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Kalman Filters in Geotechnical Monitoring of Ground Subsidence Using Data from MEMS Sensors Cheng Li 1, *, Rafig Azzam 2 and Tomás M. Fernández-Steeger 3 1 2 3

*

Chengdu Engineering Corporation Limited, Chengdu 610072, China Department of Engineering Geology and Hydrogeology, RWTH Aachen University, Aachen 52064, Germany; [email protected] Department of Applied Geosciences, TU Berlin University, Berlin 10587, Germany; [email protected] Correspondence: [email protected]; Tel.:+86-28-8739-2645

Academic Editor: Jörg F. Wagner Received: 25 March 2016; Accepted: 1 June 2016; Published: 19 July 2016

Abstract: The fast development of wireless sensor networks and MEMS make it possible to set up today real-time wireless geotechnical monitoring. To handle interferences and noises from the output data, Kalman filter can be selected as a method to achieve a more realistic estimate of the observations. In this paper, a one-day wireless measurement using accelerometers and inclinometers was deployed on top of a tunnel section under construction in order to monitor ground subsidence. The normal vectors of the sensors were firstly obtained with the help of rotation matrices, and then be projected to the plane of longitudinal section, by which the dip angles over time would be obtained via a trigonometric function. Finally, a centralized Kalman filter was applied to estimate the tilt angles of the sensor nodes based on the data from the embedded accelerometer and the inclinometer. Comparing the results from two sensor nodes deployed away and on the track respectively, the passing of the tunnel boring machine can be identified from unusual performances. Using this method, the ground settlement due to excavation can be measured and a real-time monitoring of ground subsidence can be realized. Keywords: Kalman filter; ground subsidence; rotation matrices; accelerometer; inclinometer

1. Introduction Due to the fast development of Micro Electro Mechanical Systems (MEMS) and the optimization of sensor cost, size and energy consumption in the last two decades, Wireless Sensor Networks (WSNs) has been progressively entered many areas such as disaster monitoring [1–3] and industrial sensing [4,5]. A WSN consists of spatially distributed sensor nodes to monitor various conditions such as temperature, pressure, humidity, sound, vibration, pollutants and motion. In this sense they allow us to enter Internet of Things (IoT) and provide physical information about our environment to users where ever needed. Nowadays, real-time remote surveillance of environmental conditions has been achieved and a much more comprehensive understanding of the variations of natural environments over time can be obtained. From 2007 to 2011, the Department of Engineering Geology and Hydrogeology at RWTH Aachen University and its partners carried out a joint project namely SLEWS (a Sensor based Landslide Early Warning System), aiming at developing a prototype of an alarm and early warning system for landslides. SLEWS was funded by GEOTECHNOLOGIEN, which is a geoscientific research and development program supported by the German Federal Ministry for Education and Research (BMBF) and the German Research Foundation (DFG). A self-organizing and multi-hop wireless monitoring network was created thereby [6,7]. This wireless monitoring system and its predecessor Sensors 2016, 16, 1109; doi:10.3390/s16071109

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system X-SLEWS [8] have been applied to monitor several kinds of natural hazards and geotechnical geotechnical such tiltingdeformation of rock towers deformation [9], due ground subsidence due to activities suchactivities as tilting of rockastowers [9], ground subsidence to ground improvement ground improvement measures [10], [11], tunneling construction [11], and monitoring [12]. measures [10], tunneling construction and landslide monitoring [12].landslide Figure 1 exhibits the main Figure 1 exhibits the main components of the X-SLEWS Thea node capsule a base components of the X-SLEWS network. The node capsulenetwork. comprises base board forcomprises processing and boardand for an processing and radio and an for sensing and backup storage. The radio add-on board for sensing andadd-on backupboard data storage. The add-on boarddata is easily replaced add-on board is with easilydifferent replacedsensors by another one with to allow fastThe adoption tocapsule distinct by another one to allow fastdifferent adoptionsensors to distinct tasks. battery tasks. Thewith battery capsule allocatedprovides with three 3.6-V batteries provides the power toseparating the sensor allocated three 3.6-V batteries the power supply to the sensor nodesupply capsule, node and capsule, separating nodealso andtoenergy source allows alsoortoadd exchange sources or add node energy source allows exchange energy sources modulesenergy for energy harvesting modules energy like solar gateway data receives stores the in retrieved data like solar for panels. Theharvesting gateway receives andpanels. stores The the retrieved fromand all the nodes the network frombroadcasts all the nodes the network and broadcasts the updated clockItperiodically connected and the in updated clock periodically to connected nodes. bears also a to raspberry PI nodes. with a It bears a raspberry PI withand a server to control communication data storage and up-link can be server to also control communication data storage and can be additional and equipped with a data additional equipped with operation a data up-link via 3G modem for remote operation and monitoring [8,11]. via 3G modem for remote and monitoring [8,11].

Figure 1. 1. Components Components of X-SLEWS (From [11]). The node capsule comprises a base board for basic basic and storing function. The The battery capsule allocated with operation and and an an add-on add-onboard boardfor forsensing sensing and storing function. battery capsule allocated threethree 3.6-V3.6-V batteries provides the the power supply to to the data with batteries provides power supply thenode nodecapsule capsulewhile while measuring measuring and data transmitting. The gateway gateway receives receives and and saves saves the the retrieved retrieved data data from from all all the the nodes nodes in the network and transmitting. broadcasts broadcasts the the updated updated clock clock periodically periodically to to connected connected nodes. nodes.

The X-SLEWS X-SLEWS wireless wireless monitoring monitoring system system was applied in a one-day one-day field field test test on on top top of of the the The was applied in a construction site of the South Hongmei Road super highway tunnel in Shanghai, and positional construction site of the South Hongmei Road super highway tunnel in Shanghai, and positional information ofofthe thesensor sensor nodes been obtained based onmeasurements the measurements from embedded information nodes hashas been obtained based on the from embedded MEMS MEMS accelerometers and inclinometers. Both the derived normal vectors onoutput the output of accelerometers and inclinometers. Both of the of derived normal vectors basedbased on the of the the MEMS sensors contain interferences and noises and thus a data filter was needed for a good MEMS sensors contain interferences and noises and thus a data filter was needed for a good estimate. estimate. In the following we will briefly introduce sensors and measuring principleThen applied. In the following we will briefly introduce the sensorsthe and measuring principle applied. the Then the processing of sensor data using rotation matrices will be described. Finally, the usage of the processing of sensor data using rotation matrices will be described. Finally, the usage of the Kalman Kalman filter for data estimation is described in detail and the results will be discussed. filter for data estimation is described in detail and the results will be discussed. 2. Applied AppliedMEMS MEMSSensors Sensors Each sensor node has been been equipped equipped with aa 3-axis 3-axis accelerometer accelerometer and and two two orthogonal orthogonal 1-axis 1-axis inclinometers, are produced by Murata Oy (previous VTI Technologies, inclinometers,both bothof which of which are produced by Electronics Murata Electronics Oycalled (previous called VTI Vantaa, Finland) and areFinland) mounted on are an add-on board. Inadd-on Table 1 board. a generic sheet for the two Technologies, Vantaa, and mounted on an In data Table 1 a generic datasensor sheet is forshown. the two sensor is shown. Basically, MEMS Accelerometers and inclinometers share the same principle to observe acceleration. A sketch of a MEMS accelerometer is shown below in Figure 2. The movable proof mass is suspended by the restoring springs, while the sensing plates are fixed onto the sensor board.

