CN112231821A - Reliability analysis-based basic seismic isolation structure system optimization method - Google Patents

Reliability analysis-based basic seismic isolation structure system optimization method Download PDF

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CN112231821A
CN112231821A CN202011345724.1A CN202011345724A CN112231821A CN 112231821 A CN112231821 A CN 112231821A CN 202011345724 A CN202011345724 A CN 202011345724A CN 112231821 A CN112231821 A CN 112231821A
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彭勇波
马阳颖
罗程睿
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Abstract

The invention relates to a method for optimizing a basic shock insulation structure system based on reliability analysis, which comprises the following steps: 1) calculating the random seismic response of the basic seismic isolation structure under the action of the earthquake according to the probability density evolution theory; 2) converting the first-time exceeding reliability solving problem into a probability density function solving problem of equivalent extreme value variables by using an equivalent extreme value event criterion, and then solving a corresponding probability density function by using a probability density evolution theory so as to obtain the dynamic reliability of the whole structure; 3) determining key design parameters in a resilience model of the seismic isolation support through variance sensitivity analysis; 4) and (3) constructing a probability criterion taking the integral reliability of the basic shock-isolation structure system as a constraint and a target, and performing parameter optimization on key design parameters by adopting a genetic algorithm so as to optimize the basic shock-isolation structure system. Compared with the prior art, the method has the advantages of more conveniently and quickly acquiring the calculation result with higher precision, reducing the calculation amount and the like.

Description

Reliability analysis-based basic seismic isolation structure system optimization method
Technical Field
The invention relates to the field of parameter optimization of a basic shock insulation structure system, in particular to a method for optimizing the basic shock insulation structure system based on reliability analysis.
Background
Due to uncertainty of initial conditions and basic parameters (such as physical parameters, mechanical parameters, geometric parameters and the like) of the structure and strong randomness of engineering excitation (such as earthquake, wind, sea wave and the like) in the aspects of time, space or strength, the traditional structural vibration control design may have serious safety problems. For example, the administrative building of the Tokyo technology university with viscous dampers installed in the major earthquake of the east of Japan is damaged in 2011, and the rubber support shock insulation cushion of a certain overhead bridge part of Turkey earthquake is damaged in 1999. Therefore, how to ensure the safety and reliability of the structural vibration control system is a subject with practical challenges. However, the traditional reliability analysis-based basic seismic isolation structure system optimization method has the challenges of poor theoretical solution expansibility, large calculation workload, low precision (reliability solution depends on artificial assumption of a cross-threshold process), and the like.
With the development of Reliability theory, Reliability-based Design Optimization (RBDO for short) becomes an important means for Design in the field of structure control. Spencer et al performed earlier research on reliability-based structural control, and later extended to basic seismic isolation systems, energy dissipation systems, feedback control systems, intelligent control systems, and optimal control under the reliability-based generalized probability density evolution theoretical framework. However, in the existing RBDO research and application for optimizing a base isolation system, a spectral expression method is generally adopted to carry out seismic oscillation random process modeling, and then the first exceeding failure probability is calculated based on random sampling, and the process of obtaining a higher-precision calculation result by the method is complicated. In addition, the number of optimization parameters involved in the RBDO is typically large, which tends to result in an overall under-optimization of the fabric control system.
Disclosure of Invention
The invention aims to provide a method for optimizing a basic seismic isolation structure system based on reliability analysis, aiming at overcoming the defect of high cost of obtaining a higher-precision calculation result in the prior art.
The purpose of the invention can be realized by the following technical scheme:
a method for optimizing a basic seismic isolation structure system based on reliability analysis comprises the following steps:
and a reliability calculation step: calculating the random seismic response of a basic seismic isolation structure system through a motion control equation to be used as a random variable; according to an equivalent extreme value event criterion, constructing a dynamic reliability calculation flow of a basic shock insulation structure system based on the structure response physical quantity of the concerned structure response physical quantity; according to the dynamic reliability calculation flow, combining the motion control equation, adopting a probability density evolution theory and adopting a probability density evolution equation to solve, and calculating the overall reliability of a basic shock insulation structure system;
optimizing parameters of a basic shock insulation structure system: establishing a probability criterion based on constraint and target of the overall reliability of a basic shock insulation structure system, solving the overall reliability through the reliability calculation step, and performing parameter optimization on each design parameter of the basic shock insulation structure system by adopting a genetic algorithm according to the probability criterion;
optimizing a base isolation structure system: and optimizing the basic shock insulation structure system according to the optimized design parameters.
Further, in the reliability calculation step, the dynamic reliability calculation process specifically includes:
s101: according to the failure mode of the basic shock insulation structure system, constructing a plurality of random events of the basic shock insulation structure system based on the concerned structure response physical quantity;
s102: constructing equivalent extreme events of each random event according to the plurality of random events;
s103: constructing a virtual random process, and acquiring a generalized probability density evolution equation of a basic shock insulation structure system so as to obtain a probability density function of an equivalent extreme value event;
s104: and calculating the power reliability according to the probability density function.
Further, in the reliability calculation step, the calculation of the overall reliability of the base-isolated structural system includes the following steps:
s201: according to the failure mode of the basic shock insulation structure system, constructing a plurality of random events of the basic shock insulation structure system based on the concerned structure response physical quantity, wherein each random event comprises a random vector and time;
s202: obtaining a representative point set in a sample domain of the random vector;
s203: calculating a random variable of an equivalent extreme event aiming at a certain sample point in the representative point set, and constructing a speed expression of the virtual random process;
s204: substituting the velocity expression of the virtual random process obtained in the step S203 into the generalized probability density evolution equation, and solving the generalized probability density evolution equation through a finite element difference method to obtain a joint probability density function;
s205: repeatedly executing the step S203 to the step S204 until each sample point in the representative point set is traversed, and acquiring a joint probability density function of each sample point;
s206: accumulating and summing the combined probability density function of each sample point to obtain a probability density function of the response physical quantity of the structure concerned;
s207: and calculating the overall reliability of the basic seismic isolation structure system according to the probability density function of the concerned structure response physical quantity acquired in the step S206.
