A method and system for evaluating the reliability of a pile foundation system

Abstract

The application provides a pile foundation system reliability evaluation method and system, relates to the technical field of geotechnical engineering reliability evaluation, and comprises the following steps: obtaining a training input sample representing the spatial variability of soil parameters around a pile foundation system, reconstructing a soil parameter random field according to the training input sample, and extracting a physical feature vector in combination with the spatial position relationship between the pile foundation and the soil parameter random field; calling a pile foundation system finite element model to obtain performance responses corresponding to multiple failure modes, using an uncertainty multitask neural network to establish a mapping relationship between the physical features and the performance responses; determining a to-be-verified sample according to a performance response prediction result, a prediction uncertainty, and a candidate sample feature difference, and updating a training sample set and a neural network by using a finite element calculation result; and obtaining a pile foundation system reliability evaluation result according to a system failure state corresponding to a reliability statistical sample after a verification condition is met.

Description

Technical Field

[0001] This application belongs to the field of geotechnical engineering reliability assessment technology, specifically relating to a method and system for assessing the reliability of pile foundation systems. Background Technology

[0002] With the development of geotechnical engineering and infrastructure construction, pile foundations, as an important foundation form that bears the load of the superstructure and transfers the load to the ground, are widely used in building engineering, bridge engineering, marine engineering, and large-scale infrastructure projects. Because pile foundation systems operate in complex geological environments for extended periods, their bearing capacity, settlement characteristics, and deformation compatibility among different piles are affected by various factors such as soil material parameters, geological structure, and external load conditions. Therefore, conducting reliability assessments of pile foundation systems to analyze the likelihood of failure under random environmental factors is a crucial technical means to ensure the safe operation of engineering structures.

[0003] Existing reliability assessment methods for pile foundation systems are typically based on finite element numerical simulation combined with probabilistic statistical methods. Specifically, a finite element model of the pile-soil interaction is established to calculate the structural response under different combinations of soil parameters and load conditions. Based on the calculated bearing capacity, settlement, or other performance indicators, a limit state function is constructed. Then, probabilistic analysis methods such as Monte Carlo simulation and importance sampling are used to obtain the system reliability index. In practical applications, to describe the uncertainty of soil material parameters, it is usually necessary to set statistical characteristics of the soil parameters based on experimental data or engineering experience, and generate analysis samples under different working conditions through random sampling.

[0004] However, due to the significant spatial non-homogeneity of soil in actual engineering projects, soil parameters vary at different locations. This means that the response of the pile foundation system is affected not only by the soil parameters at a single location but also by the distribution of soil around the pile and the differences in soil between different piles. Furthermore, finite element models typically have high computational complexity, requiring substantial computational resources for large-scale random sample analysis, thus limiting the efficiency of reliability assessment. In addition, traditional assessment methods based on fixed samples and a single prediction model may suffer from insufficient performance response prediction, inadequate boundary region identification, and limited stability of assessment results when faced with coupled failure modes, complex random inputs, and insufficient sample coverage. Summary of the Invention

[0005] This application provides a method and system for assessing the reliability of pile foundation systems to solve the aforementioned technical problems.

[0006] The technical solution adopted in this application is as follows: This application provides a method for assessing the reliability of a pile foundation system, executed by an electronic device, including: Acquire training input samples characterizing the spatial variability of soil parameters around the pile foundation system, and reconstruct a random field of soil parameters based on the training input samples; according to a predetermined first feature extraction rule and feature standardization parameters, extract physical features of the random field of soil parameters based on the spatial positional relationship between the pile foundation and the random field of soil parameters to obtain physical feature vectors corresponding to each training input sample; For each of the aforementioned training input samples, the finite element model of the pile foundation system is invoked to obtain the performance response corresponding to multiple failure modes; a training sample set is constructed based on the performance response and the corresponding physical feature vector; an uncertain multi-task neural network is trained based on the training sample set, so that the uncertain multi-task neural network can output the performance response prediction results and prediction uncertainty corresponding to the multiple failure modes according to the physical feature vector; Obtain active learning candidate samples, and reconstruct a random field of soil parameters based on the active learning candidate samples; extract physical features from the random field of soil parameters corresponding to the active learning candidate samples according to the first feature extraction rule and the feature standardization parameters to obtain physical feature vectors corresponding to the active learning candidate samples; input the physical feature vectors corresponding to the active learning candidate samples into the uncertain multi-task neural network to obtain performance response prediction results and prediction uncertainties corresponding to the multiple failure modes; determine the samples to be verified from the active learning candidate samples based on the performance response prediction results, the prediction uncertainties, and the feature differences between different active learning candidate samples; The finite element model of the pile foundation system is invoked for the sample to be verified to obtain the corresponding first performance response; the first performance response and the physical feature vector corresponding to the sample to be verified are incorporated into the training sample set; the uncertain multi-task neural network is updated based on the updated training sample set. Based on the prediction results of the updated uncertain multi-task neural network, the judgment parameters for system failure determination are determined, and the updated uncertain multi-task neural network is used to make a release judgment using independent verification samples. When the release conditions are met, a reliability statistical sample is obtained, and a random field of soil parameters is reconstructed based on the reliability statistical sample. Physical features are extracted from the random field of soil parameters corresponding to the reliability statistical sample according to the first feature extraction rule and the feature standardization parameters to obtain the physical feature vector corresponding to the reliability statistical sample. The physical feature vector corresponding to the reliability statistical sample is input into the updated uncertain multi-task neural network to obtain performance response prediction results and prediction uncertainties corresponding to the multiple failure modes. Based on the performance response prediction results, the prediction uncertainties, and the judgment parameters, the system failure state corresponding to each reliability statistical sample is determined. The reliability assessment result of the pile foundation system is obtained based on the system failure state.

[0007] According to an embodiment of this application, the first feature extraction rule includes: The soil influence zone is determined based on the location of each pile, and the soil influence zone is divided into multiple depth layers along the depth direction of the pile. Statistical processing is performed on the random field data of soil parameters corresponding to each depth layer to obtain the layered soil parameter characteristics corresponding to each pile. The differences between piles are determined based on the layered soil parameters at corresponding depths between adjacent piles. The physical feature vector is formed based on the layered soil parameter characteristics and the pile-to-pile difference characteristics.

[0008] According to one embodiment of this application, before extracting physical features from the random field of soil parameters, the first feature extraction rule and the feature standardization parameters are first determined, including: The first feature extraction rule is determined based on the spatial distribution of the pile foundation, the spatial distribution of the random field of the soil parameters, and the influence range of the pile foundation. The feature standardization parameters are determined based on the training input samples and the first feature extraction rule.

[0009] When extracting physical features from the random field of soil parameters corresponding to the active learning candidate samples and the reliability statistics samples, the processing is carried out according to the first feature extraction rule and the feature standardization parameters.

[0010] According to one embodiment of this application, the uncertain multi-task neural network includes a shared feature extraction part, a performance response prediction part, and a system failure classification part; during training and inference, the uncertain multi-task neural network performs the following operations on the input physical feature vector: Perform shared feature extraction operations to generate shared feature representations from the physical feature vectors; By using multiple prediction branches corresponding to the multiple failure modes respectively, and based on the shared feature representation, the performance response prediction results for the corresponding failure modes and network output parameters for determining prediction uncertainty are output. Based on the shared feature representation, a system failure classification operation is performed, and the system failure classification result corresponding to the pile foundation system is output.

