Wind power blade wrinkle damage identification method based on data driving

Abstract

The invention discloses a wind power blade wrinkle damage identification method based on data driving, and the method carries out the frequency domain and time domain analysis of the monitoring data of a blade strain sensor, carries out the analysis and judgment of the collected data according to an established full-size blade model, and achieves the feature identification of the wind power blade wrinkle damage. The method comprises the following implementation steps: 1, arranging a resistance-type strain sensor in a blade, continuously monitoring the state of the blade by using the sensor in a test process, and recording the strain change condition of the blade; 2, carrying out data processing and data analysis on sensor monitoring data; 3, establishing a fatigue test simulation model of a full-size blade, and introducing a wrinkle defect into the blade model; and 4, carrying out digital-analog combined drive analysis and comparison on finite element data extracted by the full-size finite element model and sensor monitoring data, and further judging a damage signal feature caused by wrinkles. The method solves the problems that a traditional blade damage identification method cannot specifically identify the damage type and fold damage is difficult to identify, and has great significance in reducing the operation and maintenance cost of the wind power blade and ensuring healthy and stable operation of the wind power blade.

Description

Technical Field

[0001] The present invention relates to a wind turbine blade damage identification technology, and in particular to a wind turbine blade wrinkle damage identification method based on data drive. Background Art

[0002] In recent years, renewable energy is replacing traditional energy as the main energy source. As one of the fastest growing renewable energy sources, wind power generation is increasingly valued for its safety and reliability.

[0003] The blade is the most important wind-catching structure of the wind turbine. As the scale of wind turbines increases year by year, the load on the blade is also increasing. Once the wind turbine blade is damaged, the overall safety of the wind turbine will be seriously reduced and the operation and maintenance costs will increase. The blade is usually a laminate structure composed of dozens of layers of fiber-resin composite materials. During the manufacturing process, the fiber will shrink and twist as the resin solidifies, or part of the ply will be squeezed and deformed and slip when pressurized, resulting in wrinkle defects in the main beam.

[0004] Wrinkles affect the tensile and compressive strength and fatigue performance of the blades, reduce the load-bearing capacity of the blades, and affect the service life of the blades. They are a molding defect that has a serious impact on the safety of blade operation and produces frequent damage. Wrinkles usually appear inside the blades and are not easy to be found. During the long-term operation of the blades, wrinkles will evolve into various damages such as stratification and cracks, causing increased vibration of the blades and a decrease in the stiffness of the blades. Not only will the stiffness and strength of the blades be significantly reduced, but stress concentration is likely to occur in the wrinkled area when loaded, endangering the service safety of the blades and even causing the collapse and damage of the entire machine.

[0005] Therefore, the identification of wind turbine blade wrinkle damage is of great guiding significance to ensure the safe operation of the blades. However, due to the difficulty of wrinkle identification, once it is identified, it has often entered a very serious stage. Traditional wind turbine blade damage identification methods cannot identify specific damage categories, such as wrinkles, delamination, etc., and their prediction accuracy and adaptability are limited in complex real-world environments. Summary of the invention

[0006] In view of the problems existing in the prior art, the present invention provides a data-driven method for identifying wrinkle damage on wind turbine blades.

[0007] In order to achieve the above technical purpose, the technical solution adopted by the present invention is:

[0008] A data-driven wind turbine blade wrinkle damage identification method comprises the following steps:

[0009] Step 1: Arrange a resistive strain sensor at the root of a full-size blade to monitor the strain during a shimmy fatigue test and obtain monitoring data;

[0010] Step 2: De-noise the monitoring data and extract feature values;

[0011] Step 3: Establish a blade geometry model based on aerodynamic layout and airfoil data, introduce wrinkle defects into blade analysis through body-shell coupling, apply equivalent fatigue load to the blade geometry model and extract finite element data of strain value in damaged area;

[0012] Step 4: Use the dynamic time warping method to analyze and compare the finite element data obtained in step 3 with the monitoring data to identify the damage signal characteristics of the blade caused by wrinkles.

[0013] To optimize the technical solution, further improvements were made including:

[0014] The resistive strain sensor described in step 1 is Donghua DH5908H, which is arranged at 45° relative to the actual swing direction, and the strain of the blade is monitored at a sampling frequency of 50 Hz.