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The accelerometer is Table sensitive to the linear of the sensor the earth gravitational field. 1. Generic Data Sheetacceleration of the two Sensors Used in the and Deployment. When the sensing plate deflects from the original position, the change in capacitance (C1 and C2) Table 1. Generic Data SheetAccelerometer of the two Sensors Used in theInclinometer Deployment. Sensor Type between the fingers of Product the proof mass and sensing plates can be converted into a voltage signal, which SCA3100-D04 SCA830-D07 Inclinometer Sensor Type Accelerometer 3 acceleration 3 is subsequently digitized to digital value, from which the along themm axis can be expressed Size(w × h × l) 7.0 × 3.3 × 8.6 mm 7.6 × 3.3 × 8.6 Product SCA3100-D04 SCA830-D07 Measurement Axis 3-axis 1-axis 3 3 through a given formula. Due to different precision of the sensors, the output of the accelerometer and Size(w × h × l) 7.0 × 3.3 × 8.6 mm 7.6 × 3.3 × 8.6 mm Range ±2 g ±1 g Measurement Axis 3-axisto obtain the acceleration 1-axis value [13]. inclinometer is substituted into respective formulas Sensitivity (LSB/g) 900 (0.0637°/count) 32,000 (0.00179°/count) Range ±2 g ±1 g Sensitivity (LSB/g) 900 (0.0637°/count) 32,000 (0.00179°/count) Table 1. Generic Data Sheet of the two Sensors Used in the Deployment.

Basically, MEMS Accelerometers and inclinometers share the same principle to observe acceleration. A sketch a MEMS accelerometer is shown below in Figure 2. Theprinciple movable proof mass Basically, MEMSofAccelerometers and inclinometers share the same to observe Sensor Type Accelerometer Inclinometer is suspendedA bysketch the restoring springs, while theissensing fixed onto the sensor board. The acceleration. of a MEMS accelerometer shown plates below are in Figure 2. The movable proof mass SCA3100-D04 SCA830-D07 accelerometer isProduct sensitive to the linearwhile acceleration of the sensor the earth is suspended by the restoring springs, the sensing plates areand fixed onto thegravitational sensor board.field. The 3 3 Size(w ˆhˆ l)to the from 7.0original ˆ 3.3 ˆ position, 8.6 ˆ capacitance 3.3 ˆ gravitational 8.6 mm When the sensing plate deflects the change in (C1 andfield. C2) accelerometer is sensitive linearthe acceleration of mm the sensor and7.6 the earth Measurement Axis 3-axis can be converted into1-axis between the fingersplate of thedeflects proof mass a voltage signal, which When the sensing fromand thesensing originalplates position, the change in capacitance (C1 and C2) Range to digital value, from which ˘2 g the acceleration along the˘1 g can be expressed is subsequently digitized axis between the fingers of the proof mass and sensing plates can be converted into a voltage signal, which 900 (0.0637˝ /count) 32,000 (0.00179˝ /count) Sensitivity (LSB/g) through a givendigitized formula.to Due to different precision sensors, the output of the is subsequently digital value, from which of thethe acceleration along the axis canaccelerometer be expressed and inclinometer is substituted into respective formulas to obtain thethe acceleration [13]. through a given formula. Due to different precision of the sensors, output of value the accelerometer and inclinometer is substituted into respective formulas to obtain the acceleration value [13].

C1 C2 C1 C2

Fixed Sensing Fixed Plate Sensing Plate

Movable Proof Movable Mass Proof Mass

Figure 2. Sketch of a MEMS Accelerometer (Modified from [14]). The sensing plate is fixed onto the

Figure 2. Sketch of a MEMS Accelerometer (Modified from [14]). The sensing plate is fixed onto sensor andofthe movable proof mass is(Modified suspendedfrom by the restoring spring. The isproof will Figure board 2. Sketch a MEMS Accelerometer [14]). The sensing fixedmass the the sensor board and the movable proof mass is suspended by the restoringplate spring. Theonto proof mass drift downward when a linear acceleration points upwards or the Earth’s gravitational field points sensor board and the movable proof mass is suspended by the restoring spring. The proof mass will will drift downward when a linear acceleration points upwards or the Earth’s gravitational field downwards. drift downward when a linear acceleration points upwards or the Earth’s gravitational field points points downwards. downwards.

When the accelerometer or the inclinometer is used for measuring the gravity, as the output represents weight of the earth gravitational fieldis (Figure the 3), the the tilt angle of When the accelerometer the inclinometer used for measuring gravity, as the output When thethe accelerometer ororthe inclinometer isalong usedthe foraxis measuring gravity, asthe theaxis output with respect toweight the horizontal plane can be obtained easily the via axis a sine function [11].tilt angle of the axis represents the of the earth gravitational field along (Figure 3), the

represents the weight of the earth gravitational field along the axis (Figure 3), the tilt angle of the axis with respect to horizontal the horizontal plane canbebeobtained obtained easily easily via [11]. with respect to the plane can viaaasine sinefunction function [11]. Horizontal Plane

Horizontal Plane α g' Axis

α

g'

