CN117709143A - Automatic ordering method for vibration modes of damaged structure of power battery system - Google Patents
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Abstract
The invention provides an automatic ordering method for vibration modes of a damaged structure of a power battery system, which relates to the field of structural health monitoring and comprises the following steps: determining a positioning reference of vibration mode sequencing in the damage evolution process; obtaining the natural frequency and the vibration mode of the structure in a lossless state, and sequencing the natural frequency and taking the vibration mode as an initial reference standard; obtaining the natural frequency and vibration mode of the damaged structure; ordering the vibration modes of all nodes of the damaged structure; taking the ordering of the vibration modes of each order of the structure after the current damage as a real-time reference standard of a state under the damage evolution; and finishing the damage vibration mode sorting of each state. According to the method, the structure vibration modes of different damage states can be automatically ordered without experimental data or a large amount of training data, so that the calculation efficiency is effectively improved, and the reliability and the accuracy of simulation results are ensured.
Description
Technical Field
The invention relates to the technical field of structural health monitoring, in particular to an automatic ordering method for damaged structure vibration modes of a power battery system.
Background
The power battery is damaged by vibration impact and the like in the service process, so that the risk of structural damage exists; therefore, detecting the structure of the power battery system can ensure the safety and the service performance thereof, and prolong the service life thereof. In a power cell system, various factors (such as vibration impact, temperature change, material aging, etc.) may cause damage to the structure and degradation of the performance, thereby posing a threat to the safety and reliability thereof. By detecting and locating damage to the power cell system structure, potential problems can be discovered early or timely, so that preventive maintenance measures can be taken, and the occurrence of potential risks is reduced. Thus, safe and reliable operation of the power battery system can be ensured.
In the structure detection process of a power battery system, damage identification is an important task, and the damage identification directly affects the detection precision, accuracy and the like; by analyzing the vibration response data of the structure, damage conditions in the structure can be accurately identified. The vibration response data of the structure includes natural frequencies and modes, which are closely related to the mass, stiffness and damage status of the structure. When analyzing the vibration characteristics of the damaged structure, the vibration modes of each order and the natural frequency are required to be ensured to be in one-to-one correspondence with the reference group (namely the vibration characteristics in a nondestructive state); however, with the occurrence of structural damage or the development of damage degree, if data are arranged according to the order of the natural frequencies all the time, the high/low order frequencies may be crossed, and the low order frequencies may correspond to the high order vibration modes, thereby affecting the accuracy of the characterization of the structure and the damage identification.
In the prior art, various methods for ordering the vibration modes of the damaged structure exist, such as finite element analysis and modal experiments, however, the traditional finite element analysis and modal experiment methods generally need a large amount of calculation resources and experimental data, and have high calculation cost; meanwhile, for a complex structure, vibration characteristics of the complex structure are difficult to capture accurately, errors can be introduced in calculation, and mathematical models are high in complexity, so that sequencing accuracy is low, and calculation efficiency is low. Meanwhile, in the prior art, deep learning networks (such as convolutional neural networks CNN and cyclic neural networks RNN) are used for processing structural vibration data, and although the ordering efficiency can be improved to a certain extent, a large amount of training data is required to enhance the generalization capability of a model based on a machine learning method, and a black box model is difficult to explain physical phenomena and has low reliability. In addition, some information technologies (such as image processing and machine vision methods) can convert structural vibration data into images, and then the images are sequenced by using the image processing technology, however, the image processing-based method has high computational complexity, involves multiple steps of image sampling, feature extraction and the like, and is easy to generate the problem that noise and distortion influence when vibration features are converted into images in an actual application environment. In summary, although the prior art has a means for monitoring and sorting the vibration modes of the damaged structure, the prior art has the problems of low sorting efficiency, easiness in being influenced by environmental factors, a large number of influencing factors causing errors and the like.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention aims to provide an automatic ordering method for the vibration modes of the damaged structure of a power battery system, so as to solve the problems existing in the prior art aiming at the ordering of the vibration modes of the damaged structure.
