An automatic sorting method for damaged structural vibration modes of power battery system

Abstract

The present invention provides a method for automatically sorting the vibration modes of damaged structures of a power battery system, which relates to the field of structural health monitoring, including: determining the positioning reference for vibration mode sorting during the damage evolution process; obtaining the natural frequency and vibration mode of the structure in the intact state, sorting the natural frequency, and using the vibration mode as the initial reference reference; obtaining the natural frequency and vibration mode of the damaged structure; sorting the vibration modes of each node of the damaged structure; sorting the vibration modes of each order of the current damaged structure as the real-time reference reference for the next state of damage evolution; and completing the sorting of damage vibration modes in each state. This method can realize the automatic sorting of structural vibration modes in different damage states without experimental data or a large amount of training data, effectively improving the calculation efficiency, and ensuring the reliability and accuracy of the simulation results.

Description

Technical Field

[0001] The present invention relates to the technical field of structural health monitoring, and in particular to a method for automatically sorting vibration modes of damaged structures of a power battery system. Background Art

[0002] During service, power batteries may be damaged by vibration and shock, which may lead to the risk of structural damage; therefore, detecting the structure of the power battery system can ensure its safety and performance, as well as extend its service life. In the power battery system, various factors (such as vibration and shock, temperature changes, material aging, etc.) may cause structural damage and performance degradation, thus posing a threat to its safety and reliability. By detecting and locating damage to the power battery system structure, potential problems can be discovered early or in time, so that preventive maintenance measures can be taken to reduce the occurrence of potential risks. This ensures the safe and reliable operation of the power battery system.

[0003] In the process of structural inspection of power battery systems, damage identification is a very important task, which directly affects the accuracy and precision of the inspection. By analyzing the vibration response data of the structure, the damage in the structure can be accurately identified. The vibration response data of the structure includes natural frequency and vibration mode, which are closely related to the mass, stiffness and damage state of the structure. When analyzing the vibration characteristics of the damaged structure, it is necessary to ensure that each order vibration mode and natural frequency correspond to the reference group (i.e., the vibration characteristics in the intact state); however, with the occurrence of structural damage or the development of the degree of damage, if the data is always arranged in order of the size of the natural frequency, it may cause high / low order frequencies to cross, and low order frequencies may correspond to high order vibration modes, thus affecting the accuracy of structural characterization and damage identification.

[0004] There are many methods for sorting the vibration modes of damaged structures in the prior art, such as finite element analysis and modal experiments. However, traditional finite element analysis and modal experiment methods usually require a large amount of computing resources and experimental data, and have high computing costs. At the same time, for complex structures, their vibration characteristics are difficult to capture accurately, errors may be introduced in the calculation, and the mathematical model is highly complex, resulting in low accuracy and low computational efficiency in sorting. At the same time, there are also methods in the prior art that use deep learning networks (such as convolutional neural networks CNN, recurrent neural networks RNN, etc.) to process structural vibration data. Although they can improve the efficiency of sorting to a certain extent, the machine learning-based methods require a large amount of training data to enhance the generalization ability of the model, and the black box model is difficult to explain physical phenomena and has low credibility. In addition, some information technologies (such as image processing and machine vision methods) can convert structural vibration data into images, and then use image processing technology to sort them. However, the image processing-based methods have high computational complexity and involve multiple steps such as image sampling and feature extraction. In actual application environments, problems such as noise and distortion may occur when vibration characteristics are converted into images. In summary, although there are means in the prior art that can monitor and sort the vibration modes of damaged structures, they all have problems such as low sorting efficiency, susceptibility to environmental factors, and many influencing factors that cause errors. Summary of the invention

[0005] In view of the problems existing in the above prior art, an object of the present invention is to provide a method for automatically sorting the damaged structure vibration modes of a power battery system, so as to solve the problems existing in the above prior art for sorting the damaged structure vibration modes.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] A method for automatically sorting damaged structural vibration modes of a power battery system, comprising:

[0008] Step 1: First, according to the number of damaged structures to be sorted, the order of vibration modes, node positions, etc., and the requirements of vibration analysis of damaged structures, determine the positioning benchmark for vibration mode sorting during the damage evolution process;

