Hysteretic parameter identification method of bwbn model based on improved particle swarm optimization

Abstract

The application discloses a hysteretic parameter identification method of a BWBN model based on an improved particle swarm optimization, and belongs to the field of hysteretic parameter identification. The method comprises the following steps: determining the equivalent yield point of a RC pier under a pseudo-static force reciprocating load according to a skeleton curve of a measured hysteretic curve; giving boundary constraints of hysteretic parameters to be identified; obtaining optimal values of the hysteretic parameters to be identified by using an improved particle swarm optimization; optimizing a global historical optimal position by using a Levy flight strategy and a pattern search algorithm in each step of iteration of the improved particle swarm optimization, taking the global historical optimal position output in the last step as the value of each hysteretic parameter to be identified, and completing the hysteretic parameter identification of the BWBN model. The application solves the problems that the existing method is prone to falling into a local optimal solution in the later period, premature convergence, the convergence speed and fitting precision depend on the selection of parameters, and evolution lacks sufficient exploration ability and is difficult to guarantee the diversity of a particle population when dealing with complex high-dimensional space optimization problems.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of hysteretic parameter identification, and particularly relates to a hysteretic parameter identification method of a BWBN model based on an improved particle swarm optimization. BACKGROUND

[0002] As an important load-bearing component supporting the superstructure of a bridge, a reinforced concrete (RC) pier is prone to damage and failure under the action of an earthquake, thereby endangering the service safety performance of the overall bridge structure and becoming a key research object of seismic analysis and design of a bridge structure. Under the action of an earthquake, an RC pier is usually affected by key parameters such as a reinforcement ratio, a stirrup ratio, an axial compression ratio, and a shear-span ratio, and is prone to flexural failure (FF), flexural-shear failure (FS), and shear failure (SF). For an RC pier under different failure modes, the corresponding restoring force hysteretic characteristics and seismic performance often differ greatly.

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

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

[0005] The hysteretic parameter identification process of the BWBN model is relatively complex due to its high nonlinearity and numerous parameters, which is a bottleneck problem of applying the BWBN model. However, the hysteretic parameters can be efficiently and accurately identified from the test data by selecting a suitable calculation algorithm. In combination with the measured hysteretic curve data of the RC pier, a suitable intelligent optimization algorithm is selected, and a target function related to the hysteretic parameters is constructed for parameter identification, which is the main way to identify the hysteretic parameters at present. The particle swarm optimization algorithm (PSO) has been widely concerned due to its simple algorithm structure and easy implementation, and has advantages of good global search ability, fast convergence, less parameter adjustment, strong adaptability, and good parallel processing capability. Although the standard PSO algorithm shows excellent performance in solving most optimization problems, it has disadvantages of being easy to fall into local optimal solution in the later stage, premature convergence, convergence speed and fitting precision depending on the selection of parameters (inertia weight, learning factor, etc.), and lack of sufficient exploration ability to ensure the diversity of particle population when dealing with complex high-dimensional space optimization problems. SUMMARY

[0006] In view of the above problems in the prior art, the hysteretic parameter identification method of the BWBN model based on the improved particle swarm optimization provided by the present application solves the problems of being easy to fall into local optimal solution in the later stage, premature convergence, convergence speed and fitting precision depending on the selection of parameters, and lack of sufficient exploration ability to ensure the diversity of particle population when dealing with complex high-dimensional space optimization problems.

[0007] In order to achieve the above-mentioned application purposes, the technical scheme adopted by the present application is as follows: a hysteretic parameter identification method of a BWBN model based on improved particle swarm optimization, comprising:

[0008] Obtaining the pseudo-static force reciprocating loading measured hysteretic curve of the RC pier under different failure modes, and determining the yield load and yield displacement of the final equivalent yield point based on the skeleton curve of the measured hysteretic curve;

[0009] Constructing a BWBN model with strength degradation, stiffness degradation and pinching effect, normalizing and dimensionless processing the BWBN model and the measured hysteretic curve according to the yield load and yield displacement of the final equivalent yield point, and constructing a first-order explicit differential equation set of the BWBN model according to the normalized dimensionless processing result of the BWBN model;

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

[0011] The improved particle swarm algorithm is used to obtain the optimal value of the hysteresis parameter to be identified, specifically: in each step iteration of the improved particle swarm algorithm, the global historical optimal position is deeply optimized by using the Levy flight strategy and the pattern search algorithm, and the global historical optimal position output in the last step is taken as the value of each hysteresis parameter to be identified, so as to complete the identification of the hysteresis parameters of the BWBN model; and the fitness function of the improved particle swarm algorithm is an error function between the predicted value of the restoring force obtained by solving the first-order explicit differential equation set 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 Logistic-Tent composite chaotic mapping has good randomness and ergodicity, excellent autocorrelation and complex chaotic dynamic characteristics, can generate uniformly distributed initial particle population, avoids the phenomenon that part of the search area is too dense or too sparse, and thus effectively improves particle population diversity, global search capability and convergence speed; the introduction of the nonlinear inertia weight w can balance the optimization ability of the global "exploration" and the local "development" of the particle swarm; in the early stage of iteration, a larger inertia weight is beneficial to realize a wide range of search and promote the algorithm to converge to the adjacent area of the potential optimal value, in the later stage of iteration, with the increase of the iteration number, the inertia weight gradually decreases, so that the particles carry out 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 effective regulation of the individual self-learning ability and the ability to obtain social information of the particles; in the early stage of iteration, a larger c1 and a smaller c2 are set to make the particles tend to rely on the self-learning ability to explore unknown areas, realize extensive search of each particle in the search space, thereby avoiding premature convergence and enhancing the adaptability of the algorithm, while in the later stage of iteration, c1 is gradually reduced and c2 is gradually increased to make the particles tend to rely on the ability to obtain social information to adjust the search direction, realize fine search of each particle in the vicinity of 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 jumping nature, and has wide search ability, and provides new search paths and areas through the random walk mechanism, so as to realize the position update of each particle, which increases the diversity of the particle population and makes the particles have the opportunity to jump out of the current local optimal solution, thereby improving the possibility of finding a better solution; embedding the PS algorithm into the improved PSO algorithm framework not only can maintain the global search advantage of the improved PSO algorithm, but also can implement more fine search in the key area where the entire particle swarm tends to the global historical optimal position by relying on the local search ability of the PS algorithm, make up for the limitation of the improved PSO algorithm in local search, and thus greatly improve the overall search efficiency and accuracy of the algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 Flow chart of the method of the present application.