The aim of the invention is achieved by the following technical scheme:
an automatic ordering method for damaged structure vibration modes of a power battery system comprises the following steps:
firstly, determining a positioning reference of vibration pattern sequencing in the process of damage evolution according to the number of damage structures to be sequenced, the vibration pattern order, the node position and the like and the requirements of vibration analysis of the damage structures;
performing mathematical modeling on the structure, and obtaining vibration characteristics of each node of the structure in a nondestructive state by using modal analysis; the vibration characteristics include natural frequency and vibration mode (vibration mode, i.e., vertical displacement of each node);
step three, ordering the vibration characteristics of each node of the structure in the nondestructive state obtained in the step two according to the magnitude of the natural frequency, and taking the vibration mode of each node (namely the vertical displacement of each node) after ordering as an initial reference standard;
step four, introducing vibration characteristics of the damaged structure, obtaining the natural frequency of the damaged structure through a finite element model, and sequencing all nodes of the damaged structure according to the current natural frequency;
step five, acquiring the vibration modes (namely vertical displacement) of each node of the damaged structure after the sorting in the step four by adopting the method in the step two;
step six, ordering the vibration modes of all nodes of the damaged structure;
step seven, taking the ordering of the vibration modes of each order of the structure after the current damage in the step six as a real-time reference standard of the next state of the damage evolution;
and step eight, repeating the steps four to seven until the vibration modes of each state of the damage evolution are correctly sequenced and are in one-to-one correspondence with the inherent frequencies.
Based on the further optimization of the scheme, the requirements of vibration analysis of the damaged structure in the first step include damage position, damage degree and the like.
Based on the further optimization of the scheme, the method for acquiring the natural frequency of the structure in the lossless state in the second step comprises the following steps:
firstly, assuming that the structure is acted by a group of exciting forces with the frequency w in a nondestructive state, wherein the amplitude of the exciting forces is P, the corresponding displacement is D, and the structure is divided into N component parts in the nondestructive state, the maximum strain energy V and the potential energy T of the structure in the nondestructive state are as follows:
wherein: a and B are symmetric matrixes of N.N, respectively represent a rigidity matrix and a mass matrix of the structure, and the mass and the rigidity of the structure are uniformly distributed along the longitudinal direction of the structure in a nondestructive state; t represents the transpose of the matrix;
since the stiffness matrix a is independent of the elements in the mass matrix B from w, the lagrangian equation is applied:
wherein: p is p j And d j Represents the j-th element in the amplitude P and the displacement D, respectively;
thereby obtaining: k=a-w 2 B；
Wherein K represents a dynamic stiffness matrix of the structure, and each element in the matrix is related to a frequency w;
taking the free vibration as an example, the amplitude P is 0, namely KD= (A-w) 2 B)D＝0；
The displacement vector D contains the degrees of freedom of the structure, when d=0, indicating that no vibration occurs; thus, the free vibration problem translates into solving:
det(K)＝0；
dynamic stiffness matrix K of structure in nondestructive state ES The method comprises the following steps:
wherein: k (K) 1 ,K 2 ,…,K j Representing the dynamic stiffness matrix of each unit of the structure in a nondestructive state; e (E) 1 ,E 2 ,…,E j Representing a longitudinal node constraint matrix of each unit of the structure in a lossless state; l represents the longitudinal length of the structure in the intact state; h represents a conjugate transpose;
through dynamic stiffness matrix K of structure in nondestructive state ES And solving det (K) =0 to obtain the natural frequency of each node of the structure in the lossless state.
Based on the further optimization of the scheme, the method for acquiring the vibration mode (namely vertical displacement) of the structure in the nondestructive state in the second step comprises the following steps:
firstly, a dynamic stiffness matrix K of a structure in a nondestructive state is obtained through Gaussian elimination ES Conversion to an upper triangular matrix
Then, in the interval range of 0-1, a random force is given to the last node of the structure in a lossless state, namely:
P(n)＝rand(n,1)；
then, according to the formula of p=kd and the upper triangular matrixObtaining the normalized vibration mode of the last node:
finally, the vibration modes of all nodes of the structural unit in each lossless state are calculated in sequence:
based on the further optimization of the scheme, the specific method for obtaining the natural frequency of the damaged structure through the finite element model in the fourth step is as follows:
after the vibration characteristics of the damaged structure are introduced, the homogeneity of the original structure is destroyed, the structure is divided into a lossless region and a damaged region, the lossless region adopts the model in the second step, the damaged region adopts a finite element model, and the lossless region and the damaged region are coupled through Lagrangian operators to form a semi-analytical model applicable to any damaged structure; at this time, the dynamic stiffness matrix K of the post-injury structure is:
wherein: k (K) ES A dynamic stiffness matrix representing the lossless region; k (K) FE A dynamic stiffness matrix representing the lesion area; c (C) 1 Constraint matrix representing lossless region, C 1 H Representing a conjugate transpose of the lossless region constraint matrix; c (C) 2 Constraint matrix representing damaged area, C 2 t Representing the transpose of the lesion field constraint matrix.
