Hysteresis parameter identification method of BWBN model based on improved particle swarm optimization

Abstract

The invention discloses a hysteretic parameter identification method of a BWBN model based on improved particle swarm optimization, and belongs to the field of hysteretic parameter identification, and the method comprises the steps: determining an equivalent yield point of an RC pier under quasi-static reciprocating loading according to a skeleton curve of an actually measured hysteretic curve; giving a boundary constraint of a hysteretic parameter to be identified; obtaining an optimal value of the hysteresis parameter to be identified by using an improved particle swarm algorithm; and in each step of iteration of the improved particle swarm algorithm, optimizing the global historical optimal position by using a Levy flight strategy and a pattern search algorithm, and taking the global historical optimal position output in the last step as the value of each hysteresis parameter to be identified, thereby completing the hysteresis parameter identification of the BWBN model. The method solves the problems that when an existing method is used for processing a complex high-dimensional space optimization problem, the existing method is prone to falling into a local optimal solution in the later period, premature convergence is achieved, the convergence speed and fitting precision depend on parameter selection, evolution lacks enough exploration capacity, and the diversity of particle populations is difficult to guarantee.

Description

Technical Field

[0001] The present invention belongs to the field of hysteretic parameter identification, and particularly relates to a method for identifying hysteretic parameters of a BWBN model based on improved particle swarm optimization. Background Art

[0002] Reinforced concrete (RC) bridge piers, as important load-bearing members supporting the superstructure of bridges, are prone to damage under seismic actions, thus endangering the service safety performance of the overall bridge structure, and have become the key research objects in the seismic analysis and design of bridge structures. RC bridge piers under seismic actions are usually affected by key parameters such as reinforcement ratio, stirrup ratio, axial compression ratio, shear span ratio, etc., and may undergo flexural failure (FF), flexural-shear failure (FS), and shear failure (SF). For RC bridge piers under different failure modes, their corresponding restoring force hysteretic characteristics and seismic performance often vary greatly.

[0003] Due to various reasons such as the non-linear material properties of reinforced concrete, concrete cracking, bond slip between steel bars and concrete, and cumulative fatigue damage, the restoring force-displacement curve of RC bridge piers exhibits obvious hysteretic characteristics such as strength degradation, stiffness degradation, and pinching effect. Therefore, for RC bridge piers under different failure modes, establishing a refined restoring force hysteretic model that can effectively consider hysteretic characteristics and be described by a simple mathematical equation is the basis for the seismic response analysis of RC bridge piers.

[0004] In view of this, a variety of hysteretic models (ideal elastoplastic model, bilinear model, Clough model, Takeda model, Bouc-Wen model, etc.) have been proposed to simulate the non-linear hysteretic characteristics of RC bridge piers. Among them, the Bouc-Wen-Baber-Noori (BWBN) model derived from the Bouc-Wen model has been widely used in the engineering field because it can comprehensively consider hysteretic characteristics such as strength degradation, stiffness degradation, and pinching effect, and can effectively fit experimental data by appropriately adjusting hysteretic parameters, thereby exploring the seismic performance of RC bridge piers. It is worth mentioning that the BWBN model is essentially an empirical mathematical model for determining key parameters based on experimental data, so the model parameters have clear physical meanings. Its hysteretic parameters reflect phenomena such as stiffness changes, energy dissipation characteristics, and possible strength degradation during the loading and unloading processes of the structure, but there is a lack of quantitative values for the hysteretic parameters under different failure modes. Therefore, accurately and efficiently identifying the hysteretic parameters of the BWBN model based on the pseudo-static cyclic loading test data of RC bridge piers under different failure modes is crucial for evaluating the seismic performance of the structure.

[0005] Due to the high nonlinearity and numerous parameters of the BWBN model, the process of identifying hysteretic parameters is relatively complex, which is a bottleneck problem in applying the BWBN model. However, by selecting appropriate calculation algorithms, hysteretic parameters can be efficiently and accurately identified from experimental data. Combining the measured hysteretic curve data of RC bridge piers, selecting appropriate intelligent optimization algorithms and constructing an objective function related to hysteretic parameters for parameter identification are the main ways to identify hysteretic parameters at present. The particle swarm optimization algorithm (PSO) has received extensive attention due to its simple algorithm structure and easy implementation, and has advantages such as good global search ability, fast convergence, few parameter adjustments, strong adaptability, and good parallel processing ability. Although the standard PSO algorithm shows excellent performance in solving most optimization problems, when dealing with complex high-dimensional space optimization problems, there are disadvantages such as being prone to falling into local optimal solutions in the later stage, premature convergence, the convergence speed and fitting accuracy depending on the selection of parameters (inertia weight, learning factor, etc.), and the lack of sufficient exploration ability in evolution to ensure the diversity of the particle population. Summary of the Invention

[0006] Aiming at the above deficiencies in the prior art, a method for identifying hysteretic parameters of a BWBN model based on improved particle swarm optimization provided by the present invention solves the problems that the existing methods are prone to falling into local optimal solutions in the later stage, premature convergence, the convergence speed and fitting accuracy depending on the selection of parameters, and the lack of sufficient exploration ability in evolution to ensure the diversity of the particle population when dealing with complex high-dimensional space optimization problems.

[0007] In order to achieve the above invention purpose, the technical solution adopted by the present invention is: a method for identifying hysteretic parameters of a BWBN model based on improved particle swarm optimization, including:

[0008] Obtain the measured hysteretic curves of the pseudo-static reciprocating loading of RC bridge piers under different failure modes, and determine the yield load and yield displacement of the ultimate equivalent yield point based on the skeleton curve of the measured hysteretic curves;

[0009] Construct a BWBN model with strength degradation, stiffness degradation and pinching effect, respectively perform normalized dimensionless processing on the BWBN model and the measured hysteretic curves according to the yield load and yield displacement of the ultimate equivalent yield point, and construct a first-order explicit differential equation system of the BWBN model according to the normalized dimensionless processing results of the BWBN model;

[0010] Determine the hysteretic parameters to be identified, and give the boundary constraint conditions of the hysteretic parameters to be identified;

[0011] The optimal values of the hysteretic parameters to be identified are obtained by using an improved particle swarm optimization algorithm. Specifically, in each iteration of the improved particle swarm optimization algorithm, the Levy flight strategy and the pattern search algorithm are used to deeply optimize the global historical optimal position, and the global historical optimal position output in the last step is used as the value of each hysteretic parameter to be identified, thus completing the identification of the hysteretic parameters of the BWBN model. The fitness function of the improved particle swarm optimization algorithm is the error function between the predicted value of the restoring force obtained by solving the first-order explicit differential equations of the BWBN model and the measured value of the restoring force in the normalized dimensionless processing result of the measured hysteresis curve.

[0012] The beneficial effects of the present invention are as follows: The introduction of the Logistic-Tent composite chaotic map has good randomness and ergodicity, excellent autocorrelation, and complex chaotic dynamic characteristics, and can generate an initial particle population with a uniform distribution, avoiding the phenomenon that some search regions are too dense or too sparse, thereby effectively improving the diversity of the particle population, the global search ability, and the convergence speed. The introduction of the nonlinear inertia weight w can balance the global "exploration" and local "exploitation" optimization abilities of the particle swarm. In the early stage of iteration, a larger inertia weight is given, which is beneficial to achieving a large-scale search and promoting the algorithm to converge rapidly to the vicinity of the potential optimal value. In the later stage of iteration, as the number of iterations increases, the inertia weight gradually decreases, enabling the particles to conduct a fine local search in the vicinity of the optimal value, thereby avoiding falling into a local optimal solution in the later stage of iteration and improving the solution accuracy and robustness of the algorithm. The introduction of the dynamic cognitive parameter c1 and the dynamic social parameter c2 realizes the effective regulation of the self-learning ability of the particle individuals and the ability to obtain social information. In the early stage of iteration, by setting a larger c1 and a smaller c2, the particles are prompted to tend to rely on their self-learning ability to explore unknown regions, achieving a wide search of each particle in the search space, thereby avoiding premature convergence and enhancing the adaptability of the algorithm. In the later stage of iteration, c1 is gradually decreased and c2 is increased, prompting the particles to tend to rely on the ability to obtain social information to adjust the search direction, achieving a fine search of each particle near the global optimal position, thereby accelerating the convergence speed and improving the search accuracy. The introduction of the Levy flight strategy has significant randomness and jumpiness and has a wide search ability. By providing new search paths and regions through the random walk mechanism, the position update of each particle is realized. This process increases the diversity of the particle population, enabling the particles to have the opportunity to jump out of the current local optimal solution, thereby increasing the possibility of finding a better solution. Embedding the PS algorithm into the improved PSO algorithm framework can not only maintain the original global search advantage of the improved PSO algorithm but also, relying on the local search ability of the PS algorithm, conduct a more refined search in the key region where the entire particle swarm approaches the global historical optimal position, making up for the limitations of the improved PSO algorithm in local search, and thus greatly improving the overall search efficiency and accuracy of the algorithm. Brief Description of the Drawings

[0013] Figure 1 This is the flowchart of the method of the present invention.

