A sequencing machine learning-based seismic vulnerability analysis method

Abstract

The application discloses a kind of sequencing machine learning-based seismic vulnerability analysis method, first, the ordered damage state label of structure under the action of earthquake and corresponding seismic intensity index are obtained, to obtain training data set;Then construct candidate base learning list and candidate sequencing probability structure set and carry out combination, to obtain candidate model set;Again, for each candidate model, base learning is constructed as latent function and is coupled with incremental threshold parameter, to obtain candidate sequencing probability model, according to this calculate class probability and construct negative logarithm likelihood objective function;Then using coordinate descent strategy alternately updates latent function and threshold parameter until convergence, then the optimal target model is screened by performance evaluation;Finally, the seismic intensity is input into the optimal model to obtain each damage state exceedance probability, and the seismic vulnerability curve is drawn.The design can make full use of the ordered information of damage state, compatible with various regression-type machine learning models, effectively suppress the intersection of vulnerability curve, and improve the analysis accuracy and physical rationality.

Description

Technical Field

[0001] This invention relates to a seismic vulnerability analysis method, belonging to the fields of earthquake engineering and machine learning technology, and particularly to a seismic vulnerability analysis method based on ordinal machine learning. Background Technology

[0002] Seismic vulnerability analysis quantifies the probability that a structural object will reach or exceed a specific damage state under a given seismic motion intensity. Its core is establishing the probabilistic relationship between seismic motion intensity indices and structural damage states. Traditional seismic vulnerability analysis often employs two-parameter log-normal vulnerability models or log-linear probabilistic seismic demand models. These methods are concise and physically clear, but when the structural response is affected by significant nonlinear effects and multi-source uncertainties, their fixed distribution assumptions and linear expressions cannot accurately characterize the complex probabilistic relationship between seismic motion intensity and damage states.

[0003] To improve nonlinear fitting capabilities, machine learning models have been introduced into the fields of earthquake damage prediction and vulnerability analysis in recent years. However, conventional machine learning classification models typically treat each damage state as an independent and disordered category, ignoring the inherent order of progressively increasing damage severity. This not only leads to the loss of crucial ordered information but also easily generates physically and logically illogical cross-vulnerability curves that do not conform to the actual evolution of earthquake damage.

[0004] Chinese patent application No. 202411109788.X, filed on August 14, 2024, discloses a method for assessing the seismic vulnerability of buried gas pipelines based on machine learning prediction. This method collects basic data on different buried gas pipelines under seismic action, uses pipeline material, wall thickness, and seismic intensity parameters as inputs, and the maximum stress of the pipeline as the output to train a machine learning prediction model. It then combines the predicted seismic demand with probabilistic seismic resistance to establish a seismic vulnerability model and plot failure discrimination curves. By leveraging the nonlinear fitting capability of machine learning to replace a large amount of finite element calculation, it effectively improves the efficiency of seismic vulnerability assessment of buried gas pipelines and reduces the technical threshold and time cost of analysis. However, in terms of the modeling logic of damage states, this scheme independently discriminates and calculates probabilities for different levels of damage limit states, fails to introduce a progressively increasing order constraint of damage degree in the model framework, and does not establish a progressive correlation logic between different damage levels, thus still having the following shortcomings:

[0005] It ignores the inherent order of progressively increasing damage levels.

[0006] The information disclosed in this background section is intended only to enhance understanding of the overall background of this application and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0007] The purpose of this invention is to overcome the problem in the prior art that it ignores the inherent order of progressively increasing damage levels, and to provide a seismic vulnerability analysis method based on ordered machine learning that can make full use of the inherent order of progressively increasing damage levels.

[0008] To achieve the above objectives, the technical solution of the present invention is:

[0009] A seismic vulnerability analysis method based on ordinal machine learning, the method comprising the following steps:

[0010] S1. Obtain the ordered damage state labels of the structural object to be evaluated under seismic action and the corresponding seismic intensity index to obtain the training dataset.

[0011] S2. First, construct a list of candidate base learners and a set of candidate ordered probability structures. Then, combine each base learner in the list of candidate base learners with each ordered probability structure in the set of candidate ordered probability structures to obtain a set of candidate models.

[0012] S3. For each candidate model in the candidate model set, first construct its corresponding base learner as a latent function to characterize the mapping relationship between the ground motion intensity index and the severity of damage. Then, couple the latent function with a set of incremental threshold parameters to obtain a candidate ordinal probability model. Then, calculate the category probability of each damage state based on the candidate ordinal probability model. Finally, construct a negative log-likelihood objective function based on the category probability.

[0013] S4. Using a coordinate descent strategy, the latent function and the threshold parameter are alternately updated until the preset convergence condition is met, and the trained candidate ordinal probability model is obtained.