[0014] Figure 2 Bar chart of Logistic-Tent chaotic mapping in the embodiment of the present application.

[0015] Figure 3 Scatter plot of Logistic-Tent chaotic mapping in the embodiment of the present application.

[0016] Figure 4 Trajectory diagram of the change of fitness function value with iteration process in the embodiment of the present application.

[0017] Figure 5 Schematic diagram of comparative analysis of measured data and BWBN hysteretic model hysteretic curve in the bending failure mode in the embodiment of the present application.

[0018] Figure 6 Schematic diagram of comparative analysis of measured data and BWBN hysteretic model hysteretic curve in the bending-shear failure mode in the embodiment of the present application.

[0019] Figure 7 Schematic diagram of comparative analysis of measured data and BWBN hysteretic model hysteretic curve in the shear failure mode in the embodiment of the present application.

[0020] Figure 8 Schematic diagram of comparative analysis of measured data and BWBN hysteretic model skeleton curve in the bending failure mode in the embodiment of the present application.

[0021] Figure 9 Schematic diagram of comparative analysis of measured data and BWBN hysteretic model skeleton curve in the bending-shear failure mode in the embodiment of the present application.

[0022] Figure 10 Schematic diagram of comparative analysis of measured data and BWBN hysteretic model skeleton curve in the shear failure mode in the embodiment of the present application.

[0023] Figure 11 Schematic diagram of comparative analysis of measured data and BWBN hysteretic model skeleton curve in the bending failure mode in the embodiment of the present application.

[0024] Figure 12 Schematic diagram of comparative analysis of measured data and BWBN hysteretic model skeleton curve in the bending-shear failure mode in the embodiment of the present application.

[0025] Figure 13 Schematic diagram of comparative analysis of measured data and BWBN hysteretic model skeleton curve in the shear failure mode in the embodiment of the present application.

[0026] Figure 14 Schematic diagram of comparative analysis of the measured data and the accumulated hysteretic energy dissipation of the BWBN hysteretic model under the bending failure mode in an embodiment of the present invention.

[0027] Figure 15 Schematic diagram of comparative analysis of the measured data and the accumulated hysteretic energy dissipation of the BWBN hysteretic model under the bending-shear failure mode in an embodiment of the present invention.

[0028] Figure 16 Schematic diagram of comparative analysis of the measured data under the shear failure mode in an embodiment of the present invention and the accumulated hysteresis energy dissipation of the BWBN hysteresis model.

[0029] Figure 17 Schematic diagram of the correlation coefficient distribution of RC bridge piers under different failure modes in an embodiment of the present invention. DETAILED DESCRIPTION

[0030] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0031] Example 1

[0032] like Figure 1 As shown, in one embodiment of the present invention, a hysteresis parameter identification method based on the BWBN model of improved particle swarm optimization includes:

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

[0034] A BWBN model with strength degradation, stiffness degradation, and pinching effects was constructed. The BWBN model and the measured hysteresis curves were normalized and dimensionless according to the yield load and yield displacement of the final equivalent yield point. Based on the normalized dimensionless results of the BWBN model, a set of first-order explicit differential equations for the BWBN model was constructed.

[0035] Determine the hysteresis parameter to be identified and give the boundary constraint conditions of the hysteresis parameter to be identified;

[0036] The improved particle swarm algorithm is used to obtain the optimal value of the to-be-identified hysteresis parameter, specifically: in each step of iteration of the improved particle swarm algorithm, the global historical optimal position is deeply optimized by using the Levy flight strategy and the pattern search algorithm, and the global historical optimal position output in the last step is taken as the value of each to-be-identified hysteresis parameter, so as to complete the identification of the hysteresis parameters of the BWBN model; and the fitness function of the improved particle swarm algorithm is an error function between the predicted value of the restoring force obtained by solving the first-order explicit differential equation set of the BWBN model and the measured value of the restoring force in the normalized dimensionless processing result of the measured hysteresis curve.

[0037] In the embodiment, when the improved PSO algorithm falls into search stagnation (the global historical optimal value remains unchanged for several times), the global historical optimal position of the search space of the hysteresis parameters of the BWBN model is taken as the initial value of the PS algorithm for local search, so as to overcome the problem that the PS algorithm is sensitive to the initial value. The hybrid algorithm combines the characteristics and advantages of the PSO algorithm and the PS algorithm, and exhibits more superior performance in processing the complex high-dimensional problem of the identification of the hysteresis parameters of the BWBN model.