Then, obtaining the structural rigidity loss, and updating the degree of utilization of each node of the structure by utilizing the structural rigidity loss, thereby obtaining the rigidity matrix K of each node of the damaged area * The method comprises the steps of carrying out a first treatment on the surface of the Stiffness matrix K of each node passing through damaged area * And combining the dynamic stiffness matrix K of the damaged structure to obtain the natural frequency of the damaged structure.
Based on the further optimization of the scheme, the method for obtaining the structural rigidity loss comprises the following steps: taking a damaged plate structure with cracks as an example: representing structural stiffness loss C due to cracking by a mass-free spring * ：
Wherein: d represents the crack depth and h represents the plate structure thickness.
Based on the further optimization of the scheme, the sixth step is specifically:
respectively differencing the vibration modes corresponding to the nth order and the n+1st order natural frequencies of the damaged structure obtained in the fifth step from the first order natural frequency and the vibration mode corresponding to the nth order natural frequency in the initial reference standard obtained in the third step; comparing the difference values, and marking the fixed frequency corresponding to the smaller difference value as the nth order frequency of the damaged structure; the vibration mode corresponding to the larger difference value is continuously different from the vibration mode corresponding to the natural frequency of the n+2 th order in the next stage, namely, the vibration mode corresponding to the natural frequency of the n+1 th order in the initial reference standard, the size is compared, and the cycle is performed in this way until the frequencies of all the orders of the structure after the current damage are correctly ordered;
namely: firstly, respectively obtaining the vibration mode (namely vertical displacement) d 'corresponding to the natural frequency of the j-th order' i,j,n The vibration mode (namely vertical displacement) d 'corresponding to the natural frequency of the (j+1) th order' i,j+1,n The jth order corresponding to the initial referenceVibration mode (i.e. vertical displacement) d corresponding to natural frequency i-1,j,n Difference betweenWherein:
wherein n represents the node position of the damaged structure; i represents the mode in the damaged state, and when the mode is in the lossless state, the mode is 0, namely i-1=0 in the formula;
when (when)At the time, d' i,j,n The corresponding natural frequency is taken as the natural frequency of the j th order, d' i,j+1,n Continuing to perform next-round difference calculation on the vibration modes (namely vertical displacement) corresponding to the next stage (namely j+2 steps), namely performing difference calculation on the vibration modes (namely vertical displacement) corresponding to the j+1 steps in the initial reference standard;
when (when)At the time, d' i,j+1,n The corresponding natural frequency is taken as the natural frequency of the j th order, d' i,j,n And continuing to perform the next round of difference calculation on the vibration modes (namely vertical displacement) corresponding to the next phase, namely the j+2 order, namely performing difference calculation on the vibration modes (namely vertical displacement) corresponding to the j+1 th order in the initial reference.
The invention has the following technical effects:
compared with the prior art, the method has the advantages that the vibration characteristics of the structure in the nondestructive state and the vibration characteristics of the structure after damage are modeled respectively, the vibration characteristics of the structure in the nondestructive state are used as reference, so that the vibration patterns of the structure after damage are automatically ordered by straight lines, the method can realize the automatic ordering of the vibration patterns of the structure in different damage states without a large amount of experimental data or training data, the calculation efficiency is high, the simulation reliability is good, the calculation error is small, the whole ordering process is concise, a large amount of calculation resources are not required to be consumed, the rapid and accurate ordering of the vibration patterns of the damaged structure is realized, and the identification and monitoring of different damages of the power battery system structure are promoted.
Drawings
Fig. 1 is a flow chart of automatic sorting of damaged structure vibration modes of a power battery system according to an embodiment of the invention.
FIG. 2 is a schematic diagram of a finite element model obtaining natural frequencies of a structure after damage in an embodiment of the present invention; wherein fig. 2 (a) shows a detailed representation of a finite element portion; fig. 2 (b) shows a schematic view of the degree of freedom of the damaged area node 5; fig. 2 (c) shows a display of a structural unit with crack damage.