[0014] The method for updating the latent function is as follows: first, fix the threshold parameter, then calculate the pseudo residual based on the negative gradient of the negative log-likelihood objective function with respect to the latent function, then fit the pseudo residual using the base learner, and finally update the latent function based on the fitting result.

[0015] The method for updating the threshold parameter is as follows: first, fix the latent function, then calculate the gradient of the negative log-likelihood objective function with respect to the threshold parameter, and then use the gradient descent method to update the threshold parameter based on the gradient.

[0016] S5. First, evaluate the performance of each trained candidate ordinal probability model based on the preset evaluation index, and then select the optimal target model from the candidate model set according to the performance evaluation results.

[0017] S6. First, based on the optimal target model, obtain the category probability of each damage state under each target ground motion intensity. Then, by accumulating the category probabilities of the target damage state itself and all other damage states with a greater degree of damage than the target damage state, obtain the exceedance probability corresponding to the target damage state under each target ground motion intensity. For each target damage state, plot the seismic vulnerability curve based on its exceedance probability under each target ground motion intensity to complete the seismic vulnerability analysis of the structural object to be evaluated.

[0018] In S1, the seismic intensity index is at least one of spectral acceleration, peak ground acceleration, peak ground velocity, and spectral displacement.

[0019] In S1, the ordered damage state label belongs to an ordered damage state set arranged in ascending order of damage degree, including basically intact, slightly damaged, moderately damaged, severely damaged, and destroyed.

[0020] In S1, the ordered damage status label is determined based on the comparison results between the engineering requirement parameters of the structure to be evaluated and the corresponding seismic capacity limit, or based on the results of the on-site investigation of earthquake damage.

[0021] In step S2, each base learner in the candidate base learner list is a supervised machine learning model with continuous value regression output capability.

[0022] In S2, the candidate order probability structure set includes at least one of cumulative link structure, sequential structure and adjacent category structure;

[0023] The cumulative link structure is as follows: The cumulative probability is modeled using a connection function σ, and the cumulative probability that the damage state is no higher than level k is expressed as... Where f(x) is the output of the latent function, The corresponding threshold parameter is used; and the category probability of the k-th level damage state is determined as the difference between two adjacent cumulative probabilities, i.e. ;

[0024] The sequential structure is as follows: The conditional crossing probability of each stage is modeled using a connection function σ, and the conditional crossing probability of the m-th stage is expressed as... Where f(x) is the output of the latent function, The corresponding threshold parameter is used; and the category probability of each damage state is determined as the product of the condition crossing probabilities of each stage.

[0025] The adjacent category structure is as follows: The conditional transition probability between two adjacent damage levels is modeled using a connection function σ. The conditional transition probability of taking the (k+1)th level between adjacent levels k and k+1 is expressed as follows: Where f(x) is the output of the latent function, The corresponding threshold parameter is used; and the conditional transition probabilities of each adjacent level pair are recursively normalized to obtain the category probability of each damage state.

[0026] The join function can be either the logit join function or the probit join function.

[0027] In step S3, the set of increasing threshold parameters is defined as follows: the first threshold is set as a free parameter, and the interval between adjacent thresholds is represented as an exponential function value, such that the subsequent threshold is equal to the previous threshold plus the positive interval; that is... , where j=2,…,K-1, K is the number of damage state levels, and α and δ are the parameters to be optimized.

[0028] In step S4, the preset convergence condition is: the relative change of the negative log-likelihood objective function in the current iteration relative to the previous iteration is less than the tolerance of 1 × 10⁻⁶. -5 Or the number of iterations reaches 1000.

[0029] In step S5, the specific steps for selecting the optimal target model include: first, stratifying the training dataset according to the level of ordered damage state labels, and then randomly dividing it into a training subset and a validation subset according to a preset ratio; then retraining each candidate ordinal probability model on the training subset, and calculating the evaluation index on the validation subset; then repeating the above stratification, model training and evaluation index calculation process multiple times, and taking the average of the evaluation index under multiple partitions as the performance estimate of the corresponding candidate model; finally, selecting the optimal target model from the candidate model set based on the performance estimate.

[0030] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0031] 1. In the seismic vulnerability analysis method based on ordinal machine learning of the present invention, the ordered damage state labels of the structural object to be evaluated under seismic action and the corresponding ground motion intensity index are first obtained to obtain a training dataset; then, a candidate base learner list and a candidate ordinal probability structure set are constructed, and each base learner is paired with each ordinal probability structure to obtain a candidate model set; then, for each candidate model, its corresponding base learner is constructed as a latent function to characterize the mapping relationship between ground motion intensity index and damage severity and coupled with a set of incremental threshold parameters to obtain a candidate ordinal probability model, and the category probability of each damage state is calculated accordingly and a negative log-likelihood objective function is constructed. Then, a coordinate descent strategy is used to iteratively update the latent function and threshold parameters alternately until convergence is obtained to obtain the trained candidate ordinal probability model. Next, the performance of each trained candidate ordinal probability model is evaluated based on preset evaluation indicators, and the optimal target model is selected from the candidate model set according to the evaluation results. Finally, based on the optimal target model, the category probability of each damage state under each target ground motion intensity is obtained. By accumulating the category probabilities of the target damage state itself and all other damage states with a greater degree of damage than the target damage state, the exceedance probability of the corresponding target damage state under each target ground motion intensity is obtained. Based on this, a seismic vulnerability curve is plotted, completing the seismic vulnerability analysis of the structure to be evaluated. The advantages of this invention are:

[0032] First, by using a modeling framework based on ordered probability structures, the inherent order of progressively increasing damage levels is embedded in the probability generation logic. The coupling structure of latent functions and increasing threshold parameters replaces the disordered category determination method of conventional classification models. While retaining the advantages of strong nonlinear fitting in machine learning, this fully utilizes the ordered progressive correlation between various damage states, avoids the loss of ordered damage information, and improves the rationality of the probability mapping relationship between seismic intensity and damage states.

[0033] Second, by setting strictly increasing threshold parameters and constraining the order probability structure, the model mechanism ensures that the exceedance probability of each damage state increases monotonically with the increase of earthquake intensity. This avoids the cross-vulnerability curves that are physically illogical, and makes the analysis results fully conform to the objective law of the gradual evolution of earthquake damage. This realizes a scientific vulnerability analysis based on the order of increasing damage degree.

[0034] Therefore, this invention can make full use of the inherent order of progressively increasing damage levels, effectively balancing the accuracy of nonlinear fitting with the physical rationality of the analysis results.

[0035] 2. In this invention, a seismic vulnerability analysis method based on ordinal machine learning, a candidate base learner list is constructed and paired with an ordinal probability structure for modeling. This unifies various regression-type machine learning models into a latent function representing the mapping relationship between ground motion intensity and damage severity, without requiring customized modifications to the base learner structure itself. Therefore, it is compatible with any machine learning model capable of continuous value regression output, fully leveraging the nonlinear fitting advantages of different models to accurately characterize the complex probabilistic correlations under the combined effects of nonlinear effects and multi-source uncertainties, effectively overcoming the limitations of traditional linear models and single machine learning models in terms of fitting ability. Thus, this invention possesses strong model adaptability and nonlinear expression capabilities, adaptable to the high-precision seismic vulnerability modeling needs under different data characteristics.

[0036] 3. In the seismic vulnerability analysis method based on ordinal machine learning of this invention, a candidate ordinal probability structure set including cumulative link structures, sequential structures, and adjacent category structures is constructed. This unifies the generation logic of multiple ordinal probabilities into a single modeling framework, allowing for the matching of appropriate ordinal structures to the damage evolution mechanisms of different engineering scenarios. It provides differentiated probabilistic modeling methods for various structures with different damage evolution patterns and also supports extended modeling of category-specific effects, significantly improving the flexibility and scenario adaptability of ordinal vulnerability analysis. Therefore, this invention can provide flexible ordinal modeling options for diverse engineering applications and has a wider range of engineering applicability.

[0037] 4. In the seismic vulnerability analysis method based on ordinal machine learning of this invention, a coordinate descent strategy is used to alternately update the latent function and threshold parameters. Combined with an exponentially spaced threshold parameterization method, the monotonically increasing threshold constraint is ensured. Stable joint training of the latent function and monotonic threshold can still be achieved even when the base learner is not differentiable. This training mechanism does not rely on the differentiability of the base learner and can still output stable and reliable ordinal probability prediction results even in scenarios with limited training sample size and scarce high-damage-level samples. Therefore, the training process of this invention is stable and reliable, with strong data adaptability, and can achieve stable seismic vulnerability analysis under diverse data conditions. Attached Figure Description

[0038] Figure 1 This is a flowchart of the present invention.

[0039] Figure 2 This is a schematic diagram of the longitudinal overall finite element model of the four-span reinforced concrete continuous beam bridge in Embodiment 1 of the present invention.

[0040] Figure 3 for Figure 2 Schematic diagram of fiber unit and cross-sectional structure of the middle pier.

[0041] Figure 4for Figure 2 Schematic diagram of the boundary model and constitutive relation of the middle bridge abutment.

[0042] Figure 5 This is a flowchart of the coordinate descent alternating iterative training in Embodiment 1 of the present invention.

[0043] Figure 6 This is a comparison chart of various ordered machine learning performance metrics in Embodiment 1 of the present invention.

[0044] Figure 7 This is the seismic vulnerability curve output by sequential machine learning in Embodiment 1 of the present invention. Detailed Implementation

[0045] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0046] See Figure 1 — Figure 7 A seismic vulnerability analysis method based on ordinal machine learning, the method comprising the following steps:

[0047] S1. Obtain the ordered damage state labels of the structural object to be evaluated under seismic action and the corresponding seismic intensity index to obtain the training dataset.