[0038] Specifically, the method comprises the following steps:

[0039] In the structure performance database (SPD) website of the Pacific Earthquake Engineering Research Center (PEER), the pseudo-static cyclic loading measured data of the RC bridge pier under different failure modes (flexural failure, flexural-shear failure and shear failure) is obtained;

[0040] It should be noted that 6 groups of test data samples are randomly selected for the RC bridge pier under different failure modes, and the obtained test data samples cover the measured restoring force, displacement and corresponding hysteresis curve in 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 hysteresis curve, the equivalent yield point is determined by different equivalent yield point extraction methods, and the average value of the yield load and yield displacement of the equivalent yield point determined by each method is taken as the yield load and yield displacement of the final equivalent yield point. In this way, the limitations caused by the theoretical assumptions or empirical deviations of a single method can be weakened, so as to improve the reliability of the equivalent yield point parameter.

[0043] In the embodiment, the corresponding skeleton curve is extracted according to the pseudo-static cyclic loading measured hysteresis 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 bridge 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] The BWBN model with strength degradation, stiffness degradation and pinching effect is constructed. According to the yield load and yield displacement of the final equivalent yield point, the BWBN model and the measured hysteresis curve are respectively normalized and dimensionless. Based on the normalized dimensionless processing results of the BWBN model, a first-order explicit differential equation system of the BWBN model is constructed, specifically:

[0046] Constructing a BWBN model with strength degradation, stiffness degradation, and pinching effects:

[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 hysteresis 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 hysteresis 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 that controls the smoothness of the hysteresis curve; γ is the parameter that controls the shape of the hysteresis curve; β is the parameter that controls the peak value of the hysteresis curve; is a sign function related to the hysteretic displacement z and the velocity is a sign function related to the velocity is a first order differential of u, representing the velocity; δ v is the strength degradation rate; ε is the cumulative hysteretic energy at time t; t is time; δ η is the stiffness degradation rate; ζ1 is a parameter controlling the degree of pinching; is a sign function related to the velocity is a sign function related to the velocity; q is a parameter controlling the starting position of pinching effect; z u is the maximum value of hysteretic displacement; ζ2 is a parameter controlling the spread area of pinching; ζ 10 is a parameter controlling the total slip amount; p is a parameter controlling the pinching slope; ψ0 is a parameter controlling the pinching amplitude; δ ψ is a parameter controlling the pinching rate; λ is a parameter controlling the magnitude relationship between the total amount of pinching and the pinching rate;

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

[0059] According to the yield load and the yield displacement of the final equivalent yield point, the BWBN model is normalized and dimensionless processed to obtain a 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] wherein, F n is a 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 a normalized relative lateral displacement; μ z is a normalized hysteretic displacement; is a first order differential of μ; is a first order differential of the normalized hysteretic displacement; h(μ z ) is a normalized pinching effect function; ε n is a normalized cumulative hysteretic energy; is a sign function related to μ z and product-dependent sign function; product-dependent sign function; product-dependent sign function; ε y is the accumulated hysteretic energy at the final equivalent yield point;

[0066] According to the normalized dimensionless processing results of the BWBN model, the first-order explicit differential equation set of the BWBN model is constructed:

[0067]

[0068] where 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 accumulated hysteretic energy 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, the BWBN model with strength degradation, stiffness degradation and pinch effect is constructed, and the lateral displacement is input through a linear variable amplitude displacement function. In order to ensure the universality of the hysteretic parameter identification results and avoid the time-varying nature of the initial stiffness, the BWBN model and the measured hysteretic curve are normalized and dimensionless processed, and the ductility demand index can be directly obtained after the normalization processing.

[0070] The BWBN hysteretic model is introduced, the strength degradation, stiffness degradation and pinch effect of the hysteretic characteristics are comprehensively considered by adjusting the hysteretic parameters with clear physical meaning, and then the nonlinear relationship between the restoring force and the displacement of the RC pier can be simulated with high precision. At the same time, the calculation complexity is low, and the engineering practicability and the accuracy of dynamic response analysis are considered, which is significantly better than the simplified description of the complex hysteretic behavior of the traditional hysteretic model. On this basis, the BWBN hysteretic model and the measured hysteretic curve in the measured data are normalized and dimensionless processed, the time-varying nature of the initial stiffness is effectively avoided, and the ductility demand index can be directly obtained.

[0071] The improved particle swarm algorithm is used to obtain the optimal value of the to-be-identified hysteretic parameter, specifically:

[0072] S1, according to the to-be-identified hysteretic parameter, a to-be-identified hysteretic parameter vector θ is formed:

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

[0074] wherein a is the stiffness ratio before and after yielding; n is a parameter controlling the smoothness of the hysteresis curve; g is a parameter controlling the shape of the hysteresis curve; b is a parameter controlling the peak value of the hysteresis curve; d v is the strength degradation rate; d η is the stiffness degradation rate; z 10 is a parameter controlling the total slip amount; q is a parameter controlling the initial position of the pinch effect; p is a parameter controlling the pinch slope; y0 is a parameter controlling the pinch amplitude; d ψ is a parameter controlling the pinch rate; l is a parameter controlling the magnitude relationship between the total pinch amount and the pinch rate;

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

[0076] S3, randomly initialize particle positions x N×D and particle velocities v N×D in the search space by using a Logistic-Tent composite chaotic mapping:

[0077]

[0078] wherein, 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 Dth dimension in the particle i; is the initial value of the velocity of the Dth dimension in the particle i; is the initial value of the position of the jth dimension in the particle i; is the initial value of the velocity of the jth dimension in the particle i; X ij is a chaotic sequence value of the jth dimension in the particle i in the interval [0, 1]; is the upper limit of the position searched in dimension j; is the lower limit of the position searched in dimension j; is the upper limit of the velocity searched in dimension j; is the lower limit of the velocity searched in dimension j; X (i+1)jis the chaotic sequence value of the jth dimension in the particle i+1 in the interval [0,1]; r is a control parameter;

