Detection and Quantification of Damage in Metallic Structures ... - MDPI

applied sciences Article

Detection and Quantification of Damage in Metallic Structures by Laser-Generated Ultrasonics Yongqiang Liu, Shixi Yang * and Xuekun Liu College of Mechanical Engineering &The State Key Lab of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 320027, China; [email protected] (Y.L.); [email protected] (X.L.) * Correspondence: [email protected]; Tel.: +86-0571-8795-1924 Received: 23 April 2018; Accepted: 17 May 2018; Published: 20 May 2018







Abstract: The appearance of damage on metallic structures is inevitable due to complex working environments. Non-destructive testing (NDT) of these structures is critical to the safe operation of the equipment. This paper presents a non-destructive damage detection, visualization, and quantification technique based on laser-generated ultrasonics. The undamaged and damaged metallic structures are irradiated with laser pulses to produce broadband input ultrasonic waves. Damage to the structures plays the role of a nonlinear radiation source of new frequencies. Usually these new frequencies are too weak to be detected directly. Here, the state space predictive model is proposed to address the problem. Based on the recorded responses in the time domain, the state space attractors are reconstructed. Damage to the structures is shown to change the properties of the attractors. A nonlinear damage detection feature called normalized nonlinear prediction error (NNPE) is extracted from the state space to identify the changes in the attractors—and hence the damage. Furthermore, the damage is visualized and quantified using the NNPE values extracted from the entire area by using a laser scanning technique. Experimental results validate that the proposed technique is capable of detecting, visualizing and quantifying artificial damage to aluminum alloy plates and actual fatigue cracks to a twin-screw compressor body. Keywords: damage detection; damage quantification; laser-generated ultrasonics; state space reconstruction; normalized nonlinear prediction error

1. Introduction During the life cycle of a metallic structure, the appearance of damage is inevitable due to the structure’s complex working environments [1–3]. For example, the working environment of engine blades is very severe. These blades suffer from shock, friction and high temperatures as well as heating and cooling cycles. Therefore, it is very easy to produce cracks in the engine blades [1]. According to the statistics on predecessors, the failures in metallic structures caused by fatigue cracks account for more than 90% [4]. Each year, the breakdown and disorderly closedown of equipment caused by fatigue cracks cause owners to expend large amounts of time and money, and sometimes failures even threaten the operators’ safety and lives [5,6]. These safety and economic considerations have spurred research within the field of NDT of metallic structures in the past few years. Among various structural damage detection techniques, such as infrared testing [7], eddy current testing [8,9], magnetic particle testing [10], and ultrasound testing [11,12], the ultrasound testing technique has been widely used due to its relatively high spatial resolution, portable operation, high performance ratio, and high effectiveness in damage detection. By recording the ultrasonic waves propagating through a structure, macroscopic damage such as cracks, inclusions, and notches can be detected by using this method [5]. Influenced by the linear interaction between propagating waves and damage, the ultrasonic waves experience reflection, diffraction, and mode conversion. Appl. Sci. 2018, 8, 824; doi:10.3390/app8050824

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By extracting metrics from the response waves, the damage can be defined. Notably, most damage detection techniques use linear metrics extracted from response waves to detect damage, namely, the damage is assumed only to affect the structure in a linear way. However, according to Worden’s study [12], damage evolution is a nonlinear process that initiates certain nonlinear properties in the structure. When dealing with nonlinear damage, linear ultrasonic waves may lose their effectiveness and reliability. Recent studies have shown that nonlinear ultrasonic waves are usually more sensitive to small cracks than classical linear ones. In the nonlinear ultrasonic techniques, a fatigue crack plays the role of a nonlinear radiation source [13]. It will distort the original propagating ultrasonic waves and generate different waves with new frequency components as shown in Figure 1. This makes the new nonlinear component a damage-sensitive feature for damage detection. Duffour et al. [14] investigated the application of the nonlinear vibro-acoustic modulation technique for the assessment of fatigue cracks in steel beams and nickel-based alloy plates. In their experiments, the specimens were subjected to both a low ultrasound frequency and a low structural vibration frequency. The ratio of the average first sideband amplitude over the ultrasonics carrier was proposed as a nonlinear feature to assess the cracks. Jiao et al. [13] also investigated the application of the vibro-acoustic modulation technique for the detection of cracks in steel pipes. They delimited the Modulation Index as a crack-sensitive feature. The influence of the frequency and amplitude of vibration on the sideband amplitudes was experimentally investigated. Liu et al. [15] conducted nonlinear modulation measurement for non-destructive testing of the cracks in aluminum plates and scaled steel shafts. The nonlinear spectral coefficient was used to isolate the nonlinear modulation components from noisy environments and show a higher sensitivity to fatigue cracks than the traditional nonlinear coefficient. Hess et al. [16] investigated the application of the linear surface acoustic waves and the nonlinear surface acoustic waves in non-destructive testing of surface cracks. They demonstrated that the nonlinear surface acoustic waves could be more effective to crack detection. Gusev et al. [17] developed a theoretical model for crack imagination by the nonlinear frequency-mixing technique. Based on the model, the cracks in a glass plate were successfully detected and imaged [18]. They demonstrated that the sensitivity of this technique is 20 times higher than the linear photo-acoustic techniques. In the research mentioned above, the nonlinear ultrasonic technique was demonstrated to be a good candidate for the detection of fatigue damage. However, this technique also has some shortcomings in that it is challenging to get the two most suitable independent original excitation frequencies in practice [19]. This is because the optimal choice of the excitation frequencies is also affected by the structure to be detected and the environmental condition [20]. Here we introduced the laser-generated ultrasonics technique [21] to solve this problem. Compared with traditional nonlinear techniques, only one laser pulse excitation is used to generate a broadband input signal rather than two different ultrasonic waves. So the optimal choice of the excitation frequencies is no longer a problem. But a new problem has reared up that is affected by the broadband nature of the input signal generated by the laser pulse. The new frequencies caused by the damage are submerged and cannot be detected directly. In this paper, we introduced the state space predictive model [22] to tackle this problem. The dynamic characteristics of the structure can be described by geometric figures in the state space and the damage is shown to change the properties of the geometric figure. By identifying the change in the geometric figure, the damage can be detected. Usually, the state space predictive model was applied to the vibrating structures for structural damage identification. In this paper, the model was applied to laser-generated ultrasonic signals for fatigue damage detection and quantification. This paper is organized as follows: in Section 2, the fundamental issues about the generation and modulation of laser-generated ultrasonics and attractor-based analyses are provided. How damage can be detected and quantified by normalized nonlinear prediction error is also described in Section 2; in Section 3, a laser-generated ultrasonics detecting system is built to detect the damage; in Sections 4 and 5, artificial damage to aluminum alloy plates and actual fatigue cracks in a twin-screw compressor

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body are detected and quantified by the proposed technique to validate the effectiveness of the compressorFinally, body arethe detected proposedin technique technique. resultsand of quantified this workby arethe presented Sectionto 6.validate the effectiveness of the technique. Finally, the results of this work are presented in Section 6.