[0048] S2. First, construct a list of candidate base learners and a set of candidate ordered probability structures. Then, combine each base learner in the list of candidate base learners with each ordered probability structure in the set of candidate ordered probability structures to obtain a set of candidate models.

[0049] S3. For each candidate model in the candidate model set, first construct its corresponding base learner as a latent function to characterize the mapping relationship between the ground motion intensity index and the severity of damage. Then, couple the latent function with a set of incremental threshold parameters to obtain a candidate ordinal probability model. Then, calculate the category probability of each damage state based on the candidate ordinal probability model. Finally, construct a negative log-likelihood objective function based on the category probability.

[0050] S4. Using a coordinate descent strategy, the latent function and the threshold parameter are alternately updated until the preset convergence condition is met, and the trained candidate ordinal probability model is obtained.

[0051] The method for updating the latent function is as follows: first, fix the threshold parameter, then calculate the pseudo residual based on the negative gradient of the negative log-likelihood objective function with respect to the latent function, then fit the pseudo residual using the base learner, and finally update the latent function based on the fitting result.

[0052] The method for updating the threshold parameter is as follows: first, fix the latent function, then calculate the gradient of the negative log-likelihood objective function with respect to the threshold parameter, and then use the gradient descent method to update the threshold parameter based on the gradient.

[0053] S5. First, evaluate the performance of each trained candidate ordinal probability model based on the preset evaluation index, and then select the optimal target model from the candidate model set according to the performance evaluation results.

[0054] S6. First, based on the optimal target model, obtain the category probability of each damage state under each target ground motion intensity. Then, by accumulating the category probabilities of the target damage state itself and all other damage states with a greater degree of damage than the target damage state, obtain the exceedance probability corresponding to the target damage state under each target ground motion intensity. For each target damage state, plot the seismic vulnerability curve based on its exceedance probability under each target ground motion intensity to complete the seismic vulnerability analysis of the structural object to be evaluated.

[0055] In S1, the seismic intensity index is at least one of spectral acceleration, peak ground acceleration, peak ground velocity, and spectral displacement.

[0056] In S1, the ordered damage state label belongs to an ordered damage state set arranged in ascending order of damage degree, including basically intact, slightly damaged, moderately damaged, severely damaged, and destroyed.

[0057] In S1, the ordered damage status label is determined based on the comparison results between the engineering requirement parameters of the structure to be evaluated and the corresponding seismic capacity limit, or based on the results of the on-site investigation of earthquake damage.

[0058] In step S2, each base learner in the candidate base learner list is a supervised machine learning model with continuous value regression output capability.

[0059] In S2, the candidate order probability structure set includes at least one of cumulative link structure, sequential structure and adjacent category structure;

[0060] The cumulative link structure is as follows: The cumulative probability is modeled using a connection function σ, and the cumulative probability that the damage state is no higher than level k is expressed as... Where f(x) is the output of the latent function, The corresponding threshold parameter is used; and the category probability of the k-th level damage state is determined as the difference between two adjacent cumulative probabilities, i.e. ;

[0061] The sequential structure is as follows: The conditional crossing probability of each stage is modeled using a connection function σ, and the conditional crossing probability of the m-th stage is expressed as... Where f(x) is the output of the latent function, The corresponding threshold parameter is used; and the category probability of each damage state is determined as the product of the condition crossing probabilities of each stage.

[0062] The adjacent category structure is as follows: The conditional transition probability between two adjacent damage levels is modeled using a connection function σ. The conditional transition probability of taking the (k+1)th level between adjacent levels k and k+1 is expressed as follows: Where f(x) is the output of the latent function, The corresponding threshold parameter is used; and the conditional transition probabilities of each adjacent level pair are recursively normalized to obtain the category probability of each damage state.

[0063] The join function can be either the logit join function or the probit join function.

[0064] In step S3, the set of increasing threshold parameters is defined as follows: the first threshold is set as a free parameter, and the interval between adjacent thresholds is represented as an exponential function value, such that the subsequent threshold is equal to the previous threshold plus the positive interval; that is... , where j=2,…,K-1, K is the number of damage state levels, and α and δ are the parameters to be optimized.

[0065] In step S4, the preset convergence condition is: the relative change of the negative log-likelihood objective function in the current iteration relative to the previous iteration is less than the tolerance of 1 × 10⁻⁶. -5 Or the number of iterations reaches 1000.