[0015] In step 2, the monitoring data is first denoised using a discrete wavelet threshold method, and then the LSTM analysis method is used to remove invalid data from the extracted eigenvalues, where the eigenvalues ​​include mean, variance, maximum and minimum values, and peak-to-peak values.

[0016] The specific method of using discrete wavelet threshold method to denoise the monitoring data is as follows:

[0017] The monitoring data is used as the original signal for wavelet transform, and the signal is decomposed into sub-bands of different frequencies. The sub-bands after wavelet transform are threshold processed, and the coefficients less than the threshold are set to zero, while the coefficients greater than the threshold are retained. The wavelet coefficients after threshold processing are inversely transformed to obtain the denoised signal, which is expressed as follows:

[0018] Wavelet Transform:

[0019] Inverse wavelet transform:

[0020] Thresholding:

[0021] Among them, a is the scale factor, b is the translation parameter, a and b are wavelet coefficients, x(t) is the original signal, X(a,b) is the signal after wavelet transformation, ψ a,b (t) is the wavelet function (wavelet basis), is the complex conjugate of the wavelet function, λ is the threshold;

[0022] The specific method of using the LSTM analysis method to remove invalid data from the extracted feature values ​​is:

[0023] First, the denoised signal is used to construct a time series data set in chronological order, and eigenvalues ​​are extracted from the time series data, which will be used as the input of the LSTM model. The eigenvalues ​​are divided into training set, validation set and test set, and then a model including an input layer, an LSTM layer, a fully connected layer, a softmax layer and a classification layer is constructed through the training set to make it learn the data representation of normal and abnormal states of the data, and the validation set is used to verify and set the training options, including the optimizer, the number of training iterations, and the Mini-Batch size. The trained LSTM model is used to remove abnormal data from the test set, and then the accuracy of the LSTM model in removing abnormal data is evaluated by calculating the mean square error.

[0024] The specific method of step 3 is:

[0025] A blade geometric model is established in UG software. The aerodynamic centers of all airfoil sections of the blade geometric model are located on the same straight line, and these aerodynamic centers are located at 1 / 3 of the blade chord length. The blade airfoil data is transformed into three-dimensional coordinates according to the aerodynamic shape. The blade geometric model is imported into the commercial finite element software ABAQUS for chord-wise and span-wise partitioning, laying of layers, and application of equivalent fatigue loads. The body-shell coupling method is used to introduce wrinkles into the blade, and the finite element data of the strain value in the damaged area are extracted.

[0026] The specific method of establishing the blade geometry model in UG software is:

[0027] The wind turbine blade model is constructed by twisting and scaling the wind turbine blade, and its thickness and chord length gradually change along the span direction of the blade. The principle is as follows:

[0028]

[0029] Where d is the chord length, β is the twist angle, and x p is the pitch axis of the cross section, and 1 / 3 of the blade chord length is taken. x and y are the original coordinates of the airfoil. t ,y t , z is the transformed section coordinate, r is the position of the airfoil section,

[0030] According to the three-dimensional section coordinates after conversion of formula (1), each section is saved as a sat file. In the UG software, the lofting command is selected, and the sat file of each section is imported in turn according to the points in the file to generate the blade geometry model.

[0031] The specific method of importing the blade geometry model into the commercial finite element software ABAQUS to extract the finite element data of the strain value of the damaged area is:

[0032] The blade geometry model is imported into Abaqus as an iges file for area division. After the area division is completed, the material properties and mesh division are performed on different areas in Abaqus. The different material properties, ply angles, and thicknesses of the blade design are assigned to different areas one by one to obtain a full-size blade model.

[0033] Introducing wrinkles into full-scale blade models,

[0034]

[0035] Where: A is the height of the wrinkle curve; L is the length of the wrinkle defect area, that is, the amplitude of the sine curve; Z(x) is the geometric representation of the wrinkle.

[0036] Loads were applied to the full-size blade in ABAQUS, and finite element data of strain values ​​in the damaged area were extracted.

