Bridge structure parameter correction model establishment and prediction method based on time domain data

Abstract

The application discloses a bridge structure parameter correction model establishment and prediction method based on time domain data, which comprises the following steps: selecting at least one type of to-be-corrected parameter of a bridge structure; taking each type of to-be-corrected parameter as a training sample; obtaining a series of acceleration time history data of each type of to-be-corrected parameter corresponding to each measuring point position and taking the series as a sampling point; compressing and converting the series of acceleration time history data into accumulated intensity values and inputting data, so as to construct a training sample set; establishing a blind Kriging model; inputting the training sample set into the blind Kriging model; determining important variables by using a Bayesian variable selection algorithm; starting iteration from 0 by setting a parameter k in the blind Kriging model; finally finding an optimal value of k; finding other corresponding parameters of the blind Kriging model from the optimal value; substituting the parameters into the blind Kriging model; and obtaining a final blind Kriging model. The bridge structure parameter can be corrected based on the time domain data.

Description

Technical Field

[0001] This invention relates to the field of bridge structural parameter correction technology, specifically a method for establishing and predicting bridge structural parameter correction models based on time-domain data. Background Technology

[0002] Bridges are crucial hubs in transportation infrastructure. Accidents involving bridges during operation can disrupt traffic and threaten the lives and property of the public. Therefore, health monitoring of bridge structures is a necessary and important task. Bridge structural parameters are a key aspect of bridge monitoring. Once these parameters are obtained, numerical calculation models can be established to accurately analyze and evaluate the bridge's performance. Typically, bridge structural parameters are obtained from the bridge's design drawings, and a numerical calculation module is built based on these drawings. However, this method simplifies the model building process. Furthermore, during actual bridge construction, factors such as materials and construction techniques can cause discrepancies between the numerical calculation model and the actual structural parameters. Generally, measured values ​​more accurately reflect the true bridge structural response than numerical calculation models. Therefore, measured bridge structural values ​​can be used to correct the numerical calculation model, creating a more accurate bridge structural parameter correction model, and ultimately, a model for predicting bridge structural parameters.

[0003] In the existing technology, there are many methods for correcting bridge structural parameters. Among them, the parameter correction method based on surrogate model is an important method that can be applied to the correction of bridge structural parameters.

[0004] The existing parameter correction methods based on surrogate models mainly include the following:

[0005] 1) Correction methods based on polynomial response surface methodology. The basic principle of response surface methodology is to use simple explicit functions to gradually approximate the relationship between the actual implicit (or explicit) structural excitation and response, simplifying parameter identification and correction calculations. Considering both computational efficiency and accuracy, quadratic polynomials are currently the most commonly used response surface functions. In fact, even using quadratic polynomials with intersection terms as response surface functions, it is still impossible to fit the relationship between structural excitation and response well in space. If the relationship between excitation and response has high nonlinearity, such as above quadratic, the accuracy of using quadratic polynomials is very low, and sometimes it may even yield incorrect results. Furthermore, the polynomial model is too rigid and lacks adaptability.

[0006] 2) Neural Network-Based Correction Methods. Artificial neural networks are high-performance fitting functions based on the basic structure and interaction mechanisms of neurons, the fundamental building blocks of the human brain. By learning from the input (parameters to be corrected) and output (response), the mapping relationship between them can be stored as the connection strength between neurons. Neural network methods can achieve satisfactory results when sufficient training samples are available. However, neural networks lack a rigorous mathematical foundation and suffer from the following problems: the structure of the neural network needs to be pre-defined or continuously explored during training, making this method overly reliant on the user's prior knowledge and experience, leading to difficulties in structure selection; neural networks may get trapped in local minima, causing local extrema problems; and "underlearning" or "overlearning" problems may occur.

[0007] 3) Corrective methods based on Support Vector Machines (SVMs). Statistical learning theory is built on a solid theoretical foundation, providing a unified framework for solving finite-sample learning problems. Support Vector Machines (SVMs) are a new, general-purpose learning method developed on this theoretical foundation, capable of overcoming the difficulties of structure selection, local extrema, and the curse of dimensionality in artificial neural networks. In recent years, SVMs have demonstrated superior performance compared to existing methods. However, SVMs are easily limited by the dimensionality of the recognition parameters; if the number of parameters is large, their effectiveness cannot be guaranteed.

