CN115270239A - Bridge reliability prediction method based on dynamic characteristics and intelligent algorithm response surface method - Google Patents

Bridge reliability prediction method based on dynamic characteristics and intelligent algorithm response surface method Download PDF

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CN115270239A
CN115270239A CN202210684360.2A CN202210684360A CN115270239A CN 115270239 A CN115270239 A CN 115270239A CN 202210684360 A CN202210684360 A CN 202210684360A CN 115270239 A CN115270239 A CN 115270239A
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卢彭真
李登国
武瑛
卢立波
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Abstract

The invention discloses a bridge reliability prediction method based on dynamic characteristics and a response surface method, which comprises the following steps: acquiring vibration characteristic information of an existing bridge and preprocessing data; establishing a structural analysis model by combining bridge design data and operation conditions, and screening design parameters to be corrected of the structural analysis model by adopting a sensitivity analysis method; acquiring an output sample, forming a training sample with the input sample, and correcting the initial structure analysis model; outputting a sample based on the corrected structural analysis model, building a training sample again, carrying out normalization processing on sample points, and building a response surface model; normalizing the random variable standard, converting a constrained optimization problem into an unconstrained optimization problem by adopting a penalty function, and acquiring the optimal weight of the random variable by utilizing an optimization algorithm; and establishing a mathematical model for solving the structural reliability index according to the prediction result of the constructed response surface model. The beneficial effects of the invention are: the calculation precision is high, and the estimation speed is fast.

Description

Bridge reliability prediction method based on dynamic characteristics and intelligent algorithm response surface method
Technical Field
The invention relates to the technical field of bridge engineering, in particular to a bridge reliability prediction method based on dynamic characteristics and a response surface method.
Background
The reliability problem of the existing bridge is one of the research hotspots in the civil engineering community at present, but the analysis model of the existing bridge reliability research is mainly established according to bridge design data, has larger deviation with the actual current situation of the performance degradation of the long-term service material of the existing bridge, and cannot truly and accurately reflect the reliable performance of the existing bridge structure in the using process. In addition, in the reliability analysis of the complex bridge engineering, the function is generally implicit, which makes it difficult to directly use algorithms such as a first order second moment method (FORM), a second order second moment method (SORM), and a direct integration method. However, the direct monte carlo simulation Method (MCS) is suitable for solving the reliability problem of the implicit function, and the calculation accuracy is high, but in order to ensure the calculation accuracy, the sampling times required by the MCS method are very large, and especially when the function value needs to be obtained by means of a finite element, the huge calculation amount results in very long time consumption, so that the MCS method is greatly limited in engineering application. Therefore, a small number of sampling points are utilized, regression tools such as a classical Response Surface (RSM), an Artificial Neural Network (ANN), a Kriging (Kriging) surrogate model and a Support Vector Machine (SVM) are adopted to construct a response surface of an implicit function, and then conventional methods such as FORM, SORM and MCS are combined to perform reliability analysis, so that the structure reanalysis times can be effectively reduced, the calculation efficiency is remarkably improved, and the method becomes an important way for the reliability analysis of a complex structure at present.
The method aims at the problems that the existing bridge reliability analysis process has large result deviation and can not truly reflect the reliability of the actual bridge in the using process, and the traditional response surface method is low in fitting accuracy and difficult to meet the requirement for precision when solving the reliability of the bridge in the reliability calculation process. A response surface method for predicting the reliability of a bridge structure based on finite element model correction is provided by using a finite element model correction method and combining the characteristics of a Dynamic Bayesian Network (DBN) and PSOSA optimization algorithm. Firstly, correcting a finite element model to ensure that a corrected structural analysis model is consistent with the performance parameters of an actual existing bridge; secondly, in the aspect of reliability calculation of the existing bridge structure, the method not only utilizes the advantages of the DBN in processing uncertainty problems and probability inference problems, but also utilizes the characteristic that the PSOSA algorithm can better update particle swarm coordinates so as to search an optimal solution more quickly, effectively improves the precision and efficiency of the reliability calculation of the complex structure, overcomes the limitation of the classical response surface method on the high nonlinear structure reliability problem, and solves the problems that the calculation efficiency of the MCS method is low, and the calculation precision of the existing response surface method excessively depends on the scale and distribution of a preset sample.
Disclosure of Invention
In view of the fact that the performance deviation between an analysis model and an actual bridge structure is large in the existing reliability analysis process of the bridge structure at present, when the reliability problem is solved by adopting a traditional response surface method, due to the fact that the traditional response surface method has a highly nonlinear implicit function, the fitting accuracy is not high, the precision is difficult to meet the requirements, and the like.