[0037] The specific method of step 4 is:

[0038] The dynamic time warping method is used to calculate the similarity between the monitoring data of each resistive strain sensor and the finite element data, and a similarity matrix is ​​obtained. For each pair of data points (x i ,y i ) and (x j ,y j ), calculate the Euclidean distance:

[0039]

[0040] Construct a distance matrix, where the rows represent data points on the reference curve and the columns represent data points on other curves. Each element d in the matrix ij represents the Euclidean distance between the i-th point on the reference curve and the j-th point on the other curves,

[0041] Create a matrix of the same size as the distance matrix, recorded as the cumulative distance matrix. For each element D[i,j] in the matrix, calculate as follows:

[0042] D[i,j]=d ij +min(D[i-1,j],D[i,j-1],D[i-1,j-1])

[0043] Among them, d ij is an element in the distance matrix, D[i-1,j], D[i,j-1] and D[i-1,j-1] are adjacent elements in the cumulative distance matrix,

[0044] Starting from the lower right corner of the cumulative distance matrix, backtracking to the upper left corner to determine the best path to align the finite element data and the monitoring data, find an optimal path, the points on which represent the optimal solution to align the finite element data and the monitoring data to minimize the cumulative distance between them, and use the cumulative distance value as a similarity measure. The smallest cumulative distance value indicates that wrinkle damage occurs at the corresponding resistive strain sensor.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] The present invention identifies wrinkle defects, predicts the progressive damage evolution mechanism of wrinkles, combines state monitoring technology, and combines numerical simulation with operating data after strain sensor monitoring data mining to achieve feature fusion and feature comparison of a full-size blade model with wrinkle defects and monitoring data, and realizes digital-analog joint-driven wrinkle damage feature recognition of wind turbine blades. The present invention solves the problem that traditional blade damage recognition methods cannot specifically identify damage types and that wrinkle damage identification is difficult, and is of great significance to reducing the operation and maintenance costs of wind turbine blades and ensuring the healthy and stable operation of wind turbine blades. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart of a wind turbine blade wrinkle damage identification method based on data-driven;

[0048] Figure 2 It is a schematic diagram of the sensor distribution location;

[0049] Figure 3 It is the geometric parameter diagram of the airfoil;

[0050] Figure 4 It is a schematic diagram of chord-wise and span-wise partitioning;

[0051] Figure 5 This is a schematic diagram of the coupling between the body and shell of a wind turbine blade;

[0052] Figure 6 It is the wind turbine blade load coordinate system diagram. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application is described and illustrated below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application. Based on the embodiments provided in the present application, all other embodiments obtained by ordinary technicians in the field without making creative work are within the scope of protection of the present application.

[0054] The technical solution of the present invention is: a data-driven wind turbine blade wrinkle damage identification method, which specifically includes the following steps:

[0055] Step 1: Arrange 8 sensors with a total of 8 channels in the full-size blade, of which 4 are used at 1m from the blade root and 4 are used at 21.5m from the blade root to evaluate the strain monitoring scenario where the strain is large and relatively flat. The points are arranged at 45° relative to the actual flapping direction. The specific distribution of the sensors is as follows: Figure 2 As shown;

[0056] The arrangement process of the sensor is as follows: polish and clean the surface. Apply structural glue to the sensor installation surface. Use a hot air gun to heat at 80 degrees Celsius for 30 minutes. Connect the signal line and crimp it with a cold-press terminal. Connect the signal line to the sensor's air socket, and the other end of the signal line to the collector of the control cabinet. Connect the industrial computer to the keyboard, mouse and monitor for settings, and turn on the automatic collection frequency of 50Hz.

[0057] Step 2: First, the sensor data is denoised using the discrete wavelet threshold method, and the LSTM analysis method is used to remove invalid data from the extracted eigenvalues.

[0058] The original signal is subjected to wavelet transform, and the signal is decomposed into sub-bands of different frequencies. The sub-bands after wavelet transform are subjected to threshold processing, and the coefficients less than the threshold are set to zero, while the coefficients greater than the threshold are retained. This can set the noise coefficient to zero, thereby removing the noise. The wavelet coefficients after threshold processing are subjected to inverse wavelet transform to obtain the denoised signal. Its expression is:

[0059] Wavelet Transform:

[0060] Inverse wavelet transform:

[0061] Thresholding:

[0062] Among them, a is the scale factor, b is the translation parameter, is the wavelet coefficient, x(t) is the original signal, X(a,b) is the signal after wavelet transformation, ψ a,b (t) is the wavelet function (wavelet basis), is the complex conjugate of the wavelet function, and λ is the threshold.

