Nonlinear post-buckling stability calculation method based on deep learning

Abstract

The application discloses a nonlinear structure post-buckling stability calculation method based on deep learning, relates to the technical field of structural engineering calculation and data processing, and comprises the following steps: constructing nonlinear behavior data of a structure under different loading conditions; establishing a buckling critical state prior perception model to identify potential buckling critical regions in the loading process of the structure; further constructing a post-buckling path generation model based on bifurcation guide constraints to predict various response paths of the structure after buckling; establishing a stability evolution determination model to analyze and determine the stability state of the structure at different loading stages; and comprehensively calculating the overall stability of the structure to output stability determination results, stability change trends and key critical state identification results. The application can realize systematic analysis of the post-buckling multi-path response and stability evolution process of a complex structure, improve the accuracy and integrity of structural stability evaluation, and has good engineering application value.

Description

Technical Field

[0001] This invention relates to the field of structural engineering calculation and data processing technology, specifically to a method for calculating the post-buckling stability of nonlinear structures based on deep learning. Background Technology

[0002] The deep learning-based method for calculating the post-buckling stability of nonlinear structures is a computational approach for analyzing the nonlinear response of complex structures. Its core lies in constructing structural nonlinear behavior representation data and combining it with prior perception modeling of the buckling critical state, prediction of post-buckling path generation, and modeling of stability evolution to achieve comprehensive calculation and evaluation of the stability state of the structure in the buckling and post-buckling stages.

[0003] In existing technologies, the main analytical methods for structural buckling problems include eigenvalue buckling analysis based on the finite element method and nonlinear numerical simulation methods. Eigenvalue buckling analysis is typically used to solve for the critical buckling load of a structure, but this method relies on linearization assumptions and is difficult to accurately describe the structure's response behavior after buckling. While nonlinear numerical simulation methods can simulate the actual response of a structure during loading, they usually only yield single-path results and lack effective characterization of the multi-path bifurcation behavior that may occur in the post-buckling stage.

[0004] Furthermore, in practical engineering, structures often undergo a complex critical state evolution process before entering the buckling stage. Existing methods mostly rely on empirical judgment or simple indicators for identification, making it difficult to capture potential instability risks in a timely and accurate manner. At the same time, for the assessment of structural stability in the post-buckling stage, existing technologies are usually based on a single response index or static judgment method, lacking the ability to systematically model and quantitatively analyze the dynamic evolution process of stability.

[0005] Therefore, how to effectively identify the critical buckling state, reasonably predict the multi-path response of post-buckling, and comprehensively evaluate the evolution of structural stability based on the characteristics of the nonlinear response of the structure has become a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0006] To address the above situation and overcome the shortcomings of existing technologies, the technical solution adopted by this invention is as follows: This invention provides a deep learning-based method for calculating the post-buckling stability of nonlinear structures, which includes the following steps:

[0007] Step S1: Construction of structural nonlinear behavior data;

[0008] Step S2: Prior perception modeling of the buckling critical state;

[0009] Step S3: Post-buckling path generation and prediction;

[0010] Step S4: Stability evolution determination modeling;

[0011] Step S5: Calculation of post-buckling stability of nonlinear structure.

[0012] Further, in step S1, the construction of the structural nonlinear behavior data is used to obtain nonlinear response data of the target structure under different loading conditions. Specifically, numerical simulation calculations are performed on the target structure under a preset loading path to obtain displacement response data, stress-strain data, and energy response data of the structure during the loading process; the obtained data are subjected to time series alignment, data standardization processing, and outlier data removal to construct a structural nonlinear behavior dataset; based on the structural nonlinear behavior dataset, structural response feature data for subsequent modeling is extracted to obtain structural nonlinear behavior characterization data.

[0013] Furthermore, based on the aforementioned structural nonlinear behavior dataset, structural response feature data for subsequent modeling is extracted. Specifically, according to preset feature extraction rules, feature quantities that can characterize the trend of structural response changes are extracted from the dataset, including at least one of displacement change features, stress distribution features, and energy change features. The extracted feature data is then uniformly packaged to form structural nonlinear behavior characterization data.

[0014] The structural nonlinear behavior characterization data serves as the input data basis for subsequent buckling critical state prior perception modeling and post-buckling path generation prediction.

[0015] Further, in step S2, the prior perception modeling of the buckling critical state is used to identify and characterize the buckling critical state that may occur in the structure during loading. Specifically, it adopts a prior perception method for the buckling critical state based on energy perturbation response consistency calculation. Based on the structural nonlinear behavior characterization data, it constructs joint characterization data reflecting the structural energy change characteristics and perturbation response characteristics. According to the joint characterization data, it performs critical feature extraction processing on the response state of the structure during loading to obtain state feature data for characterizing the buckling critical trend. Based on the state feature data, it establishes a buckling critical state identification model to determine the potential buckling critical region during loading and obtain the prior perception result data of the buckling critical state.

[0016] The prior sensing method for buckling critical state based on energy perturbation response consistency calculation specifically includes the following steps:

[0017] Step S21: Energy response gradient field construction, used to characterize the energy change characteristics of the structure during loading. Specifically, based on the energy response data in the structural nonlinear behavior characterization data, the energy change gradient between adjacent loading steps is calculated, and the second-order gradient of energy change is further calculated to obtain energy response gradient characteristic data that reflects the rate and trend of energy change.

[0018] Step S22: Disturbance response amplification modeling is used to characterize the disturbance sensitivity of the structure during loading. Specifically, based on the displacement response data in the structural nonlinear behavior characterization data, the displacement change between adjacent loading steps is calculated, and the disturbance response amplification index is constructed based on the displacement change relationship between consecutive loading steps to characterize the amplification degree of the disturbance response and obtain disturbance response characteristic data.

[0019] Step S23: Constructing an energy perturbation consistency index to integrate energy change characteristics and perturbation response characteristics to form a unified criterion. Specifically, based on the energy response gradient characteristic data and perturbation response characteristic data, an energy perturbation consistency index is constructed to characterize the relationship between energy change trend and perturbation amplification degree. The response state of the structure during the loading process is comprehensively characterized according to the consistency index to obtain joint characterization data.

[0020] Step S24: Critical feature state encoding, used to extract and express the critical trend in the structural response state. Specifically, based on the joint characterization data, the consistency index is analyzed for change trend and threshold determination is performed to identify candidate positions that may correspond to the buckling critical state. The energy change characteristics, disturbance response characteristics and consistency index are combined and encoded to form state feature data that describes the critical state of the structure, and the state feature data is obtained.

[0021] Step S25: Construct a buckling critical state identification model to determine the potential buckling critical region of the structure during the loading process. Specifically, based on the state feature data, construct a buckling critical state identification model, and use the identification model to determine the state of each loading stage, outputting the corresponding critical risk result or state label to obtain the prior perception result data of the buckling critical state.