Further, the expression of the generalized probability density evolution equation is:
Figure BDA0002799859210000031
Figure BDA0002799859210000032
Figure BDA0002799859210000033
in the formula, thetaqIs the qth representative point, and tau is the generalized timeY is the physical quantity of the structure response of interest, pYΘ(y,θqτ) is the joint probability density function of the probability conservative system (Y (τ), Θ),
Figure BDA0002799859210000034
velocity expression, Z, for a pseudo-random processeq(θqT) is the equivalent extremum event of the qth random vector, T is the duration corresponding to Z (-) and ZBiFor random events { Zi(Θ, t) } safety threshold, { Zi(Θ, t) } is the ith random event, and m is the number of random events.
Further, the calculation expression of the probability density function of the structure of interest responding to the physical quantity is:
Figure BDA0002799859210000035
in the formula, nptIs the total number of representative points.
Further, the calculation expression of the dynamic reliability is as follows:
Figure BDA0002799859210000036
wherein R (t) is the calculation result of the overall reliability.
Further, the method for optimizing the base-isolated structural system further comprises the following steps:
determining key design parameters: calculating the total effect index of each random input variable of the basic seismic isolation structure system through variance sensitivity analysis, and taking the partial random input variable with the highest total effect index as a key design parameter; the total effect index comprises the individual contribution of a certain random input variable to the corresponding variance of the structure and the cross contribution of the random input variable and other random input variables;
and in the step of optimizing parameters of the basic shock insulation structure system, the parameters of the key design parameters are optimized.
Further, in the step of determining the key design parameter, the calculation expression of the total effect index of the random input variable is as follows:
Figure BDA0002799859210000041
Figure BDA0002799859210000042
Figure BDA0002799859210000043
Figure BDA0002799859210000044
Figure BDA0002799859210000045
Figure BDA0002799859210000046
in the formula (I), the compound is shown in the specification,
Figure BDA0002799859210000047
is an indicator of the total effect of the random input variable i,
Figure BDA0002799859210000048
to remove XiCross-contributions of other random input variables to the mean of the structural response,
Figure BDA0002799859210000049
to remove XiCross-contribution of other random input variables to the variance of the structural response, E·(. is.) the conditional expectation operator, Var (. is.) the variance of the structural response, Z is the structural response, Z ═ f (X), X is the vector of n random input variables, i and j are the serial numbers of the random input variables,Xiis a vector of a random input variable i, Xi∈[0,1],i＝1,2,...,n，Vi,Vi,j,…,V1,2,...,nVariance of structural response, X, contributed for each random input variable～iRemoving X from all random input variablesiThe vector of (a) is determined,
Figure BDA00027998592100000410
is Xi、XjCross-contributions to the structural response variance.
Further, the total effect index is calculated by adopting a quasi-Monte Carlo simulation method, wherein the quasi-Monte Carlo simulation method comprises the following steps:
s301: acquiring N random events based on the concerned structure response physical quantity according to the failure mode of the basic shock insulation structure system, and generating an Nx 2N sample matrix, wherein each row is a 2N-dimensional sample point in the hyperspace;
s302: and taking the first n columns of the sample matrix as a matrix A, and taking the rest n columns as a matrix B. This gives independent samples of N sample points in two N-dimensional unit hypercubes;
s303: building N N x N matrices
Figure BDA00027998592100000411
Matrix array
Figure BDA00027998592100000412
The value of the ith column in the matrix B is the value of the ith column in the matrix B, and the rest values are the same as the matrix A;
s304: the matrix A, the matrix B and N matrixes form N (N +2) sample points, and the structural response functions are substituted into the sample points to give N (N +2) structural response values, namely f (A), f (B) and
Figure BDA00027998592100000413
s305: estimating the total effect indicator using:
Figure BDA00027998592100000414
Figure BDA00027998592100000415
further, in the step of optimizing parameters of the basic seismic isolation structure system, the step of optimizing parameters of the key design parameters by adopting a genetic algorithm according to the probability criterion specifically comprises the following steps:
s401: constructing an IMB model of the basic shock insulation structure system, determining the parameter range of the IMB model, and randomly generating an initial population;
s402: taking the overall reliability calculated in the reliability calculation step as the fitness of the individual, and calculating the fitness of each individual in the population;
s403: selecting a father and a mother which participate in reproduction according to the fitness of each individual, wherein the selection principle is that the individuals with higher fitness are more likely to be selected;
s404: performing genetic operation on the selected parents and the parents, wherein the genetic operation comprises copying genes of the parents and the parents, and generating filial generations by adopting operators such as crossover, mutation and the like;
s405: and judging whether a preset algorithm termination judgment condition is met or not according to the calculation result of the individual fitness, and determining the optimal parameters of the IMB model.
Compared with the prior art, the invention has the following advantages:
(1) the method is based on the dynamic reliability analysis of the equivalent extreme event criterion, converts the first-time exceeding reliability solving problem into the probability density function solving problem of the equivalent extreme variable, and solves the corresponding probability density function by using the probability density evolution theory to obtain the integral reliability of the structure; the calculation process of the scheme can more conveniently and quickly obtain a calculation result with higher precision; and then, design parameters of the shock insulation structure are optimized through a genetic algorithm, and the method is stable and reliable and is suitable for reliability optimization design of a general basic shock insulation structure system.
