Sensor fault diagnosis method based on weighted coefficient of array modal sensor

Abstract

The present invention is applicable to sensor fault diagnosis in situations where piezoelectric sensor arrays are required in fields such as active vibration control or structural health monitoring, and proposes a method for fault determination and positioning of sensor units in large sensor arrays. The method is based on the design principle of array piezoelectric modal sensors, and includes: obtaining weighting coefficients; calculating damage factors; and setting damage thresholds. The obtained weighting coefficients are interpolated with cubic splines, and the damage factors and damage thresholds are calculated based on the interpolated weighting coefficients. Whether there is a faulty sensor in the sensor array is determined based on whether the damage threshold is exceeded, and the location of the faulty sensor is determined based on the maximum damage factor.

Description

Technical Field

[0001] The present invention belongs to the technical field of sensor fault diagnosis in active vibration control or structural health monitoring (SHM) technology, and specifically relates to a method for judging and locating faults of sensor units of a sensor array. Background Art

[0002] When performing active vibration control or structural health monitoring on large flexible structures, a large number of sensors need to be arranged on the surface of the structure. Piezoelectric sensors are widely used in the fields of active vibration control and structural health monitoring due to their many advantages such as wide operating frequency range, simple structure, light weight, high sensitivity, and fast frequency response time. However, piezoelectric sensors may fail due to long-term use, which may lead to failure of the control system or misjudgment of SHM system failure. For large sensor arrays, when the system fails, it is a huge and complicated task to check the sensor units one by one according to the relevant equipment. Therefore, it is very important to judge and locate the faulty sensor unit in the sensor array directly based on the output of the sensor array.

[0003] The fault diagnosis method based on the weighted coefficient of the array modal sensor is to calculate the weighted coefficient of the array piezoelectric modal sensor using the initial output of the sensor array, and use the weighted coefficient as the standard parameter for the normal operation of each sensor unit. When a sensor unit fails, the weighted coefficient of the corresponding sensor unit will change. At the same time, by setting the damage threshold, the interference of the working environment changes and other factors on the diagnosis results is eliminated, so as to further improve the reliability of the method. This method is based on the output changes of the sensor array, and uses the damage threshold to compare the changes in the parameters of each sensor horizontally. It does not require the detection of a single sensor unit, which can greatly improve the efficiency of sensor array fault diagnosis. At the same time, this method is simple to operate and has strong practicality. Summary of the invention

[0004] The purpose of the present invention is to provide a sensor fault diagnosis method based on weighted coefficients of array modal sensors.

[0005] The technical solution of the present invention is: a sensor fault diagnosis method based on array modal sensor weighting coefficients, comprising:

[0006] Step 1: When the system is working stably, the initial weighting coefficient matrix of each piezoelectric sensing unit is calculated according to the actual conditions using the design method of the array piezoelectric modal sensor. As the original parameters of each piezoelectric unit in the system.

[0007] Step 2: When inspecting or troubleshooting the system, use the method in step 1 to calculate the monitoring weighted coefficient matrix of each piezoelectric sensor unit again. As the state parameters of each piezoelectric unit in the current system

[0008] Step 3: Perform cubic spline interpolation on the initial weighting coefficient matrix in step 1 and the monitoring weighting coefficient matrix in step 2, and calculate the damage threshold and the damage factor of each interpolation point.

[0009] Step 4: Determine whether there is a damaged sensing unit in the piezoelectric sensing array based on whether the damage factor of each interpolation point exceeds the damage threshold; and locate the faulty sensor based on the coordinates of the interpolation point where the damage threshold is exceeded.