[0022] Further, in step S3, the post-buckling path generation prediction is used to predict and model multiple possible response paths of the structure after buckling occurs. Specifically, it employs a post-buckling path generation prediction method based on bifurcation-guided constraints. Based on the structural nonlinear behavior characterization data and the prior perception results of the buckling critical state, it constructs input data for post-buckling response modeling; it performs path feature extraction processing on the input data for post-buckling response modeling to establish a path generation model describing the relationship between loading parameters and structural response; based on the path generation model, it predicts and calculates the response path of the structure after buckling to obtain the post-buckling path prediction result data under the corresponding loading conditions.

[0023] The post-buckling path generation and prediction method based on bifurcation guidance constraints specifically includes the following steps:

[0024] Step S31: Constructing input data for post-buckling response modeling, which forms a unified input basis for subsequent path generation models. Specifically, based on the structural nonlinear behavior characterization data and the prior perception results of the buckling critical state, the loading parameters, structural response state, energy characteristics and critical state information are aligned and combined to construct the input vector for post-buckling response modeling, thus obtaining the input data for post-buckling response modeling.

[0025] Step S32: Bifurcation guidance feature construction, used to characterize the trend of the structure entering the post-buckling bifurcation region during loading. Specifically, based on the critical risk information and structural energy change characteristics in the prior perception results of the buckling critical state, a bifurcation guidance coefficient reflecting the bifurcation tendency is constructed, and combined with the structural response change information to form a bifurcation guidance feature vector, thus obtaining bifurcation guidance feature data.

[0026] Step S33: Path identification feature construction, used to distinguish and control multiple possible post-buckling paths. Specifically, a preset number of path branches is set, corresponding path identification variables are constructed for different path branches, and the path identification variables are encoded to form a path identification feature vector, which serves as branch control information in the path generation process, thus obtaining path identification feature data.

[0027] Step S34: Path generation model construction, used to establish the generation relationship between loading parameters and structural post-buckling response and output multiple candidate paths. Specifically, based on the post-buckling response modeling input data, bifurcation guidance feature data and path identification feature data, a path generation model is constructed, and the post-buckling response of the structure is predicted and calculated under different path identification conditions to generate multiple corresponding candidate post-buckling paths and obtain candidate post-buckling path data.

[0028] Step S35: Path difference characterization processing, used to improve the distinguishability between different candidate paths. Specifically, based on the candidate post-buckling path data, the degree of response difference between different paths is calculated, and the similarity between paths is determined according to a preset difference threshold. Paths with insufficient distinguishability are subjected to separation constraint processing to obtain path difference characterization data.

[0029] Step S36: Path correction, used to improve the physical rationality and continuity of candidate paths. Specifically, based on the candidate post-buckling path data, a consistency analysis is performed on the continuous change characteristics and energy change characteristics of the path to identify path segments with abnormal fluctuations or discontinuous changes, and correction processing is performed on the path segments to obtain path rationality verification result data and corrected path data.

[0030] Step S37: Output the post-buckling path prediction results to form the final post-buckling path prediction results. Specifically, based on the corrected path data, each candidate path is sorted and output, and the correspondence between the path and the loading parameters is established to obtain the post-buckling path prediction result data.

[0031] Further, in step S4, the stability evolution determination modeling is used to analyze and determine the stability change process of the structure in the post-buckling stage. Specifically, based on the post-buckling path prediction result data, evolutionary feature data of the structural response changing with loading is extracted; according to the evolutionary feature data, a stability analysis model for determining the change of the structural stability state is established; through the stability analysis model, the stability state of the structure in different loading stages is determined to obtain stability evolution determination result data.

[0032] The stability evolution determination results data specifically include the stability state labels, stability change trend sequences, and stability level classification results corresponding to each loading stage;

[0033] Further, in step S5, the nonlinear structure post-buckling stability calculation is used to comprehensively calculate and output the overall stability of the structure based on the above modeling results. Specifically, it is to comprehensively analyze the stability state of the structure within the target loading range based on the post-buckling path prediction results and stability evolution judgment results; to quantitatively calculate the stability of the structure at different loading stages according to the preset stability evaluation rules; and to output the post-buckling stability calculation results of the structure.

[0034] The post-buckling stability calculation results specifically include structural stability determination results, stability change trend results, and key critical state identification results.

[0035] The beneficial effects achieved by the present invention using the above solution are as follows:

[0036] (1) In view of the technical problem that existing nonlinear structural stability analysis methods usually rely on single finite element path calculation or linearized approximate analysis, which makes it difficult to accurately characterize the complex nonlinear response behavior of the structure after buckling, especially in the case of multi-path bifurcation and sudden instability, the overall stability assessment results are incomplete and unstable. This solution creatively adopts a nonlinear structural post-buckling stability calculation framework based on deep learning, thereby realizing multi-path and multi-stage dynamic assessment of the overall stability of the structure, significantly improving the integrity and engineering applicability of stability analysis.

[0037] (2) In view of the technical problem that the identification of buckling critical state in existing technologies mainly relies on eigenvalue analysis or empirical judgment, which makes it difficult to accurately capture potential critical turning points in complex nonlinear loading processes, especially the insufficient characterization of local disturbance sensitivity and energy change response, this solution creatively adopts a priori perception modeling method for buckling critical state based on energy disturbance response consistency calculation. By constructing energy response gradient field, disturbance response amplification rate and energy disturbance consistency index, a multidimensional joint characterization of critical state is achieved, thereby improving the advance and accuracy of buckling critical state identification.

[0038] (3) In view of the technical problem that existing post-buckling analysis methods can usually only obtain a single evolution path or rely on artificial perturbation to set path branches, making it difficult to systematically characterize the bifurcation behavior and path differences of multiple paths, this scheme creatively adopts a post-buckling path generation and prediction method based on bifurcation guidance constraints. By introducing bifurcation guidance features and path identification features, it realizes parallel generation of multiple paths and path separation constraints, thereby realizing systematic modeling of multiple possible response modes and improving the completeness and physical rationality of post-buckling path prediction.

[0039] (4) In view of the technical problems that existing structural stability assessment methods rely on single indicators or static judgment methods, which make it difficult to reflect the dynamic evolution characteristics of structural stability with loading process and lack the ability to accurately locate key instability stages, this solution creatively adopts a stability evolution judgment and comprehensive quantitative calculation method based on the fusion of evolution characteristics. By constructing a stability characterization index that integrates displacement change, energy change and path continuity, and combining it with a hierarchical judgment model and global stability evaluation rules, dynamic analysis and quantitative output of stability state can be achieved. Attached Figure Description

[0040] Figure 1 A flowchart illustrating the deep learning-based method for calculating the post-buckling stability of nonlinear structures provided by this invention.

[0041] Figure 2 A flowchart illustrating the prior perception modeling of the buckling critical state in step S2;

[0042] Figure 3 This is a schematic diagram of the process for generating and predicting the buckling path after step S3.

[0043] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof. Detailed Implementation

[0044] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0045] In the description of this invention, it should be understood that the terms "upper", "lower", "front", "rear", "left", "right", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0046] Example 1, see Figure 1 The present invention provides a method for calculating the post-buckling stability of nonlinear structures based on deep learning, the method comprising the following steps:

[0047] Step S1: Construction of structural nonlinear behavior data;

[0048] Step S2: Prior perception modeling of the buckling critical state;

[0049] Step S3: Post-buckling path generation and prediction;

[0050] Step S4: Stability evolution determination modeling;

[0051] Step S5: Calculation of post-buckling stability of nonlinear structure.