[0014] Figure 2 This is the bar chart of the Logistic-Tent chaotic map in the embodiment of the present invention.

[0015] Figure 3 This is the scatter plot distribution diagram of the Logistic-Tent chaotic map in the embodiment of the present invention.

[0016] Figure 4 This is the schematic diagram of the change trajectory of the fitness function value with the iterative process in the embodiment of the present invention.

[0017] Figure 5 This is the schematic diagram of the comparative analysis of the measured data and the hysteretic curve of the BWBN hysteretic model under the bending failure mode in the embodiment of the present invention.

[0018] Figure 6 This is the schematic diagram of the comparative analysis of the measured data and the hysteretic curve of the BWBN hysteretic model under the flexure-shear failure mode in the embodiment of the present invention.

[0019] Figure 7 This is the schematic diagram of the comparative analysis of the measured data and the hysteretic curve of the BWBN hysteretic model under the shear failure mode in the embodiment of the present invention.

[0020] Figure 8 This is the schematic diagram of the comparative analysis of the measured time history curve and the predicted time history curve of the restoring force under the bending failure mode in the embodiment of the present invention.

[0021] Figure 9 This is the schematic diagram of the comparative analysis of the measured time history curve and the predicted time history curve of the restoring force under the flexure-shear failure mode in the embodiment of the present invention.

[0022] Figure 10 This is the schematic diagram of the comparative analysis of the measured time history curve and the predicted time history curve of the restoring force under the shear failure mode in the embodiment of the present invention.

[0023] Figure 11 This is the schematic diagram of the comparative analysis of the measured data and the backbone curve of the BWBN hysteretic model under the bending failure mode in the embodiment of the present invention.

[0024] Figure 12 This is the schematic diagram of the comparative analysis of the measured data and the backbone curve of the BWBN hysteretic model under the flexure-shear failure mode in the embodiment of the present invention.

[0025] Figure 13 This is the schematic diagram of the comparative analysis of the measured data and the backbone curve of the BWBN hysteretic model under the shear failure mode in the embodiment of the present invention.

[0026] Figure 14 Schematic diagram for comparative analysis of measured data and cumulative hysteretic energy dissipation of BWBN hysteretic model under flexural failure mode in the embodiments of the present invention.

[0027] Figure 15 Schematic diagram for comparative analysis of measured data and cumulative hysteretic energy dissipation of BWBN hysteretic model under flexure-shear failure mode in the embodiments of the present invention.

[0028] Figure 16 Schematic diagram for comparative analysis of measured data and cumulative hysteretic energy dissipation of BWBN hysteretic model under shear failure mode in the embodiments of the present invention.

[0029] Figure 17 Schematic diagram for distribution of correlation coefficients of RC bridge piers under different failure modes in the embodiments of the present invention. Detailed implementation manners

[0030] The following describes the detailed implementation manners of the present invention to facilitate those skilled in the art to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the detailed implementation manners. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions created using the concept of the present invention are within the scope of protection.

[0031] Embodiment 1

[0032] As Figure 1 shown, in an embodiment of the present invention, a method for identifying hysteretic parameters of a BWBN model based on improved particle swarm optimization includes:

[0033] Obtain the measured hysteretic curves of RC bridge piers under pseudo-static cyclic loading in different failure modes, and determine the yield load and yield displacement of the ultimate equivalent yield point based on the skeleton curve of the measured hysteretic curves;

[0034] Construct a BWBN model with strength degradation, stiffness degradation, and pinching effect. According to the yield load and yield displacement of the ultimate equivalent yield point, perform normalized dimensionless processing on the BWBN model and the measured hysteretic curves respectively, and construct a first-order explicit differential equation system of the BWBN model according to the normalized dimensionless processing results of the BWBN model;

[0035] Determine the hysteretic parameters to be identified, and give the boundary constraint conditions of the hysteretic parameters to be identified;

[0036] The optimal values of the hysteretic parameters to be identified are obtained by using an improved particle swarm optimization algorithm. Specifically, in each iteration of the improved particle swarm optimization algorithm, the Levy flight strategy and the pattern search algorithm are used to deeply optimize the globally historically optimal position. The globally historically optimal position output in the last step is used as the value of each hysteretic parameter to be identified, completing the identification of the hysteretic parameters of the BWBN model. The fitness function of the improved particle swarm optimization algorithm is an error function between the predicted value of the restoring force obtained by solving the first-order explicit differential equation system of the BWBN model and the measured value of the restoring force in the normalized dimensionless processing result of the measured hysteretic curve.

[0037] In this embodiment, when the improved PSO algorithm falls into search stagnation (the globally historically optimal value remains unchanged for several times), the globally historically optimal position in the search space of the hysteretic parameters of the BWBN model is used as the initial value of the PS algorithm for local search, thereby overcoming the problem that the PS algorithm is sensitive to the initial value. This hybrid algorithm combines the characteristics and advantages of the PSO algorithm and the PS algorithm, and shows more excellent performance when dealing with the complex high-dimensional problem of identifying the hysteretic parameters of the BWBN model.

[0038] Specifically, it includes the following steps:

[0039] In the Structural Performance Database (SPD) website of the Pacific Earthquake Engineering Research Center (PEER), the measured data of the pseudo-static cyclic loading of RC bridge piers under different failure modes (flexure failure, flexure-shear failure, shear failure) are obtained.

[0040] It should be noted that for each RC bridge pier under different failure modes, 6 groups of test data samples are randomly selected. The obtained test data samples cover the measured restoring force, displacement, and the corresponding hysteretic curve during the loading process.

[0041] The yield load and yield displacement of the final equivalent yield point are specifically:

[0042] Based on the skeleton curve of the measured hysteretic curve, the equivalent yield point is determined by different equivalent yield point extraction methods, and the average values of the yield load and yield displacement of the equivalent yield point determined by each method are used as the yield load and yield displacement of the final equivalent yield point. This can weaken the limitations caused by theoretical assumptions or empirical deviations of a single method, thereby improving the reliability of the equivalent yield point parameters.

[0043] In this embodiment, the corresponding skeleton curve is extracted according to the measured pseudo-static cyclic loading hysteretic curve, and the equivalent yield point (peak point) of the RC bridge pier under the pseudo-static cyclic loading is determined based on the skeleton curve.

[0044] It should be noted that the equivalent yield point of the RC pier is determined by the classical geometric construction method, the equivalent energy method, and the R. Park method, and the average value of the three methods is used as the yield load and yield displacement of the equivalent yield point.