[0066] In step S5, the specific steps for selecting the optimal target model include: first, stratifying the training dataset according to the level of ordered damage state labels, and then randomly dividing it into a training subset and a validation subset according to a preset ratio; then retraining each candidate ordinal probability model on the training subset, and calculating the evaluation index on the validation subset; then repeating the above stratification, model training and evaluation index calculation process multiple times, and taking the average of the evaluation index under multiple partitions as the performance estimate of the corresponding candidate model; finally, selecting the optimal target model from the candidate model set based on the performance estimate.

[0067] Example 1:

[0068] This embodiment uses a four-span reinforced concrete continuous beam bridge as the structural object to explain in detail the implementation process of the structural seismic vulnerability analysis method based on ordinal machine learning.

[0069] S1. Obtain the ordered damage state labels of the structural object to be evaluated under seismic action and the corresponding seismic intensity index to obtain the training dataset.

[0070] In this embodiment, the training data includes multiple samples, each consisting of a seismic intensity index and its corresponding damage state label. The seismic intensity index is a one-dimensional scalar; in this embodiment, the spectral acceleration at the longitudinal fundamental natural period of the bridge is taken. Damage status labels are ordered discrete labels, denoted in ascending order of damage severity. D K This represents the k-th level of damage, where K is the number of damage level categories.

[0071] Training data can be obtained from numerical simulations or earthquake damage surveys. For numerical simulation data, the acquisition process includes four steps: finite element modeling, seismic motion input, nonlinear time history analysis, and damage state determination. For earthquake damage survey data, damage state labels are obtained based on on-site assessment results. This embodiment uses the numerical simulation method.

[0072] (1) Finite element modeling

[0073] This embodiment uses the OpenSees finite element platform to establish a nonlinear analysis model of the bridge, such as... Figure 2 , 3 As shown in Figure 4, the bridge piers were simulated using fiber-reinforced beam-column elements. The steel reinforcement constitutive model used the Menegotto-Pinto model (Steel02), and the concrete constitutive model used the modified Kent-Park model (Concrete02), considering the differences in constraint effects between the core concrete and the protective layer concrete. The plate rubber bearings were simulated using elastoplastic spring elements to model their horizontal mechanical behavior. The interaction between the abutment and the soil behind it was characterized by nonlinear springs. The active direction used a bilinear skeleton curve, the passive direction used a hyperbolic model based on Caltrans's recommendations, and the lateral direction was treated as a friction slip model.

[0074] (2) Seismic motion input and nonlinear analysis

[0075] The seismic motion input employs a multi-strip analysis method. The spectral acceleration at the bridge's longitudinal fundamental natural period is used as the input. As an indicator of seismic intensity, no fewer than 20 natural seismic ground motion records are selected from the NGA-West2 strong earthquake database, requiring their magnitude, distance, and site conditions to be compatible with the engineering site. The selected records are amplitude-adjusted at multiple intensity levels, covering the complete range from elastic response to severe damage. In this embodiment, [the following is used]... =20 intensity levels: 0.1g, 0.2g, 0.3g, ..., 2.0g. At each intensity level, the amplitude modulation coefficient of each record was calculated. Records with amplitude modulation coefficients exceeding the reasonable range of 0.25 to 4.0 were removed to avoid severe distortion of the spectral characteristics due to excessive amplitude modulation. The retained records were randomly paired with bridge model samples to form a complete analysis sample library.

[0076] Nonlinear time history analysis was performed on each pair of bridge models and ground motion records to record the maximum response values ​​of each key component, including the maximum curvature ductility coefficient of the pier bottom section, the maximum displacement of the abutment in the active direction, the maximum displacement of the abutment in the passive direction, the maximum lateral displacement of the abutment, and the maximum horizontal displacement of each support.

[0077] (3) Damage status assessment

[0078] For each component type, multiple damage state levels, ranging from no damage to complete damage, and their corresponding thresholds are defined. This embodiment defines five damage states: basically intact, slightly damaged, moderately damaged, severely damaged, and completely destroyed, corresponding to levels D0 to D... 4， The thresholds listed in Table 1 are used for determination. The thresholds listed in Table 1 are representative values ​​for this embodiment and can be adjusted according to specific structural types and relevant specifications.

[0079]

[0080] Table 1. Thresholds for Determining Damage Status of Each Component

[0081] For each analysis sample, the maximum response of each component is compared with its corresponding damage threshold to determine the damage state level of that component. The damage state of the bridge system is determined using the series system assumption, meaning the most unfavorable damage level among all critical components is taken as the overall system damage level for that sample. All the strength index-damage state data pairs obtained after these steps constitute the training dataset. The established training dataset is... ,in As an indicator of seismic intensity, For ordered damage state labels, The total number of samples.

[0082] S2. Construct a list of candidate base learners and a set of candidate ordered probability structures. Combine each base learner in the list of candidate base learners with each ordered probability structure in the set of candidate ordered probability structures to obtain a set of candidate models.