[0052] By performing the above operations, this solution addresses the technical problem that existing nonlinear structural stability analysis methods typically rely on single finite element path calculations or linearized approximation analyses, making it difficult to accurately characterize the complex nonlinear response behavior of structures after buckling, especially in cases of multi-path bifurcation and abrupt instability, resulting in incomplete and unstable overall stability assessments. This solution creatively adopts a deep learning-based nonlinear structural post-buckling stability calculation framework. For example, in the compressive buckling analysis of thin-walled shell structures, traditional methods often only yield a single buckling path, while this solution can simultaneously predict multiple post-buckling evolution paths through a path generation model and combine this with the stability evolution judgment results for comprehensive analysis. This enables multi-path, multi-stage dynamic assessment of the overall structural stability, significantly improving the completeness and engineering applicability of the stability analysis.

[0053] Example 2, see Figure 1 This embodiment is based on the above embodiment. In step S1, the construction of the structural nonlinear behavior data is used to obtain nonlinear response data of the target structure under different loading conditions. Specifically, numerical simulation calculations are performed on the target structure under a preset loading path to obtain displacement response data, stress-strain data, and energy response data of the structure during the loading process. The obtained data is then subjected to time series alignment, data standardization, and outlier removal to construct a structural nonlinear behavior dataset. Based on the structural nonlinear behavior dataset, structural response feature data for subsequent modeling is extracted to obtain structural nonlinear behavior characterization data.

[0054] In one specific implementation, the construction of the structural nonlinear behavior data first involves determining the basic geometric model and material property parameters of the target structure, selecting the corresponding modeling method according to the structure type, discretizing the structure, and constructing a finite element analysis model.

[0055] The discretization process can be implemented using one or more combinations of beam elements, shell elements, or solid elements, and the mesh density is determined according to the structural scale and computational accuracy requirements.

[0056] After structural modeling is completed, nonlinear numerical simulation calculations are performed on the finite element model based on a preset loading path. The loading path is used to describe the change process of external load with time or loading step size, and can be a monotonic loading path or a phased loading path. During the simulation calculation, the geometric nonlinear effects of the structure are considered, and the nonlinear characteristics of the material are further considered when necessary to obtain the true response behavior of the structure during the loading process.

[0057] During the simulation, the structural response data corresponding to each loading step is recorded step by step. The structural response data includes: displacement response data at structural nodes, stress and strain response data of structural elements, and energy response data of the whole structure or local areas.

[0058] The energy response data may include strain energy, external force work, or total system potential energy, which are used to characterize the energy change features of the structure during the loading process.

[0059] After obtaining the above-mentioned raw response data, the data is subjected to unified processing, specifically including time series alignment processing, data standardization processing, and outlier data removal processing.

[0060] The time series alignment process synchronizes and aligns different types of response data according to the loading step number or timestamp, so that all types of data have a consistent time reference in the same loading stage.

[0061] The standardization process is used to perform normalization or standardization on data with different dimensions to eliminate scale differences between different physical quantities and make them meet the requirements of unified modeling input.

[0062] The data removal process identifies and removes abnormal fluctuations or non-physical mutations in the response data. Abnormal data can be identified through threshold judgment, rate of change detection, or statistical methods to ensure the stability and reliability of the data.

[0063] After data processing is completed, a structural nonlinear behavior dataset is constructed; the structural nonlinear behavior dataset can be stored in the form of a data structure organized by loading steps, with each loading step corresponding to a set of structural response state data;

[0064] Furthermore, based on the aforementioned structural nonlinear behavior dataset, structural response feature data for subsequent modeling is extracted. Specifically, according to preset feature extraction rules, feature quantities that can characterize the trend of structural response changes are extracted from the dataset, including at least one of displacement change features, stress distribution features, and energy change features. The extracted feature data is then uniformly packaged to form structural nonlinear behavior characterization data.

[0065] The structural nonlinear behavior characterization data serves as the input data basis for subsequent buckling critical state prior perception modeling and post-buckling path generation prediction.

[0066] Example 3, see Figure 1 , Figure 2This embodiment is based on the above embodiment. In step S2, the prior perception modeling of the buckling critical state is used to identify and characterize the buckling critical state that may occur in the structure during loading. Specifically, it adopts a prior perception method for the buckling critical state based on the consistency calculation of energy perturbation response. Based on the structural nonlinear behavior characterization data, it constructs joint characterization data reflecting the structural energy change characteristics and perturbation response characteristics. According to the joint characterization data, it performs critical feature extraction processing on the response state of the structure during loading to obtain state feature data for characterizing the buckling critical trend. Based on the state feature data, it establishes a buckling critical state identification model to determine the potential buckling critical region during loading and obtain the prior perception result data of the buckling critical state.

[0067] In some implementations, the critical state identification process can be further enhanced by introducing the structural local response change rate or energy change characteristics to improve the identification accuracy under complex nonlinear conditions.

[0068] The prior sensing method for buckling critical state based on energy perturbation response consistency calculation specifically includes the following steps:

[0069] Step S21: Energy response gradient field construction, used to characterize the energy change characteristics of the structure during loading. Specifically, based on the energy response data in the structural nonlinear behavior characterization data, the energy change gradient between adjacent loading steps is calculated, and the second-order gradient of energy change is further calculated to obtain energy response gradient characteristic data that reflects the rate and trend of energy change.

[0070] In specific implementation, let the first... The energy response value corresponding to each loading step is , No. The energy response value corresponding to each loading step is The loading parameter increment is Then the first-order energy gradient and energy second gradient They are represented as follows:

[0071] ;

[0072] ;

[0073] In the formula, It is the first-order energy gradient, used to characterize the rate of change of structural energy with the loading process. The second-order energy gradient is used to characterize the abrupt change in the rate of energy change. For initial loading steps where the first-order gradient, second-order gradient, or perturbation response amplification cannot be calculated, the eigenvalues ​​of adjacent effective loading steps can be used to complete the calculation, or these steps can be marked as non-candidate critical loading steps and not included in the critical position selection. It is a small constant to prevent the denominator from being zero, and its preferred value is [value missing]. As a structure gradually approaches the buckling critical state, the energy response typically tends to shift from gradual accumulation to rapid change or local abrupt change. Therefore, through the aforementioned first-order energy gradient... and energy second gradient It can quantify and express this type of critical precursor;

[0074] Furthermore, to avoid excessive differences in energy gradient amplitude due to different structural dimensions, material parameters, or load scales, after obtaining... and Then, it is normalized to obtain the normalized energy gradient feature. and normalized energy mutation characteristics The normalization process can be implemented using maximum-minimum normalization or standard deviation normalization to ensure that the energy change characteristics corresponding to different loading steps are within a uniform numerical scale.

[0075] Step S22: Disturbance response amplification modeling is used to characterize the disturbance sensitivity of the structure during loading. Specifically, based on the displacement response data in the structural nonlinear behavior characterization data, the displacement change between adjacent loading steps is calculated, and the disturbance response amplification index is constructed based on the displacement change relationship between consecutive loading steps to characterize the amplification degree of the disturbance response and obtain disturbance response characteristic data.

