Method and system for surrogate model assisted rbdo of suction anchors under spatially variable soil conditions
By combining global and local proxy models, the problems of high computational cost and insufficient accuracy in suction anchor design optimization under spatially variable soil conditions are solved, achieving more efficient and accurate reliability design.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SOUTH CHINA UNIV OF TECH
- Filing Date
- 2026-06-26
- Publication Date
- 2026-07-31
AI Technical Summary
Under spatially variable soil conditions, the reliability design optimization of suction anchors faces the problems of high computational cost and insufficient accuracy. In particular, the traditional two-layer cyclic RBDO method has high computational cost, and the global proxy model lacks local accuracy near the feasibility boundary.
A two-level hierarchical adaptive proxy architecture combining a global proxy model and a local proxy model is adopted. Through global screening and local iterative updates, combined with an active learning function, high-fidelity evaluation samples are selected, reducing the input dimension of the proxy model and increasing the training density of key regions.
It improves the computational efficiency and local accuracy of suction anchor reliability design optimization, reduces invalid high-fidelity calculations, explicitly considers soil spatial variability, and improves the credibility of design results.
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Figure CN122491069A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of marine geotechnical engineering and reliability design optimization technology, and in particular to a method, system, terminal equipment, computer-readable storage medium, and computer program product for RBDO assisted by suction anchor proxy model under spatially variable soil conditions. Background Technology
[0002] Suction anchors are critical foundational components widely used in deepwater oil and gas platforms, floating offshore wind turbines, and other marine renewable energy installations. Their design must simultaneously meet the requirements of structural reliability and cost-effectiveness throughout their service life. A key challenge in suction anchor design lies in the inherent spatial variability of natural soil parameters; therefore, a design framework capable of explicitly accounting for such uncertainties is urgently needed.
[0003] Reliability-Based Design Optimization (RBDO) provides a rigorous framework for design optimization under uncertainty by requiring the optimized design to meet a target reliability level, rather than relying on empirical safety factors. In RBDO, the traditional two-loop approach involves two nested computational loops: the outer loop iterates through different design options, while the inner loop performs a reliability analysis on each candidate design to evaluate its reliability metrics. The outer loop often needs to evaluate hundreds to thousands of candidate designs, while each inner reliability analysis requires tens of thousands of model calls. When complex numerical models are involved, the computational cost of traditional two-loop RBDO becomes unacceptably high.
[0004] To alleviate the aforementioned computational burden, existing research has proposed surrogate model-assisted RBDO methods, which replace high-fidelity models with less computationally expensive approximation models. However, most existing methods still require building a surrogate model for each candidate design, resulting in high computational costs. Other methods train a single global surrogate model across the entire extended design-random variable space, but these global surrogate models often lack sufficient local accuracy near the feasibility boundary, leading to suboptimal design results.
[0005] Furthermore, when using random fields (RF) to characterize the spatial variability of soil parameters, the high-dimensional features of the RF input introduce the "curse of dimensionality," making training the surrogate model computationally unsustainable. Even with Karhunen-Loève expansion (KLE) discretization, dozens to hundreds of random variables are obtained as inputs, making it impractical to directly construct the surrogate model in the original space. Summary of the Invention
[0006] To address at least one of the technical problems in the prior art, the present invention provides a method, system, terminal device, computer-readable storage medium, and computer program product for suction anchor proxy model-assisted RBDO under spatially variable soil conditions (HAS-RBDO-RF).
[0007] The first objective of this invention is to provide a method for RBDO assisted by a suction anchor proxy model under spatially variable soil conditions.
[0008] The second objective of this invention is to provide a system for RBDO assisted by a suction anchor proxy model under spatially variable soil conditions.
[0009] The third objective of this invention is to provide a terminal device.
[0010] A fourth objective of this invention is to provide a computer-readable storage medium.
[0011] The fifth objective of this invention is to provide a computer program product.
[0012] The first objective of this invention can be achieved by adopting the following technical solution:
[0013] A method for RBDO assisted by a suction anchor surrogate model under spatially variable soil conditions, the method comprising:
[0014] Based on the geometric parameters of the suction anchor, a design variable space is constructed; based on the design variable space, a reliability-based suction anchor design optimization problem is constructed; the suction anchor design optimization problem includes deterministic constraints and reliability constraints.
[0015] Based on the design variable space and deterministic constraints, an initial screening design set is generated; based on the field survey data, a random field sample set is constructed to characterize the spatial variability of soil parameters.
[0016] The candidate designs for attracting anchors in the initial screening design set are combined with random field samples in the random field sample set to obtain the initial combination; the candidate designs for attracting anchors in the initial combination are combined with the low-dimensional latent vectors of the corresponding random field samples to obtain the initial extended combination; the initial extended combination sets are formed by the initial extended combination sets.
[0017] The global surrogate model is trained by taking the initial extended combination as input and the limit state function value of the corresponding initial combination as output; the trained global surrogate model is used to predict the initial extended combination set; and the global feasible design set is obtained based on the predicted limit state function value and reliability constraints.
[0018] Based on the candidate designs for suction anchors in the global feasible design set, the corresponding initial extended combination is selected from the initial extended combination set; the limit state function values of the selected initial extended combination and its corresponding initial combination are used as local training samples to train the local proxy model, and the final top-ranked design set is obtained.
[0019] Preferably, the local proxy model is a multinomial chaotic kriging model;
[0020] The selected initial extended combination and its corresponding limit state function value are used as the local training set. ;
[0021] The step of using the selected initial extended combination and its corresponding initial combination's limit state function value as local training samples to train the local proxy model, and obtaining the final top-ranked design set, includes:
[0022] When the iteration round hour:
[0023] Let the local proxy model be denoted as Using local training sets For local proxy model Training is performed; where the input data is the selected initial extended combination, and the output data is the limit state function value corresponding to the input data in the initial combination;
[0024] When the iteration round hour:
[0025] Will The locally trained proxy model in each round is used as the first... Round-based local proxy model ;
[0026] Using the local proxy model Predict the initial extended combination corresponding to each suction anchor candidate design in the initial screening design set; calculate the reliability index of each suction anchor candidate design based on the predicted limit state function value.