[0011] According to one embodiment of this application, training an uncertain multi-task neural network based on the training sample set includes: The training sample set is trained using multiple network members respectively; The model uncertainty is determined based on the differences in the performance response prediction results output by different network members; The conditional response uncertainty is determined based on the uncertainty parameters corresponding to the performance response prediction results output by the performance response prediction section. The prediction uncertainty is determined based on the model uncertainty and the conditional response uncertainty.

[0012] According to one embodiment of this application, obtaining active learning candidate samples includes: Generate global candidate samples in the random input space corresponding to the training input samples; Based on the identified failure samples in the training sample set, candidate failure neighborhood samples are generated in the random input region corresponding to the failure samples. Based on the safe samples that are close to the failure boundary in the training sample set, critical safety candidate samples are generated in the random input region corresponding to the safe samples. The active learning candidate samples are formed based on the global candidate samples, the failure neighborhood candidate samples, and the critical safety candidate samples.

[0013] According to one embodiment of this application, determining the sample to be verified from the active learning candidate samples based on the obtained performance response prediction results, prediction uncertainty, and feature differences between different active learning candidate samples includes: Based on the performance response prediction results and prediction uncertainties corresponding to each active learning candidate sample, the logical region to which each active learning candidate sample belongs is determined; the logical region includes the prediction boundary region corresponding to different failure modes, the multi-failure mode interaction region, the sparse failure mode region, and the classification divergence region. Determine the corresponding number of samples to be selected for each of the aforementioned logical regions; Based on the distance relationship between the active learning candidate samples in the feature space formed by the physical feature vectors, candidate samples are selected in each logical region according to the corresponding number of samples to obtain the sample to be verified.

[0014] According to one embodiment of this application, determining the determination parameters for system failure determination based on the updated prediction results of the uncertain multi-task neural network includes: Based on the out-of-place prediction results of the training sample set, a conservative decision parameter is determined for correcting the performance response prediction results according to the prediction uncertainty. Determine the corresponding classification threshold based on the system failure classification results; The system failure state determination rule is determined based on the conservative determination parameter and the classification determination threshold.

[0015] This application also provides a reliability assessment system for pile foundation systems, including: The physical feature construction module is used to obtain training input samples that characterize the spatial variability of soil parameters around the pile foundation system, reconstruct a random field of soil parameters based on the training input samples, and obtain a physical feature vector by combining the spatial positional relationship between the pile foundation and the random field of soil parameters. The proxy model training module is used to call the finite element model of the pile foundation system to obtain the performance response corresponding to the training input sample, construct a training sample set based on the performance response and the physical feature vector, and train an uncertain multi-task neural network. The active learning update module is used to determine the sample to be verified based on the performance response prediction results, prediction uncertainty and feature differences corresponding to the active learning candidate samples, and to update the training sample set and the uncertain multi-task neural network based on the finite element model calculation results corresponding to the sample to be verified. The calibration judgment module is used to determine the system failure judgment parameters based on the updated uncertain multi-task neural network, and to make a release judgment on the uncertain multi-task neural network using independent verification samples; The reliability assessment module is used to determine the system failure state based on the prediction results corresponding to the reliability statistical samples when the release conditions are met, and output the reliability assessment results of the pile foundation system.

[0016] This application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the pile foundation system reliability assessment method.

[0017] Due to the adoption of the above technical solution, the beneficial effects achieved by this application are as follows: This application obtains training input samples that characterize the spatial variability of soil parameters around the pile foundation system, reconstructs a random field of soil parameters based on the training input samples, and extracts physical feature vectors by combining the spatial positional relationship between the pile foundation and the random field of soil parameters. This allows the input data to not only characterize the random changes of soil parameters, but also reflect the influence of pile foundation location, pile depth, and differences in soil between piles on the pile foundation response, thereby improving the state characterization capability of the pile foundation system under complex random environments.

[0018] This application obtains the performance response corresponding to multiple failure modes by calling the finite element model of the pile foundation system for the training input sample, and constructs a training sample set based on the performance response and the corresponding physical feature vector. It uses an uncertain multi-task neural network to simultaneously output the performance response prediction results and prediction uncertainty corresponding to multiple failure modes, so that the same model can jointly analyze multiple failure modes, and uses the prediction uncertainty to describe the credibility of the model prediction results, thereby improving the accuracy of reliability assessment under complex failure mode conditions.

[0019] This application enables multiple failure modes to share soil spatial feature information and learn the differences between different performance responses by setting up a shared feature extraction part, multiple performance response prediction branches and a system failure classification part. This avoids insufficient information utilization caused by building independent models for different failure modes and improves the joint prediction capability of multiple failure modes.

[0020] This application employs multiple network members to construct an uncertain multi-task neural network, and determines the model uncertainty based on the differences between the output results of different network members. At the same time, it combines the conditional response uncertainty to obtain the comprehensive prediction uncertainty. This allows the reliability assessment process to simultaneously consider the prediction bias caused by insufficient model parameters and insufficient input sample coverage, thereby improving the reliability of system failure determination.

[0021] This application obtains global candidate samples, failure neighborhood candidate samples, and critical safety candidate samples, and determines the samples to be verified based on the performance response prediction results, prediction uncertainties, and characteristic differences between different candidate samples. This allows finite element computing resources to be prioritized for sample regions that contribute significantly to model updates, thereby reducing invalid computations and improving the targeting of active sample selection.

[0022] This application determines the number of samples to be selected based on the predicted boundary regions, multi-failure mode interaction regions, and sparse failure mode regions corresponding to different failure modes, and combines the distance relationship in the physical feature space to screen the samples, so that the newly added verification samples can cover different failure regions and different feature space regions, thereby improving the balance of the training sample distribution and enhancing the surrogate model's ability to identify complex failure boundaries.

[0023] This application obtains the real performance response by calling the finite element model of the pile foundation system on the sample to be verified, and updates the training sample set and the uncertain multi-task neural network according to the real performance response. This enables the surrogate model to continuously improve its prediction ability based on the newly added real calculation results, forming a closed loop process between candidate sample selection, finite element verification and model update, thereby improving the adaptability of the reliability assessment model.

[0024] This application determines system failure judgment parameters based on the prediction results of an updated uncertain multi-task neural network and uses independent verification samples for release judgment, making the determination process of judgment parameters independent of the final model verification process, reducing the data influence during model training, and improving the credibility of system failure judgment results.

[0025] This application obtains reliability statistics samples after the release conditions are met, and uses an updated uncertainty multi-task neural network to predict the performance response prediction results, prediction uncertainty, and system failure state corresponding to each reliability statistics sample. This enables the large-scale reliability statistics process to reduce the direct use of high-computation-cost finite element models, thereby improving the reliability calculation efficiency while ensuring the reliability of the assessment.