[0076] In specific implementation, let the first... The structural displacement response vector corresponding to each loading step is: , No. The structural displacement response vector corresponding to each loading step is: The displacement change between adjacent loading steps Represented as:

[0077] ;

[0078] In the formula, It is the displacement change amplitude between adjacent loading steps. It is the first The structural displacement response vector corresponding to each loading step. It is the first The structural displacement response vector corresponding to each loading step. Represents the L2 norm;

[0079] Based on the displacement change amplitude between consecutive loading steps, the disturbance response amplification factor is constructed. The calculation formula is:

[0080] ;

[0081] In the formula, It is a disturbance response amplification index, used to characterize the degree of amplification of the structural response during continuous loading. When the load increases continuously or a significant peak appears in the local loading range, it indicates that the structure is more sensitive to loading disturbances, which may correspond to the critical buckling state or a precursor to the subsequent bifurcation response.

[0082] Furthermore, to reduce the impact of local numerical fluctuations in a single loading step on the amplification rate of the disturbance response, the following can be done: Sliding window smoothing is performed to obtain the smoothed perturbation response amplification. The length of the sliding window is preferably 3 to 5 loading steps; in one specific embodiment, the length of the sliding window is 3, so as to balance the timeliness of capturing critical changes and the effect of suppressing local noise.

[0083] Step S23: Constructing an energy perturbation consistency index to integrate energy change characteristics and perturbation response characteristics to form a unified criterion. Specifically, based on the energy response gradient characteristic data and perturbation response characteristic data, an energy perturbation consistency index is constructed to characterize the relationship between energy change trend and perturbation amplification degree. The response state of the structure during the loading process is comprehensively characterized according to the consistency index to obtain joint characterization data.

[0084] Preferably, based on normalized energy gradient characteristics Normalized energy mutation characteristics and smooth perturbation response amplification Constructing an energy perturbation consistency index The calculation formula is:

[0085] ;

[0086] In the formula, It is the first Energy perturbation consistency index corresponding to each loading step It's the Sigmoid function, used to map indicator values ​​to a range of 0 to 1. β and γ are the weights for the rate of energy change, the energy mutation, and the perturbation amplification, respectively, and satisfy the following conditions: ;

[0087] In a preferred embodiment, it is advisable to , , ;

[0088] Among them, the rate of energy change and the degree of perturbation amplification are used together to reflect the gradual enhancement trend of the structural response before the buckling criticality, and the energy mutation feature is used to supplement the reflection of the local nonlinear changes near the criticality. Through the above weight configuration, it is possible to avoid relying solely on a single energy feature or a single displacement change feature for critical state determination, thereby improving the stability of the critical state identification results.

[0089] Furthermore, the joint characterization data includes first-order energy gradient features, second-order energy gradient features, perturbation response amplification rate, and energy perturbation consistency index; wherein, the energy perturbation consistency index... The closer it is to 1, the more likely the structural response corresponding to the current loading step is to be in the vicinity of the buckling critical region; The closer it is to 0, the more stable the structural response is for the current loading step;

[0090] Step S24: Critical feature state encoding, used to extract and express the critical trend in the structural response state. Specifically, based on the joint characterization data, the consistency index is analyzed for change trend and threshold determination is performed to identify candidate positions that may correspond to the buckling critical state. The energy change characteristics, disturbance response characteristics and consistency index are combined and encoded to form state feature data that describes the critical state of the structure, and the state feature data is obtained.

[0091] State feature data is constructed based on the joint characterization data. The calculation formula is:

[0092] ;

[0093] In the formula, It is the first State feature data corresponding to each loading step It is the magnitude of displacement change. It is the change in the energy perturbation consistency index, and ;

[0094] By introducing It can characterize the changing trend of the energy perturbation consistency index between consecutive loading steps, thereby avoiding the determination of critical state based solely on the index amplitude at a single moment.

[0095] Furthermore, regarding the energy perturbation consistency index and its change Perform candidate critical position screening, when Greater than the preset consistency threshold ,and Greater than the preset change threshold At that time, the corresponding loading step is marked as the initial screening candidate buckling critical position; in a preferred embodiment, The value range is from 0.65 to 0.75. The value range is from 0.05 to 0.10; in specific implementation, a preferred value can be selected. ;

[0096] It should be noted that the above threshold is used to screen candidates for loading steps that may have a critical trend. Subsequently, the critical risk result or state label is further output by the buckling critical state identification model to reduce misjudgment caused by simple threshold determination.

[0097] Step S25: Buckling critical state identification model construction, used to determine the potential buckling critical region of the structure during the loading process. Specifically, based on the state feature data, a buckling critical state identification model is constructed, and the identification model is used to determine the state of each loading stage, outputting the corresponding critical risk result or state label to obtain the prior perception result data of the buckling critical state.

[0098] In this embodiment, the buckling critical state identification model uses state feature data. As input, the critical risk value As output, the calculated expression is:

[0099] ;

[0100] In the formula, This represents the buckling critical state identification model. It is the first The critical risk value corresponding to each loading step ranges from 0 to 1. The larger the value, the more likely the corresponding loading step is to be in a critical buckling state or a critical proximity region;

[0101] In one specific embodiment, the buckling critical state identification model is implemented using a lightweight multilayer perceptron model, including an input layer, a first fully connected layer, a second fully connected layer, and an output layer; wherein, the number of nodes in the first fully connected layer is preferably 16, the number of nodes in the second fully connected layer is preferably 8, the activation function is the ReLU function, and the output layer uses the Sigmoid function; this model structure can fit the nonlinear relationship between energy change, perturbation amplification, and consistency trend under low computational conditions, and is suitable for structural stability calculation scenarios with limited loading step sequence size;

[0102] Furthermore, the buckling critical state identification model can be trained based on historical nonlinear simulation data or data annotated by finite element post-processing; the input of the training samples is the state feature vector corresponding to each loading step. The training labels are state labels indicating whether the corresponding loading step is in the vicinity of the buckling critical region. These state labels can be determined based on one or more of the following: eigenvalue buckling results, locations of abrupt changes in the nonlinear path, inflection points of the load-displacement curve, or annotations by engineers.

[0103] During model training, the cross-entropy loss function can be used for parameter optimization, and the calculation formula is as follows:

[0104] ;

[0105] In the formula, It is the critical state recognition loss function. The number of training samples. For the first The actual status label corresponding to each loading step. It is the critical risk value output by the model;

[0106] Furthermore, during the model inference process, based on the initial screening of candidate buckling critical positions and their adjacent loading intervals, the buckling critical state identification model outputs a critical risk value, and the critical risk judgment threshold is denoted as... This is used to determine whether the critical risk value output by the model reaches the buckling critical candidate region. When, the corresponding loading step is determined as a candidate region for buckling criticality; when When this occurs, the corresponding loading step is determined to be a non-critical region; in a preferred embodiment, The range of values ​​is to The preferred value is If multiple consecutive loading steps satisfy If the continuous loading interval is considered as the critical risk interval in the prior perception result data of the buckling critical state, then the critical risk interval is considered in conjunction with the data of adjacent loading steps. and To reduce the risk of misjudgment caused by isolated noise points;

[0107] The prior perception results of the buckling critical state include a critical risk value sequence, candidate buckling critical loading steps, critical risk intervals, and corresponding state labels. The critical risk value sequence is used for the construction of bifurcation guidance features in the subsequent post-buckling path generation prediction process, and the candidate buckling critical loading steps and critical risk intervals are used to limit the key analysis scope of post-buckling path generation prediction.

