However, the LMS to be matched are easily is hardly influenced by spectrum the spectrum position. However, thedesired LMS desired to be matched areshifted easily out of the WMS as a result of the different spectrum shift direction of the tensile and compressive shifted out of the WMS as a result of the different spectrum shift direction of the tensile and distributed strain. Considering measurable the range of the tensile or compressive distributed strain, compressive distributed strain.theConsidering measurable range of the tensile or compressive the local spectrum position finally set as 5.0 is nm at theset middle theatwhole spectrum. is distributed strain, the local is spectrum position finally as 5.0ofnm the middle of theSNR whole most stable at the center of the swept. In our method, a spectrum segment is chosen in the reference spectrum. SNR is most stable at the center of the swept. In our method, a spectrum segment is spectrum thereference local reference spectrum (LRS). the measurement spectrum considered chosen inasthe spectrum as the localThen, reference spectrum (LRS). Then,may the be measurement as a shift reference spectrum. This matchesspectrum. the LRS segment on the measurement spectrum may be considered as a method shift reference This method matches the LRSspectrum segment and finds the shift between the center of LRS and the matched spectrum segment in the measurement on the measurement spectrum and finds the shift between the center of LRS and the matched spectrum. matter in whether under stretching or compression, the center spectrum in the spectrum No segment the measurement spectrum. No matter whether undersegment stretching or reference spectrum is the last to lose its similar segment part in the measurement spectrum, so the SNR compression, the center spectrum segment in the reference spectrum is the last to lose its similar would notpart drop the center. segment inin the measurement spectrum, so the SNR would not drop in the center.

Based on the results of Figure 12, the spectrum length and location should be carefully selected. Excessive reduction of cross-correlation points would yield a lower SNR, however, appropriate reduction points could improve the SNR. So a conclusion about how to enhance the similarity