FIG. 3 is a flow chart of vibration mode ordering of a damaged structure in an embodiment of the invention; wherein A 'is' m,r Representing default ordering of vibration modes of damaged structures, A m,r The method is characterized in that the method is used for accurately sequencing the vibration modes of the damaged structure, m is the damage position or damage degree, the lossless structure is m=0, i is the number of groups of the vibration modes of the structure, j is the j-th order vibration mode, r is the vibration mode order, and n is the node position.
FIG. 4 is a diagram showing a structure of a damage structure to be checked in order of vibration mode in an embodiment of the present invention; fig. 4 (a) shows x=0.01, l=0.01, and default mode number r =2; fig. 4 (b) is x=0.01, l=0.01, default mode number r =3; fig. 4 (c) is x=0.04, l=0.01, default mode number r =2; fig. 4 (d) is x=0.04, l=0.01, default mode number r =4.
Detailed Description
In the following description, for purposes of explanation and not limitation, specific details are set forth such as the particular system architecture, techniques, etc., in order to provide a thorough understanding of the embodiments of the present invention.
Example 1:
an automatic ordering method for damaged structure vibration modes of a power battery system comprises the following steps:
firstly, determining a positioning reference of vibration pattern sequencing in the process of damage evolution according to the number m, vibration pattern order r, node position n and the like of the damage structures to be sequenced and the requirements of vibration analysis of the damage structures, including damage positions, damage degree and the like;
performing mathematical modeling on the structure, and obtaining vibration characteristics of each node of the structure in a nondestructive state by using modal analysis; the vibration characteristics include natural frequency and vibration mode (vibration mode, i.e., vertical displacement of each node);
the method for acquiring the natural frequency of the structure in the lossless state comprises the following steps:
firstly, taking a plate structure in a non-destructive state as an example, assuming that the plate structure meets the non-damping line elasticity assumption, assuming that the structure in the non-destructive state is subjected to a group of exciting forces with the frequency w, the amplitude of the exciting forces is P, the corresponding displacement is D, and the structure in the non-destructive state is divided into N components, wherein the maximum strain energy V and the potential energy T of the structure in the non-destructive state are as follows:
wherein: a and B are symmetric matrixes of N.N, respectively represent a rigidity matrix and a mass matrix of the structure, and the mass and the rigidity of the structure are uniformly distributed along the longitudinal direction of the structure in a nondestructive state; t represents the transpose of the matrix;
since the stiffness matrix a is independent of the elements in the mass matrix B from w, the lagrangian equation is applied:
wherein: p is p j And d j Respectively are provided withRepresents the j-th element in amplitude P and displacement D;
thereby obtaining: k=a-w 2 B；
Wherein K represents a dynamic stiffness matrix of the structure, and each element in the matrix is related to a frequency w;
taking the free vibration as an example, the amplitude P is 0, namely KD= (A-w) 2 B)D＝0；
The displacement vector D contains the degrees of freedom of the structure, when d=0, indicating that no vibration occurs; thus, the free vibration problem translates into solving:
det(K)＝0；
according to the accurate strip method, dynamic stiffness matrix K of structure in lossless state in accurate strip model ES The method comprises the following steps:
wherein: k (K) 1 ,K 2 ,…,K j Representing the dynamic stiffness matrix of each unit of the structure in a nondestructive state; e (E) 1 ,E 2 ,…,E j Representing a longitudinal node constraint matrix of each unit of the structure in a lossless state; l represents the longitudinal length of the structure in the intact state; h represents a conjugate transpose;
through dynamic stiffness matrix K of structure in nondestructive state ES And solving det (K) =0 to obtain the natural frequency of each node of the structure in the lossless state.
