Structural damage identification method based on benchmark Bayesian principle and sparse regularization

Abstract

The present invention discloses a structural damage identification method based on the benchmark Bayesian principle and sparse regularization, including performing an environmental vibration test on the structure and collecting acceleration signal data; performing fast Bayesian FFT modal identification on the collected signal to obtain measured modal information of the structure; establishing a finite element model and parameterizing the stiffness matrix; constructing a damage identification objective function based on the benchmark Bayesian principle and sparse regularization; setting a regularization parameter selection range and an iteration step, and using a swarm intelligence optimization algorithm to solve the objective function for any of the regularization parameters; selecting regularization parameters based on the DP criterion, and solving to obtain the optimal structural parameters. The present invention establishes a fitting function (i.e., a damage identification objective function) between measured modal parameters and theoretical modal parameters calculated according to the finite element model based on the benchmark Bayesian principle and sparse regularization technology, and uses an intelligent optimization algorithm to solve the optimal structural parameters, thereby realizing the positioning and quantification of structural damage.

Description

Technical Field

[0001] The invention relates to a method for structural damage identification using a computer program. Background Art

[0002] Under the combined effects of environmental erosion, material aging, design defects, load fatigue effects, and natural disasters, the structural system will inevitably accumulate damage and attenuate resistance, which will in turn affect the safety of the structure. If the structural damage is not discovered in time and the structure is not maintained, it is very likely to cause an engineering accident, which will have a direct and significant impact on people's lives and property and social stability, and may even lead to catastrophic consequences in extreme cases. In order to ensure the safety of engineering structures and extend the service life of structures, structural health monitoring has become a hot issue in the field of civil engineering. Among them, structural damage identification technology is the core issue of structural health monitoring. It uses the information collected by the structural health monitoring system to locate and quantify structural damage, providing a decision-making basis for structural safety status assessment and maintenance. Damage identification is roughly divided into the following four levels: determine whether structural damage exists; determine the location of damage; quantify the degree of structural damage; and predict the remaining life of the structure.

[0003] Structural damage identification is a typical inverse problem, which infers unknown structural parameters (input) based on the output (structural response), that is, to find the optimal system parameters that respond to the structural state. The data used in the identification process are usually the time history data of the structural response recorded at different locations (such as displacement, acceleration, etc.), and the time history data of the excitation are input when possible. The parameter to be identified can be any physical quantity of the structural system (such as structural mass, damping, stiffness, etc.). Existing damage identification methods can be roughly divided into deterministic methods and probabilistic methods. So far, deterministic methods, such as methods based on least squares, heuristic algorithms, filtering techniques, etc., have been well developed. These methods have been used to solve inverse problems such as model updating and damage identification. By providing well-defined values ​​of structural parameters, when the identification problem is well-posed, deterministic methods can be effectively used to determine the structural health state (damage degree). However, in actual engineering, there are often measurement errors and modeling errors, and the measurement data are often incomplete, which all cause the ill-posedness of the inverse problem solution, and the deterministic method often cannot give satisfactory results. In contrast, probabilistic methods are more robust in dealing with uncertainty because they are able to consider all possible models conditioned on the measured data and prior information. One of the most popular probabilistic methods is called the Bayesian method. This method considers the complete information in the measured data for statistical inference while giving an appropriate likelihood function, which can obtain a robust prediction of the structural response and a reliable assessment of the structural damage, alleviating the ill-posedness of the inverse problem solution to a certain extent. However, the Bayesian inversion process generally requires high-dimensional multiple integrals, the formula derivation is complex, and the solution calculation is very difficult, which limits its application to a certain extent.

[0004] Regularization method is a method used to deal with the ill-posedness of inverse problem solving. Its basic idea is to use the solution of a well-posed problem close to the original problem to approximate the solution of the original problem. In the process of solving ill-posed inverse problems such as structural damage identification, there is often overfitting of structural parameters to measurement errors and noise, resulting in multiple sets of local optimal solutions or even no solution. Therefore, the introduction of regularization technology can ensure that the data fitting error is small enough while maintaining a relatively smooth model without overfitting. Common regularization methods include: 1 Norm regularization (sparse regularization) and l 2 Norm regularization (Tikhonov regularization). Compared to l 2 Norm regularized smooth solution, l 1 Norm regularization can retain more mutation information and obtain a sparser solution. Since the damage of actual structures often only occurs in local locations, that is, the damage is sparse, l 1 Norm regularization is more suitable for structural damage identification. Summary of the invention

[0005] The technical problem to be solved by the present invention is: in order to reduce the influence of uncertain factors such as measurement error, modeling error, incomplete measurement acquisition signal on the structural damage identification effect, improve the accuracy and robustness of damage identification results, and reduce the occurrence of erroneous damage identification results, the present invention proposes a damage identification method that combines the benchmark Bayesian principle with sparse regularization, and adopts an intelligent swarm optimization algorithm for analysis and calculation, thereby realizing the organic combination of deterministic method and probabilistic method, and can achieve accurate positioning and quantification of damage results with a lower amount of calculation.