[0010] The advantages of the present invention are: the sensor fault diagnosis method based on the weighted coefficient of the array modal sensor realizes the judgment and positioning of the faulty sensor unit in the piezoelectric sensor array by processing the output of the sensor array. The advantages of this method are briefly summarized as follows: 1. This method analyzes the output of the piezoelectric array at the same time, that is, when calculating the weighted coefficient twice, the working time and working environment of each piezoelectric unit in the piezoelectric array are consistent, thereby eliminating the influence of the performance reduction of the piezoelectric unit or environmental interference on the fault diagnosis result; 2. The present invention establishes a damage threshold for damage statistics based on the "3σ" principle in mathematical statistics, and uses this to determine whether there is a faulty sensor unit in the sensor array, eliminating the influence of the difference in individual parameter changes of the sensor unit on the diagnosis result, and improving the reliability and robustness of the fault diagnosis result. 3. The fault diagnosis method proposed by the present invention can evaluate the working conditions of all sensor units in the piezoelectric sensor array at one time, without the need to measure a single sensor unit, and without adding additional detection equipment, and has the advantages of simple operation and high reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 Flowchart for sensor fault diagnosis

[0012] Figure 2 This is the fault diagnosis result diagram of the one-dimensional structure sensor array

[0013] Figure 3 The fault diagnosis result diagram of the two-dimensional structure sensor array DETAILED DESCRIPTION

[0014] The present invention is described in further detail below.

[0015] Figure 1 This is a flow chart of sensor fault diagnosis based on the weighted coefficients of array modal sensors.

[0016] The sensor fault diagnosis method based on the weighted coefficient of the array modal sensor includes:

[0017] Step 1: When the system is working stably, the initial weighting coefficient matrix of each piezoelectric sensing unit is calculated according to the actual conditions using the design method of the array piezoelectric modal sensor. As the original parameters of each piezoelectric unit in the system.

[0018] Step 2: When the system is being repaired, the monitoring weighting coefficient matrix of each piezoelectric sensor unit is calculated again using the method in step 1. As the state parameters of each piezoelectric unit in the current system

[0019] Step 3: Perform cubic spline interpolation on the initial weighting coefficient matrix in step 1 and the monitoring weighting coefficient matrix in step 2, and calculate the damage threshold and the damage factor of each interpolation point.

[0020] Step 4: Determine whether there is a damaged sensing unit in the piezoelectric sensing array based on whether the damage factor of each interpolation point exceeds the damage threshold; locate the faulty sensor based on the coordinates of the interpolation point where the damage threshold is exceeded.

[0021] Step 1 is as follows:

[0022] When the system is working stably, the frequency response function between the output of each sensor unit in the array and the system input and the natural frequencies of each order of the vibrating structure are obtained. P frequency points are selected from the measured frequency response function to form the frequency response function matrix H, and the modal coordinate matrix A of the corresponding frequency band is calculated according to the modal coordinate formula (Formula 1). Assume that the initial weighting coefficient of the system is The initial weighting coefficient Substitute the frequency response function matrix H and the modal coordinate matrix A into the array piezoelectric modal sensor model formula (2):

[0023]

[0024]

[0025] In the formula, H N (ω p ) is the value of the pth frequency point of the Nth piezoelectric unit in the piezoelectric sensor array; W Nm A is the weighting coefficient of the mth order modal sensor of the Nth piezoelectric unit in the piezoelectric sensor array, where m can be any order and can be determined according to the actual measurement conditions; m (ω p ) is the value at the pth frequency point in the modal coordinates calculated based on the mth order natural frequency of the measured structure.

[0026] To find W in formula (2) Nm Parameters, rewrite formula (2) into a matrix form H×W=A. Since the number of frequency points P is much larger than the number of piezoelectric units N, a pseudo-inverse solution is required:

[0027] W=H + A (3)

[0028] In the formula, H + =[H H H] -1 H H (H H The conjugate transposed matrix of matrix H) is the pseudo-inverse of matrix H. If the measured frequency response function matrix is ​​singular or ill-conditioned, the pseudo-inverse H of the frequency response function can be solved by matrix processing methods such as singular value decomposition or Tikhonov regularization. + The following takes singular value decomposition as an example to further illustrate this step.