[0045] Construct the BWBN model with strength degradation, stiffness degradation, and pinching effect. According to the yield load and yield displacement of the final equivalent yield point, normalize and dimensionless process the BWBN model and the measured hysteresis curve respectively, and construct the first-order explicit differential equations of the BWBN model according to the normalized and dimensionless processing results of the BWBN model, specifically:

[0046] Construct the BWBN model with strength degradation, stiffness degradation, and pinching effect:

[0047] F m = F e + F h

[0048] F e = αku

[0049] F h = (1 - α)kz

[0050]

[0051] v = 1 + δ v ε

[0052] η = 1 + δ η ε

[0053]

[0054] ζ1 = ζ 10 [1 - exp(-pε)]

[0055] ζ2 = (ψ0 + δ ψ ε)(λ + ζ1)

[0056]

[0057] Among them, F m is the inelastic restoring force of the BWBN model; F e is the elastic force; F h is the hysteretic force; α is the stiffness ratio before and after yielding; k is the initial stiffness of the structure; u is the relative lateral displacement; z is the hysteretic displacement; is the first-order differential of z; h(z) is the function used to control the pinching effect of the hysteresis curve; η is the stiffness degradation parameter; v is the strength degradation parameter; n is the parameter used to control the smoothness of the hysteresis curve; γ is the parameter used to control the shape of the hysteresis curve; β is the parameter used to control the peak value of the hysteresis curve; is the sign function related to the product of the hysteretic displacement z and the velocity ; is the first-order differential of u, representing the velocity; δ v is the strength degradation rate; ε is the cumulative hysteretic energy dissipation at time t; t is the time; δ η is the stiffness degradation rate; ζ1 is the parameter controlling the pinching degree; is the sign function related to the velocity ; q is the parameter controlling the starting position of the pinching effect; z u is the maximum value of the hysteretic displacement; ζ2 is the parameter controlling the pinching diffusion region; ζ 10 is the parameter controlling the total slip amount; p is the parameter controlling the pinching slope; ψ0 is the parameter controlling the pinching amplitude; δ ψ is the parameter controlling the pinching rate; λ is the parameter controlling the magnitude relationship between the total pinching amount and the pinching rate;

[0058] According to the yield load and yield displacement of the final equivalent yield point, the measured hysteretic curve is normalized and dimensionless processed to obtain the normalized and dimensionless processing result of the measured hysteretic curve;

[0059] According to the yield load and yield displacement of the final equivalent yield point, the BWBN model is normalized and dimensionless processed to obtain the normalized and dimensionless processing result of the BWBN model:

[0060]

[0061] μ = u / u y

[0062] μ z = z / u y

[0063] F y = ku y

[0064]

[0065] where F n is the normalized restoring force; F y is the yield load of the final equivalent yield point; u y is the yield displacement of the final equivalent yield point; μ is the normalized relative lateral displacement; μ z is the normalized hysteretic displacement; is the first-order differential of μ; is the first-order differential of the normalized hysteretic displacement; h(μ z ) is the normalized pinching effect function; ε n is the normalized cumulative hysteretic energy dissipation; is related to μ z and Product-related sign function; Is related to Related sign function; ε y Is the cumulative hysteretic energy dissipation at the ultimate equivalent yield point;

[0066] Based on the normalized dimensionless processing results of the BWBN model, construct the first-order explicit differential equations of the BWBN model:

[0067]

[0068] Among them, Y is the introduced state vector; Y1 is the normalized relative lateral displacement μ; Y2 is the normalized hysteretic displacement μ z ; Y3 is the normalized cumulative hysteretic energy dissipation ε n ; Is the first-order differential of Y; Is the first-order differential of Y1; Is the first-order differential of Y2; Is the first-order differential of Y3.

[0069] In this embodiment, based on the MATLAB platform, construct a BWBN model with strength degradation, stiffness degradation and pinching effect, and input the lateral displacement through a linear amplitude-varying displacement function. To ensure the universality of the hysteretic parameter identification results and avoid the time-variation of the initial stiffness, perform normalized dimensionless processing on the BWBN model and the measured hysteretic curve, and the ductility demand index can be directly obtained after the normalization process.

[0070] Introduce the BWBN hysteretic model, comprehensively consider the hysteretic characteristics such as strength degradation, stiffness degradation and pinching effect by adjusting the hysteretic parameters with clear physical meanings, and then be able to accurately simulate the nonlinear relationship between the restoring force and displacement of RC bridge piers with high precision. At the same time, it takes into account the engineering practicability and the accuracy of dynamic response analysis with a low computational complexity, which is significantly better than the simplified description of complex hysteretic behaviors by traditional hysteretic models. On this basis, perform normalized dimensionless processing on the BWBN hysteretic model and the measured hysteretic curve in the measured data, effectively avoid the time-variation of the initial stiffness and can directly obtain the ductility demand index.

[0071] The method for obtaining the optimal values of the hysteretic parameters to be identified by using the improved particle swarm algorithm is specifically as follows:

[0072] S1. According to the hysteretic parameters to be identified, form the hysteretic parameter vector θ to be identified:

[0073] θ = [α, β, γ, n, δ v , δ η , ζ 10 , q, p, ψ0, δ ψ , λ]

[0074] Among them, α is the stiffness ratio before and after yielding; n is the parameter controlling the smoothness of the hysteresis curve; γ is the parameter controlling the shape of the hysteresis curve; β is the parameter controlling the peak value of the hysteresis curve; δ v is the strength degradation rate; δ η is the stiffness degradation rate; ζ 10 is the parameter controlling the total slip; q is the parameter controlling the starting position of the pinching effect; p is the parameter controlling the pinching slope; ψ0 is the parameter controlling the pinching amplitude; δ ψ is the parameter controlling the pinching rate; λ is the parameter controlling the order relationship between the total pinching amount and the pinching rate;

[0075] S2, initialize the parameters of the particle swarm optimization algorithm; the parameters of the particle swarm optimization algorithm include the particle population size N, the dimension D of the hysteresis parameter to be identified, the maximum inertia weight w max , the minimum inertia weight w min , the cognitive parameter c1, the social parameter c2, the maximum number of iteration steps T, the maximum search position column vector x max , the minimum search position column vector x min , the maximum search velocity column vector v max and the minimum search velocity column vector v min ; the dimension D of the hysteresis parameter to be identified is equal to the number of hysteresis parameters to be identified;

[0076] S3, randomly initialize the particle position x N×D and the particle velocity v N×D :

[0077]

[0078] Among them, is the initial position of the particle swarm; is the initial velocity of the particle swarm; is the initial value of the position of the D-th dimension in particle i; is the initial value of the velocity of the D-th dimension in particle i; is the initial value of the position of the j-th dimension in particle i; is the initial value of the velocity of the j-th dimension in particle i; X ij is the chaotic sequence value of the j-th dimension of particle i in the interval [0,1]; is the upper limit of the search position of dimension j; is the lower limit of the search position of dimension j; is the upper limit of the search velocity of dimension j; is the lower limit of the search velocity of dimension j; X (i+1)jIt is the chaotic sequence value of the j-th dimension in the range of [0, 1] for particle i + 1; r is the control parameter;

[0079] S4. Calculate the fitness value of each particle, and initialize the individual historical optimal position p N×D and the individual historical optimal value pbest N×1 as well as the global historical optimal position g 1×D and the global historical optimal value gbest 1×1 ;

[0080] S5. Based on the adaptive strategy, dynamically update the inertia weight w, the cognitive parameter c1, and the social parameter c2, and update the particle velocity and particle position based on the updated inertia weight w, cognitive parameter c1, and social parameter c2 with boundary constraints;

[0081] S6. Update the individual historical optimal position p N×D and the individual historical optimal value pbest N×1 as well as the global historical optimal position g 1×D and the global historical optimal value gbest 1×1 ;

[0082] S7. Introduce the Levy flight strategy to update the position of each particle, and update the global historical optimal position g 1×D (t) update and the global historical optimal value gbest 1×1 (t) update ;

[0083] S8. Determine whether the prerequisite conditions of the embedded pattern search algorithm are met. If so, go to step S9; otherwise, return to step S5. The prerequisite conditions of the embedded pattern search algorithm are that the current iteration step t > T / 2, and the global historical optimal value gbest 1×1 (t) update has not changed for 5 consecutive iterations;

[0084] S9. Take the global historical optimal position g 1×D (t) update as the iterative initial value K 1×D (0), and update the global historical optimal position and global historical optimal value of the particle population through the pattern search algorithm;

[0085] S10. Determine whether the preset maximum number of iterations T is met. If so, output the final position g 1×D (T) final of the global historical optimum of the entire particle population at the T-th iteration and the final value gbest 1×1 (T)final , otherwise, return to S5 for continued iteration.