[0006] The first technical solution of the present invention is:

[0007] A structural damage identification method based on the benchmark Bayesian principle comprises: performing an environmental vibration test on the structure and collecting acceleration signal data; performing fast Bayesian FFT modal identification on the collected signal and obtaining measured modal information of the structure; establishing a finite element model and a parameterized stiffness matrix of the component; constructing a damage identification objective function based on the benchmark Bayesian principle and performing identification in two stages. In the first stage, the modal characteristics, i.e., the natural frequency, damping ratio, vibration mode, etc., are firstly identified, and then the structural parameters of the second stage are identified using their identification results; and a swarm intelligence optimization algorithm is used to solve the objective function.

[0008] The specific steps are:

[0009] A. Arrange acceleration sensors on the structure to be identified, conduct vibration tests under environmental excitation conditions, and obtain the vibration signal of the structure.

[0010] B. Based on the collected structural acceleration signal Perform fast Bayesian FFT modal identification to obtain measured modal information of the structure Including measured natural frequencies and formation and the corresponding posterior covariance matrix Where i represents the order of the mode;

[0011] C. Establish a finite element model of the structure and obtain the computational modal information of the structure based on the finite element model Including calculation of natural frequencies and formation Where i represents the order of the mode; D. Based on the benchmark Bayesian principle, combined with the structural modal information, a fitting function between the measured modal parameters and the theoretical modal parameters calculated according to the finite element model is established, that is, a damage identification objective function is constructed; the objective function is:

[0012]

[0013] 1.E. Intelligent swarm optimization algorithm is used to solve the objective function and locate and quantify structural damage.

[0014] Further in step B: Assume that the acceleration signal collected by the structural vibration test is (where n is the number of channels for collecting signals, and N is the number of samples for each channel.) Perform fast Fourier transform, the expression is:

[0015]

[0016] Assumptions is the set of modal parameters, where f is the modal frequency, is the damping ratio, S ij is the cross power spectrum density of modal excitation, σ 2 is the power spectral density of the prediction error, Φ is the formation; the posterior distribution of α can be expressed as

[0017]

[0018] The posterior distribution of αp(α|{Z k}) can be rewritten as:

[0019]

[0020] In the formula is the posterior covariance matrix.

[0021] Further in step E: the intelligent swarm optimization algorithm adopted is Jaya algorithm, which achieves the goal of global optimization by continuously approaching the current optimal solution and avoiding the current worst solution. The basic procedure includes three parts: population initialization, local search strategy and greedy selection mechanism.

[0022] The second technical solution of the present invention is:

[0023] A structural damage identification method based on the benchmark Bayesian principle and sparse regularization includes: conducting environmental vibration tests on the structure and collecting acceleration signal data; performing fast Bayesian FFT modal identification on the collected signal to obtain the measured modal information of the structure; establishing a finite element model and a parameterized stiffness matrix of the component; constructing a damage identification objective function based on the benchmark Bayesian principle and sparse regularization; setting the regularization parameter selection range and iteration step size, and using a swarm intelligence optimization algorithm to solve the objective function for any of the regularization parameters; selecting the regularization parameter based on the DP criterion and solving for the optimal structural parameters. The specific steps are:

[0024] A. Arrange acceleration sensors on the structure to be identified, conduct vibration tests under environmental excitation conditions, and obtain the vibration signal of the structure.

[0025] B. Based on the collected structural acceleration signal Perform fast Bayesian FFT modal identification to obtain measured modal information of the structure Including measured natural frequencies and formation and the corresponding posterior covariance matrix Where i represents the order of the mode;

[0026] C. Establish a finite element model of the structure and obtain the computational modal information of the structure based on the finite element model Including calculation of natural frequencies and formation Where i represents the order of the mode; D. Based on the benchmark Bayesian principle and sparse regularization technology, combined with the structural modal information, a fitting function between the measured modal parameters and the theoretical modal parameters calculated according to the finite element model is established, that is, a damage identification objective function is constructed; the identification is divided into two stages. In the first stage, the modal characteristics, namely the natural frequency, damping ratio, vibration mode, etc., are first identified, and then their identification results are used to identify the structural parameters of the second stage.

[0027] The objective function is:

[0028]

[0029] E. Determine the range of regularization parameter selection, set a reasonable step size, and use the intelligent swarm optimization algorithm to solve the objective function for each regularization parameter within the value range; realize the location and quantification of structural damage.

