A method for calculating dynamic reliability of nonlinear random structure

Abstract

The application discloses a nonlinear random structure dynamic reliability calculation method, and belongs to the field of structure health monitoring, comprising the following steps: collecting structure dynamic response data, and extracting high-order component signals of the structure dynamic response; correcting a random structure nonlinear model of an actual structure, and determining the probability distribution of the random structure nonlinear model parameters; applying external excitation load to the random structure nonlinear model, establishing a nonlinear random structure dynamic response state equation, and obtaining a probability density evolution equation; applying an absorbing boundary condition to the structure dynamic response according to a first exceeding failure criterion, combining a finite difference method and a nonlinear time-history integration method, obtaining the structure dynamic reliability changing with time under the dynamic load, and realizing the quantification of the reliability evolution process of the actual structure under the external load, avoiding the response assumption in the traditional reliability calculation process, and improving the calculation precision of the structure reliability.

Description

Technical fields:

[0001] This invention relates to the field of structural health monitoring, and in particular to a method for calculating the dynamic reliability of nonlinear stochastic structures. Background technology:

[0002] As a crucial component of national infrastructure, the safety and reliability of civil engineering structures directly impact the safety of people's lives and property. Assessing the dynamic reliability of civil engineering structures using measured response data during their service life can provide a relatively accurate reflection of their actual safety status. Based on the first-breakdown criterion for random vibration, conducting dynamic reliability analysis of composite random vibration systems is one of the main methods for assessing structural safety status.

[0003] However, dynamic reliability theories based on traversal analysis require simultaneous assumptions about the joint probability density function of the structural response and the traversal process, such as the Poisson assumption or the Markov assumption, which leads to a certain deviation between the calculated structural dynamic reliability and the actual value. Furthermore, traditional stochastic structural dynamic reliability analysis methods focus on the numerical characteristics of the structural response, only grasping the structural response information from a macroscopic perspective.

[0004] Therefore, conducting measured structural dynamic reliability analysis based on the evolution of the probability density distribution of structural dynamic response using probability and statistics theory has significant theoretical research value. Traditional structural dynamic reliability calculations suffer from inadequate model correction theories, are limited to linear structures, and rely on arbitrary assumptions about the probability distribution of model parameters, lacking factual basis.

[0005] Based on this, the present invention aims to propose a method for calculating the dynamic reliability of nonlinear stochastic structures, which can more realistically reflect the safety status of engineering structures. Summary of the Invention:

[0006] To overcome the shortcomings of existing technologies, the purpose of this invention is to provide a method for calculating the dynamic reliability of nonlinear stochastic structures. Based on a nonlinear model of a stochastic structure, an external excitation load with stochastic characteristics is applied to establish a state equation for the dynamic response of the nonlinear stochastic structure. This solves the problem that traditional dynamic reliability analysis methods can only reflect the overall reliability of a structure from a macroscopic perspective by calculating the statistics of the structural response, lacking the quantification of the actual structural reliability evolution process under external loads. Furthermore, this invention utilizes measured structural dynamic response information to correct the nonlinear model of the actual structure, avoiding the need for response assumptions in traditional reliability calculations, improving the accuracy of structural reliability calculations, and more realistically reflecting the safety state of engineering structures. In addition, based on the corrected structural nonlinear model, the probability distribution of the calculated structural dynamic response time history can more clearly reflect its reliability change trend.

[0007] The technical solution of the present invention is as follows:

[0008] A method for calculating the dynamic reliability of nonlinear stochastic structures includes the following steps:

[0009] S1. Select a sensor with appropriate sampling frequency and resolution, and use the sensor to collect structural dynamic response data.

[0010] S2. Perform low-frequency noise reduction on the collected dynamic response data and use signal decomposition technology to extract the high-order component signals of the structural dynamic response.

[0011] S3. Based on the high-order component signal data of the structural dynamic response extracted in S2, the stochastic nonlinear model of the actual structure is corrected, and the probability distribution of the parameters of the stochastic nonlinear model is determined.

[0012] S4. Based on the nonlinear model of the stochastic structure in S3, an external excitation load with stochastic characteristics is applied to establish the dynamic response state equation of the nonlinear stochastic structure. By introducing an extended state vector, its probability density evolution equation is obtained:

[0013]

[0014] in, The dynamic response vector x of the structural model l and external excitation load vector x ζ The joint probability distribution; combined with the initial state conditions of the equation. Obtain the dynamic response X of the random structure l The probability density function of (t):

[0015]

[0016] In the formula, Ω ζ Let n be the probability space of random variables in a composite random structure system, where n is the total number of mutually independent subdomains in the probability space.