(2) The invention further performs dimension reduction of the design parameters of the shock insulation support through variance sensitivity analysis, so that the genetic algorithm only needs to perform parameter optimization on the key design parameters, the calculated amount is reduced, and the reliability of the overall parameter optimization result of the basic shock insulation structure system can be ensured.
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FIG. 1 is a block diagram of a method for optimizing a base-isolated architecture based on reliability analysis;
FIG. 2 is a flow chart of reliability optimization of an embedded magnet type sliding vibration isolation structure system (IMB) based on a genetic algorithm;
FIG. 3 is a schematic diagram of a probability density function of equivalent extreme displacement of a built-in magnet type sliding seismic isolation layer before optimization;
FIG. 4 is a schematic diagram of a probability distribution function of equivalent extreme value displacement of the built-in magnet type sliding seismic isolation layer before optimization;
FIG. 5 is a schematic diagram of a first time-course change of parameters of a built-in magnet type sliding seismic isolation layer with a total effect index ranking of the first three under sinusoidal displacement;
FIG. 6 is a schematic diagram of a second time-course variation of parameters of a built-in magnet type sliding seismic isolation layer with a total effect index ranking of the first three under sinusoidal displacement;
FIG. 7 is a schematic diagram of a probability density function for optimizing the displacement of an equivalent extreme value of a postposition magnet type sliding shock insulation layer;
FIG. 8 is a schematic diagram of a probability distribution function for optimizing the equivalent extreme displacement of the postposition magnet type sliding seismic isolation layer;
in the figure, 0.11g represents a frequently encountered earthquake, 0.2g represents a design earthquake, 0.51g represents a rarely encountered earthquake, PDF represents a probability density function, CDF represents a probability distribution function, Displacement represents equivalent extreme Displacement of seismic isolation layers, Random Variable represents a Random input Variable, and Time represents Time.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
Example 1
The embodiment provides a method for optimizing a base isolation structure system based on reliability analysis, which comprises the following steps:
and a reliability calculation step: calculating the random seismic response of a basic seismic isolation structure system through a kinetic equation to serve as a random variable; according to an equivalent extreme value event criterion, constructing a dynamic reliability calculation flow of a basic shock insulation structure system based on the structure response physical quantity of the concerned structure response physical quantity; according to the dynamic reliability calculation flow, combining the motion control equation, adopting a probability density evolution theory and adopting a probability density evolution equation to solve, and calculating the overall reliability of a basic shock insulation structure system;
optimizing parameters of a basic shock insulation structure system: establishing a probability criterion based on constraint and target of the overall reliability of a basic shock insulation structure system, solving the overall reliability through the reliability calculation step, and performing parameter optimization on each design parameter of the basic shock insulation structure system by adopting a genetic algorithm according to the probability criterion;
optimizing a base isolation structure system: and optimizing the basic shock insulation structure system according to the optimized design parameters.
In the reliability calculation step, the dynamic reliability calculation process specifically comprises:
s101: according to the failure mode of the basic shock insulation structure system, constructing a plurality of random events of the basic shock insulation structure system based on the concerned structure response physical quantity;
s102: constructing equivalent extreme events of each random event according to the plurality of random events;
s103: constructing a virtual random process, and acquiring a generalized probability density evolution equation of a basic shock insulation structure system so as to obtain a probability density function of an equivalent extreme value event;
s104: and calculating the power reliability according to the probability density function.
In the reliability calculation step, the calculation of the overall reliability of the base isolation structure system comprises the following steps:
s201: according to the failure mode of the basic shock insulation structure system, constructing a plurality of random events of the basic shock insulation structure system based on the concerned structure response physical quantity, wherein each random event comprises a random vector and time;
s202: obtaining a representative point set in a sample domain of the random vector;
s203: calculating a random variable of an equivalent extreme event aiming at a certain sample point in the representative point set, and constructing a speed expression of the virtual random process;
s204: substituting the velocity expression of the virtual random process obtained in the step S203 into the generalized probability density evolution equation, and solving the generalized probability density evolution equation through a finite element difference method to obtain a joint probability density function;
s205: repeatedly executing the step S203 to the step S204 until each sample point in the representative point set is traversed, and acquiring a joint probability density function of each sample point;
s206: accumulating and summing the combined probability density function of each sample point to obtain a probability density function of the response physical quantity of the structure concerned;
s207: and calculating the overall reliability of the basic seismic isolation structure system according to the probability density function of the concerned structure response physical quantity acquired in the step S206.
The generalized probability density evolution equation has the expression:
Figure BDA0002799859210000071
Figure BDA0002799859210000072
Figure BDA0002799859210000073
in the formula, thetaqIs the q-th representative point, and τ isGeneralized time, y being the physical quantity of response of the structure of interest, pYΘ(y,θqτ) is the joint probability density function of the probability conservative system (Y (τ), Θ),
Figure BDA0002799859210000074
velocity expression, Z, for a pseudo-random processeq(θqT) is the equivalent extremum event of the qth random vector, T is the duration corresponding to Z (-) and ZBiFor random events { Zi(Θ, t) } safety threshold, { Zi(Θ, t) } is the ith random event, and m is the number of random events.
The calculation expression of the probability density function of the concerned structure response physical quantity is as follows:
Figure BDA0002799859210000075
in the formula, nptIs the total number of representative points.
The calculation expression of the power reliability is as follows:
Figure BDA0002799859210000081
wherein R (t) is the calculation result of the overall reliability.