[0030] Further, in step E: a suitable regularization parameter λ is selected based on the DP criterion to obtain the optimal structural damage parameter and realize the location and quantification of structural damage.

[0031] Determine the regularization parameter selection range [a, a+nΔ] based on experience, set a reasonable step size Δ, and for each regularization parameter λ within the value range i =a+iΔ (where i=0, 1, ..., n) uses an intelligent swarm optimization algorithm to solve the objective function.

[0032] The intelligent swarm optimization algorithm adopted is Jaya algorithm, which includes three parts: population initialization, local search strategy and greedy selection mechanism. At the beginning of the algorithm, an initial population will be randomly generated in the solution space. After the initial population is generated, each individual will be updated through the local search strategy, constantly approaching the current optimal solution and away from the current worst solution. After all individuals in the population are updated to generate offspring, the greedy selection strategy is used to determine the individual entering the next iteration.

[0033] The beneficial effects of the present invention are:

[0034] The present invention establishes a fitting function (i.e., damage identification objective function) between measured modal parameters and theoretical modal parameters calculated according to the finite element model based on the benchmark Bayesian principle and sparse regularization technology, and uses an intelligent optimization algorithm to solve the optimal structural parameters (structural stiffness), thereby realizing the location and quantification of structural damage. This method combines the theoretical derivation of the Bayesian probability method with the simple and fast calculation of the deterministic optimization method, and alleviates the ill-posedness of the solution of the damage identification problem from the two aspects of benchmark Bayesian and sparse regularization, reduces the probability of erroneous damage, and improves the accuracy and robustness of the damage identification results. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a logic flow chart of the present invention.

[0036] Figure 2 It is a schematic diagram of the two-stage Bayesian recognition problem.

[0037] Figure 3 It is a schematic diagram of the IASC-ASCE Benchmark steel frame structure.

[0038] Figure 4 It is the degree of freedom analysis model of Benchmark steel frame structure.

[0039] Figure 5 It is the Benchmark structure floor distribution and sensor and excitation locations.

[0040] Figure 6-Figure 9 This is a comparison chart of the structural damage identification results and reference values ​​of the IASC-ASCE Benchmark under different damage modes. DETAILED DESCRIPTION

[0041] Embodiment 1:

[0042] (1) Arrange acceleration sensors reasonably on the actual structure, conduct vibration tests under environmental excitation conditions, and obtain the vibration signal of the structure.

[0043] (2) Perform fast Bayesian FFT modal identification based on the acquired structural acceleration signal to obtain the measured modal information of the structure (including measured natural frequency and formation ) and the corresponding posterior covariance matrix Where i = 1, ... n represents the order of the mode, and n is the number of degrees of freedom tested;

[0044] (3) Establish a finite element model of the structure and obtain the computational modal information of the structure based on the finite element model (including calculation of natural frequency and formation ), where i represents the order of the mode;

[0045] (4) Based on the benchmark Bayesian principle and sparse regularization technology, combined with the structural modal information, a fitting function between the measured modal parameters and the theoretical modal parameters calculated according to the finite element model is established, that is, the damage identification objective function is constructed;

[0046] The objective function is:

[0047]

[0048] in It is similar to the fitting function between the measured modal parameters and the theoretical modal parameters calculated according to the finite element model, which is used to measure the difference between the finite element model and the actual structure; λ||θ|| 1 For the introduced 1 The norm regularization term can improve the sparsity of parameters and alleviate the ill-posedness of the inverse problem solution.

[0049] (5) Determine the range of regularization parameter selection, set a reasonable step size, and use an intelligent swarm optimization algorithm to solve the objective function for each regularization parameter within the value range.

[0050] (6) Based on the DP criterion, a suitable regularization parameter λ is selected to obtain the optimal structural damage parameter and realize the location and quantification of structural damage.

[0051] Embodiment 2:

[0052] (1) Arrange acceleration sensors reasonably on the actual structure, conduct vibration tests under environmental excitation conditions, and obtain the vibration signal of the structure.

[0053] (2) Perform fast Bayesian FFT modal identification based on the acquired structural acceleration signal to obtain the measured modal information of the structure (including measured natural frequency and formation ) and the corresponding posterior covariance matrix Where i = 1, ... n represents the order of the mode, and n is the number of degrees of freedom tested;

[0054] (3) Establish a finite element model of the structure and obtain the computational modal information of the structure based on the finite element model (including calculation of natural frequency and formation ), where i represents the order of the mode;

[0055] (4) Based on the benchmark Bayesian principle and combined with the structural modal information, a fitting function is established between the measured modal parameters and the theoretical modal parameters calculated according to the finite element model, that is, a damage identification objective function is constructed;

[0056] The objective function is:

[0057]

[0058] in It is similar to the fitting function between the measured modal parameters and the theoretical modal parameters calculated according to the finite element model, which is used to measure the difference between the finite element model and the actual structure.