Figure illustration of nonlinear modulation of two ultrasonic waves. waves. Figure1.The 1. The illustration of nonlinear modulation of two ultrasonic

2. Background

2. Background The fundamental issues of laser-generated ultrasonics and attractor-based analyses are briefly The fundamental of laser-generated ultrasonics reviewed in this section.issues The framework for damage detectionand andattractor-based quantification isanalyses provided.are briefly reviewed in this section. The framework for damage detection and quantification is provided. Transforming the dynamic properties of a structure into a geometric figure in the state space is shown Transforming dynamic properties a quantification. structure into a geometric figure in the state space is to be especially the useful for damage detectionof and

shown to be especially useful for damage detection and quantification. 2.1. Generation and Modulation of Laser-Generated Ultrasonics

2.1. Generation and Modulation of Laser-Generated Ultrasonics The ultrasonics technique has been used for damage detection for a long time, and the generation of ultrasonic waves by using laser in the 1960s [21]. the surface of generation a The ultrasonics technique haspulses been was useddeveloped for damage detection for aWhen long time, and the material is illuminated by a laser pulse, the material absorbs a part of the laser energy, resulting in a of ultrasonic waves by using laser pulses was developed in the 1960s [21]. When the surface of a rapid temperature rise in the local area. Elastic waves are generated due to the thermal expansion. material is illuminated by a laser pulse, the material absorbs a part of the laser energy, resulting in Based on the power density of the irradiating pulse laser, there are two thermal models for the a rapid temperature rise in the local area. Elastic waves are generated due to the thermal expansion. generation of ultrasonic waves, namely, ablation generation and thermo-elastic generation [23]. For Based on the thepower power density of laser the irradiating pulse there threshold are two of thermal models for the the latter, density of the pulse is lower than laser, the ablation the irradiated generation of ultrasonic namely, wave ablation generation andpaper, thermo-elastic generation [23]. For the material, which indicates waves, non-destructive generation. In this thermo-elastic generation latter, the power density of the laser pulse is lower than the ablation threshold of the irradiated is considered. material, indicates non-destructive waveultrasonics generation. In this paper, generation Afterwhich irradiation by a laser pulse, a broadband is generated. The thermo-elastic ultrasonics is then as an excitation signal to detect the damaged structure. When the wave is propagating in the isused considered. structure, wave occur because of the damage and new After nonlinear irradiation by amodulation laser pulse,will a broadband ultrasonics is generated. The frequency ultrasonics is then components are generated as shown in Figure 2. Taking a closer look at Figure 2, the high-order used as an excitation signal to detect the damaged structure. When the wave is propagating in nonlinear modulation signals are easily submerged by the original signal because of the broadband the structure, nonlinear wave modulation will occur because of the damage and new frequency characteristic of the input signal, which means that traditional nonlinear damage detection components are generated as shown in Figure 2. Taking a closer look at Figure 2, the high-order technologies are unsuitable for this situation. State-space predictive models [22,24] are introduced to nonlinear modulation signals are easily submerged by the original signal because of the broadband tackle this issue.

characteristic of the input signal, which means that traditional nonlinear damage detection technologies are unsuitable for this situation. State-space predictive models [22,24] are introduced to tackle this issue.

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Figure 2.The illustration of laser-generated ultrasonics modulations. Figure 2. The illustration of laser-generated ultrasonics modulations.

2.2. Reconstruction of the State-Space Attractor

2.2. Reconstruction of the State-Space Attractor Usually, a dynamic system can be described by a first-order differential equation:

Usually, a dynamic system can be described by a first-order differential equation:

x  F ( x, t ) , .

(1)

x = F ( x, t),

(1)

where F is a function of the variables x and t. Variable x represents the state variable and t represents time. where F is a function of the variables x and t. Variable x represents the state variable and t If we plot x1(t) against x2(t), the resulted space is called to be ‘state space’. If the solution of the

represents time. equation is visualized as a trajectory in state space, for a given set of initial conditions, xi (0) , the If we plot x1 (t) against x2 (t), the resulted space is called to be ‘state space’. If the solution of trajectories representing the dynamic properties of the system in the state space will trace out a the equation is visualized as a trajectory in state space, for a given set of initial conditions, xi (0), the unique path. After a certain period of disturbance, the path will gradually migrate towards an trajectories representing the dynamic properties of the system in the state space will trace out a unique invariant geometric figure in state space. This geometric figure is called to be ‘attractor’ [22].This path. After a certain period ofthe disturbance, path gradually towards an invariant attractor in state space represents steady statethe point of awill dynamic systemmigrate and exhibits sensitive geometric figure in state space. This geometric figure is called to be ‘attractor’ [22].This attractor dependence on the initial conditions of the system. This is the reason why the state space predictive in state space theforsteady state point of a dynamic exhibits sensitive on the modelrepresents can be used identifying the dynamic change system (usuallyand caused by damage) ofdependence a system [22,24–26]. Usually,ofan initial baseline is reconstructed for an intact system and compared initial conditions the system. Thisattractor is the reason why the state space predictive model can be used for with the attractor reconstructed for (usually a damaged one. Damage has been to change the geometry identifying the dynamic change caused by damage) of ashown system [22,24–26]. Usually, an initial of the attractor. Hence, by identifying a change in the geometric properties, damage can be detected baseline attractor is reconstructed for an intact system and compared with the attractor reconstructed andaeven quantified. is the basic detection principlethe of this paper. of the attractor. Hence, by for damaged one.This Damage has damage been shown to change geometry In theory, all the vector variables of the system are needed to reconstruct the attractor. identifying a change in the geometric properties, damage can be detected and even quantified. This is Unfortunately, it is difficult to obtain every vector variable in practice. Luckily, according to the the basic damage detection principle of this paper. embedding algorithm proposed by Takens [27], the unknown variables can be reconstructed by the In theory, all the vector variables of time the series, system needed measured ones. Assuming x(n) is the measured theare attractor X(n)to canreconstruct be expressedthe as attractor. Unfortunately, it is difficult to obtain every vector variable in practice. Luckily, according to the follows: embedding algorithm proposed by Takens [27], the unknown variables can be reconstructed by the X (n)  [ x(n), x(n  T ),..., x(n  (m 1)T )], (2) measured ones. Assuming x(n) is the measured time series, the attractor X(n) can be expressed as where n is the discrete time index of the sampled value; m is the embedding dimension, it is the follows: dimension of the reconstructed of 1the reconstructed vectors X (state n) =space; [ x (n)T, xis(nthe + time T ), . delay, . . , x (nand + (all m− ) T )] , (2) are simply time-delayed versions of the measured signal with a lag of T. The choice of parameters T

where n is the discrete time index of the sampled m is the embeddingmethods dimension, and m influences the reconstruction result. In this study, value; the commonly acknowledged for it is the dimension reconstructed state space; T is them, time delay, all of the reconstructed the choice ofof thethe time delay T and embedding dimension namely, theand average mutual information vectors function (AMI) [28] and Cao’s function[29], proposedsignal to calculate embedding are simply time-delayed versions of the are measured with athe lag of T. The parameters. choice of parameters T and m influences the reconstruction result. In this study, the commonly acknowledged methods for the choice of the time delay T and embedding dimension m, namely, the average mutual information function (AMI) [28] and Cao’s function [29], are proposed to calculate the embedding parameters.