[0079] S4, calculate the fitness value of each particle, and initialize the individual historical optimal position p of each particle according to the fitness value of each particle N×D and the individual historical optimal value pbest N×1 , and 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 based on the updated inertia weight w, the cognitive parameter c1 and the social parameter c2, update the particle speed and the particle position based on the boundary constraint;

[0081] S6, update the individual historical optimal position p of each particle N×D and the individual historical optimal value pbest N×1 , and 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 of the particle population based on the greedy algorithm update evaluation strategy;

[0083] S8, judge whether the precondition of the embedded mode search algorithm is met, if yes, go to step S9, otherwise, return to step S5; the precondition of the embedded mode search algorithm is that the current iteration step t>T / 2, and the global historical optimal value gbest 1×1 (t) update of the particle population has not changed for 5 consecutive iterations;

[0084] S9, take the global historical optimal position g 1×D (t) update of the particle population as the iteration initial value K 1×D (0), and update the global historical optimal position and the global historical optimal value of the particle population by the mode search algorithm;

[0085] S10, judge whether the preset maximum iteration step T is met, if yes, output the final position g 1×D (T) final and the final value gbest 1×1 (T) of the global historical optimal of the entire particle population when iteration is T steps.final , otherwise, return to S5 and continue iteration.

[0086] In this embodiment, the corresponding boundary constraints are given for the hysteresis parameters under different failure modes (bending failure, bending-shear failure, and shear failure). In order to generate a uniformly distributed search space, the position x of the particle swarm is randomly initialized using the Logistic-Tent composite chaotic map. N×D and speed v N×D .

[0087] The fitness value of each particle in S4 is:

[0088]

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

[0090] The fitness function provides the particle swarm with an initial collaborative search direction and individual experience retention. An error function is also introduced as the fitness function, and an efficient optimization algorithm is used to quickly converge to the optimal hysteresis parameter combination, minimizing the error between the predicted and measured restoring force values ​​and reducing computational time.

[0091] The first-order explicit differential equations of the BWBN model are iteratively solved using the fourth-order Runge-Kutta method 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 equation system of the BWBN model; For nth t Under each loading step, input the time corresponding to the normalized lateral displacement μ; for The state vector at the moment, including the normalized hysteresis displacement μ z and normalized cumulative hysteresis energy ε n ; h is the time step; k1 is the time Status is The slope of the time; k2 is the time Status is the slope at time t; k3 is the slope at time t the state at time t is the slope at time t; k4 is the slope at time t the state at time t is the slope at time t.

[0094] In this embodiment, the "ODE15s" solver in the MATLAB platform is called to solve the differential equation set by using the fourth-order Runge-Kutta iterative method with high calculation accuracy. The method is based on the Taylor formula and uses the slope to approximate the differential. The derivative values (i.e., the slope) of multiple intermediate points are estimated within one time step, and then the weighted average of these slopes is used to approximate the real change of the function within the step, which is used as the basis for the next point.

[0095] The expression for updating the particle velocity and particle position in S5 is:

[0096]

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

[0098] In this embodiment, The right side of the equation consists of three components: the first reflects the inertia of particle motion, i.e., the tendency of particles to maintain their previous iterative search speed; the second reflects the ability of individual particles to learn from their past experiences, i.e., the tendency of particles to converge towards their individual historical optimal positions; and the third reflects the ability of particles to acquire social information through collaboration and experience sharing, i.e., the tendency of particles to converge towards the global historical optimal position of the entire population. r1 and r2 are both uniformly distributed random numbers in the range [0, 1] to enhance the randomness of the particle search.

[0099] In S6, the individual historical optimal position p of each particle is updated N×D and individual historical optimal value pbest N×1 And the global historical optimal position g 1×D and the global historical optimal value gbest 1×1 The expression is:

[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 best historical 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 updates in S6 guide the particle population to move towards a better search space, improve the convergence efficiency and accuracy of the algorithm, avoid blind dispersion, and thus form an effective balance between global "exploration" and local "exploitation".

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

[0104]

[0105] σ χ =1

[0106] in, is the updated position of particle i after Levy flight when iterating to step t; g 1×D (t) is the global historical optimal position when iterating to step t; for 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 in the range of [0, 1]; is the dot product; Levy(ρ) is the random search path, which obeys the Levy distribution with parameter ρ; s is the random step size; ρ is a parameter with a value range of [1,3]; κ and χ are both random step size related parameters and obey the standard normal distribution; and are variances; Γ is the gamma function.

[0107] In this embodiment, the Levy Flight strategy is introduced to generate random steps through the random walk mechanism, change the position of each particle in the current iteration step, and then update the state of each particle to x. N×D (t) new Subsequently, an update evaluation strategy based on a greedy algorithm is adopted, and only the update value that can improve the global historical optimal value of the current iteration step is accepted, where the superscript represents the dimension of the generator matrix;

[0108] It should be noted that the Lévy flight strategy is an efficient random search strategy that alternates short-distance walks and occasional longer-distance walks that obey the Lévy 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 capability. It is widely present in nature. For example, similar behaviors can be observed in animals and insects foraging for food and pollen dissemination.

[0109] Considering that the Levy flight strategy cannot guarantee that the updated particles can improve the global historical optimal value of the current iteration step, an update evaluation strategy based on a greedy algorithm is adopted. The fitness value of each particle after the Levy flight update is calculated and compared with the global historical optimal value gbest of the entire population in the current iteration step. 1×1(t) to perform a comparison analysis, according to which it is determined whether to accept the updated particle, thereby avoiding blind movement of the particle in the search space, and improving the convergence and stability of the algorithm.