In order to solve the problems, the invention provides a bridge reliability prediction method based on dynamic characteristics and a response surface method, which is characterized by comprising the following steps of:
s1, acquiring vibration characteristic information of an existing bridge and preprocessing data;
s2, establishing a structural analysis model by combining bridge design data and operation conditions, and screening design parameters to be corrected of the structural analysis model by adopting a sensitivity analysis method;
s3, calculating target variables corresponding to the input samples to obtain output samples, forming training samples with the input samples, and correcting the initial structure analysis model by using the dynamic characteristic data of the step S1 in combination with an intelligent algorithm;
s4, calculating target variables corresponding to the input samples again based on the corrected structural analysis model to obtain output samples, constructing training samples again, carrying out normalization processing on sample points, and constructing a response surface model based on an intelligent algorithm;
s5, normalizing the random variable standard, converting the constrained optimization problem into an unconstrained optimization problem by adopting a penalty function, and acquiring the optimal weight of the random variable by utilizing an optimization algorithm;
s6, establishing a mathematical model for solving the structural reliability index according to the prediction result of the constructed response surface model:
and comparing the constructed prediction result of the response surface model with the structure real extreme state function result, and directly calculating the structure reliability by using the response surface prediction result when the prediction result of the response surface model is converged to the structure real extreme state function result. When the prediction result of the response surface model does not converge to the real extreme state function, updating and optimizing a sample of the DBN prediction model are needed, so that the DBN prediction model can well approach to a sample point until the model constructs a response surface with enough precision, and the structural extreme state function can be simulated really.
The extreme state function of the structure should be determined based on a plurality of factors such as the concrete form of the structure and the analysis object of the reliability.
Further, in step S1, a direct measurement method or an indirect measurement method is used to obtain actual vibration characteristic information of the bridge structure, and a signal processing method is used to process the collected vibration information.
Further, the direct measurement method in step S1: directly arranging a vibration pickup on a bridge control section, collecting bridge vibration response signals through a digital signal collector, and reading bridge frequency and other responses through a power spectrogram peak value and a time domain history curve which are actually measured and recorded by a collecting system;
indirect measurement method: the sensor is arranged on the mobile trolley, when the mobile trolley drives the bridge to generate axle coupling effect, the dynamic characteristic method of the bridge is extracted from the acceleration response of the trolley body, and the information such as bridge frequency is obtained;
the signal processing method comprises the following steps: and (3) carrying out Fourier transformation on the time domain signal acquired by the vibration pickup to obtain a frequency domain result of the bridge frequency characteristic. The fourier transform equation is:
Figure BDA0003697487670000041
in the formula: j is a virtual unit, j ^2= -1, and no unit is used; t is the period and the unit is second; x is a primitive function of X; t is time in seconds; ω is the frequency and x (t) is the continuous time signal.
Preferably, in the step S1, a direct measurement method is adopted to test the dynamic characteristic result of the bridge, and the specific method is to arrange a vibration pickup device at the positions of the typical cross sections of the existing bridge, such as 1/2 and 1/4, and the cross section of the fulcrum, collect the vibration response signal of the bridge through a digital signal collector, and read the response of the bridge, such as the frequency, etc., through the power spectrogram peak value and the time domain history curve which are actually measured and recorded by a collection system. During signal processing, a frequency domain result (such as frequency, vibration mode and the like) of bridge frequency characteristics can be obtained by performing Fourier transform on a time domain signal acquired by a vibration pickup, wherein the Fourier transform formula is as follows:
Figure BDA0003697487670000042
in the formula: j is a virtual unit, j ^2= -1, and no unit is used; t is the period and the unit is second; x is a primitive function of X; t is time in seconds; ω is the frequency and x (t) is the continuous time signal.
Further, step S2 determines values of bridge design parameters (such as material elastic modulus E, material volume weight γ, boundary conditions, load application, and other parameters) according to existing bridge design data, establishes an initial structure analysis model of the bridge, performs sensitivity analysis on each design parameter, and screens out design parameters with large response to the bridge structure.
Further, step S2 is to build a numerical analysis model of the bridge structure by using finite element software (such as ANSYS, ABAQUS, midas, etc.) according to the design data of the bridge. And (3) carrying out sensitivity analysis on the design parameters by adopting a Morris method, and screening out the design parameters which have larger influence on the vibration response of the bridge as the design parameters to be corrected subsequently. The Morris method causes the change of output response through the variable quantity of a single factor, and the calculation formula is as follows:
Figure BDA0003697487670000051
in the formula: di(j) J =1,2,3, \ 8230for the base effect of the jth group of samples of the ith parameter, R (R is the repeated sampling times), and n is the number of the parameters; x is the number ofiFor the ith parameter, Δ is the small variation of the single parameter, and f (X) is the response output of the corresponding parameter set. Morris proposes two calculation indexes to judge the sensitivity of parameters, namely a mean value mu and a standard deviation sigma of a basal effect. Wherein μ characterizes the sensitivity of the parameters, determines the ordering of the parameters, and σ characterizes the degree of non-linearity between the parameters. And screening out the key design parameters needing to be corrected according to the Morris calculation result.