[0009] Step 2: mathematically model the structure and use modal analysis to obtain the vibration characteristics of each node of the structure in a lossless state; the vibration characteristics include natural frequency and vibration mode (vibration mode is the vertical displacement of each node);

[0010] Step 3: sort the vibration characteristics of each node of the structure in the intact state obtained in step 2 according to the size of the natural frequency, and use the vibration mode of each node after sorting (i.e., the vertical displacement of each node) as the initial reference benchmark;

[0011] Step 4: Introduce the vibration characteristics of the damaged structure, and obtain the natural frequency of the damaged structure through the finite element model, and sort the nodes of the damaged structure according to the current natural frequency;

[0012] Step 5: Use the method in step 2 to obtain the vibration mode (i.e., vertical displacement) of each node of the damaged structure sorted in step 4;

[0013] Step 6: Sort the vibration modes of each node of the damaged structure;

[0014] Step 7: sorting the vibration modes of the current damaged structure in step 6 as a real-time reference benchmark for the next state of damage evolution;

[0015] Step 8: Repeat steps 4 to 7 until the vibration modes of each state of damage evolution are correctly sorted and correspond one by one to the natural frequencies.

[0016] Based on further optimization of the above solution, the requirements for vibration analysis of the damaged structure in step 1 include damage location, damage degree, etc.

[0017] Based on the further optimization of the above scheme, the method for obtaining the natural frequency of the structure in the lossless state in step 2 is:

[0018] First, assume that the structure is subjected to a set of exciting forces with a frequency of w in the lossless state, the amplitude of the exciting force is P, the corresponding displacement is D, and the structure is divided into N components in the lossless state. Then, the maximum strain energy V and potential energy T of the structure in the lossless state are:

[0019]

[0020]

[0021] Where: A and B are both N·N symmetric matrices, representing the stiffness matrix and mass matrix of the structure respectively. In the lossless state, the mass and stiffness of the structure are uniformly distributed along the longitudinal direction of the structure; t represents the transpose of the matrix;

[0022] Since the elements in the stiffness matrix A and the mass matrix B are independent of w, the Lagrange equation is applied:

[0023]

[0024] Where: p j and d j represent the jth element in the amplitude P and displacement D respectively;

[0025] Thus we get: K = Aw 2 B;

[0026] In the formula, K represents the dynamic stiffness matrix of the structure, and each element in the matrix is ​​related to the frequency w;

[0027] Taking free vibration as an example, its amplitude P is 0, that is, KD = (Aw 2 B) D = 0;

[0028] The displacement vector D includes all degrees of freedom of the structure. When D = 0, it means that no vibration occurs; therefore, the free vibration problem is transformed into the solution:

[0029] det(K)=0;

[0030] The dynamic stiffness matrix K of the structure in the damage-free state ES for:

[0031]

[0032] Where: K1, K2, …, K j represents the dynamic stiffness matrix of each unit of the structure in the lossless state; E1, E2, …, E j represents the longitudinal node constraint matrix of each unit of the structure in the lossless state; l represents the longitudinal length of the structure in the lossless state; H represents the conjugate transpose;

[0033] The dynamic stiffness matrix K of the structure in the undamaged state ES And the solution of det(K)=0 is used to obtain the natural frequency of each node of the structure in the lossless state.

[0034] Based on the further optimization of the above scheme, the method for obtaining the vibration mode (i.e., vertical displacement) of the structure in the non-destructive state in step 2 is:

[0035] First, the dynamic stiffness matrix K of the structure in the lossless state is converted into ES Convert to upper triangular matrix

[0036] Then, a random force is assigned to the last node of the structure in the lossless state within the range of 0-1, that is:

[0037] P(n)=rand(n,1);

[0038] Afterwards, according to the formula P = KD and the upper triangular matrix Get the normalized mode shape of the last node:

[0039]

[0040] Finally, the vibration modes of each node of the structural unit in each lossless state are calculated in turn:

[0041]

[0042] Based on the further optimization of the above scheme, the specific method of obtaining the natural frequency of the damaged structure through the finite element model in step 4 is:

[0043] After the vibration characteristics of the damaged structure are introduced, the homogeneous characteristics of the original structure are destroyed. The structure is divided into two parts: the intact area and the damaged area. The intact area adopts the model described in the above step 2, and the damaged area adopts the finite element model. The intact area and the damaged area are coupled through the Lagrangian operator to form a semi-analytical model suitable for any damaged structure. At this time, the dynamic stiffness matrix K of the damaged structure is:

[0044]

[0045] Where: K ES represents the dynamic stiffness matrix of the lossless region; K FE represents the dynamic stiffness matrix of the damaged area; C1 represents the constraint matrix of the intact area, C1 H represents the conjugate transpose of the constraint matrix of the intact region; C2 represents the constraint matrix of the damaged region, C2 t represents the transpose of the damage region constraint matrix.