Axis

α α g

g Figure 3. Measurement of Inclination from the Accelerometer. The accelerometer measures the value Figure 3.′,Measurement of for Inclination the Accelerometer. The accelerometer the value of which represents the weightfrom of the earth’s gravitational acceleration inmeasures themeasures axial the direction Figure 3. Measurement of Inclination from the Accelerometer. The accelerometer value 1 on the sensor board. The tilt angle of the axis ∝ with respect to the horizontal plane can be calculated of g , of which represents for the weight of of thethe earth’s in the theaxial axialdirection direction on ′, which represents for the weight earth’sgravitational gravitational acceleration acceleration g in '

via an board. inverse trigonometric function: ∝= . respect the sensor The tiltThe angle of theofaxis 9arcsin with respect to the horizontal be calculated calculated via on the sensor board. tilt angle the axis ∝ with to the horizontalplane plane can can be ' g1 via an trigonometric inverse trigonometric function: ∝= arcsin . an inverse function: 9 “ arcsin . g

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3. Acquiring Sensor Motion Using Inertial Navigation Algorithm During the monitoring, a 3-axis accelerometer returns three values in each measurement, Sensors 2016,the 16, 1109 4 of 14 axial representing respective weights of the earth’s gravitational acceleration along the three directions. In this sense each axis can be seen and handled equally to an independent sensor, like 3. Acquiring Sensor Motion Using Inertial Navigation Algorithm the two orthogonal 1-axis inclinometers which provide from each sensor a perpendicular inclination. During the the monitoring, 3-axis returns three values measurement, Processing output, tilt anglea of eachaccelerometer axis of the accelerometers and in theeach inclinometers can be representing the respective weights of the earth’s gravitational acceleration along the three axial deduced. However, we cannot gain an understanding of the spatial variations of the sensors by only directions. In this sense each axis can be seen and handled equally to an independent sensor, like the comparing the three values from accelerometers and the two values from inclinometers over time. two orthogonal 1-axis inclinometers which provide from each sensor a perpendicular inclination. Indeed, there is lack of a unified spatial parameter that enables a comparison of the results from Processing output, the tilt angle of each axis of the accelerometers and the inclinometers can be distinct sensors. Hence, before the study of the spatial variations of the sensors, a normal vector should deduced. However, we cannot gain an understanding of the spatial variations of the sensors by only be calculated a standard expression, representing offrom a sensor in a three dimensional comparingasthe three values from accelerometers and the the position two values inclinometers over time. Cartesian coordinate system. The deviation of the normal vectora can be divided into threefrom gradual Indeed, there is lack of a unified spatial parameter that enables comparison of the results stepsdistinct [15] and will beHence, brieflybefore explained as follows. sensors. the study of the spatial variations of the sensors, a normal vector should be calculated as a standard expression, representing the position of a sensor in a three

3.1. Expression of Cartesian g’ dimensional coordinate system. The deviation of the normal vector can be divided into three gradual steps [15] and will be briefly explained as follows.

We define a coordinate system OX0 Y0 Z0 , which is transformed to a new coordinate system 1 Z1 by rotating a roll angle φ, a pitch angle θ and a yaw angle ψ around x-, y- and z-axis OX 1 Y3.1. Expression of g’ respectively (Figure 4). For each step of rotation, there is a corresponding rotation matrix R that We define a coordinate system , which is transformed to a new coordinate system transfers the expression of a vector based on the old coordinate system to an expression based on the ′ ′ ′ by rotating a roll angle ϕ, a pitch angle θ and a yaw angle ψ around x-, y- and z-axis new one. There are six possible orders for the rotation of the coordinate system but only the orders of respectively (Figure 4). For each step of rotation, there is a corresponding rotation matrix that Z-Y-Xtransfers or Z-X-Y assure aofsolution, since aonspatial has two degrees of freedombased [14]. on Taking thecan expression a vector based the oldvector coordinate system to an expression the the Z-Y-Xnew order instance, being rotated z-, y- and x-axis, rotated vector of one.for There are sixafter possible orders for successively the rotation ofaround the coordinate system butthe only the orders earthofgravitational acceleration 0, ´1q1since can abespatial expressed Z-Y-X or Z-X-Y can assure ap0, solution, vectoras: has two degrees of freedom [14]. Taking the Z-Y-X order for instance, after being rotated ¨ successively around z-, y- and ˛ ¨ ˛ x-axis, the rotated vector of earth gravitational acceleration (0,0, −1)′ can 0 be expressed as: sinθ

˚ ‹ ˚ ‹ g1xyz “ R x pϕq Ry pθq Rz pψq ˝ 0 0 ‚ “ ˝ ´cosθsinϕ ‚ ′ = ( ) ( ) ( ) ´10 = − ´cosθcosϕ −

−1

Z’

(1) (1)

Z0 Yaw

ψ

Y’ O Roll

Pitch

ϴ

Y0

φ

X0 X’

Figure 4. Coordinate System Transforming Through the Order of X-Y-Z (modified from [11]). The Figure 4. Coordinate System Transforming Through the Order of X-Y-Z (modified from [11]). The initial initial coordinate system is transformed to considering the roll, pitch and yaw coordinate system OX0 Y0 Z0 is transformed to OX 1 Y 1 Z1 considering the roll, pitch and yaw angles angles around the x-, y- and z-axis respectively. around the x-, y- and z-axis respectively.

3.2. Acquirement of Rotation Angles

3.2. Acquirement of Rotation Angles

In this step, based on the equivalent relations between the sensor output value and the

corresponding of the ′ vector,relations the roll between and pitchthecan be resolved rotation In this step, components based on the equivalent sensor outputand value and the matrices arecomponents hereby obtained. As ag1result of the an accelerometer, the vector of rotation the corresponding of the vector, themechanism roll ϕ andofpitch θ can be resolved and earth’s gravitational acceleration is exported as (0,0,1) instead of (0,0, −1) [11]. Similarly, theof the matrices are hereby obtained. As a result of the mechanism of an accelerometer, the vector components of ′ are correspondingly equal to the magnitude of the normalized accelerometer T T earth’s gravitational acceleration is exported as p0, 0, 1q instead of p0, 0, ´1q [11]. Similarly, the reading

(

,

,

) after multiplying with −1, which can be presented as:

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components of g1xyz are correspondingly equal to the magnitude of the normalized accelerometer ` ˘T reading G p G px , G py , G pz after multiplying with ´1, which can be presented as: ¨

Gp “ ´g1 xyz k Gp k

˛ sinθ ˚ ‹ “ ´ ˝ ´cosθsinϕ ‚ ´cosθcosϕ

Solving the equation, the roll ϕ and the pitch θ can be expressed as: Accelerometer: ˙ ˆ G py ϕ “ arctan G pz θ “ ´arcsin b Inclinometer:

G px G2px ` G2py ` G2pz

(2)

(3) (4)

G py ϕ “ arcsin b 1 ´ G2px

(5)

θ “ ´arcsinG px

(6)