[0027] Based on the reliability indices and reliability constraints of the suction anchor candidate design, the first... The design set prioritizes rounds;
[0028] Based on the reliability indices and reliability constraint boundaries of the suction anchor candidate design, the first... Design set near the feasibility boundary of each round;
[0029] The first The design sets ranked at the top of the round and the design sets near the feasibility boundary are merged; the suction anchor candidate designs in the merged design set are combined with the low-dimensional latent vectors of each random field sample in the random field sample set to form extended latent sample points; based on the values of the extended latent sample points calculated by the active learning function, the extended latent sample points are selected as new high-fidelity evaluation samples.
[0030] The newly added high-fidelity evaluation samples and the corresponding limit state function values of the initial combination are added as new samples to the local training set. In the middle; using local training sets Training local proxy model , to obtain the trained first Round-based local proxy model ;
[0031] If the termination condition is met, stop the iteration; otherwise: let and return the iteration number. If necessary, continue with the subsequent operations.
[0032] Preferably, the suction anchor design optimization problem further includes an objective cost function; the objective cost function is used to represent the material cost of the candidate suction anchor designs;
[0033] Based on the reliability indicators and reliability constraints of the suction anchor candidate design, the first... The design set with the rounds prioritized includes:
[0034] If the reliability index of the suction anchor candidate design meets the reliability constraint, then the suction anchor candidate design is added to the local feasible design set.
[0035] Based on the objective cost function, calculate the objective cost function value of the suction anchor candidate designs; rank the suction anchor candidate designs in the local feasible design set according to the objective cost function values in ascending order, and select the top-ranked, predetermined number of suction anchor candidate designs as the first... The design set is prioritized by the order of rounds.
[0036] Preferably, the first The candidate design with the smallest objective cost function value in the highest-ranked design set is selected as the current optimal design. ;
[0037] Based on the reliability indices and reliability constraint boundaries of the suction anchor candidate design, the first... The design set near the feasibility boundary of each round includes:
[0038] Calculate the minimum distance between the reliability index and the reliability constraint boundary of the suction anchor candidate design;
[0039] If the minimum distance is less than or equal to the preset reliability neighborhood threshold, then the corresponding suction anchor candidate design is added to the first... Design set near the feasibility boundary of each round;
[0040] For the initial selection of design sets, if the objective cost function value of the suction anchor candidate design is less than that of the current optimal design... If a candidate design for a suction anchor is selected, and the reliability index of the candidate design is lower than the allowable lower limit of the reliability constraint boundary and the difference between the two does not exceed the preset reliability neighborhood threshold, then the candidate design for the suction anchor is added to the first... Design set near the feasibility boundary of each round.
[0041] Preferably, the termination condition is:
[0042] No. The order of rounds is prioritized in the design set and the first round. The design set ranked at the top of the rounds remained consistent in the composition and ranking of the suction anchor candidate designs multiple times.
[0043] Or, until the preset maximum number of iterations is reached;
[0044] Alternatively, all newly added candidate samples may have values calculated using the active learning function that are greater than the preset active learning threshold.
[0045] Preferably, obtaining the globally feasible design set based on the predicted limit state function value and reliability constraints includes:
[0046] Based on the predicted limit state function value, calculate the reliability index of each suction anchor candidate design;
[0047] Candidate suction anchor designs that do not meet the reliability constraints in the initial screening design set are deleted, and the remaining candidate suction anchor designs in the initial screening design set are used as the global feasible design set.
[0048] Preferably, the step of calculating the reliability index of each suction anchor candidate design based on the predicted limit state function value includes:
[0049] Based on the limit state function value, design for each suction anchor candidate Calculate the failure probability ;
[0050] Calculate candidate designs for suction anchors based on failure probability. Reliability indicators :
[0051] ;
[0052] In the formula, (·) is the inverse function of the standard normal distribution function.
[0053] Preferably, the step of constructing a random field sample set to characterize the spatial variability of soil parameters based on field survey data includes:
[0054] Based on the field investigation data, soil parameters were obtained; the field investigation data included static cone penetration test data, and the soil parameters included undrained shear strength s. u and soil undrained deformation modulus E u ;
[0055] For the soil parameter Y, a one-dimensional random field is constructed along the depth direction and discretized using the Karhunen-Loève theorem expansion;
[0056] Based on the discrete results and the truncation criterion, s are generated respectively. u Random field samples and E u Random field samples;
[0057] s under the same random event u Random field samples and E u Random field samples are combined to form random field samples used to characterize the spatial variability of soil parameters; random field samples constitute a random field sample set.
[0058] Preferably, the step of constructing the design variable space based on the geometric parameters of the suction anchor includes:
[0059] Due to the length of the suction anchor Suction anchor diameter and the depth position of the mooring lugs The ratio of the length of the suction anchor to the length of the suction anchor together constitutes the design variables of the suction anchor. , denoted as:
[0060] ;
[0061] in, Design variable boundary constraints must be met:
[0062] C-1: ;
[0063] In the formula, and These are the set lower and upper limits of permission, respectively.
[0064] The design variable space is determined by the suction anchor design variables and the design variable boundary constraints.
[0065] The second objective of this invention can be achieved by adopting the following technical solution:
[0066] A system for RBDO assisted by a suction anchor proxy model under spatially variable soil conditions, the system comprising:
[0067] The module is used to construct the design variable space based on the geometric parameters of the suction anchor; and to construct the reliability-based suction anchor design optimization problem based on the design variable space. The suction anchor design optimization problem includes deterministic constraints and reliability constraints.
[0068] The generation module is used to generate an initial screening design set based on the design variable space and deterministic constraints; and to construct a random field sample set to characterize the spatial variability of soil parameters based on field survey data.
[0069] The combination module is used to combine the suction anchor candidate designs in the initial screening design set with the random field samples in the random field sample set to obtain the initial combination; combine the suction anchor candidate designs in the initial combination with the low-dimensional latent vectors of the corresponding random field samples to obtain the initial extended combination; and form the initial extended combination set from the initial extended combination.