Further, step S3, calculating target variables corresponding to all input samples, constructing training samples between the design parameters and the vibration response which are distributed in the space based on a uniform design theory, and substituting the training samples into an intelligent algorithm program to perform learning training; and calling the bridge vibration characteristic information obtained in the step S1 as an input parameter, substituting the input parameter into the response surface model, predicting the actual value of each design parameter, substituting the predicted value of the design parameter into the initial structure analysis model established in the step S2, and realizing the correction of the bridge structure analysis model, wherein the corrected analysis model is matched with the actual state of the existing bridge.
Furthermore, in the step S3, a Latin Hypercube Sampling (LHS) method is adopted to carry out efficient sampling from the distribution interval of the design parameters, and K variables x are subjected to1,x2,...,xkAnd extracting N samples from the variable, dividing the cumulative distribution of each variable into N same small intervals, randomly selecting one value from each interval, and randomly combining the N values of each variable and the values of other variables. Using each design parameter as input data, and using the structural vibration response corresponding to each set of design parameters asAnd outputting data to generate a training sample. And establishing a Gaussian process response surface model on the basis of the completion of the construction of the training sample. Gaussian process response surface model to training sample set (x)1,t1)、(x2,t2)...(xN,tN)，tiIs xiPredicting a new set of input quantities x corresponding to the target valuesN+1Corresponding target value t can be obtainedN+1The training set is as follows:
R＝{(Xi,Ti),i＝1,2,3,...,i,...,N} (3)；
the joint probability distribution of the training set obeys a gaussian distribution:
f(TN)～GP(m(x),K(x,x')) (4)；
wherein:
m(x)＝E[f(x)] (5)；
K(x,x')＝E[f(x)-m(x)(f(x')-m(x'))] (6)；
wherein m (x) is a mean value; f (x) is a function with respect to the sample points; e is the sign of the mean; k (x, x') is a covariance matrix;
determining a corresponding Gaussian process response surface model by determining the mean value m (x) and the covariance matrix K (x, x');
and after the Gaussian process response surface model is built, inputting the bridge dynamic characteristic result obtained in the step S1 into the Gaussian process response surface model, calculating a prediction result of the design parameters, substituting the prediction result into the initial structure analysis model in the step S1, and finishing the correction of the initial structure analysis model.
Further, in the step S4, on the basis of the corrected structural analysis model, the target variables corresponding to the input samples are calculated again to obtain output samples, the training samples are constructed again, the sample points are normalized, the basic DBN model is established based on the BN toolbox in the MATLAB, and the unsupervised training and model parameter optimization processes are performed on the basic model through the input sample points to obtain the DBN response surface model related to the structure.
Further, step S4 normalizes the training sample by a normalization processing method based on the modified structural analysis model, so that the normalized result is between 0 and 1, and normalizes the formula:
Figure BDA0003697487670000071
in the formula: x is the number ofiFor sample point data, yiIs the result after normalization;
substituting the normalized training sample into a DBN tool box in MATLAB software, and calculating to obtain a DBN corresponding face model related to the DBN random variable;
the construction of the response surface model is to input training sample data into an algorithm of a DBN (database-based laboratory) toolbox by utilizing a DBN toolbox in MATLAB software, so that the response surface model can be constructed;
wherein DBN can be represented as (B)0,B→) In which B is0Is a static BN, showing the probability distribution P (X) of the node at the initial time0)，B→The method is a transition network comprising two adjacent time slices, and represents the state transition probability between nodes of the two adjacent time slices, and the expression is as follows:
Figure BDA0003697487670000072
in the formula:
Figure BDA0003697487670000073
is the ith node on t time slices;
Figure BDA0003697487670000074
of parent node
Figure BDA0003697487670000075
Can be combined with
Figure BDA0003697487670000076
In the same time slice or the previous time slice, the DBN response surface model related to the structure is obtained through the process of carrying out unsupervised training and model parameter optimization on the basic model by inputting sample points。
Further, step S5 normalizes the random variable standard, converts the constrained optimization problem into an unconstrained optimization problem by adopting a penalty function, constructs a fitness equation suitable for solving the PSOSA algorithm, updates the optimal positions of the search particles and the particle swarm through the PSOSA algorithm, and iteratively obtains the optimal weight of the random variable to support the unsupervised learning process of the DBN model.
Further, step S5 normalizes the random variables, and assumes that each random variable complies with the standard normal distribution in the normalization of the random variables, which is the normalization of the random variables.
And converting the random variable constraint optimization problem into an unconstrained optimization problem by adopting a penalty function method, and converting the constrained optimization problem into the unconstrained optimization problem by introducing a penalty function (9):
Figure BDA0003697487670000081
wherein F (x, sigma) is a penalty function, F (x) is an objective function, sigma is a penalty factor,
Figure BDA0003697487670000082
for the penalty term, the parameter x in F (x, σ) is not limited and may take any value.