[0017] S5. Based on the first-break failure criterion, apply an absorbing boundary condition to the structural dynamic response:

[0018] When x l ∈Ω f ;

[0019] In the formula Ω f The failure domain is defined as the region where the structural model response enters the failure domain Ω. f If the probability of the event occurring is 0, then the probability of the event occurring is 0.

[0020] S6, combining the initial state conditions of the stochastic structure and the absorbing boundary conditions of S5, are substituted into the partial differential equation for the probability density evolution in S4 to calculate the probability density function. Through security domain Ω s The dynamic reliability R(t) of the structure under the first-failure criterion is obtained by inner integration, denoted as:

[0021]

[0022] S7. Combining the finite difference method and the nonlinear time history integral method, the probability density evolution partial differential equation in S6 is solved to obtain the time-varying structural dynamic reliability under dynamic load.

[0023] Step S3, the correction of the nonlinear model of the stochastic structure, specifically includes the following steps:

[0024] S31. Based on the higher-order component signals of the structural dynamic response in step S2, construct the likelihood function of the parameters of the nonlinear model of the stochastic structure.

[0025] S32. Based on the Jeffery information criterion, determine the prior distribution of parameters of the stochastic structure nonlinear model;

[0026] S33. Combining S31 and S32, based on the Bayesian theoretical framework, derive the posterior probability density function expression for the parameters of the nonlinear model of the random structure to be modified.

[0027] S34. Using the differential evolution adaptive algorithm, posterior samples of the parameters of the random structure nonlinear model to be corrected are obtained by sampling, and the probability distribution of the parameters of the random structure nonlinear model is determined based on the statistics of the posterior samples.

[0028] Step S7, solving for the structural dynamic reliability under dynamic loads, specifically includes the following steps:

[0029] S71. First, the real-valued parameter interval corresponding to the random parameter variable ζ is discretized, and the discretized parameter vector is denoted as... Meanwhile, the initial state condition in S4 is discretized to obtain its discrete representation as follows:

[0030]

[0031] S72. Combining the discrete scheme expression of S71, the probability density evolution equation in S4 is transformed using the finite difference method of the total variation decreasing difference scheme, with the grid ratio set to... Its difference scheme is obtained:

[0032]

[0033] Where, p j,m for The simplified form, For flux limiter;

[0034] S73. For the difference scheme of the probability density evolution equation in S72, the stability and convergence CFL conditions that need to be satisfied are: |rg m |≤1;

[0035] S74. In the process of solving the partial differential equation S4 using the difference scheme, first estimate |g in S72. m The maximum limit of | is then determined by continuously adjusting the parameter r based on the CFL condition in S73. During the difference operation, the satisfaction of the CFL condition is continuously verified, thus yielding the probability density in S4.

[0036] S75. Regarding the function expression obtained in S74, about By performing integration, the probability density function of the structural dynamic response is obtained.

[0037] S76. Based on the expression for the structural dynamic reliability R(t) under the first failure criterion in S6, the structural dynamic reliability is obtained by integrating the probability density function in S75:

[0038]

[0039] In the S7 finite difference calculation process, the incremental variable stiffness method is used to calculate the given random parameter vector ζ at each discrete point t. m The structural dynamic response at point mΔt.

[0040] Compared with the prior art, the advantages of the present invention are:

[0041] 1. Based on the nonlinear model of a stochastic structure, this invention applies an external excitation load with stochastic characteristics to establish the dynamic response state equation of the nonlinear stochastic structure. By introducing an extended state vector, its probability density evolution equation is obtained. This solves the problem that traditional dynamic reliability analysis methods can only reflect the overall reliability of the structure from a macroscopic perspective by calculating the statistics of the structural response, and lack the quantification of the actual reliability evolution process of the structure under external loads. The probability distribution of the calculated dynamic response time history of the structure can more clearly reflect its reliability change trend.

[0042] 2. This invention utilizes measured structural dynamic response information to correct the actual structure using a stochastic nonlinear model, avoiding the need for response assumptions in traditional reliability calculations and improving the accuracy of structural reliability calculations.

[0043] 3. This invention combines nonlinear numerical integration and finite difference methods to solve the probability density evolution partial differential equation, thereby improving the computational efficiency of structural dynamic reliability. Attached image description:

[0044] Figure 1 This is a flowchart of the method of the present invention.

[0045] Figure 2 This is a flowchart of the differential evolution adaptive algorithm of the present invention.