[0026] This application executes the reliability assessment process in the order of random field reconstruction, physical feature extraction, uncertain multi-task prediction, active learning update, decision parameter calibration, and reliability statistics. This allows the data features obtained in the preceding steps to serve as the input basis for subsequent steps, and enables the active learning update process to supplement areas where the model is insufficient. This improves the consistency of data processing and the stability of assessment results in the reliability assessment of pile foundation systems. Attached Figure Description

[0027] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a schematic diagram of the overall process and active sampling closed loop provided for embodiments of the present invention; Figure 2 A schematic diagram of KL discretization, variable correlation transformation, and marginal distribution mapping of a relevant soil random field provided in an embodiment of the present invention; Figure 3 This is a diagram showing the influence domain, depth stratification, and inter-pillar corresponding layer differences in a dual-pile configuration provided in an embodiment of the present invention. Figure 4 This is a schematic diagram of a shared encoder, a multi-regression head, a system classification head, and a deep integration structure provided in an embodiment of the present invention; Figure 5This is a schematic diagram illustrating the generation of global candidates, failure neighborhood candidates, and critical safe neighborhood candidates according to embodiments of the present invention. Figure 6 A schematic diagram of quota-based point selection for single-mode boundaries, multi-mode intersection areas, scarce mode areas, and classification divergence areas provided in embodiments of the present invention; Figure 7 This is a schematic diagram illustrating the out-of-flush prediction calibration, independent gating, and return-to-increment sampling when failing, provided in an embodiment of the present invention. Figure 8 This is a schematic diagram illustrating the center determination, lower confidence boundary determination, classification alarm, and composite system failure determination provided in an embodiment of the present invention. Figure 9 A schematic diagram of the reliability assessment system modules and data flow provided in an embodiment of the present invention; Figure 10 This is a schematic diagram of the electronic device, finite element calculation node, and communication relationship provided in an embodiment of the present invention. Detailed Implementation

[0028] The embodiments of this application are described below with reference to the accompanying drawings. It should be understood that the following embodiments are only for illustrating the technical solutions of this application and are not intended to limit the scope of protection of this application. Unless otherwise specified, the embodiments and technical features in the embodiments of this application can be combined with each other.

[0029] In the description of this application, the terms "comprising" or "including" are used to indicate the presence of a described feature, step, operation, module, or component, but do not exclude the presence or addition of one or more other features, steps, operations, modules, or components.

[0030] The pile foundation system involved in the embodiments of this application can be a single pile foundation, a pile group foundation, or a pile foundation system in which multiple piles jointly bear the load of the superstructure. Soil parameters may include one or more of the following: cohesion, internal friction angle, elastic modulus, unit weight, compression modulus, permeability coefficient, or other material parameters that can affect pile-soil interaction.

[0031] The parameters of natural soil typically vary with spatial location. Therefore, in this embodiment, instead of simply treating all soil parameters as several independent scalar random variables, a random field of soil parameters is reconstructed using random input samples that can characterize the spatial variability of soil parameters. Furthermore, physical features related to pile-soil interaction are extracted by combining the spatial location of the pile foundation in the random field of soil parameters, and these physical features are used as input to the surrogate model.

[0032] Figure 1 The overall flow of the pile foundation system reliability assessment method provided in the embodiments of this application can be schematically illustrated. For example... Figure 1As shown, the method can be executed by an electronic device, which can be a server, workstation, engineering computer, or a computing platform composed of multiple computing nodes.

[0033] In some embodiments, the method may include steps S100 to S600.

[0034] S100: Obtain training input samples, reconstruct the random field of soil parameters based on the training input samples, and extract physical features by combining the spatial positional relationship between the pile foundation and the random field of soil parameters to obtain the physical feature vector corresponding to the training input samples.

[0035] Specifically, before conducting a reliability assessment, a finite element foundation model and a random field generation model of soil parameters can be established for the pile foundation system.

[0036] For finite element foundation models of pile foundations, model data such as pile diameter, pile length, pile spacing, pile material parameters, pile cap dimensions, load conditions, soil interface coordinates, soil constitutive parameters, and analysis stages can be obtained, and a three-dimensional finite element model can be established according to the actual engineering structure.

[0037] For the first that needs to consider spatial variability Soil-like parameters Its mean can be predetermined. Standard deviation or coefficient of variation and horizontal related length , Vertical related length When considering multiple soil parameters simultaneously, the correlation matrix between different soil parameters can also be determined. .

[0038] As an alternative implementation, the spatial correlation function can be an exponential correlation function:

[0039] Where s and s′ represent two spatial locations, and Δx, Δy and Δz represent the distances between the two spatial locations in different coordinate directions.

[0040] In other implementations, quadratic exponential correlation functions, Matérn correlation functions, or other correlation functions that can describe the spatial correlation of soil in the actual site can also be used.

[0041] Figure 2 The process of constructing a random field in soil can be illustrated schematically.

[0042] In one implementation, the Karhunen-Loève expansion, or KL expansion, can be used to represent a spatially continuous random field as a combination of a finite number of random variables.

[0043] The covariance matrix formed after discretizing the random field is decomposed into eigenvalues ​​to obtain eigenvalues ​​and their corresponding eigenvectors. The retention order is then determined according to the proportion of accumulated eigenvalues. The corresponding standard Gaussian field can be expressed as:

[0044] in, For the corresponding to the first Standard random variables for quasi-random fields.

[0045] For example, a cumulative random field energy of 0.90 to 0.99 can be used as a cutoff condition for KL expansion. In one specific embodiment, the cumulative energy threshold can be set to 0.95.

[0046] When there is a correlation between multiple soil parameters, corresponding Gaussian random fields can be generated first, and then correlation transformations between variables can be performed based on the correlation matrix. For example, Cholesky decomposition can be used to perform correlation transformations on multiple Gaussian variables at the same spatial location.

[0047] For soil parameters with positive values, the Gaussian field can be further converted into the target distribution through edge distribution mapping.

[0048] For example, when the soil parameters follow a log-normal distribution, it can be determined according to:

[0049]

[0050]

[0051] Obtain the corresponding random field of soil parameters.

[0052] It should be noted that the KL expansion is only one specific implementation method of this application. The training input samples are essentially used to determine a random soil state. Therefore, in other embodiments, spectral representation, local averaging, cyclic embedding, or other random field simulation methods can also be used to generate the corresponding training input samples.

[0053] After forming the random input space, multiple training input samples can be generated using methods such as Latin hypercube sampling, low-discrepancy sequence sampling, or random sampling. Each training input sample corresponds to a specific random field implementation.

[0054] To ensure data tracking between subsequent finite element calculations, network training, and reliability statistics, a unique sample number can be saved for each training input sample, along with the random seed, random field basis version, random input vector, and corresponding finite element model version.

[0055] After obtaining the training input samples, the complete random field of soil parameters is reconstructed based on the corresponding random input variables. Figure 3 The spatial relationship between the pile foundation and the random field of soil parameters, as well as the process of physical feature extraction, can be schematically shown.

[0056] In some embodiments, the soil influence zone is determined based on the location of each pile. Specifically, the soil influence zone can be established with the pile axis of the p-th pile as the center. The soil influence zone can be a cylindrical region, and its influence radius can be expressed as:

[0057] in, For the first The diameter of the root pile, This is a preset influence coefficient. For example, You can choose from 1 to 8.

[0058] It should be noted that the cylindrical influence domain is only one specific method. In other embodiments, a conical influence domain, an influence domain with segmented varying radii, or the influence domain can be determined based on the strain energy distribution and plastic zone range obtained from finite element calculations.

[0059] After determining the soil influence zone, it can be divided into multiple depth layers along the pile depth direction. Depth layers can be divided according to the soil layer interfaces in the actual project, or by combining the pile tip location and the location where the pile load transfer changes significantly. When there is no clear soil layer interface, equal-thickness division can also be performed according to a preset layer thickness.

[0060] Subsequently, statistical processing was performed on the random field data corresponding to each depth layer to obtain the layered soil parameter characteristics corresponding to each pile.

[0061] For example, for the first Root pile, first The depth layer and the first Soil-like parameters can be used to obtain layered characteristics. .

[0062] The stratification features can be determined by the average value of material units within the corresponding influence domain, or by distance-weighted average value, minimum value, or preset quantiles. When using the distance-weighted method, material units closer to the pile axis can have a greater weight, thus making the obtained stratification features more focused on the adjacent soil that actually participates in the pile-soil interaction.