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2.3. Feature Extraction As indicated earlier, damage to a system is expected to alter the geometric portrait of the attractor in the state space. The difference between the undamaged and damaged attractors then becomes a good candidate feature for damage detection. Here, we introduce a certain metric called NNPE as the feature to identify the difference between the attractors. A schematic overview of feature NNPE extraction from the reconstructed state-space attractors is provided in Figure 3. First, P random points x(i) (i = 1,2, . . . ,P) are selected from the baseline attractor reconstructed from the undamaged system. The selection of the value of P influences the feature extraction result. P is set to N/100 in this study based on Pecora’s work [30], where N is the number of recorded data. Next, Q points y(j) (j = 1,2, . . . ,Q) closest to each point x(i) are selected from the current-line attractor reconstructed from the compared system, which may suffer from certain damage. When selecting the closest Q points in current-line attractor, the same P points x(i) (i = 1,2, . . . ,P) will be used in the baseline attractor. For example, if point (1, 1) was selected as the random point in baseline attractor, then the point (1,1) will still be selected as the point in the current-line attractor. Even though in most cases, this point may not be contained on the trajectory in the current-line attractor. When the point x(i) is selected in the current-line, the closest Q points in the current-line attractor will be selected by the Euclidean distance of the specific point from the point x(i) in the state space. The Q points that have the shortest Euclidean distance from the point x(i) in current-line attractor will be selected as the closest Q points. Also, the choice of the value of Q should guarantee that the local dynamic properties of the attractor can be described clearly and that the feature extraction results will not be hidden by the noise. A proper choice is Q = N/1000 [31]. Meanwhile, to avoid the time correlation between x(i) and y(j), a Theiler Window with a step 2T is proposed when selecting the neighboring points. In this way, the minimum separation between x(i) and its closest neighbors in time will be at least 2T. After that, x(i) and y(j) will be evolved with L steps (L = 2 in this study) into the future. The prediction value of x(i) after L steps in time, xˆ (i + L), can be computed by xˆ (i + L) =

1 Q y j ( i + L ). Q j∑ =1

(3)

Once the prediction has been made, the prediction error can be computed by eri = k xˆ (i + L) − x (i + L)k

(4)

where k · k is the Euclidean norm. Finally, NNPEis proposed to capture the differences between the baseline and current-line attractors. NNPE is defined as [32] NNPE =

1 P eri 2 P i∑ =1 σi

(5)

where σi2 is the variance of the baseline signal. Obviously, this NNPE value is the quantity used for determining the differences between the baseline attractor and the current-line attractor caused by damage. The NNPE is selected as the damage-sensitive feature in this study.

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Figure The schematic of feature extraction. Figure 3. The3.schematic of feature extraction. Figure 3. The schematic of feature extraction.

2.4.2.4. Damage Detection and and Quantification Damage Detection Quantification

2.4. Damage Detection andtechnique Quantification TheThe laser scanning is introduced to visualize and quantify the damage. Any desired laser scanning technique is introduced to visualize and quantify the damage. Any desired point on the structure surface can be irradiated by a laser pulse using a galvanometer, and thedesired pitchand the point on the structure surfaceiscan be irradiated by a and laserquantify pulse using a galvanometer, The laser scanning technique introduced to visualize the damage. Any between thestructure two adjacent setirradiated to a constant. a laserusing pulseaisgalvanometer, at a point, point on the canisbe by atoWhen laser pulse the pitch pitch between thesurface twopoints adjacent points is set a constant. When shot a laser pulseand isultrasonic shot at a point, waves are generated because of the thermal expansion of the material. The ultrasonic waves between the two adjacent points is because set to a constant. Whenexpansion a laser pulse is shot at a point, ultrasonicwaves ultrasonic waves are generated of the thermal of the material. The ultrasonic propagating in the structure are then recorded by the transducer placed at a fixed point. The recorded waves are generated because of expansion of the material. ultrasonic waves propagating in the structure arethe thenthermal recorded by the transducer placed atThe a fixed point. The recorded ultrasonic responses from undamaged and damaged structures are used to calculate NNPE values propagating inresponses the structure areundamaged then recorded by damaged the transducer placedare at aused fixedtopoint. The recorded ultrasonic from and structures calculate NNPE values for each excitation point to capture the differences between the baseline and current-line attractors. ultrasonic responses from undamaged structures to calculate NNPE values for each excitation point to captureand the damaged differences betweenare theused baseline and current-line attractors. The most significant differences should occur at the damage location. Therefore, the damage can be for each excitation point to capture the differences between the baseline and current-line attractors. The most significant differences should occur at the damage location. Therefore, the damage detected by the calculated NNPE values. Notably, only a small area covering the damaged location can be Thedetected most significant differences should occurNotably, at the damage location. Therefore, the can be by the calculated NNPE values. only adetect small the area covering the damage damaged location in in the damaged structure was scanned in this study to readily damage because the damage detected by the calculated NNPE values. Notably, only a small area covering the damaged location the damaged structure was scanned in this study to readily detect the damage because the damage location is not known in advance. Furthermore, the pitch between two adjacent points in the scanned inarea the damaged structure was scanned in this study tothe readily detect thetwo damage because the damage location is not known advance. Furthermore, pitch between adjacent points the scanned is determined before in laser scanning, by countingthe number of points that correspond toinlarger location is not known in advance. Furthermore, the pitch between two adjacent points in the scanned areavalues is determined before laserpicture. scanning, the number points that NNPE in the visualization The by sizecounting of the damage can be of quantified too.correspond to larger areaNNPE isAdetermined before laser scanning, bytechnique counting points that correspond values in the visualization picture. The size ofnumber the damage can4.be quantified too.to larger schematic diagram of the proposed isthe provided inofFigure NNPE values in the visualization picture. The size of the damage can be A schematic diagram of the proposed technique is provided in quantified Figure 4. too. A schematic diagram of the proposed technique is provided in Figure 4.

Figure 4.The schematic diagram of the damage detection technique.

Figure The schematic diagram the damage detection technique. Figure 4.The4.schematic diagram of theof damage detection technique.

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3. Experimental Setup and Testing Structures

3.1. Laser-Generated Ultrasonics Damage Detection System

3.1. Laser-Generated Ultrasonics Damage Detection A laser-generated ultrasonics damageSystem detection system was built in this study to verify the

accuracy of the detection technique. A pulsed lasersystem beam was withbuilt a duration 20 nstoand at a the repetition A laser-generated ultrasonics damage detection in this of study verify of 20 KHz is generated by a Q-switched Nd:YAG pulse laser. The wavelength of the pulse is 1064 nm. accuracy of the detection technique. A pulsed laser beam with a duration of 20 ns and at a repetition laser pulse is slightly focused to a 0.3 mm diameter bywavelength a lens, andofthe pulse of The 20 KHz is generated by a Q-switched Nd:YAG pulse laser. The themaximum pulse is 1064 nm. energy 7 W/cm2 to avoid ablating the material. Through the galvanometric density is controlled below 1 × 10 The laser pulse is slightly focused to a 0.3 mm diameter by a lens, and the maximum pulse energy 7 W/cm 2 to scanner, the laser below pulse 1can be shot at any desired place the structure. generated ultrasonic density is controlled × 10 avoid ablating theon material. ThroughThe the galvanometric waves the are laser recorded a focused transducer mounted at the a fixed point on structure. The transducer scanner, pulseby can be shot at any desired place on structure. Thethe generated ultrasonic usedare here is a high-frequency transducer product by Olympus (VB213 -RM) a bandwidth waves recorded by a focused transducer mounted at a fixed point on the structure. Thewith transducer used here is aofhigh-frequency transducer product by Olympus (VB213 -RM)is with a bandwidth frequency 0–30.0 MHz, and the crystal diameter of the transducer 6 mm. This transducer frequency of 0–30.0 MHz, and the crystal diameter of generated the transducer is 6laser mm. pulse. This transducer is used for receiving the surface acoustic waves by the Glycerin is isused used as the forcouplant receivingto the acoustic waves the laser pulse. Glycerin is used as the couplant fixsurface the transducer to thegenerated structure by surface. Each dynamic response is post-amplified and to recorded fix the transducer to the structure surface. Each dynamic response is post-amplified and recorded by a 14-bit high-speed data acquisition card at a sampling frequency of 100 MHz. There is byaasync 14-bit high-speed datacontained acquisitionincard at a sampling frequency of 100MHz. is signals a sync to the signal generator the detection system who will send twoThere enable signal generator contained in laser the detection system who willacquisition send two card enable signals to theInQQ-switched Nd:YAG pulse and the high–speed data synchronously. this way, switched Nd:YAG pulse laser and the high–speed data acquisition card synchronously. this the synchronization of the laser excitation and the reception of the ultrasonic waves In can beway, guaranteed. the synchronization of the laser excitation and the reception of the ultrasonic waves can be The recorded data are transferred to a personal computer (PC) for further analysis. The process of data guaranteed. The recorded data are transferred to a personal computer (PC) for further analysis. The collection is started by a trigger signal sent out by the PC. A three-dimensional transition stage is used process of data collection is started by a trigger signal sent out by the PC. A three-dimensional to determine the relative position of the structure. The step interval of the stage is 0.01 mm, which is a transition stage is used to determine the relative position of the structure. The step interval of the sufficient interval to guarantee the repeatability of the test. All the recorded data are averaged 64 times stage is 0.01 mm, which is a sufficient interval to guarantee the repeatability of the test. All the in the time domain to improve the signal to noise ratio. recorded data are averaged 64 times in the time domain to improve the signal to noise ratio. Anoverall overallschematic schematic laser-generated ultrasonics damage detection An ofof thethe laser-generated ultrasonics damage detection systemsystem used inused this in this study is is shown shownininFigure Figure5.5. study