[0059] (5) An intelligent swarm optimization algorithm is used to solve the objective function and locate and quantify structural damage.

[0060] Embodiment 3:

[0061] (1) Arrange acceleration sensors reasonably on the actual structure, conduct vibration tests under environmental excitation conditions, and obtain the vibration signal of the structure.

[0062] (2) Based on the collected structural acceleration signal Perform fast Bayesian FFT modal identification to obtain measured modal information of the structure (including measured natural frequency and formation ) and the corresponding posterior covariance matrix Where i represents the order of the mode;

[0063] The fast Bayesian FFT mode recognition process is as follows:

[0064] (2.1) Assume that the acceleration signal collected by the structural vibration test is (where n is the number of channels for collecting signals, and N is the number of samples for each channel.) Perform fast Fourier transform (FFT), the expression is:

[0065]

[0066] Where i is an imaginary number, i 2 =1; Δt is the sampling time interval; k=1,...,N; F k yes The real part, G k for The imaginary part of .

[0067] (2.2) Assumptions is the set of modal parameters, where f is the modal frequency, is the damping ratio, Sij is the cross power spectrum density of modal excitation, σ 2 is the power spectral density of the prediction error, and Φ is the formation. According to Bayesian theory, assuming that the prior distribution of the modal parameter α is a normal distribution, the posterior distribution of α can be expressed as

[0068]

[0069] Where: N q =int[N / 2]+1 is the Nyquist frequency; C k is the matrix Z k The covariance matrix of α. When the posterior distribution p(α|{Z k}) Take the corresponding maximum That is, it is the modal parameter with the highest probability of occurring under the measured signal conditions, and it is naturally taken as the final modal parameter result.

[0070] For the convenience of expression, the above formula is written in the form of log-likelihood function L(α), that is:

[0071] p(α|{Z k})∝exp[-L(α)] (2-4)

[0072] Then we have:

[0073]

[0074] When the structural acceleration signal is fully collected, the posterior probability density function is in the form of a Gaussian probability density, so L(α) can be approximately expressed by its second-order Taylor expansion, that is:

[0075]

[0076] In the formula, when is the best estimate of α, For L(α) The Hessian matrix at .

[0077] Substituting equation (2-6) into equation (2-4), the posterior distribution of α p(α|{Z k}) can be rewritten as:

[0078]

[0079] In the formula is the posterior covariance matrix.

[0080] Assuming that the environmental load on the structure is similar to white noise excitation, the cross power spectrum density S between each modal excitation is ijAssuming it is a constant, after mathematical derivation and calculation, formula (2-7) can be rewritten as

[0081] L(α)=-nN f ln2+(n-1)N f lnσ 2 +∑ k ln(SD k +σ 2 )+σ -2 (d-Φ T AΦ) (2-8)

[0082] Where:

[0083] A=∑ k [1+(σ 2 / SD k )] -1 D k (2-9)

[0084]

[0085]

[0086] From formula (2-4), we can see that when the posterior p(α|{Z k}) takes the maximum value, L(α) should take the minimum value. From the expression (2-8), we can see that when L(α) is the minimum, Φ T AΦ should take the maximum value, then Φ should be taken as the eigenvector corresponding to the largest eigenvalue of matrix A (the array is unit normalized). The remaining 4 parameters in the modal parameter α It can be obtained by unconstrained numerical optimization of equation (2-8). The posterior covariance matrix It can be obtained by inverting the Hessian matrix of formula (2-8).

[0087] (3) Establish a finite element model of the structure and obtain the computational modal information of the structure based on the finite element model (including calculation of natural frequency and formation ), where i represents the order of the mode;

[0088] The overall structural stiffness matrix K can be parameterized by the substructure stiffness as follows:

[0089]

[0090] Where K 0 is the stiffness matrix calculated based on the model assumptions and does not change with the substructure. i is the stiffness matrix of the ith substructure, θ iis the stiffness variation parameter introduced, and its value range is set to [0, 1], which is used for damage location and quantification. i When the value is 0, it means that the stiffness of the i-th substructure is completely lost. i When the value is 1, it means that the stiffness of the i-th substructure has not changed. It is generally believed that the quality of the structure does not change significantly over time or that when the quality of the structure changes significantly, it is easily detected by the naked eye. Therefore, the quality of the structure is usually considered to be known and unchanged, and the identification of structural damage is basically equivalent to the identification of changes in structural stiffness.

[0091] Using the linear dynamic model under classical modal theory, the natural frequency and formation of the structure can be obtained by the eigenvalue equation:

[0092]

[0093] Where K and M represent the structural stiffness and mass matrix respectively; and They represent the calculation frequency and formation of the i-th order respectively.