[0063] The LSTM (Long Short-Term Memory) method is used to filter valid data and eliminate invalid data. The processed sensor data is used to construct a time series data set in chronological order. Feature values ​​are extracted from the time series data for LSTM model training. Feature values ​​include mean, variance, maximum and minimum values, and peak-to-peak values. These feature values ​​are used as the input of the LSTM model and are divided into training set, validation set, and test set. The LSTM model is then constructed using the training set. The input layer is set to define the number of data features, the LSTM layer is set to capture long-term dependencies in the time series, and the number of hidden units and layers are specified. The output of the LSTM layer is converted into a form suitable for the softmax layer input using a fully connected layer. The input values ​​are then converted into probability distributions through the softmax layer. The classification layer makes classification decisions based on the output of the softmax layer. The validation set is then used to verify and set training options, including optimizer, number of training iterations, and Mini-Batch size. The trained LSTM model is used to eliminate abnormal data from the test set, and the accuracy of the LSTM model in eliminating abnormal data is then evaluated by calculating the mean square error.

[0064] Step 3: Establish the blade geometry model in UG software. The aerodynamic centers of all airfoil sections are located on the same straight line, and these aerodynamic centers are located at 1 / 3 of the blade chord length. According to the aerodynamic shape, the blade airfoil data is transformed into three-dimensional coordinates according to this method. The geometry model is imported into the commercial finite element software ABAQUS to partition it in the chord direction and span direction, lay the layers, and apply equivalent fatigue loads. The body-shell coupling method is used to introduce wrinkles into the blade, and the finite element data of the strain value of the damaged area is extracted.

[0065] like Figure 3 As shown in the figure, the wind turbine blade model is constructed by twisting and scaling the wind turbine blade at a certain angle, and its thickness and chord length gradually change along the span direction of the blade. The principle is as follows:

[0066]

[0067] Where d is the chord length, β is the twist angle, and x p is the cross-section pitch axis (take 1 / 3 of the blade chord length), x and y are the original coordinates of the airfoil, x t ,y t , z is the transformed section coordinate, and r is the position of the airfoil section.

[0068] According to the three-dimensional section coordinates after conversion of the above formula, each section is saved as a sat file. Select the lofting command in the UG software, select the points in the file, and import the sat file of each section in turn to generate the geometric model of the blade.

[0069] The generated geometric model is imported into ABAQUS as an iges file for region division. Figure 4 As shown in (a), there is one spanwise partition between each airfoil section, and a total of 27 spanwise partitions are divided. The chordwise partitions divided according to the structural design are as follows Figure 4 As shown in (b), S1 represents the windward front edge strip, S2 and S6 represent the windward sandwich, S3, S4 and S5 represent the windward main beam, and S7 represents the windward trailing edge beam; P1 represents the windward front edge strip, P2 and P6 represent the windward sandwich, P3, P4 and P5 represent the windward main beam, and P7 represents the windward trailing edge beam.

[0070] After the model area is divided, the material properties of different areas are assigned and the mesh is divided in abaqus. The different material properties, ply angles, and thicknesses of the blade design are assigned to different areas one by one. The shell element S4R is used for the entire blade, and the final mesh size is determined to be approximately 50mm×50mm, the number of meshes is 84740, and the number of nodes is 83349.

[0071] Introducing wrinkles into full-scale blade models, such as Figure 5 The main beam of the 8th blade is selected, and the finite element model of the fold is established using the solid unit C3D8R according to the geometric morphology characteristics of the fold as follows. Figure 6 , body-shell coupling contact is adopted in ABAQUS to introduce wrinkle defects into the blade.

[0072]

[0073] Where: A is the height of the wrinkle curve; L is the length of the wrinkle defect area, that is, the amplitude of the sine curve; Z(x) is the geometric representation of the wrinkle.

[0074] In ABAQUS, loads are applied to the full-scale blade including the bending moment M. XS and M YS , torque M ZS , shear force F XS and F YS , and the axial force F ZS , extract the finite element data of the strain value of the damaged area. The cross-sectional coordinate system of the wind turbine blade is as follows: Figure 6As shown in the figure, when describing the blade section coordinate system, YS represents the direction along the blade chord line, which extends from the leading edge to the trailing edge; ZS represents the direction along the blade span, that is, the direction from the blade root to the blade tip; and XS is determined according to the right-hand rule, and the starting point OS of the coordinate system is set at the intersection of the blade's pitch axis and the chord line. As for the blade root coordinate system, ZB is exactly along the blade span, XB and ZB are at right angles, pointing to the tower in the upwind direction and away from the tower in the downwind direction. YB is also obtained according to the right-hand rule, and the origin OB of the coordinate system is located in the center of the circular area of ​​the blade root. When performing load analysis on a wind turbine, the load calculation software Bladed can provide force and moment data in three directions on each section, and load the obtained loads to the blade model.