[0070] The first training module is used to train the global proxy model by taking the initial extended combination as input and the limit state function value of the corresponding initial combination as output; using the trained global proxy model to predict the initial extended combination set; and obtaining the global feasible design set based on the predicted limit state function value and reliability constraints.
[0071] The second training module is used to select the corresponding initial extended combination from the initial extended combination set based on the suction anchor candidate designs in the global feasible design set; and to train the local proxy model using the limit state function values of the selected initial extended combination and its corresponding initial combination as local training samples to obtain the final top-ranked design set.
[0072] The third objective of this invention can be achieved by adopting the following technical solution:
[0073] A terminal device includes a processor and a memory for storing a processor-executable program, wherein when the processor executes the program stored in the memory, it implements the above-described method for suction anchor proxy model-assisted RBDO under spatially variable soil conditions.
[0074] The fourth objective of this invention can be achieved by adopting the following technical solution:
[0075] A computer-readable storage medium storing a program that, when executed by a processor, implements the above-described method for using a suction anchor proxy model to assist RBDO under spatially variable soil conditions.
[0076] The fifth objective of this invention can be achieved by adopting the following technical solution:
[0077] A computer program product includes a computer program that, when executed by a processor, implements the above-described method for using a suction anchor proxy model to assist RBDO under spatially variable soil conditions.
[0078] The present invention has the following advantages over the prior art:
[0079] (1) This invention employs a two-tiered hierarchical adaptive proxy architecture combining a global proxy model and a local proxy model. The global proxy model first performs rapid filtering of the extended design space to obtain a globally feasible design set; the local proxy model then iteratively updates the top-ranked designs and designs near the reliability constraint boundary within the globally feasible design set. Specifically, this invention combines the top-ranked design set and the design set near the feasibility boundary to form a candidate design set to be encrypted. The candidate designs are combined with the low-dimensional latent vectors corresponding to the random field samples to generate extended latent sample points, and new high-fidelity evaluation samples are added to the local training set, thereby increasing the training sample density in key areas. Through this sample encryption method, the local proxy model achieves higher prediction accuracy in the potential optimal region and near the reliability constraint boundary, thereby reducing the impact of feasibility misjudgment on the optimization results.
[0080] (2) This invention addresses the problem of high-dimensional random field input caused by the spatial variability of soil parameters by compressing random field samples into low-dimensional potential vectors. While retaining the main spatial variability features, it reduces the input dimension of the surrogate model and alleviates the training burden of the surrogate model caused by the high input dimension after KLE discretization.
[0081] (3) This invention utilizes an active learning function to measure the amount of information updated by the extended potential sample points to the local proxy model, thereby selecting new high-fidelity evaluation samples and concentrating the random finite element model calls on areas near the limit state surface, regions with high prediction uncertainty, and boundary candidate design regions that may affect the optimal design, thus reducing invalid high-fidelity calculations. Therefore, this invention can improve the computational efficiency, local accuracy, and result reliability of suction anchor reliability design optimization under the condition of explicitly taking into account the spatial variability of soil. Attached Figure Description
[0082] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.
[0083] Figure 1 This is a flowchart of the method for using a suction anchor proxy model to assist RBDO under spatially variable soil conditions, as described in Embodiment 1 of the present invention.
[0084] Figure 2 This is a schematic diagram of the method for using a suction anchor proxy model to assist RBDO under spatially variable soil conditions, as described in Embodiment 1 of the present invention.
[0085] Figure 3 This is a schematic diagram of the deep learning autoencoder (AE) structure for random field dimensionality reduction according to Embodiment 1 of the present invention, and a schematic diagram of the process for selecting AE training samples.
[0086] Figure 4 This is a schematic diagram of the two-level hierarchical adaptive proxy modeling method in Embodiment 1 of the present invention;
[0087] Figure 5 This is a structural block diagram of the system for RBDO assisted by suction anchor proxy model under spatially variable soil conditions, as shown in Embodiment 2 of the present invention.
[0088] Figure 6 This is a structural block diagram of the terminal device according to Embodiment 3 of the present invention. Detailed Implementation
[0089] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be understood that the specific embodiments described are merely used to explain this application and are not intended to limit this application.
[0090] The terminology used in the embodiments is explained as follows: "Suction anchor" refers to a hollow cylindrical foundation component with one open end, which is installed into the seabed by applying suction negative pressure inside; "Non-drained shear strength S" u "" refers to the shear strength of saturated cohesive soil under undrained loading conditions; "undrained deformation modulus of soil E" u "" refers to the modulus of soil used to characterize deformation characteristics under undrained conditions; "Random Field (RF)" refers to a random process indexed by spatial coordinates, which in this paper mainly corresponds to the spatial depth coordinate z; "Proxy Model" refers to a low-cost mathematical model that approximates a high-fidelity model with high computational cost; "Reliability Index β" is used to characterize the safety margin of the design scheme relative to the limit state surface, and the larger the β, the smaller the probability of failure; "Pad-Eye" refers to the attachment point on the suction anchor used to connect the mooring cable.
[0091] Example 1:
[0092] like Figure 1 , Figure 2 As shown, this embodiment provides a method for RBDO assisted by a suction anchor proxy model under spatially variable soil conditions, including the following steps:
[0093] S101. Based on the geometric parameters of the suction anchor, construct the design variable space; based on the design variable space, construct the suction anchor design optimization problem based on reliability; the suction anchor design optimization problem includes deterministic constraints and reliability constraints.
[0094] Furthermore, step S101 specifically includes:
[0095] (1) Construct the design variable space based on the geometric parameters of the suction anchor.
[0096] In this embodiment, the suction anchor design variables are composed of the suction anchor length, suction anchor diameter, and the ratio of the mooring lug depth position to the suction anchor length. , denoted as:
[0097] ;
[0098] In the formula, Indicates the length of the suction anchor. Indicates the diameter of the suction anchor. Indicates the depth of the mooring lugs. The relative positions of the mooring lugs are dimensionless.
[0099] in, Design variable boundary constraints (C-1) must be satisfied:
[0100] C-1: ;
[0101] In the formula, and These represent the lower and upper bound vectors of the suction anchor design variables, respectively.