[0094] (4) Based on the benchmark Bayesian principle and sparse regularization technology, combined with the structural modal information, a fitting function between the measured modal parameters and the theoretical modal parameters calculated according to the finite element model is established, that is, the damage identification objective function is constructed;

[0095] Assuming that θ is the structural system parameter to be identified, and D is used to simplify the measured structural vibration response, the posterior probability density function of the structural parameter can be obtained according to the Bayesian theory:

[0096] p(θ|D)=c·p(D|θ)·p(θ) (2-14)

[0097] Where: c = 1 / p (D) - normalization constant;

[0098] p(θ) — prior distribution of θ;

[0099] p(D|θ)——Likelihood function.

[0100] Since the relationship between the structural system parameter θ and the structural vibration response is very complex, it is difficult to express the likelihood function p(D|θ) in an explicit form that is conducive to analysis. Therefore, it is difficult for us to directly obtain the posterior distribution of θ. In view of the difficulty of identifying θ directly from the data D, a "two-stage" method is proposed to transform the original problem into two more intuitive sub-problems, such as Figure 2 In the first stage, the modal characteristics are first identified, namely the natural frequency, damping ratio, vibration mode, etc. Then their identification results are used to identify the structural parameters in the second stage.

[0101] Assumptions is the structural modal parameter, including the natural frequency and vibration mode, that is, According to the two-stage benchmark Bayesian theory, the posterior distribution p(θ|D) can be re-expressed as follows:

[0102]

[0103] Where: —— The quasi-posterior distribution of The prior probability of can be taken as uniform distribution;

[0104] ——Conditional probability.

[0105] Will Modeled as the most likely value is the multivariate Gaussian distribution of the mean, see formula 2-16:

[0106]

[0107] Where: —— The most likely value of

[0108] n—— Dimensions;

[0109] —— The posterior covariance matrix of ;

[0110] —— The determinant of .

[0111] Assuming the modal parameters can be completely determined by the structural system parameter θ, then Modeled as a Dirac function, see formula 2-17:

[0112]

[0113] Where: ——Theoretical modal parameters calculated from the structural system parameters θ according to the characteristic equation.

[0114] Take the prior distribution of θ as uniform distribution, and substitute equation 2-16 and equation 2-17 into equation 2-15, and we can get

[0115]

[0116] In this way, we get the posterior distribution of θ. For the convenience of calculation, we rewrite Equation 2-18 mathematically, as shown in Equation 2-19:

[0117]

[0118] Where: ——The covariance matrix corresponding to the i-th order mode The reciprocal of the j-th non-zero eigenvalue of ;

[0119] ——The covariance matrix corresponding to the i-th order mode Corresponds to The eigenvector of

[0120] ——The i-th order theoretical modal parameter calculated from the structural system parameter θ according to the characteristic equation, where

[0121] ——The most likely value obtained from the vibration response, that is, the measured modal parameter of the i-th order, where

[0122] The posterior distribution p(θ|D), that is, θ when the value of Formula 2-6 is the largest, is considered to be the most likely structural parameter.

[0123] Maximizing Equation 2-6, using a deterministic approach and adding a sparse regularization term on its basis, we can get the final objective function as follows:

[0124]

[0125] in is the fitting function between the measured modal parameters and the theoretical modal parameters calculated according to the finite element model, which is used to measure the difference between the finite element model and the actual structure; λ||θ|| 1 for l 1 The norm regularization term can alleviate the ill-posedness of the inverse problem solution.

[0126] (5) Determine the range of regularization parameter selection [a, a+nΔ] based on experience, set a reasonable step size Δ, and for each regularization parameter λ within the range i =a+iΔ (where i=0, 1, ..., n) uses an intelligent swarm optimization algorithm to solve the objective function. The present invention adopts the Jaya algorithm. The Jaya algorithm is a new type of intelligent swarm optimization algorithm proposed by Indian scholar Rao in 2016. It does not require setting any algorithm-specific parameters during execution, and does not require initial guesses of optimization parameters, does not require gradient information and sensitivity analysis, and has irreplaceable advantages over traditional intelligent optimization algorithms. The core strategy of the Jaya algorithm is to achieve the goal of global optimization by continuously approaching the current optimal solution and avoiding the current worst solution. The basic procedure includes three parts: population initialization, local search strategy, and greedy selection mechanism.

[0127] (5.1) Population initialization

[0128] At the beginning of the algorithm, an initial population is randomly generated in the solution space. , the population contains CS individuals, each individual is denoted by x i . Each individual contains n variables, namely x i =[x 1 , x 2 , ..., x n ]. The initial value generation formula is shown in formula 2-20:

[0129]

[0130] Where: ——Individual x i The initial value of the jth variable;

[0131] --variable x i，j The upper limit value of

[0132] --variable x i，j The lower limit of

[0133] r——A random number in the closed interval [0, 1].