The method for acquiring the vibration mode (namely vertical displacement) of the structure in the nondestructive state comprises the following steps:
firstly, a dynamic stiffness matrix K of a structure in a nondestructive state is obtained through Gaussian elimination ES Conversion to an upper triangular matrix
Then, according to the random force method, in the interval range of 0-1, a random force is given to the last node of the structure in a lossless state, namely:
P(n)＝rand(n,1)；
then, according to the formula of p=kd and the upper triangular matrixObtaining the normalized vibration mode of the last node:
finally, the vibration modes of all nodes of the structural unit in each lossless state are calculated in sequence:
step three, ordering the vibration characteristics of each node of the structure in the nondestructive state obtained in the step two according to the magnitude of the natural frequency, and taking the vibration mode of each node (namely the vertical displacement of each node) after ordering as an initial reference standard;
step four, introducing vibration characteristics of the damaged structure, and obtaining natural frequency of the damaged structure through a finite element model, wherein the method specifically comprises the following steps: after the vibration characteristics of the damaged structure are introduced, the homogeneity of the original structure is destroyed, the structure is divided into a lossless region and a damaged region, the lossless region adopts the model in the second step, the damaged region adopts a finite element model, and the lossless region and the damaged region are coupled through Lagrangian operators to form a semi-analytical model applicable to any damaged structure; at this time, the dynamic stiffness matrix K of the post-injury structure is:
wherein: k (K) ES A dynamic stiffness matrix representing the lossless region; k (K) FE A dynamic stiffness matrix representing the lesion area; c (C) 1 Constraint matrix representing lossless region, C 1 H Representing a conjugate transpose of the lossless region constraint matrix; c (C) 2 Constraint matrix representing damaged area，C 2 t Representing a transpose of the lesion field constraint matrix;
after that, a structural rigidity loss is obtained, taking a damaged structure with cracks as an example, the structural rigidity loss due to the cracks is represented by a mass-free spring:
wherein: d represents the crack depth and h represents the plate structure thickness.
The self-utilization degree of each node of the structure is updated by utilizing the loss of the rigidity of the structure, so that the rigidity matrix K of each node of the damaged area is obtained * Taking a damaged structural unit as shown in FIG. 2 (c) as an example, the structural rigidity loss formula and the shape function N are based on 1 、N 2 、N 3 、N 4 ：
The compliance of each node in the damaged structural unit is updated as:
taking node 5 of the damaged area in fig. 2 (b) as an example: because of the existence of cracks, the degree of freedom of the node 5 is expanded from three to five, two degrees of freedom of angles are increased, and the degree of freedom of the node 5 is updated as follows:
(w 5 ,θ x5L ,θ x5U ,θ y5L ,θ y5U ) The stiffness matrix is:
thus, the stiffness matrix of each node of the damaged area can be written out sequentially, taking fig. 2 (a) as an example, the stiffness matrix of 9 nodes shown in fig. 2 (a) is:
wherein: stiffness matrix K of each node in damaged area i The roman numerals of (a) are the numbers of the subunits in fig. 2 (a), i.e., I, II, IV denote the numbers of the node subunits.
Stiffness matrix K of each node passing through damaged area * Combining the dynamic stiffness matrix K of the damaged structure to obtain the natural frequency of the damaged structure; meanwhile, ordering all nodes of the damaged structure according to the current natural frequency;
step five, acquiring the vibration modes (namely vertical displacement) of each node of the damaged structure after the sorting in the step four by adopting the method in the step two;
step six, starting from the first order natural frequency, respectively differentiating the vibration modes (namely vertical displacement) corresponding to the nth order and the n+1st order natural frequency of the damaged structure obtained in the step five and the vibration mode (namely vertical displacement) corresponding to the nth order natural frequency in the initial reference standard obtained in the step three; comparing the difference values, and marking the fixed frequency corresponding to the smaller difference value as the nth order frequency of the damaged structure; the vibration mode (namely vertical displacement) corresponding to the larger difference value is continuously differed from the vibration mode (namely vertical displacement) corresponding to the natural frequency of the n+2 th order in the next stage, namely the vibration mode (namely vertical displacement) corresponding to the natural frequency of the n+1 th order in the initial reference standard, the size is compared, and the circulation is carried out in this way until the frequencies of all the orders of the structure after the current damage are correctly ordered;
the method comprises the following steps:
firstly, respectively obtaining the vibration mode (namely vertical displacement) d corresponding to the natural frequency of the jth order i ′ ,j,n Mode shape (i.e. vertical displacement) d corresponding to the (j+1) -th order natural frequency i ′ ,j+1,n Mode shape (i.e. vertical displacement) d corresponding to the jth order natural frequency corresponding to the initial reference i-1,j,n Difference betweenWherein:
wherein n represents the node position of the damaged structure; i represents the mode in the damaged state, and when the mode is in the lossless state, the mode is 0, namely i-1=0 in the formula;
when (when)When d is to i ′ ,j,n The corresponding natural frequency is taken as the natural frequency of the j th order; d, d i ′ ,j+1,n Continue and go downThe next round of difference calculation is carried out on the vibration modes (namely vertical displacement) corresponding to the j+2 steps at one stage, namely, the difference calculation is carried out on the vibration modes (namely vertical displacement) corresponding to the j+1 steps in the initial reference standard, for example:
comparison ofAnd->The natural frequency corresponding to the smaller value is used as the natural frequency of the j+1st order, and the vibration mode (namely vertical displacement) corresponding to the larger value is continuously calculated in the next round;
when (when)When d is to i ′ ,j+1,n The corresponding natural frequency is taken as the natural frequency of the j th order; d, d i ′ ,j,n Continuing to perform the next round of difference calculation on the vibration modes (i.e. vertical displacements) corresponding to the next phase, i.e. the j+2 steps, i.e. respectively performing difference calculation on the vibration modes (i.e. vertical displacements) corresponding to the j+1 steps in the initial reference, for example:
comparison ofAnd->The natural frequency corresponding to the smaller value is used as the natural frequency of the j+1st order, and the vibration mode (namely vertical displacement) corresponding to the larger value is continuously calculated in the next round;
and finishing the sequencing of the frequencies of each order in the current state.