[0008] 4) Kriging-based Correction Method. Kriging is a widely used statistical forecasting method in mathematical geology based on stochastic processes. It can find optimal and linear unbiased interpolation estimates for regionalized variables, exhibiting smoothing effects and minimizing estimation variance. It holds an important position in linear geostatistics. This method was first proposed by the South African geologist Krige in 1951. Before being introduced into the field of optimization design, it was mainly used in geology to determine the distribution of mineral reserves. Subsequently, Matheron of France theorized and systematized Krige's results, proposing the concept of regionalized variables. As an improved technique of linear regression analysis, Kriging includes both linear regression and nonparametric components, with the nonparametric component considered as an unrealized stochastic distribution. Kriging simulations at a given point rely on information from known variables surrounding that point; that is, they estimate the unknown information at that point through a weighted linear combination of information within a certain range. The weighting is determined by minimizing the error variance of the estimate; therefore, the Kriging model is considered the optimal linear unbiased estimate. Kriging modeling is more flexible, as it can not only provide estimated values ​​for corrected parameters but also provide estimates of the errors in those values. This is the main difference between Kriging models and other proxy models.

[0009] Existing parameter correction methods based on surrogate models have the following two main drawbacks:

[0010] First, existing technologies, when using bridge structural response information, primarily select the natural frequencies of the bridge structure in the frequency domain (rather than time-domain information) as feature data for parameter correction. The main reason is that in Kriging models, complex, multi-dimensional time-domain information (such as acceleration time histories, which are time-series data, similar to tensor data) is extremely difficult to use as input; while the natural frequencies of a finite-order bridge structure are simple scalar data and are easily used as input. As mentioned earlier, due to the limited number of frequency orders actually obtainable (containing limited information), correction methods based on the structure's natural frequencies often cannot guarantee the accuracy of the results when there are many parameters to be corrected. Furthermore, if the structure has dense modes or high damping, the difficulty of identification increases significantly. Compared to frequency-domain information, time-domain information contains the most comprehensive and original information, effectively avoiding errors caused by secondary data analysis. In short, existing technologies in bridge structural parameter correction methods basically lack effective utilization of time-domain information.

[0011] Second, the proxy models used in existing technologies are basically typical general Kriging models, without any corresponding improvements based on the actual bridge engineering situation. This is mainly reflected in the following two aspects:

[0012] a. First, for the Kriging model, the basis functions in the regression model [f1(x)...f p The selection of (x)] often depends on the complexity of the actual engineering problem. In existing technologies, standard-Kriging (where the regression part is taken as a constant) is basically used, which lacks flexibility and robustness and may not be consistent with the actual situation.

[0013] 2) Secondly, in actual bridge structures, there are numerous structural parameters. Some parameters have a significant impact on the response (i.e., high sensitivity), while others have a small impact (some are even negligible). In kriging models, a more complex regression model (e.g., considering all parameters) does not necessarily lead to better predictive performance. This mainly depends on the importance of the selected factor variables (i.e., the action terms related to the structural parameters, including interaction terms). Unimportant factor variables may actually reduce prediction accuracy and computational efficiency. Therefore, when building a kriging model, the regression model should prioritize important factor variables and ignore some unimportant ones. This greatly helps ensure both accuracy and efficiency. Of course, some existing techniques pre-determine the importance of factors through sensitivity analysis, but this approach leads to extremely low efficiency because the intermediate process requires multiple manual trial calculations, and often results in coarse segmentation due to computational constraints, causing the sensitivity analysis results to deviate significantly from reality.

[0014] The following are relevant references on using numerical calculation models to correct bridge structural parameters:

[0015] [1] Zhou Chiwei. Research on bridge finite element model correction based on Taylor expansion and wind-driven optimization algorithm [D] Beijing Jiaotong University, 2016.

[0016] [2] Zhang Xueqiang. Research on the Correction of Multiple Solutions Problem of Finite Element Model of Bridge Structure Based on Crowd Intelligence Algorithm [D] Wuhan University of Technology, 2020.

[0017] [3] Mao Jianping. Correction of static finite element model of bridge structure based on neural network [D] Jilin University, 2011.

[0018] [4] Zhang Kezan. Parameter identification and correction of static finite element model of reinforced rigid frame arch bridge based on different neural networks [D] Chang'an University, 2018.

[0019] [5] Liu, Shengzhong. Prediction of main beam elevation and parameter identification during construction of long-span concrete cable-stayed bridges [D]. South China University of Technology, 2017.