[0046] After that, the loss of structural stiffness is obtained, and the loss of structural stiffness is used to update the self-use of each node of the structure, so as to obtain the stiffness matrix K of each node in the damaged area. * ; Through the stiffness matrix K of each node in the damaged area * Combined with the dynamic stiffness matrix K of the damaged structure, the natural frequency of the damaged structure is obtained.

[0047] Based on the further optimization of the above scheme, the method for obtaining the structural stiffness loss is as follows: Taking a damaged plate structure with a crack as an example: the structural stiffness loss C caused by the crack is represented by a massless spring * :

[0048]

[0049] Where: d represents the crack depth, h represents the thickness of the plate structure.

[0050] Based on the further optimization of the above scheme, the step six is ​​specifically as follows:

[0051] Starting from the first-order natural frequency, the vibration modes corresponding to the n-order and n+1-order natural frequencies of the damaged structure obtained in step five are respectively subtracted from the vibration modes corresponding to the n-order natural frequency in the initial reference datum obtained in step three; the difference values ​​are compared, and the fixed frequency corresponding to the smaller difference value is marked as the n-order frequency of the damaged structure; the vibration mode corresponding to the larger difference value continues to be subtracted from the vibration mode corresponding to the next stage, that is, the n+2-order natural frequency, and the vibration mode corresponding to the n+1-order natural frequency in the initial reference datum, and the sizes are compared, and this cycle is repeated until all the frequencies of the current damaged structure are correctly sorted;

[0052] That is: First, obtain the vibration mode (i.e. vertical displacement) d′ corresponding to the j-th order natural frequency i,j,n , the vibration mode (i.e. vertical displacement) d′ corresponding to the j+1th order natural frequency i,j+1,n The vibration mode (i.e. vertical displacement) corresponding to the jth natural frequency in the initial reference datum is d i-1,j,n The difference between in:

[0053]

[0054]

[0055] In the formula, n represents the node position of the damaged structure; i represents the mode in the damaged state. When it is in the intact state, the mode is 0, that is, i-1=0 in the above formula;

[0056] when When d′ i,j,n The corresponding natural frequency is taken as the natural frequency of the jth order, d′ i,j+1,n Continue to perform the next round of difference calculation with the vibration mode (i.e., vertical displacement) corresponding to the next stage, i.e., they respectively perform difference calculation with the vibration mode (i.e., vertical displacement) corresponding to the j+1th order in the initial reference datum;

[0057] when When d′ i,j+1,n The corresponding natural frequency is taken as the natural frequency of the jth order, d′ i,j,n Continue to perform the next round of difference calculation with the vibration mode (i.e. vertical displacement) corresponding to the next stage, i.e. j+2 order, that is, perform difference calculation with the vibration mode (i.e. vertical displacement) corresponding to the j+1th order in the initial reference datum.

[0058] The present invention has the following technical effects:

[0059] Compared with the prior art, the present application models the vibration characteristics of the structure in the intact state and the vibration characteristics of the structure after damage respectively, and uses the vibration characteristics of the structure in the intact state as a reference benchmark, thereby automatically sorting the vibration modes of the damaged structure in a straight line. The method of the present application does not require a large amount of experimental data or training data, and can realize automatic sorting of structural vibration modes in different damage states. It has high calculation efficiency, good simulation reliability, and small calculation error. The entire sorting process is simple and does not require a large amount of computing resources, thereby achieving faster and more accurate sorting of damaged structure vibration modes, and promoting the identification and monitoring of different damages to the power battery system structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 The flowchart is a flow chart of automatic sorting of damaged structural vibration modes of a power battery system in an embodiment of the present invention.