[0110] The introduction of the Levy Flight strategy has significant randomness and jumping, and has wide search ability. A new search path and area are provided through a random walk mechanism to realize the position update of each particle. This process increases the diversity of the particle population, so that the particle has the opportunity to jump out of the current local optimal solution, thereby improving the possibility of finding a better solution.

[0111] The S9 is specifically:

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

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

[0114] S903, a detection movement process is performed, specifically:

[0115] For the current search direction e E , 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 are calculated. 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 Ethe point with a small fitness value in the current search direction as a new search point, otherwise, moving the current search point L 1×D (E-1) as an initial search point of the next search direction, i.e., setting L 1×D (E) = L 1×D (E-1);

[0116] S904, determining whether E = R is satisfied, if yes, going to step S905, otherwise, returning to S903 to perform a search movement process on the next search direction;

[0117] S905, if fitness[L 1×D (R)] < fitness[K 1×D (M)], going to step S906, otherwise, going to step S907; L 1×D (R) is a search point after performing the search movement; K 1×D (M) is a base point of the mode movement in the Mth iteration;

[0118] S906, performing a mode movement process, specifically:

[0119] updating the base point K 1×D (M+1) = L 1×D (R), and updating the initial search point from the updated base point, i.e., L 1×D (0) = K 1×D (M+1) + a s [K 1×D (M+1) - K 1×D (M)], setting M = M+1, E = 1, and returning to step S903;

[0120] S907, determining whether a mode search algorithm termination condition is satisfied, if yes, outputting the current point K 1×D (M) as a final result, updating the global historical optimal position and the global historical optimal value of the particle population 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), otherwise, contracting the step size δ s = β s δ s , updating the initial search point L 1×D (0) = K 1×D (M), setting M = M+1, E = 1, and returning to step S903; the mode search algorithm termination condition is that a preset maximum iteration number MaxIteration is reached or the fitness values of K 1×D (M) and K 1×D (M-1) change by less than a threshold value TolFun or the step size δ sless than a preset allowable error TolX.

[0121] In this embodiment, in order to solve the problems of the improved PSO algorithm, such as easy falling into local optimal solution and premature convergence in the later stage, the iteration process is divided into two stages: the early global search stage and the later local search enhancement stage. Specifically, when the iteration step reaches half of the maximum iteration step T, i.e. t > T / 2, the later local search enhancement stage is entered. In this stage, the PS algorithm is embedded to strengthen the local search ability, thereby effectively avoiding the decline of search efficiency caused by excessive calculation. At the same time, in the iteration process of the later local search enhancement stage, a discrimination mechanism for detecting premature convergence of particles is introduced: gbest 1 ×1 (t-5) update = gbest 1×1 (t) update When the signs of premature convergence are detected, the mode search is performed on the updated position of the global historical optimum found by the current entire population, so as to make it jump out of the local optimal state and promote the algorithm to converge to the global optimal value.

[0122] For the particle population after the Lévy flight update, the updated position g 1×D (t) update of the global historical optimum of the entire population in the current iteration step is taken as the initial value K 1×D (0) of iteration, and the optimization solver options (including the maximum iteration number MaxIteration, the function tolerance TolFun and the allowable error TolX) are configured, and the objective function (i.e. the fitness function fitness) and the constraint conditions (including the boundary conditions u b ,l b , the equality constraints A eq ,b eq , the inequality constraints A ineq ,b ineq and the nonlinear constraints nonlcon) are defined, and 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 iteration parameters M = 1, E = 1 are set. For this, the “Patternsearch” toolbox in the MATLAB platform is called, and the two cooperative processes of probe movement (probe descent in the favorable direction) and pattern movement (movement along the favorable direction) are alternately executed, the search is gradually performed along the optimal direction of the fitness value decrease, and finally converges to the optimal position.

[0123] In this embodiment, 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 is calculated, denoted as ρp ,According to this, the correlation between the two is quantitatively judged, which serves as the key indicator for evaluating the effectiveness of the IPSO-PS algorithm;

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

[0125]

[0126] Where: F e (n t ) is the nth t Measured value of step restoring force; F m (n t ) is the nth t Step restoring force prediction value; is the mean of the measured values ​​of the restoring force; is the mean predicted value of resilience.

[0127] In mathematical statistics, Pearson correlation coefficient ρ p The closer it is to 1, the stronger the correlation between the two data sets. Usually, ρ p When the correlation is between 0.8 and 1.0, the two data sets are considered to have a strong correlation.

[0128] Example 2

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

[0130] Step 1: From the Structural Performance Database (SPD) website of the Pacific Earthquake Engineering Research Center (PEER), for each RC bridge pier with different failure modes (flexure failure, flexural-shear failure, and shear failure), randomly select 6 sets of pseudo-static reciprocating loading measured data samples, corresponding to the cross-sectional dimensions b×h or diameter d, pier height H0, and concrete strength f′. c , reinforcement ratio ρ l , stirrup ratio ρ t , axial load N A , axial pressure ratio n A and shear span ratio λ s The key parameters are detailed in the table below:

[0131] Table 1 Sample of measured data of pseudo-static reciprocating loading

[0132]

[0133]

[0134]

[0135] Subsequently, based on the MATLAB platform, the BWBN model with strength degradation, stiffness degradation and pinch effect is constructed, and the lateral displacement is input through the linear variable amplitude displacement function. In particular, in order to ensure the universality of the hysteretic parameter identification results and avoid the time-varying nature of the initial stiffness, the BWBN model and the measured hysteretic curve need to be normalized and dimensionless. To this end, the "ODE15s" solver in the MATLAB platform is called, and the fourth-order Runge-Kutta iterative method with high calculation accuracy is used to solve the differential equation set.