[0020] [6] Wei Tuo. Bridge structural damage identification based on support vector machine and modal curvature [J]. Northern Transportation, 2011, 08: 40-42.

[0021] [7] Zhao Yunpeng, Yu Tianlai, Jiao Yubo, Gong Yafeng, Song Gang. Damage identification method and parameter influence analysis of irregular bridges [J]. Journal of Jilin University (Engineering Science), 2016, 46(06):1858-1866.

[0022] [8] Chen Yuxuan. Modal extension and finite element model correction of long-span arch bridges based on Kriging method [D]. South China University of Technology, 2019.

[0023] [9] Ding Xi. Load test and ultimate bearing capacity analysis of irregular steel truss bridge [D]. Hefei University of Technology, 2020.

[0024]

[10] Hong Yu. Research on Modal Parameter Identification and Model Correction of Bridge Structures Based on Vibration Signals [D] Southwest Jiaotong University, 2019.

[0025]

[11] Liu Bing. Parameter identification of bridge construction stage based on PC-Kriging substitution model [D]. South China University of Technology, 2018.

[0026]

[12] Qin Chao. Research on Fast Bayesian Method for Identification of Modal Parameters and Model Correction of Bridge Structures [D]. Hefei University of Technology, 2020.

[0027]

[13] Sun Cheng. Correction of the finite element model of Taiping Lake Bridge based on Kriging model [D]. Hefei University of Technology, 2018.

[0028]

[14] Ding Xi, Wang Zuocai. Correction of Finite Element Model of Irregular Steel Truss Bridge Based on Kriging Proxy Model [J]. Anhui Architecture, 2020, 27(03):91-95.

[0029]

[15] Kaymaz I.Application of kriging method to structural reliabilityproblems[J].Structural Safety,2005,27(2):133-151.

[0030]

[16] Sacks J., Schiller SB, Welch WJDesigns for computer experiments[J].Technometrics, 1989, 31(1):41-7. Summary of the Invention

[0031] In view of the shortcomings of the prior art, one of the objectives of this invention is to provide a method for establishing a bridge structural parameter correction model based on time domain data, which can solve the problems described in the background art.

[0032] The second objective of this invention is to provide a method for predicting bridge structural parameters based on time-domain data, which can solve the problems described in the background art.

[0033] One of the technical solutions to achieve the objective of this invention is: a method for establishing a bridge structural parameter correction model based on time-domain data, comprising the following steps:

[0034] Step 1: Select at least one type of bridge structure parameters to be corrected;

[0035] Step 2: Use each type of parameter to be corrected as a training sample y. The number of sample points of the training sample y is N×n, where N and n are both positive integers greater than 1.

[0036] Step 3: Determine the measurement point locations of at least two sets of dynamic time histories, perform measurements at each measurement point location, and obtain the measurement point acceleration time history data series corresponding to each type of parameter to be corrected at each measurement point location. The measurement point acceleration time history series is used as the sampling point.

[0037] Step 4: Compress the acceleration time history data series at the measuring points according to formula ① to obtain the cumulative intensity value CI(δ):

[0038]

[0039] In the formula, a(t) represents the acceleration value at time t, which is the time history data series of acceleration at the measuring point. d This represents the duration from the start of the measurement to the present. δ is a hyperparameter that can take multiple different values.

[0040] The cumulative intensity value CI(δ) is used as the input data x of the blind kriging model Y(x), and combined with the training sample y obtained in step 1, so as to obtain the training sample set [x,y] with a one-to-one mapping relationship.

[0041] Step 5: Establish the blind kriging model Y(x) as shown in Equation ②:

[0042]

[0043] In the formula, f k (x)′=[f1(x),f2(x),…,f k (x)],f k (x)′ is also the basis function, μ k =[μ0,μ1,…μ k ],

[0044] Kriging predictions based on formula ② As shown in formula ③:

[0045]

[0046] In the formula, F k =(f k (x1),f k (x2),…,f k (x m ))′, x i Let i = 1, 2, ..., m represent the i-th input data, and m represent the total number of input data.

[0047] The Bayesian variable selection algorithm was used to select important variables from candidate variables, which included linear terms, quadratic terms, and two-factor interaction terms.