Step seven, taking the ordering of the vibration modes of each order of the structure after the current damage in the step six as a real-time reference standard of the next state of the damage evolution;
and step eight, repeating the steps four to seven until the vibration modes of each state of the damage evolution are correctly sequenced and are in one-to-one correspondence with the inherent frequencies.
Example 2:
as a further optimization of the solution of the present application, based on the solution of embodiment 1, a method for sorting vibration modes of a damaged structure of a (isotropic material) simply supported thin plate with a crack, which is applicable to damage detection of a plate structure in a power battery module, includes:
the default modes of the cracked (isotropic material) simply supported sheet with different crack locations and different damage levels are shown in figure 4,
first, the natural frequency w of the structure is obtained based on the modal analysis of example 1 with the crack positions as the positioning references for the vibration mode ordering m,r And normalized mode shape (i.e. vertical displacement) d m,r,n Wherein the crack is parallel to the transverse axis y and takes the projection of the crack on the longitudinal axis x as the coordinate thereof; crack length l represents the extent of damage; r represents the vibration mode order; m represents the crack position of the damaged structure to be checked; n represents the structure node position. Next, the natural frequencies w of the nodes of the simply supported sheet in the lossless state were obtained according to the method described in step two of example 1 0,r Vibration mode d 0,r,n Sorting according to the magnitude of the natural frequency (sorting is 1,2,3, …, n), and taking the corresponding vibration mode as an initial reference standard; crack initiation position x=0.01, initial damage degree l=0.01, obtained according to the method described in step four, step five of example 1Natural frequency w 'of simply supported sheet in current state' 1,r Vertical displacement d 'of each node' 1,r,n And are arranged in order of natural frequency by default.
Then, the vibration mode sorting of the damaged structure is performed by the method described in step six of example 1, specifically: starting from the first order natural frequency (i=1, j=1), if the lesion continues to evolve, i.e. i=2, 3, …, n, the vertical displacement d 'of its default first and second order frequencies is extracted' 1,1,n And d' 1,2,n The method comprises the steps of carrying out a first treatment on the surface of the According to the first-order vertical displacement d of the non-destructive structure 0,1,n Obtaining the offset degree of the vertical displacement of each node relative to the vertical displacement of the nondestructive structure, namely:
comparison ofAnd->If->D is then 1 ′ ,1,n The corresponding natural frequency is used as the first-order natural frequency of the current damage state; d, d 1 ′ ,2,n The vertical displacement of the natural frequency of the third order is taken into the next round of calculation together, and the vertical displacement d of the second order of the lossless structure is respectively calculated 0,2,n The difference is made and compared, the second order natural frequency with smaller difference is used as the current damage state, the vertical displacement with larger difference and the vertical displacement of the fourth order natural frequency are jointly taken into the next round of calculation and respectively combined with the vertical displacement d of the third section of the lossless structure 0,3,n Making and comparing differences, and circulating untilAll vibration modes of the current damage state are ordered.