[0086] In this embodiment, corresponding boundary constraint conditions are given for the hysteretic parameters under different failure modes (flexural failure, flexure-shear failure, shear failure). To generate a uniformly distributed search space, the positions x of the particle swarm are randomly initialized using the Logistic-Tent composite chaotic map N×D and the velocities v N×D .

[0087] The fitness values of the particles in S4 are as follows:

[0088]

[0089] where is the fitness value of particle i; is the position of particle i; n t is the loading step index; N t is the total number of loading steps; F e (n t ) is the measured value of the restoring force at the nth t step; is the predicted value of the restoring force at the nth t step calculated by particle i.

[0090] The fitness function provides an initial cooperative search direction for the particle swarm and retains individual experience. At the same time, an error function is introduced as the fitness function fitness, and an efficient optimization algorithm is used to quickly converge to the optimal hysteretic parameter combination, ensuring that the error between the predicted value of the restoring force and the measured value of the restoring force is minimized and reducing the computational time consumption.

[0091] The fourth-order Runge-Kutta method is used to iteratively solve the first-order explicit differential equations of the BWBN model to obtain the predicted value of the restoring force; the calculation formula of the fourth-order Runge-Kutta method is:

[0092]

[0093] where f() is the first-order explicit differential equations of the BWBN model; is the time corresponding to the input normalized lateral displacement μ at the nth t loading step; is the state vector at time, including the normalized hysteretic displacement μ z and the normalized cumulative hysteretic energy dissipation ε n ; h is the time step; k1 is the slope at time with the state ; k2 is the slope at time with the state The slope at time; k3 is the time when The state is The slope at time; k4 is the time when The state is The slope at time.

[0094] In this embodiment, the "ODE15s" solver in the MATLAB platform is called, and the fourth-order Runge-Kutta method with higher calculation accuracy is used to iteratively solve the differential equation system. It is based on the Taylor formula and uses the slope to approximately express the differential. By predicting the derivative values (i.e., slopes) of multiple intermediate points within a time step, and then performing a weighted average on these slopes to approximate the true change of the function within this step, and using this as the basis for the next point.

[0095] The expressions for updating the particle velocity and particle position in S5 are:

[0096]

[0097] Among them, is the velocity of the j-th dimension in particle i at the t-th iteration; is the velocity iteration value of the j-th dimension in particle i at the t-th iteration; t is the current iteration step number, t = 1, 2,... T; is the velocity of the j-th dimension in particle i at the (t - 1)-th iteration; r1 and r2 are both uniformly distributed random numbers within [0, 1]; is the individual historical optimal position of the j-th dimension in particle i at the (t - 1)-th iteration; is the position of the j-th dimension in particle i at the (t - 1)-th iteration; g 1×D (t - 1) is the global historical optimal position at the (t - 1)-th iteration; is the position of the j-th dimension in particle i at the t-th iteration; is the position iteration value of the j-th dimension in particle i at the t-th iteration; is the position of the j-th dimension in particle i at the (t - 1)-th iteration; m is the balance factor; c ini-1 is the initial cognitive parameter; c ini-2 is the initial social parameter.

[0098] In this embodiment, The right side of the equation to be solved consists of three parts: the first part reflects the inertia of particle movement, that is, the particle has the characteristic of maintaining its search speed in the previous iteration step; the second part reflects the learning ability of the particle individual to its historical experience, that is, the particle has the characteristic of approaching its individual historical optimal position; the third part reflects the social information acquisition ability of collaborative cooperation and experience sharing among particles, that is, the particle has the characteristic of approaching the global historical optimal position of the entire population. Both r1 and r2 are uniformly distributed random numbers within [0, 1] to enhance the randomness of particle search.

[0099] In the above S6, update the individual historical optimal position p N×D of each particle and the individual historical optimal value pbest N×1 as well as the global historical optimal position g 1×D and the global historical optimal value gbest 1×1 The expressions are as follows:

[0100]

[0101] Among them, p N×D (t) is the individual historical optimal position of each particle when iterating to step t; is the individual historical optimal position of particle i when iterating to step t; pbest N×1 (t) is the individual historical optimal value of each particle when iterating to step t; is the individual historical optimal value of particle i when iterating to step t; is the position of particle i when iterating to step t; is the fitness value of particle i when iterating to step t; is the individual historical optimal value of particle i when iterating to step t - 1; is the individual historical optimal position of particle i when iterating to step t - 1; g 1×D (t) is the global historical optimal position when iterating to step t; gbest 1×1 (t - 1) is the global historical optimal value when iterating to step t - 1; g 1×D (t - 1) is the global historical optimal position when iterating to step t - 1; gbest 1×1 (t) is the global historical optimal value when iterating to step t.

[0102] The update in S6 guides the particle population to move towards a better search space, improves the convergence efficiency and accuracy of the algorithm, and avoids blind dispersion, thus forming an effective balance between global "exploration" and local "exploitation".

[0103] In the above step S7, update the global historical optimal position g 1×D (t) update of the particle population and the global historical optimal value gbest1×1 (t) update The expression of

[0104]

[0105] σ χ = 1

[0106] where is the position of particle i after being updated by Levy flight at the t-th iteration step; g 1×D (t) is the global historical optimal position at the t-th iteration step; is the corresponding fitness value; gbest 1×1 (t) is the global historical optimal value at the t-th iteration step; is the position of particle i at the t-th iteration step; is the step size control factor within the range of [0, 1]; is the dot product; Levy(ρ) is the random search path, following the Levy distribution with parameter ρ; s is the random step size; ρ is a parameter with a value range between [1, 3]; κ and χ are both random step size related parameters and follow the standard normal distribution; and are both variances; Γ is the gamma function.

[0107] In this embodiment, the Levy flight strategy (Levy Flight) is introduced. By means of the random walk mechanism, a random step size is generated to change the positions of each particle at the current iteration step, and then the states of each particle are updated to x N×D (t) new . Subsequently, an update evaluation strategy based on the greedy algorithm is adopted, and only the update value that can improve the global historical optimal value at the current iteration step is accepted, where the superscript represents the dimension of the generation matrix;

[0108] It should be noted that the Levy flight strategy is an efficient random search strategy that alternates between short-distance walks and occasional long-distance walks following the Levy distribution. During the search process, it can take into account both local fine search and global large-scale exploration, thereby increasing the diversity of the particle population and improving the global search ability. It widely exists in nature. For example, similar behaviors can be observed in the foraging of animals and insects, pollen dissemination, etc.

[0109] Considering that the Levy flight strategy cannot guarantee that the updated particles will definitely improve the global historical optimal value at the current iteration step, an update evaluation strategy based on the greedy algorithm is adopted. By calculating the fitness values of each particle after being updated by Levy flight and comparing them with the global historical optimal value gbest of the entire population at the current iteration step 1×1(t) is compared and analyzed to decide whether to accept the updated particle, thus avoiding the blind movement of particles in the search space and improving the convergence and stability of the algorithm.

[0110] Introducing the Levy Flight strategy has significant randomness and jumpiness, and has extensive search capabilities. It provides new search paths and regions through the random walk mechanism to update the positions of each particle. This process increases the diversity of the particle population, enabling the particles to have the opportunity to jump out of the current local optimal solution, thereby increasing the possibility of finding a better solution.