[0102] Design variable boundary constraints are limited by elements. , as well as All are located within the preset design range, thus ensuring that the candidate designs meet the requirements for engineering layout, manufacturing and installation.
[0103] The design variable space is determined by the suction anchor design variables and design variable boundary constraints mentioned above.
[0104] (2) Based on the design variable space and the target reliability level, construct a reliability-based suction anchor design optimization problem.
[0105] Establish a target cost function based on the weight of the steel used in the suction anchor. And the optimization objective is to minimize material costs, that is:
[0106] ;
[0107] The objective function represents the goal of maximizing the steel cost function while satisfying all constraints. Obtain the minimum value. It can be calculated from the geometry of the suction anchor, the volume or weight of the steel, and the unit material cost, and is used to measure the economics of candidate designs.
[0108] The suction anchor RBDO problem can be summarized as: finding the design scheme with the lowest steel cost within the design variable space, while requiring that the scheme simultaneously satisfies engineering determinism constraints and target reliability constraints. This step can be referenced... Figure 2 The M1 part.
[0109] Among them, the deterministic constraint (C-2) is:
[0110] , ;
[0111] In the formula, This indicates a preset upper limit for steel costs; and These represent the lower and upper limits of the allowable length-to-diameter ratio L / D, respectively.
[0112] Deterministic constraints are used to simultaneously control material consumption and structural geometry to avoid cost overruns or designs with aspect ratios that are unfavorable to construction, installation, and overall stability.
[0113] The reliability constraint (C-3) is:
[0114] C-3: ;
[0115] In the formula, In order to be in Reliability indices after considering soil random fields; and These represent the lower and upper limits of the reliability index, respectively.
[0116] The lower limit of the reliability constraint is used to ensure design safety, while the upper limit is used to avoid unnecessarily overly conservative designs through excessive material consumption; in embodiments where only the lower limit of reliability needs to be set, the upper limit can be taken as a sufficiently large value.
[0117] S102. Generate an initial screening design set based on the design variable space and deterministic constraints; construct a random field sample set to characterize the spatial variability of soil parameters based on field survey data.
[0118] Furthermore, step S102 specifically includes:
[0119] (1) Generate an initial screening design set based on the design variable space and deterministic constraints.
[0120] Within the design space defined by the boundary constraints of the design variables, multiple suction anchor candidate designs (hereinafter referred to as candidate designs) are generated according to a preset sampling interval or experimental design method, forming the initial screening design set. This set covers multiple possible design schemes within the design variable space.
[0121] The first stage of screening is performed on the candidate designs in the initial screening design set, and the candidate designs that meet the deterministic constraints are used as the initial screening design set. The samples in.
[0122] (2) Based on the field survey data, construct a random field sample set to characterize the spatial variability of soil parameters.
[0123] A one-dimensional random field of soil parameters varying along the depth direction is constructed based on field survey data. Field survey data may include static cone penetration test data, or other survey data that can characterize the properties of the soil profile.
[0124] In this embodiment, the soil parameter Y representing a random location includes the undrained shear strength s. u and soil undrained deformation modulus E u In other embodiments, additional soil parameters related to the suction anchor bearing capacity or deformation response may also be included.
[0125] For the soil parameter Y, a one-dimensional random field is constructed along the depth direction and discretized using the Karhunen-Loève (KLE) expansion, which is expressed as:
[0126] ;
[0127] In the formula, Y represents the soil parameter being modeled (s) u With E u z represents the depth coordinate, and θ represents the random event or random field sample number. and Let Y represent the mean function value and standard deviation function value of the soil parameter Y at depth z, respectively; and Let represent the k-th eigenvalue and the eigenfunction value corresponding to the autocorrelation function of soil parameter Y, respectively; N represents mutually independent standard normal random variables; RF This represents the number of KLE cutoff terms in the random field corresponding to the soil parameter Y.
[0128] The covariance function of the soil parameter Y is determined by both the standard deviation function and the autocorrelation function, that is:
[0129] ;
[0130] In the formula, This indicates the soil parameter Y at depth. and Covariance between them; and These represent the soil parameter Y at depths of [depth value missing]. and The standard deviation function value at; Indicates the soil parameter Y at depth and The autocorrelation function between them.
[0131] This formula shows that the correlation between soil parameters at different depths is determined by both the standard deviation function and the autocorrelation function.
[0132] From a physical perspective, by using KLE expansion, the random fluctuations of soil parameters along the depth direction are decomposed into several independent random components. The more expansion terms retained, the higher the accuracy of random field reconstruction, but the higher the input dimension for subsequent reliability analysis and surrogate model training.
[0133] The number of expansion terms N retained after determining KLE truncation. RF In this process, the eigenvalues of the random field corresponding to the soil parameter Y are arranged in descending order and truncated according to the cumulative variance contribution rate. Specifically, the expanded terms corresponding to the first few eigenvalues are retained, such that the cumulative contribution rate of the retained eigenvalues reaches or exceeds a preset cumulative variance contribution rate threshold. The preset cumulative variance contribution rate threshold can be determined according to the accuracy requirements of the random field reconstruction.
[0134] In one embodiment, the preset cumulative variance contribution rate threshold is 95%.
[0135] Based on the above KLE discretization results and truncation criteria, s are generated respectively. u Random field samples and E u Random field samples, and the same random event The s below u Random field samples and E u Random field sample combinations constitute random field samples V used to characterize the spatial variability of soil parameters. RF .
[0136] Discrete V RF Including s along the depth direction u Random field components and E u The random field components can then be mapped to the stress integration points of the stochastic finite element model to reflect the spatial variability of soil parameters with depth. This step can be referenced... Figure 2The M2 part.
[0137] S103. Dimensionally reduce the samples in the random field sample set to obtain low-dimensional latent vectors.
[0138] A one-dimensional convolutional neural network-long short-term memory autoencoder (1D-CNN-LSTM autoencoder) is trained using a random field sample set. The encoder in the trained 1D-CNN-LSTM autoencoder is then used to reduce the dimensionality of the samples in the random field sample set, resulting in a low-dimensional latent vector.