[0061] Figure 2 Schematic diagram of obtaining the natural frequency of a damaged structure using a finite element model in an embodiment of the present invention; wherein: Figure 2 (a) shows the detailed diagram of the finite element part; Figure 2 (b) Schematic diagram showing the rotational freedom of node 5 in the damaged area; Figure 2 (c) is a diagram showing a structural unit with crack damage.

[0062] Figure 3 is a flowchart of the damage structure vibration mode sorting in the embodiment of the present invention; wherein A′ m,r Indicates the default sorting of the damaged structure vibration modes, A m,r It indicates the correct sorting of the damaged structure vibration modes, m indicates the damage location or damage degree, m=0 for the intact structure, i indicates the number of structural vibration mode groups, j indicates the jth vibration mode, r indicates the vibration mode order, and n indicates the node position.

[0063] Figure 4 is a damaged structure diagram of the vibration mode sequence to be verified in the embodiment of the present invention; wherein, Figure 4 (a) is x=0.01, l=0.01, default mode number r=2; Figure 4 (b) is x=0.01, l=0.01, default mode number r=3; Figure 4 (c) is x=0.04, l=0.01, default mode number r=2; Figure 4 (d) is x=0.04, l=0.01, and default mode number r=4. DETAILED DESCRIPTION

[0064] The technical solutions in the embodiments of the present invention will be described clearly and completely below. In the following description, for the purpose of explanation rather than limitation, specific details such as specific system structures and technologies are proposed to facilitate a thorough understanding of the embodiments of the present invention.

[0065] Embodiment 1:

[0066] A method for automatically sorting damaged structural vibration modes of a power battery system, comprising:

[0067] Step 1: First, according to the number m, mode order r, node position n, etc. of damaged structures to be sorted, and the requirements of vibration analysis of damaged structures, including damage location, damage degree, etc., determine the positioning benchmark for mode sorting during damage evolution;

[0068] Step 2: mathematically model the structure and use modal analysis to obtain the vibration characteristics of each node of the structure in a lossless state; the vibration characteristics include natural frequency and vibration mode (vibration mode is the vertical displacement of each node);

[0069] Among them, the method for obtaining the natural frequency of the structure in the lossless state is:

[0070] First, take the plate structure in the lossless state as an example, assuming that it satisfies the undamped linear elastic assumption, assuming that the structure in the lossless state is subjected to a set of exciting forces with a frequency of w, the amplitude of the exciting force is P, and the corresponding displacement is D. The structure in the lossless state is divided into N components, then the maximum strain energy V and potential energy T of the structure in the lossless state are:

[0071]

[0072]

[0073] Where: A and B are both N·N symmetric matrices, representing the stiffness matrix and mass matrix of the structure respectively. In the lossless state, the mass and stiffness of the structure are uniformly distributed along the longitudinal direction of the structure; t represents the transpose of the matrix;

[0074] Since the elements in the stiffness matrix A and the mass matrix B are independent of w, the Lagrange equation is applied:

[0075]

[0076] Where: p j and d j represent the jth element in the amplitude P and displacement D respectively;

[0077] Thus we get: K = Aw 2 B;

[0078] In the formula, K represents the dynamic stiffness matrix of the structure, and each element in the matrix is ​​related to the frequency w;

[0079] Taking free vibration as an example, its amplitude P is 0, that is, KD = (Aw 2 B) D = 0;

[0080] The displacement vector D includes all degrees of freedom of the structure. When D = 0, it means that no vibration occurs; therefore, the free vibration problem is transformed into the solution:

[0081] det(K)=0;

[0082] According to the exact strip method, the dynamic stiffness matrix K of the structure in the undamaged state in the exact strip model is ES for:

[0083]

[0084] Where: K1, K2, …, K j represents the dynamic stiffness matrix of each unit of the structure in the lossless state; E1, E2, …, E j represents the longitudinal node constraint matrix of each unit of the structure in the lossless state; l represents the longitudinal length of the structure in the lossless state; H represents the conjugate transpose;

[0085] The dynamic stiffness matrix K of the structure in the undamaged state ES And the solution of det(K)=0 is used to obtain the natural frequency of each node of the structure in the lossless state.