[0048] Assume u0, u1, ..., u t As candidate variables, formula ③ is simplified to formula ④:

[0049]

[0050] Where u0=1, v1,…,v i ,…,v k ∈{u1,…,u tIf x1 and x2 are the only two factor variables, then formula ④ becomes formula ⑤:

[0051]

[0052] Where u0 = 1, When t > m-1, for all β i Dense estimation is impossible; in this case, a Bayesian variable selection algorithm is used to solve the problem. To do this, assume β = (β0, β1, ... β) t The prior distribution of ) is shown in formula ⑥:

[0053]

[0054] In the formula, Let ψ be the prior covariance matrix, and let ψ be a (t+1)×(t+1) diagonal matrix. ψ is determined as follows:

[0055] Assuming the correlation function in the Kriging model has a multi-correlation structure, by Given that if β i Includes the first-order effect of factor j, l ij =1, otherwise l ij =0, similarly, β i If the quadratic effect of factor j is included, then q ij =1, otherwise q ij =0, therefore the i-th diagonal element of ψ is in: Assuming that Z(x) in formula ① follows a Gaussian process, then, based on Bayesian theory, the posterior mean of β is approximately given by formula ⑦:

[0056]

[0057] In the formula, U is the model matrix. Taking a 3-level model as an example, its orthogonal polynomial basis form model matrix is:

[0058]

[0059] If a variable has a large absolute coefficient, it is considered an important variable. In each step, k = 0, 1, 2, ..., select those variables with the largest absolute coefficient. The variable is set as an important variable, without loss of generality, in formula ⑦.

[0060] The leave-one-out method in cross-validation is used, selecting one set of samples for validation and using the rest for model training, as detailed below:

[0061] Pick As the prediction result after deleting the i-th data point, the leave-one-out cross-validation error is then defined as...

[0062]

[0063] Therefore, the verification prediction error is:

[0064]

[0065] Next, solve...

[0066]

[0067] The optimal value of k can be obtained.

[0068] After selecting the key variables, the next step is to determine the undetermined parameters θ in the blind kriging model. First, assume the correlation function r(x) is a Gaussian kernel function:

[0069]

[0070] Define θ = [θ1, θ2, ... θ] p ], parameter θ, Estimate using maximum likelihood.

[0071] Under the assumption that Z(x) follows a Gaussian process, the negative value of the log-likelihood function is expressed as:

[0072]

[0073] Assuming θ is known, pair NLH Finding the minimum, we get:

[0074]

[0075]

[0076] At this point, the corresponding minimum NLH value is:

[0077]

[0078] Now consider the case where θ is unknown, then θ is estimated only when k = 0:

[0079]

[0080] Starting by setting k=0, and using the formula... Calculate Then based on the calculations... Substituting into formula ⑦ will give you the result. exist Select The variable corresponding to the maximum value is the first important variable v1. Then, k is set sequentially to 1, 2, ..., and the above process is repeated to obtain the corresponding important variables until the validation prediction error CVPE in the leave-one-out method reaches its minimum value. At this point, the formula is obtained. The corresponding optimal k value, denoted as k. opt ,

[0081] Then, according to k opt Corresponding and formula Calculated Establish the final blind Kriging model, formula As shown below:

[0082]

[0083] The above steps establish a model that can correct the bridge structural parameters.

[0084] Furthermore, the parameters to be corrected include concrete elastic modulus, section moment of inertia, beam unit weight, and support stiffness. Each of these parameters corresponds to a class of parameters to be corrected.

[0085] Furthermore, the Latin hypercube experimental design method was used to design corresponding training samples for each class of parameters to be corrected.

[0086] Furthermore, δ = [0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0].

[0087] One of the technical solutions to achieve the objective of this invention is: a method for predicting bridge structural parameters based on time-domain data, comprising the following steps:

[0088] Step S1: Obtain the actual measured acceleration time history data series at the measuring points, compress the acceleration time history data series at the measuring points into cumulative strength values, and input the cumulative strength values ​​as input data into the blind kriging model to predict the bridge structure parameters. The predicted parameters are recorded as the predicted parameters.

[0089] Step S2: Replace the predicted parameters with the corresponding parameters to be corrected in the initial blind kriging model to complete the parameter correction.

[0090] The beneficial effects of the present invention are as follows: Compared with the prior art, the present invention has the following advantages:

[0091] 1) It can make full and limited use of measured data, with fewer restrictions on engineering applications. Compared with existing technologies (which use frequency domain information), this invention uses time domain data instead of frequency domain information as input data (time domain data is the most comprehensive and original), while overcoming the problem that frequency domain information cannot be applied to structural modes with high damping in existing technologies.