[0083] The ordinal probability model of this invention is composed of two elements: an ordinal probability structure and a regressive base learner. To include any machine learning model and select the best one, this step first establishes a candidate base learner list and a candidate ordinal probability structure set, and then combines the two to generate a complete candidate model set.

[0084] The candidate base learner list includes supervised machine learning models with continuous value regression output capabilities. This embodiment sets them to five types: Support Vector Regression, Random Forest, Multilayer Perceptron, Gradient Boosting Tree, and Linear Model. Users can also add or replace candidate models according to specific project needs.

[0085] The candidate ordinal probability structure set includes the following three structures:

[0086] The first type is the cumulative link structure, which accumulates probabilities. Modeling. Let f(x) be the latent function output. If the threshold parameter is ordered, then Where σ is the connection function, such as the logistic function or the standard normal cumulative distribution function; the category probability of each injury level is obtained by the difference between adjacent cumulative probabilities. get.

[0087] Because the cumulative probability monotonically increases with respect to the threshold and shares the same latent function, this structure naturally guarantees an ordering relationship between different damage levels. In this bridge embodiment, this means... As the damage increases, the probability of exceeding the damage level remains monotonically constant, and the probability of exceeding the damage level at a higher level is never higher than the probability of exceeding the damage level at a lower level.

[0088] The second type is the sequential structure, which treats the evolution of damage levels as a phased process: the sample first determines whether it has crossed the first damage threshold (from D0 to D1 and above), and if it has, it continues to determine whether it has crossed the second threshold (from D1 to D2 and above), and so on. Let the conditional crossing probability of the m-th stage be... ,in The latent function can be shared across all stages or be stage-specific, with the category probability determined by the product of the conditional traversal probabilities of each stage. This structure is suitable for describing the physical process of damage progressing from low to high levels; for example, the progression of a bridge pier from protective layer cracking to core area damage conforms to this stage-traversal scenario.

[0089] The third type is the adjacent category structure, which models the log probability ratio between adjacent damage levels, i.e. The probability of each category is obtained by recursively calculating and normalizing the logarithmic probability ratio of all adjacent level pairs. This structure can directly characterize the transformation mechanism between adjacent levels. When the physical driving factors across different damage levels are different, such as support damage and pier damage being dominated by different deformation modes, the adjacent category structure can capture this difference by setting independent latent functions for different level pairs.

[0090] By pairwise combining the three ordinal probability structures with each base learner in the candidate base learner list, a set of candidate models is obtained. In this embodiment, the three structures and five base learners generate a total of 15 candidate combinations. Furthermore, to provide a non-ordinal benchmark for comparison, the nominal multi-class structure can also be included in the candidate list and combined with each base learner, increasing the total number of candidate models to 20.

[0091] S3. For each candidate model in the candidate model set, first construct its corresponding base learner as a latent function to characterize the mapping relationship between the ground motion intensity index and the severity of damage. Then, couple the latent function with a set of incremental threshold parameters to obtain a candidate ordinal probability model. Next, calculate the category probability of each damage state based on the candidate ordinal probability model. Finally, construct a negative log-likelihood objective function based on the category probability.

[0092] Specifically, for each combination of ordinal probability structures and base learners in the candidate set, a latent function and an objective function are constructed respectively. The selected regression-type base learners are then used to construct the latent function. The latent function is used to characterize the nonlinear relationship between the seismic intensity index x and the severity of damage. It receives the seismic intensity index as input and outputs a continuous scalar value, which can be physically understood as a measure of the severity of damage to the structure under a given seismic intensity. For category-specific effects, i.e., scenarios where independent latent functions are set for different stages in sequential structures or adjacent categories of structures, multiple latent functions need to be constructed. Each latent function corresponds to a stage or level pair crossing judgment, and each latent function uses a base learner of the same type but independently parameterized.

[0093] The probability of each training sample belonging to each damage state is calculated based on the selected ordering probability structure. Taking the cumulative link structure as an example, for the training sample... It belongs to a damaged state. The probability is and agreed (Right now (where is a fixed boundary that does not participate in optimization). The training objective is to minimize the negative log-likelihood of all training samples. , where N is the total number of samples.

[0094] S4. Using a coordinate descent strategy, the latent function and the threshold parameter are alternately updated until the preset convergence condition is met, and the trained candidate ordinal probability model is obtained.

[0095] This embodiment uses a coordinate descent strategy to train an ordered probability model, alternately performing latent function updates and threshold parameter updates, as follows: Figure 5 As shown.

[0096] During the latent function update step, the threshold parameter τ remains fixed for each training sample. Based on the current latent function value Calculate class probabilities with a fixed threshold τ The negative log-likelihood of the latent function with respect to its output value Find the negative gradient to obtain the pseudo residual. ; then with all pseudo-residuals Training the regression model for supervision signals And update the latent function to , where η is the learning rate.