[0108] By performing the above operations, this solution addresses the technical problem that existing technologies mainly rely on eigenvalue analysis or empirical judgment for buckling critical state identification, making it difficult to accurately capture potential critical inflection points during complex nonlinear loading processes, especially in terms of insufficient characterization of local perturbation sensitivity and energy mutation response. This solution creatively adopts a priori perception modeling method for buckling critical states based on energy perturbation response consistency calculation. By constructing an energy response gradient field, perturbation response amplification rate, and energy perturbation consistency index, a multidimensional joint characterization of the critical state is achieved. For example, during the loading process of a beam structure with initial defects, when the structure enters the pre-buckling stage, its displacement change may not be significant, but the energy gradient and perturbation amplification rate have already shown abnormal changes. This solution can identify such potential critical intervals in advance through the consistency index, thereby improving the advance capability and accuracy of buckling critical state identification.

[0109] Example 4, see Figure 1 , Figure 3 This embodiment is based on the above embodiment. In step S3, the post-buckling path generation and prediction is used to predict and model multiple possible response paths of the structure after buckling occurs. Specifically, it adopts a post-buckling path generation and prediction method based on bifurcation-guided constraints. Based on the structural nonlinear behavior characterization data and the prior perception results of the buckling critical state, post-buckling response modeling input data is constructed. The post-buckling response modeling input data is processed by path feature extraction to establish a path generation model for describing the relationship between loading parameters and structural response. Based on the path generation model, the response path of the structure after buckling is predicted and calculated to obtain the post-buckling path prediction result data under the corresponding loading conditions.

[0110] Furthermore, in some embodiments, the path generation model can be used to generate a variety of different post-buckling response paths and characterize the differences between different paths to reflect the differences in the structure's response under different perturbation conditions or initial states.

[0111] In some implementations, the post-buckling path prediction results data can also be subjected to path rationality verification processing to improve the consistency between the prediction results and the actual physical behavior.

[0112] The post-buckling path generation and prediction method based on bifurcation guidance constraints specifically includes the following steps:

[0113] Step S31: Constructing input data for post-buckling response modeling, which forms a unified input basis for subsequent path generation models. Specifically, based on the structural nonlinear behavior characterization data and the prior perception results of the buckling critical state, the loading parameters, structural response state, energy characteristics and critical state information are aligned and combined to construct the input vector for post-buckling response modeling, thus obtaining the input data for post-buckling response modeling.

[0114] Preferably, the loading parameters include at least one of loading step number, loading amplitude, loading increment, or normalized loading ratio; the structural response state includes at least one of displacement response characteristics, stress-strain response characteristics, or response prediction results of the previous loading step; the energy characteristics include at least one of energy response value, energy change gradient, or energy mutation characteristics; and the critical state information includes at least one of critical risk value sequence, candidate buckling critical loading step, or critical risk interval.

[0115] In practice, the loading step is used as a unified index to synchronize and align the above data. The loading parameters, structural response state, energy characteristics and critical state information corresponding to the same loading step are spliced ​​together to form the input vector for post-buckling response modeling. For data with different dimensions, normalization can be performed before splicing. For missing loading step data, interpolation of adjacent loading steps or forward padding can be used to fill in the missing data to ensure the continuity of the input data for the path generation model.

[0116] Step S32: Bifurcation guidance feature construction, used to characterize the trend of the structure entering the post-buckling bifurcation region during loading. Specifically, based on the critical risk information and structural energy change characteristics in the prior perception results of the buckling critical state, a bifurcation guidance coefficient reflecting the bifurcation tendency is constructed, and combined with the structural response change information to form a bifurcation guidance feature vector, thus obtaining bifurcation guidance feature data.

[0117] Preferably, let the first The critical risk value corresponding to each loading step is The energy perturbation consistency index is The normalized energy mutation characteristic is Then construct the bifurcation guidance coefficient. The calculation formula is:

[0118] ;

[0119] In the formula, It is the first The bifurcation guidance coefficients corresponding to each loading step are used to characterize the tendency of the structural response to enter the post-buckling bifurcation region. It is a critical risk value, derived from the prior perception results of the buckling critical state, used to characterize the critical risk corresponding to the loading step; It is an energy perturbation consistency index, used to characterize the degree of consistency in the energy perturbation response; It is a normalized energy mutation characteristic, used to characterize the degree of mutation in the rate of energy change; , , These are the critical risk bifurcation guidance weight coefficient, the energy perturbation consistency bifurcation guidance weight coefficient, and the normalized energy mutation bifurcation guidance weight coefficient, respectively, and satisfy the following conditions: ;

[0120] In a preferred embodiment, it is advisable to , , Among them, the critical risk value is used to reflect the dominant role of the buckling critical state identification result in bifurcation prediction, the energy perturbation consistency index is used to reflect the synergistic trend between energy change and perturbation amplification, and the energy mutation feature is used to supplement and reflect the local nonlinear changes that may occur in the post-buckling stage.

[0121] Furthermore, based on the bifurcation guidance coefficient By combining displacement change amplitude, loading parameters, and critical risk interval identifiers, bifurcation guidance feature data is formed. The bifurcation guidance feature data is used to indicate loading intervals in the path generation model where the structure may diverge, enabling the path generation model to output candidate post-buckling paths with differences in the vicinity of the buckling critical region.

[0122] Step S33: Path identification feature construction, used to distinguish and control multiple possible post-buckling paths. Specifically, a preset number of path branches is set, corresponding path identification variables are constructed for different path branches, and the path identification variables are encoded to form a path identification feature vector, which serves as branch control information in the path generation process, thus obtaining path identification feature data.

[0123] The number of path branches can be preset based on the historical simulation results of the target structure, structural symmetry, initial disturbance type, or engineering analysis requirements.

[0124] In one specific implementation, the number of path branches can preferably be set to 3 to 5, so as to avoid generating too many low-discrimination paths while covering the main post-buckling response modes.

[0125] For the k-th candidate path, set the corresponding path identifier variable p. k The path identification feature vector is formed by one-hot encoding or learnable embedding encoding. The path identification feature vector does not directly represent the real physical disturbance, but serves as the branch control information of the path generation model, which is used to enable different candidate paths under the same loading conditions to have different response evolution directions.

[0126] In a preferred embodiment, when the number of candidate paths is small, a one-hot encoding method is used to construct the path identifier feature vector; when the number of candidate paths is large or the training sample size is large, a learnable embedding encoding method can be used to construct the path identifier feature vector to enhance the expressive ability of the path identifier features to complex bifurcation responses.