Figure 5. The schematic diagram of the laser-generated ultrasonics detection system; 1: Laser Figure 5. The schematic diagram of the laser-generated ultrasonics detection system; 1: Laser generator; generator; 2: Galvanometric scanner; 3: Structure to be tested; 4: Transducer; 5:Three-dimensional 2: Galvanometric scanner; 3: Structure tested; 4: Transducer; transition stage; 6: Data acquisition system;to7:be Data processing system. 5:Three-dimensional transition stage; 6: Data acquisition system; 7: Data processing system.

3.2. Testing Structures

3.2. Testing Structures

Eight identical aluminum alloy plates with different sizes of artificial rectangular grooves on Eight as identical plates with sizes artificialand rectangular grooves on their surfaces well as aaluminum twin-screwalloy compressor body different with actual sandofinclusions fatigue cracks ontheir its connection are introduced for verifying feasibility the damage detection surfaces transverse as well asplane a twin-screw compressor bodythewith actualofsand inclusions and fatigue technique. cracks on its connection transverse plane are introduced for verifying the feasibility of the damage The aluminum alloy plates are fabricated out of 5052 aluminum alloy with a dimension of 150 × detection technique. 150 × 10 mm3, and the artificial rectangular grooves have the same depths of 0.1mm but different widths, varying from 0.05mm to 0.8mm, as shown in Figure 6. Meanwhile, an actual twin-screw

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The aluminum alloy plates are fabricated out of 5052 aluminum alloy with a dimension of 150 × 150 × 10 mm3 , and the artificial rectangular grooves have the same depths of 0.1 mm but Appl. Sci. 2018, 8, x FOR PEER REVIEW 8 of 18 different widths, varying from 0.05 mm to 0.8 mm, as shown in Figure 6. Meanwhile, an actual twin-screw compressor body is introduced for the additional validation of the technique. The compressor body is introduced for the additional validation of the technique. The twin-screw twin-screw compressor body is produced by casting with grey cast iron. The connection transverse compressor body is produced by casting with grey cast iron. The connection transverse plane of the plane of the body is turned for the purpose of assembly, and sand inclusions and fatigue cracks on its body is turned for the purpose of assembly, and sand inclusions and fatigue cracks on its connection connection surface are explored. surface are explored.

Figure 6. The dimension of the plates, damage, laser excitation, and detection arrangement:(a) Figure 6.undamaged The dimension plates,undamaged damage, laser excitation, and detection arrangement:(a) Reference plate;of (b)the currently plate;(c)damage width: 0.05 mm; (d) damage Reference undamaged plate; (b) currently undamaged plate;(c)damage width: 0.05 mm; (d)mm; damage width: 0.1 mm; (e) damage width: 0.2 mm; (f) damage width: 0.4 mm; (g) damage width: 0.6 (h) width: 0.1 mm; (e) damage width: 0.2 mm; (f) damage width: 0.4 mm; (g) damage width: 0.6 mm; (h) damage width: 0.8 mm. damage width: 0.8 mm.

4. Artificial Damage Detection and Quantification for Aluminum Alloy Plates 4. Artificial Damage Detection and Quantification for Aluminum Alloy Plates 4.1. Ultrasonic Responses in Time Domain 4.1. Ultrasonic Responses in Time Domain The damage detection and quantification process contains two steps. First, a single laser pulse The damage detection and quantification process contains two steps. First, aultrasonic single laser pulse irradiating a fixed excitation point on one side of the damage is used to generate waves. irradiating fixed excitation point one side of the damage is used ultrasonic waves. The ultrasonica waves are recorded by aontransducer placed on the other sidetoofgenerate the damage. The distance The ultrasonic waves and are detection recorded point by a transducer on the other side of the6c. damage. The between the excitation is 40 mm inplaced this study, as shown in Figure Using the distance between the excitation and detection point is 40 mm in this study, as shown in Figure 6c. nonlinear state-space-based predictive feature NNPE, the differences among the ultrasonic responses Using the nonlinear predictive NNPE, the differences ultrasonic can be detected, and state-space-based thereby the damage. Next, feature the laser scanning technique among is usedthe and all the responses can be detected, and thereby the damage. Next, the laser scanning technique is used and ultrasonic responses from the irradiated points are recorded by the data acquisition system. According all the ultrasonic responses from the irradiated points are recorded by the data acquisition system. to the NNPE values calculated from each excitation point, the damage can be quantified successfully. According to of thethe NNPE calculated each in excitation point, the damage can be quantified The schematic laser values scanning progressfrom is shown Figure 6d. successfully. The schematic of the laser scanning progress is shown 6d. responses of the Using the laser-generated ultrasonics damage detection system,in theFigure ultrasonic Using the plates laser-generated ultrasonics detection the ultrasonic responses of the aluminum alloy under the excitation ofdamage a single laser pulsesystem, were recorded and plotted in Figure 7. aluminum alloy plates under the excitation of a single laser pulse were recorded and plotted in Figure 7.

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Figure 7. The recorded ultrasoinc responses the time domain: (a) Reference undamaged Figure 7. The recorded ultrasoinc responses in theintime domain: (a) Reference undamaged plate; plate; (b) (b) currently undamaged plate;(c)damage width: 0.05 mm; (d) damage width: 0.1(e) mm; (e) damage currently undamaged plate;(c)damage width: 0.05 mm; (d) damage width: 0.1 mm; damage width:width: 0.2 mm; (f) damage width: 0.4 mm; (g) damage width: 0.6 mm; damage width:width: 0.8 mm. 0.2 mm; (f) damage width: 0.4 mm; (g) damage width: 0.6 (h) mm; (h) damage 0.8 mm.