[0097] During the threshold parameter update step, the latent function remains fixed. To ensure that the threshold is strictly increasing, the threshold τ is parameterized as a function of unconstrained parameters α and δ, i.e. Subsequent thresholds , Calculate the gradient of the objective function L with respect to α and δ, update the parameters using gradient descent, and determine the step size using backtracking search.

[0098] After each latent function update and threshold update, the convergence condition is determined: if the relative improvement of the objective function is less than the preset tolerance of 1×10⁻⁶, then the convergence condition is determined. -5 If the number of iterations reaches the preset limit of 1000, training stops; otherwise, the next round of alternating updates continues. The above training process is repeated for each combination in the candidate model set until all candidate models have been trained.

[0099] S5. First, evaluate the performance of each trained candidate ordinal probability model based on the preset evaluation index, and then select the optimal target model from the candidate model set according to the performance evaluation results.

[0100] After all candidate models have been trained, a repeated stratified partitioning strategy is used to evaluate the predictive performance of each model. First, the training dataset is stratified according to the level of ordered damage state labels, and then randomly divided into training subsets and validation subsets according to a preset ratio. Next, each candidate ordinal probability model is retrained on the training subset, and the evaluation index is calculated on the validation subset. Then, the stratified partitioning is repeated multiple times, and the average of the evaluation index under multiple partitions is taken as the performance estimate of the corresponding candidate model. Finally, the optimal target model is selected from the candidate model set based on the performance estimate.

[0101] In this embodiment, the data is randomly divided at a ratio of 80% to 20%, and this division is repeated 50 times. The evaluation metrics include the quadratic weighted Kappa coefficient, the macro-average Brier score, the ranking probability score, and the expected calibration error. Figure 6 As shown.

[0102] In this implementation, the ranking probability score is used as the main evaluation index, and the average of multiple divisions of this evaluation index is used as the ranking basis. The candidate model with the best index is selected as the optimal target model. When the main evaluation indexes of multiple candidate models are not significantly different, the base learner with lower complexity is selected first to balance interpretability and generalization ability.

[0103] The optimal model is selected from the candidate model set based on the evaluation results: when the main indicators of multiple candidate models are not significantly different, the base learner with shorter training time is selected first to balance interpretability and generalization ability.

[0104] S6. First, based on the optimal target model, obtain the category probability of each damage state under each target ground motion intensity. Then, by accumulating the category probabilities of the target damage state itself and all other damage states with a greater degree of damage than the target damage state, obtain the exceedance probability corresponding to the target damage state under each target ground motion intensity. For each target damage state, plot the seismic vulnerability curve based on its exceedance probability under each target ground motion intensity to complete the seismic vulnerability analysis of the structural object to be evaluated.

[0105] The final vulnerability analysis results are output using the optimal target model selected in S5. First, within the preset seismic intensity range... Multiple intensity points are selected at equal intervals within the model, and each is input into the optimal target model. The probability of each damage state at each intensity point is then calculated using the optimal target model. Then, the class probabilities of damage states at level k and above are summed to obtain the transcendence probability of that damage state. .

[0106] Earthquake intensity index Multiple seismic vulnerability curves can be plotted by using the horizontal axis as the plotting factor and the exceedance probability of reaching or exceeding the corresponding damage state as the vertical axis. In this embodiment, the output results for a four-span continuous beam bridge include four vulnerability curves, corresponding to minor damage and above. Moderate damage and above Severe damage and above and destruction The probability of exceeding, such as Figure 7 As shown, because the model utilizes the ordered structure of damage levels and strictly increasing threshold parameters, the output vulnerability curves satisfy the damage level order constraint throughout the entire intensity range, which is consistent with the physical evolution law of structural seismic damage.

[0107] The above description is only a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. Any equivalent modifications or changes made by those skilled in the art based on the content disclosed in the present invention should be included within the scope of protection set forth in the claims.