As a preferred embodiment, the method for optimizing a base-isolated structure system further includes:
determining key design parameters: calculating the total effect index of each random input variable of the basic seismic isolation structure system through variance sensitivity analysis, and taking the partial random input variable with the highest total effect index as a key design parameter; the total effect index comprises the individual contribution of a certain random input variable to the corresponding variance of the structure and the cross contribution of the random input variable and other random input variables;
and in the step of optimizing parameters of the basic shock insulation structure system, the parameters of the key design parameters are optimized.
In the step of determining the key design parameter, the calculation expression of the total effect index of the random input variable is as follows:
Figure BDA0002799859210000082
Figure BDA0002799859210000083
Figure BDA0002799859210000084
Figure BDA0002799859210000085
Figure BDA0002799859210000086
Figure BDA0002799859210000087
in the formula (I), the compound is shown in the specification,
Figure BDA0002799859210000088
is an indicator of the total effect of the random input variable i,
Figure BDA0002799859210000089
to remove XiCross-contributions of other random input variables to the mean of the structural response,
Figure BDA00027998592100000810
to remove XiCross-contribution of other random input variables to the variance of the structural response, E·(. is. the conditional expectation operator), Var. the variance of the structural response, Z is the structural response, Z ═ f (X), X is the vector of n random input variables, i and j are the serial numbers of the random input variables, X is the variance of the structural response, andiis a vector of a random input variable i, Xi∈[0,1],i＝1,2,...,n，Vi,Vi,j,…,V1,2,...,nVariance of structural response, X, contributed for each random input variable～iRemoving X from all random input variablesiThe vector of (a) is determined,
Figure BDA00027998592100000811
is Xi、XjCross-contributions to the structural response variance.
Calculating the total effect index by adopting a quasi-Monte Carlo simulation method, wherein the quasi-Monte Carlo simulation method comprises the following steps:
s301: acquiring N random events based on the concerned structure response physical quantity according to the failure mode of the basic shock insulation structure system, and generating an Nx 2N sample matrix, wherein each row is a 2N-dimensional sample point in the hyperspace;
s302: and taking the first n columns of the sample matrix as a matrix A, and taking the rest n columns as a matrix B. This gives independent samples of N sample points in two N-dimensional unit hypercubes;
s303: building N N x N matrices
Figure BDA0002799859210000091
Matrix array
Figure BDA0002799859210000092
The value of the ith column in the matrix B is the value of the ith column in the matrix B, and the rest values are the same as the matrix A;
s304: the matrix A, the matrix B and N matrixes form N (N +2) sample points, and the structural response functions are substituted into the sample points to give N (N +2) structural response values, namely f (A), f (B) and
Figure BDA0002799859210000093
s305: estimating the total effect indicator using:
Figure BDA0002799859210000094
Figure BDA0002799859210000095
in the step of optimizing parameters of the basic seismic isolation structure system, the step of optimizing parameters of the key design parameters by adopting a genetic algorithm according to the probability criterion specifically comprises the following steps:
s401: constructing an IMB model of the basic shock insulation structure system, determining the parameter range of the IMB model, and randomly generating an initial population;
s402: taking the overall reliability calculated in the reliability calculation step as the fitness of the individual, and calculating the fitness of each individual in the population;
s403: selecting a father and a mother which participate in reproduction according to the fitness of each individual, wherein the selection principle is that the individuals with higher fitness are more likely to be selected;
s404: performing genetic operation on the selected parents and the parents, wherein the genetic operation comprises copying genes of the parents and the parents, and generating filial generations by adopting operators such as crossover, mutation and the like;
s405: and judging whether a preset algorithm termination judgment condition is met or not according to the calculation result of the individual fitness, and determining the optimal parameters of the IMB model.
The above two preferred embodiments are combined to obtain an optimal embodiment, and the following describes the process and implementation results of the optimal embodiment in detail.
The reliability optimization design method of the base isolation structure system is shown in a flow chart 1 and comprises the following steps:
1) and according to a basic seismic isolation structure system, performing random seismic response analysis and overall reliability evaluation on the n-degree-of-freedom seismic isolation structure model under the action of random seismic motion according to a probability density evolution theory and an equivalent extreme value event criterion.
2) And carrying out sensitivity analysis on the resilience parameter of the isolation bearing by adopting a variance sensitivity analysis method to obtain a key parameter in the resilience model of the isolation bearing.
3) And obtaining the optimal solution of the key parameters by adopting a genetic algorithm, and carrying out the optimal design of a basic shock insulation structure system based on the reliability.
The variance sensitivity analysis is a global sensitivity analysis method. Within the probabilistic framework, it decomposes the variance of the structural response into random input variables and their cross terms. And introducing a total effect index to describe the individual contribution of the structural response variance and the cross contribution of the structural response variance and other variables, and calculating the index by adopting a quasi-Monte Carlo simulation method.
The genetic algorithm is a calculation method for obtaining a high-precision optimal solution by simulating biological evolution such as mutation, intersection and selection. The method optimizes the sensitive parameters of the vibration isolation support by using GA in Optimization Tool carried by Matlab program, and carries out reliability Optimization design by using a built-in magnet type sliding vibration isolation structure system as an example.
The specific description is as follows:
1. dynamic reliability analysis based on equivalence extremum event criterion
The motion control equation of the n layers of basic shock insulation structure concentrated mass models under the action of the earthquake is as follows:
Figure BDA0002799859210000101
Figure BDA0002799859210000102
Figure BDA0002799859210000103
Figure BDA0002799859210000104
in the formula, miIs the superstructure layer i mass, i ═ 1,2,3,. n; m isbThe quality of the shock insulation layer; c. CiAnd kiDamping coefficient and rigidity of the ith layer are respectively; fIMBRestoring force of the built-in magnet type sliding shock insulation layer; x is the number ofiDisplacement of the ith layer relative to the seismic isolation layer; x is the number ofbDisplacement of the seismic isolation layer relative to the ground; m is a mass matrix of a basic shock insulation structure;
Figure BDA0002799859210000105
the restoring force of the base isolation structure; x is the sum of the total weight of the components,
Figure BDA0002799859210000106
respectively the displacement and the speed of the base shock insulation structure; t is time;
Figure BDA0002799859210000107
acceleration of the base isolation structure;
Figure BDA0002799859210000108
is a random earthquake motion acceleration function, and theta is a random vector related to earthquake ground motion; i is a column vector with element 1.