[0139] Specifically, the large number of random field samples obtained in step S102 The 1D-CNN-LSTM autoencoder is trained using the training samples. This autoencoder consists of an encoder and a decoder; the encoder includes one-dimensional convolutional layers, activation layers, max-pooling layers, long short-term memory network layers, and fully connected layers; the decoder is used to reconstruct random field samples from the latent vectors. .
[0140] One-dimensional convolutional layers are used to extract local features of the random field along the depth profile, long short-term memory (LSTM) network layers are used to capture the sequence correlations of the random field along the depth direction, and fully connected layers are used to form low-dimensional latent representations. After training, the encoder part of the 1D-CNN-LSTM autoencoder is saved, and the encoder is used to process high-dimensional random field samples. Mapped to low-dimensional latent vectors ,Right now:
[0141] ;
[0142] In the formula, Encoder(·) represents the encoder after training, V L Indicates samples from a random field The low-dimensional latent vector obtained by compression.
[0143] V L It retains the main spatial variation features that affect the bearing capacity response, but its dimension is significantly lower than that of the original random field sample, so it is suitable as input for the surrogate model.
[0144] In one embodiment, the number of training samples for the autoencoder can be determined by comparing the training loss and latent representation distribution corresponding to 1000, 2500, 5000, and 10000 training samples. In this embodiment, 5000 random field samples are selected as the initial training samples to ensure that the latent representation retains as much of the statistical properties of the original random field input as possible while maintaining a small reconstruction error.
[0145] This step can be referred to. Figure 3 .
[0146] To address the problem of high-dimensional random field input caused by the spatial variability of soil parameters, this embodiment utilizes a deep learning autoencoder to compress random field samples into low-dimensional latent vectors. While preserving the main spatial variability features, this reduces the input dimension of the surrogate model, alleviating the training burden of the surrogate model caused by the high input dimension after KLE discretization.
[0147] S104. Combine the candidate designs for the suction anchor in the initial screening design set with the samples in the random field sample set to obtain the limit state function value corresponding to the combination; combine the candidate designs for the suction anchor in the combination with the low-dimensional latent vector of the corresponding sample to obtain the initial extended combination; the initial extended combination constitutes the initial extended combination set.
[0148] For any candidate design in the initial screening design set On the one hand, it is compared with any random field sample Combine to obtain a combination and combine Input a stochastic finite element model (RFEM) to obtain a high-fidelity ultimate bearing capacity response. On the other hand, the same random field sample The low-dimensional latent vector obtained by the encoder With candidate designs Combine to obtain the initial extended combination. .
[0149] The stochastic finite element model (RFEM) is used to calculate the ultimate bearing capacity response of suction anchors under spatially variable soil conditions. Based on the relationship between the ultimate bearing capacity response and the given mooring load requirements, the limit state function is constructed:
[0150] ;
[0151] In the formula, express and The corresponding safety margin, The stochastic finite element model is based on and The calculated ultimate bearing capacity response, This indicates a given mooring load requirement.
[0152] when When the value is greater than 0, it indicates that the ultimate bearing capacity response is greater than the given mooring load requirement, and the sample is determined to be a safe sample; when... When the value is ≤0, it is determined to be in a failed state, that is, the sample is a failed sample.
[0153] This yields high-fidelity response data for training the global agent model. as well as Corresponding limit state function value .
[0154] This step can be referred to. Figure 2 Part 301 of M3 and Figure 4 The S1 part.
[0155] S105. Use the limit state function values of the initial extended combination and the corresponding combination as global training samples to train the global surrogate model; use the trained global surrogate model to predict the initial extended combination set; obtain the global feasible design set based on the predicted limit state function values and reliability constraints.
[0156] Furthermore, step S105 specifically includes:
[0157] (1) Use the initial extended combination and the limit state function values of the corresponding combination as global training samples to train the global agent model.
[0158] In this embodiment, the global proxy model is the polynomial-chaos kriging (PCK) model.
[0159] The initial extended combination As input data for the global proxy model; to combine The corresponding limit state function value is used as the output data of the global proxy model.
[0160] By training a global proxy model ,make It can approximate the limit state response of a stochastic finite element model in an extended potential space.
[0161] (2) Use the trained global proxy model to predict the limit state function value of the initial extended combination in the initial extended combination set; calculate the reliability index of the suction anchor candidate design based on the limit state function value; add the suction anchor candidate design that satisfies the reliability constraint to the global feasible design set.
[0162] Input the initial extended combinations from the initial extended combination set into the trained global proxy model, and output the corresponding limit state function values; based on the output results, for each candidate design The number of failure samples corresponding to each candidate design is counted, and the proportion of this number of failure samples to the total number of initial extended combinations corresponding to the candidate design is calculated to obtain the failure probability of the candidate design. Based on failure probability Candidate designs were obtained Reliability indicators :
[0163] ;
[0164] In the formula, (·) denotes the inverse function of the standard normal distribution function.
[0165] As can be seen from this formula, the smaller the failure probability, the higher the reliability index. The larger the reliability index, the better. Therefore, reliability indices can serve as a unified measure for evaluating the safety level of candidate designs.
[0166] Based on reliability constraints, a second-stage reliability screening is conducted on candidate designs, using reliability indicators... Not within the target reliability index range ( , Candidate designs within the range are eliminated to obtain the globally feasible design set. .
[0167] S106. Based on the candidate designs in the global feasible design set, select the corresponding initial extended combination from the initial extended combination set; use the limit state function values of the selected initial extended combination and its corresponding initial combination as local training samples to train the local proxy model, and obtain the final top-ranked design set.
[0168] From the initial extended combination set obtained in step S104, select the initial extended combination corresponding to the globally feasible design set obtained in step S105 and its corresponding limit state function value to form the initial local training set. .
[0169] Specifically, if a candidate design in the initial extended combinatorial set is included in the global feasible design set, then the initial extended combinatorial set corresponding to that candidate design and the corresponding limit state function value are used as the initial local training set. The sample.