[0046] Figure 3 This is a model diagram of the nonlinear interlayer shear frame structure of the present invention.

[0047] Figure 4 This is the posterior distribution diagram of the parameters of the model to be corrected in this invention.

[0048] Figure 5 This is a probability distribution diagram of the top-level displacement response of the structure at a typical moment according to the present invention.

[0049] Figure 6 This is a comparison chart of the mean and standard deviation of the top-level displacement of the structure of the present invention.

[0050] Figure 7 This is a dynamic reliability curve of the frame structure of the present invention under different displacement limit conditions.

[0051] Figure 8 This is a dynamic reliability curve of the frame structure of the present invention under different speed limit conditions. Detailed implementation method:

[0052] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0053] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0054] Example 1

[0055] like Figure 1 As shown in Example 1, a method for calculating the dynamic reliability of a nonlinear stochastic structure includes the following steps:

[0056] S1. Select a sensor with appropriate sampling frequency and resolution to collect structural dynamic response data;

[0057] S2. Perform low-frequency noise reduction on the dynamic response data collected in S1, and use signal decomposition technology to extract the high-order component signals of the structural dynamic response.

[0058] S3. Based on the high-order component signal data of the structural dynamic response extracted in S2, perform stochastic structural nonlinear model correction on the actual structure and determine the probability distribution of the stochastic structural nonlinear model parameters. The stochastic structural nonlinear model correction process specifically includes the following steps:

[0059] S31. Using the higher-order component signals of the structural dynamic response of S2 as the target response, construct the likelihood function of the parameters of the nonlinear model of the stochastic structure.

[0060] S32. Based on the Jeffery information criterion, determine the prior distribution of parameters of the stochastic structure nonlinear model;

[0061] S33. Combining S31 and S32, based on the Bayesian theoretical framework, derive the posterior probability density function expression for the parameters of the nonlinear model of the random structure to be modified.

[0062] S34. Using the differential evolution adaptive algorithm, posterior samples of the parameters of the stochastic structure nonlinear model to be corrected are obtained, and the probability distribution of the stochastic structure nonlinear model parameters is determined based on the statistics of the posterior samples. The flowchart of the differential evolution adaptive algorithm is as follows: Figure 2 As shown.

[0063] S4. Based on the nonlinear model of the stochastic structure in S3, an external excitation load with stochastic characteristics is applied to establish the dynamic response state equation of the nonlinear stochastic structure. By introducing an extended state vector, its probability density evolution equation is obtained:

[0064]

[0065] in, The dynamic response vector x of the structural model l and external excitation load vector x ζ The joint probability distribution. Combined with the initial state conditions of this equation. Obtain the dynamic response X of the random structure l The probability density function of (t):

[0066]

[0067] In the formula, Ω ζ Let n be the probability space of random variables in a composite random structure system, and n be the total number of mutually independent subdomains in the probability space.

[0068] S5. Based on the first-break failure criterion, apply an absorbing boundary condition to the structural dynamic response:

[0069]

[0070] In the formula Ω fThe failure domain is defined as the region where the structural model response enters the failure domain Ω. f If the probability of the event occurring is 0, then the probability of the event occurring is 0.

[0071] S6, combining the initial state conditions of the stochastic structure and the absorbing boundary conditions of S5, are substituted into the partial differential equation for the probability density evolution in S4 to calculate the probability density function. Through security domain Ω s The dynamic reliability R(t) of the structure under the first-failure criterion is obtained by inner integration, denoted as:

[0072]

[0073] S7. Combining the finite difference method and the nonlinear time history integral method, the probability density evolution partial differential equation in S6 is solved to obtain the time-varying structural dynamic reliability under dynamic load. In the finite difference calculation, the incremental variable stiffness method is used to calculate the given random parameter vector ζ at each discrete point t. m The structural dynamic response at point mΔt and the solution for structural dynamic reliability include the following steps:

[0074] S71. First, the real-valued parameter interval corresponding to the random parameter variable ζ is discretized, and the discretized parameter vector is denoted as... Meanwhile, the initial state condition in S4 is discretized to obtain its discrete representation as follows:

[0075]

[0076] S72. Combining the discrete scheme expression of S71, the probability density evolution equation in S4 is transformed using the finite difference method of the total variation decreasing difference scheme, with the grid ratio set to... Its difference scheme is obtained:

[0077]

[0078] Where, p j,m for The simplified form, It is a flux limiter.