[0063] For performance responses that are significantly affected by local weak interlayers, minimum or low quantile values ​​can be used to characterize the soil features at the corresponding depth, thereby reducing the problem of smoothing out local weak areas when only the average value is used.

[0064] After obtaining the layered soil parameter characteristics corresponding to different piles, the inter-pile differences can be further determined based on the characteristics of the corresponding depth layers between adjacent piles. For example, for two adjacent piles, the inter-pile differences in soil parameters corresponding to the l-th layer and the q-th type can be expressed as:

[0065] In other implementations, the difference between piles can also be expressed as an absolute difference:

[0066] Alternatively, the ratio between the two can be used. Through the above processing, the layered soil parameter characteristics and inter-pile differences of each pile can be spliced ​​together in a predetermined order to form a physical feature vector corresponding to the training input sample. Thus, the physical feature vector not only retains the spatial variation of the soil random field itself, but also incorporates the pile location, depth, and relative soil state between different piles.

[0067] For example, in an embodiment that includes two piles, eight depth layers, and two types of random soil parameters, the layered soil parameter features of the two piles may include 2×8×2=32 dimensions; the pile difference features between corresponding depth layers may include 8×2=16 dimensions, thus forming a 48-dimensional physical feature vector.

[0068] As a further specific embodiment, material units within a horizontal range of no more than 4.0m from the axes of the two piles can be selected, and divided into eight depth layers according to center depths of -2.5m, -7.5m, -12.5m, -17.5m, -22.5m, -27.5m, -32.5m, and -37.5m. The statistical characteristics of cohesion and internal friction angle are calculated for each depth layer to form the aforementioned 48-dimensional physical characteristics.

[0069] In some embodiments, a first feature extraction rule and feature standardization parameters are determined before physical feature extraction is performed. Specifically, before the surrogate model is trained for the first time, the influence domain, depth layer division method, statistics used for each depth layer, and calculation order of inter-pile difference features are determined based on the spatial distribution of the pile foundation, the spatial distribution of the random field of soil parameters, and the influence range of the pile foundation, and these are used as the first feature extraction rule.

[0070] Within a model version, physical features are extracted from training input samples, active learning candidate samples, and subsequent reliability statistics samples according to the first feature extraction rule.

[0071] After forming multiple physical feature vectors corresponding to the training input samples according to the first feature extraction rule, the feature standardization parameters corresponding to each dimension of the physical feature can be determined based on the training data. For example, for the i-th physical feature, its mean and standard deviation can be calculated based on the training samples, and then:

[0072] Obtain the standardized physical features. After determining the feature standardization parameters, freeze the feature standardization parameters. Subsequent active learning candidate samples, independent validation samples, and reliability statistics samples all use the same feature standardization parameters, without recalculating them based on subsequent samples.

[0073] By using the above methods, we can avoid changes in the feature space caused by using different feature transformation rules at different sample stages, and ensure that the meaning of the data remains consistent in the model training stage, active learning stage, and reliability statistics stage.

[0074] It should be noted that when no effective material units are found in a combination of influence domain and depth layer, the influence radius can be expanded first according to preset rules. If effective material units still cannot be obtained, adjacent depth layers of the same type can be merged or interpolation can be performed based on nearby effective material units. When effective physical features still cannot be formed, the sample can be marked as an anomalous sample instead of directly using zero value as the corresponding physical feature, thereby reducing the impact of anomalous inputs on the training results of the surrogate model.

[0075] S200 uses the finite element model of the pile foundation system to obtain the performance response corresponding to multiple failure modes for the training input samples, constructs a training sample set, and trains an uncertain multi-task neural network.

[0076] Specifically, after reconstructing the random field of soil parameters from each training input sample, the corresponding random field values ​​can be written into the finite element model of the pile foundation system according to the pre-established material element number.

[0077] The finite element model is then sequentially assigned material parameters, loaded stage settings, finite element solution, and structural response extraction to obtain performance responses related to multiple failure modes.

[0078] In one embodiment, the pile foundation system can simultaneously consider three failure modes: the bearing capacity of the first pile, the bearing capacity of the second pile, and the differential settlement between the two piles. The corresponding performance functions can be expressed as follows:

[0079]

[0080]

[0081] Where Rp,40 represents the load corresponding to the settlement of the p-th pile reaching 40mm, Qp,d represents the design load corresponding to the p-th pile; S1 and S2 represent the settlement of the two piles under the design conditions, respectively; ΔSallow represents the allowable differential settlement. For example, Qp,d can be taken as 2750kN, and ΔSallow can be taken as 5.6mm.

[0082] In this embodiment, it is specified that:

[0083] This indicates that the j-th mode is in a safe state;

[0084] This indicates that the j-th mode has failed.

[0085] For a series-type pile foundation system, when any failure mode satisfies the corresponding performance function being no greater than zero, it can be determined that the pile foundation system has experienced a system failure.

[0086] It should be noted that the above three performance responses are only used to illustrate the specific implementation of this application. This application can also establish corresponding performance functions for total settlement, pile bending moment, pile axial force, pile cap rotation angle, or other performance responses that can constitute the ultimate state of the pile foundation.

[0087] For each training input sample, a correspondence can be established between its physical feature vector and the multiple performance responses obtained from the corresponding finite element calculation, thus forming a training sample set. For samples that do not converge normally during the finite element calculation, they can be recorded as numerical calculation anomalies, and the mesh density, load step size, and material constitutive parameters can be checked, rather than directly identifying the non-converged samples as pile foundation system failures.

[0088] Figure 4 The uncertain multitasking neural network provided in the embodiments of this application can be illustrated schematically.

[0089] In some embodiments, the uncertain multi-task neural network includes a shared feature extraction part, a performance response prediction part, and a system failure classification part.

[0090] During training and inference, the standardized physical feature vectors are input into the shared feature extraction part to perform shared feature extraction operations, generating a shared feature representation that can be used by multiple failure modes. For example, the shared feature extraction part can be configured with an input layer, a fully connected layer, a normalization layer, an activation layer, and a residual structure in sequence.

[0091] As an example, when the physical feature vector is 48-dimensional, the shared feature extraction part can use a 48-dimensional input layer, a 128-node fully connected layer, a layer normalization layer, a SiLU activation layer, a 128-node residual block, and a 64-node fully connected layer.

[0092] The performance response prediction section may include multiple prediction branches corresponding to multiple failure modes. In the j-th prediction branch, the predicted value of the j-th performance response and parameters representing the uncertainty of the conditional response are output based on the shared feature representation.

[0093] For example, the j-th prediction branch can output the prediction mean and log-variance, based on:

[0094] Determine the corresponding conditional response uncertainty, where ε is a small positive number used to ensure numerical stability.

[0095] Based on the shared feature representation, a system failure classification operation is performed, and the system failure classification result corresponding to the pile foundation system is output. For example, the Sigmoid function can be used to output the system failure probability.

[0096] When the pile foundation system is a series system, training labels can be constructed based on the actual finite element performance response:

[0097] In some embodiments, an uncertain multi-task neural network can be constructed using multiple network members. For example, M network members can be trained with different random initialization parameters, where M can be 3 to 10. Furthermore, different training samples can be resampled using different parameters for different network members.