[0075] Step 4: Using the characteristic that the peak-to-peak value in the monitoring data eigenvalue can reflect the change of stiffness, the dynamic time warping method (DTW) is used to compare and analyze the peak-to-peak values ​​of the eight channels with the finite element data.

[0076] The DTW algorithm is used to calculate the similarity between the peak-to-peak data of each of the eight channels and the finite element data, and a similarity matrix is ​​obtained. For each pair of data points (x i ,y i ) and (x j ,y j ), calculate the Euclidean distance:

[0077]

[0078] Construct a distance matrix in which the rows represent data points on the reference curve and the columns represent data points on other curves. Each element d in the matrix ij It represents the Euclidean distance between the i-th point on the reference curve and the j-th point on the other curves.

[0079] Create a matrix of the same size as the distance matrix, recorded as the cumulative distance matrix. For each element D[i,j] in the matrix, calculate as follows:

[0080] D[i,j]=d ij +min(D[i-1,j],D[i,j-1],D[i-1,j-1])

[0081] Among them, d ij is an element in the distance matrix, and D[i-1,j], D[i,j-1], and D[i-1,j-1] are adjacent elements in the cumulative distance matrix.

[0082] Starting from the lower right corner of the cumulative distance matrix, trace back to the upper left corner to determine the best path to align the finite element data and the monitoring data, and find an optimal path. The points on the path represent the optimal solution to align the finite element data and the monitoring data to minimize the cumulative distance between them. The cumulative distance value is used as a similarity metric. A total of 8 cumulative distance values ​​are obtained for the 8 channel monitoring data. The smallest cumulative distance value indicates that wrinkle damage occurs at the sensor of this channel. The cumulative distance calculated from the monitoring data of channel 8 and the finite element data is the smallest. Therefore, according to the position of channel 8, wrinkle damage occurs near the leading edge 21.5m away from the blade.

[0083] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A data-driven wind turbine blade wrinkle damage identification method, characterized in that: The following steps are involved: Step 1: Arrange a resistive strain sensor at the root of a full-size blade to monitor the strain during a shimmy fatigue test and obtain monitoring data; Step 2: De-noise the monitoring data and extract feature values; Step 3: Establish a blade geometry model based on aerodynamic layout and airfoil data, introduce wrinkle defects into blade analysis through body-shell coupling, apply equivalent fatigue load to the blade geometry model and extract finite element data of strain value in damaged area; Step 4: Use the dynamic time warping method to analyze and compare the finite element data obtained in step 3 with the monitoring data to identify the damage signal characteristics of the blade caused by wrinkles.

2. The data-driven wind turbine blade wrinkle damage identification method according to claim 1 is characterized in that: The resistive strain sensor described in step 1 is Donghua DH5908H, which is arranged at 45° relative to the actual swing direction, and the strain of the blade is monitored at a sampling frequency of 50 Hz.

3. The data-driven wind turbine blade wrinkle damage identification method according to claim 1 is characterized in that: In step 2, the monitoring data is first denoised using a discrete wavelet threshold method, and then the LSTM analysis method is used to remove invalid data from the extracted eigenvalues, where the eigenvalues ​​include mean, variance, maximum and minimum values, and peak-to-peak values.

4. The data-driven wind turbine blade wrinkle damage identification method according to claim 3 is characterized in that: The specific method of using discrete wavelet threshold method to denoise the monitoring data is as follows: The monitoring data is used as the original signal for wavelet transform, and the signal is decomposed into sub-bands of different frequencies. The sub-bands after wavelet transform are threshold processed, and the coefficients less than the threshold are set to zero, while the coefficients greater than the threshold are retained. The wavelet coefficients after threshold processing are inversely transformed to obtain the denoised signal, which is expressed as follows: Wavelet Transform: Inverse wavelet transform: Thresholding: Among them, a is the scale factor, b is the translation parameter, a and b are wavelet coefficients, x(t) is the original signal, X(a,b) is the signal after wavelet transformation, ψ a,b (t) is the wavelet function (wavelet basis), is the complex conjugate of the wavelet function, λ is the threshold; The specific method of using the LSTM analysis method to remove invalid data from the extracted feature values ​​is: First, the denoised signal is constructed into a time series dataset in chronological order, and feature values ​​are extracted from the time series data. These features will be used as the input of the LSTM model. Then, the extracted feature values ​​are divided into training set, validation set and test set. Subsequently, a model including an input layer, an LSTM layer, a fully connected layer, a softmax layer and a classification layer is constructed through the training set to enable it to learn the data representation of normal and abnormal states of the data. The validation set is used for verification to set the training options, and the trained LSTM model is used to remove abnormal data from the test set. Subsequently, the accuracy of the LSTM model in removing abnormal data is evaluated by calculating the mean square error.