4.2.4.2. Calculation of Embedding Parameters Calculation of Embedding Parameters TheThe proposed technique attempts to detect changes in the geometric figure in the statein space proposed technique attempts to the detect the changes in the geometric figure the state resulting from damage. First, theFirst, baseline and current-line attractors are reconstructed by theby the space resulting from damage. the baseline and current-line attractors are reconstructed response datadata recorded from both thethe undamaged and damaged structures. Notably, thethe attractors response recorded from both undamaged and damaged structures. Notably, attractors are are reconstructed reconstructed using using the thesame sameembedding embeddingparameters. parameters.An Anaccurate accuratereconstruction reconstructionrequires requiresa proper a proper choice of embedding parameters,as as mentioned mentioned above. thethe choice of the choice of embedding parameters, above.Generally, Generally, choice ofembedding the embedding dimension m should guarantee that the reconstructed attractor is unfolding in the state space. dimension m should guarantee that the reconstructed attractor is unfolding in the stateInspace. addition, the choice of the time delay T depends on the appearance location of the first minimum In addition, the choice of the time delay T depends on the appearance location of the first minimum value of the function. Here, the AMI function for time delaydelay T andTCao’s function for for value of auto-covariance the auto-covariance function. Here, the AMI function for time and Cao’s function dimension m are used. For the recorded response data x(n) (n = 1,2,…,N), the AMI quantifies the dimension m are used. For the recorded response data x(n) (n = 1,2, . . . ,N), the AMI quantifies the average amount of information obtained about x(n + T) through x(n). If x(n + T) and x(n) are average amount of information obtained about x(n + T) through x(n). If x(n + T) and x(n) are completely completely independent, the AMI value becomes zero. However, in practice, the value of T independent, the AMI value becomes zero. However, in practice, the value of T corresponding to corresponding to the first minimum of the AMI function is considered sufficient, which means that the first minimum of the AMI function is considered sufficient, which means that the first minimum the first minimum value of T can be chosen as the proper time delay. Figure 8 shows the AMI values value of T can be chosen as the proper time delay. Figure 8 shows the AMI values for the eight plates’ for the eight plates’ responses. When T reached 12, all the AMI values were reaching their minimum responses. When T reached 12, all the AMI values were reaching their minimum values. Hence, the values. Hence, the time delay was chosen to be 12 for this experiment. A proper choice of embedding time delay was chosen to be 12 for this experiment. A proper choice of embedding dimension m should dimension m should guarantee that no false neighbors exist in the reconstructed state space. Cao’s guarantee that no false neighbors exist in the reconstructed state space. Cao’s functions for the eight functions for the eight plates’ responses are provided in Figure 9a. Figure 9b is Cao’s function for the plates’ responses are provided in Figure 9a. Figure 9b is Cao’s function for the plate whose minimum plate whose minimum embedding dimension is largest compared with the others’. E1 and E2 are two embedding dimension is largest compared with the others’. E1 and E2 are two quantities defined by quantities defined by Cao [29] for determining the minimum embedding dimension of a scalar time Cao [29] for determining the minimum embedding dimension of a scalar time series. Suppose a time series. Suppose a time series, x1, x2, …,xN. The attractor Xi(m)can be reconstructed as follows [29]: series, x1 , x2 , . . . ,xN . The attractor Xi (m)can be reconstructed as follows [29]: X i (m)  ( xi , xi T ,..., xi ( m1)T ), i  1, 2,..., N  (m 1)T . (6) Xi (m) = ( xi , xi+T , . . . , xi+(m−1)T ), i = 1, 2, . . . , N − (m − 1) T. (6) Define: Define: Xki X (m  1) m)(m 1) + 1)k +1)X−n (iX,mn)((i,m i (m a(ai(, i,mm ) )= i  1,i2,..., = 1,N 2,  . . mT . , N ,− mT, (7) (7) X k(X mi)(m  )X− Xn((i,m m))(m)k i

n (i ,m)

where ||·|| is some measurement of Euclidian distance and is given by the maximum norm, i.e., where ||·|| is some measurement of Euclidian distance and is given by the maximum norm, i.e., k X ( n ) − X ( n )k = max − x (8) x X k (nk )  X l (nl)  max xk  jT k+ jT xl  jT l + (0jT (j0≤n j≤ 1) n. − 1). (8) Define:

Sci. 2018, 8, x FOR PEER REVIEW Appl.Appl. Sci. 2018, 8, x FOR PEER REVIEW Appl. Sci. 2018, 8, 824 N  mT 1 1 N mT E ( m )  E (m)  a(i,am(i),.m) .    mT i 1 N NmT i 1N − mT

Define:

E(m) =

Then Then

1 N − mT

∑

(9) (9)

a(i, m).

(9)

i =1

E1)( m)E(mE(m E1 (m 1)/ 1) E (/mE)(.m) .

Then Define: Define: Define:

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E1 (m) = E(m + 1)/E(m). N  mT −mT * 1 1 1 N NmT xi mTx  xn ( i , m ) .mT . E ( m )  EE ((mm))= x  − x x  i  mT n ( i , m )  mT ∑i 1 i+mT n(i,m)+mT . mT mT − NNN mT i 1 i =1 *∗

(10)(10) (10)

(11)(11) (11)

Then Then

E2 (m) =* E∗*(m + 1)*/E∗* (m). (12) m)E(E E2 (E m2)( m (m 1)/ 1) E /(E m)(.m) . (12)(12) Equations (10) and (12) are the definitions of E1 and E2 , respectively. Notably, the values of E1 Equations the definitions Eembedding 1 and E2, respectively. Notably, values E1 Equations (10)(10) andand (12)(12) are are the definitions Eof 1an and E2, respectively. Notably, the the values offor Eof 1this and E2 stopped changing after m exceeded 15 of and dimension of 16 was selected and E 2 stopped changing after m exceeded 15 and an embedding dimension of 16 was selected for andexperiment. E2 stopped The changing after m exceeded 15 and dimension of 16 was selected for detailed selection procedure cananbeembedding found in [29]. experiment. detailed selection procedure be found in [29]. thisthis experiment. TheThe detailed selection procedure cancan be found in [29].

Figure 8. The The average mutual information (AMI) function for time time delay Figure8. average mutual information (AMI) function for delay Figure8. The average mutual information (AMI) function for time delay T. T.

Figure9. function for dimension m: (a) function for the plates’ responses; Figure 9.Cao’s Cao’s function forembedding embedding dimension m:Cao’s (a)Cao’s Cao’s function foreight theeight eight plates’ responses; Figure9. Cao’s function for embedding dimension m: (a) function for the plates’ responses; (b) Cao’s function for the plate with the largest embedding dimension. largest embedding dimension. (b) Cao’s function for the plate with the largest embedding dimension.

Damage-Sensitive Feature: NNPE 4.3.4.3. Damage-Sensitive Feature: NNPE

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4.3. Damage-Sensitive Feature: NNPE Appl. Sci. 2018, 8, x FOR PEER REVIEW 11 of 18 Once the embedding parameters are selected, all segments with the same embedding parameters are used to reconstruct the attractors. Then, the NNPE values for the ultrasonic responses of Once the embedding parameters are selected, all segments with the same embedding parameters specimens (b)–(h) are calculated by comparing their attractors with the reference undamaged attractor are used to reconstruct the attractors. Then, the NNPE values for the ultrasonic responses of reconstructed the are ultrasonic response of specimen specimensfrom (b)–(h) calculated by comparing their (a). attractors with the reference undamaged Several linear features, including the root mean xrms , (a). standard deviation, and shape factor attractor reconstructed from the ultrasonic responsesquare of specimen were calculated thefeatures, eight plates’ response data in addition to ,the NNPEdeviation, values. These features Several for linear including the root mean square xrms standard and shape are chosen not only for their ability to reflect the vibration amplitude and energy in the time domain factor were calculated for the eight plates’ response data in addition to the NNPE values. These but also for their power to represent the time series distribution of the responses [33]. To compare features are chosen not only for their ability to reflect the vibration amplitude and energy in the time the performances of also these all the calculation results aredistribution normalizedofby undamaged value. domain but forfeatures, their power to represent the time series thethe responses [33]. To The features calculated by following comparecan thebeperformances ofthe these features,equations: all the calculation results are normalized by the

undamaged value. The features can be calculated v by the following equations:

xrms =

u N u N u ∑ ( x (n))2 2 t n=1( x(n))

xrms 

 n 1

N

N

,

,

v u N u N u ∑ (( xx((nn)) −xxm) 2)2 t n =1 m

xstdx = 

 n 1

N−1

N 1

std

xs f =

xsf 

, and , and

(13) (13)