Since current monitoring system is not equipped with a magnetometer or a gyroscope, the value of yaw ψ cannot be solved. Nevertheless, taking account of the relatively simple deformation mode in geotechnical projects and the slight relevance to construction safety, the yaw ψ that represents the rotation around z-axis could be considered as zero. 3.3. Derivation of the Normal Vector After retrieving the expression of rotation matrices, we operate the matrices inversely and intend to convert the normal vector from the transformed coordinate system into a description according to the old one. Defining the upward direction that is perpendicular to the sensor board plane as the normal direction; following the Z-Y-X order, the equation that describes the correlation between initial normal vector Vn and the converted normal vector p0, 0, 1qT in the rotated coordinate system can be expressed as: ¨ ˛ 0 ˚ ‹ R x pϕq Ry pθq Rz pψq Vn “ ˝ 0 ‚ (7) 1 As the rotation matrices Rz pψq, Ry pθq and R x pϕq are unit orthogonal matrices (Unit Orthogonal Matrix: is a unitized square matrix, the transpose of which equals to its inverse, which can be expressed as Q T “ Q´1 , QQ T “ Q T Q “ E, where E is the identity matrix), they satisfy the principle that the transpose equals to their inverse. Hence Vn can be solved by: ¨

˛ 0 ˚ ‹ Vn “ RzT pψq RyT pθq R Tx pϕq ˝ 0 ‚ 1

(8)

¨

˛ cosϕsinθ ˚ ‹ ñ Vn “ ˝ ´sinϕ ‚ cosϕcosθ

(9)

The normal vector represents the tilt direction and the tilt angle of the sensor board, which moves along with the monitored objects during geotechnical events.

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4. Positional Estimate Using Kalman Filter The normal vectors calculated from raw data of the MEMS sensor have inherited interferences and noises from different sources and thus should not be used directly to represent the position. Therefore, Kalman filter is used subsequently to estimate the state of the observations. In particular, this allows also to apply the concept of sensor fusion if more than one sensor is used e.g., to monitor inclination or acceleration. Kalman filter goes back on 1960, when R. E. Kalman proposed a recursive solution to the discrete-data linear filtering problem [16]. As one of the primary developers of the linear quadratic estimation (LQE), this method is named after his name. Kalman filter is a set of mathematical equations that uses a recursive means to estimate the underlying system state by minimizing the mean square error [17]. Nowadays, Kalman filter and its extended version have been widely used in target tracking, navigation, and other relevant fields in data processing [18,19]. In the following a brief introduction of Kalman filter followed by his application to our problem of noisy positional data is given. 4.1. A Brief Introduction of Kalman Filter The first step of the Kalman filter is to build a model that represents the series of data. The state variable x is addressed as an expression of discrete linear stochastic difference equation and the measurement value z is described as a linear function of x: xk “ Axk´1 ` Buk´1 ` wk´1

(10)

zk “ Hxk ` vk

(11)

where: A—State transition matrix relating the state at the previous time step k ´ 1 to that at the current step k; u—Optional control input; B—Control matrix that relates u to the state x; w—Process noise vector, w(i) is normally distributed denoted by N(0, Q) and the covariance # 0 if i ‰ j cov rw piq , w pjqs “ Q ¨ δij , where δij “ ; 1 if i “ j H—Meaurement transition matrix relating the state x to the measurement z; v—Measurement noise vector, v piq is normally distributed denoted by N p0, Rq and the # 0 if i ‰ j covariance cov rv piq , v pjqs “ R ¨ δij , where δij “ , and w and v are 1 if i “ j statistically independent. Once the Kalman filter model is established, the estimating process is applied by a predictor-corrector cycle. As is shown in Figure 5, when the initial state value is established, the iteration can be immediately started. Specifically, time update equations and measurement update equations are respectively grouped that are responsible for the priori estimate for the next time step and the feedback of the priori estimate. Table 2 provides the update equations from groups of time and measurement. A detailed explanation of Kalman filter can be found in [17,20]. There are several formulations Kalman filter update equations; in this paper, a specific form of Kalman gain K and a posteriori estimate error covariance P are selected on purpose of a concise expression of Kalman filter algorithms (Tables 2 and 3) for both single and multi-sensor systems. More information can be found in [21].

feedback of the priori estimate. Table 2 provides the update equations from groups of time and measurement. A detailed explanation of Kalman filter can be found in [17,20]. There are several formulations Kalman filter update equations; in this paper, a specific form of Kalman gain and a posteriori estimate error covariance are selected on purpose of a concise expression of Kalman filter algorithms (Tables 2 and 3) for both single and multi-sensor systems. More information can be Sensors 2016, 16, 1109 7 of 15 found in [21].

Time Update (Predictor)

Measurement Update (Corrector)

Figure 5. Kalman Predictor-Corrector Cycle. Theupdate time projects update the projects Figure 5. KalmanFilter Filter Predictor-Corrector Cycle. The time currentthe statecurrent estimatestate estimate ahead, and then the measurement adjusts the projected estimate based on the ahead, and then the measurement update update adjusts the projected estimate based on the actual actualmeasurement. measurement. Table 2. Kalman Filter Update Equations (xˆ k´ —A priori state estimate at step k, Pk´ —A priori estimate Sensors 2016, 16, 1109 7 oferror 14 error covariance at step k, xˆ k —A posteriori state estimate at step k, Pk —A posteriori estimate covariance at step k, Kk —Kalman Gain that is deduced by minimizing Pk ). Table 2. Kalman Filter Update Equations ( —A priori state estimate at step , —A priori estimate covariance at step , —A posteriori state estimate at step , —A posteriori Time Updateerror Equations Measurement Update Equations ´ ´1 T estimate error covariance at step , —Kalman Gain that is deduced by minimizing ). (12) (14) xˆ k “ A xˆ k´1 ` Buk´1 Kk “ Pk H` Rk ˘ (13) (15) Pk´ “ APk´1 A T ` Qk´1 xˆ k “ xˆ k´ ` Kk zk ´ H xˆ k´ Time Update Equations Measurement Update¯´1 Equations ´ ´ ´1 ´1 T − (16) (14) Pk “ Pk `H (12) = + = Rk H −1 −

=

−1

−1

+

−1

−1



=

(13)

−

+

− −1

(

− −1

−

)

(15)