[0086] The method for obtaining the vibration mode (i.e. vertical displacement) of the structure in the lossless state is:

[0087] First, the dynamic stiffness matrix K of the structure in the lossless state is converted into ES Convert to upper triangular matrix

[0088] Then, according to the random force method, a random force is assigned to the last node of the structure in the range of 0-1 in the lossless state, that is:

[0089] P(n)=rand(n,1);

[0090] Afterwards, according to the formula P = KD and the upper triangular matrix Get the normalized mode shape of the last node:

[0091]

[0092] Finally, the vibration modes of each node of the structural unit in each lossless state are calculated in turn:

[0093]

[0094] Step 3: sort the vibration characteristics of each node of the structure in the intact state obtained in step 2 according to the size of the natural frequency, and use the vibration mode of each node after sorting (i.e., the vertical displacement of each node) as the initial reference benchmark;

[0095] Step 4: Introduce the vibration characteristics of the damaged structure and obtain the natural frequency of the damaged structure through the finite element model. Specifically, after the vibration characteristics of the damaged structure are introduced, the homogeneous characteristics of the original structure are destroyed. The structure is divided into two parts: the intact area and the damaged area. The intact area adopts the model described in the above step 2, and the damaged area adopts the finite element model. The intact area and the damaged area are coupled through the Lagrangian operator to form a semi-analytical model suitable for any damaged structure. At this time, the dynamic stiffness matrix K of the damaged structure is:

[0096]

[0097] Where: K ES represents the dynamic stiffness matrix of the lossless region; K FE represents the dynamic stiffness matrix of the damaged area; C1 represents the constraint matrix of the intact area, C1 H represents the conjugate transpose of the constraint matrix of the intact region; C2 represents the constraint matrix of the damaged region, C2 t represents the transpose of the damage region constraint matrix;

[0098] After that, the structural stiffness loss is obtained. Taking the damaged structure with cracks as an example, the structural stiffness loss caused by the cracks is represented by a massless spring:

[0099]

[0100] Where: d represents the crack depth, h represents the thickness of the plate structure.

[0101] The loss of structural stiffness is used to update the self-use of each node of the structure, so as to obtain the stiffness matrix K of each node in the damaged area. * ,by Figure 2 Taking a damaged structural unit shown in (c) as an example, based on the above structural stiffness loss formula and shape functions N1, N2, N3, N4:

[0102]

[0103]

[0104]

[0105]

[0106] The flexibility of each node in the damaged structural element is updated as:

[0107]

[0108]

[0109]

[0110]

[0111] by Figure 2 Take node 5 in the damaged area in (b) as an example: Due to the existence of cracks, the degrees of freedom of node 5 are expanded from three to five, and two rotational degrees of freedom are added. The degrees of freedom of node 5 are updated as follows:

[0112] (w5,θ x5L ,θ x5U ,θ y5L ,θ y5U ), its stiffness matrix is:

[0113]

[0114] Therefore, the stiffness matrix of each node in the damaged area can be written in sequence as Figure 2 Take (a) as an example, Figure 2 The stiffness matrix of the 9 nodes shown in (a) is:

[0115]

[0116] Where: The stiffness matrix K of each node in the damaged area i The Roman numeral superscript is Figure 2 The serial numbers of each subunit in (a), i.e., I, II, and IV, represent the serial numbers of each node subunit.

[0117] The stiffness matrix K of each node in the damaged area * Combined with the dynamic stiffness matrix K of the damaged structure, the natural frequency of the damaged structure is obtained; at the same time, the nodes of the damaged structure are sorted according to the current natural frequency;

[0118] Step 5: Use the method in step 2 to obtain the vibration mode (i.e., vertical displacement) of each node of the damaged structure sorted in step 4;

[0119] Step 6: Starting from the first-order natural frequency, the vibration modes (i.e., vertical displacements) corresponding to the n-order and n+1-order natural frequencies of the damaged structure obtained in step 5 are respectively subtracted from the vibration modes (i.e., vertical displacements) corresponding to the n-order natural frequency in the initial reference datum obtained in step 3; the difference values ​​are compared, and the fixed frequency corresponding to the smaller difference is marked as the n-order frequency of the damaged structure; the vibration mode (i.e., vertical displacement) corresponding to the larger difference continues to be subtracted from the vibration mode (i.e., vertical displacement) corresponding to the next stage, i.e., the vibration mode (i.e., vertical displacement) corresponding to the n+2-order natural frequency and the vibration mode (i.e., vertical displacement) corresponding to the n+1-order natural frequency in the initial reference datum, and the sizes are compared, and the cycle is repeated until all the frequencies of the current damaged structure are correctly sorted;