[0111] The specific content of S9 is as follows:

[0112] S901: Take the global historical optimal position g 1×D (t) update of the particle population as the base point K 1×D (0) and the initial detection point L 1×D (0);

[0113] S902: Take the standard basis vectors e1, e2,..., e of the R coordinate axes R as the preset search direction set, and initialize the parameters of the pattern search algorithm at the same time; the parameters of the pattern search algorithm include the step size δ s , the acceleration factor α s , the contraction factor β s , the allowable error TolX, the iteration parameter M, and the search direction index E;

[0114] S903: Execute the detection movement process, specifically:

[0115] For the current search direction e E , calculate the fitness values at the two detection points [L 1×D (E - 1)+δ s e E and [L 1×D (E - 1)-δ s e E in the neighborhood. If there is a point in [L 1×D (E - 1)+δ s e E and [L 1×D (E - 1)-δ s e E whose fitness value is less than the fitness value of the current detection point, then [L 1×D (E - 1)+δ s e E and [L 1×D (E - 1)-δ s e EPoints with small fitness values are used as new exploration points. Otherwise, the current exploration point L 1×D (E - 1) is used as the initial exploration point for the next search direction, that is, set L 1×D (E) = L 1×D (E - 1);

[0116] S904. Determine whether E = R is satisfied. If so, go to step S905. Otherwise, return to S903 to perform the exploration and movement process for the next search direction;

[0117] S905. If fitness[L 1×D (R)] < fitness[K 1×D (M)], go to step S906. Otherwise, go to step S907; L 1×D (R) is the exploration point after performing the exploration movement; K 1×D (M) is the base point for performing the pattern movement in the M - th iteration;

[0118] S906. Perform the pattern movement process, specifically:

[0119] Update the base point K 1×D (M + 1) = L 1×D (R), and starting from the updated base point, update the initial exploration point, that is, L 1×D (0) = K 1×D (M + 1)+α s [K 1×D (M + 1)-K 1×D (M)], set M = M + 1, E = 1, and return to step S903;

[0120] S907. Determine whether the pattern search algorithm termination condition is satisfied. If so, output the current point K 1×D (M) as the final result. Based on the output final result K 1×D (M) and the fitness value fitness[K 1×D (M)] corresponding to K 1×D (M), update the global historical optimal position and global historical optimal value of the particle swarm. Otherwise, shrink the step size δ s =β s δ s , update the initial exploration point L 1×D (0) = K 1×D (M), set M = M + 1, E = 1, and return to step S903; The pattern search algorithm termination condition is to reach the preset maximum number of iterations MaxIteration or the change in the fitness values of K 1×D (M) and K 1×D (M - 1) is less than the threshold TolFun or the step size δ sLess than the preset allowable error TolX.

[0121] In this embodiment, aiming at the problems that the improved PSO algorithm is prone to fall into local optimal solutions and premature convergence in the later stage, the iterative process is divided into two stages: the early global search stage and the later local search enhancement stage. Specifically, when the number of iterative steps reaches half of the maximum number of iterative steps T, that is, t > T / 2, it will enter the later local search enhancement stage. In this stage, the local search ability is strengthened by embedding the PS algorithm, so as to effectively avoid the decrease in search efficiency caused by excessive calculation. At the same time, in the iterative process of the later local search enhancement stage, a discrimination mechanism for detecting the premature convergence of particles is introduced: gbest 1 ×1 (t - 5) update = gbest 1×1 (t) update , when signs of premature convergence are detected, immediately perform a pattern search on the updated position of the global historical optimum found by the current entire population, so that it jumps out of the local optimal state and promotes the algorithm to converge to the global optimal value.

[0122] For the particle population after Levy flight update, take the updated position g 1×D (t) update of the global historical optimum of the entire population at the current iteration step as the iterative initial value K 1×D (0), and configure the optimization solver options (including the maximum number of iterations MaxIteration, the function tolerance TolFun, and the allowable error TolX), and at the same time define the objective function (i.e., the fitness function fitness) and the constraint conditions (including the boundary conditions u b , l b , the equality constraint A eq , b eq , the inequality constraint A ineq , b ineq and the non - linear constraint nonlcon), and at the same time set the initial step size δ s > 0, the acceleration factor α s ≥ 1, the contraction factor β s ∈(0, 1), the allowable error TolX > 0, and the initial iterative parameters M = 1, E = 1, etc. For this, call the "Patternsearch" toolbox in the MATLAB platform, and gradually search along the optimal direction of the fitness value decrease by alternately executing two cooperative processes: the probe move (detecting the favorable direction of descent) and the pattern move (moving along the favorable direction), and finally converge to the optimal position.

[0123] In this embodiment, calculate the Pearson correlation coefficient between the measured value of the restoring force and the predicted value of the restoring force based on the BWBN model, denoted as ρp , based on which the correlation between the two is quantitatively judged, serving as the key index for evaluating the performance of the IPSO-PS algorithm;

[0124] It should be noted that the Pearson correlation coefficient ρ p is used to quantify the linear correlation degree between two groups of data sets, and is solved by calling the "Corr" function in the MATLAB platform. The specific calculation formula is as follows:

[0125]

[0126] In the formula: F e (n t ) is the measured value of the restoring force at the nth t step; F m (n t ) is the predicted value of the restoring force at the nth t step; is the mean value of the measured values of the restoring force; is the mean value of the predicted values of the restoring force.

[0127] In mathematical statistics, the Pearson correlation coefficient ρ p is closer to 1, indicating that the correlation between the two groups of data sets is stronger. Generally, when ρ p is between 0.8 and 1.0, it is considered that the two groups of data sets have a very strong correlation.

[0128] Example 2

[0129] The present invention specifically includes the following steps:

[0130] Step 1: In the Structural Performance Database (SPD) website of the Pacific Earthquake Engineering Research Center (PEER), for RC bridge piers under different failure modes (flexure failure, flexure-shear failure, shear failure), 6 groups of measured data samples of pseudo-static cyclic loading are randomly selected respectively. The corresponding cross-sectional dimensions b×h or diameter d, pier height H0, concrete strength f′ c , reinforcement ratio ρ l , stirrup ratio ρ t , axial load N A , axial compression ratio n A , and shear span ratio λ s and other key parameters are shown in the following table:

[0131] Table 1 Measured data samples of pseudo-static cyclic loading

[0132]

[0133]

[0134]

[0135] Subsequently, based on the MATLAB platform, a BWBN model with strength degradation, stiffness degradation, and pinching effect is constructed, and the lateral displacement is input through a linearly varying displacement function. In particular, to ensure the universality of the hysteretic parameter identification results and avoid the time-variation of the initial stiffness, it is necessary to perform normalized dimensionless processing on the BWBN model and the measured hysteretic curve. For this purpose, the "ODE15s" solver in the MATLAB platform is called, and the fourth-order Runge-Kutta method with higher calculation accuracy is used to iteratively solve the differential equation system.

[0136] Step 2: For different failure modes, determine the hysteretic parameters to be identified, and give the boundary constraint conditions of the hysteretic parameters to be identified. Set the particle swarm optimization parameters including the particle population size N, the dimension D of the hysteretic parameters to be identified, the maximum value w max of the initial inertia weight and the minimum value w min of the initial inertia weight, the initial cognitive parameter c ini-1 and the initial social parameter c ini-2 of the initial social parameter, the maximum number of iteration steps T, the maximum value column vector x max of the search position and the minimum value column vector x min of the search position, as well as the maximum value column vector v max of the search speed and the minimum value column vector v min of the search speed. Tables 2 and 3 respectively summarize the boundary constraint conditions and the particle swarm optimization parameters of the embodiments of the present invention.