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Based onxthe of Figure 12, the spectrum length and location should be carefully selected. Sensors 2018, 18, FORresults PEER REVIEW 13 of 17 Excessive reduction of cross-correlation points would yield a lower SNR, however, appropriate between reference and measurement and improve duringthe thesimilarity determination of reduction points could improve the SNR.spectra So a conclusion aboutthe howSNR to enhance between spectrumand shifts. This is a great contribution and the significant discovery of this paper.of spectrum shifts. reference measurement spectra and improve SNR during the determination This is a great contribution and significant discovery of this paper. 3.3. Experiments on Testing the Distributed Sensing Performances of the Proposed Method 3.3. Experiments on Testing the Distributed Sensing Performances of the Proposed Method The performances of the proposed OFDR method are experimentally tested and compared The performances of the proposed OFDR method are experimentally tested and compared with with conventional OFDR methods, including the improvement of SNR, the sensing performance of conventional OFDR methods, including the distributed improvement of SNR, performance large distributed strain, resolution of the strain and the thesensing repeatability across of thelarge full distributed strain, resolution of the distributed strain and the repeatability across the full strain range. strain range. Experiments Experiments on on the the improvement improvement of of SNR SNR are areconducted conductedfirst. first. This This experiment experiment is is aimed aimed at at comparing of the evaluating functionfunction between the proposed the conventional comparingthe theSNR SNR of similarity the similarity evaluating between theand proposed and the method during the determination of spectrum shift. Inshift. the In conventional method based on conventional method during the determination of spectrum the conventional method based cross-correlation, SNR is defined as the amplitude ratio of the secondary highest peak amplitude to on cross-correlation, SNR is defined as the amplitude ratio of the secondary highest peak amplitude the highest peak amplitude when the local spectra are all matched. SNR SNR is defined as zero to the highest peak amplitude when the local spectra arecorrectly all correctly matched. is defined as once fake peak or multi-peaks exits in cross-correlation and wavelength shift cannot be distinguished zero once fake peak or multi-peaks exits in cross-correlation and wavelength shift cannot be the cross-correlation wavelength shiftwavelength can’t be determined. Experimental resultsExperimental shown in Figure 13 distinguished the cross-correlation shift can’t be determined. results are derived from the distributed sensing in a range from fiber 1.3 mintoa1.6 m. The shown in Figure 13 are derived from thefiber distributed sensing range fromexperiments 1.3 m to 1.6are m. conducted 30 times under a same condition and the SNR is an averaged result of the distributed The experiments are conducted 30 times under a same condition and the SNR is an averaged result sensing region of 0.2 m subjected to a0.2strain. The statistical results shown in Figure SNR is of the distributed sensing region of m subjected to a strain. Theare statistical results are13.shown in defined as zero once there is a mistaken match. The dotted lines represent the SNR under different Figure 13. SNR is defined as zero once there is a mistaken match. The dotted lines represent the spatial using the conventional method dealing cross-correlation, and the solid lines SNR resolutions under different spatial resolutions using thewith conventional method dealing with represent the SNRand under spatial resolutions using thedifferent proposed method dealing using with the cross-correlation, thedifferent solid lines represent the SNR under spatial resolutions the least-square method. SNR achieved by the conventional method is lower than 2 when the distributed proposed method dealing with the least-square method. SNR achieved by the conventional method strain is larger 1000 and multistrain or fake peaksthan begin to appear leads the failure is lower than 2than when the µε distributed is larger 1000 µε andwhich multi or faketopeaks begin of to the distributed straintosensing. However, SNR of thestrain proposed method is in aSNR range from 2 to 12 appear which leads the failure of the distributed sensing. However, of the proposed which verifies it isfrom robust large distributed strain. for In summary, the proposed method method is in athat range 2 tofor 12sensing which verifies that it is robust sensing large distributed strain. can improve SNR the similarity evaluating function distributed strainfunction and make the In summary, the of proposed method can improve SNRunder of thesmall similarity evaluating under distributed strain sensing of larger than 1000 µε range possible when the conventional method is small distributed strain and make the distributed strain sensing of larger than 1000 µε range thoroughly invalid. The proposed method could raise the strain measurable range to 3000 µε which possible when the conventional method is thoroughly invalid. The proposed method could raise exceeds themeasurable reported OFDR [6].which exceeds the reported OFDR methods [6]. the strain rangemethods to 3000 µε

Figure on on comparing SNR SNR of theof similarity evaluating function function between the proposed Figure13. 13.Experiment Experiment comparing the similarity evaluating between the (P) and the(P) conventional method (C)method under different spatial resolutions. proposed and the conventional (C) under different spatial resolutions.

Then, thethe sensing performance of a of large distributed strain under spatial Then,experiments experimentsonon sensing performance a large distributed strain different under different resolutions are conducted. Distributed strainsstrains from 1000 to µε 3000 µε inµε anin interval of 400 spatial resolutions are conducted. Distributed from µε 1000 to 3000 an interval of µε 400are µε loaded on the FUT between 1.3 m to 1.6 m. The proposed method is utilized to process sensing signal are loaded on the FUT between 1.3 m to 1.6 m. The proposed method is utilized to process sensing and senses distributed strain. The experimental results are illustrated in Figure in 14.Figure It indicates signal and the senses the distributed strain. The experimental results are illustrated 14. It that the strain measurable range of the proposed method can reach 3000 µε under a 3 mm higha indicates that the strain measurable range of the proposed method can reach 3000 µε under spatial resolution and there is no mistaken point in the distributed sensing region. On the other hand, 3 mm high spatial resolution and there is no mistaken point in the distributed sensing region. On

the other hand, the smoothness of the distributed strain gets worse when the distributed strain becomes larger and the spatial resolution becomes higher. It would be caused by that SNR is influence by the amount of distributed sensing data and similarity. Based on the theory of STFT, the resolution of spatial and spectrum has an interaction relationship. The similarity degenerates due to