In M, the horizontal ellipses represent 0, and the diagonal ellipses represent MnThe positive integer n is an incremental change with a tolerance of 1 from 2, and the vertical ellipsis in F is a formula
Figure BDA0002799859210000109
The positive integer n is increased from 2 by a tolerance of 1, and the vertical ellipses in X represent the formula Xn+xbThe positive middle integer n varies from 2 with an increasing tolerance of 1.
Structural dynamic reliability function:
Figure BDA0002799859210000111
in the formula, Pr {. is a probability operator of the random event; z (Θ, t) is a random event in which the structure of interest responds to physical quantities (e.g., stress, internal force, and deflection); omegasIs a safe area; t is the duration corresponding to Z (-) toAnd (3) removing the solvent.
When the system has a plurality of failure modes, the power reliability can be expressed as:
Figure BDA0002799859210000112
in the formula, m is the number of random events; { zBiIs a random event { Z }i(Θ, t) }.
Constructing an equivalent extreme value:
Figure BDA0002799859210000113
then, equation (3) is equivalent to:
R(T)＝Pr{Zeq(Θ,T)≤0} (6)
formula (6) may be expressed as:
Figure BDA0002799859210000114
in the formula (I), the compound is shown in the specification,
Figure BDA0002799859210000115
is Zeq(Θ, T) and Z is a random input variable ZeqSample value of (Θ, T).
Thus, the equivalent extreme event criterion translates the power reliability problem into a one-dimensional integration problem.
In order to obtain the probability density evolution function of the extreme value distribution in the random process, a virtual random process is constructed:
Y(τ)＝ψ[Zeq(Θ,T),τ] (8)
the random process satisfies the condition:
Figure BDA0002799859210000116
in the formula, when τ is in a broad senseA (c) is added; tau is0,τcRespectively the initial and final moments of the pseudo-random process, psi [ ·]Is equal extreme event Zeq(Θ, T) and generalized time τ related functions.
Thus, Zeqτ of extremum information of (Θ, t) in random process Y (τ)cThe time of day is reflected and the random information of Y (tau) is derived from Zeq(Θ, t), the system (Y (τ), Θ) constitutes a probability-conservative system, satisfying the generalized probability density evolution equation:
Figure BDA0002799859210000117
solving equation (10) yields:
Figure BDA0002799859210000121
in the formula, omegaΘSample space, p, of random vector ΘY(y, τ) is a probability density function of the determined physical quantity y and time τ, pYΘ(Y, theta, tau) is a joint probability density function of the probability conservative system (Y (tau), theta),
Figure BDA0002799859210000122
is the velocity course of (Y (τ), Θ).
Further, τ ═ τ can be obtainedcTime ZeqProbability density function of equivalent extremum events of (Θ, t):
Figure BDA0002799859210000123
wherein Z is a random input variable ZeqSample value of (Θ, T).
Then, the power reliability formula (3) of the structure is equivalent to:
Figure BDA0002799859210000124
2. solving overall reliability by probability density evolution theory
Solving the overall reliability by using a probability density evolution theory comprises the following steps:
2-1) selecting a set of representative points in the sample domain for a random vector Θ
Figure BDA0002799859210000125
Wherein n isresFor the number of representative point sets, the assigned probability of each representative point is determined.
2-2) for each specified θqSolving the power equation to obtain the random input variable Z of the equivalent extreme value eventeq(θqT), constructing a velocity expression for a pseudo-random process
Figure BDA0002799859210000126
Zeq(θqT) can be expressed as:
Figure BDA0002799859210000127
Figure BDA0002799859210000128
can be expressed as:
Figure BDA0002799859210000129
2-3) mixing
Figure BDA00027998592100001210
Substituting into generalized probability density evolution equation to obtain combined probability density function p by finite difference methodYΘ(y,θq,τ)。
Figure BDA00027998592100001211
Obtaining a union by a finite difference methodProbability density function pYΘ(y,θq,τ)。
2-4) reacting pYΘ(y,θq,τ),q＝1,2,…,nresThe sum is accumulated to obtain a probability density function of the physical quantity of interest, namely:
Figure BDA00027998592100001212
further, the overall reliability is obtained by combining the equations (12) and (13).
Therefore, the dynamic reliability analysis based on the equivalent extreme value event criterion converts the first-time exceeding reliability solving problem into the probability density function solving problem of the equivalent extreme value variable, and solves the corresponding probability density function by utilizing the probability density evolution theory to obtain the integral reliability of the structure.
3. Variance sensitivity analysis
The variance sensitivity analysis is a global sensitivity analysis method. Within the probabilistic framework, it decomposes the variance of the structural response into random input variables and their cross terms. For a structural response function Z ═ f (X), where X is n random input variables { X ═ X1,x2,...,xnThe vector of, Z is the structural response. Furthermore, assuming that the random input variables are independently and uniformly distributed within the unit hypercube, Xi∈[0,1]1, 2.., n. And (f) (X) is subjected to high-dimensional model description, namely:
Figure BDA0002799859210000131
wherein Var (. cndot.) is the variance of the structural response; vi,Vi,j,…,V1,2,...,nThe variance of the structural response contributed for each random input variable is defined as follows
Figure BDA0002799859210000132
In the formula, E·(. is. a.) conditional expectationA seed; x～iRemoving X from all variablesi。
Figure BDA0002799859210000133
Is XiIndividual contributions to the structural response variance (averaging of contributions from other random input variables),
Figure BDA0002799859210000134
Is Xi、XjCross-contributions to the structural response variance (averaging of cross-contributions of other random input variables),
Figure BDA0002799859210000135
Is X1、X2…XnCross-contributions to the structural response variance.