[0098] For the j-th performance response, each network member obtains its predicted mean, from which the ensemble predicted mean can be obtained:

[0099] The differences in predictions among different network members can be used to determine model uncertainty, i.e., cognitive uncertainty caused by factors such as insufficient coverage of the current training samples. Accordingly:

[0100] The variance of the conditional response output by each network member is used to represent the uncertainty of the conditional response given physical characteristics:

[0101] Therefore, the total forecast uncertainty can be expressed as:

[0102] By simultaneously considering both the uncertainty of the conditional response and the model uncertainty among network members, the subsequent active learning process not only focuses on whether the predicted response is close to the failure boundary, but also identifies areas where the current training data is insufficiently covered.

[0103] When training the uncertain multi-task neural network, both performance response regression loss and system failure classification loss can be used simultaneously. Furthermore, a loss term can be set to constrain the consistency between the performance response prediction results and the system failure classification results.

[0104] For example, the total loss can be expressed as:

[0105] Where Lreg represents the performance response regression loss, Lcls represents the system failure classification loss, Lcons represents the consistency loss between the regression and classification results, and θ represents the network parameters. For heteroscedastic performance response prediction, Lreg can be a heteroscedastic Gaussian negative log-likelihood loss. For system classification, class-weighted binary cross-entropy or focus loss can be used to improve the network's attention to failure samples when the number of failure samples is small.

[0106] S300: Obtain active learning candidate samples, obtain corresponding physical feature vectors based on active learning candidate samples, and determine the samples to be verified based on performance response prediction results, prediction uncertainty, and feature differences between different candidate samples.

[0107] Figure 5 The process of generating candidate samples through active learning can be illustrated schematically.

[0108] In some embodiments, the active learning candidate samples include global candidate samples, failure neighborhood candidate samples, and critical safety candidate samples.

[0109] Global candidate samples can be regenerated in the same random input space as the training input samples. For example, when using KL expansion, global candidate samples can be generated in the corresponding standard normal latent variable space using the Latin hypercube method or low-discrepancy sequences. These global candidate samples are used to maintain coverage of the entire random input space, reducing the problem of the active learning process focusing on the vicinity of the existing failure boundary and missing other possible failure regions.

[0110] Failure neighborhood candidate samples are generated based on real samples that have been identified as failures using the finite element model in the training sample set. For example, a Gaussian perturbation can be added centered on the random input vector corresponding to the failure sample to form candidate samples located near the known failure region.

[0111] Critical safety candidate samples are generated from real samples that have been determined to be safe through the finite element model, but whose corresponding performance responses are close to the failure boundary. For example, real safe samples can be sorted from smallest to largest according to the minimum value among multiple performance functions, and the sample closest to the limit state can be selected as the center, and perturbation can be applied to the vicinity of the corresponding random input variable.

[0112] As one implementation method, the standard deviation of random perturbation of candidate samples can be set to 0.1 to 0.6.

[0113] After all active learning candidate samples are generated, the finite element model is not immediately invoked. First, a random field of soil parameters is reconstructed based on the active learning candidate samples. Then, the corresponding physical feature vectors are obtained according to the previously determined and frozen first feature extraction rules and feature standardization parameters. Subsequently, the physical feature vectors are input into the current uncertain multi-task neural network to obtain the performance response prediction results and prediction uncertainties corresponding to each failure mode.

[0114] Figure 6 It can schematically illustrate the logical region affiliation of candidate samples and the selection process of samples to be verified.

[0115] In some embodiments, the logical region to which an active learning candidate sample belongs can be determined based on the performance response prediction result and prediction uncertainty corresponding to each active learning candidate sample. The logical region includes prediction boundary regions corresponding to different failure modes, multi-failure mode interaction regions, sparse failure mode regions, and classification divergence regions.

[0116] For example, for the j-th failure mode, the boundary uncertainty can be defined as follows:

[0117] The smaller the boundary uncertainty, the closer the predicted result of the sample is to the predicted failure boundary of the j-th mode, and the greater the uncertainty of the prediction sign. Therefore, candidate samples whose boundary uncertainty meets the preset conditions can be identified as the predicted boundary region belonging to the j-th failure mode.

[0118] The interaction region between the j-th mode and the k-th mode can be further defined as follows:

[0119] When the above indicators are small, it means that the same candidate sample is close to the prediction boundary of two failure modes at the same time, and the candidate sample can be identified as belonging to the multi-failure mode interaction region.

[0120] For failure modes with a small number of actual failures in the training samples or where no actual failure samples have yet appeared, the sparse failure mode region can be determined based on the prediction uncertainty corresponding to the failure mode and the number of existing actual failure samples. Furthermore, the classification divergence region can be determined based on the differences in the system failure classification probabilities output by multiple network members.

[0121] For the different logical regions mentioned above, the corresponding number of samples can be determined. For example, assuming that one active learning round allows for the addition of B finite element verification samples, a portion of these samples can be used for the prediction boundaries of each single mode, a portion for the multi-mode interaction region, and another portion for the sparse and ineffective mode region or the global coverage region.

[0122] As an example, 60% of the quota can be used for single-mode prediction boundaries, 20% for multi-mode interaction regions, and the remaining 20% ​​for scarce modes, classification divergences, or global coverage regions. The number of samples for each single mode can be dynamically adjusted based on the actual number of failure samples for each failure mode, the number of out-of-bounds false safety samples, and prediction uncertainty. This reduces the problem of common failure modes consistently consuming the entire new finite element budget.

[0123] After determining the ranking of candidate samples within each logical region, diversity screening can be performed based on the feature differences between candidate samples. Specifically, the distances between candidate samples and existing training samples, as well as the selected samples to be verified in the current round, can be calculated in the standardized physical feature space. A candidate sample is only identified as a sample to be verified if the minimum distance between it and the aforementioned samples meets a preset distance condition.

[0124] For example, Euclidean distance can be used as a measure of feature difference, and the initial minimum distance threshold δ can be set to 0.3–1.5. In one example, δ can be 0.65.

[0125] When a candidate region cannot select a sufficient number of samples to be validated according to the current distance threshold, the distance threshold can be gradually reduced, for example, according to:

[0126] Gradually increase the distance until the preset minimum distance is reached.

[0127] When the same candidate sample satisfies multiple regional conditions, it can occupy only one finite element verification slot. For example, its unique affiliation can be determined in the order of "sparse and ineffective mode region - multi-mode interaction region - single-mode prediction boundary region - classification divergence region - global coverage region", thereby avoiding the repeated use of the finite element model for the same candidate sample.

[0128] S400 calls the finite element model of the pile foundation system for the samples to be verified, and updates the training sample set and the uncertain multi-task neural network based on the finite element calculation results.

[0129] Specifically, high-cost finite element calculations are performed only on the samples to be verified obtained after screening in step S300.

[0130] For each sample to be validated, the random field of soil parameters is reconstructed in the same way as the initial training input sample. The random field parameters are written into the finite element model, and the true performance responses corresponding to multiple failure modes are obtained. Subsequently, the physical feature vectors corresponding to the sample to be validated and the true performance responses are added to the training sample set.

[0131] After updating the training sample set, the uncertain multi-task neural network is retrained or incrementally trained to obtain the updated network version. This forms an active learning closed loop of "candidate sample generation - surrogate prediction - candidate screening - finite element verification - training sample update - network update".

[0132] In some embodiments, steps S300 and S400 can be repeated until a pre-set active learning stopping condition is met. The active learning stopping condition can simultaneously consider the security of the surrogate model and the stability of the prediction results.

[0133] For example, it may include: the number of false safe samples in the out-of-boundary prediction is lower than a preset upper limit; the rate of change of the system failure probability estimate in multiple consecutive active learning rounds is lower than a preset threshold; the proportion of low boundary uncertainty samples corresponding to the main failure modes in the candidate samples is lower than a preset threshold; and the finite element calculation budget reaches one or more of the preset upper limits.