If it isD is then 1 ′ ,2,n The corresponding natural frequency is used as the first-order natural frequency of the current damage state; d, d 1 ′ ,1,n The vertical displacement of the natural frequency of the third order is taken into the next round of calculation together, and the vertical displacement d of the second order of the lossless structure is respectively calculated 0,2,n The difference is made and compared, the second order natural frequency with smaller difference is used as the current damage state, the vertical displacement with larger difference and the vertical displacement of the fourth order natural frequency are jointly taken into the next round of calculation and respectively combined with the vertical displacement d of the third section of the lossless structure 0,3,n And (4) performing difference and comparison on the difference values, and circulating in this way until all vibration modes in the current damage state are ordered.
And then, taking the vibration characteristic of the current damage state as a vibration mode sequencing reference standard of the next stage of damage evolution until the vibration mode sequencing of each stage of damage evolution is completed.
Claims (6)
1. A damage structure vibration mode automatic ordering method of a power battery system is characterized in that: comprising the following steps:
firstly, determining a positioning reference of vibration pattern sequencing in the process of damage evolution according to the number of damage structures to be sequenced, the vibration pattern order, the node position and the like and the requirements of vibration analysis of the damage structures;
performing mathematical modeling on the structure, and obtaining vibration characteristics of each node of the structure in a nondestructive state by using modal analysis; the vibration characteristics comprise natural frequency and vibration mode;
step three, ordering the vibration characteristics of each node of the structure in the nondestructive state obtained in the step two according to the magnitude of the natural frequency, and taking the vibration modes of each node after ordering as initial reference standard;
step four, introducing vibration characteristics of the damaged structure, obtaining the natural frequency of the damaged structure through a finite element model, and sequencing all nodes of the damaged structure according to the current natural frequency;
step five, acquiring the vibration modes of the nodes of the damaged structure after the sorting in the step four by adopting the method in the step two;
step six, ordering the vibration modes of all nodes of the damaged structure;
step seven, taking the ordering of the vibration modes of each order of the structure after the current damage in the step six as a real-time reference standard of the next state of the damage evolution;
and step eight, repeating the steps four to seven until the vibration modes of each state of the damage evolution are correctly sequenced and are in one-to-one correspondence with the inherent frequencies.
2. The automatic ordering method for damaged structure vibration modes of a power battery system according to claim 1, wherein the automatic ordering method is characterized by comprising the following steps: the requirements of vibration analysis of the damaged structure in the first step include damage position, damage degree and the like.
3. The automatic ordering method for damaged structure vibration modes of a power battery system according to claim 1 or 2, characterized in that: the method for acquiring the natural frequency of the structure in the lossless state in the second step comprises the following steps:
firstly, assuming that the structure is acted by a group of exciting forces with the frequency w in a nondestructive state, wherein the amplitude of the exciting forces is P, the corresponding displacement is D, and the structure is divided into N component parts in the nondestructive state, the maximum strain energy V and the potential energy T of the structure in the nondestructive state are as follows:
wherein: a and B are symmetric matrixes of N.N, respectively represent a rigidity matrix and a mass matrix of the structure, and the mass and the rigidity of the structure are uniformly distributed along the longitudinal direction of the structure in a nondestructive state; t represents the transpose of the matrix;
since the stiffness matrix a is independent of the elements in the mass matrix B from w, the lagrangian equation is applied:
wherein: p is p j And d j Represents the j-th element in the amplitude P and the displacement D, respectively;
thereby obtaining: k=a-w 2 B；
Wherein K represents a dynamic stiffness matrix of the structure, and each element in the matrix is related to a frequency w;
taking the free vibration as an example, the amplitude P is 0, namely KD= (A-w) 2 B)D＝0；
The displacement vector D contains the degrees of freedom of the structure, when d=0, indicating that no vibration occurs; thus, the free vibration problem translates into solving:
det(K)＝0；
dynamic stiffness matrix K of structure in nondestructive state ES The method comprises the following steps:
wherein: k (K) 1 ,K 2 ,…,K j Representing the dynamic stiffness matrix of each unit of the structure in a nondestructive state; e (E) 1 ,E 2 ,…,E j Representing a longitudinal node constraint matrix of each unit of the structure in a lossless state; l represents the longitudinal length of the structure in the intact state; h represents a conjugate transpose;
through dynamic stiffness matrix K of structure in nondestructive state ES And solving det (K) =0 to obtain the natural frequency of each node of the structure in the lossless state.