The optimal weight of the random variable is solved by adopting a particle swarm optimization algorithm (PSOSA), and the principle is as follows:
Figure BDA0003697487670000083
in the formula: i is the particle number, d is the particle dimension number, k is the number of iterations, w is the inertial weight, c1For an individual learning factor, c2As a group learning factor, r1,r2Is the interval of [0-1 ]]Internal random numbers, increasing the search randomness,
Figure BDA0003697487670000084
dimension d for particle i in k iterationThe velocity vector of (a) is calculated,
Figure BDA0003697487670000085
for the position vector of particle i in dimension d in the kth iteration,
Figure BDA0003697487670000086
for the historical optimal position of particle i in dimension d in the kth iteration,
Figure BDA0003697487670000091
the historical optimal position of the d-th dimension in the k-th iteration is obtained;
the optimal weight of the random variable can be obtained through the gradual iteration of the formula.
Further, step S6 is to establish a mathematical model for solving the structural reliability index through the prediction result of the DBN model, and in this process, updating and optimizing the sample of the DBN prediction model each time is required, so that the DBN prediction model can well approach the sample point until the model constructs a response surface with sufficient precision, and the extreme state function of the structure can be simulated really.
Further, in step S6, the prediction result of the constructed response surface model is compared with the result of the structure true extreme state function, and when the prediction result of the response surface model converges to the result of the structure true extreme state function, the structure reliability is calculated by directly using the prediction result of the response surface. When the prediction result of the response surface model does not converge to the real extreme state function, updating and optimizing a sample of the DBN prediction model are needed, so that the DBN prediction model can well approach to a sample point until the model constructs a response surface with enough precision, and the structural extreme state function can be simulated really.
The extreme state function of the structure is determined according to a plurality of factors such as a specific form of the structure, an analysis object of reliability and the like.
The invention has the beneficial effects that:
(1) The method is based on a finite element model correction technology, so that an analysis model is more consistent with the actual structure of the existing bridge, and the calculation result is more accurate.
(2) The method is used for bridge reliability analysis by a hybrid fast response surface method combining a Dynamic Bayesian Network (DBN) and a Particle Swarm Optimization (PSOSA) based on a simulated annealing algorithm idea, and not only utilizes the advantages of the DBN in processing uncertainty problems and probability reasoning problems, but also utilizes the characteristic that the PSOSA algorithm can better update particle swarm coordinates so as to search an optimal solution more quickly, and effectively improves the precision and efficiency of complex structure reliability calculation.
(3) The method overcomes the limitation of the classical response surface method on the problem of high nonlinear structure reliability, and solves the problems that the MCS method is low in calculation efficiency, the calculation accuracy of the existing response surface method excessively depends on the scale and distribution of the preset sample, and the like.
(4) Compared with the traditional bridge reliability analysis method, the DBN-PSOSA mixed response surface method has the advantages of high calculation precision, high estimation speed and easiness in combination with the existing finite element analysis software, is convenient for engineering application, and is particularly suitable for the reliability problems of high structural analysis cost and high nonlinear implicit function.
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FIG. 1a is a block flow diagram of the present invention.
FIG. 1b is a graph of the dynamic characteristic acquisition spectrum of an actual bridge structure;
FIG. 2 is a flow chart of bridge finite element model modification;
FIG. 3 is a flow chart of bridge reliability prediction based on dynamic characteristics and response surface method;
FIG. 4 is a diagram of PSOSA parameter optimization for actual bridge reliability calculation;
FIG. 5 is a diagram of the DBN prediction results of an actual bridge reliability calculation.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating embodiments of the invention, are given by way of illustration and explanation only, not limitation.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The invention will be described in detail hereinafter with reference to the drawings and in connection with exemplary embodiments.
The invention provides a bridge reliability prediction method based on dynamic characteristics and a response surface method, which comprises the following steps:
s1, acquiring vibration characteristic information of an existing bridge and preprocessing data:
measuring dynamic characteristics of the bridge by adopting a contact or non-contact method, a direct method or an indirect method (such as a machine vision method, a field test method and the like); the dynamic characteristic parameters comprise the frequency, the vibration mode, the damping, the impact coefficient and the like of the bridge; FIG. 1b is a diagram showing the result of a field dynamic load test of a bridge by using an environmental excitation method in a direct measurement method, wherein the test result is used as an input parameter of a machine learning intelligent algorithm prediction model established subsequently to further predict parameters to be corrected;
in this embodiment, in step S1, a direct measurement method is used to test a dynamic characteristic result of a bridge, and the specific method includes arranging vibration pickup devices on the cross sections of the existing bridge, such as 1/2, 1/4, and the cross section of the fulcrum, collecting a vibration response signal of the bridge through a digital signal collector, and reading a response such as a bridge frequency through a power spectrogram peak value and a time domain history curve which are actually measured and recorded by a collection system. During signal processing, a frequency domain result (such as frequency, vibration mode and the like) of bridge frequency characteristics can be obtained by performing Fourier transform on a time domain signal collected by a vibration pickup, wherein the Fourier transform formula is as follows:
Figure BDA0003697487670000111
in the formula: j is an imaginary unit, j ^2= -1, and no unit exists; t is the period and the unit is second; x is a primitive function of X; t is time in seconds; ω is the frequency and x (t) is the continuous time signal.