[0127] Step S34: Path generation model construction, used to establish the generation relationship between loading parameters and structural post-buckling response and output multiple candidate paths. Specifically, based on the post-buckling response modeling input data, bifurcation guidance feature data and path identification feature data, a path generation model is constructed, and the post-buckling response of the structure is predicted and calculated under different path identification conditions to generate multiple corresponding candidate post-buckling paths and obtain candidate post-buckling path data.

[0128] In specific implementation, let the first... The input vector for modeling the post-buckling response corresponding to each loading step is: The bifurcation guidance coefficient is , No. The path identifier feature vectors corresponding to the candidate paths are The input to the path generation model is... , and Together they constitute; the path generation model outputs the first... The structural response prediction results of the candidate paths in the next loading step are calculated using the following formula:

[0129] ;

[0130] In the formula, It is the first The candidate paths in the th The structural response prediction results corresponding to each loading step include at least one of displacement response prediction values, energy response prediction values, and stress-strain response prediction values. This represents the path generation model. These are model parameters;

[0131] In one specific implementation, the path generation model is implemented using a gated recurrent unit network (GRU), which is used to capture the temporal dependencies in the loading step sequence; the number of hidden layer nodes is preferably 32 to 64, and the number of network layers is preferably 1 to 2.

[0132] In another specific embodiment, the path generation model can also be implemented using a feedforward generation network with path branch embedding. The feedforward generation network includes a path identifier embedding layer, a feature encoding layer, a path response output layer, and an energy response output layer. The path identifier embedding layer is used to convert path identifier variables into path identifier feature vectors. The feature encoding layer is used to fuse post-buckling response modeling input data, bifurcation guidance feature data, and path identifier feature data. The path response output layer is used to output candidate path response prediction results, and the energy response output layer is used to output energy change prediction results.

[0133] When the training sample size is small or engineering computing resources are limited, a single-layer GRU network can be used with 32 hidden layer nodes; when the training sample size is large or the structural response sequence is long, a two-layer GRU network can be used with 64 hidden layer nodes.

[0134] Furthermore, to improve the smoothness and continuity of the path generation results, a response prediction error term can be introduced during the training process of the path generation model, so that the candidate paths output by the model are as close as possible to the historical simulation paths or finite element calculation paths; at the same time, the similarity between different candidate paths is constrained through subsequent path difference characterization processing, thereby avoiding multiple paths from degenerating into approximately the same response curve.

[0135] Step S35: Path difference characterization processing, used to improve the distinguishability between different candidate paths. Specifically, based on the candidate post-buckling path data, the degree of response difference between different paths is calculated, and the similarity between paths is determined according to a preset difference threshold. Paths with insufficient distinguishability are subjected to separation constraint processing to obtain path difference characterization data.

[0136] For the Candidate paths and the first The candidate paths are calculated based on the structural response prediction results of the two paths within the target loading interval. :

[0137] ;

[0138] In the formula, It is the first Candidate paths and the first Path difference between candidate paths It is the number of loading steps within the target loading range. and They are the first Candidate paths and the first The candidate paths in the th Structural response prediction results corresponding to each loading step;

[0139] when Less than the preset path difference threshold At that time, the judgment of the first Candidate paths and the first The candidate paths lack sufficient distinguishability, and a path separation constraint is imposed during the training of the path generation model or the post-processing of candidate paths. This path separation constraint can be expressed as:

[0140] ;

[0141] In the formula, It is a path separation constraint term. It is a preset path difference threshold;

[0142] In a preferred embodiment, It can be determined based on the average response differences between different post-buckling paths in the training set; when historical statistics are lacking, it can be set based on the normalized response quantity. to The preferred value is Furthermore, the path difference characterization data includes a path difference matrix, low-discrimination path identification results, and path separation constraint results; wherein, the path difference matrix is ​​used to characterize the overall degree of difference between different candidate post-buckling paths, and the low-discrimination path identification results are used to indicate candidate paths that need further separation or correction;

[0143] Step S36: Path correction, used to improve the physical rationality and continuity of candidate paths. Specifically, based on the candidate post-buckling path data, a consistency analysis is performed on the continuous change characteristics and energy change characteristics of the path to identify path segments with abnormal fluctuations or discontinuous changes, and correction processing is performed on the path segments to obtain path rationality verification result data and corrected path data.

[0144] The path rationality verification includes continuity verification and energy consistency verification; the continuity verification is used to determine whether there are non-physical jumps between adjacent loading steps in the candidate path; when the response change amplitude of a certain loading step is significantly higher than the average change amplitude of adjacent loading intervals, the path segment near that loading step is marked as an abnormal fluctuation path segment.

[0145] The energy consistency check is used to determine whether the energy response in the candidate path matches the loading process and the trend of structural response changes; when the energy response shows an abnormal sudden change that is significantly inconsistent with the trend of displacement response changes, the corresponding path segment is marked as an energy abnormal path segment.

[0146] For the abnormal fluctuation path segment or energy abnormal path segment, the following methods can be used for processing: local smoothing, interpolation between adjacent loading steps, correction based on the response trend of the previous and subsequent loading steps, or re-calling the path generation model for local prediction.

[0147] In practice, three-point moving average or local linear interpolation can be used as a priority for correction. For path segments with anomalies in multiple consecutive loading steps, the path generation model is used to re-predict the structural response of the path segment based on the state of the previous effective loading step of the anomaly segment.

[0148] Furthermore, the path rationality verification result data includes the location of abnormal path segments, the type of abnormality, the correction method, and the corrected path response data; the type of abnormality includes at least one of response jump abnormality, energy mutation abnormality, and path continuity abnormality;

[0149] Step S37: Output the post-buckling path prediction results to form the final post-buckling path prediction results. Specifically, based on the corrected path data, each candidate path is sorted and output, and the correspondence between the path and the loading parameters is established to obtain the post-buckling path prediction result data.

[0150] The post-buckling path prediction results include the loading step sequence, structural response prediction sequence, path identification information, bifurcation guidance coefficient sequence, path difference results, and path rationality verification results for each candidate path. The structural response prediction sequence includes at least one of displacement response prediction sequence, energy response prediction sequence, and stress-strain response prediction sequence.

[0151] Furthermore, a mapping relationship is established between each candidate path and its corresponding loading parameters, so that each candidate post-buckling path can be mapped to specific loading conditions and loading stages. At the same time, the path difference characterization data and path rationality verification results are output as additional information so that stability comparison analysis can be performed on different candidate paths in the subsequent stability evolution judgment modeling process.

[0152] By performing the above operations, this scheme creatively adopts a post-buckling path generation and prediction method based on bifurcation guidance constraints to address the technical problem that existing post-buckling analysis methods typically only obtain a single evolution path or rely on artificial perturbation to set path branches, making it difficult to systematically characterize multi-path bifurcation behavior and path differences. By introducing bifurcation guidance features and path identification features, it realizes parallel generation of multiple paths and path separation constraints. For example, in the post-buckling process of plate and shell structures, different initial perturbation conditions may lead to different instability modes. This scheme can generate multiple candidate paths through path identification variables, and separate and optimize similar paths through path difference characterization and path correction mechanisms, thereby realizing systematic modeling of multiple possible response modes and improving the completeness and physical rationality of post-buckling path prediction.