[0134] For example, the threshold for the rate of change of the system's central failure probability between two consecutive active learning rounds can be set to 1% to 5%. For a failure mode for which no real failure samples have been obtained, targeted sampling can be performed on its prediction boundary or high uncertainty region instead of directly using the surrogate prediction result of the mode as the failure probability conclusion that has been verified by real finite element samples.

[0135] S500 determines system failure judgment parameters based on the prediction results of the updated uncertain multi-task neural network and makes release judgments using independent verification samples.

[0136] Figure 7 The process of out-of-flight prediction calibration and independent verification sample release can be illustrated schematically.

[0137] In some embodiments, the training sample set can first be divided into multiple training subsets, and the out-of-fold prediction results of each training sample can be obtained through cross-validation. For example, five-fold cross-validation can be used.

[0138] In each fold, a feature normalizer is fitted using only the training subset corresponding to the current fold, and the neural network is trained. Then, predictions are made for samples that did not participate in the training of this fold, thus obtaining the out-of-fold prediction results.

[0139] Based on the aforementioned out-of-range prediction results, conservative decision parameters can be determined for correcting the performance response prediction results according to the prediction uncertainty. For example, a conservative coefficient k can be set, and the following can be used:

[0140] As the conservative performance response corresponding to the j-th mode. When:

[0141] If the sample meets the system failure condition through the performance response prediction channel, it can be determined that the sample meets the system failure condition.

[0142] Furthermore, the classification threshold τ can be determined based on the system failure classification results output by the system failure classification section. When:

[0143] In such cases, the system classification channel can be used to determine if a sample is in a system failure state. Therefore, in one specific implementation, the system failure state can be determined using the following composite judgment rule:

[0144] Where F(f)=1 indicates that the system has failed.

[0145] The conservatism coefficient k and the classification decision threshold τ can be jointly selected based on the out-of-place prediction results corresponding to the training samples. For example, k can be selected from candidate parameters such as 0, 0.5, 1, 1.5, 1.96, 2.5, and 3; τ can be searched in the range of 0.10 to 0.90.

[0146] First, parameter combinations that have a failure recall rate not lower than a preset value and a false safety number not exceeding a preset upper limit can be selected. Then, among multiple combinations that meet the safety requirements, the final judgment parameters can be further determined based on the false failure number, failure recall rate, k value, and τ value.

[0147] The term "false safety" here refers to a situation where the finite element analysis results indicate that the sample is actually in a system failure state, while the composite judgment result of the surrogate model determines that the sample is safe.

[0148] After determining the decision parameters, the updated uncertain multi-task neural network is further evaluated using independent validation samples. It should be noted that these independent validation samples do not participate in network structure selection, network parameter training, feature extraction rule selection, standardized parameter selection, conservative coefficient k selection, or classification threshold τ selection.

[0149] For example, "the out-of-bounds predicted failure recall rate is not less than 0.90, the out-of-bounds false safety number is not greater than 3, and the number of false safety in the independently validated samples is 0" can be set as an approval condition. The above values ​​are only for specific implementation methods and are not intended to limit the scope of protection of this application.

[0150] When the independent verification results meet the release conditions, the corresponding uncertain multi-task neural network, feature transformation rules, standardized parameters, and system failure judgment parameters are locked together as the model version for subsequent reliability statistics.

[0151] If the release conditions are not met, the final reliability assessment result is not output directly. Instead, the process returns to the active learning candidate sample generation process to continue adding samples to be verified and updating the surrogate model.

[0152] By separating the calibration of decision parameters from independent release, data leakage caused by repeatedly selecting network parameters and decision thresholds using the same batch of samples can be reduced, and the risk of real failed samples being misjudged as safe by the proxy model can be lowered.

[0153] S600, under the condition of meeting the release conditions, obtains the reliability statistics sample, and obtains the reliability assessment result of the pile foundation system based on the system failure state corresponding to the reliability statistics sample.

[0154] Figure 8 The system failure determination process in the reliability statistics stage can be illustrated schematically.

[0155] After the release conditions in step S500 are met, a large number of reliability statistics samples are generated in the same random input space as the training input samples. For example, when using KL random field representation, NMCS mutually independent reliability statistics samples can be generated in the corresponding standard normal latent variable space.

[0156] For each reliability statistical sample, a random field of soil parameters is reconstructed based on the reliability statistical sample, and the corresponding physical feature vector is obtained according to the determined and frozen first feature extraction rule and feature standardization parameters. Subsequently, the physical feature vector corresponding to the reliability statistical sample is input into an uncertain multi-task neural network that has passed the release judgment to obtain the prediction results of each performance response, the corresponding prediction uncertainty, and the system failure classification results.

[0157] Then, using the conservative judgment parameters and classification judgment threshold determined in step S500, the system failure state corresponding to each reliability statistical sample is determined. Assuming that Nfail samples out of NMCS reliability statistical samples are judged as system failures, the system failure probability can be expressed as:

[0158] Furthermore, reliability indicators can be obtained based on the failure probability:

[0159] Where Φ raised to the power of negative one represents the inverse function of the standard normal distribution function.

[0160] Reliability assessment results may include one or more of the following: system failure probability, reliability index, failure probability corresponding to each individual failure mode, and confidence interval for failure probability. Furthermore, Wilson confidence intervals or bootstrap sampling methods can be used to determine the confidence intervals corresponding to the failure probabilities.

[0161] When executing a large number of reliability statistics samples, network inference can be performed in batches, and the change in failure probability as the cumulative number of statistics samples increases can be recorded to obtain the convergence curve corresponding to the reliability assessment results.

[0162] In some embodiments, both center prediction results and conservative screening results can be output simultaneously. The center failure status can be determined based on:

[0163] A determination is made; for conservative system failure states, a composite determination can be made using the prediction uncertainty correction rule determined in step S500 and the system classification results.

[0164] The central failure probability can be used as a probability estimate corresponding to the central prediction of the surrogate model, while the conservative system failure ratio is mainly used for engineering safety screening. The two can be output separately to avoid directly interpreting the conservative screening ratio as the unbiased system failure probability.

[0165] Through the above steps, this embodiment first converts the spatial random field corresponding to the original high-dimensional random input into physical features that have a clear physical correspondence with the pile location, pile depth, and differences in soil between piles; then, it uses a surrogate model that can simultaneously obtain multiple performance responses and prediction uncertainties to determine finite element verification samples; after the surrogate model is updated, calibrated, and independently verified, it is used to replace large-scale finite element calculations to perform reliability statistics, thereby reducing the number of finite element calls while controlling the boundaries of multiple failure modes and the prediction uncertainty of the surrogate model.

[0166] To further illustrate the implementation process of the above method, in a specific embodiment, a three-dimensional finite element model containing two piles and layered soil can be established.

[0167] Soil cohesion and internal friction angle These are two log-normal random fields that are cross-correlated.

[0168] In the finite element model, 288 material element centers can be used as discrete locations for the random field. The mean of the cohesion can be taken as 15, and the standard deviation as 4.5; the mean of the internal friction angle can be taken as 25, and the standard deviation as 3.75; the correlation coefficient between the two random parameters can be taken as -0.3.

[0169] KL decomposition was performed on the discrete covariance matrices corresponding to the two types of random fields, and the cumulative energy threshold was set to 0.95. Each type of random field retained 240 order, so that the two types of random fields corresponded to 480-dimensional standard normal random input variables.