[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 initial inertia weight w max , the minimum initial inertia weight w min , the initial cognitive parameter c ini-1 , the initial social parameter c ini-2 , the maximum iteration step T, the maximum search position column vector x max , the minimum search position column vector x min , and the maximum search velocity column vector v max , the minimum search velocity column vector v min . Table 2 and Table 3 summarize the boundary constraint conditions and particle swarm optimization parameters of the embodiments of the present application, respectively.

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

[0138]

[0139] Table 3 Particle swarm optimization parameters

[0140]

[0141]

[0142] Further, as shown in Figure 2 and Figure 3 , the position x N×D and the velocity v N×D of the particle swarm are randomly initialized in the search space using the Logistic-Tent composite chaotic mapping.

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

[0144] Step 4: Based on the adaptive strategy, dynamically update the nonlinear inertia weight w, cognitive parameter c1 and social parameter c2 to realize the iterative update of particle velocity and position. Further, perform boundary constraint condition processing on the search space of the particle

[0145] Step 5: For each particle after iterative update, update the individual historical best position p N×D and best value pbest N×1 of each particle, and global historical best position g 1×D and best value gbest 1×1 of the whole population

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

[0147] Step 7: Judge whether the prerequisite condition of embedded pattern search algorithm (PS) is met. If the embedding condition is not met, return to step 4 to continue iteration. If the embedding condition is met, take the updated position g 1×D (t) update of the global historical best of the whole population after Levy flight update of the particle population as the iteration initial value K 1×D (0), and configure the optimization solver options (including maximum iteration number MaxIteration = 30, function tolerance TolFun = 10 -6 and variable tolerance TolX = 10 -6 ), define the objective function (i.e. fitness function fitness) and constraint conditions (including boundary condition u b = x max , l b = x min , equality constraint A eq , b eq , and inequality constraint A ineq , b ineqand nonlinear constraint nonlcon). On this basis, the "Patternsearch" toolbox in MATLAB platform is called to use the pattern search algorithm (PS) to expand the depth of optimization and development;

[0148] The identification results of the BWBN model hysteretic parameters of the RC bridge pier under different failure modes are counted, and the specific identification results are shown in Table 4.

[0149] Table 4 Identification results of hysteretic parameters of BWBN model

[0150]

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

[0152] Further, to evaluate the identification accuracy, the fitness function convergence value of the IPSO-PS algorithm is extracted, and the error between the measured data and the BWBN hysteretic model in the peak load and the cumulative hysteretic energy is calculated, and the calculation results are shown in Table 5.

[0153] Generally, when the fitness function convergence value is less than 0.2, it is considered to meet the requirement of identification error accuracy. In the embodiment of the present application, the fitness function convergence value is less than 0.2, so the fitness function convergence value obtained meets the established accuracy requirement.

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

[0155]

[0156] For RC bridge piers under different failure modes, referring to Figures 5-7 The comparative analysis results of the hysteretic curve show that the measured hysteretic curve and the hysteretic curve based on the BWBN model have a high degree of agreement, not only can accurately represent the overall hysteretic form, but also can 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 is worth noting that since the nonlinear evolution of the RC bridge pier under the bending failure mode has more significant regularity, the identification accuracy of the IPSO-PS algorithm under the bending failure mode is optimal, and the identified hysteretic curve exhibits high consistency.

[0157] Referring toFigures 8-10 The comparative analysis of the time history curves shows that the fitting effect of the measured restoring force and the restoring force predicted based on the BWBN model is excellent throughout the loading process. Meanwhile, it can be observed that the restoring force predicted based on the BWBN model at the initial stage is lower than the measured restoring force, which is mainly due to the underestimation of the stiffness ratio α before and after yielding, so that the elastic force is insufficient at the initial small displacement stage, thereby leading to the smaller restoring force prediction value.

[0158] Referring to Table 5 and Figures 11-13 The 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 two have a high degree of coincidence, and the relative error of the positive and negative peak loads is 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 of the positive and negative displacement amplitudes, the measured peak load and the peak displacement are not synchronized, and the positive and negative peak loads are asymmetric, and the phenomenon that the measured peak load is close to the peak load based on the BWBN model but the corresponding displacement presents a significant deviation occurs.

[0159] Referring to Table 5 and Figures 14-16 The error and comparative analysis of the cumulative hysteresis energy show that the measured cumulative hysteresis energy and the cumulative hysteresis energy based on the BWBN model have basic correlation. Different failure modes have a significant influence on the energy dissipation capacity of the RC pier, and the bending failure has the highest energy dissipation capacity due to the full development of the plastic hinge, and the shear failure has the lowest energy dissipation capacity due to the brittle fracture characteristics.

[0160] The present application uses the lateral displacement difference between the two loading steps as the weight of the time proportion, and combines the actual positive and negative displacement amplitudes to solve the differential equation set, so as to truly and effectively simulate the actual loading process, and to a certain extent, to improve the disadvantages of the asymmetry of the positive and negative loading and the difference of the displacement amplitudes.