[0092] 2) The small training sample size and high computational efficiency ensure the applicability of time-domain data in the Kriging model. This invention compresses the acceleration time history data, converting it into cumulative intensity values. This transforms the time history sequence with its large number of sample points into one-dimensional data represented by simple scalars, significantly reducing the input sample size and improving computational efficiency. This successfully enables the use of the Kriging model to correct the parameters of bridge structures based on time-domain data.

[0093] 3) The application effect will be closer to reality. Existing technologies, when correcting parameters based on Kriging models, indiscriminately pre-set the basis functions in the regression terms to a standard form. This adds unnecessary computational workload to parameter correction and often has a counterproductive effect. This invention believes that the basis functions in the regression terms of traditional Kriging models should not be set as known, but should be optimized and confirmed through primary and secondary selection techniques. Therefore, a blind Kriging model is adopted. It can automatically select important variables and discard unimportant variables, effectively combining the actual situation in bridge parameter correction, and further ensuring the accuracy and efficiency of bridge structural parameter correction. Attached Figure Description

[0094] Figure 1 A flowchart illustrating the method for building the model;

[0095] Figure 2 This is a flowchart illustrating a method for predicting bridge structural parameters. Detailed Implementation

[0096] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0097] Example 1

[0098] like Figure 1 As shown, a method for establishing a bridge structural parameter correction model based on time-domain data includes the following steps:

[0099] Step 1: Select different types of parameters to be corrected for the bridge structure. The parameters to be corrected include concrete elastic modulus, section moment of inertia, beam unit weight, and support stiffness. Among them, concrete elastic modulus, section moment of inertia, beam unit weight, and support stiffness are all corresponding to one type of parameter to be corrected.

[0100] Step 2: Take each type of parameter to be corrected as a corresponding training sample y. The number of sample points of the training sample y is N×n, where N and n are both positive integers greater than 1. Usually, N = 5-10, and n is the number of variables. In this embodiment, the value is 4.

[0101] Specifically, the Latin hypercube experimental design method can be used to design corresponding training samples for each type of parameter to be corrected. That is, through the Latin hypercube experimental design method, the concrete elastic modulus can be used to obtain the corresponding concrete elastic modulus training sample y, the section moment of inertia can be used to obtain the corresponding section moment of inertia y, the beam unit weight can be used to obtain the corresponding beam unit weight training sample y, and the support stiffness can be used to obtain the corresponding support stiffness training sample y.

[0102] Step 3: Determine the measurement point locations for at least two sets of dynamic time histories. Perform measurements at each measurement point location to obtain the acceleration time histories data series corresponding to each type of parameter to be corrected at each measurement point location. The acceleration time histories series at each measurement point location are used as sampling points. Generally, the number of sampling points corresponding to each type of parameter to be corrected at each measurement point location is set to 1000-2000.

[0103] Step 4: Compress the acceleration time history data series at the measuring points according to formula ① to obtain the cumulative intensity value CI(δ):

[0104]

[0105] In the formula, a(t) represents the acceleration value at time t, which is the time history data series of acceleration at the measuring point. d This represents the duration from the start of the measurement to the present. δ is a hyperparameter, and δ can take multiple different values. In this embodiment, δ = [0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0], a total of 10 values.

[0106] Formula ① transforms a large number of sampling points into cumulative intensity values ​​with 10 different δ values, where CI(δ) is a one-dimensional scalar array. If the original acceleration time history data series from a single measurement point is directly imported into the numerical model without the compression transformation using Formula ①, two drawbacks exist: First, the number of sampling points from a single measurement point's acceleration time history data is enormous, potentially tens of thousands, leading to a massive computational burden and significant computational challenges. Second, sampling points from different measurement point locations need to have the same number of time steps multiplied by the time length, which is difficult to guarantee in practice. This embodiment avoids these two drawbacks by compressing the original acceleration time history data series into cumulative intensity values. The cumulative intensity value is a highly compressed feature value that retains the original time-domain characteristics. After integration, the dimension of the data is reduced to 1, significantly reducing the computational burden. Furthermore, its time-domain relevant information is preserved, enabling model building based on time-domain data. Compared to the traditional time-domain to frequency-domain conversion method, which contains limited information in the frequency domain of modes of finite order and is also constrained by the dense structure modes and large damping, this embodiment contains the most comprehensive and original information, which can effectively avoid errors caused by secondary data analysis.