(14) (14)

xrms Nxrms

1 N N1 ∑ | x ( n )| n =1 x ( n )

 N n 1

(15) (15)

where xm is the mean value of x(n). Figure shows the value values each feature calculated from the dynamic responses for specimens where x10 the mean ofof x(n). m is (b)–(h). ItFigure is clear that: (1) damage exceeded 0.4 mm, all the feature values were 10 shows the when values the of each featurewidth calculated from the dynamic responses for specimens changing, which means that all the the features had the ability to detect damage larger than 0.4were mm; (2) (b)–(h). It is clear that:(1) when damage width exceeded 0.4 mm, all the feature values changing,linear whichfeatures means that all the featuresinsensitive had the ability to detect damage 0.4mm; (2)the the proposed were relatively to damage smallerlarger than than 0.4 mm, as evidenced were relatively damage 0.4mm, as evidenced by by theproposed tangent linear slopesfeatures of the linear features’insensitive plots that to were closesmaller to zerothan when the damage was smaller the tangent slopes of the linear features’ plots that were close to zero when the damage was smaller than 0.4 mm; and (3) compared to the linear features, the plot of the NNPE had the steepest tangent 0.4mm; and (3) compared to the linear features, the plot of the NNPE had the steepest tangent slope than when the damage width changed from 0 to 0.8 mm. The value of the tangent slope of the NNPE slope when the damage width changed from 0 to 0.8mm. The value of the tangent slope of the NNPE plot is almost 10 times larger than those of the others, especially when the damage width is smaller plot is almost 10times larger than those of the others, especially when the damage width is smaller than 0.4 mm. This result reveals that the NNPE feature outperformed the other linear features and can than 0.4mm. This result reveals that the NNPE feature outperformed the other linear features and be used damage. canto bedetect used tosmaller detect smaller damage.

Figure 10. A comparison of the normalized features at different damage widths.

Figure 10. A comparison of the normalized features at different damage widths.

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4.4. Damage Visualization and Quantification As mentioned in Section 2.3, the excitation laser pulse scans over both the damaged area and the comparison undamaged area while the ultrasonic responses from the excitation point are recorded by a transducer placed at a fixed point. The scanning area covering the damage was 5 × 5 mm2 in this experiment. The scanning process continues until the whole area is covered. The calculated NNPE values can be used to visualize the entire scanned area, and the spatial distribution of the values is expected to help in detecting the damage. Furthermore, because the pitch between two adjacent points in the scanned area is known before scanning (0.02 mm for this experiment), the size of the damage can be quantified by counting the number of points that contain damage in the visualization picture. The results are summarized in Figure 11. For simplicity’s sake, only the visualization pictures for specimens (c) and (d) with the smallest damage widths are plotted. One thing deserves to be mentioned is that when the laser beam spot irradiates in the front of the damage, the focal distance of the laser beam will change and result in a varying diameter of the laser beam spot. It means that the presence of the damage changes the characteristics of the structure as well as the laser beam. However, we should notice that the changing in the received signal caused by a varying laser beam spot is very limited. According to the work conducted by Aindow et al. [34], the diameter of the laser beam spot mainly affects the pulse duration of the surface waves. Compared with the nonlinear modulation caused by the damage as shown in Figure 2, the effects caused by a varying laser beam spot is almost negligible. From another perspective, the state-space predictive model mainly focuses on the changing of the received signal. Generally speaking, the changing of the laser beam spot caused by damage is helpful for the damage detection. From Figure 11 we can see that a strongest nonlinearity was observed when damage appeared. Thus, the damage could be localized by the proposed technique successfully. Notably, the distribution of the damage is uniform through the Y direction. This is caused by the limitation of the transducer. When the laser pulse irradiates at the edge of the transducer, the laser generated ultrasonic waves will be propagating to the transducer obliquely. Some of the signals may be missed in this situation. So the calculated NNPE values are not uniformly distributed, especially at the edge of the scanning area. By extracting the coordinate values of the damage in Figure 11, the damage size can be quantified too. In Figure 11a, the longest distance of the damage width along the X direction was 59.7 − 57.1 = 2.6. The width of the damage was then 2.6 × 0.02 = 0.052 mm, which matched the actual width. Similarly, the width of the damage to structure (d) was 5.1 × 0.02 = 0.102 mm. Using this method, the damage was not only localized, but its size was quantified too. Especially noteworthy is the number of scanning points and the pitches between two adjacent points being adjustable, which means, proper visualization parameters can be chosen to detect the different damage dimensions to obtain the best visualization results. For example, a larger distance between the scanning points should be chosen to visualize lager dimensioned damage. In the above damage detection process, the crack is contained in the scanning area. However, if the damage is located between the scanning area and the transducer, the damage detection process is relatively cumbersome. In this situation, the detection process is as follows: Three plates are needed, as shown in Figure 6a–c. Plates (a) and (b) are undamaged and plate (c) is a damaged plate with a crack. First of all, we make plate (a) the reference undamaged plate and plate (b) the current undamaged plate to be detected. Calculate the NNPE values in the scan area for plate (b). It is reasonable to predict that the calculated NNPE values will be basically the same. Secondly, make plate (a) the reference undamaged plate and plate (c) the current plate to be detected. Calculate the NNPE values in the scan area for plate (c). Again, the calculated NNPE values will be basically the same. Thirdly, compare the NNPE values calculated from plate (c) with the NNPE values calculated from plate (b). It is not hard to predict that the NNPE values calculated from plate (c) will be larger than the NNPE values calculated from plate (b) as a result of the damage. In this case, we can tell that there is a crack in plate (c), but the location of the crack is still unknown. This damage detection process is relatively cumbersome for practical applications. In the following, different scanning modes will be proposed to simplify the damage detection process.

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Figure 11. Damage visualization by the values: (a) Damage width: 0.05 0.05 mm;mm; (b) damage width: Figure 11. Damage visualization by NNPE the NNPE values: (a) Damage width: (b) damage width: Figure 11. Damage visualization by the NNPE values: (a) Damage width: 0.05 mm; (b) damage width: 0.1 mm. 0.1 mm. 0.1 mm.

5. Actual Damage Detection and Quantification of a Twin-Screw Compressor Body 5. 5. Actual Actual Damage Damage Detection Detection and and Quantification Quantification of of aa Twin-Screw Twin-ScrewCompressor CompressorBody Body 5.1. 5.1. Description of the of a of Twin-Screw Compressor Body Description of Detection the Detection a Twin-Screw Compressor Body 5.1. Description of the Detection of a Twin-Screw Compressor Body An An actual 22 kW twin-screw compressor body (218A) is introduced for further verification of the actual 22 kW twin-screw compressor body (218A) is introduced for further verification of the An actual 22 kW twin-screw compressor body (218A) is introduced for further verification of the effectiveness of the damage detection technique. TheThe body is made of grey castcast ironiron (No.35) by casting effectiveness of the damage detection technique. body is made of grey (No.35) by casting effectiveness of the damage detection technique. The body is made of grey cast iron (No.35) by casting andand hashas rough dimensions of 370 × 230 × 180 , as 3shown in Figure 12. The upper andand lower parts rough dimensions of 370 × 230 × mm 180 3mm , as shown in Figure 12. The upper lower parts and has rough dimensions of 370 × 230 × 180 mm3, as shown in Figure 12. The upper and lower parts of the body areare connected byby positioning pins and of the body connected positioning pins andbolts. bolts.There Thereisisaastrict strictdemand demandfor for the the quality of the of the body are connected by positioning pins and bolts. There is a strict demand for the quality of the body body because becauseany anysmall smallcrack crackininthe thebody bodymay maycause causeanan extremely horrible production accident extremely horrible production accident under the body because any small crack in the body may cause an extremely horrible production accident under high temperature high-pressure working conditions. However, in practice, it is to easy to high temperature andand high-pressure working conditions. However, in practice, it is easy produce under high temperature and high-pressure working conditions. However, in practice, it is easy to produce sand inclusions and the resulting into theduring body during the casting process. sand inclusions and the resulting fatiguefatigue crackscracks into the body the casting process. Using the produce sand inclusions and the resulting fatigue cracks into the body during the casting process. Using the proposed technique the experimental setup proved in thisthe study, the damage on the proposed technique and theand experimental setup proved in this study, damage on the connection Using the proposed technique and the experimental setup proved in this study, the damage on the connection transverse plane was detected and quantified. of the damage actual damage are shown in 13. transverse plane was detected and quantified. ImagesImages of the actual are shown in Figure connection transverse plane was detected and quantified. Images of the actual damage are shown in Figure Both images were taken with amicroscope digital microscope by KEYENCE (VHX-100). 13a is Both13. images were taken with a digital by KEYENCE (VHX-100). Figure 13aFigure is a global view Figure 13. Both images were taken with a digital microscope by KEYENCE (VHX-100). Figure 13a is a global view of the damage and contains both the sand inclusions and fatigue cracks. The of the damage and contains both the sand inclusions and fatigue cracks. The magnification is 25 times a global view of the damage and contains both the sand inclusions and fatigue cracks. The magnification 25 times Figure 13b isofa Figure local enlarged of Figure 13a. The the originalissize. Figurethe 13boriginal is a localsize. enlarged picture 13a. The picture area containing a fatigue crack magnification is 25 times the original size. Figure 13b is a local enlarged picture of Figure 13a. The areaincontaining fatigue crack in Figure 13a was extracted and look enlarged obtain a The closer look at the is Figure 13aa was extracted and enlarged to obtain a closer at thetodamage. magnification area containing a fatigue crack in Figure 13a was extracted and enlarged to obtain a closer look at the damage. The the magnification is 100 times the original size. 100 times original size. damage. The magnification is 100 times the original size.