−1

(16) ( + In a multi-sensor system, the main fusion methods include=centralized and)distributed means [22], the sketches of which are illustrated in Figure 6. Specifically, for centralized fusion methods, Willner, In a multi-sensor system, the main fusion methods include centralized and distributed means Chang [23] introduced threeare main linear Kalman algorithms a multi-sensor [22], has the sketches of which illustrated in Figurefilter 6. Specifically, forfor centralized fusion system, methods,namely parallelWillner, filter, sequentially filter and datathree compression andfilter all the three filters equivalent and Chang [23] has introduced main linearfilter, Kalman algorithms for a are multi-sensor system, parallel filter, methods, sequentially filter and compression filter, and all the three optimum. For namely distributed fusion Carson hasdata proposed a federated Kalman filterfilters as a typical are equivalent and optimum. For distributed fusion methods, Carson has proposed a federated representation [24,25]. Generally speaking, the centralized fusion consumes intensive resources during Kalman as a typical representation [24,25]. Generally speaking, the centralized fusioncalculates consumes faster calculating butfilter assures a limited loss of information, while the distributed fusion intensive resources during calculating but assures a limited loss of information, while the distributed but has a less accuracy. In the following application, the centralized fusion method will be applied fusion calculates faster but has a less accuracy. In the following application, the centralized fusion considering the relatively small amount processed data at the time. method will be applied considering theofrelatively small amount of same processed data at the same time. Fusion Center

S. 1

S. 2

S. 3 Sensors

Centralized Fusion

Fusion Center

Local Center 1

Local Center 2

S. 1

S

S. 2

Local Center N

...

S

S

S. m

Sensors Distributed Fusion

6. Centralized Fusion DistributedFusion. Fusion. In fusion, all measurements are sentare sent Figure Figure 6. Centralized Fusion andand Distributed Incentralized centralized fusion, all measurements to the fusion center; while in distributed fusion, the sensors supply data to a set of local processors to to the fusion center; while in distributed fusion, the sensors supply data to a set of local processors to conduct pretreatment firstly, and then the result will be sent to the fusion center for a global estimate. conduct pretreatment firstly, and then the result will be sent to the fusion center for a global estimate.

4.2. Application of Kalman Filter to Monitor Tunneling-Induced Ground Subsidence from Sensor Motion A one-day field test of the X-SLEWS wireless sensor network was conducted from 10 a.m. to 5 p.m. on 27 January in 2013 at a tunneling construction site in Shanghai. The sensor nodes were deployed at the surface above the underground super highway tunnel at South Hongmei Road, while the shield machine would pass below the area at a depth of 41.65 m. Due to the subsidence related to the tunnel excavation, subsurface deformations was expected to monitor. Each node contains a 3-axis

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change of the orientation of the normal vector and define it as the expected motion due to the tunnel

4.2. Application of Kalman Filter to Monitor Tunneling-Induced Subsidence Motion driving. Figure 7 shows the orientation of the MEMS sensorGround nodes in relation tofrom the Sensor tunnel axis as well as the expected stages of motion caused by shield tunneling. Whenwas the excavation causes A one-day field test of the X-SLEWS wireless sensor network conducted fromground 10 a.m. to subsidence, the sensor node will firstly incline to the shield head, secondly restore to a certain extent 5 p.m. on 27 January in 2013 at a tunneling construction site in Shanghai. The sensor nodes were with the expansion of the settlement area, and then tilt to the shield head again following the deployed at the surface above the underground super highway tunnel at South Hongmei Road, while succeeding subsidence. the shieldThe machine would pass the area at ahave depth of processed 41.65 m. Due to paper the subsidence related to data retrieved frombelow two sensor nodes been in this as an example. the tunnel excavation, subsurface deformations was expected to monitor. Each node contains a 3-axis Firstly, the normal vectors over time have been derived as briefly described above and in detail accelerometer and twotheorthogonal 1-axis inclinometers, and both of them are able to measure in [11]. To monitor ground deformation, the change in inclination of the surface, respectively the the tiltingsensor of thenode, sensor with a settable frequency to the station via wirelessthe network MEMS as depicted in Figure 7, can be used as base a measure and to avisualize changes[8]. overThe time. Theof normal vectorsnode have been consequently the longitudinal the we tunnel, and the sensors the sensor are orientated onprojected a planeinto defined as sensor section plane,ofand observe theof dip angle values have been herebyvector solvedand to express the bestmotion tilting of thetosensor. change the orientation of the normal define itthe asvertical the expected due the tunnel Figure 8 illustrates the derivation of the dip angle from the projected normal vector in the axis _ driving. Figure 7 shows the orientation of the MEMS sensor nodes in relation to the tunnel longitudinal section, and Figure 9 shows the plots of dip angles of two sensor nodes located away as well as the expected stages of motion caused by shield tunneling. When the excavation causes from and on the track in the longitudinal section over the observing day. Particularly, Node 102 was ground subsidence, the sensor node will firstly incline to the shield head, secondly restore to a certain deployed on the surface on the track of the tunnel for the purpose of an observation of ground extent with the expansion the settlement area,from and the then tilt to thecenter shield again following subsidence, while Nodeof 101 located 16 m away excavation is head used as a reference of the succeeding subsidence. Node 102.

Figure 7. Schematic DiagramofofSpatial SpatialRelation Relation Between and thethe Shield Machine (a) and Figure 7. Schematic Diagram BetweenSensors Sensors and Shield Machine (a) and Expected Motion Stages of a Sensor Node Caused by Shield Tunneling (b) (modified from [11]). Expected Motion Stages of a Sensor Node Caused by Shield Tunneling (b) (modified from [11]).

N

The data retrieved from two sensor nodesZhave been processed in this paper as an example. Firstly, the normal vectors over time have been derived as briefly described above and in detail in [11]. To monitor the ground deformation, the change in inclination of the surface, respectively Vn_prj the sensor node, as depicted in Figure 7, can be used as a measure and to visualize the changes over time. The normal vectors have been consequently Dip Angle projected into the longitudinal section of the tunnel, and the dip angle values have been hereby solved to express the vertical the best tilting of the sensor. Figure 8 illustrates the derivationOof the dip angle from the projected normal vector Vn_prj in the longitudinal section, and Figure 9 shows the plots of dip angles of two sensor nodes located Y away from and on the track in the longitudinal section over the observing day. Particularly, Node 102 Dip Angle was deployed on the surface on the track of the tunnel for the purpose of an observation of ground subsidence, while Node 101 located 16 m away from the excavation center is used as a reference of Node 102. X Figure 8. Derivation of the Dip Angle From the Projected Normal Vector _ in the Longitudinal and z positive semi-axis, as well as Section (modified from [15]). The dip is the angle between _ the angle between the sensor board and the horizontal plane.