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

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

[0163] Table 6 Pearson correlation coefficient statistics

[0164]

[0165]

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

Claims

1. A hysteresis parameter identification method for the BWBN model based on improved particle swarm optimization, characterized in that: include: Obtain the measured hysteresis curves of RC bridge piers under pseudo-static reciprocating loading under different failure modes, and determine the yield load and yield displacement of the final equivalent yield point based on the skeleton curve of the measured hysteresis curves; A BWBN model with strength degradation, stiffness degradation, and pinching effects was constructed. The BWBN model and the measured hysteresis curves were normalized and dimensionless according to the yield load and yield displacement of the final equivalent yield point. Based on the normalized dimensionless results of the BWBN model, a set of first-order explicit differential equations for the BWBN model was constructed. Determine the hysteresis parameter to be identified and give the boundary constraint conditions of the hysteresis parameter to be identified; The improved particle swarm algorithm is used to obtain the optimal value of the hysteresis parameter to be identified. In each iteration of the improved particle swarm algorithm, the Levy flight strategy and pattern search algorithm are used to deeply optimize the global historical optimal position. The global historical optimal position output in the last step is used as the value of each hysteresis parameter to be identified to complete the hysteresis parameter identification of the BWBN model. The fitness function of the improved particle swarm 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, specifically: S1. According to the hysteresis parameters to be identified, a hysteresis parameter vector to be identified is formed ; S2, initialize the particle swarm optimization algorithm parameters; S3. Use Logistic-Tent composite chaotic mapping to randomly initialize particle positions in the search space and particle speed ; S4. Calculate the fitness value of each particle and initialize the individual historical optimal position of each particle according to the fitness value of each particle and individual historical optimal value And the global historical optimal position and the global historical optimal value ; S5. Dynamically update inertia weight based on adaptive strategy , cognitive parameters and social parameters , and according to the updated inertia weight , cognitive parameters and social parameters , update particle velocity and particle position based on boundary constraints; S6. Update the individual historical optimal position of each particle and individual historical optimal value And the global historical optimal position and the global historical optimal value ; S7, introduce the Levy flight strategy to update the position of each particle, and update the global historical optimal position of the particle population based on the update evaluation strategy of the greedy algorithm and the global historical optimal value ; S8, determine whether the precondition of the embedded pattern search algorithm is met, if so, go to step S9, otherwise, return to step S5; the precondition of the embedded pattern search algorithm is that the current iteration step , and the global historical optimal value of the particle population No changes were observed for 5 consecutive iterations; S9, the global historical optimal position of the particle population As the initial value of the iteration , 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 iteration steps is met If so, output iteration to The final position of the global historical optimal of the entire particle population at step and the final value , otherwise, return to S5 and continue iteration.

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

3. The hysteresis parameter identification method of the BWBN model based on the improved particle swarm optimization according to claim 1 is characterized in that: The BWBN model with strength degradation, stiffness degradation and pinching effect is constructed. According to the yield load and yield displacement of the final equivalent yield point, the BWBN model and the measured hysteresis curve are respectively normalized and dimensionless. Based on the normalized dimensionless processing results of the BWBN model, a first-order explicit differential equation system of the BWBN model is constructed, specifically: Constructing a BWBN model with strength degradation, stiffness degradation, and pinching effects: in, is the inelastic restoring force of the BWBN model; is the elastic force; is the hysteresis force; is the stiffness ratio before and after yielding; is the initial stiffness of the structure; is the relative lateral displacement; is the hysteresis displacement; for The first differential of is the function used to control the pinching effect of the hysteresis curve; is the stiffness degradation parameter; is the strength degradation parameter; It is a parameter that controls the smoothness of the hysteresis curve; is the parameter that controls the shape of the hysteresis curve; is the parameter that controls the peak value of the hysteresis curve; is the hysteresis displacement and speed Sign functions related to products; for The first-order differential of represents the velocity; is the strength degradation rate; for The accumulated hysteresis energy consumption within a certain time period; For time; is the stiffness degradation rate; Parameters to control the degree of pinching; For speed Related symbolic functions; Parameters that control the starting position of the pinching effect; is the maximum value of the hysteresis displacement; Parameters to control the pinch diffusion area; is the parameter that controls the total slip; is the parameter that controls the pinch slope; Parameters for controlling the pinching amplitude; is the parameter to control the pinching rate; It is a parameter that controls the magnitude relationship between the total amount of pinching and the pinching rate; According to the yield load and yield displacement of the final equivalent yield point, the measured hysteresis curve is normalized and dimensionless, and the normalized dimensionless processing result of the measured hysteresis curve is obtained; According to the yield load and yield displacement of the final equivalent yield point, the BWBN model is normalized and dimensionless, and the normalized dimensionless processing results of the BWBN model are obtained: in, is the normalized restoring force; is the yield load of the final equivalent yield point; is the yield displacement of the final equivalent yield point; is the normalized relative lateral displacement; is the normalized hysteresis displacement; for The first differential of is the first-order differential of the normalized hysteresis displacement; is the normalized pinching effect function; is the normalized cumulative hysteresis energy; For and Sign functions related to products; For Related symbolic functions; is the yield accumulated hysteresis energy at the final equivalent yield point; According to the normalized dimensionless processing results of the BWBN model, the first-order explicit differential equations of the BWBN model are constructed: in, is the introduced state vector; is the normalized relative lateral displacement ; is the normalized hysteresis displacement ; is the normalized cumulative hysteresis energy ; for The first differential of for The first differential of for The first differential of for The first-order differential of .