[0170] One hundred initial samples are generated in the standard normal random input space, and the cohesion random field and internal friction angle random field are reconstructed for each sample. According to the material element number, each random field is implemented and assigned to the corresponding finite element model, and three performance functions are obtained.

[0171] During physical feature extraction, material units with a horizontal distance of no more than 4.0m centered on the two piles were selected, and the pile body was divided into eight depth layers. The cohesion and internal friction angle statistical characteristics of each pile in each depth layer were calculated to form a 32-dimensional double-pile layered soil parameter feature. Furthermore, the differences in cohesion and internal friction angle between the two piles in the corresponding depth layers were calculated according to a fixed pile number order to form a 16-dimensional pile difference feature, thus obtaining a 48-dimensional physical feature vector.

[0172] The existing data foundation for this project includes 100 initial finite element samples and 50 supplementary finite element samples obtained from existing surrogate methods, forming a total of 150 sets of real finite element data. These 150 sets of data can be used to demonstrate that the above-mentioned random field reconstruction, pile perimeter physical feature extraction, and multi-task network training processes have a practical data basis.

[0173] It should be noted that the subsequent 50 finite element samples are from the existing Gaussian process active point selection process. Therefore, this part of the data is not used as proof that the uncertain multi-task neural network of this application has actually completed active learning point selection.

[0174] In an existing neural network training implementation, a shared encoder can be used to encode 48-dimensional physical features and simultaneously output the predicted mean of three performance responses, three corresponding heteroscedasticity parameters, and the system failure classification probability. A deep ensemble can be constructed using five differently randomly initialized network members, and the model uncertainty can be determined based on the prediction differences among the different members. The existing data can be used for training and comparing the network structure, physical feature inputs, and uncertainty outputs.

[0175] When deploying the complete reliability assessment process of this application in actual engineering, the active learning candidate generation, finite element verification, network update, extrapolation parameter calibration and independent verification release are re-executed using the uncertain multi-task neural network according to the aforementioned steps S300 to S500, and the large sample reliability statistics process in step S600 is only entered after the model meets the release conditions.

[0176] Therefore, it is possible to clearly distinguish between the two different implementation processes: "network training and feature comparison on existing limited metadata" and "uncertain multi-task neural network completing active learning - independent release - reliability statistical closed loop".

[0177] This application also provides a reliability assessment system for pile foundation systems. Figure 9 The composition of the reliability assessment system for the pile foundation system can be schematically shown.

[0178] In some embodiments, the pile foundation system reliability assessment system may include a physical feature construction module, a surrogate model training module, an active learning update module, a calibration judgment module, and a reliability assessment module.

[0179] The physical feature construction module is used to obtain training input samples characterizing the spatial variability of soil parameters around the pile foundation system, reconstruct a random field of soil parameters based on the training input samples, and obtain physical feature vectors by combining the spatial positional relationship between the pile foundation and the random field of soil parameters. Specifically, the physical feature construction module can perform the random field reconstruction, pile perimeter influence domain determination, depth layer division, layered soil parameter statistics, pile inter-pile difference feature calculation, and feature standardization operation corresponding to the aforementioned step S100.

[0180] The surrogate model training module is used to call the finite element model of the pile foundation system to obtain multiple performance responses corresponding to the training input samples, construct a training sample set based on the performance responses and physical feature vectors, and train an uncertain multi-task neural network. Specifically, the surrogate model training module can perform the aforementioned step S200.

[0181] The active learning update module is used to determine the samples to be verified based on the performance response prediction results, prediction uncertainty, and feature differences between different candidate samples corresponding to the active learning candidate samples, and to update the training sample set and the uncertain multi-task neural network based on the finite element model calculation results corresponding to the samples to be verified. Therefore, the active learning update module can execute the aforementioned steps S300 and S400.

[0182] The calibration and judgment module is used to determine system failure judgment parameters based on the prediction results of the updated uncertain multi-task neural network, and to make a release judgment on the updated uncertain multi-task neural network using independent verification samples. The calibration and judgment module can perform the out-of-bounds prediction generation, conservative judgment parameter selection, classification threshold determination, and independent verification process corresponding to the aforementioned step S500.

[0183] The reliability assessment module is used to generate or obtain reliability statistical samples when the release conditions are met, obtain performance response prediction results and prediction uncertainties based on the reliability statistical samples, determine the system failure state of each reliability statistical sample based on the corresponding judgment parameters, and obtain the reliability assessment results corresponding to the pile foundation system.

[0184] It should be noted that the above modules are divided according to their functions. In a specific computing platform, multiple modules can be executed by the same processor or deployed on different computing nodes.

[0185] For example, random field reconstruction, physical feature extraction, and neural network inference can be deployed on the main computing server, high-cost pile foundation finite element analysis tasks can be distributed to multiple finite element computing nodes, and the real performance responses returned by each finite element computing node can be written into a unified sample database.

[0186] Figure 10The communication relationships between electronic devices, finite element computing nodes, and data storage units can be schematically illustrated.

[0187] The reliability assessment method for the pile foundation system in this application embodiment can be executed by an electronic device. The electronic device may include one or more processors and a memory.

[0188] The memory can store computer programs used to execute the reliability assessment method for the pile foundation system of this application, as well as data such as random field parameters, random input samples, KL basis, feature extraction rules, feature standardization parameters, finite element model version, uncertain multi-task neural network parameters, active learning sample records, decision parameters, and reliability statistics.

[0189] When the processor executes the computer program, it can perform the above steps S100 to S600.

[0190] This application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the above-described pile foundation system reliability assessment method.

[0191] The computer-readable storage medium may include, but is not limited to, read-only memory, random access memory, solid-state memory, disk, optical disk, or other non-transitory storage medium capable of storing computer programs.

[0192] It should be noted that the above embodiments using KL expansion, pile perimeter layered features, deep ensemble neural networks, and Monte Carlo statistics are only used to illustrate one specific implementation of this application.

[0193] Without altering the technical chain of this application—"soil random field reconstruction—physical feature extraction combined with pile foundation spatial location—uncertainty multi-task prediction—active sample selection based on prediction results and uncertainties—finite element verification and update—judgment parameter calibration and independent release—reliability statistics"—the specific implementation method can be adjusted.

[0194] For example, random field generation can employ truncated spectrum representation, local averaging, or other random field simulation methods; the cylindrical influence domain in physical features can be replaced with a conical influence domain or other influence domains determined based on the pile-soil action range; and the stratified statistical features can employ average value, distance-weighted average value, minimum value, quantile, gradient, or interlayer difference.

[0195] For multi-pile systems, adjacency relationships between piles can be established based on pile spacing, common pile cap connection, or load transfer relationship, and pile difference characteristics can be formed only for piles with adjacency relationships.

[0196] In addition to deep ensembles, uncertainty prediction can also employ MC Dropout, Bayesian neural networks, or other network forms capable of outputting prediction uncertainties.

[0197] Boundary uncertainty in the active learning process is not limited to the U function; it can also be achieved by using prediction entropy, committee disagreement, or other indicators that can reflect the value of candidate sample information.

[0198] In addition to ordinary Monte Carlo simulation, reliability statistics can also employ importance sampling, subset simulation, or quasi-Monte Carlo methods.

[0199] The above alternatives can be selected based on the structural form of the pile foundation system to be evaluated, the dimension of the random field, the cost of finite element calculation, and the accuracy requirements of reliability assessment.