[0120] Specifically:

[0121] First, the vibration mode (i.e. vertical displacement) d corresponding to the j-th order natural frequency is obtained respectively. i ' ,j,n , the vibration mode corresponding to the j+1th order natural frequency (i.e. vertical displacement) d i ' ,j+1,n The vibration mode (i.e. vertical displacement) corresponding to the jth order natural frequency in the initial reference datum is d i-1,j,n The difference between in:

[0122]

[0123]

[0124] In the formula, n represents the node position of the damaged structure; i represents the mode in the damaged state. When it is in the intact state, the mode is 0, that is, i-1=0 in the above formula;

[0125] when When d i ' ,j,n The corresponding natural frequency is taken as the natural frequency of the jth order; d i ' ,j+1,n Continue to perform the next round of difference calculation with the vibration mode (i.e., vertical displacement) corresponding to the next stage, i.e., perform difference calculation with the vibration mode (i.e., vertical displacement) corresponding to the j+2th order in the initial reference datum, such as:

[0126]

[0127]

[0128] Compare and The smaller value corresponds to the natural frequency as the j+1th order natural frequency, and the larger value corresponds to the vibration mode (i.e. vertical displacement) to continue the next round of calculation;

[0129] when When d i ' ,j+1,n The corresponding natural frequency is taken as the natural frequency of the jth order; d i ' ,j,n Continue to perform the next round of difference calculation with the vibration mode (i.e., vertical displacement) corresponding to the next stage, i.e., perform difference calculation with the vibration mode (i.e., vertical displacement) corresponding to the j+2th order in the initial reference datum, such as:

[0130]

[0131]

[0132] Compare and The smaller value corresponds to the natural frequency as the j+1th order natural frequency, and the larger value corresponds to the vibration mode (i.e. vertical displacement) to continue the next round of calculation;

[0133] Until the sorting of each order frequency in the current state is completed.

[0134] Step 7: sorting the vibration modes of the current damaged structure in step 6 as a real-time reference benchmark for the next state of damage evolution;

[0135] Step 8: Repeat steps 4 to 7 until the vibration modes of each state of damage evolution are correctly sorted and correspond one by one to the natural frequencies.

[0136] Embodiment 2:

[0137] As a further optimization of the scheme of the present application, based on the scheme of Example 1, a method for sorting the vibration modes of a damaged structure of a simply supported thin plate (isotropic material) with a crack can be applied to damage detection of the plate structure in a power battery module, including:

[0138] The default vibration modes of a cracked (isotropic material) simply supported thin plate with different crack positions and different damage degrees are as follows: Figure 4 As shown,

[0139] First, the crack position is used as the positioning reference for vibration mode sorting, and the natural frequency w of the structure is obtained based on the modal analysis of Example 1. m,r and the normalized vibration mode (i.e. vertical displacement) d m,r,n, where the crack is parallel to the horizontal axis y, and the projection of the crack on the vertical axis x is its coordinate; the crack length l represents the degree of damage; r represents the vibration mode order; m represents the crack position of the damaged structure to be verified; and n represents the structural node position. Secondly, the natural frequency w of each node of the simply supported thin plate in the undamaged state is obtained according to the method described in step 2 of embodiment 1. 0,r And vibration mode d 0,r,n , sort them according to the size of the natural frequency (sorted as 1, 2, 3, ..., n), and use the corresponding vibration mode as the initial reference benchmark; the initial crack position x = 0.01, the initial damage degree l = 0.01, and the natural frequency w' of the simply supported thin plate in the current state is obtained according to the method described in step 4 and step 5 of embodiment 1 1,r And the vertical displacement d' of each node 1,r,n , and are arranged in order of natural frequency by default.