Figure 7. Schematic Diagram of Spatial Relation Between Sensors and the Shield Machine (a) and Sensors 2016, 16, 1109 Expected Motion Stages of a Sensor Node Caused by Shield Tunneling (b) (modified from [11]).

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N

Z

Vn_prj Dip Angle

O Y Dip Angle

X

Dip Angle in Longitudinal Section/ °

Figure 8. Derivation of the DipAngle AngleFrom From the the Projected Vector in the Longitudinal Figure 8. Derivation of the Dip ProjectedNormal Normal Vector _Vn_prj in the Longitudinal semi-axis, as well as as Section (modified from [15]). Thedip dipisisthe the angle angle between Section (modified from [15]). The between V_n_prjand andz positive z positive semi-axis, as well the angle between the sensor board and the horizontal plane. the angle between the sensor board and the horizontal plane. Sensors 2016, 16, 1109 9 of 14 Projected Dip Angle of Node 101 (away from Track)

4

Dip Angle ACC Dip Angle INC

3.5

3

2.5

2 10:54:25

11:55:51

12:57:18

13:58:45

15:00:11

16:01:38

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Dip Angle in Longitudinal Section/ °

Time Projected Dip Angle of Node 102 (on the Track)

2

Dip Angle ACC Dip Angle INC

1.5

1

0.5

0 10:54:25

11:55:38

12:56:51

13:58:04

14:59:17

16:00:30

17:01:44

Time

Figure Plots DipAngles AnglesofofSensor SensorNode Node 101 101 (away (away from Figure 9. 9. Plots ofofDip from Track) Track) and andNode Node102 102(on (onthe theTrack) Track)inin the Longitudinal Section over the Observing Day. Blue and green lines stand for the performances of the Longitudinal Section over the Observing Day. Blue and green lines stand for the performances of the accelerometer and the inclinometer. Vertical bars can be recognized as outliers. the accelerometer and the inclinometer. Vertical bars can be recognized as outliers.

The change of the inclination has been simplified as a uniform motion. Hereby, the movement The of change of the inclination has node been can simplified as aas: uniform motion. Hereby, the movement model the inclination of the sensor be defined model of the inclination of the sensor node be defined (17) = + can + , = as: 1,2, … (18) = + , = 1,2, … θk´angle ` wangular 1, 2, . . . at time , is the measuring (17) k “ tilt 1 ` Tω k´1the k´1 , k “velocity In which and areθthe and time interval, is the process noise vector at time . ω “ ωk´1 ` wk´were 1, 2, . . . (18) 1 , k “ conducted During the monitoring, the kmeasurements every ten seconds, thus the measuring interval is taken as 10.and Therefore, the Kalman filter model is is built In whichtime θk and ωk are the tilt angle the angular velocity at time k, T theas: measuring time (19) = + δ , = 1,2, … interval, wk is the process noise vector at time k. 1 10 1 where = , = , δ= , is the process noise vector and it is normally distributed 0 1 1 0 ≠ . = denoted by (0, ) and the covariance [ ( ), ( )] = ⋅ , where 1 = Because the state transition matrix has a high reliability, the result will not be influenced much by , hence we define a relatively small value of covariance as 10−7 and thus = 0.0000001 0 . 0 0.0000001 Since there are two types of sensors (accelerometers and an inclinometers) have been embedded

Sensors 2016, 16, 1109

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During the monitoring, the measurements were conducted every ten seconds, thus the measuring time interval T is taken as 10. Therefore, the Kalman filter model is built as: xk “ Axk´1 ` δwk´1 , k “ 1, 2, . . . « where xk “

ff θk ωk

«

, A “

1 0

10 1

ff

«

1 1

(19)

ff

, w is the process noise vector and it is normally # 0 if i ‰ j distributed denoted by N p0, Qq and the covariance cov rw piq , w pjqs “ Q ¨ δij , where δij “ . 1 if i “ j Because the state transition matrix A has a high reliability, the result will not be influenced much« by w, hence we define a relatively small value of covariance as 10´7 and thus ff 0.0000001 0 Q“ . 0 0.0000001 Since there are two types of sensors (accelerometers and an inclinometers) have been embedded in a sensor node, both of the measurements are going to be processed in the fusion center. Hereby the measurement value z known as the tilt angle at step k is defined as: ,δ “

zk “ Hxk ` vk , k “ 0, 1, 2, . . . (20) « ff « ff « ff « ff zk,1 H1 1 0 vk,1 In which zk “ ,H“ “ , vk “ . Assuming the measurement zk,2 H2 1 0 vk,2 « ff « ff Rk,1 1 noise vector v is white noise with a covariance of 1, and thus Rk “ “ . Rk,2 1 « ff « ff 0 1 0 The initial values of the model are defined as x0 “ , P0 “ . These values are 0 0 1 substituted into Equation (21) to Equation (25) in Table 3, following the Kalman filter cycle as shown in Figure 5. Table 3. Kalman Filter Equations for Centralized Fusion. Time Update Equations xˆ k´ “ A xˆ k´1

(21)

Pk´ “ APk´1 A T ` Qk´1

(22)

Measurement Update Equations Kk,i “ Pk HiT R´1 k,i 2 “ ‰ ř Kk,i zk,i ´ Hi xˆ k´ xˆ k “ xˆ k´ ` i“1

Pk “ pPk´

´1

`

2 ř i“1

(23) (24)

´1

HiT R´1 k,i Hi q

(25)

Before the application of Kalman filter, the values of dip angles of Nodes 101 and 102 were subtracted by their initial values individually, as there was an initial offset for each sensor due to the soldering. In this way the variation of dip angles of both sensors of Nodes 101 and 102 can be plotted, which are presented in Figure 10 together with the filtered result. In general, the filtered dip angles show much lower variances compared to the values from the accelerometer and the inclinometer. A discussion and evaluation is given in the following.