[0137] Table 2 Physical meanings and boundary constraint conditions of the hysteretic parameters of the BWBN model

[0138]

[0139] Table 3 Particle swarm optimization parameters

[0140]

[0141]

[0142] Furthermore, as shown in Figure 2 and Figure 3 , the positions x N×D and velocities v N×D of the particle swarm are randomly initialized in the search space by using the Logistic-Tent composite chaotic map;

[0143] Step 3: Establish the fitness function (objective function) fitness of the optimization problem of the embodiment, and calculate the fitness values of each particle in the initial particle swarm. Initialize the individual historical optimal position p of each particle by evaluating and replacing the fitness values of each particle N×D and the optimal value pbest N×1 as well as the global historical optimal position g of the entire population 1×D and the optimal value gbest 1×1 ;

[0144] Step 4: Based on the adaptive strategy, dynamically update the non - linear inertia weight w, cognitive parameter c1, and social parameter c2 to achieve iterative updates of the particle velocity and position. Further, process the boundary constraint conditions for the particle search space;

[0145] Step 5: For each particle after iterative update, the individual historical optimal position p N×D and the optimal value pbest N×1 as well as the global historical optimal position g of the entire population 1×D and the optimal value gbest 1×1 should be updated accordingly;

[0146] Step 6: Introduce the Levy Flight strategy, generate a random step size s through a random walk mechanism N×D , change the positions of each particle at the current iteration step, and then update the state of each particle to x N×D (t) new . Subsequently, adopt an update evaluation strategy based on the greedy algorithm, and only accept the update values that can improve the global historical optimal value at the current iteration step;

[0147] Step 7: Determine whether the prerequisite conditions of the Pattern Search algorithm (PS) are met. If not, return to Step 4 for continued iteration. If the embedding conditions are met, for the particle population after Levy flight update, use the updated position g 1×D (t) update of the global history optimum of the entire population at the current iteration step as the iterative initial value K 1×D (0), and configure the optimization solver options (including the maximum number of iterations MaxIteration = 30, function tolerance TolFun = 10 -6 and variable tolerance TolX = 10 -6 ), and at the same time define the objective function (i.e., the fitness function fitness) and constraint conditions (including the boundary conditions u b =x max , l b =x min , equality constraints A eq , b eq , inequality constraints A ineq , b ineqand the non - linear constraint (nonlcon). On this basis, call the "Patternsearch" toolbox in the MATLAB platform and use the pattern search algorithm (PS) to carry out in - depth optimization and development;

[0148] Statistically analyze the hysteretic parameter identification results of the BWBN model of RC piers under different failure modes. The specific identification results are shown in Table 4.

[0149] Table 4 Hysteretic parameter identification results of the BWBN model

[0150]

[0151] Refer to Figure 4 The change trajectory of the iteration process shows that the fitness function value exhibits typical optimization convergence characteristics: it shows a rapid downward trend in the initial stage, and then the convergence speed gradually slows down and finally stabilizes, which reflects the dynamic process of enhanced global search in the early stage and local search in the later stage of the IPSO - PS algorithm. At the same time, when the number of iteration steps reaches 100 steps, the fitness function value tends to be stable, indicating that the IPSO - PS algorithm has significant superiority in terms of convergence speed and search efficiency.

[0152] Furthermore, to evaluate the identification accuracy, extract the convergence value of the fitness function of the IPSO - PS algorithm, and calculate the errors between the measured data and the BWBN hysteretic model in terms of peak load and cumulative hysteretic energy dissipation. The calculation results are shown in Table 5.

[0153] Generally, when the convergence value of the fitness function is lower than 0.2, it can be considered that it meets the requirements of the identification error accuracy. In the embodiments of the present invention, the convergence values of the fitness function are all lower than 0.2, so the obtained convergence values of the fitness function meet the established accuracy requirements.

[0154] Table 5 Error comparison between measured data and the BWBN model

[0155]

[0156] For RC piers under different failure modes, refer to Figures 5 - 7 From the comparative analysis results of the hysteretic curves, it can be seen that the measured hysteretic curves are in good agreement with the hysteretic curves based on the BWBN model. It can not only accurately represent the overall hysteretic shape, but also better simulate the strength degradation, stiffness degradation and pinching effect, indicating the applicability and reliability of the IPSO - PS algorithm in hysteretic parameter identification. It should be noted that due to the more significant regularity of the non - linear evolution of RC piers in the flexural failure mode, the IPSO - PS algorithm has the best identification accuracy in the flexural failure mode, and the hysteretic curves obtained by its identification show a high degree of consistency.

[0157] Refer toFigures 8 - 10 Comparative analysis of the time history curves shows that during the entire loading process, the fitting effect between the measured restoring force values and the predicted restoring force values based on the BWBN model is excellent. At the same time, it can be observed that in the initial stage, the predicted restoring force values of the time history curves based on the BWBN model are lower than the measured restoring force values, mainly due to the underestimation of the stiffness ratio α before and after yielding, resulting in insufficient contribution of the elastic force in the initial small-displacement stage, thus leading to a smaller predicted restoring force value.

[0158] Refer to Table 5 and Figures 11 - 13 Comparative analysis of the peak load error and the skeleton curve shows that the measured skeleton curve and the skeleton curve based on the BWBN model have similar mechanical behaviors in the elastic deformation, plastic yielding, and strength degradation stages, and the degree of coincidence between the two is relatively high. The relative errors of the positive and negative peak loads are basically controlled within 15%. During the loading process, due to the asymmetry of the positive and negative loading, the deviation of the displacement loading rate, and the difference in the positive and negative displacement amplitudes, the asynchrony of the peak load and peak displacement of the measured hysteresis curve and the asymmetry of the positive and negative peak loads occur, resulting in a phenomenon where the measured peak load is close to the peak load based on the BWBN model while the corresponding displacement shows a significant deviation.

[0159] Refer to Table 5 and Figures 14 - 16 Error and comparative analysis of the cumulative hysteretic energy dissipation show that there is a basic correlation between the measured cumulative hysteretic energy dissipation and the cumulative hysteretic energy dissipation based on the BWBN model. Different failure modes have a significant impact on the energy dissipation capacity of RC bridge piers. The flexural failure has the highest energy dissipation capacity due to the full development of plastic hinges, while the shear failure has the lowest energy dissipation capacity due to the restriction of brittle fracture characteristics.

[0160] In the present invention, by taking the lateral displacement difference between two consecutive loading steps as the weight of the time ratio and combining the positive and negative displacement amplitudes of the actual loading, the solution of the differential equation system is carried out, thereby truly and effectively simulating the actual loading process, and to a certain extent, improving the disadvantages of the asymmetry of the positive and negative loading and the difference in displacement amplitudes.

[0161] Step 8: Calculate the Pearson correlation coefficient between the measured restoring force value and the predicted restoring force value based on the BWBN model, denoted as ρ p , and quantitatively judge the correlation between the two based on this, which is the key index for evaluating the performance of the IPSO-PS algorithm. For this, by calling the "Corr" function in the MATLAB platform, the Pearson correlation coefficient ρ between the measured restoring force value and the predicted restoring force value based on the BWBN model is calculated p , and the specific values are shown in Table 6.

[0162] Refer to Table 6 and Figure 17 The correlation coefficient ρ pFor the distribution of the Pearson correlation coefficient ρ between the measured restoring force and the predicted restoring force based on the BWBN model for RC bridge piers under different failure modes p All reached above 0.94, showing a very strong correlation, verifying the efficiency and reliability of the IPSO-PS algorithm for identifying the hysteretic parameters of the BWBN model.

[0163] Table 6 Pearson correlation coefficient statistics

[0164]

[0165]

[0166] In summary, the IPSO-PS algorithm combines the swarm intelligence cooperation mechanism of the improved PSO algorithm and the local search guidance strategy of the PS algorithm. By balancing the global "exploration" and local "exploitation" optimization capabilities of the particle swarm, it effectively improves the diversity of the particle population, the global search traversal ability and the convergence speed, and avoids problems such as falling into local optimal solutions and premature convergence in the later stage of iteration. Compared with the standard PSO algorithm, the IPSO-PS algorithm has significantly improved in overall search efficiency, optimization accuracy and robustness, and shows more superior comprehensive performance when dealing with the complex high-dimensional problem of identifying the hysteretic parameters of the BWBN model, providing a reliable theoretical basis and technical implementation path for solving the parameter identification of complex hysteretic models.