Introduction of "Total Effect index" STi。STiComprises XiThe individual contributions to the structural response variance and their cross contributions with other variables, of the form:
Figure BDA0002799859210000136
in the formula (I), the compound is shown in the specification,
Figure BDA0002799859210000137
to remove XiCross-contribution (X) of other random input variables to the mean of the structural responseiThe variance of the contribution of),
Figure BDA0002799859210000138
to remove XiCross-contribution (X) of other random input variables to the variance of the structural responseiAveraging the contributions of (a).
The steps of calculating the sensitivity index using a simulated monte carlo simulation method are as follows:
(1) generating an N x 2N sample matrix, each row being a sample point in a 2N-dimensional hyperspace, which should be related to the probability distribution of the input variables;
(2) the first n columns of the matrix are taken as matrix a, and the remaining n columns are taken as matrix B. This gives independent samples of N sample points in two N-dimensional unit hypercubes;
(3) building N N x N matrices
Figure BDA0002799859210000141
Matrix array
Figure BDA0002799859210000142
The value of the ith column in the matrix B is the value of the ith column in the matrix B, and the rest values are the same as the matrix A;
(4) the matrix A, the matrix B and the N matrixes form N (N +2) sample points. By substituting the structural response function into these sample points, N (N +2) structural response values can be given, namely f (A), f (B) and
Figure BDA0002799859210000143
(5) the total effect indicator is estimated using the following equation:
Figure BDA0002799859210000144
Figure BDA0002799859210000145
the accuracy of the estimation depends on N, and the estimated value can be made to converge by increasing the number of samples N.
4. Parameter optimization based on genetic algorithm
The sensitive parameters of the vibration isolation bearing are optimized by using GA in Optimization Tool carried by Matlab program. The physical quantities concerned are the peak value of the interlayer displacement and the reliability of the displacement of the seismic isolation layer. The joint committee for international security (JCSS) stipulates "Probabilistic Model Code" that the failure probability of a structural member at moderate construction cost is 0.05, and therefore the reliability for a seismic isolation mount should be greater than 0.95. And obtaining the parameters of the shock insulation support corresponding to the optimal solution of the interlayer displacement peak value on the basis.
The probability criterion taking the response reliability of the seismic isolation structure as a constraint and a target is as follows:
Figure BDA0002799859210000146
in the formula, RdAnd RbThe interlayer displacement and the reliability of the shock insulation layer are respectively; α, β, γ are the key design parameters to optimize.
Optimization of genetic algorithms typically involves a number of iterations following random initial generation, and each iteration involves an assessment of individual fitness, defined as the reliability of the displacement between layers of the superstructure. A flow chart of parameter optimization of the built-in magnet type base-isolated structure based on the genetic algorithm is shown in fig. 2. 1) Determining the parameter range of the IMB model, and randomly generating an initial population; 2) taking the overall reliability solution obtained based on the probability density evolution theory as the fitness of the individual, and calculating the fitness of each individual in the population (the calculated fitness provides a basis for subsequent individual selection); 3) selecting parents and parents participating in reproduction according to the fitness, wherein the selection principle is that individuals with higher fitness are more likely to be selected; 4) performing genetic operation on the selected parents and parents, namely copying genes of the parents and the parents, and generating filial generations by adopting operators such as crossing, mutation and the like; 5) and determining an optimization range as an algorithm termination judgment condition, and finally determining the optimal parameters of the IMB model.
5. Working state of built-in magnet type sliding shock insulation structure
Selecting the maximum interlayer displacement of the upper structure as a concerned physical quantity, carrying out first exceeding damage probability analysis based on a probability density evolution theory and an equivalent extreme value event criterion, and comparing a probability density function and a probability distribution function of a non-seismic isolation structure and a seismic isolation structure. As shown in figures 3 and 4, equivalent extreme displacement of seismic isolation layers is mainly distributed at 10-70mm under the action of a frequent earthquake, is mainly distributed at 10-80mm under the action of a design earthquake, and is mainly distributed at 20-130mm under the action of a rare earthquake. The displacement of the seismic isolation layer under the action of the multi-earthquake and the design earthquake is far less than the limit value of 109mm, and the reliability is 1.000; under the action of rare earthquakes, the reliability of the displacement of the seismic isolation layer is relatively low and is only 0.842. The displacement of the shock insulation layer under the action of rare earthquakes has higher failure probability, and the shock insulation system needs to be further optimally designed.
quasi-Monte Carlo sampling is carried out on 500,000 sample points, under the condition of loading of sinusoidal displacement with loading frequency of 0.1Hz and 0.2Hz and loading amplitude of 50mm, the global sensitivity of each parameter of the built-in magnet type sliding shock insulation layer is considered, the first three parameters in the total effect index are selected, and the parameter time course change diagram of the first three parameters is drawn, as shown in figures 5 and 6. FIGS. 5 and 6 show that under different working conditions and different moments, each parameter has a history of entering the first three, but the friction coefficients mu at high speed and low speed related to the dynamic friction of the seismic isolation layer are considered according to the occupancy rates of the first threehv,μlvAnd attenuation coefficient alpha is the most sensitive three parameters.