[0170] In this embodiment, the local proxy model is the polynomial-chaos kriging (PCK) model.
[0171] (1) When the initial iteration round hour:
[0172] Let the local proxy model be denoted as Using the initial local training set All samples are used to train the initial local proxy model .
[0173] (2) When the iteration round hour:
[0174] Will The locally trained proxy model in each round is used as the first... Round-based local proxy model .
[0175] (2-1) Using the local proxy model For each suction anchor candidate design in the initial screening design set, the initial extended combination corresponding to it is predicted; based on the predicted limit state function value and reliability constraints, the first... The design set is prioritized by the order of rounds.
[0176] Each candidate design in the initial screening design set The corresponding initial extended combined input local proxy model Based on the predicted limit state function values, a reliability analysis is performed to obtain the candidate design. The corresponding reliability index; the candidate designs that meet the reliability constraints constitute the first... Wheel Local Feasibility Design Set .
[0177] Subsequently, according to the Wheel Local Feasibility Design Set Target cost function value of candidate design Sort the candidate designs in ascending order, and select the preset number of candidate designs from the previous sorting as the first. The current sorting of the design set .
[0178] Specifically, the preset quantity is a positive integer and can be determined according to engineering design needs. In one embodiment, the preset quantity is 3.
[0179] When the Wheel Local Feasibility Design Set When the number of candidate designs is less than the preset number, the local feasible design set will be... All candidate designs in the set are used as the top-ranked designs in the current order. At the same time, the design sets that are currently ranked first will be... The candidate design that minimizes the objective cost function value is selected as the first... Current optimal design .
[0180] (2-2) Using the local proxy model For each suction anchor candidate design in the initial screening design set, the initial extended combination corresponding to it is predicted; based on the predicted limit state function value and reliability constraint boundary, the first... Design set near the feasibility boundary of each round.
[0181] Get the first The design set near the feasibility boundary of each round falls into two cases. The first case is:
[0182] For each candidate design in the initial screening design set, its reliability index is calculated. Minimum distance between the reliability constraint boundary and the boundary :
[0183] .
[0184] when Not greater than the preset reliability neighborhood threshold At that time, it was determined that the candidate design was near the feasibility boundary, and Included in the Design set near the feasibility boundary of the wheel .
[0185] Specifically, This is a preset positive number used to characterize the allowed boundary neighborhood range of the reliability metric. In one embodiment, The value is 0.1.
[0186] The second scenario is:
[0187] For the objective cost function value is less than the current optimal design Candidate designs whose reliability index is lower than the allowable lower limit of reliability index. However, if the following conditions are met, the candidate design will also be included in the first round. Design set near the feasibility boundary of the wheel :
[0188] .
[0189] Although this type of candidate design does not yet meet the reliability constraints under the current local proxy model evaluation, its cost is lower than the current optimal design and close to the reliability constraint boundary. There is a possibility that it may be misjudged as an infeasible design due to the error of the proxy model. Therefore, it is necessary to prioritize local encrypted evaluation.
[0190] (2-3) The first The design sets ranked at the top of the round and the design sets near the feasibility boundary are merged; the suction anchor candidate designs in the merged design set are combined with the low-dimensional latent vectors of each random field sample in the random field sample set to form extended latent sample points; based on the values of the extended latent sample points calculated by the active learning function, the extended latent sample points are selected as new high-fidelity evaluation samples.
[0191] Specifically, the first Wheel sorting design set Design set near the feasibility boundary Merge to obtain the set of candidate designs to be encrypted. .
[0192] Will Each candidate design in the dataset corresponds to a low-dimensional latent vector for each random field sample. Combination, as an extension of potential sample points .
[0193] Based on the current local proxy model Expanding potential sample points mean of the predicted distribution at location and the predicted standard deviation Calculate the value of the active learning function:
[0194] ;
[0195] In the formula, To avoid the default small positive number with a denominator of zero.
[0196] Used to measure expanded potential sample points The amount of information updated in the local agent model. The smaller the value, the closer the extended potential sample point is to the limiting state surface. The greater the uncertainty in the prediction of the local proxy model at that point, the more necessary it is to conduct a high-fidelity evaluation.
[0197] All sample points according to Sort the values in ascending order; select Not greater than the preset active learning threshold And the sample size is no greater than The expanded potential sample points are used as new high-fidelity evaluation samples. Among them, and All parameters are preset active learning parameters.
[0198] (2-4) Add the newly added high-fidelity evaluation samples and their corresponding limit state function values as new samples to the local training set. In this process, the updated local training set is obtained. ; Utilizing the updated local training set Training local proxy model , to obtain the trained first A round-based local proxy model.
[0199] (2-5) If one of the following termination conditions is met, then stop the iteration; otherwise: Let Then return to step (2-1) to continue with the subsequent operations;
[0200] The termination condition is:
[0201] (I) No. The current sorting of the design set Compared to the previous round, the current top-ranked design set Continuous in candidate design composition and ranking order Keep it consistent;
[0202] (II) Reaching the preset maximum number of iterations ;
[0203] (III) There is no condition that satisfies this condition. The newly added candidate samples.
[0204] In one embodiment, Take 3.
[0205] When the iteration stops, the local proxy model of the current round is taken as the final local proxy model, and the top-ranked design set of the current round is taken as the final top-ranked design set.
[0206] Based on the final ranked design set, multiple suction anchor design schemes are output. Each suction anchor design scheme includes the corresponding suction anchor geometric parameters and its ultimate bearing capacity response.
[0207] In one embodiment, the output may further include the bearing capacity probability distribution, bearing capacity statistical parameters, confidence intervals, and system parameters related to the soil random field for each suction anchor design scheme. The results can provide engineers with multiple alternative schemes that meet the target reliability level and have lower material costs. This step corresponds to... Figure 2 M4 in the middle.
[0208] In one validation embodiment, the method was validated using two benchmark examples. The first validation example employed a 40-dimensional mathematical performance function; compared to a double-loop RBDO using the original model, the method identified three optimal designs with errors of less than 0.4% relative to the reference results, requiring only 396 calls to the original model, while the direct double-loop method typically requires thousands of calls. The second validation example employed a simplified pile foundation bearing capacity model with 146-dimensional extended input; the method identified three optimal designs with errors of less than 8% relative to the reference results, requiring only 700 evaluations of the original model.