[0153] Example 5, see Figure 1This embodiment is based on the above embodiment. In step S4, the stability evolution judgment modeling is used to analyze and judge the stability change process of the structure in the post-buckling stage. Specifically, based on the post-buckling path prediction result data, evolution feature data of structural response changing with loading is extracted; according to the evolution feature data, a stability analysis model for judging the change of structural stability state is established; through the stability analysis model, the stability state of the structure in different loading stages is judged to obtain stability evolution judgment result data.

[0154] In practice, the structural response sequences corresponding to each candidate path at each loading step are first extracted from the post-buckling path prediction results data, including displacement response sequences, energy response sequences, and path continuity-related features. The response sequences are aligned according to the loading steps, and a unified time series data structure is constructed for subsequent stability analysis.

[0155] Based on this, evolution feature extraction processing is performed on the response sequence, specifically including calculating the change amplitude between adjacent loading steps for the displacement response sequence to characterize the structural deformation growth rate; calculating the change trend during the loading process for the energy response sequence to reflect the structural energy release or accumulation characteristics; and performing statistical analysis on the path continuity characteristics to identify whether there are abrupt or discontinuous changes in the path.

[0156] Furthermore, to improve the robustness of stability determination, the aforementioned multiple features are uniformly quantified to construct a comprehensive index describing the trend of stability changes. The calculation formula is as follows:

[0157] ;

[0158] In the formula, It is a sequence of stability characterization values, specifically the stability characterization value at the t-th loading step. It is the magnitude of displacement change. It is a change in energy. It is a normalized path continuity indicator. It is the displacement change amplitude weighting coefficient. It is the energy change weighting coefficient. This is the weighting coefficient for the path continuity index, with the preferred value being [value missing]. It can also be adjusted according to different structural types;

[0159] Based on the stability characterization value sequence A stability analysis model is established to determine the stability state of the structure during the loading process. In specific implementation, the stability analysis model can be implemented using a threshold-based determination method or a lightweight sequence classification model.

[0160] In a preferred embodiment, a threshold-based hierarchical determination rule is used to classify the stability states, specifically as follows:

[0161] when When the structure is in a stable state, it is determined that the structure is stable.

[0162] when At that time, the structure is determined to be in a metastable state;

[0163] when When this occurs, the structure is determined to be in an unstable or indeterminate state.

[0164] Among them, threshold and The optimal value can be determined based on historical simulation data or engineering experience. ;

[0165] In another implementation, a lightweight neural network model can be introduced to determine the stability state. For example, a single-layer long short-term memory network (LSTM) or gated recurrent unit network (GRU) can be used to model the stability characterization value sequence to capture the dynamic evolution characteristics of stability during the loading process. The network structure can be set to a single-layer recurrent unit, and the number of hidden layer nodes is preferably 16 to 32 to improve the accuracy of determination while ensuring computational efficiency.

[0166] After completing the stability determination, the determination results of each loading step are organized to form a stability evolution sequence, and the stability change trend of the structure during the loading process can be further output.

[0167] The stability evolution determination results data specifically include the stability state labels, stability change trend sequences, and stability level classification results corresponding to each loading stage;

[0168] In some implementations, the stability determination results of different candidate paths can be compared and analyzed by combining the post-buckling path prediction results data, thereby identifying the stability differences corresponding to different paths and providing a reference for subsequent structural safety assessment.

[0169] In some implementations, the stability state can be graded by combining the trend of structural response changes or the characteristics of energy changes, so as to form a structural stability level result.

[0170] By performing the above operations, this solution addresses the technical problems of existing structural stability assessment methods, which often rely on single indicators or static judgment methods, making it difficult to reflect the dynamic evolution characteristics of structural stability during loading and lacking the ability to accurately locate key instability stages. It creatively adopts a stability evolution judgment and comprehensive quantitative calculation method based on the fusion of evolutionary characteristics. By constructing a stability characterization index that integrates displacement change, energy change, and path continuity, and combining it with a hierarchical judgment model and global stability evaluation rules, it achieves dynamic analysis and quantitative output of stability states. For example, during the loading process of actual engineering structures, the transition process from stable to metastable to unstable can be identified through the stability characterization value sequence, and the location of key instability loading steps can be further identified. This provides a clear decision-making basis for structural safety design and operation control, significantly improving the interpretability and engineering guidance value of stability assessment results.

[0171] Example 6, see Figure 1 This embodiment is based on the above embodiment. In step S5, the nonlinear structure post-buckling stability calculation is used to comprehensively calculate and output the overall stability of the structure based on the above modeling results. Specifically, it is to comprehensively analyze the stability state of the structure within the target loading range based on the post-buckling path prediction result data and the stability evolution judgment result data; according to the preset stability evaluation rules, it is to quantitatively calculate the stability of the structure at different loading stages; and output the post-buckling stability calculation result data of the structure.

[0172] The post-buckling stability calculation results specifically include structural stability determination results, stability change trend results, and key critical state identification results.

[0173] Example 7, see Figure 1 This embodiment is based on the above embodiment. In step S5, when it is specifically implemented, the correspondence between the post-buckling path prediction result data output in step S3 and the stability evolution judgment result data output in step S4 is first established. That is, the loading step is used as a unified index to match the response sequence of each candidate post-buckling path with the stability judgment result of the corresponding loading stage one by one, and a unified stability analysis data structure is constructed.

[0174] After data alignment, a comprehensive analysis of the structure's stability state throughout the entire loading range is conducted. This includes statistically analyzing the stability evolution sequences of each candidate path and calculating the proportion of different paths in stable, metastable, and unstable states; performing aggregate analysis on the stability judgment results of each loading stage to identify key loading intervals where the stability state changes significantly; and comparing the stability differences between different paths to identify the differences in structural stability performance under different bifurcation paths.

[0175] Furthermore, the structural stability is quantitatively calculated according to the preset stability evaluation rules. In a preferred embodiment, a comprehensive stability evaluation index can be constructed to uniformly represent the overall stability of the structure. Specifically, the overall structural stability score is obtained by weighting and fusing the proportion of stable states, the location of instability, and the rate of change of stability. The weight parameters can be set according to engineering experience or historical data. For example, the weight of the proportion of stable states is 0.5, the weight of the key instability location is 0.3, and the weight of the rate of change is 0.2.

[0176] In practical implementation, the following processing methods can be adopted:

[0177] The proportion of stable states is normalized to characterize the overall stability of the structure;

[0178] The loading steps at which critical states occur are identified to reflect the main locations where structural instability occurs;

[0179] The stability change trend is fitted to identify the main trend direction of structural stability evolution;

[0180] After completing the quantification calculation, the results are uniformly packaged and output to obtain the post-buckling stability calculation results data;

[0181] The post-buckling stability calculation results specifically include structural stability determination results, used to characterize whether the overall structure meets the stability requirements; stability change trend results, used to describe the stability evolution process of the structure during loading; and key critical state identification results, used to indicate the key loading locations where the structure experiences a sudden change in stability or instability.