Claims

1. A method for identifying hysteretic parameters of a BWBN model based on improved particle swarm optimization, characterized in that, Including: Obtain the measured hysteretic curves of the pseudo-static cyclic loading of RC piers under different failure modes, and determine the yield load and yield displacement of the ultimate equivalent yield point based on the skeleton curve of the measured hysteretic curve; Construct a BWBN model with strength degradation, stiffness degradation and pinching effect. According to the yield load and yield displacement of the ultimate equivalent yield point, perform normalized dimensionless processing on the BWBN model and the measured hysteretic curve respectively, and construct the first-order explicit differential equations of the BWBN model according to the normalized dimensionless processing results of the BWBN model; Determine the hysteretic parameters to be identified, and give the boundary constraint conditions of the hysteretic parameters to be identified; Use the improved particle swarm optimization algorithm to obtain the optimal values of the hysteretic parameters to be identified. Specifically: in each iteration of the improved particle swarm optimization algorithm, use the Lévy flight strategy and the pattern search algorithm to deeply optimize the global historical optimal position, and take the global historical optimal position output in the last step as the value of each hysteretic parameter to be identified, and complete the identification of the hysteretic parameters of the BWBN model; the fitness function of the improved particle swarm optimization algorithm is the error function between the predicted restoring force obtained by solving the first-order explicit differential equations of the BWBN model and the measured restoring force value in the normalized dimensionless processing results of the measured hysteretic curve.

2. The hysteretic parameter identification method of the BWBN model based on improved particle swarm optimization according to claim 1, characterized in that The yield load and yield displacement of the ultimate equivalent yield point are specifically: Based on the skeleton curve of the measured hysteretic curve, determine the equivalent yield point through different equivalent yield point extraction methods, and take the average value of the yield load and yield displacement of the equivalent yield point determined by each method as the yield load and yield displacement of the ultimate equivalent yield point.

3. The hysteretic parameter identification method of the BWBN model based on improved particle swarm optimization according to claim 1, characterized in that, The construction of the BWBN model with strength degradation, stiffness degradation and pinching effect, and the normalization and dimensionless processing of the BWBN model and the measured hysteretic curve according to the yield load and yield displacement of the ultimate equivalent yield point, and the construction of the first-order explicit differential equations of the BWBN model according to the normalized dimensionless processing results of the BWBN model are specifically: Construct a BWBN model with strength degradation, stiffness degradation and pinching effect: F m = F e + F h F e = αku F h = (1 - α)kz v = 1 + δ v ε η = 1 + δ η ε ζ1 = ζ 10 [1 - exp(-pε)] ζ2 = (ψ0 + δ ψ ε)(λ + ζ1) Among them, F m is the inelastic restoring force of the BWBN model; F e is the elastic force; F h is the hysteretic force; α is the stiffness ratio before and after yielding; k is the initial stiffness of the structure; u is the relative lateral displacement; z is the hysteretic displacement; is the first derivative of z; h(z) is a function used to control the pinching effect of the hysteresis curve; η is the stiffness degradation parameter; v is the strength degradation parameter; n is the parameter controlling the smoothness of the hysteresis curve; γ is the parameter controlling the shape of the hysteresis curve; β is the parameter controlling the peak value of the hysteresis curve; is the sign function related to the product of the hysteretic displacement z and the velocity ; is the first derivative of u, representing the velocity; δ v is the strength degradation rate; ε is the cumulative hysteretic energy dissipation at time t; t is the time; δ η is the stiffness degradation rate; ζ1 is the parameter controlling the pinching degree; is the sign function related to the velocity ; q is the parameter controlling the starting position of the pinching effect; z u is the maximum value of the hysteretic displacement; ζ2 is the parameter controlling the pinching diffusion region; ζ 10 is the parameter controlling the total slip amount; p is the parameter controlling the pinching slope; ψ0 is the parameter controlling the pinching amplitude; δ ψ is the parameter controlling the pinching rate; λ is the parameter controlling the magnitude relationship between the total pinching amount and the pinching rate; According to the yield load and yield displacement of the ultimate equivalent yield point, perform normalized dimensionless processing on the measured hysteretic curve to obtain the normalized dimensionless processing results of the measured hysteretic curve; According to the yield load and yield displacement of the ultimate equivalent yield point, perform normalized dimensionless processing on the BWBN model to obtain the normalized dimensionless processing results of the BWBN model: μ = u / u y μ z = z / u y F y = ku y Among them, F n is the normalized restoring force; F y is the yield load at the final equivalent yield point; u y is the yield displacement at the final equivalent yield point; μ is the normalized relative lateral displacement; μ z is the normalized hysteretic displacement; is the first derivative of μ; is the first derivative of the normalized hysteretic displacement; h(μ z ) is the normalized pinching effect function; ε n is the normalized cumulative hysteretic energy dissipation; is the sign function related to the product of μ z and ; is the sign function related to ; ε y is the yield cumulative hysteretic energy dissipation at the final equivalent yield point; Construct the first-order explicit differential equations of the BWBN model according to the normalized dimensionless processing results of the BWBN model: Among them, Y is the introduced state vector; Y1 is the normalized relative lateral displacement μ; Y2 is the normalized hysteretic displacement μ z ; Y3 is the normalized cumulative hysteretic energy dissipation ε n ; is the first derivative of Y; is the first derivative of Y1; is the first derivative of Y2; is the first derivative of Y3.

4. The hysteretic parameter identification method of the BWBN model based on improved particle swarm optimization according to claim 1, characterized in that The use of the improved particle swarm optimization algorithm to obtain the optimal values of the hysteretic parameters to be identified is specifically: S1. According to the hysteretic parameters to be identified, form the hysteretic parameter vector θ to be identified: θ = [α, β, γ, n, δ v , δ η , ζ 10 , q, p, ψ0, δ ψ , λ] Among them, α is the stiffness ratio before and after yielding; n is the parameter controlling the smoothness of the hysteresis curve; γ is the parameter controlling the shape of the hysteresis curve; β is the parameter controlling the peak value of the hysteresis curve; δ v is the strength degradation rate; δ η is the stiffness degradation rate; ζ 10 is the parameter controlling the total slip; q is the parameter controlling the starting position of the pinching effect; p is the parameter controlling the pinching slope; ψ0 is the parameter controlling the pinching amplitude; δ ψ is the parameter controlling the pinching rate; λ is the parameter controlling the order relationship between the total pinching amount and the pinching rate; S2. Initialize the parameters of the particle swarm optimization algorithm; the parameters of the particle swarm optimization algorithm include the particle population size N, the dimension D of the hysteresis parameters to be identified, the maximum inertia weight w max , the minimum inertia weight w min , the cognitive parameter c1, the social parameter c2, the maximum number of iteration steps T, the maximum search position column vector x max , the minimum search position column vector x min , the maximum search velocity column vector v max and the minimum search velocity column vector v min ; the dimension D of the hysteresis parameters to be identified is equal to the number of the hysteresis parameters to be identified; S3. Randomly initialize the particle position \(x\) and the particle velocity \(v\) within the search space using the Logistic-Tent composite chaotic map N×D and particle velocity \(v\) N×D :[[]]END]] Among them, is the initial position of the particle swarm; is the initial velocity of the particle swarm; is the initial value of the position of the D-th dimension in particle i; is the initial value of the velocity of the D-th dimension in particle i; is the initial value of the position of the j-th dimension in particle i; is the initial value of the velocity of the j-th dimension in particle i; X ij is the chaotic sequence value of the j-th dimension in particle i within the interval [0, 1]; is the upper limit of the position searched for dimension j; is the lower limit of the position searched for dimension j; is the upper limit of the velocity searched for dimension j; is the lower limit of the velocity searched for dimension j; X (i+1)j is the chaotic sequence value of the j-th dimension in particle i + 1 within the interval [0, 1]; r is the control parameter; S4. Calculate the fitness value of each particle, and initialize the individual historical best position p N×D and the individual historical best value pbest N×1 of each particle, as well as the global historical best position g 1×D and the global historical best value gbest 1 ×1 ; S5. Based on the adaptive strategy, dynamically update the inertia weight w, the cognitive parameter c1 and the social parameter c2, and update the particle velocity and particle position based on the boundary constraints according to the updated inertia weight w, the cognitive parameter c1 and the social parameter c2; S6. Update the individual historical optimal position p N×D and the individual historical optimal value pbest N×1 as well as the global historical optimal position g 1×D and the global historical optimal value gbest 1×1 ; S7. Introduce the Levy flight strategy to update the positions of each particle, and update the evaluation strategy based on the greedy algorithm to update the global historical optimal position g of the particle population 1×D (t) update and the global historical optimal value gbest 1×1 (t) update ; S8. Determine whether the preconditions of the embedded pattern search algorithm are met. If so, proceed to step S9; otherwise, return to step S5. The preconditions of the embedded pattern search algorithm are that the current iteration step t > T / 2, and the global historical optimal value gbest 1×1 (t) update of the particle swarm has not changed for 5 consecutive iterations; S9. Use the global historical optimal position g 1×D (t) update of the particle population as the initial iteration value K 1×D (0), and update the global historical optimal position and global historical optimal value of the particle population through the pattern search algorithm; S10. Determine whether the preset maximum number of iterations T is satisfied. If so, output the final position g of the global historical optimum of the entire particle population at the T-th step, 1×D (T) final and the final value gbest 1×1 (T) final , otherwise, return to S5 to continue the iteration.