[0209] In the RBDO suction anchor application example, the RFEM method is used to perform high-fidelity simulation of the suction anchor in spatially variable undrained clay; wherein, the undrained shear strength s u and soil undrained deformation modulus E uAll models were constructed as one-dimensional random fields represented by field survey data. The optimization results identified several suction anchor designs with low material consumption while meeting the target reliability level, such as suction anchors with lengths of approximately 11.5m to 12m, anchor diameters of approximately 3m, and mooring lug relative positions of approximately 0.55 to 0.65. This application example requires approximately 1000 finite element evaluations, a computational reduction of several orders of magnitude compared to direct double-layer cyclic RBDOs that typically require millions of evaluations.
[0210] Example 2:
[0211] like Figure 5 As shown, this embodiment provides a system for RBDO assisted by a suction anchor surrogate model under spatially variable soil conditions. The system includes a construction module 501, a generation module 502, a combination module 503, a first training module 504, and a second training module 505, wherein:
[0212] Module 501 is used to construct the design variable space based on the geometric parameters of the suction anchor; and to construct a reliability-based suction anchor design optimization problem based on the design variable space; the suction anchor design optimization problem includes deterministic constraints and reliability constraints.
[0213] The generation module 502 is used to generate an initial screening design set based on the design variable space and deterministic constraints; and to construct a random field sample set to characterize the spatial variability of soil parameters based on field survey data.
[0214] Combination module 503 is used to combine the suction anchor candidate designs in the initial screening design set with the random field samples in the random field sample set to obtain an initial combination; combine the suction anchor candidate designs in the initial combination with the low-dimensional latent vectors of the corresponding random field samples to obtain an initial extended combination; and form an initial extended combination set from the initial extended combination.
[0215] The first training module 504 is used to train the global proxy model by taking the initial extended combination as input and the limit state function value of the corresponding initial combination as output; using the trained global proxy model to predict the initial extended combination set; and obtaining the global feasible design set based on the predicted limit state function value and reliability constraints.
[0216] The second training module 505 is used to select the corresponding initial extended combination from the initial extended combination set based on the suction anchor candidate designs in the global feasible design set; and to train the local proxy model by using the limit state function values of the selected initial extended combination and its corresponding initial combination as local training samples to obtain the final top-ranked design set.
[0217] The specific implementation of each module in this embodiment can be found in Embodiment 1 above, and will not be repeated here. It should be noted that the system provided in this embodiment is only illustrated by the division of the above functional modules. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure can be divided into different functional modules to complete all or part of the functions described above.
[0218] Example 3:
[0219] This embodiment provides a terminal device, which can be a computer, such as... Figure 6 As shown, it is connected via a system bus 601 to a processor 602, a memory, an input device 603, a display 604, and a network interface 605. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium 606 and an internal memory 607. The non-volatile storage medium 606 stores an operating system, computer programs, and a database. The internal memory 607 provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. When the processor 602 executes the computer programs stored in the memory, it implements the method of suction anchor proxy model-assisted RBDO under spatially variable soil conditions described in Embodiment 1 above.
[0220] Example 4:
[0221] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method of suction anchor proxy model-assisted RBDO under spatially variable soil conditions described in Embodiment 1 above.
[0222] It should be noted that the computer-readable storage medium in this embodiment can be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof.
[0223] Example 5:
[0224] This embodiment provides a computer program product, including a computer program that, when executed by a processor, implements the method of suction anchor proxy model assisted RBDO under spatially variable soil conditions described in Embodiment 1 above.
[0225] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope disclosed in the present invention, based on the technical solution and inventive concept of the present invention, shall fall within the scope of protection of the present invention.
Claims
1. A method for using a suction anchor proxy model to assist RBDO under spatially variable soil conditions, characterized in that, The method includes: Based on the geometric parameters of the suction anchor, a design variable space is constructed; based on the design variable space, a reliability-based suction anchor design optimization problem is constructed; the suction anchor design optimization problem includes deterministic constraints and reliability constraints. Based on the design variable space and deterministic constraints, an initial screening design set is generated; based on the field survey data, a random field sample set is constructed to characterize the spatial variability of soil parameters. The candidate designs for attracting anchors in the initial screening design set are combined with random field samples in the random field sample set to obtain the initial combination; the candidate designs for attracting anchors in the initial combination are combined with the low-dimensional latent vectors of the corresponding random field samples to obtain the initial extended combination; the initial extended combination sets are formed by the initial extended combination sets. The global surrogate model is trained by taking the initial extended combination as input and the limit state function value of the corresponding initial combination as output; the trained global surrogate model is used to predict the initial extended combination set; and the global feasible design set is obtained based on the predicted limit state function value and reliability constraints. Based on the candidate designs for suction anchors in the global feasible design set, the corresponding initial extended combination is selected from the initial extended combination set; the limit state function values of the selected initial extended combination and its corresponding initial combination are used as local training samples to train the local proxy model, and the final top-ranked design set is obtained.
2. The method according to claim 1, characterized in that, The local proxy model is a multinomial chaotic kriging model. The selected initial extended combination and its corresponding limit state function value are used as the local training set. ; The step of using the selected initial extended combination and its corresponding initial combination's limit state function value as local training samples to train the local proxy model, and obtaining the final top-ranked design set, includes: When the iteration round hour: Let the local proxy model be denoted as Using local training sets For local proxy model Training is performed; where the input data is the selected initial extended combination, and the output data is the limit state function value corresponding to the input data in the initial combination; When the iteration round hour: Will The locally trained proxy model in each round is used as the first... Round-based local proxy model ; Using the local proxy model Predict the initial extended combination corresponding to each suction anchor candidate design in the initial screening design set; calculate the reliability index of each suction anchor candidate design based on the predicted limit state function value. Based on the reliability indices and reliability constraints of the suction anchor candidate design, the first... The design set prioritizes rounds; Based on the reliability indices and reliability constraint boundaries of the suction anchor candidate design, the first... Design set near the feasibility boundary of each round; The first The design sets ranked at the top of the round and the design sets near the feasibility boundary are merged; the suction anchor candidate designs in the merged design set are combined with the low-dimensional latent vectors of each random field sample in the random field sample set to form extended latent sample points; based on the values of the extended latent sample points calculated by the active learning function, the extended latent sample points are selected as new high-fidelity evaluation samples. The newly added high-fidelity evaluation samples and the corresponding limit state function values of the initial combination are added as new samples to the local training set. In the middle; using local training sets Training local proxy model , to obtain the trained first Round-based local proxy model ; If the termination condition is met, stop the iteration; otherwise: let and return the iteration number. If necessary, continue with the subsequent operations.