4. The hysteresis parameter identification method of the BWBN model based on the improved particle swarm optimization according to claim 1 is characterized in that: The hysteresis parameter vector to be identified The expression is: in, is the stiffness ratio before and after yielding; It is a parameter that controls the smoothness of the hysteresis curve; is the parameter that controls the shape of the hysteresis curve; is the parameter that controls the peak value of the hysteresis curve; is the strength degradation rate; is the stiffness degradation rate; is the parameter that controls the total slip; Parameters that control the starting position of the pinching effect; is the parameter that controls the pinch slope; Parameters for controlling the pinching amplitude; is the parameter to control the pinching rate; It is a parameter that controls the magnitude relationship between the total amount of pinching and the pinching rate; The particle swarm optimization algorithm parameters include particle swarm size N , Dimension of hysteresis parameter to be identified , maximum inertia weight , minimum inertia weight , cognitive parameters , social parameters , maximum number of iterations T , search position maximum column vector , search position minimum column vector , search speed maximum column vector and search speed minimum column vector ; The dimension of the hysteresis parameter to be identified is equal to the number of hysteresis parameters to be identified; The initialization particle position and particle speed The expression is: in, is the initial position of the particle swarm; is the initial velocity of the particle swarm; For particles Middle The initial value of the position of the dimension; For particles Middle The initial value of the velocity in each dimension; For particles Middle The initial value of the position of the dimension; For particles Middle The initial value of the velocity in each dimension; For particles Middle Dimensions in Chaotic sequence value within the interval; Dimension Upper limit of the search position; Dimension The lower limit of the search position; Dimension The upper limit of search speed; Dimension The lower limit of search speed; For particles Middle Dimensions in Chaotic sequence value within the interval; is the control parameter.

5. The hysteresis parameter identification method of the BWBN model based on the improved particle swarm optimization according to claim 4 is characterized in that: The fitness value of each particle in S4 is: in, For particles The fitness value of For particles location; is the load step index; is the total number of loading steps; For the The measured value of the restoring force of the step; For particles The calculated The predicted value of the restoring force of the step.

6. The hysteresis parameter identification method of the BWBN model based on the improved particle swarm optimization according to claim 5 is 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 value of the restoring force. The calculation formula of the fourth-order Runge-Kutta method is: in, is the first-order explicit differential equation system of the BWBN model; For the Under each loading step, the normalized lateral displacement is input corresponding moments; for The state vector at time t, including the normalized hysteresis displacement and normalized cumulative hysteresis energy ; is the time step; For time , the status is The slope when For time , the status is The slope when For time , the status is The slope when For time , the status is The slope when .

7. The hysteresis parameter identification method of the BWBN model based on the improved particle swarm optimization according to claim 4 is characterized in that: The expressions for updating the particle velocity and particle position in S5 are: in, Iterate to When the particle Middle The speed of the dimension; Iterate to When the particle Middle The speed iteration value of each dimension; is the current iteration number, ; Iterate to When the particle Middle The speed of the dimension; and Both Uniformly distributed random numbers within; Iterate to When the particle Middle The individual's historical optimal position in each dimension; Iterate to When the particle Middle The location of the dimension; Iterate to The global historical optimal position at step time; Iterate to When the particle Middle The location of the dimension; Iterate to When the particle Middle Position iteration value of the dimension; Iterate to When the particle Middle The location of the dimension; is the balance factor; is the initial cognitive parameter; are the initial social parameters.

8. The hysteresis parameter identification method of the BWBN model based on improved particle swarm optimization according to claim 4 is characterized in that: In S6, the individual historical optimal position of each particle is updated and individual historical optimal value And the global historical optimal position and the global historical optimal value The expression is: in, Iterate to At step , the individual historical optimal position of each particle; Iterate to When the particle The individual historical optimal position of Iterate to At step , the individual historical optimal value of each particle; Iterate to When the particle The individual historical optimal value of Iterate to When the particle location; Iterate to When the particle The fitness value of Iterate to When the particle The individual historical optimal value of Iterate to When the particle The individual historical optimal position of Iterate to The global historical optimal position at step time; Iterate to The global historical optimal value at step time; Iterate to The global historical optimal position at step time; Iterate to The global historical optimal value at step .

9. The hysteresis parameter identification method of the BWBN model based on the improved particle swarm optimization according to claim 4 is characterized in that: In step S7, the global historical optimal position of the particle population is updated and the global historical optimal value The expression is: in, Iterate to Step Particle Updated location via Levi Flight; Iterate to The global historical optimal position at step time; for The corresponding fitness value; Iterate to The global historical optimal value at step time; Iterate to When the particle location; for Step size control factor within the range; is the dot product; is a random search path, subject to the parameter The Levy distribution; is a random step size; The value range is Parameters between; and All are random step-related parameters and obey the standard normal distribution; and All are variances; is the gamma function.

10. The hysteresis parameter identification method of the BWBN model based on improved particle swarm optimization according to claim 7, characterized in that: The S9 is specifically: S901, the global historical optimal position of the particle population As a base point and initial detection point ; S902, will The standard basis vectors of the coordinate axes As a preset search direction set, the pattern search algorithm parameters are initialized at the same time; the pattern search algorithm parameters include step size , acceleration factor , shrinkage factor , allowable error , iteration parameters and search direction index ; S903: Execute the detection movement process, specifically: For the current search direction , calculate the neighborhood and The fitness value at two detection points, if and If there is a point whose fitness value is less than the fitness value of the current detection point, and The point with the smallest fitness value is used as the new detection point, otherwise, the current detection point As the initial detection point for the next search direction, ; S904: Determine whether If yes, proceed to step S905, otherwise, return to S903 to perform the detection movement process in the next search direction; S905, if , go to step S906, otherwise go to step S907; To perform the detection point after the detection movement; For the The base point of the execution mode movement of the iteration; S906: Execute the mode shift process, specifically: Update base point , and starting from the updated base point, the initial detection point is updated, that is, , set , , and returns to step S903; S907, determine whether the termination condition of the pattern search algorithm is met, if so, output the current point As a final result, the final result based on the output and The corresponding fitness value , update the global historical optimal position and global historical optimal value of the particle population, otherwise, shrink the step size , update the initial detection point , set , , return to step S903; the termination condition of the pattern search algorithm is to reach the preset maximum number of iterations or and The change in fitness value is less than the threshold or step length Smaller than the preset allowable error .

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