Fig. 1b shows the result of the field dynamic load test of a bridge by using the environmental excitation method in the direct measurement method, wherein the abscissa represents the sampling time and the ordinate represents the amplitude.
S2, establishing a structural analysis model by combining bridge design data and operation conditions, and screening design parameters to be corrected of the structural analysis model by adopting a sensitivity analysis method:
according to the design data of the existing bridge, values of the geometric shapes, specific sizes and material properties of all parts of the bridge and the forms of boundary conditions are determined, an initial structure analysis model of the bridge structure is established by using structural analysis software, the influence degree of different design parameters on the bridge structure is analyzed by using a global sensitivity analysis method, and finally the key design parameters of the bridge structure are screened out.
Specifically, according to the design data of the bridge, finite element software (such as ANSYS, ABAQUS, midas and the like) is adopted to establish a numerical analysis model of the bridge structure. And screening the sensitivity design parameters of the bridge by adopting a sensitivity analysis method. The sensitivity analysis method adopts a Morris method, the Morris method causes the change of output response through the variable quantity of a single factor, and the calculation formula is as follows:
Figure BDA0003697487670000121
in the formula: di(j) J =1,2,3, \8230forthe base effect of the jth group of samples of the ith parameter, R (R is the repeated sampling times), and n is the number of the parameters; x is the number ofiFor the ith parameter, Δ is the small variation of the single parameter, and f (X) is the response output of the corresponding parameter set. Morris proposes two calculation indexes to judge the sensitivity of parameters, namely a mean value mu and a standard deviation sigma of a basal effect. Where μ characterizes the sensitivity of the parameters, determines the ordering of the parameters, and σ characterizes the degree of non-linearity between the parameters. And screening out the key design parameters needing to be corrected according to the Morris calculation result.
And S3, calculating target variables corresponding to the design parameter samples to obtain output samples, forming training samples with the input samples, inputting the bridge dynamic characteristic data obtained in the step 1, predicting an optimal value of a group of parameters to be corrected through a machine learning intelligent algorithm, and substituting the predicted value into the initial structure analysis model to realize correction of the structure analysis model. FIG. 2 is a flowchart of a finite element model modification of an existing bridge; the machine learning intelligent algorithm comprises a Kriging model algorithm, a Gaussian process algorithm, a Bayesian algorithm, a random forest algorithm, a cloud theory algorithm, various agent models and the like. In this embodiment, a gaussian process response surface model algorithm is used.
In the embodiment, a Latin Hypercube Sampling (LHS) method is adopted to carry out high-efficiency sampling from a distribution interval of design parameters, and K variables x are subjected to sampling1,x2,...,xkAnd extracting N samples from the variable, dividing the cumulative distribution of each variable into N same small intervals, randomly selecting one value from each interval, and randomly combining the N values of each variable and the values of other variables. And generating a training sample by taking each design parameter as input data and taking the structural vibration response corresponding to each group of design parameters as output data. And establishing a Gaussian process response surface model on the basis of the completion of the construction of the training sample. Gaussian Process response surface model to training sample set (x)1,t1)、(x2,t2)...(xN,tN)，tiIs xiPredicting a new set of input quantities x corresponding to the target valuesN+1The corresponding target value t can be obtainedN+1The training set is as follows:
R＝{(Xi,Ti),i＝1,2,3,...,i,...,N} (3)；
the joint probability distribution of the training set follows a gaussian distribution:
f(TN)～GP(m(x),K(x,x')) (4)；
wherein:
m(x)＝E[f(x)] (5)；
K(x,x')＝E[f(x)-m(x)(f(x')-m(x'))] (6)；
wherein m (x) is a mean value; f (x) is a function with respect to the sample points; e is the sign of the mean; k (x, x') is a covariance matrix;
the corresponding Gaussian process response surface model can be determined by determining the mean m (x) and the covariance matrix K (x, x'). And after the Gaussian process response surface model is built, inputting the bridge dynamic characteristic result obtained in the step S1 into the Gaussian process response surface model, calculating a prediction result of the design parameters, substituting the prediction result into the initial structure analysis model in the step S1, and finishing the correction of the initial structure analysis model.
S4, on the basis of the corrected structural analysis model, calculating target variables corresponding to all input samples again to obtain output samples, constructing training samples again, carrying out normalization processing on sample points, and establishing a basic DBN model based on a BN tool box in MATLAB;
based on the corrected structure analysis model, the training sample is normalized by a normalization processing method, so that the result after normalization is between 0 and 1, and the normalization formula is as follows:
Figure BDA0003697487670000141
in the formula: x is a radical of a fluorine atomiFor the sample point data, yiIs the result after normalization. And substituting the normalized training sample into a DBN tool box in MATLAB software, and calculating to obtain a DBN corresponding face model related to the DBN random variable.
The construction of the response surface model is to input training sample data into an algorithm of a DBN toolbox by utilizing a DBN toolbox in MATLAB software, so that the response surface model can be constructed.