3. The method according to claim 2, characterized in that, The suction anchor design optimization problem also includes an objective cost function; the objective cost function is used to represent the material cost of the candidate suction anchor designs. Based on the reliability indicators and reliability constraints of the suction anchor candidate design, the first... The design set with the rounds prioritized includes: If the reliability index of the suction anchor candidate design meets the reliability constraint, then the suction anchor candidate design is added to the local feasible design set. Based on the objective cost function, calculate the objective cost function value of the suction anchor candidate designs; rank the suction anchor candidate designs in the local feasible design set according to the objective cost function values in ascending order, and select the top-ranked, predetermined number of suction anchor candidate designs as the first... The design set is prioritized by the order of rounds.
4. The method according to claim 3, characterized in that, The first The candidate design with the smallest objective cost function value in the highest-ranked design set is selected as the current optimal design. ; Based on the reliability indices and reliability constraint boundaries of the suction anchor candidate design, the first... The design set near the feasibility boundary of each round includes: Calculate the minimum distance between the reliability index and the reliability constraint boundary of the suction anchor candidate design; If the minimum distance is less than or equal to the preset reliability neighborhood threshold, then the corresponding suction anchor candidate design is added to the first... Design set near the feasibility boundary of each round; For the initial selection of design sets, if the objective cost function value of the suction anchor candidate design is less than that of the current optimal design... If a candidate design for a suction anchor is selected, and the reliability index of the candidate design is lower than the allowable lower limit of the reliability constraint boundary and the difference between the two does not exceed the preset reliability neighborhood threshold, then the candidate design for the suction anchor is added to the first... Design set near the feasibility boundary of each round.
5. The method according to claim 2, characterized in that, The termination condition is: No. The order of rounds is prioritized in the design set and the first round. The design set ranked at the top of the rounds remained consistent in the composition and ranking of the suction anchor candidate designs multiple times. Or, until the preset maximum number of iterations is reached; Alternatively, all newly added candidate samples may have values calculated using the active learning function that are greater than the preset active learning threshold.
6. The method according to claim 1, characterized in that, The global feasible design set, obtained based on the predicted limit state function value and reliability constraints, includes: Based on the predicted limit state function value, calculate the reliability index of each suction anchor candidate design; Candidate suction anchor designs that do not meet the reliability constraints in the initial screening design set are deleted, and the remaining candidate suction anchor designs in the initial screening design set are used as the global feasible design set.
7. The method according to any one of claims 2 and 6, characterized in that, The calculation of reliability indices for each suction anchor candidate design based on the predicted limit state function value includes: Based on the limit state function value, design for each suction anchor candidate Calculate the failure probability ; Calculate candidate designs for suction anchors based on failure probability. Reliability indicators : ； In the formula, (·) is the inverse function of the standard normal distribution function.
8. The method according to any one of claims 1 to 6, characterized in that, The process of constructing a random field sample set to characterize the spatial variability of soil parameters based on field survey data includes: According to the field survey data, the soil parameters are obtained; wherein the field survey data include static cone penetration test data, and the soil parameters include undrained shear strength s u and soil undrained deformation modulus E u ; For the soil parameter Y, a one-dimensional random field is constructed along the depth direction and discretized using the Karhunen-Loève theorem expansion; Based on the discrete results and the truncation criterion, s are generated respectively. u Random field samples and E u Random field samples; s under the same random event u Random field samples and E u Random field samples are combined to form random field samples used to characterize the spatial variability of soil parameters; random field samples constitute a random field sample set.
9. The method according to any one of claims 1 to 6, characterized in that, The construction of the design variable space based on the geometric parameters of the suction anchor includes: Due to the length of the suction anchor Suction anchor diameter and the depth position of the mooring lugs The ratio of the length of the suction anchor to the length of the suction anchor together constitutes the design variables of the suction anchor. , denoted as: ； in, Design variable boundary constraints must be met: C-1： ； In the formula, and These are the set lower and upper limits of permission, respectively. The design variable space is determined by the suction anchor design variables and the design variable boundary constraints.
10. A system for RBDO assisted by a suction anchor surrogate model under spatially variable soil conditions, characterized in that, The system includes: The module is used to construct the design variable space based on the geometric parameters of the suction anchor; and to construct the reliability-based suction anchor design optimization problem based on the design variable space. The suction anchor design optimization problem includes deterministic constraints and reliability constraints. The generation module is used to generate an initial screening design set based on the design variable space and deterministic constraints; and to construct a random field sample set to characterize the spatial variability of soil parameters based on field survey data. The combination module is used to combine the suction anchor candidate designs in the initial screening design set with the random field samples in the random field sample set to obtain the initial combination; combine the suction anchor candidate designs in the initial combination with the low-dimensional latent vectors of the corresponding random field samples to obtain the initial extended combination; and form the initial extended combination set from the initial extended combination. The first training module is used to train the global proxy model by taking the initial extended combination as input and the limit state function value of the corresponding initial combination as output; using the trained global proxy model to predict the initial extended combination set; and obtaining the global feasible design set based on the predicted limit state function value and reliability constraints. The second training module is used to select the corresponding initial extended combination from the initial extended combination set based on the suction anchor candidate designs in the global feasible design set; and to train the local proxy model using the limit state function values of the selected initial extended combination and its corresponding initial combination as local training samples to obtain the final top-ranked design set.