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the smoothness of the distributed strain gets worse when the distributed strain becomes larger and the spatial resolution becomes Sensors 2018, 18, x FOR PEER REVIEW higher. It would be caused by that SNR is influence by the amount 14 of 17 of distributed sensing data and similarity. Based on the theory of STFT, the resolution of spatial and spectrum has ansegments interaction relationship. similarity degenerates the duerising to new segments new spectrum appearing in theThe whole MeS. Furthermore, orspectrum falling phase of the appearing in the whole MeS. Furthermore, the rising or falling phase of the distributed strain under a distributed strain under a spatial resolution of 20 mm is longer than that under a higher spatial spatial resolution of 20 mm is longer than thatwindow under a higher spatial resolution. It is points mainlyreflecting induced resolution. It is mainly induced by the STFT containing more or less data by the STFT window containing more or less data points reflecting the distributed strain when the distributed strain when the STFT windows are sliding in and out of the strain region. It canthe be STFT windows andmultiple out of the strain It caneliminated be concluded thatproposed fake peaks and concluded that are fakesliding peaksin and peaks areregion. thoroughly by the OFDR multiple are strain thoroughly eliminated by the OFDR method and the strain measurable method peaks and the measurable range up proposed to 3000 µε is achieved under a highest spatial range up to 3000 µε is achieved under a highest spatial resolution downwards to 3 mm. resolution downwards to 3 mm.

(a)

(b)

(c)

(d)

Figure on sensing large large distributed strain under resolutions: (a) 20 mm, Figure14. 14.Experiments Experiments on sensing distributed straindifferent under spatial different spatial resolutions: (b) and andand 3 mm. (a) 10 20 mm, (c) (b)510mm mm, (c)(d) 5 mm (d) and 3 mm.

According thethe spectrum shift varies linearly withwith the increase of the of distributed strain AccordingtotoFigure Figure14,14, spectrum shift varies linearly the increase the distributed and so and sensitivity can be calibrated as follows. The average spectrum shift of shift the fiber gauges strain so sensitivity can be calibrated as follows. The average spectrum of the fiber within gauges the sensing region isregion extracted under different strains and is fitted a linear The sensing within the sensing is extracted under different strains and into is fitted into function. a linear function. The curve can be written as: sensing curve can be written as: ∆λ = kε (9) Δλ = kε (9) where, ∆λ is the spectrum shift, k is the sensitivity coefficient and ε is the strain. where, Δλ is the spectrum shift, k is the sensitivity coefficient and ε is the strain. Figure 15 illustrates the results of sensing sensitivity under different spatial resolutions of 20, 10, Figure 15 illustrates the results of sensing sensitivity under different spatial resolutions of 20, 10, 5 and 3 mm are respectively 0.1586, 0.1587, 0.1586 and 0.1587 GHz/µε. The diversity of sensitivities 5 and 3 mm are respectively 0.1586, 0.1587, 0.1586 and 0.1587 GHz/µε. The diversity of sensitivities under different spatial resolutions is less than 0.03%. The sensing curves or the relationship between under different spatial resolutions is less than 0.03%. The sensing curves or the relationship spectrum shifts and strain are quite stable under the same condition even with different spatial between spectrum shifts and strain are quite stable under the same condition even with different resolutions. Furthermore, the nonlinearity of the sensing curves is less than 0.5%. spatial resolutions. Furthermore, the nonlinearity of the sensing curves is less than 0.5%.

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(a) (a)

(b) (b)

(c) (c)

(d) (d)

Figure 15. Experiments on the sensing sensitivity of the distributed strain under different spatial Figure 15. 15. Experiments distributed strain strain under under different different spatial spatial resolutions: (a) 20 mm, (b) mm, (c) 5 mm and (d) of and 3 mm. Figure on10the sensing sensitivity the distributed resolutions: (a) 20 mm, mm, (b) (b) 10 10 mm, mm, (c) (c) 55 mm mm and and (d) (d) and and 33 mm. mm. resolutions:

The repeatability across the full strain range can be derived from the Figure 14. Repeatability Thestrain repeatability full range be from Repeatability repeatability the full strain strain range can can be derived derivedover from the the Figure Figure 14. Repeatability across the fullacross rangethe refers to average repeatability full strain 14. range 3000 µε. across strain the full range refers to average repeatability over full strain range 3000 µε. Repeatability across strain isthe full range overthe full strain range 3000 µε. Repeatability measured and refers reflectsto2σaverage standardrepeatability deviation from stable distributed sensing is measured and reflects 2σ and standard deviation from the stable sensing region. Figure 16 Repeatability is16measured reflects 2σ standard deviation from stable distributed sensing region. Figure indicates that the repeatability across the fulldistributed strainthe range under different spatial indicates that repeatability across the full strain0.85, range under spatial resolutions ofa3, 10 region. Figure indicates the across the fulldifferent strain range under different spatial resolutions ofthe 3,165, 10 and 20that mm is repeatability respectively 0.48, 0.26 and 0.12 GHz. The result of 55,mm and 20 mm is respectively 0.85, 0.48, 0.26 and 0.12 GHz. The result of a 5 mm gauge length is better resolutions of is3, better 5, 10 and mmofisLUNA respectively 0.85, 0.48, 0.26representing and 0.12 GHz. resultlevel of a of 5 mm gauge length than20that ODiSI-B (0.79 GHz) theThe leading the than that of LUNA ODiSI-B (0.79of GHz) representing the leading level of the OFDR. gauge length is better than that LUNA ODiSI-B (0.79 GHz) representing the leading level of the OFDR. OFDR.

Figure Experiments repeatability across the strain full strain different Figure 16. Experiments on on the the repeatability across the full range range under under different spatial spatial Figure resolutions. 16. Experiments on the repeatability across the full strain range under different spatial resolutions. resolutions.

Finally, In Figure Figure 10c, 10c, Finally, the the strain strain resolution resolution of of the the proposed proposed method method is is experimentally experimentally tested. tested. In the sensing fiber between 0.85 m to 0.9 m is glued on a silico-manganese bronze cantilever and aa Finally,fiber the strain resolution of 0.9 the m proposed is experimentally tested. In Figure 10c, the sensing between 0.85 m to is gluedmethod on a silico-manganese bronze cantilever and stepping motor isisutilized to0.85 generate micro steps. 17 illustrates the experimental results the sensing fiber between m to 0.9 m strain is glued onsteps. aFigure silico-manganese bronze cantilever and a stepping motor utilized to generate micro strain Figure 17 illustrates the experimental and it indicates that micro strain steps of 10 µε (limited by the device generating strain) can be clearly stepping motor is utilized to generate microofstrain Figure 17 device illustrates the experimental results and it indicates that micro strain steps 10 µεsteps. (limited by the generating strain) can distinguished under a high spatial resolution ofof3 10 mm. results anddistinguished it indicates that micro strain stepsresolution µε (limited be clearly under a high spatial of 3 mm.by the device generating strain) can

be clearly distinguished under a high spatial resolution of 3 mm.

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Figure 17. 17. Experiments Experiments on on sensing sensing micro micro distributed distributed strain strain or or strain strain resolution resolution under under the the highest highest Figure spatial resolution resolution of of 33 mm. mm. spatial