[0029] For the selected frequency response function matrix H∈C N×P (rank(H)=r) performs singular value decomposition to obtain:

[0030]

[0031]

[0032] Where U H =U -1 , V H =V -1 is a unit orthogonal matrix (unitary matrix), ∑ is a diagonal matrix. σ1≥σ2≥…≥σ1>0 is the singular value of the frequency response function matrix H.

[0033] Expanding formula (4) yields:

[0034]

[0035] Substituting equation (6) into equation (3), we can obtain

[0036]

[0037] When the singular value of the frequency response function is very small, 1 / σ in equation (7) n It will tend to infinity. To avoid this situation from having a greater impact on the calculation results. In practical applications, some items corresponding to smaller singular values ​​in the frequency response function matrix are often omitted. For example, only the first k singular values ​​are taken, and equation (7) can be rewritten as:

[0038]

[0039] According to formula (8), the initial weighting coefficient matrix of the piezoelectric array is obtained:

[0040] Step 2 is as follows:

[0041] When the system is repaired or fault diagnosed, the output frequency response function of the piezoelectric array is obtained. The frequency response function matrix and the modal coordinate matrix are obtained in turn according to the method in step 1, and then the monitoring weighting coefficient matrix of the piezoelectric array is calculated according to formula (8):

[0042] Step 3 is as follows:

[0043] The initial weighting coefficient of the piezoelectric sensor unit and monitoring weighting factor Perform cubic spline interpolation, and the number of interpolation points is appropriately selected according to the size of the actual structure and the damage location accuracy requirements. The weighted coefficient damage factor model formula (9) and formula (10) after interpolation

[0044]

[0045]

[0046] Assuming that the damage statistics of the system present a normal distribution, the damage threshold can be determined based on the 3σ principle of normal distribution (σ is the standard deviation of the data set). norm Substitute into formula (11)

[0047] UCL norm =mean(SF norm )+a×std(SF norm ) (11)

[0048] In the formula, mean() and std() represent the mean and standard deviation of the data in the brackets respectively. a=(1,2,3) is a constant. When a=1, the confidence level is 68.26%; when a=2, the confidence level is 95.44%; when a=3, the confidence level is 99.74%. In practical applications, appropriate damage thresholds can be set according to actual confidence requirements.

[0049] Step 4 is as follows:

[0050] According to the calculated damage factor and damage threshold, the sensor fault is judged and located, as shown in formula (12):

[0051]

[0052] The faulty sensor unit can be located according to the coordinate value of the sensor unit whose damage factor exceeds the damage threshold.

[0053] The sensor fault diagnosis method in this patent can judge and locate the faulty sensor unit in a large sensor array. The following uses a one-dimensional beam structure and a two-dimensional plate structure as examples and uses PZT as a piezoelectric sensor unit to experimentally verify the method.

[0054] Figure 2 The following is the fault diagnosis result of helicopter blades as an example. 10 pieces of lead zirconate titanate piezoelectric ceramics (PZT) are evenly arranged on the helicopter blades, and three different degrees of damage simulation are performed on the third PZT. The thin solid line represents the damage factor of each interpolation point. The dotted line represents the damage threshold when the confidence level is 99.74%, and the thick solid line represents the actual position of the faulty PZT. It can be seen from the experimental results that only the damage factor of the third PZT exceeds the set damage threshold, which indicates that the third PZT is damaged, which is consistent with the actual damage simulation results. Therefore, the sensor fault diagnosis method based on the weighted coefficient of the array piezoelectric modal sensor can accurately locate the faulty sensing unit in the piezoelectric array, and the diagnosis result has a high confidence level.