Through the optimization of a genetic algorithm, the optimal values of the sensitivity parameters of the built-in magnet type sliding shock insulation support are respectively muhv＝0.164，μlv0.053 and α -69.8. Fig. 7 and 8 show probability density function and probability distribution function of equivalent extreme displacement of the optimized seismic isolation layer, and it can be seen that: the probability density distribution of the displacement of the shock insulation layer after optimization is more concentrated, and the displacement reliability of the shock insulation layer under the action of frequent earthquake, design earthquake and rare earthquake is 1.000, 1.000 and 0.966 respectively. Therefore, the overall reliability of the seismic isolation structure is obviously improved by optimizing the parameters of the seismic isolation system.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (10)

1. A method for optimizing a basic seismic isolation structure system based on reliability analysis is characterized by comprising the following steps:
and a reliability calculation step: calculating the random seismic response of a basic seismic isolation structure system through a kinetic equation to serve as a random variable; according to the equivalent extreme value event criterion, constructing a dynamic reliability calculation flow of a basic shock insulation structure system based on preset concerned structure response physical quantity; solving by adopting a probability density evolution equation, and calculating the integral reliability of the basic shock insulation structure system;
optimizing parameters of a basic shock insulation structure system: solving the overall reliability through the reliability calculation step according to a probability criterion taking the overall reliability of the basic shock insulation structure system as a constraint and a target, and performing parameter optimization on each design parameter of the basic shock insulation structure system by adopting a genetic algorithm according to the probability criterion;
optimizing a base isolation structure system: and optimizing the basic shock insulation structure system according to the optimized design parameters.
2. The method for optimizing a base-isolated structure system based on reliability analysis according to claim 1, wherein in the reliability calculation step, the dynamic reliability calculation process specifically comprises:
s101: according to the failure mode of the basic shock insulation structure system, constructing a plurality of random events of the basic shock insulation structure system based on the concerned structure response physical quantity;
s102: constructing equivalent extreme events of each random event according to the plurality of random events;
s103: constructing a virtual random process, and acquiring a generalized probability density evolution equation of a basic shock insulation structure system so as to obtain a probability density function of an equivalent extreme value event;
s104: and calculating the power reliability according to the probability density function.
3. The method for optimizing a seismic isolation structural system based on reliability analysis according to claim 2, wherein in the reliability calculation step, the calculation of the overall reliability of the seismic isolation structural system comprises the following steps:
s201: according to the failure mode of the basic shock insulation structure system, constructing a plurality of random events of the basic shock insulation structure system based on the concerned structure response physical quantity, wherein each random event comprises a random vector and time;
s202: obtaining a representative point set in a sample domain of the random vector;
s203: calculating a random variable of an equivalent extreme event aiming at a certain sample point in the representative point set, and constructing a speed expression of the virtual random process;
s204: substituting the velocity expression of the virtual random process obtained in the step S203 into the generalized probability density evolution equation, and solving the generalized probability density evolution equation through a finite element difference method to obtain a joint probability density function;
s205: repeatedly executing the step S203 to the step S204 until each sample point in the representative point set is traversed, and acquiring a joint probability density function of each sample point;
s206: accumulating and summing the combined probability density function of each sample point to obtain a probability density function of the response physical quantity of the structure concerned;
s207: and calculating the overall reliability of the basic seismic isolation structure system according to the probability density function of the concerned structure response physical quantity acquired in the step S206.
4. The method for optimizing a seismic isolation structure system based on reliability analysis according to claim 3, wherein the generalized probability density evolution equation has an expression as follows:
Figure FDA0002799859200000021
Figure FDA0002799859200000022
Figure FDA0002799859200000023
in the formula, thetaqFor the q-th representative point, τ is the generalized time, y is the physical quantity of the response of the structure of interest, pYΘ(y,θqτ) is the joint probability density function of the probability conservative system (Y (τ), Θ),
Figure FDA0002799859200000024
velocity expression, Z, for a pseudo-random processeq(θqT) is the equivalent extremum event of the qth random vector, T is the duration corresponding to Z (-) and ZBiFor random events { Zi(Θ, t) } safety threshold, { Zi(Θ, t) } is the ith random event, and m is the number of random events.
5. The method for optimizing a seismic isolation structure system based on reliability analysis according to claim 4, wherein the computational expression of the probability density function of the structure response physical quantity of interest is as follows:
Figure FDA0002799859200000025
in the formula, nptIs the total number of representative points.
6. The method for optimizing a seismic isolation structure system based on reliability analysis according to claim 5, wherein the computational expression of the dynamic reliability is as follows:
Figure FDA0002799859200000026
wherein R (t) is the calculation result of the overall reliability.
7. The method of claim 1, wherein the method further comprises:
determining key design parameters: calculating the total effect index of each random input variable of the basic seismic isolation structure system through variance sensitivity analysis, and taking the partial random input variable with the highest total effect index as a key design parameter; the total effect index comprises the individual contribution of a certain random input variable to the corresponding variance of the structure and the cross contribution of the random input variable and other random input variables;
and in the step of optimizing parameters of the basic shock insulation structure system, the parameters of the key design parameters are optimized.