On the floor in the region of sensing distributed strainstrain is about 2 µε which On the other otherhand, hand,the thenoise noise floor in the region of sensing distributed is ± about ±2 µε meansmeans that thethat strain is on the level 2 µε.ofFurthermore, the noise of the which the resolution strain resolution is on theoflevel 2 µε. Furthermore, thefloor noiseout floor out region of the of sensing distributed strain isstrain loweristhan ±0.4 GHz the repeatability at zero region of sensing distributed lower than ±0.4which GHz could whichrepresent could represent the repeatability strain is better ±0.75 by the by LUNA ODiSI-B. at zeroand strain and isthan better thanGHz ±0.75achieved GHz achieved the LUNA ODiSI-B. 4. Conclusions 4. Conclusions In this paper, the restrictions on the measurable range strain using a narrow swept spectrum range In this paper, the restrictions on the measurable range strain using a narrow swept spectrum are investigated and a new similarity evaluation function is built to improve the data processing rate range are investigated and a new similarity evaluation function is built to improve the data and SNR during determination of the spectrum shift. The new spectrum segment in the MeS spectrum processing rate and SNR during determination of the spectrum shift. The new spectrum segment in without similarity to ReS segment is the primary reason causing the similarity degeneration between the MeS spectrum without similarity to ReS segment is the primary reason causing the similarity ReS and MeS. The local spectrum characteristics are found and SNR of the similarity evaluating results degeneration between ReS and MeS. The local spectrum characteristics are found and SNR of the is enhanced by the proposed method so that the fake peaks and multi peaks are thoroughly eliminated. similarity evaluating results is enhanced by the proposed method so that the fake peaks and multi Then, a new similarity evaluation function based on least-square method is built to replace the Pearson peaks are thoroughly eliminated. Then, a new similarity evaluation function based on least-square correlation coefficient and the amount of calculation is decreased significantly. By combining these two method is built to replace the Pearson correlation coefficient and the amount of calculation is variations, the proposed OFDR method matches the local ReS in the MeS to find the most similar MeS decreased significantly. By combining these two variations, the proposed OFDR method matches segment wherein the least-squares method is employed to evaluate similarity. By the proposed method, the local ReS in the MeS to find the most similar MeS segment wherein the least-squares method is the measurable strain range can reach 3000 µε under a highest spatial resolution of 3 mm when the employed to evaluate similarity. By the proposed method, the measurable strain range can reach sweep wavelength range is only 10 nm. The data processing rate is raised by at least 10 times than 3000 µε under a highest spatial resolution of 3 mm when the sweep wavelength range is only 10 nm. that employing Pearson correlation coefficients. Experimental results indicate that a nonlinearity of The data processing rate is raised by at least 10 times than that employing Pearson correlation less than 0.5%, a strain resolution of better than 10 µε, a repeatability at zero strain of below ±0.4 GHz coefficients. Experimental results indicate that a nonlinearity of less than 0.5%, a strain resolution of and a repeatability across the full strain range of less than 0.85 GHz are achievable under a highest better than 10 µε, a repeatability at zero strain of below ±0.4 GHz and a repeatability across the full spatial resolution of 3 mm. This work solves the problem of the invalidation of conventional methods strain range of less than 0.85 GHz are achievable under a highest spatial resolution of 3 mm. This when measuring a large strain and the failure to find the true cross-correlation peak when the sweep work solves the problem of the invalidation of conventional methods when measuring a large is insufficient. The performances of the proposed method are better than those of a LUNA ODiSI-B strain and the failure to find the true cross-correlation peak when the sweep is insufficient. The device representing the leading level of OFDR. performances of the proposed method are better than those of a LUNA ODiSI-B device representing the leading level of OFDR.K.F.; Formal analysis, Y.J., D.J. and Y.N.; Funding acquisition, J.C.; Author Contributions: Conceptualization, Project administration, J.T.; Writing-original draft, K.F.; Writing-review & editing, K.F., X.S. and H.D. Author Contributions: Conceptualization, K.F.;Natural FormalScience analysis, Y.J., D.J. and Y.N.;51575140 Fundingand acquisition, J.C.; Funding: This research was funded by National Foundation of China Science Fund Project administration, J.T.; Writing-original draft, K.F.; Writing-review & editing, K.F., X.S. and H.D. for Distinguished Young Scholars of Harbin RC2016JQ006007. Conflicts of Interest: Thewas authors declare no conflict of interest. Funding: This research funded by National Natural Science Foundation of China 51575140 and Science Fund for Distinguished Young Scholars of Harbin RC2016JQ006007.

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