[0107] The cumulative intensity value CI(δ) is used as the input data x of the blind kriging model Y(x), and combined with the training sample y obtained in step 1, so as to obtain a training sample set [x,y] with a one-to-one mapping relationship.

[0108] Step 5: The blind kriging model is obtained based on the traditional kriging model Y(x), as shown in Equation ②:

[0109]

[0110] In the formula, f k (x)′=[f1(x),f2(x),…,f k (x)],f k (x)′ is also the basis function, μ k =[μ0,μ1,…μ k [k is unknown.] The Kriging prediction based on formula ② is... As shown in formula ③:

[0111]

[0112] In the formula, F k =(f k (x1),f k (x2),…,f k (x m ))′, xi Let i = 1, 2, ..., m represent the i-th input data, and m represent the total number of input data.

[0113] In the blind kriging model represented by formula ②, the most important thing is to determine f. k (x), which refers to variable selection. Since there are a vast number of bridge structural parameters to be corrected in bridge structural parameter correction, it is nearly impossible to obtain the closest model by searching through all these variables. Therefore, it is necessary to select important variables and discard unimportant ones. This embodiment uses a Bayesian variable selection algorithm to select important variables, that is, to choose important variables from the candidate variables.

[0114] The candidate variables include linear terms, quadratic terms, and two-factor interaction terms. The two-factor interaction terms include linear-linear interaction terms, linear-quadratic interaction terms, and quadratic-quadratic interaction terms, totaling 2n. 2 There are n, where n is the number of candidate variables.

[0115] Taking low-order terms as an example, this section explains the process and principle of the Bayesian variable selection algorithm. First, the candidate variables are regularized to a certain interval [a, b], where b > a > 0. For example, regularization to [1, 3] yields the following orthogonal polynomial basis:

[0116]

[0117] In the formula, Let j represent the j-th linear term. Let x represent the j-th quadratic term. j When the values ​​are 1, 2, and 3, the linear term and quadratic terms Having the same length Therefore, these variables can be used instead of defining the two-factor interaction term. For example, the first- and second-order interaction term of x1 and x2 can be defined as...

[0118] Assume u0, u1, ..., u t As candidate variables, formula ③ is simplified to formula ④:

[0119]

[0120] Where u0=1, v1,…,v i ,…,v k ∈{u1,…,u t} are important variables, responsible for explaining most of the changes in the response. Taking two factor variables, x1 and x2, as an example, equation ④ becomes equation ⑤:

[0121]

[0122] Where u0 = 1, When t > m-1, for all β i Dense estimation is impossible; however, this is precisely the case where the Bayesian variable selection algorithm can be used to solve this problem. To do this, assume β = (β0, β1, ... β2). t The prior distribution of ) is shown in formula ⑥:

[0123]

[0124] In the formula, Let ψ be the prior covariance matrix, and let ψ be a (t+1)×(t+1) diagonal matrix. ψ can be determined as follows:

[0125] Assuming the correlation function in the Kriging model has a multi-correlation structure, by Given. If β i Includes the first-order effect of factor j, l ij =1, otherwise l ij =0. Similarly, β i If the quadratic effect of factor j is included, then q ij =1, otherwise q ij =0. Therefore, the i-th diagonal element of ψ is in: Assume that Z(x) in formula ① follows a Gaussian process. Then, based on Bayesian theory, the posterior mean of β can be approximated by formula ⑦:

[0126]

[0127] In the formula, U is the model matrix. Taking a 3-level model as an example, the 3 levels are a concept in positive pricing design methods, meaning that each variable factor varies within a range of 3 levels. The model matrix in orthogonal polynomial basis form is:

[0128]

[0129] A variable is considered important if its absolute coefficient is large. Therefore, in each step k = 0, 1, 2…, variables with the largest absolute coefficients can be selected. The variable is taken as an important variable. Without loss of generality, we can set it in formula ⑦. This further simplifies the calculation.