Claims

1. A seismic vulnerability analysis method based on ordinal machine learning, characterized in that: The method includes the following steps: S1. Obtain the ordered damage state labels of the structural object to be evaluated under seismic action and the corresponding seismic intensity index to obtain the training dataset. S2. First, construct a list of candidate base learners and a set of candidate ordered probability structures. Then, combine each base learner in the list of candidate base learners with each ordered probability structure in the set of candidate ordered probability structures to obtain a set of candidate models. S3. For each candidate model in the candidate model set, first construct its corresponding base learner as a latent function to characterize the mapping relationship between the ground motion intensity index and the severity of damage. Then, couple the latent function with a set of incremental threshold parameters to obtain a candidate ordinal probability model. Then, calculate the category probability of each damage state based on the candidate ordinal probability model. Finally, construct a negative log-likelihood objective function based on the category probability. S4. Using a coordinate descent strategy, the latent function and the threshold parameter are alternately updated until the preset convergence condition is met, and the trained candidate ordinal probability model is obtained. The method for updating the latent function is as follows: first, fix the threshold parameter, then calculate the pseudo residual based on the negative gradient of the negative log-likelihood objective function with respect to the latent function, then fit the pseudo residual using the base learner, and finally update the latent function based on the fitting result. The method for updating the threshold parameter is as follows: first, fix the latent function, then calculate the gradient of the negative log-likelihood objective function with respect to the threshold parameter, and then use the gradient descent method to update the threshold parameter based on the gradient. S5. First, evaluate the performance of each trained candidate ordinal probability model based on the preset evaluation index, and then select the optimal target model from the candidate model set according to the performance evaluation results. S6. First, based on the optimal target model, obtain the category probability of each damage state under each target ground motion intensity. Then, by accumulating the category probabilities of the target damage state itself and all other damage states with a greater degree of damage than the target damage state, obtain the exceedance probability corresponding to the target damage state under each target ground motion intensity. For each target damage state, plot the seismic vulnerability curve based on its exceedance probability under each target ground motion intensity to complete the seismic vulnerability analysis of the structural object to be evaluated.

2. The seismic vulnerability analysis method based on ordinal machine learning according to claim 1, characterized in that: In S1, the seismic intensity index is at least one of spectral acceleration, peak ground acceleration, peak ground velocity, and spectral displacement.

3. The seismic vulnerability analysis method based on ordinal machine learning according to claim 1, characterized in that: In S1, the ordered damage state label belongs to an ordered damage state set arranged in ascending order of damage degree, including basically intact, slightly damaged, moderately damaged, severely damaged, and destroyed.

4. The seismic vulnerability analysis method based on ordinal machine learning according to claim 1, characterized in that: In S1, the ordered damage status label is determined based on the comparison results between the engineering requirement parameters of the structure to be evaluated and the corresponding seismic capacity limit, or based on the results of the on-site investigation of earthquake damage.

5. The seismic vulnerability analysis method based on ordinal machine learning according to claim 1, characterized in that: In step S2, each base learner in the candidate base learner list is a supervised machine learning model with continuous value regression output capability.

6. The seismic vulnerability analysis method based on ordinal machine learning according to claim 1, characterized in that: In S2, the candidate order probability structure set includes at least one of cumulative link structure, sequential structure and adjacent category structure; The cumulative link structure is as follows: The cumulative probability is modeled using a connection function σ, and the cumulative probability that the damage state is no higher than level k is expressed as... Where f(x) is the output of the latent function, The corresponding threshold parameter is used; and the category probability of the k-th level damage state is determined as the difference between two adjacent cumulative probabilities, i.e. ; The sequential structure is as follows: The conditional crossing probability of each stage is modeled using a connection function σ, and the conditional crossing probability of the m-th stage is expressed as... Where f(x) is the output of the latent function, The corresponding threshold parameter is used; and the category probability of each damage state is determined as the product of the condition crossing probabilities of each stage. The adjacent category structure is as follows: The conditional transition probability between two adjacent damage levels is modeled using a connection function σ. The conditional transition probability of taking the (k+1)th level between adjacent levels k and k+1 is expressed as follows: Where f(x) is the output of the latent function, The corresponding threshold parameter is used; and the conditional transition probabilities of each adjacent level pair are recursively normalized to obtain the category probability of each damage state.

7. The seismic vulnerability analysis method based on ordinal machine learning according to claim 6, characterized in that: The join function can be either the logit join function or the probit join function.

8. The seismic vulnerability analysis method based on ordinal machine learning according to claim 1, characterized in that: In step S3, the set of increasing threshold parameters is defined as follows: the first threshold is set as a free parameter, and the interval between adjacent thresholds is represented as an exponential function value, such that the subsequent threshold is equal to the previous threshold plus the positive interval; that is... , where j=2,…,K-1, K is the number of damage state levels, and α and δ are the parameters to be optimized.

9. The seismic vulnerability analysis method based on ordinal machine learning according to claim 1, characterized in that: In step S4, the preset convergence condition is: the relative change of the negative log-likelihood objective function in the current iteration relative to the previous iteration is less than the tolerance of 1 × 10⁻⁶. -5 Or the number of iterations reaches 1000.

10. The seismic vulnerability analysis method based on ordinal machine learning according to claim 1, characterized in that: In step S5, the specific steps for selecting the optimal target model include: first, stratifying the training dataset according to the level of ordered damage state labels, and then randomly dividing it into a training subset and a validation subset according to a preset ratio; then retraining each candidate ordinal probability model on the training subset, and calculating the evaluation index on the validation subset; then repeating the above stratification, model training and evaluation index calculation process multiple times, and taking the average of the evaluation index under multiple partitions as the performance estimate of the corresponding candidate model; finally, selecting the optimal target model from the candidate model set based on the performance estimate.

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