[0134] (5.2) Local search strategy

[0135] After the initial population is generated, each individual will be updated through a local search strategy. The basic idea is to continuously approach the current optimal solution and move away from the current worst solution. The offspring generation formula is shown in Formula 2-21, where the second and third terms respectively show the trend of the offspring approaching the current optimal solution and moving away from the contemporary worst solution.

[0136] θ′ g，i，j =θ g，i，j +r 1 (θ g，best，j -|θ g，i，j |)-r 2 (θ g，worst，j -|θ g，i，j |) (2-21)

[0137] Where: θ g，i，j ——the jth variable of the ith individual in the gth iteration;

[0138] θ′ g，i，j ——θ in the gth iteration g，i，j Update the generated children;

[0139] θ g，best，j ——the jth variable of the best individual in the gth iteration;

[0140] θ g，worst，j ——the jth variable of the worst individual in the gth iteration;

[0141] r 1 and r 2 ——A random number in the closed interval [0, 1].

[0142] After the offspring is generated, the boundary condition needs to be judged. If the value of the variable in the offspring after the update exceeds the upper limit or is lower than the lower limit, the variable should take its upper or lower limit value. The boundary judgment condition is shown in formula 2-22:

[0143]

[0144] (5.3) Greedy selection

[0145] After all individuals in the population are updated to generate offspring, a greedy selection strategy is used to determine the individuals that enter the next iteration. Specifically, first calculate θ g，i，j and θ′ g，i，j Their respective fitness, that is, the objective function value f(θ g，i ) and f(θ′ g，i ), individuals with smaller fitness are selected to enter the next iteration. The greedy selection mechanism is shown in formula 2-23:

[0146]

[0147] After the initial population is generated, the Jaya algorithm will continuously cycle the second and third steps until the convergence conditions are met, such as reaching the maximum number of iterations or the accuracy of the objective function value reaches a certain level.

[0148] It is worth mentioning that this algorithm can be replaced by any intelligent group optimization algorithm such as artificial bee colony algorithm, particle swarm algorithm, etc. The optimization results will vary depending on the performance of the optimization algorithm.

[0149] (6) Based on the DP criterion, a suitable regularization parameter λ is selected to obtain the optimal structural damage parameter and realize the location and quantification of structural damage.

[0150] Embodiment 4:

[0151] Application example: Damage identification of Benchmark steel frame structure

[0152] In 1999, the IASC-ASCE Structural Health Monitoring Group was established and proposed to establish a Benchmark structure to provide a unified analysis and comparison platform for different structural health methods. In 2000, the IASC-ASCE SHM Group proposed an analysis model of the Benchmark structure and tested the experimental model built in the Earthquake Engineering Research Laboratory of the University of British Columbia, Canada. Figure 3 As shown, the IASC-ASCE Benchmark structure is a 4-story, 2-span x 2-span steel frame scale model with a length and width of 2.5 meters and a height of 3.6 meters. The steel frame components are all made of hot-rolled 300W grade steel. The beams and columns are fixed, and the supports and structures are hinged to facilitate disassembly. Each bay on each floor has a floor slab: the first floor has four 800 kg floor slabs, the second and third floors each have four 600 kg floor slabs, and the fourth floor has four 400 kg floor slabs (or three 400 kg floor slabs plus one 550 kg floor slab to create an asymmetric mass distribution). This example uses the 12-degree-of-freedom shear building model of Case 4 of the first phase of the Benchmark structure ( Figure 4 ) was used for numerical simulation. Case 4 adds 150kg of mass to a slab on the top floor to introduce asymmetric mass distribution. The five working conditions considered are shown in Table 5-1.

[0153] Table 5-1 IASC-ASCE Benchmark structural damage mode

[0154]

[0155] The steps of structural damage identification using this method are as follows:

[0156] (1): Rationally arrange acceleration sensors on the actual structure, conduct vibration tests, and obtain the vibration signal of the structure.

[0157] Apply oblique unknown excitation to the top floor of the structure. See the floor distribution and excitation position for details. Figure 5 Four acceleration sensors are installed on each floor, and a total of 16 channels of acceleration data are recorded. The location of the sensors on each floor is shown in Figure 5 In each damage mode, the datagen package released by the IASC-ASCE SHM group was used to generate a 100-second acceleration data with a sampling frequency of 1000 Hz for subsequent structural damage identification. In order to make the simulated data closer to the real data, Gaussian white noise with a root mean square size of 10% was added to the acceleration signal.

[0158] (2) Rapid Bayesian modal identification is performed based on the acquired structural acceleration signal, and the first three modal information in the x and y directions (including the measured natural frequency And the measured formation and the corresponding posterior covariance matrix ) are identified and used for subsequent damage identification, see Tables 5-2 and 5-3.