Claims

1. A method for reliability assessment of a pile foundation system, characterized in that, Performed by electronic devices, including: Acquire training input samples characterizing the spatial variability of soil parameters around the pile foundation system, and reconstruct a random field of soil parameters based on the training input samples; according to a predetermined first feature extraction rule and feature standardization parameters, extract physical features of the random field of soil parameters based on the spatial positional relationship between the pile foundation and the random field of soil parameters to obtain physical feature vectors corresponding to each training input sample; For each of the aforementioned training input samples, the finite element model of the pile foundation system is invoked to obtain the performance response corresponding to multiple failure modes; a training sample set is constructed based on the performance response and the corresponding physical feature vector; an uncertain multi-task neural network is trained based on the training sample set, so that the uncertain multi-task neural network can output the performance response prediction results and prediction uncertainty corresponding to the multiple failure modes according to the physical feature vector; Obtain active learning candidate samples, and reconstruct a random field of soil parameters based on the active learning candidate samples; extract physical features from the random field of soil parameters corresponding to the active learning candidate samples according to the first feature extraction rule and the feature standardization parameters to obtain physical feature vectors corresponding to the active learning candidate samples; input the physical feature vectors corresponding to the active learning candidate samples into the uncertain multi-task neural network to obtain performance response prediction results and prediction uncertainties corresponding to the multiple failure modes; determine the samples to be verified from the active learning candidate samples based on the performance response prediction results, the prediction uncertainties, and the feature differences between different active learning candidate samples; The finite element model of the pile foundation system is invoked for the sample to be verified to obtain the corresponding first performance response; the first performance response and the physical feature vector corresponding to the sample to be verified are incorporated into the training sample set; the uncertain multi-task neural network is updated based on the updated training sample set. Based on the prediction results of the updated uncertain multi-task neural network, the judgment parameters for system failure determination are determined, and the updated uncertain multi-task neural network is used to make a release judgment using independent verification samples. When the release conditions are met, a reliability statistical sample is obtained, and a random field of soil parameters is reconstructed based on the reliability statistical sample. Physical features are extracted from the random field of soil parameters corresponding to the reliability statistical sample according to the first feature extraction rule and the feature standardization parameters to obtain the physical feature vector corresponding to the reliability statistical sample. The physical feature vector corresponding to the reliability statistical sample is input into the updated uncertain multi-task neural network to obtain performance response prediction results and prediction uncertainties corresponding to the multiple failure modes. Based on the performance response prediction results, the prediction uncertainties, and the judgment parameters, the system failure state corresponding to each reliability statistical sample is determined. The reliability assessment result of the pile foundation system is obtained based on the system failure state.

2. The reliability assessment method for pile foundation systems according to claim 1, characterized in that, The first feature extraction rule includes: The soil influence zone is determined based on the location of each pile, and the soil influence zone is divided into multiple depth layers along the depth direction of the pile. Statistical processing is performed on the random field data of soil parameters corresponding to each depth layer to obtain the layered soil parameter characteristics corresponding to each pile. The differences between piles are determined based on the layered soil parameters at corresponding depths between adjacent piles. The physical feature vector is formed based on the layered soil parameter characteristics and the pile-to-pile difference characteristics.

3. The reliability assessment method for pile foundation systems according to claim 2, characterized in that, Before extracting physical features from the random field of soil parameters, the method further includes: The first feature extraction rule is determined based on the spatial distribution of the pile foundation, the spatial distribution of the random field of the soil parameters, and the influence range of the pile foundation. The feature standardization parameters are determined based on the training input samples and the first feature extraction rule.

4. The reliability assessment method for pile foundation systems according to claim 1, characterized in that, The uncertain multi-task neural network includes a shared feature extraction part, a performance response prediction part, and a system failure classification part; during training and inference, the uncertain multi-task neural network performs the following operations on the input physical feature vector: Perform shared feature extraction operations to generate shared feature representations from the physical feature vectors; By using multiple prediction branches corresponding to the multiple failure modes respectively, and based on the shared feature representation, the performance response prediction results for the corresponding failure modes and network output parameters for determining prediction uncertainty are output. Based on the shared feature representation, a system failure classification operation is performed, and the system failure classification result corresponding to the pile foundation system is output.

5. The reliability assessment method for pile foundation systems according to claim 1, characterized in that, The training of the uncertain multi-task neural network based on the training sample set includes: The training sample set is trained using multiple network members respectively; The model uncertainty is determined based on the differences in the performance response prediction results output by different network members; The conditional response uncertainty is determined based on the uncertainty parameters corresponding to the performance response prediction results output by the performance response prediction section. The prediction uncertainty is determined based on the model uncertainty and the conditional response uncertainty.

6. The reliability assessment method for pile foundation systems according to claim 1, characterized in that, The process of obtaining active learning candidate samples includes: Generate global candidate samples in the random input space corresponding to the training input samples; Based on the identified failure samples in the training sample set, candidate failure neighborhood samples are generated in the random input region corresponding to the failure samples. Based on the safe samples that are close to the failure boundary in the training sample set, critical safety candidate samples are generated in the random input region corresponding to the safe samples. The active learning candidate samples are formed based on the global candidate samples, the failure neighborhood candidate samples, and the critical safety candidate samples.

7. The reliability assessment method for pile foundation systems according to claim 6, characterized in that, Based on the obtained performance response prediction results, prediction uncertainty, and feature differences between different active learning candidate samples, samples to be verified are determined from the active learning candidate samples, including: Based on the performance response prediction results and prediction uncertainties corresponding to each active learning candidate sample, the logical region to which each active learning candidate sample belongs is determined; the logical region includes the prediction boundary region corresponding to different failure modes, the multi-failure mode interaction region, the sparse failure mode region, and the classification divergence region. Determine the corresponding number of samples to be selected for each of the aforementioned logical regions; Based on the distance relationship between the active learning candidate samples in the feature space formed by the physical feature vectors, candidate samples are selected in each logical region according to the corresponding number of samples to obtain the sample to be verified.

8. The reliability assessment method for pile foundation systems according to claim 1, characterized in that, The determination of judgment parameters for system failure based on the prediction results of the updated uncertain multi-task neural network includes: Based on the out-of-place prediction results of the training sample set, a conservative decision parameter is determined for correcting the performance response prediction results according to the prediction uncertainty. Determine the corresponding classification threshold based on the system failure classification results; The system failure state determination rule is determined based on the conservative determination parameter and the classification determination threshold.

9. A reliability assessment system for pile foundation systems, characterized in that, include: The physical feature construction module is used to obtain training input samples that characterize the spatial variability of soil parameters around the pile foundation system, reconstruct a random field of soil parameters based on the training input samples, and obtain a physical feature vector by combining the spatial positional relationship between the pile foundation and the random field of soil parameters. The proxy model training module is used to call the finite element model of the pile foundation system to obtain the performance response corresponding to the training input sample, construct a training sample set based on the performance response and the physical feature vector, and train an uncertain multi-task neural network. The active learning update module is used to determine the sample to be verified based on the performance response prediction results, prediction uncertainty and feature differences corresponding to the active learning candidate samples, and to update the training sample set and the uncertain multi-task neural network based on the finite element model calculation results corresponding to the sample to be verified. The calibration judgment module is used to determine the system failure judgment parameters based on the updated uncertain multi-task neural network, and to make a release judgment on the uncertain multi-task neural network using independent verification samples; The reliability assessment module is used to determine the system failure state based on the prediction results corresponding to the reliability statistical samples when the release conditions are met, and output the reliability assessment results of the pile foundation system.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the pile foundation system reliability assessment method according to any one of claims 1-8.

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