[0079] S73. For the difference scheme of the probability density evolution equation in S72, the stability and convergence CFL conditions that need to be satisfied are: |rg m |≤1;

[0080] S74. In the process of solving the partial differential equation S4 using the difference scheme, first estimate |g in S72. m The maximum limit of | is then determined by continuously adjusting the parameter r based on the CFL condition in S73. During the difference operation, the satisfaction of the CFL condition is continuously verified, thus yielding the probability density in S4.

[0081] S75. Regarding the function expression obtained in S74, about By performing integration, the probability density function of the structural dynamic response is obtained.

[0082] S76. Based on the expression for the structural dynamic reliability R(t) under the first failure criterion in S6, the structural dynamic reliability can be obtained by integrating the probability density function in S75:

[0083]

[0084] Example 2

[0085] A specific method for calculating the dynamic reliability of nonlinear stochastic structures based on the first-break failure criterion is provided:

[0086] S1. Taking a two-span, six-story inter-story shear-type frame structure with stochastic nonlinear model parameters as an example, such as... Figure 3 As shown, the shear frame structure has a bottom floor height of 4m and each of the remaining floors is 3m high. The column cross-section is 500mm × 500mm, and the elastic modulus E = 2.5 × 10⁻⁶. 4 MPa, the mass of each layer from the bottom to the top of the structure is 5.4 × 10 MPa. 4 kg, 5.2×10 4 kg, 4.8×10 4 kg, 3.1×10 4 kg, 2.5×10 4 kg, 1.7×10 4 kg. The structure was subjected to El-centro waveform seismic excitation. Peak ground acceleration and nonlinear Bouc-Wen model parameters were used as random variables. Thirty sets of structural dynamic responses were taken as measured data to calculate the dynamic reliability of the shear frame structure under random seismic excitation.

[0087] S2. Perform low-frequency noise reduction on the collected dynamic response data and use signal decomposition technology to extract the high-order component signals of the structural dynamic response.

[0088] S3. Based on the high-order component signals of the structural dynamic response extracted in S2, a stochastic structural nonlinear model is modified for the actual structure to determine the probability distribution of the stochastic structural nonlinear model parameters. The rejection-delay adaptive Monte Carlo algorithm is used to sample the posterior samples of the parameters to be modified. Taking parameter γ as an example, the posterior samples are as follows: Figure 4 As shown;

[0089] S4. Based on the nonlinear model of the stochastic structure in S3, an external excitation load with stochastic characteristics is applied to establish the dynamic response state equation of the nonlinear stochastic structure. By introducing an extended state vector, its probability density evolution equation is obtained:

[0090]

[0091] in, The dynamic response vector x of the structural model l and external excitation load vector x ζ The joint probability distribution. Combined with the initial state conditions of this equation. Obtain the dynamic response X of the random structure l The probability density function of (t):

[0092]

[0093] In the formula, Ω ζ Let n be the probability space of random variables in a composite stochastic structure system, and n be the total number of mutually independent subdomains in the probability space. The probability density function of the top-level displacement response of the structure at a typical moment is calculated, as follows: Figure 5 As shown. To verify the accuracy of the calculation results, the Monte Carlo method was used for comparison, and the time history curves of the mean and standard deviation of the top-level displacement of the structure were obtained, as shown. Figure 6 As shown, from Figure 6 It can be seen that the calculation results of the method proposed in this invention are close to those of the Monte Carlo method, indicating that the proposed method can accurately calculate the probability distribution of the evolution process of structural dynamic response;

[0094] S5. Based on the first-break failure criterion, apply an absorbing boundary condition to the structural dynamic response:

[0095] When x l ∈Ω f

[0096] In the formula Ω f The failure domain is defined as the region where the structural model response enters the failure domain Ω. f If the probability of the event occurring is 0, then the probability of the event occurring is 0.

[0097] Substituting the initial conditions of the combined random structure (S6) and the absorbing boundary conditions (S5) into the partial differential equation for the probability density evolution in S4, the probability density function is calculated. Through security domain Ω s The dynamic reliability R(t) of the structure under the first-failure criterion is obtained by inner integration, denoted as:

[0098]

[0099] S7. Combining the finite difference method and the nonlinear time history integral method, the probability density evolution partial differential equation in S6 is solved to obtain the time-varying structural dynamic reliability under dynamic load. To verify the accuracy of the calculation results, the Monte Carlo method is used for comparison, and the dynamic reliability curves of the frame structure under different displacement limit conditions and different velocity limit conditions are obtained, as shown below. Figure 7 and Figure 8 As shown, from Figure 7 and Figure 8 The calculation results show that the dynamic reliability calculation results of the proposed method are close to those of the Monte Carlo method, indicating that the proposed method has high accuracy and is suitable for dynamic reliability calculation of nonlinear stochastic structures.