Figure 12. The twin-screw compressor body. body. Figure 12. The twin-screw compressor body.

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Figure 13. The The images images of of the the damage damage in in two two different different scanning scanning modes: modes: (a) (a) aa global global view view of of the the damage; damage; Figure 13. (b) (b) enlarged enlarged local local fatigue fatigue crack. crack.

5.2. Damage Visualization and Quantification In this section, we discuss the detection, visualization and quantification of the damage on the connection of aoftwin-screw compressor body using experimental setup presented connection transverse transverseplane plane a twin-screw compressor bodythe using the experimental setup in Section 3. this damage scanning with different presented in In Section 3. In thisdetection damage process, detectiontwo process, twomodes scanning modes withdamage differentdetection damage accuracies were used were in theused experiment to identify the damage the withdamage differentwith dimensions. mode one, detection accuracies in the experiment to identify different In dimensions. 2 , and the distance the scanning the laserarea pulse set to pulse 10 × 10 mm between the two between adjacent In mode one,area the of scanning of was the laser was set to 10 × 10mm2, and the distance points 0.2 mm, yielding scanning points. damage was quickly located in quickly this wide range the twowas adjacent points was 2500 0.2mm, yielding 2500The scanning points. The damage was located 2 2 scanning mode. The scanning area of thescanning laser pulse was set to 5 ×pulse 5 mmwas in set mode The distance in this wide range scanning mode. The area of the laser to 5two. × 5mm in mode between two adjacent wasadjacent 0.1 mm,points yielding 2500 scanning points. More information the two. Thethe distance betweenpoints the two was 0.1mm, yielding 2500 scanning points.on More tiny damage was acquired by using this scanning mode. A schematic of the second scanning mode information on the tiny damage was acquired by using this scanning mode. A schematic of the second was shown in Figure 13a. Inin this experiment, the baseline datathe wasbaseline acquired from theacquired same connection scanning mode was shown Figure 13a. In this experiment, data was from the transverse plane on the same plane twin-screw body. The only difference thatonly the scanned area same connection transverse on thecompressor same twin-screw compressor body.isThe difference is used for scanned acquiringarea the baseline was examined carefully withexamined the digitalcarefully microscope to the make sure that the used for data acquiring the baseline data was with digital there is no obvious the is area. In this way, thisin area be In treated as thethis ‘reference microscope to makedefect sure in there no obvious defect thecan area. this way, area canundamaged be treated structure’ in the experiment. embedding be chosen parameters before computing as the ‘reference undamaged The structure’ in the parameters experiment.should The embedding shouldthe be NNPE embedding parameters of ten selected ultrasonic responses recorded by chosenvalues. before The computing the NNPE values. Therandomly embedding parameters of ten randomly selected aultrasonic transducer placed at a fixed point were calculated AMI and were Cao’scalculated function. by Thethe calculation responses recorded by a transducer placedby at the a fixed point AMI and results are provided Figures 14results and 15,are respectively. The results14 calculated by Cao’s function for the Cao’s function. The in calculation provided in Figures and 15, respectively. The results response, minimum dimension was the largest compared with those of the largest others, calculatedwhose by Cao’s functionembedding for the response, whose minimum embedding dimension was are shown with in Figure From Figures 14 andin 15, when15b. the time T reached 4, the calculation compared those15b. of the others, are shown Figure Fromdelay Figures 14 and 15, when the time results all the4,responses by using the for AMI were by close to the value, andclose the delay Tfor reached the calculation results allfunction the responses using theminimum AMI function were values of E1 and value, E2 didand not the change after = 4 and m = 24 were selected to the minimum values of Em1 exceeded and E2 did23. notHence, changeTafter m exceeded 23. Hence, T =in4 this the time delay T and embedding scanning modedimension two were and experiment. m = 24 were Similarly, selected in this experiment. Similarly, the dimension time delay m T in and embedding calculated to bemode 3 andtwo 19, respectively. Next,toall the same Next, embedding parameters m in scanning were calculated beresponses 3 and 19,with respectively. all responses withwere the used reconstructparameters the attractors. Based attractors reconstructed bothonthethe undamaged same toembedding were usedontothereconstruct the attractors.from Based attractors and damaged sections, the 2500 NNPE valuesand weredamaged computedsections, and are summarized in Figure 16. Here, reconstructed from both the undamaged the 2500 NNPE values were the detection by linear feature root mean square also calculated shown in Figure 17 in computed andresult are summarized in Figure 16. Here, thewas detection result by as linear feature root mean addition to the values. Figure the 17 values of the feature sand inclusion square was alsoNNPE calculated as In shown in16a, Figure in addition to the NNPE NNPE around values. the In Figure 16a, the are the of largest compared with othersthe in the scanning area. the sand inclusion canothers be detected values the feature NNPE around sand inclusion areThus, the largest compared with in the and visualized clearly.theFurthermore, the can shape direction the resulting fatigue crack canthe be scanning area. Thus, sand inclusion be and detected and of visualized clearly. Furthermore, vaguely distinguished the picture too. crack But, the of thedistinguished fatigue crack from is almost submerged shape and direction of from the resulting fatigue canpicture be vaguely the picture too. in thethe environmental duecrack to the detection accuracy. Inenvironmental Figure 16b, thenoise shapedue andtodirection But, picture of thenoise fatigue is low almost submerged in the the low information of the fatigue crack can beshape identified clearly, which means that in fatigue scanning mode detection accuracy. In Figure 16b, the and direction information of the crack cantwo be the damage detection accuracy has been greatly improved as a result of changes in the visualization identified clearly, which means that in scanning mode two the damage detection accuracy has been greatly improved as a result of changes in the visualization parameters. In Figure 17, the sand inclusion has been detected and visualized successfully. However, the detection of the resulting

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15 of 18 inclusion has been detected and visualized successfully. However, the detection of the resulting has failed since thereabout is no the obvious information about 17. the fatigue crack has failed since fatigue there iscrack no obvious information fatigue crack in Figure fatigue crack has failed since there is no obvious information about the fatigue crack in Figure 17. fatigue crack inresult Figure 17. surprised This detection is not surprised since the nonlinear ultrasonic features This detection is not sinceresult the nonlinear ultrasonic features are usually more sensitive This detection result is not surprised since the nonlinear ultrasonic features are usually more sensitive are usually more sensitive to small cracks than the linear ones as mentioned above. This detection to small cracks than the linear ones as mentioned above. This detection result is consistent with the to small thanwith the the linear ones as mentioned above. This detection result is consistent with the result is cracks consistent result given in Figure 10. result given in Figure 10. result given in Figure 10.