[0159] Table 5-2 Modal frequencies identified under different damage modes in Case 4

[0160]

[0161] Note: The unit of frequency is Hz and the unit of relative error is %.

[0162] Table 5-3 MAC values ​​in different damage modes in Case 4

[0163]

[0164]

[0165] (3) Establish a finite element model of the structure and obtain the computational modal information of the structure based on the finite element model.

[0166] In order to locate the damage in all directions of the floor, each lateral direction of each floor is defined as a sub-element, and the overall stiffness matrix is ​​parameterized as follows:

[0167] K(θ)=K 0 +∑ s ∑ d (1-θ sd )K sd

[0168] Where s = 1, ..., 4 represents the number of floors; d = x, y represents the direction; K sd Represents the sub-element stiffness matrix in the undamaged state of the structure; K 0 Represents the rotational stiffness matrix calculated based on the model assumptions; θ sd That is, the stiffness reduction parameter to be identified. There are 8 stiffness reduction parameters involved in the identification, corresponding to {k 1x , k 1y , k 2x , k 2y , k 3x , k 3y , k 4x , k 4y}.

[0169] Using the linear dynamic model under classical modal theory, the natural frequency and formation of the structure can be obtained by the eigenvalue equation:

[0170]

[0171] Where K and M represent the structural stiffness and mass matrix respectively; and They represent the calculation frequency and formation of the i-th order respectively.

[0172] (4) Based on the benchmark Bayesian principle and sparse regularization technology, combined with the structural modal information, a fitting function between the measured modal parameters and the theoretical modal parameters calculated according to the finite element model is established, that is, the damage identification objective function is constructed;

[0173]

[0174] Where: ——The covariance matrix corresponding to the i-th order mode The reciprocal of the j-th non-zero eigenvalue of ;

[0175] ——The covariance matrix corresponding to the i-th order mode Corresponds to The eigenvector of

[0176] ——The i-th order theoretical modal parameter calculated from the structural system parameter θ according to the characteristic equation, where

[0177]

[0178] ——The most likely value obtained from the vibration response, that is, the measured modal parameter of the i-th order.

[0179] λ——Regularization parameter.

[0180] (5) Determine the regularization parameter selection range [0, 1e-5] based on experience, set the step size to 1e-7, and for each regularization parameter λ within the range i =i×1e-7 (where i=0, 1, ..., n) Jaya algorithm is used to solve the objective function. The parameters of Jaya algorithm are set as follows: the number of individuals in the initial population is 100, and the maximum number of iterations is 500. To prevent accidental errors in the algorithm, each case is run independently 30 times and the average value is taken as the final statistical result.

[0181] (6) Based on the DP criterion, the appropriate regularization parameter λ is selected, and the Jaya algorithm is used to optimize and solve the optimal structural damage parameter to achieve the location and quantification of structural damage. The regularization parameters selected for different damage conditions are shown in Table 5-4, and the optimal damage identification results are shown in Figure 6-Figure 9 .

[0182] According to the damage identification results, the objective function established based on the benchmark Bayesian principle and sparse regularization has achieved good results. The structural damage is accurately located and quantified, and there are almost no erroneous results, which proves the powerful ability of the benchmark Bayesian principle and sparse regularization in dealing with the ill-posed inverse problem of damage identification.

[0183] Table 5-4 Regularization parameter values ​​under different damage modes

[0184]

[0185]

Claims

1. A structural damage identification method based on the benchmark Bayesian principle, Features include: Conduct environmental vibration tests on the structure and collect acceleration signal data; Perform fast Bayesian FFT modal identification on the collected signals to obtain the measured modal information of the structure; Establish a finite element model and parameterize the stiffness matrix; construct a damage identification objective function based on the benchmark Bayesian principle; use a swarm intelligence optimization algorithm to solve the objective function; The specific steps are: A. Arrange acceleration sensors on the structure to be identified, conduct vibration tests under environmental excitation conditions, and obtain the vibration signal of the structure. B. Based on the acquired structural acceleration signal Perform fast Bayesian FFT modal identification to obtain measured modal information of the structure Including measured natural frequencies and formation and the corresponding posterior covariance matrix , where i represents the order of the mode; assuming that the acceleration signal collected by the structural vibration test is , where n represents the number of channels for collecting signals, and N represents the number of samples for each channel. Perform fast Fourier transform, the expression is: Assumptions is the set of modal parameters, where is the modal frequency, is the damping ratio, is the cross power spectral density of the modal excitation, is the power spectral density of the prediction error, For the formation; The posterior distribution of ; The posterior distribution of Rewritten as: ； C. Establish a finite element model of the structure and obtain the computational modal information of the structure based on the finite element model Including calculation of natural frequencies and formation , where i represents the order of the mode; The posterior distribution of Where: ——The covariance matrix corresponding to the i-th order mode The reciprocal of the j-th non-zero eigenvalue of ; ——The covariance matrix corresponding to the i-th order mode Corresponds to The eigenvector of ——By structural system parameters The i-th order theoretical modal parameters calculated according to the characteristic equation are: ; ——The most likely value obtained from the vibration response, that is, the measured modal parameter of the i-th order, where ; Posterior distribution When the value is maximum are considered to be the most likely structural parameters; D. Based on the benchmark Bayesian principle and combined with the structural modal information, a fitting function between the measured modal parameters and the theoretical modal parameters calculated according to the finite element model is established to construct the damage identification objective function; the objective function is: E. Use intelligent swarm optimization algorithm to solve the objective function and locate and quantify structural damage.