[0130] In this Bayesian positive variable selection strategy, an important question remains: when should we stop adding terms to the mean? In other words, what is the optimal value of k? The difficulty in choosing k lies in the fact that regardless of its value, the Kriging prediction model will interpolate the data to give a perfect fit (with a prediction error of 0), making it impossible to use traditional model selection criteria (such as C) in regression analysis. p (Statistical standard). Fortunately, cross-validation can be used as a criterion for selecting the optimal k value. The basic idea of ​​cross-validation is to divide the data into two parts: one part is used to train the model, and the other part is used to validate the model's predictive performance. Here, we use the leave-one-out method in cross-validation, which selects only one set of samples for validation and uses the rest to train the model. Specifically:

[0131] Pick As the prediction result after deleting the i-th data point, the leave-one-out cross-validation error is then defined as...

[0132]

[0133] Therefore, the verification prediction error is:

[0134]

[0135] Next, solve...

[0136]

[0137] The optimal value of k can be obtained.

[0138] After selecting the key variables, the next step is to determine the parameters to be determined in the blind kriging model (parameters θ, ...). First, assume the correlation function r(x) is a Gaussian kernel function:

[0139]

[0140] Define θ = [θ1, θ2, ... θ] p ]. Parameter θ, Maximum likelihood estimation can be used. Since the model is selected based on the cross-validation criterion, it seems more appropriate to use the same criterion for estimation. However, many empirical studies have shown that maximum likelihood estimation outperforms cross-validation-based estimation.

[0141] Under the assumption that Z(x) follows a Gaussian process, the negative value of the log-likelihood function can be expressed as:

[0142]

[0143] Currently, assume θ is known. Pair NLH with... Finding the minimum, we get:

[0144]

[0145]

[0146] At this point, the corresponding minimum NLH value is:

[0147]

[0148] Now, consider the case where θ is unknown. It can also be estimated by minimizing NLH in equation ⑩. However, minimization is not a simple task (finding the global minimum is not easy). θ can only be estimated when k = 0:

[0149]

[0150] From the above formula, we can start by setting k=0, and then use the formula... Calculate Then based on the calculations... Substituting into formula ⑦ will give you the result. exist Select The variable corresponding to the maximum value is the first important variable, v1. Then, k is set sequentially to 1, 2, ..., and the above process is repeated to obtain the corresponding important variables until the validation prediction error (CVPE) in the leave-one-out method reaches its minimum value. At this point, the formula is obtained. The corresponding optimal k value, denoted as k. opt .

[0151] Then, according to k opt Corresponding and formula Calculated Establish the final blind Kriging model. Formula As shown below:

[0152]

[0153] The above steps establish a model capable of correcting bridge structural parameters. This model is a blind kriging model, using time-domain data to preserve the original effective information to the greatest extent possible. Using time-domain data instead of frequency-domain information as input avoids information leakage caused by time-domain to frequency-domain conversion and avoids limitations imposed by dense structural modes and large damping. Simultaneously, using cumulative intensity values ​​instead of the original acceleration time sequence achieves high-dimensional compression while retaining the original time-domain information, significantly improving computational efficiency.

[0154] Example 2

[0155] Example 1 establishes a blind kriging model that can correct bridge structural parameters. This model can predict bridge structural parameters, and the predicted parameters can then replace the previously set parameters to be corrected in the blind kriging model, thus correcting the bridge structural parameters. This includes the following steps:

[0156] Step S1: Obtain the actual measured acceleration time history data series, compress the acceleration time history data series into cumulative strength values, and input the cumulative strength values ​​as input data into the blind kriging model obtained in Step 1 to predict the bridge structure parameters. The predicted parameters are recorded as the predicted parameters.

[0157] Step S2: Replace the predicted parameters with the corresponding parameters to be corrected in the initial blind kriging model to complete the parameter correction.

[0158] The embodiments disclosed in this specification are merely illustrative of one aspect of the invention, and the scope of protection of the invention is not limited to these embodiments. Any other functionally equivalent embodiments fall within the scope of protection of the invention. Those skilled in the art can make various other corresponding changes and modifications based on the technical solutions and concepts described above, and all such changes and modifications should fall within the scope of protection of the claims of this invention.