[0182] In some implementations, the stability calculation results can be compared with preset safety thresholds according to actual engineering needs, and used to output structural safety evaluation results or early warning information, thereby providing a basis for decision-making for structural design optimization or operation control.

[0183] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0184] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention.

[0185] The present invention and its embodiments have been described above. This description is not restrictive, and the accompanying drawings are only one embodiment of the present invention; the actual structure is not limited thereto. In conclusion, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the invention, such designs should fall within the protection scope of the present invention.

Claims

1. A method for calculating the post-buckling stability of nonlinear structures based on deep learning, characterized in that: The method includes the following steps: Step S1: Construct structural nonlinear behavior data to obtain structural nonlinear behavior characterization data; Step S2: Buckling critical state prior perception modeling. A buckling critical state prior perception method based on energy perturbation response consistency calculation is adopted. Based on the structural nonlinear behavior characterization data, joint characterization data reflecting the structural energy change characteristics and perturbation response characteristics are constructed. Critical feature extraction processing is performed on the response state of the structure during loading to obtain state feature data. A buckling critical state identification model is established to determine the potential buckling critical region during loading, and the buckling critical state prior perception result data is obtained. The prior perception method for buckling critical state based on energy perturbation response consistency calculation specifically includes the following steps: energy response gradient field construction, perturbation response amplification modeling, energy perturbation consistency index construction, critical feature state encoding, and buckling critical state identification model construction; The energy response gradient field is constructed by calculating the energy change gradient between adjacent loading steps based on the energy response data in the structural nonlinear behavior characterization data, and further calculating the second-order gradient of energy change to obtain energy response gradient feature data that reflects the rate and trend of energy change. The disturbance response amplification modeling is based on the displacement response data in the structural nonlinear behavior characterization data, calculates the displacement change between adjacent loading steps, and constructs a disturbance response amplification index based on the displacement change relationship between consecutive loading steps to characterize the amplification degree of the disturbance response and obtain disturbance response characteristic data. Step S3: Post-buckling path generation and prediction. A post-buckling path generation and prediction method based on bifurcation-guided constraints is adopted. Based on the structural nonlinear behavior characterization data and the prior perception results of the buckling critical state, the input data for post-buckling response modeling is constructed; path feature extraction processing is performed to establish a path generation model; the response path of the structure after buckling is predicted and calculated to obtain the post-buckling path prediction results data under the corresponding loading conditions. The post-buckling path generation and prediction method based on bifurcation guidance constraints specifically includes the following steps: constructing input data for post-buckling response modeling, constructing bifurcation guidance features, constructing path identification features, constructing a path generation model, processing path difference characterization, path correction, and outputting post-buckling path prediction results; The post-buckling response modeling input data is constructed by aligning and combining the loading parameters, structural response state, energy characteristics and critical state information based on the structural nonlinear behavior characterization data and the prior perception results of the buckling critical state, and constructing the post-buckling response modeling input vector to obtain the post-buckling response modeling input data. The bifurcation guidance feature construction is based on the critical risk information and structural energy change characteristics in the prior perception results of the buckling critical state. A bifurcation guidance coefficient reflecting the bifurcation tendency is constructed, and combined with the structural response change information to form a bifurcation guidance feature vector, thus obtaining bifurcation guidance feature data. Step S4: Stability evolution determination modeling. Based on the post-buckling path prediction results data, extract the evolution characteristic data of the structural response changing with loading, establish a stability analysis model, determine the stability state of the structure at different loading stages, and obtain stability evolution determination results data. Step S5: Calculate the post-buckling stability of the nonlinear structure. Based on the post-buckling path prediction results and stability evolution determination results, comprehensively analyze the stability state of the structure within the target loading range, and quantify the stability of the structure at different loading stages; output the post-buckling stability calculation results of the structure.

2. The method for calculating the post-buckling stability of nonlinear structures based on deep learning according to claim 1, characterized in that: In step S1, the nonlinear behavior data of the structure is constructed by performing numerical simulation calculations on the target structure under a preset loading path to obtain displacement response data, stress-strain data and energy response data of the structure during the loading process. The acquired data is subjected to time series alignment, data standardization, and outlier removal to construct a dataset with non-linear behavior. Based on the aforementioned structural nonlinear behavior dataset, structural response feature data for subsequent modeling is extracted to obtain structural nonlinear behavior characterization data.

3. The method for calculating the post-buckling stability of nonlinear structures based on deep learning according to claim 1, characterized in that: In step S2, the energy perturbation consistency index is constructed. Based on the energy response gradient feature data and the perturbation response feature data, an energy-perturbation consistency index is constructed to characterize the relationship between the energy change trend and the perturbation amplification degree. The response state of the structure during the loading process is comprehensively characterized according to the consistency index to obtain joint characterization data. The critical characteristic state encoding, based on the joint characterization data, performs trend analysis and threshold determination on the consistency index to identify candidate positions that may correspond to the buckling critical state, and combines and encodes the energy change characteristics, disturbance response characteristics and consistency index to form state characteristic data for describing the critical state of the structure, thus obtaining state characteristic data. The buckling critical state identification model is constructed based on the state feature data. The identification model is then used to determine the state of each loading stage and output the corresponding critical risk result or state label to obtain the prior perception result data of the buckling critical state.

4. The method for calculating the post-buckling stability of nonlinear structures based on deep learning according to claim 1, characterized in that: In step S3, the path identifier feature construction involves constructing corresponding path identifier variables for different path branches by setting a preset number of path branches, and encoding the path identifier variables to form a path identifier feature vector, which serves as branch control information in the path generation process, thereby obtaining path identifier feature data. The path generation model is constructed based on the post-buckling response modeling input data, bifurcation guidance feature data, and path identification feature data. The model is then used to predict and calculate the post-buckling response of the structure under different path identification conditions, generating multiple candidate post-buckling paths and obtaining candidate post-buckling path data. The path difference characterization process calculates the degree of response difference between different paths based on the candidate post-buckling path data, and determines the similarity between paths according to a preset difference threshold. Paths with insufficient distinguishability are subjected to separation constraint processing to obtain path difference characterization data.

5. The method for calculating the post-buckling stability of nonlinear structures based on deep learning according to claim 4, characterized in that: In step S3, the path correction involves performing a consistency analysis on the continuous change characteristics and energy change characteristics of the path based on the candidate post-buckling path data, identifying path segments with abnormal fluctuations or discontinuous changes, and performing correction processing on the path segments to obtain path rationality verification result data and corrected path data. The post-buckling path prediction results are output by organizing and outputting each candidate path based on the corrected path data, and establishing the correspondence between the path and the loading parameters to obtain the post-buckling path prediction results data.

6. The method for calculating the post-buckling stability of nonlinear structures based on deep learning according to claim 1, characterized in that: The stability evolution determination results data specifically include the stability state labels, stability change trend sequences, and stability level classification results corresponding to each loading stage.

7. The method for calculating the post-buckling stability of nonlinear structures based on deep learning according to claim 6, characterized in that: The post-buckling stability calculation results specifically include structural stability determination results, stability change trend results, and key critical state identification results.

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