Dip Angle in Longitudinal Section/ °

Before the application of Kalman filter, the values of dip angles of Nodes 101 and 102 were subtracted by their initial values individually, as there was an initial offset for each sensor due to the soldering. In this way the variation of dip angles of both sensors of Nodes 101 and 102 can be plotted, which are presented in Figure 10 together with the filtered result. In general, the filtered dip angles show 2016, much A Sensors 16,lower 1109 variances compared to the values from the accelerometer and the inclinometer. 11 of 15 discussion and evaluation is given in the following. Variations of Projected Dip Angle of Node 101 (away from Track)

1.5

Dip Angle INC Dip Angle ACC Dip Angle KF

1 0.5 0 -0.5 -1 -1.5 10:54:25

11:55:51

12:57:18

13:58:45

15:00:11

16:01:38

17:03:05

Dip Angle in Longitudinal Section/ °

Time Variations of Projected Dip Angle of Node 102 (on the Track)

1.5

Dip Angle INC Dip Angle ACC Dip Angle KF

1 0.5 0 -0.5 -1 -1.5 10:54:25

11:55:38

12:56:51

13:58:04

14:59:17

16:00:30

17:01:44

Time

Figure 10. 10. Plots and Node Node 102 102 (on (on the the Figure Plots of of Dip Dip Angle Angle Variations Variations of of Sensor Sensor Node Node 101 101 (away (away from from Track) Track) and Track) in inthe theLongitudinal LongitudinalSection Sectionover overthe theObserving Observing Day. The absolute values were subtracted by Track) Day. The absolute values were subtracted by the the initial value to obtain variations of dip angles, and the changes detected from the accelerometer initial value to obtain variations of dip angles, and the changes detected from the accelerometer and and inclinometer can thus be compared directly. green stand for performances the performances of inclinometer can thus be compared directly. BlueBlue and and green lineslines stand for the of the the accelerometer and the inclinometer, and the red line is the result after the application of Kalman accelerometer and the inclinometer, and the red line is the result after the application of Kalman filter. filter. Vertical bars be recognized as outliers. Vertical bars can becan recognized as outliers.

4.3. Evaluation 4.3. Evaluation and and Discussion Discussion of of the the Filtering Filtering As is is shown shown in in Figure Figure 10, 10, vertical vertical bars bars in in blue blue and and green green indicate indicate outliers outliers caused caused by by noise noise As interferences from electrical fields and ground vibration when the tunnel boring machine and other interferences from electrical fields and ground vibration when the tunnel boring machine and construction measures approach, where where the sensor node would be affected and thus obtain other construction measures approach, the sensor node would be affected andwould thus would inaccurate measurements. Regarding the accelerometer, the the combination of ofthe 1-axis obtain inaccurate measurements. Regarding the accelerometer, combination thethree three 1-axis accelerometer has enabled a normalization in calculating the normal vector, but the relatively low accelerometer has enabled a normalization in calculating the normal vector, but the relatively sensitivity of 0.0637°/count has has reduced the the reliability of of thethededuced the low sensitivity of 0.0637˝ /count reduced reliability deduceddip dipangle. angle. As As for for the inclinometer, in spite of the high sensitivity of 0.00179°/count compared to the accelerometer, the ˝ inclinometer, in spite of the high sensitivity of 0.00179 /count compared to the accelerometer, the output from the inclinometer could not be normalized because only two orthogonal axes were output from the inclinometer could not be normalized because only two orthogonal axes were deployed deployed with inclinometers. carryfilter out to a data filter identifyonthe ondata the with inclinometers. Therefore, Therefore, to carry outtoa data identify thetooutliers theoutliers observed before they are used for an assessment is necessary and valuable. In Figure 10, the scale of the outliers for the inclinometer is evidently much bigger than that of the accelerometer for both nodes. Hence, it can be inferred that with a strong effect of noise interferences and ground vibration, the difference of sensitivity would not be the main factor of malfunction any more. Instead, the defect of normalization of the inclinometer has resulted in higher ratio of outliers and an unstable performance. To explore more information hidden from the variations of dip angles, standard deviations of the filtered dip angles were calculated every hour for both sensor nodes, and amplified filtered variations of dip angles with sectional standard deviation values is presented in Figure 11. The standard deviation values are mostly between 0.0172 and 0.0266, but two exceptions appear in the first two hours for Node 102 with a value of 0.0481 and 0.0373 respectively. On the other hand, Node 101 that was deployed 16 meters away performed regularly in the first two hours compared to its latter performance. Hereby, the abnormality of Node 102 indicates a disturbance of the data when the tunnel boring machine passed through the area underground.

Dip Angle in Longitudinal Section Section/ °

variations of dip angles with sectional standard deviation values is presented in Figure 11. The standard deviation values are mostly between 0.0172 and 0.0266, but two exceptions appear in the first two hours for Node 102 with a value of 0.0481 and 0.0373 respectively. On the other hand, Node 101 that was deployed 16 meters away performed regularly in the first two hours compared to its latter 2016, performance. Hereby, the abnormality of Node 102 indicates a disturbance of the data 12 when Sensors 16, 1109 of 15 the tunnel boring machine passed through the area underground. Variations of Projected Dip Angle of Node 101 After Kalman Filter (away from Track) 0.1 Dip Angle KF

0

Sn = 0.0206

Sn = 0.0236

Sn = 0.0235

Sn = 0.0215

Sn = 0.0172

Sn = 0.0185

-0.1

-0.2

-0.3 11:04:53

12:04:35

13:04:17

14:03:59

15:03:41

16:03:23

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Dip Angle in Longitudinal Section/ °

Variations of Projected Dip Angle of Node 102 After Kalman Filter (on the Track) 0.1 Dip Angle KF

0

-0.1

-0.2

-0.3 11:04:53

Sn = 0.0481

Sn = 0.0373

12:04:21

Sn = 0.0220

13:03:50

Sn = 0.0235

14:03:18

Sn = 0.0266

15:02:47

Sn = 0.0229

16:02:15

17:01:44

Time

Figure 11. 11. Plots Plots of after Kalman Kalman Filter Figure of Dip Dip Angle Angle Variations Variations after Filter of of Sensor Sensor Node Node 101 101 (away (away from from Track) Track) and Node 102 (on the Track) in the Longitudinal Section over the Observing Day with Hourly and Node 102 (on the Track) in the Longitudinal Section over the Observing Day with Hourly Standard Deviations. Deviations.The Thevalues valuesofofstandard standarddeviations deviations mostly between 0.0172 0.0266, Standard areare mostly between 0.0172 andand 0.0266, andand the the two exceptions appear in the first two hours for Node 102 indicating a disturbance of the two exceptions appear in the first two hours for Node 102 indicating a disturbance of the data.data.