DBN can be represented as (B)0,B→) In which B is0Is a static BN, showing the probability distribution P (X) of the node at the initial time0)，B→The method is a transition network comprising two adjacent time slices, and represents the state transition probability between nodes of the two adjacent time slices, and the expression is as follows:
Figure BDA0003697487670000142
in the formula:
Figure BDA0003697487670000143
is the ith node on t time slices;
Figure BDA0003697487670000144
of parent node
Figure BDA0003697487670000145
Can be combined with
Figure BDA0003697487670000146
In the same time slice or the previous time slice, carrying out the process of unsupervised training and model parameter optimization on the basic model by inputting sample points to obtain a DBN response surface model related to the structure; FIG. 3 is a flow chart of bridge reliability prediction based on dynamic characteristics and response surface method.
S5, normalizing the random variable standard, converting the constrained optimization problem into an unconstrained optimization problem by adopting a penalty function, constructing a fitness equation suitable for solving a PSOSA algorithm, updating the optimal positions of the searched particles and the particle swarm through the PSOSA algorithm, and iterating to obtain the optimal weight of the random variable so as to support the unsupervised learning process of the DBN model.
And (3) standard normalization of the random variables, wherein in the standard normalization of the random variables, each random variable is assumed to be subjected to standard normal distribution, and the process is the standard normalization of the random variables.
And converting the random variable constraint optimization problem into an unconstrained optimization problem by adopting a penalty function method, and converting the constrained optimization problem into the unconstrained optimization problem by introducing a penalty function (9):
Figure BDA0003697487670000151
wherein F (x, sigma) is a penalty function, F (x) is an objective function, sigma is a penalty factor,
Figure BDA0003697487670000152
for the penalty term, the parameter x in F (x, σ) is not limited and may take any value.
The optimal weight of the random variable is solved by adopting a particle swarm optimization algorithm (PSOSA), and the principle is as follows:
Figure BDA0003697487670000153
in the formula: i is the particle number, d is the particle dimension number, k is the number of iterations, w is the inertial weight, c1Learning factors for individuals, c2As a group learning factor, r1,r2Is the interval of [0-1 ]]Internal random numbers, increasing the search randomness,
Figure BDA0003697487670000154
for the velocity vector of particle i in dimension d in the kth iteration,
Figure BDA0003697487670000161
for the position vector of particle i in dimension d in the kth iteration,
Figure BDA0003697487670000162
for the historical optimal position of the particle i in the d-th dimension in the k-th iteration,
Figure BDA0003697487670000163
the historical optimal position of the d-th dimension in the k-th iteration. The optimal weight of the random variable can be obtained through the gradual iteration of the formula. In the embodiment of FIG. 4 w1-w17The root mean square error of 17 random variables after 100 iterations reaches the minimum value of 0.1107%, and the optimal weight of each random variable is shown in fig. 4. FIG. 4 is a state equation containing 17 random variables, where a sample input point and a sample output point are combined to form a training sample, the normalized sample points are input into a basic DBN model for training, and a PSOSA algorithm is used for parameter optimization to obtain an optimal weight parameter w of the model1-w17The optimization process of (2) is shown in fig. 4.
S6, establishing a mathematical model for solving the structural reliability index through the prediction result of the DBN model, wherein in the process, updating and optimizing the sample of the DBN prediction model every time is needed, so that the DBN prediction model can well approach the sample point until the model constructs a response surface with enough precision, a structural extreme state function can be simulated really, and FIG. 5 shows the DBN prediction result constructed by 50 groups of training samples generated by uniformly designing random variables.
In this embodiment, the prediction result of the constructed response surface model is compared with the result of the structure true extreme state function, and when the prediction result of the response surface model converges to the result of the structure true extreme state function, the structure reliability is calculated by directly using the prediction result of the response surface. When the prediction result of the response surface model does not converge to the real extreme state function, updating and optimizing a sample of the DBN prediction model are needed, so that the DBN prediction model can well approach to a sample point until the model constructs a response surface with enough precision, and the structural extreme state function can be simulated really. As can be seen from the embodiment of fig. 5, the predicted result of the response surface model of 50 training samples of the random variable test design is consistent with the result of the actual state function of the structure, which indicates that the DBN model can truly simulate the extreme state function of the structure and has good accuracy.
The limit state function of the structure is determined based on a plurality of factors such as a structure specific form and an analysis target of reliability.
Specific embodiments of the present invention have been described above in detail. 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 concept. Therefore, the technical solutions which can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concepts of the present invention and on the prior art are within the scope of protection defined by the claims.

Claims (10)

1. The bridge reliability prediction method based on the dynamic characteristics and the intelligent algorithm response surface method is characterized by comprising the following steps of:
s1, acquiring vibration characteristic information of an existing bridge and preprocessing data;
s2, establishing a structural analysis model by combining bridge design data and operation conditions, and screening design parameters to be corrected of the structural analysis model by adopting a sensitivity analysis method;
s3, calculating target variables corresponding to the input samples to obtain output samples, forming training samples with the input samples, and correcting the initial structure analysis model by using the dynamic characteristic data of the step S1 in combination with an intelligent algorithm;
s4, calculating target variables corresponding to all input samples again based on the corrected structural analysis model to obtain output samples, constructing training samples again, carrying out normalization processing on sample points, and constructing a response surface model based on an intelligent algorithm;
s5, normalizing the random variable standard, converting the constrained optimization problem into an unconstrained optimization problem by adopting a penalty function, and acquiring the optimal weight of the random variable by utilizing an optimization algorithm;
and S6, establishing a mathematical model for solving the structural reliability index according to the prediction result of the constructed response surface model.