Claims

1. A method for establishing a bridge structural parameter correction model based on time-domain data, characterized in that, Includes the following steps: Step 1: Select at least one type of parameter to be corrected for the bridge structure. The parameters to be corrected include concrete elastic modulus, section moment of inertia, beam unit weight, and support stiffness. Each of these parameters corresponds to one type of parameter to be corrected. Step 2: Use each type of parameter to be corrected as a training sample y. The number of sample points of the training sample y is N×n, where N and n are both positive integers greater than 1. Step 3: Determine the measurement point locations of at least two sets of dynamic time histories, perform measurements at each measurement point location, and obtain the measurement point acceleration time history data series corresponding to each type of parameter to be corrected at each measurement point location. The measurement point acceleration time history series is used as the sampling point. Step 4: Compress the acceleration time history data series at the measuring points according to formula ① to obtain the cumulative intensity value. : ------① In the formula, This represents the acceleration value at time t, which is also the time history data series of the acceleration at the measuring point. This indicates the duration from the start of the measurement to the present. It's a hyperparameter. Take multiple different values, Cumulative intensity value As a blind Kriging model The input data x is combined with the training samples y obtained in step 1 to obtain a training sample set [x,y] with a one-to-one mapping relationship. Step 5: Establish a blind kriging model as shown in Formula ② : ------② In the formula, , That is, basis functions. , Kriging predictions based on formula ② As shown in formula ③: ------③ In the formula, , , This represents the i-th input data, and m represents the total number of input data. The Bayesian variable selection algorithm was used to select important variables from candidate variables, which included linear terms, quadratic terms, and two-factor interaction terms. Assumption As candidate variables, formula ③ is simplified to formula ④: ------④ in, , As important variables, if there are only two factor variables and At this point, formula ④ becomes formula ⑤: ------⑤ in, , , , , , , , , ,when At that time, for all Dense estimation is impossible; in this case, the Bayesian variable selection algorithm is used to solve the problem. To achieve this, it is assumed that... The prior distribution is shown in formula ⑥: ------⑥ In the formula, The prior covariance matrix, for diagonal matrix Determine using the following method: Assuming the correlation function in the Kriging model has a multi-correlation structure, by Given, if Inclusion factor One effect, ,otherwise Similarly, Inclusion factor The secondary effect, then ,otherwise ,then The The diagonal elements are ,in: Assuming formula ① Following a Gaussian process, then, based on Bayesian theory, The posterior mean is approximately given by formula ⑦: ------⑦ In the formula, For the model matrix, If the absolute coefficient of a variable is large, it is considered an important variable and is included in each step. Choose those with the largest The variable is set as an important variable, without loss of generality, in formula ⑦. , The leave-one-out method in cross-validation is used, selecting one set of samples for validation and using the rest for model training, as detailed below: Pick As the deletion of the first The prediction results after 100 data points, and then the leave-one-out cross-validation error is defined as... Therefore, the verification prediction error is: Next, solve... ------ The optimal result can be obtained. value, After selecting the key variables, the next step is to determine the parameters to be determined in the blind kriging model. , , First, let's assume the relevant function For Gaussian kernel function: definition ,parameter , , Estimate using maximum likelihood. exist Under the assumption of following a Gaussian process, the negative value of the log-likelihood function is expressed as: Assumption It is known that, right , Finding the minimum, we get: ------⑧ ------⑨ At this time, the corresponding The minimum value is: ------⑩ Now consider In the case of unknown circumstances, only Time estimation : ------ Starting by setting k=0, and using formula ⑧- Calculate , , Then based on the calculations obtained , , Substituting into formula ⑦ will give you the result. ,exist Select The variable corresponding to the maximum value is the first important variable. Then, set them in sequence. Repeat the above process to obtain the corresponding important variables until the validation prediction error (CVPE) in the leave-one-out method reaches its minimum value, at which point the formula is obtained. The corresponding optimal k value is denoted as . , Then, according to Corresponding , and formula Calculated Establish the final blind Kriging model, formula As shown below: ------ The above steps establish a model that can correct the bridge structural parameters.

2. The method for establishing a bridge structural parameter correction model based on time-domain data according to claim 1, characterized in that, The Latin hypercube experimental design method was used to design corresponding training samples for each class of parameters to be corrected.

3. The method for establishing a bridge structural parameter correction model based on time-domain data according to claim 2, characterized in that, 。 4. A method for predicting bridge structural parameters based on time-domain data, comprising the following steps: Step S1: Obtain the actual measured acceleration time history data series, compress the acceleration time history data series into cumulative strength values, and input the cumulative strength values ​​as input data into the blind kriging model obtained as claimed in any one of claims 1-3 to predict the bridge structure parameters. The predicted parameters are recorded as the predicted parameters. Step S2: Replace the predicted parameters with the corresponding parameters to be corrected in the initial blind kriging model to complete the parameter correction.

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