5. The hysteretic parameter identification method of the BWBN model based on improved particle swarm optimization according to claim 4, characterized in that, The fitness value of each particle in S4 is: Among them, is the fitness value of particle i; is the position of particle i; n t is the loading step index; N t is the total number of loading steps; F e (n t ) is the measured value of the restoring force at the nth t step; is the predicted value of the restoring force at the nth t step calculated by particle i.

6. The hysteretic parameter identification method for the BWBN model based on improved particle swarm optimization according to claim 5, characterized in that The first-order explicit differential equations of the BWBN model are iteratively solved using the fourth-order Runge-Kutta method to obtain the predicted values of the restoring force; the calculation formula of the fourth-order Runge-Kutta method is as follows: where f() is the first-order explicit differential equation system of the BWBN model; is the time corresponding to the input normalized lateral displacement μ at the n t -th loading step; is the state vector at time , including the normalized hysteretic displacement μ z and the normalized cumulative hysteretic energy dissipation ε n ; h is the time step; k1 is the slope at time with the state ; k2 is the slope at time with the state ; k3 is the slope at time with the state ; k4 is the slope at time with the state .

7. The hysteretic parameter identification method of the BWBN model based on improved particle swarm optimization according to claim 4, characterized in that, The expressions for updating the particle velocity and particle position in S5 are as follows: Among them, is the velocity of the j-th dimension in particle i at the t-th iteration step; is the velocity iteration value of the j-th dimension in particle i at the t-th iteration step; t is the current iteration step number, t = 1, 2, …, T; is the velocity of the j-th dimension in particle i at the (t - 1)-th iteration step; both r1 and r2 are uniformly distributed random numbers within [0, 1]; is the individual historical best position of the j-th dimension in particle i at the (t - 1)-th iteration step; is the position of the j-th dimension in particle i at the (t - 1)-th iteration step; g 1×D (t - 1) is the global historical best position at the (t - 1)-th iteration step; is the position of the j-th dimension in particle i at the t-th iteration step; is the position iteration value of the j-th dimension in particle i at the t-th iteration step; is the position of the j-th dimension in particle i at the (t - 1)-th iteration step; m is the balance factor; c ini-1 is the initial cognitive parameter; c ini-2 is the initial social parameter.

8. The hysteretic parameter identification method of the BWBN model based on improved particle swarm optimization according to claim 4, characterized in that In S6, update the individual historical optimal position p of each particle N×D and the individual historical optimal value pbest N×1 as well as the global historical optimal position g 1×D and the global historical optimal value gbest 1×1 The expressions are as follows: Among them, p N×D (t) is the individual historical best position of each particle at the t-th iteration step; is the individual historical best position of particle i at the t-th iteration step; pbest N×1 (t) is the individual historical best value of each particle at the t-th iteration step; is the individual historical best value of particle i at the t-th iteration step; is the position of particle i at the t-th iteration step; is the fitness value of particle i at the t-th iteration step; is the individual historical best value of particle i at the (t - 1)-th iteration step; is the individual historical best position of particle i at the (t - 1)-th iteration step; g 1×D (t) is the global historical best position at the t-th iteration step; gbest 1×1 (t - 1) is the global historical best value at the (t - 1)-th iteration step; g 1×D (t - 1) is the global historical best position at the (t - 1)-th iteration step; gbest 1×1 (t) is the global historical best value at the t-th iteration step.

9. The hysteretic parameter identification method for the BWBN model based on improved particle swarm optimization according to claim 4, characterized in that, In step S7, update the global historical optimal position g 1×D (t) update and the global historical optimal value gbest 1×1 (t) update The expressions are as follows: σ χ = 1 Among them, is the position of particle i after being updated by Levy flight when iterating to step t; g 1×D (t) is the global historical optimal position when iterating to step t; The corresponding fitness value; gbest 1×1 (t) is the global historical optimal value when iterating to step t; is the position of particle i when iterating to step t; is the step size control factor within the range of [0, 1]; is the dot product; Levy(ρ) is the random search path, following the Levy distribution with parameter ρ; s is the random step size; ρ is a parameter with a value range between [1, 3]; κ and χ are both random step size related parameters and follow the standard normal distribution; and are both variances; Γ is the gamma function.

10. The hysteretic parameter identification method of the BWBN model based on improved particle swarm optimization according to claim 7, characterized in that, Specifically, S9 is as follows: S901. Take the global historical optimal position g of the particle population 1×D (t) update as the base point K 1×D (0) and the initial detection point L 1×D (0); S902. Take the standard basis vectors e1, e2, …, e of the R coordinate axes R as the preset search direction set, and initialize the pattern search algorithm parameters at the same time. The pattern search algorithm parameters include the step size δ s , the acceleration factor α s , the contraction factor β s , the allowable error TolX, the iteration parameter M, and the search direction index E; S903. Execute the exploration movement process, specifically: For the current search direction e E , calculate the fitness values at two detection points within the neighborhood [L 1×D (E - 1)+δ s e E and [L 1×D (E - 1)-δ s e E . If there is a point in [L 1×D (E - 1)+δ s e E and [L 1×D (E - 1)-δ s e E whose fitness value is less than the fitness value of the current detection point, then take the point with the smaller fitness value in [L 1×D (E - 1)+δ s e E and [L 1×D (E - 1)-δ s e E as the new detection point. Otherwise, take the current detection point L 1×D (E - 1) as the initial detection point of the next search direction, that is, set L 1×D (E)=L 1×D (E - 1); S904. Determine whether E = R is satisfied. If so, proceed to step S905; otherwise, return to S903 to perform the exploration movement process for the next search direction; S905. If fitness[L 1×D (R)] < fitness[K 1×D (M)], go to step S906; otherwise, go to step S907; L 1 ×D (R) is the detection point after performing the detection movement; K 1×D (M) is the base point for performing the pattern movement in the M-th iteration; S906. Execute the pattern movement process, specifically: Updated base point K 1×D (M + 1)=L 1×D (R), and starting from the updated base point, update the initial detection point, i.e., L 1×D (0)=K 1×D (M + 1)+α s [K 1×D (M + 1)-K 1×D (M)], set M = M + 1, E = 1, and return to step S903; S907. Determine whether the termination condition of the pattern search algorithm is satisfied. If so, output the current point K 1×D (M) As the final result, based on the output final result K 1×D (M) and K 1×D (M) corresponding fitness value fitness[K 1×D (M)], update the global historical optimal position and global historical optimal value of the particle swarm. Otherwise, shrink the step size δ s = β s δ s , update the initial exploration point L 1×D (0)= K 1×D (M), set M = M + 1, E = 1, and return to step S903; the termination condition of the pattern search algorithm is to reach the preset maximum number of iterations MaxIteration or the change in the fitness values of K 1×D (M) and K 1×D (M - 1) is less than the threshold TolFun or the step size δ s is less than the preset allowable error TolX.

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