[0100] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the dynamic reliability of nonlinear stochastic structures, characterized in that, Includes the following steps: S1. Select a sensor with appropriate sampling frequency and resolution, and use the sensor to collect structural dynamic response data. S2. Perform low-frequency noise reduction on the collected dynamic response data and use signal decomposition technology to extract the high-order component signals of the structural dynamic response. S3. Based on the high-order component signal data of the structural dynamic response extracted in S2, the stochastic nonlinear model of the actual structure is corrected, and the probability distribution of the parameters of the stochastic nonlinear model is determined. S4. Based on the nonlinear model of the stochastic structure in S3, an external excitation load with stochastic characteristics is applied to establish the dynamic response state equation of the nonlinear stochastic structure. By introducing an extended state vector, its probability density evolution equation is obtained: in, The dynamic response vector x of the structural model l and external excitation load vector x ζ The joint probability distribution; combined with the initial state conditions of the equation. Obtain the dynamic response X of the random structure l The probability density function of (t): In the formula, Ω ζ Let n be the probability space of random variables in a composite random structure system, where n is the total number of mutually independent subdomains in the probability space. S5. Based on the first-break failure criterion, apply an absorbing boundary condition to the structural dynamic response: When x l ∈Ω f ; In the formula Ω f The failure domain is defined as the region where the structural model response enters the failure domain Ω. f If the probability of the event occurring is 0, then the probability of the event occurring is 0. S6, combining the initial state conditions of the stochastic structure and the absorbing boundary conditions of S5, are substituted into the partial differential equation for the probability density evolution in S4 to calculate the probability density function. Through security domain Ω s The dynamic reliability R(t) of the structure under the first-failure criterion is obtained by inner integration, denoted as: S7. Combining the finite difference method and the nonlinear time history integral method, the probability density evolution partial differential equation in S6 is solved to obtain the time-varying structural dynamic reliability under dynamic load.

2. The method for calculating the dynamic reliability of a nonlinear stochastic structure according to claim 1, characterized in that, Step S3, the correction of the nonlinear model of the stochastic structure, specifically includes the following steps: S31. Based on the higher-order component signals of the structural dynamic response in step S2, construct the likelihood function of the parameters of the nonlinear model of the stochastic structure. S32. Based on the Jeffery information criterion, determine the prior distribution of parameters of the stochastic structure nonlinear model; S33. Combining S31 and S32, based on the Bayesian theoretical framework, derive the posterior probability density function expression for the parameters of the nonlinear model of the random structure to be modified. S34. Using the differential evolution adaptive algorithm, posterior samples of the parameters of the random structure nonlinear model to be corrected are obtained by sampling, and the probability distribution of the parameters of the random structure nonlinear model is determined based on the statistics of the posterior samples.

3. The method for calculating the dynamic reliability of a nonlinear stochastic structure according to claim 1, characterized in that, Step S7, solving for the structural dynamic reliability under dynamic loads, specifically includes the following steps: S71. First, the real-valued parameter interval corresponding to the random parameter variable ζ is discretized, and the discretized parameter vector is denoted as... Meanwhile, the initial state condition in S4 is discretized to obtain its discrete representation as follows: S72. Combining the discrete scheme expression of S71, the probability density evolution equation in S4 is transformed using the finite difference method of the total variation decreasing difference scheme, with the grid ratio set to... Its difference scheme is obtained: Where, p j,m for The simplified form, For flux limiter; S73. For the difference scheme of the probability density evolution equation in S72, the stability and convergence CFL conditions that need to be satisfied are: |rg m |≤1; S74. In the process of solving the partial differential equation S4 using the difference scheme, first estimate |g in S72. m The maximum limit of | is then determined by continuously adjusting the parameter r based on the CFL condition in S73. During the difference operation, the satisfaction of the CFL condition is continuously verified, thus yielding the probability density in S4. S75. Regarding the function expression obtained in S74, about By performing integration, the probability density function of the structural dynamic response is obtained. S76. Based on the expression for the structural dynamic reliability R(t) under the first failure criterion in S6, the structural dynamic reliability is obtained by integrating the probability density function in S75: In the S7 finite difference calculation process, the incremental variable stiffness method is used to calculate the given random parameter vector ζ at each discrete point t. m The structural dynamic response at point mΔt.

Images