2. The bridge reliability prediction method based on the dynamic characteristic and response surface method as claimed in claim 1, characterized in that: step S1, acquiring actual vibration characteristic information of the bridge structure by adopting a direct measurement method or an indirect measurement method, and processing the acquired vibration information by adopting a signal processing method; wherein:
direct measurement method: directly arranging a vibration pickup on a bridge control section, collecting bridge vibration response signals through a digital signal collector, and reading bridge frequency and other responses through a power spectrogram peak value and a time domain history curve which are actually measured and recorded by a collecting system;
indirect measurement method: the sensor is arranged on the mobile trolley, when the mobile trolley drives the bridge to generate axle coupling effect, the dynamic characteristic method of the bridge is extracted from the acceleration response of the trolley body, and the information such as bridge frequency is obtained;
the signal processing method comprises the following steps: the time domain signal collected by the vibration pickup is subjected to Fourier transform, and a frequency domain result of the bridge frequency characteristic can be obtained; the fourier transform equation is:
Figure FDA0003697487660000021
in the formula: j is an imaginary unit, j ^2= -1, and no unit exists; t is a period and has a unit of second; x is a primitive function of X; t is time in seconds; ω is the frequency and x (t) is the continuous time signal.
3. The bridge reliability prediction method based on the dynamic characteristic and response surface method as claimed in claim 2, characterized in that: and S2, determining the values of bridge design parameters according to existing bridge design data, establishing an initial structure analysis model of the bridge, carrying out sensitivity analysis on each design parameter, and screening out design parameters with large response to the bridge structure.
4. The bridge reliability prediction method based on the dynamic characteristic and response surface method as claimed in claim 3, characterized in that: s2, establishing a numerical analysis model of the bridge structure by adopting finite element software according to the design data of the existing bridge; screening the sensitivity design parameters of the bridge by adopting a sensitivity analysis method; the sensitivity analysis method adopts a Morris method, the Morris method causes the change of output response through the variable quantity of a single factor, and the calculation formula is as follows:
Figure FDA0003697487660000022
in the formula: d is a radical ofi(j) J =1,2,3, \ 8230for the base effect of the jth group of samples of the ith parameter, R (R is the repeated sampling times), and n is the number of the parameters; x is the number ofiFor the ith parameter, Δ is the small variation of a single parameter, and f (·) is the response output of the corresponding parameter set;
the Morris method provides two calculation indexes to judge the sensitivity of parameters, namely a base effect mean value mu and a standard deviation sigma; mu characterizes the sensitivity of parameters, determines the sequence of the parameters, and sigma characterizes the non-linear degree between the parameters; and screening out key design parameters needing to be corrected through a Morris method calculation result.
5. The bridge reliability prediction method based on the dynamic characteristic and response surface method as claimed in claim 1, characterized in that: s3, calculating target variables corresponding to all input samples, constructing training samples between design parameters with full space and vibration response based on a uniform design theory, and substituting the training samples into an intelligent algorithm program to perform learning training; and calling the bridge vibration characteristic information obtained in the step S1 as an input parameter, substituting the input parameter into the response surface model, predicting the actual value of each design parameter, substituting the predicted value of the design parameter into the initial structure analysis model established in the step S2, and realizing the correction of the bridge structure analysis model, wherein the corrected analysis model is matched with the actual state of the existing bridge.
6. The bridge reliability prediction method based on the dynamic characteristic and response surface method as claimed in claim 5, characterized in that: s3, adopting a Latin hypercube sampling method to carry out efficient sampling from the distribution interval of design parameters, and carrying out efficient sampling on K variables x1,x2,...,xkExtracting N samples from the variable, dividing the cumulative distribution of each variable into N same small intervals, randomly selecting a value from each interval, and randomly combining the N values of each variable with the values of other variables, wherein the method can ensure the full coverage of each variable range; generating a training sample by taking each design parameter as input data and taking the structural vibration response corresponding to each set of design parameters as output data; establishing a Gaussian process response surface model on the basis of the completion of the construction of the training sample; gaussian process response surface model to training sample set (x)1,t1)、(x2,t2)...(xN,tN)，tiIs xiPredicting a new set of input quantities x corresponding to the target valuesN+1Corresponding target value t can be obtainedN+1The training set is as follows:
R＝{(Xi,Ti),i＝1,2,3,...,i,...,N} (3)；
the joint probability distribution of the training set obeys a gaussian distribution:
f(TN)～GP(m(x),K(x,x')) (4)；
wherein:
m(x)＝E[f(x)] (5)；
K(x,x')＝E[f(x)-m(x)(f(x')-m(x'))] (6)；
wherein m (x) is a mean value; f (x) is a function with respect to the sample points; e is the sign of the mean; k (x, x') is a covariance matrix;
determining a corresponding Gaussian process response surface model by determining the mean value m (x) and the covariance matrix K (x, x');
and (3) after the Gaussian process response surface model is built, inputting the bridge dynamic characteristic result obtained in the step (S1) into the Gaussian process response surface model, calculating a prediction result of the design parameters, substituting the prediction result into the initial structure analysis model in the step (S1), and finishing the correction of the initial structure analysis model.