Taking the second measuring hour for Node 102 as an example, a comparison was made Taking the second measuring hour for Node 102 as an example, a comparison was made between between the filtered dip angles based on different algorithms of Kalman filter. Figure 12 shows the the filtered dip angles based on different algorithms of Kalman filter. Figure 12 shows the plots of plots of dip angle variations over time after distinct filtering. The blue line corresponds to the filtered dip angle variations over time after distinct filtering. The blue line corresponds to the filtered dip dip angles based on measurements from the 3-axis accelerometer, while the green line represents the angles based on measurements from the 3-axis accelerometer, while the green line represents the result result corresponding to the two orthogonal 1-axis inclinometers. The red line shows centralized corresponding to the two orthogonal 1-axis inclinometers. The red line shows centralized filtered dip filtered dip angles on the basis of both the accelerometer and the inclinometer, and the average of angles on the basis of both the accelerometer and the inclinometer, and the average of two individual two individual filtering (blue and green line) is also indicated with purple dot line. It can be observed filtering (blue and green line) is also indicated with purple dot line. It can be observed that the that the centralized filtering is not always consistent with the curve of the average. The standard centralized filtering is not always consistent with the curve of the average. The standard deviation of deviation of the inclinometer line is much higher than the accelerometer line, which indicates that the the inclinometer line is much higher than the accelerometer line, which indicates that the lack of z-axis lack of z-axis of the inclinometer combination has led an instable performance. Nevertheless, of the inclinometer combination has led an instable performance. Nevertheless, considering its higher considering its higher sensitivity, the variations calculated by inclinometers should still be taken into sensitivity, the variations calculated by inclinometers should still be taken into account, especially account, especially when the variations of dip angle are not notable. The standard deviation of the when the variations of dip angle are not notable. The standard deviation of the dip angle variations dip angle variations based on both sensor values is higher than that from the accelerometer and lower based on both sensor values is higher than that from the accelerometer and lower than that from the inclinometer, which have combined the advantages from both sensors and reduced to the instability to a certain level. If the sensor node was deployed exactly on the ground above the tunneling center, it is not possible to evaluate the ground settlement by just calculating the tilt angle from only one single node located at the center along the longitudinal or the transversal direction. Nevertheless, when a series of sensor nodes are closely located on the ground from a distance away to the excavating center, a smooth subsidence map can be achieved. Figure 13 presents a sketch showing the way of deploying sensor nodes in order to draw a settlement curve in the cross section. Simplifying the subsided ground surfaces between two adjacent sensor nodes are even, the absolute ground subsidence in the section can be calculated via the tangent function presented as a polyline. After that, a smooth subsidence curve can be obtained by interpolating the polyline (Figure 13). Anyhow, it has to be considered that modern tunnel driving in urban areas and especially in the Shanghai areas is carried out with

of sensor nodes are closely located on the ground from a distance away to the excavating center, a smooth subsidence map can be achieved. Figure 13 presents a sketch showing the way of deploying sensor nodes in order to draw a settlement curve in the cross section. Simplifying the subsided ground surfaces between two adjacent sensor nodes are even, the absolute ground subsidence in the section can be calculated via the tangent function presented as a polyline. After that, a smooth Sensors 2016, 16, 1109 13 of 15 subsidence curve can be obtained by interpolating the polyline (Figure 13). Anyhow, it has to be considered that modern tunnel driving in urban areas and especially in the Shanghai areas is carried large experience and considering larger safety margins reducetosettlements. Therefore, ground out with large experience and considering larger safety to margins reduce settlements. Therefore, displacements and tilt motion always low. ground displacements and tiltare motion areconsiderably always considerably low. Variations of Projected KF Dip Angle of Node 102 After Kalman Filter (on the Track)

0.15

KF Dip Angle ACC KF Dip Angle INC Centralized KF Dip Angle Average of ACC and INC

Sn = 0.0174

0.1

KF Dip Angle in Longitudinal Section/ °

0.05

Sn = 0.0373

0

-0.05

-0.1

Sn = 0.0643

-0.15

-0.2

-0.25

-0.3 12:04:23

12:14:25

12:24:27

12:34:29

12:44:31

12:54:33

13:04:36

Time

Figure 12. 12. Plots Track) in in the the Figure Plots of of Dip Dip Angle Angle Variations Variations after after Kalman Kalman Filter Filter of of Node Node 102 102 (on (on the the Track) Longitudinal Section Section During During the the Second Second Measuring Measuring Hour. Hour. Blue lines are are results results after after Longitudinal Blue and and green green lines Kalman filter filter for for the the accelerometer accelerometer and and inclinometer inclinometer respectively, respectively, and and the the red red line line shows shows the the result result Kalman solved by by aa centralized centralized Kalman Kalman filter filter based based on on the the tilt tilt values values from from two two sensors. sensors. The deviation solved The standard standard deviation of the red line is higher than that of the blue line and lower than that of the green line. The purple dot of the red line is higher than that of the blue line and lower than that of the green line. The purple dot line displays displays the the average average of of the the blue blue and and green green lines. lines. line

Finally, as Kalman filter is a recursive solution that can be continually applied to estimate the situation in the next time step and then be updated after obtaining the observation, the a priori estimate made by Kalman filter can be taken into account into a Building Information Model (BIM) to support the management and facility operation. Furthermore, it can be used as a kind of early warning systems to indicate changes in the ground response to the excavation.

Figure 13. Planned Distribution of Sensor Nodes along the Transversal Direction and Drawing of a Settlement Curve. The settlement is gradually accumulated from the node deployed at a distance showing no variations to the one at the excavating center on the ground. Starting with a value of zero, a smooth curve of vertical ground settlement can be obtained using the tangent function and interpolation.

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Finally, as Kalman filter is a recursive solution that can be continually applied to estimate the situation in the next time step and then be updated after obtaining the observation, the a priori estimate made by Kalman filter can be taken into account into a Building Information Model (BIM) to support the management and facility operation. Furthermore, it can be used as a kind of early warning systems to indicate changes in the ground response to the excavation. 5. Conclusions In this paper, a one-day field test was deployed on top of a tunnel section under construction and MEMS sensor nodes equipped with both accelerometers and inclinometers were used to measure the changes of the surface caused by excavation. Normal vectors of the sensors were deduced using rotation matrices and consequently were projected to the longitudinal section for the purpose of an assessment of ground settlement. Aiming at an improved data reliability and a better estimate of the inclination, a centralized Kalman filter was conducted based on the results from accelerometers and inclinometers. Furthermore, a discussion based on the filtered result was provided afterwards to evaluate the performance of the sensors and the process of tunneling. Author Contributions: Cheng Li analyzed the data and wrote the paper, Tomás Fernández-Steeger provided the data and contributed in writing and interpretation, Rafig Azzam took part in the final discussion. Conflicts of Interest: The authors declare no conflict of interest.

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