[0140] Then, the method described in step 6 of Example 1 is used to sort the vibration modes of the damaged structure, specifically: starting from the first-order natural frequency (i=1, j=1), if the damage continues to evolve, that is, i=2,3,…,n, extract the vertical displacement d' of its default first-order and second-order frequencies 1,1,n With d' 1,2,n ; According to the first-order vertical displacement d of the lossless structure 0,1,n , the degree of deviation of the vertical displacement of each node relative to the vertical displacement of the lossless structure is obtained, that is:

[0141]

[0142]

[0143] Compare and like Then d1′ ,1,n The corresponding natural frequency is taken as the first-order natural frequency of the current damage state; d1′ ,2,n The vertical displacement of the third-order natural frequency is taken into account in the next round of calculation and is respectively combined with the second-order vertical displacement of the lossless structure d 0,2,n The difference is compared and the smaller difference is taken as the second-order natural frequency of the current damage state. The vertical displacement with the larger difference and the vertical displacement of the fourth-order natural frequency are included in the next round of calculation and are respectively compared with the vertical displacement d 0,3,n Make a difference and compare the difference, and repeat this cycle until all vibration modes of the current damage state are sorted.

[0144] like Then d1′ ,2,n The corresponding natural frequency is taken as the first-order natural frequency of the current damage state; d1′ ,1,nThe vertical displacement of the third-order natural frequency is taken into account in the next round of calculation and is respectively combined with the second-order vertical displacement of the lossless structure d 0,2,n The difference is compared and the smaller difference is taken as the second-order natural frequency of the current damage state. The vertical displacement with the larger difference and the vertical displacement of the fourth-order natural frequency are included in the next round of calculation and are respectively compared with the vertical displacement d 0,3,n Make a difference and compare the difference, and repeat this cycle until all vibration modes of the current damage state are sorted.

[0145] Subsequently, the vibration characteristics of the current damage state are used as a reference for the vibration mode sorting of the next stage of damage evolution until the vibration mode sorting of each stage of damage evolution is completed.

Claims

1. A method for automatically sorting the vibration modes of damaged structures of a power battery system, characterized in that: include: Step 1: First, according to the number of damaged structures to be sorted, the order of vibration modes, and the node positions, and according to the requirements of vibration analysis of damaged structures, determine the positioning benchmark for vibration mode sorting during the damage evolution process; Step 2: mathematically model the structure and use modal analysis to obtain the vibration characteristics of each node of the structure in a lossless state; the vibration characteristics include natural frequency and vibration mode; Step 3: sort the vibration characteristics of each node of the structure in the lossless state obtained in step 2 according to the size of the natural frequency, and use the vibration mode of each node after sorting as the initial reference benchmark; Step 4: Introduce the vibration characteristics of the damaged structure, and obtain the natural frequency of the damaged structure through the finite element model, and sort the nodes of the damaged structure according to the current natural frequency; Step 5: Use the method in step 2 to obtain the vibration mode of each node of the damaged structure sorted in step 4; Step 6: Sort the vibration modes of each node of the damaged structure, specifically: Starting from the first-order natural frequency, the vibration modes corresponding to the n-order and n+1-order natural frequencies of the damaged structure obtained in step five are respectively subtracted from the vibration modes corresponding to the n-order natural frequency in the initial reference datum obtained in step three; the sizes of the differences are compared, and the fixed frequency corresponding to the small difference is marked as the n-order frequency of the damaged structure; the vibration mode corresponding to the large difference continues to be subtracted from the vibration mode corresponding to the next stage, that is, the n+2-order natural frequency and the vibration mode corresponding to the n+1-order natural frequency in the initial reference datum, and the sizes are compared, and this cycle is repeated until all the frequencies of the current damaged structure are correctly sorted; That is: First, obtain the j The vibration mode corresponding to the natural frequency , No. j+1 The vibration mode corresponding to the natural frequency The corresponding first j The vibration mode corresponding to the natural frequency The difference between , ,in: In the formula, n Indicates the node position of the structure after damage; i Indicates the mode under the damaged state. When it is in the lossless state, the mode is 0, that is, i-1=0 ; when When The corresponding natural frequency is taken as j The natural frequency of the order, Continue with the next stage, j+2 The vibration modes corresponding to the first order are calculated for the next round of difference, that is, they are respectively compared with the first order corresponding to the initial reference standard. j+1 The difference calculation is performed on the vibration mode corresponding to the order; when When The corresponding natural frequency is taken as the natural frequency of the jth order, Continue with the next stage, j+2 The vibration modes corresponding to the first order are calculated for the next round of difference, that is, they are respectively compared with the first order corresponding to the initial reference standard. j+1 The difference calculation is performed on the vibration mode corresponding to the order; Step 7: sorting the vibration modes of the current damaged structure in step 6 as a real-time reference benchmark for the next state of damage evolution; Step 8: Repeat steps 4 to 7 until the vibration modes of each state of damage evolution are correctly sorted and correspond one by one to the natural frequencies.