8. The method for optimizing a seismic isolation structure system based on reliability analysis according to claim 7, wherein in the step of determining the key design parameters, the calculation expression of the total effect index of the random input variables is as follows:
Figure FDA0002799859200000031
Figure FDA0002799859200000032
Figure FDA0002799859200000033
in the formula (I), the compound is shown in the specification,
Figure FDA0002799859200000034
is an indicator of the total effect of the random input variable i,
Figure FDA0002799859200000035
to remove XiCross-contributions of other random input variables to the mean of the structural response,
Figure FDA0002799859200000036
to remove XiCross contribution of other random input variables to the structural response variance, E. (. smallcircle.) is a conditional expectation operator, Var (. smallcircle.) is the structural response variance, Z is the structural response, Z ═ f (X), X is the vector of n random input variables, i and j are the serial numbers of the random input variables, X is the sum of the random input variables, and X is the sum of the random input variables and the structural response varianceiIs a vector of a random input variable i, Xi∈[0,1],i＝1,2,...,n，Vi,Vi,j,…,V1,2,...,nVariance of structural response, X, contributed for each random input variable～iRemoving X from all random input variablesiThe vector of (a) is determined,
Figure FDA0002799859200000037
is Xi、XjCross-contributions to the structural response variance.
9. The method for optimizing a seismic isolation structure system based on reliability analysis according to claim 8, wherein the total effect index is calculated by using a quasi-Monte Carlo simulation method, and the quasi-Monte Carlo simulation method comprises the following steps:
s301: acquiring N random events based on the concerned structure response physical quantity according to the failure mode of the basic shock insulation structure system, and generating an Nx 2N sample matrix, wherein each row is a 2N-dimensional sample point in the hyperspace;
s302: and taking the first n columns of the sample matrix as a matrix A, and taking the rest n columns as a matrix B. This gives independent samples of N sample points in two N-dimensional unit hypercubes;
s303: building N N x N matrices
Figure FDA0002799859200000043
Matrix array
Figure FDA0002799859200000044
The value of the ith column in (1) is the value of the ith column in the matrix B, and the rest values and momentsThe arrays A are the same;
s304: the matrix A, the matrix B and N matrixes form N (N +2) sample points, and the structural response functions are substituted into the sample points to give N (N +2) structural response values, namely f (A), f (B) and
Figure FDA0002799859200000045
s305: estimating the total effect indicator using:
Figure FDA0002799859200000041
Figure FDA0002799859200000042
10. the method for optimizing a base-isolated structure system based on reliability analysis according to claim 1, wherein in the step of optimizing the parameters of the base-isolated structure system, the step of optimizing the parameters of the key design parameters by using a genetic algorithm according to the probability criterion specifically comprises the following steps:
s401: constructing an IMB model of the basic shock insulation structure system, determining the parameter range of the IMB model, and randomly generating an initial population;
s402: taking the overall reliability calculated in the reliability calculation step as the fitness of the individual, and calculating the fitness of each individual in the population;
s403: selecting a father and a mother which participate in reproduction according to the fitness of each individual, wherein the selection principle is that the individuals with higher fitness are more likely to be selected;
s404: performing genetic operation on the selected parents and the parents, wherein the genetic operation comprises copying genes of the parents and the parents, and generating filial generations by adopting operators such as crossover, mutation and the like;
s405: and judging whether a preset algorithm termination judgment condition is met or not according to the calculation result of the individual fitness, and determining the optimal parameters of the IMB model.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112800651A (en) * 2021-01-27 2021-05-14 重庆大学 Structural reliability analysis method of isometric supersphere screening method
CN114217525A (en) * 2021-11-12 2022-03-22 大连理工大学 Random optimal control method for frame building structure based on power reliability

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20080234974A1 (en) * 2007-03-20 2008-09-25 Raytheon Company Efficient design process for the allocation of variability to non-normally distributed components of complex systems and for the estimation of the system response probability density
CN104361219A (en) * 2014-10-31 2015-02-18 华北水利水电大学 Method for evaluating anti-seismic property of building

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20080234974A1 (en) * 2007-03-20 2008-09-25 Raytheon Company Efficient design process for the allocation of variability to non-normally distributed components of complex systems and for the estimation of the system response probability density
CN104361219A (en) * 2014-10-31 2015-02-18 华北水利水电大学 Method for evaluating anti-seismic property of building

Non-Patent Citations (11)

* Cited by examiner, † Cited by third party
Title
刘章军等: "基于概率密度演化理论的结构抗震可靠性分析", 《振动与冲击》 *
周通等: "结构可靠度分析的概率密度演化理论——自适应代理模型方法", 《振动工程学报》 *
孙永等: "基于随机概率密度演化的结构-TMD参数优化", 《上海理工大学学报》 *
孙香红等: "基于体系可靠度的粘滞阻尼拓扑优化分析", 《武汉理工大学学报》 *
徐婉贞: "基于IMB模型的干预在支气管哮喘患者护理中的应用价值", 《河南医学研究》 *
曾波等: "基于概率密度演化的渡槽结构抗震分析", 《地震工程学报》 *
王磊等: "随机结构-TMD优化设计与概率密度演化研究", 《振动工程学报》 *
谭平等: "新型消能伸臂体系的动力可靠度", 《西南交通大学学报》 *
陈健云等: "地震作用下混凝土坝时变动力可靠度的概率密度演化方法研究", 《水利学报》 *
陈建兵等: "随机结构动力可靠度分析的极值概率密度方法", 《随机结构动力可靠度分析的极值概率密度方法》 *
顾镇媛等: "基于概率密度演化法的隔震结构随机地震响应与可靠度分析", 《振动与冲击》 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112800651A (en) * 2021-01-27 2021-05-14 重庆大学 Structural reliability analysis method of isometric supersphere screening method
CN112800651B (en) * 2021-01-27 2022-10-18 重庆大学 Structural reliability analysis method of isometric supersphere screening method
CN114217525A (en) * 2021-11-12 2022-03-22 大连理工大学 Random optimal control method for frame building structure based on power reliability
CN114217525B (en) * 2021-11-12 2024-03-01 大连理工大学 Frame building structure random optimal control method based on power reliability

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