5. The data-driven wind turbine blade wrinkle damage identification method according to claim 4 is characterized in that: The specific method of step 3 is: A blade geometric model is established in UG software. The aerodynamic centers of all airfoil sections of the blade geometric model are located on the same straight line, and these aerodynamic centers are located at 1 / 3 of the blade chord length. The blade airfoil data is transformed into three-dimensional coordinates according to the aerodynamic shape. The blade geometric model is imported into the commercial finite element software ABAQUS for chord-wise and span-wise partitioning, laying of layers, and application of equivalent fatigue loads. The body-shell coupling method is used to introduce wrinkles into the blade, and the finite element data of the strain value in the damaged area are extracted.

6. The data-driven wind turbine blade wrinkle damage identification method according to claim 5, characterized in that: The specific method of establishing the blade geometry model in UG software is: The wind turbine blade model is constructed by twisting and scaling the wind turbine blade, and its thickness and chord length gradually change along the span direction of the blade. The principle is as follows: Where d is the chord length, β is the twist angle, and x p is the pitch axis of the cross section, and 1 / 3 of the blade chord length is taken. x and y are the original coordinates of the airfoil. t ,y t , z is the transformed section coordinate, r is the position of the airfoil section, According to the three-dimensional section coordinates after conversion of formula (1), each section is saved as a sat file. In the UG software, the lofting command is selected, and the sat file of each section is imported in turn according to the points in the file to generate the blade geometry model.

7. The data-driven wind turbine blade wrinkle damage identification method according to claim 6 is characterized in that: The specific method of importing the blade geometry model into the commercial finite element software ABAQUS to extract the finite element data of the strain value of the damaged area is as follows: The blade geometry model is imported into ABAQUS as an iges file for regional division. After the regional division is completed, material properties are assigned and meshes are divided for different regions in ABAQUS. Different material properties, ply angles, and thicknesses of the blade design are assigned to different regions one by one to obtain a full-size blade model. Introducing wrinkles into full-scale blade models, Where: A is the height of the wrinkle curve; L is the length of the wrinkle defect area, that is, the amplitude of the sine curve; Z(x) is the geometric representation of the wrinkle. Loads were applied to the full-size blade in ABAQUS, and finite element data of strain values ​​in the damaged area were extracted.

8. The data-driven wind turbine blade wrinkle damage identification method according to claim 7 is characterized in that: The specific method of step 4 is: The dynamic time warping method is used to calculate the similarity between the monitoring data of each resistive strain sensor and the finite element data, and a similarity matrix is ​​obtained. For each pair of data points (x i ,y i ) and (x j ,y j ), calculate the Euclidean distance: Construct a distance matrix, where the rows represent data points on the reference curve and the columns represent data points on other curves. Each element d in the matrix ij represents the Euclidean distance between the i-th point on the reference curve and the j-th point on the other curves, Create a matrix of the same size as the distance matrix, recorded as the cumulative distance matrix. For each element D[i,j] in the matrix, calculate as follows: D[i,j]=d ij +min(D[i-1,j],D[i,j-1],D[i-1,j-1]) Among them, d ij is an element in the distance matrix, D[i-1,j], D[i,j-1] and D[i-1,j-1] are adjacent elements in the cumulative distance matrix, Starting from the lower right corner of the cumulative distance matrix, backtracking to the upper left corner to determine the best path to align the finite element data and the monitoring data, find an optimal path, the points on which represent the optimal solution to align the finite element data and the monitoring data to minimize the cumulative distance between them, and use the cumulative distance value as a similarity measure. The smallest cumulative distance value indicates that wrinkle damage occurs at the corresponding resistive strain sensor.

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