2. The method for automatically sorting the damaged structural vibration modes of a power battery system according to claim 1, characterized in that: The requirements for the vibration analysis of the damaged structure in step 1 include the damage location and the damage degree.

3. The method for automatically sorting the damaged structural vibration modes of a power battery system according to claim 1 or 2, characterized in that: The method for obtaining the natural frequency of the structure in the lossless state in step 2 is: First, assume that the structure is subjected to a set of frequencies in a lossless state. w The excitation force acts on the P The corresponding displacement is D , the structure is divided into N components, the maximum strain energy of the structure in the damage-free state is V With potential energy T for: Where: A and B Both N·N The symmetric matrices of represent the stiffness matrix and mass matrix of the structure respectively. In the lossless state, the mass and stiffness of the structure are evenly distributed along the longitudinal direction of the structure. t Represents the transpose of a matrix; Since the stiffness matrix A With the mass matrix B The elements in w Therefore, the Lagrange equation applies: Where: p j and d j Represents the amplitude P and displacement D The j elements; Thus we obtain: In the formula, K represents the dynamic stiffness matrix of the structure, and each element in the matrix is ​​related to the frequency w related; Taking free vibration as an example, its amplitude P is 0, that is Displacement Vector D Contains all degrees of freedom of the structure. D=0 When , it means that no vibration occurs; therefore, the free vibration problem is transformed into solving: Dynamic stiffness matrix of the structure in the undamaged state K ES for: Where: Represents the dynamic stiffness matrix of each unit of the structure in the damage-free state; It represents the longitudinal node constraint matrix of each unit of the structure in the damage-free state; l It represents the longitudinal length of the structure in the damage-free state; H represents conjugate transpose; Through the dynamic stiffness matrix of the structure in the undamaged state K ES And the solution of det(K)=0 is used to obtain the natural frequency of each node of the structure in the lossless state.

4. The method for automatically sorting the damaged structural vibration modes of a power battery system according to claim 3, characterized in that: The method for obtaining the vibration mode of the structure in the lossless state in step 2 is: First, the dynamic stiffness matrix of the structure in the intact state is transformed into K ES Convert to upper triangular matrix ; Then, a random force is assigned to the last node of the structure in the lossless state within the range of 0-1, that is: Afterwards, according to P=KD The formula and upper triangular matrix Get the normalized mode shape of the last node: Finally, the vibration modes of each node of the structural unit in each lossless state are calculated in turn:

5. The method for automatically sorting the damaged structural vibration modes of a power battery system according to claim 4, characterized in that: The specific method for obtaining the natural frequency of the damaged structure through the finite element model in step 4 is: After the vibration characteristics of the damaged structure are introduced, the homogeneous characteristics of the original structure are destroyed. The structure is divided into two parts: the intact area and the damaged area. The intact area adopts the model described in the above step 2, and the damaged area adopts the finite element model. The intact area and the damaged area are coupled through the Lagrangian operator to form a semi-analytical model suitable for any damaged structure. At this time, the dynamic stiffness matrix of the damaged structure is K for: Where: K ES represents the dynamic stiffness matrix of the lossless region; K FE represents the dynamic stiffness matrix of the damaged area; C 1 represents the constraint matrix of the lossless region, represents the conjugate transpose of the lossless region constraint matrix; C 2 represents the constraint matrix of the damaged area, represents the transpose of the damage region constraint matrix; After that, the loss of structural stiffness is obtained, and the loss of structural stiffness is used to update the self-use of each node of the structure, so as to obtain the stiffness matrix of each node in the damaged area. K * ; The stiffness matrix of each node in the damaged area K * The dynamic stiffness matrix of the damaged structure K Combined to obtain the natural frequency of the damaged structure; The specific method for obtaining the structural stiffness loss is as follows: Taking a damaged structure with cracks as an example: the structural stiffness loss caused by the cracks is represented by a massless spring: Where: d Indicates the crack depth, h Indicates the thickness of the plate structure.

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