7. The bridge reliability prediction method based on the dynamic characteristic and response surface method as claimed in claim 6, characterized in that: in step S4, based on the modified structural analysis model, the training sample is normalized by a normalization processing method, so that the normalized result is between 0 and 1, and the normalization formula:
Figure FDA0003697487660000041
in the formula: x is the number ofiFor the sample point data, yiIs the result after normalization;
substituting the normalized training sample into a DBN tool box in MATLAB software, and calculating to obtain a DBN corresponding face model related to the DBN random variable;
the construction of the response surface model is to input training sample data into an algorithm of a DBN (database-based laboratory) toolbox by utilizing a DBN toolbox in MATLAB software, so that the response surface model can be constructed; wherein: DBN can be represented as (B)0,B→) In which B is0Is a static BN, showing the probability distribution P (X) of the node at the initial moment0)，B→Is a transition network comprising two adjacent time slices,the state transition probability between nodes of two adjacent time slices is represented, and the expression is as follows:
Figure FDA0003697487660000051
in the formula:
Figure FDA0003697487660000052
is the ith node on t time slices;
Figure FDA0003697487660000053
of parent node
Figure FDA0003697487660000054
Can be combined with
Figure FDA0003697487660000055
Within the same time slice, or within a time slice preceding it.
8. The bridge reliability prediction method based on the dynamic characteristic and response surface method as claimed in claim 7, characterized in that: and S5, normalizing the random variable standard, converting the constrained optimization problem into an unconstrained optimization problem by adopting a penalty function, constructing a fitness equation suitable for solving a PSOSA algorithm, updating the optimal positions of the search particles and the particle swarm through the PSOSA algorithm, and iteratively obtaining the optimal weight of the random variable to support the unsupervised learning process of the DBN model, wherein the random variable standard normalization is carried out on the assumption that all the random variables obey standard normal distribution, and the process is the random variable standard normalization.
9. The bridge reliability prediction method based on the dynamic characteristic and response surface method as claimed in claim 8, characterized in that:
and converting the random variable constraint optimization problem into an unconstrained optimization problem by adopting a penalty function method, and converting the constrained optimization problem into the unconstrained optimization problem by introducing a penalty function (9):
Figure FDA0003697487660000056
wherein F (x, sigma) is a penalty function, sigma is a penalty factor,
Figure FDA0003697487660000061
for the penalty term, the parameter x in F (x, sigma) is not limited and can take any value;
the optimal weight of the random variable is solved by adopting a particle swarm optimization algorithm, and the principle is as follows:
Figure FDA0003697487660000062
in the formula: i is the particle number, d is the particle dimension number, k is the number of iterations, w is the inertial weight, c1For an individual learning factor, c2As a group learning factor, r1,r2Is the interval of [0-1 ]]Internal random numbers, increasing the search randomness,
Figure FDA0003697487660000063
for the velocity vector of particle i in dimension d in the kth iteration,
Figure FDA0003697487660000064
for the position vector of particle i in dimension d in the kth iteration,
Figure FDA0003697487660000065
for the historical optimal position of the particle i in the d-th dimension in the k-th iteration,
Figure FDA0003697487660000066
the historical optimal position of the d-th dimension in the k-th iteration is obtained;
the optimal weight of the random variable can be obtained through the gradual iteration of the formula.
10. The bridge reliability prediction method based on the dynamic characteristic and response surface method as claimed in claim 9, characterized in that: and S6, establishing a mathematical model for solving the structure reliability index through the prediction result of the DBN model, wherein in the process, updating and optimizing samples of the DBN prediction model every time are required, so that the DBN prediction model can approach sample points well until the model constructs a response surface with enough precision, and a structure extreme state function can be simulated really.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115828762A (en) * 2022-12-20 2023-03-21 湘潭大学 Flexural beam material constitutive parameter model correction and discrimination method
CN117875949A (en) * 2024-03-13 2024-04-12 山东交通学院 Intelligent bridge apparent disease detection method

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115828762A (en) * 2022-12-20 2023-03-21 湘潭大学 Flexural beam material constitutive parameter model correction and discrimination method
CN115828762B (en) * 2022-12-20 2024-01-05 湘潭大学 Method for correcting and judging constitutive parameter model of bent beam material
CN117875949A (en) * 2024-03-13 2024-04-12 山东交通学院 Intelligent bridge apparent disease detection method

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