[0055] In order to further prove the applicability of the sensor fault diagnosis method based on the weighted coefficient of the array modal sensor to other structures, this patent further conducts experiments on a two-dimensional fixed support plate. During the experiment, a 4×5 sensor array is arranged on a 44cm×34cm fixed support plate. And the damage simulation of the sensor unit with coordinates (3,2) is carried out. Figure 3 The experimental fault diagnosis results of the two-dimensional plate are given. It can be seen from the experimental results that the sensor fault diagnosis method based on the weighted coefficient of the array modal sensor can accurately locate the faulty sensor unit in the two-dimensional structure piezoelectric array, and this method can be easily extended to other structures.

Claims

1. A sensor fault diagnosis method based on array modal sensor weighting coefficients, characterized in that: include: Step 1: When the system is working stably, the initial weighting coefficient matrix of each piezoelectric sensing unit is calculated according to the actual conditions using the design method of the array piezoelectric modal sensor. As the original parameters of each piezoelectric unit in the system; specifically: When the system is working normally, the sensor array is used to measure the natural frequency of the structure and obtain the frequency response function between the output of each sensor unit and the system input, and substitute it into the modal coordinate formula (1) to obtain the modal coordinate matrix A of the structure: m , In the formula, ω m is the mth order natural frequency of the structure, ω is the excitation force frequency, ξ m represents the mth-order damping ratio of the structure, i 2 =-1 is the imaginary unit; If the piezoelectric sensor array consists of N piezoelectric units, m Take P discrete data points within the range to form a frequency response function matrix; substitute the modal coordinate matrix and the frequency response function matrix into formula (2): Rewrite formula (2) into a matrix form H×W=A. Since the number of frequency points P is much larger than the number of piezoelectric units N, in order to obtain the initial weighting coefficient matrix Need to find the pseudo-inverse: W=H + A (3) In the formula, H + =[H H H] -1 H H is the pseudo-inverse of matrix H, H Represents the conjugate transposed matrix of the matrix H; if the measured frequency response function matrix is ​​singular or ill-conditioned, use singular value decomposition or Tikhonov regularization matrix processing method to solve the pseudo-inverse H of the frequency response function + ; Step 2: When the system is being repaired, the monitoring weighting coefficient matrix of each piezoelectric sensor unit is calculated again using the method in step 1. As the state parameters of each piezoelectric unit in the current system; Step 3: Perform cubic spline interpolation on the initial weighted coefficient matrix in step 1 and the monitoring weighted coefficient matrix in step 2, and calculate the damage threshold and the damage factor of the weighted coefficient at each interpolation point; Specifically: the initial weighting coefficient of the piezoelectric sensor unit and monitoring weighting factor Perform cubic spline interpolation and substitute the interpolated weighted coefficients into the defined damage factor calculation formulas (9) and (10): Assuming that the damage statistics of the system present a normal distribution, the damage threshold is determined based on the 3σ principle of normal distribution, where σ is the standard deviation of the data set; the damage factor SF norm Substitute into formula (11) UCL norm =mean(SF norm )+a×std(SF norm ) (11) In the formula, mean() and std() represent the mean and standard deviation of the data in the brackets respectively; a=1,2,3, a is a constant; when a=1, the confidence level is 68.26%; when a=2, the confidence level is 95.44%; when a=3, the confidence level is 99.74%; Step 4: Determine whether there is a damaged sensing unit in the piezoelectric sensing array based on whether the damage factor of each interpolation point exceeds the damage threshold; locate the faulty sensor based on the coordinates of the interpolation point where the damage threshold is exceeded.

2. A sensor fault diagnosis method based on array modal sensor weighting coefficients as claimed in claim 1, characterized in that: Step 2 is as follows: When inspecting or troubleshooting the system, repeat the process in step 1 to obtain the monitoring weighted coefficient matrix of each sensor unit.

3. A sensor fault diagnosis method based on array modal sensor weighting coefficients as claimed in claim 1, characterized in that: Step 4 is as follows: According to the calculated damage factor and damage threshold, the sensor fault is judged and located, as shown in formula (12): The sensor unit whose damage factor exceeds the damage threshold is a faulty sensor unit.

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