2. According to the structural damage identification method based on the benchmark Bayesian principle of claim 1, Features Step E: The intelligent swarm optimization algorithm used is Jaya algorithm, which achieves the goal of global optimization by continuously approaching the current optimal solution and avoiding the current worst solution. The basic procedure includes three parts: population initialization, local search strategy and greedy selection mechanism.

3. A structural damage identification method based on the baseline Bayesian principle and sparse regularization, Features include: Conduct environmental vibration tests on the structure and collect acceleration signal data; Perform fast Bayesian FFT modal identification on the collected signals to obtain the measured modal information of the structure; Establish finite element model and parameterize stiffness matrix; The damage identification objective function is constructed based on the benchmark Bayesian principle and sparse regularization; the regularization parameter selection range and iteration step are set, and the swarm intelligence optimization algorithm is used to solve the objective function for any of the regularization parameters; Regularization parameters are selected based on the DP criterion to obtain the optimal structural parameters; When constructing the damage identification objective function based on the benchmark Bayesian principle, the identification is divided into two stages. In the first stage, the modal characteristics are first identified, and the modal characteristics include natural frequency, damping ratio, and vibration mode. Then, the structural parameters of the second stage are identified using their identification results. The specific steps are: A. Arrange acceleration sensors on the structure to be identified, conduct vibration tests under environmental excitation conditions, and obtain the vibration signal of the structure. B. Based on the acquired structural acceleration signal Perform fast Bayesian FFT modal identification to obtain measured modal information of the structure Including measured natural frequencies and formation , and the corresponding posterior covariance matrix , where i represents the order of the mode; assuming that the acceleration signal collected by the structural vibration test is , where n represents the number of channels for collecting signals, and N represents the number of samples for each channel. Perform fast Fourier transform, the expression is: Establish a finite element model of the structure and obtain the computational modal information of the structure based on the finite element model. Including calculation of natural frequencies and formation Where i represents the order of the mode; The posterior distribution of Where: ——The covariance matrix corresponding to the i-th order mode The reciprocal of the j-th non-zero eigenvalue of ; ——The covariance matrix corresponding to the i-th order mode Corresponds to The eigenvector of ——By structural system parameters The i-th order theoretical modal parameters calculated according to the characteristic equation are: ; ——The most likely value obtained from the vibration response, that is, the measured modal parameter of the i-th order, where ; D. Based on the benchmark Bayesian principle and sparse regularization technology, combined with structural modal information, a fitting function between the measured modal parameters and the theoretical modal parameters calculated according to the finite element model is established to construct a damage identification objective function; the objective function is: E. Determine the range of regularization parameter selection, set a reasonable step size, and use the intelligent swarm optimization algorithm to solve the objective function for each regularization parameter within the value range; realize the location and quantification of structural damage.

4. According to the structural damage identification method based on the benchmark Bayesian principle and sparse regularization according to claim 3, Features Step E: Based on the DP criterion, a suitable regularization parameter λ is selected to obtain the optimal structural damage parameter to locate and quantify the structural damage.

5. According to the structural damage identification method based on the benchmark Bayesian principle and sparse regularization according to claim 4, Features Step E: Determine the range of regularization parameters based on experience , set a reasonable step size , for each regularization parameter in the range (where i=0,1,…,n) an intelligent swarm optimization algorithm is used to solve the objective function.

6. According to the structural damage identification method based on the baseline Bayesian principle and sparse regularization according to claim 5, Features Step E: The intelligent swarm optimization algorithm used is the Jaya algorithm, which includes three parts: population initialization, local search strategy and greedy selection mechanism. At the beginning of the algorithm, an initial population will be randomly generated in the solution space. After the initial population is generated, each individual will be updated through the local search strategy, constantly approaching the current optimal solution and moving away from the current worst solution. After all individuals in the population are updated to generate offspring, the greedy selection strategy is used to determine the individual entering the next iteration.

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