Figure 14. The AMI versus time delay T. Figure 14. 14. The The AMI AMI versus versus time time delay delay T. T. Figure

Figure 15. The Cao’s function versus the embedding dimension m: (a) Cao’s function for the ten Figure 15. The Cao’s function versus the embedding dimension m: (a) Cao’s function for the ten Figure 15.selected The Cao’s function versus the embedding dimension m: (a) Cao’s function ten randomly ultrasonic responses; (b) Cao’s function for the ultrasonic response with for the the largest randomly selected ultrasonic responses; (b) Cao’s function for the ultrasonic response with the largest randomly selected ultrasonic responses; (b) Cao’s function for the ultrasonic response with the largest embedding dimension. embedding dimension. embedding dimension.

By extracting the coordinate values of the damage, the size of the cracks can also be quantified. By extracting the coordinate values of the damage, the size of the cracks can also be quantified. The largest width ofthe the sand inclusion in Figure 16 was 1.24(0.2 18.3)) mm. The be largest width By extracting values the damage, the size×× (24.5 of the−−cracks can also quantified. The largest width of thecoordinate sand inclusion in of Figure 16 was 1.24(0.2 (24.5 18.3)) mm. The largest width of thelargest sand inclusion Figure was 1.12in(0.2 × (24.9 19.3)) mm. Both of the calculated were The width of in the sand 17 inclusion Figure 16 −−was 1.24(0.2 × (24.5 − 18.3)) mm.values The largest of the sand inclusion in Figure 17 was 1.12 (0.2 × (24.9 19.3)) mm. Both of the calculated values were in line with itssand actual size of 1.21 mm, but the value calculated by−NNPE values is more accurate. The width of the inclusion in Figure 17 was 1.12 (0.2 × (24.9 19.3)) mm. Both of the calculated in line with its actual size of 1.21 mm, but the value calculated by NNPE values is more accurate. The widths of the measuring points in Figure 16b are 380 (0.1 × (17.1 − 13.3)) um, 250 (0.1 × (25.1 − 22.6)) values were line with its actual of 1.21 but(0.1 the×value by250 NNPE more widths of theinmeasuring points in size Figure 16b mm, are 380 (17.1 calculated − 13.3)) um, (0.1 ×values (25.1 −is22.6)) um, and 110 (0.1 × (28.4 −measuring 27.3)) um,points respectively, which match the actual measurements well. accurate. The widths of the in Figure 16b are 380 (0.1 × (17.1 − 13.3)) um, 250 (0.1 × um, and 110 (0.1 × (28.4 − 27.3)) um, respectively, which match the actual measurements well. Therefore, theum, proposed technique was again able to detectwhich and match quantify the damage on the (25.1 − 22.6)) and 110 (0.1 × (28.4 − 27.3)) um, respectively, the actual measurements Therefore, the proposed technique was again able to detect and quantify the damage on the connection transverse plane of the twin-screw body. Also from the result can see well. Therefore, the proposed technique was compressor again able to detect and quantify the we damage onthat the connection transverse plane of the twin-screw compressor body. Also from the result we can see that the nonlinear feature NNPE is more sensitive to the damage thanAlso the linear feature. connection transverse plane of the twin-screw compressor body. from the result we can see that the nonlinear feature NNPE is more sensitive to the damage than the linear feature. the nonlinear feature NNPE is more sensitive to the damage than the linear feature.

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Figure 16.The damage visualization by theby NNPE valuesvalues (the pitches between the two points Figure Thedamage damage visualization the NNPE NNPE (the pitches pitches between theadjacent two adjacent adjacent points Figure 16. 16.The visualization by the values (the between the two points are: (a) 0.2 mm; (b) 0.1 mm. are: are: (a) (a) 0.2 0.2 mm; mm; (b) (b) 0.1 0.1 mm. mm.

Figure 17. The damage visualization by the linear RMS values. Figure 17. The damage visualization by the linear RMS values. Figure 17. The damage visualization by the linear RMS values.

6. Conclusions 6. Conclusions 6. Conclusions This paper presents a non-destructive damage detection, visualization, and quantification This paper presents a non-destructive damage detection, visualization, and quantification techniqueThis based on laser-generated ultrasonics anddamage state-space predictive models. Different types of paper presents a non-destructive detection, visualization, and quantification technique based on laser-generated ultrasonics and state-space predictive models. Different types of damage to aluminum alloy plates and a ultrasonics twin-screwand compressor body were detected quantified technique based on laser-generated state-space predictive models.and Different types of damage to aluminum alloy plates and a twin-screw compressor body were detected and quantified by using NNPE. This feature is extracted from the attractors reconstructed by thedetected ultrasonic damage to aluminum alloy plates and a twin-screw compressor body were andresponses quantified by by using NNPE. This feature is extracted from the attractors reconstructed by the ultrasonic responses in the timeNNPE. domain recorded a transducer at thereconstructed surface of thebystructure. By capturing using This featureby is extracted frommounted the attractors the ultrasonic responses in in the time domain recorded by a transducer mounted at the surface of the structure. By capturing the the differences in the NNPEbyvalues between the undamaged and damaged structures, the the time domain recorded a transducer mounted at the surface of the structure. By capturing the differences in the NNPE values between the undamaged and damaged structures, the nonlinearity of the structures, whichbetween are usually caused by damage, can bestructures, detected. the Furthermore, differences in the NNPE values the undamaged and damaged nonlinearity of nonlinearity of the structures, which are usually caused by damage, can be detected. Furthermore, the damage can bewhich visualized and even quantified by observing the spatial distribution of NNPE the structures, are usually caused by damage, can be detected. Furthermore, the damage can be the damage can be visualized and even quantified by observing the spatial distribution of NNPE values calculated thequantified ultrasonic the area excited of byNNPE a scanning laser pulse. visualized andby even byresponses observing from the spatial distribution values calculated by the values calculated by the ultrasonic responses from the area excited by a scanning laser pulse. Artificial damage to aluminum alloy plates, as by well as the actual inclusions fatigue ultrasonic responses from the area excited a scanning lasersand pulse. Artificialand damage to cracks aluminum Artificial damage to aluminum alloy plates, as well as the actual sand inclusions and fatigue cracks in a twin-screw compressor body, have been successfully detected and quantified by using the in a twin-screw compressor body, have been successfully detected and quantified by using the proposed technique. proposed technique.

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alloy plates, as well as the actual sand inclusions and fatigue cracks in a twin-screw compressor body, have been successfully detected and quantified by using the proposed technique. Some important issues that are not considered in this paper are the capability of the technique in detecting the depth of the damage, the internal damage, and the damage on curved surface. A follow-up study with the proposed feature NNPE will focus on those issues. Author Contributions: Y.L. and S.Y. conceived and designed the experiments; Y.L. and X.L. performed the experiments; Y.L. and X.L. analyzed the data; Y.L. contributed reagents/materials/analysis tools; Y.L. wrote the paper. Acknowledgments: This research was funded by National Natural Science Foundation of China under Grant Number 51375434. Conflicts of Interest: The authors declare no conflict of interest.

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