4. The automatic ordering method for damaged structure vibration modes of a power battery system according to any one of claims 1 to 3, characterized in that: the method for acquiring the vibration mode of the structure in the nondestructive state in the second step comprises the following steps:
firstly, a dynamic stiffness matrix K of a structure in a nondestructive state is obtained through Gaussian elimination ES Conversion to an upper triangular matrix
Then, in the interval range of 0-1, a random force is given to the last node of the structure in a lossless state, namely:
P(n)＝rand(n,1)；
then, according to the formula of p=kd and the upper triangular matrixObtaining the normalized vibration mode of the last node:
finally, the vibration modes of all nodes of the structural unit in each lossless state are calculated in sequence:
5. the automatic ordering method for damaged structure vibration modes of a power battery system according to claim 4, wherein the automatic ordering method is characterized by comprising the following steps: the specific method for obtaining the natural frequency of the damaged structure through the finite element model in the fourth step is as follows:
after the vibration characteristics of the damaged structure are introduced, the homogeneity of the original structure is destroyed, the structure is divided into a lossless region and a damaged region, the lossless region adopts the model in the second step, the damaged region adopts a finite element model, and the lossless region and the damaged region are coupled through Lagrangian operators to form a semi-analytical model applicable to any damaged structure; at this time, the dynamic stiffness matrix K of the post-injury structure is:
wherein: k (K) ES A dynamic stiffness matrix representing the lossless region; k (K) FE A dynamic stiffness matrix representing the lesion area; c (C) 1 Constraint matrix representing lossless region, C 1 H Representing a conjugate transpose of the lossless region constraint matrix; c (C) 2 Constraint matrix representing damaged area, C 2 t Representing a transpose of the lesion field constraint matrix;
then, obtaining the structural rigidity loss, and updating the degree of utilization of each node of the structure by utilizing the structural rigidity loss, thereby obtaining the rigidity matrix K of each node of the damaged area * The method comprises the steps of carrying out a first treatment on the surface of the Stiffness matrix K of each node passing through damaged area * And combining the dynamic stiffness matrix K of the damaged structure to obtain the natural frequency of the damaged structure.
Based on the further optimization of the scheme, the method for obtaining the structural rigidity loss comprises the following steps: taking a damaged structure with cracks as an example: the loss of structural stiffness due to cracking is represented by a mass-free spring:
wherein: d represents the crack depth and h represents the plate structure thickness.
6. The automatic ordering method for damaged structure vibration modes of a power battery system according to claim 1 or 5, wherein the automatic ordering method is characterized by comprising the following steps: the sixth step is specifically as follows:
respectively differencing the vibration modes corresponding to the nth order and the n+1st order natural frequencies of the damaged structure obtained in the fifth step from the first order natural frequency and the vibration mode corresponding to the nth order natural frequency in the initial reference standard obtained in the third step; comparing the difference values, and marking the fixed frequency corresponding to the smaller difference value as the nth order frequency of the damaged structure; the vibration mode corresponding to the larger difference value is continuously different from the vibration mode corresponding to the natural frequency of the n+2 th order in the next stage, namely, the vibration mode corresponding to the natural frequency of the n+1 th order in the initial reference standard, the size is compared, and the cycle is performed in this way until the frequencies of all the orders of the structure after the current damage are correctly ordered;
namely: firstly, respectively obtaining the vibration mode d 'corresponding to the natural frequency of the j-th order' i,j,n Mode d 'corresponding to the j+1st order natural frequency' i,j+1,n Mode d corresponding to the jth order natural frequency corresponding to the initial reference i-1,j,n Difference betweenWherein:
wherein n represents the node position of the damaged structure; i represents the mode in the damaged state, and when the mode is in the lossless state, the mode is 0, namely i-1=0 in the formula;
when (when)At the time, d' i,j,n The corresponding natural frequency is taken as the natural frequency of the j th order, d' i,j+1,n Continuing to perform next-round difference calculation on the vibration modes corresponding to the next stage, namely j+2 steps, namely performing difference calculation on the vibration modes corresponding to the j+1 steps corresponding to the initial reference standard;
when (when)At the time, d' i,j+1,n Corresponding natural frequencyThe rate is taken as the natural frequency of the j th order, d' i,j,n And continuing to perform the next round of difference calculation on the vibration modes corresponding to the next phase, namely j+2 steps, namely respectively performing difference calculation on the vibration modes corresponding to the j+1 steps corresponding to the initial reference standard.
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