Mooring system adaptive sampling acceleration simulation method based on proxy model array

Abstract

The application provides a mooring system adaptive sampling acceleration simulation method based on an agent model array, a multi-dimensional mooring environment parameter discrete grid space is constructed, initial sampling is performed, and a basic sample set is constructed; agent models corresponding to a plurality of physical response indexes are independently established and trained; a trained model array is used to predict candidate grid points, a confidence upper limit is constructed based on a predicted mean value and a predicted standard deviation to intercept a high-risk working condition, and a high-risk candidate set is formed; a comprehensive collection function is constructed based on the predicted mean value, the predicted standard deviation and local nonlinear perturbation to score points one by one, and after spatial clustering is performed on the high-risk candidate set, extreme points in each cluster are extracted as adaptive sampling points to perform high-fidelity simulation verification; the verification result is integrated into the basic sample set, and the model is iteratively trained until convergence, and then the modeling data set is output. The application improves the identification efficiency and sampling acceleration ratio of a multi-dimensional asynchronous nonlinear boundary.

Description

Technical Field

[0001] This invention belongs to the field of operational safety assessment and numerical simulation technology for ships and other waterborne vehicles, and particularly relates to an adaptive sampling accelerated simulation method for the dynamic response of mooring systems based on a parallel agent model array. Background Technology

[0002] In the field of ship and waterborne vehicle engineering, assessing the safety of mooring systems under complex sea conditions typically requires dynamic response analysis using high-fidelity time-domain simulation software. However, the safety boundary of a mooring system is influenced by the interplay of multiple environmental parameters such as waves, wind, and currents, resulting in a high-dimensional parameter space.

[0003] Traditional mooring system safety assessments primarily rely on high-fidelity time-domain simulation software to perform traversal calculations on a grid of sea state parameters composed of multi-dimensional environmental parameters (such as wind, waves, and currents). However, the parameter space formed by the interweaving of multi-dimensional environmental parameters is extremely large (typically reaching hundreds of millions or even billions of parameters), and directly using high-fidelity software for full-domain traversal would incur extremely high computational costs, making it impractical in real-world engineering applications.

[0004] To alleviate computational bottlenecks, existing technologies typically incorporate machine learning surrogate models and adaptive sampling algorithms, training the model with a small number of samples to predict system responses. For example, existing technologies employ a single surrogate model combined with an expected improvement sampling function for iterative sampling. This involves establishing an initial mooring model using OrcaFlex, creating an initial sample set using adaptive Latin hypercube sampling, constructing the surrogate model, calculating the expected improvement to determine sampling points, and iteratively updating the model. However, when facing high-dimensional and complex mooring scenarios, existing acceleration technologies still face significant application challenges. (1) Inaccurate extreme value capture. The response of the mooring system has strong nonlinear characteristics (such as the violent jump caused by the physical break of the cable). Traditional single surrogate models are difficult to capture such characteristics, resulting in a significant decrease in prediction accuracy at dangerous boundaries.

[0005] (2) The “asynchronous deterioration” phenomenon cannot be solved. The six degrees of freedom motion of the mooring system and the stress on the multiple cables deteriorate at different paces under different sea conditions. Conventional single-objective optimization or simple multi-objective weighted algorithms are prone to risk dilution and miss potential dangers in a single dimension.

[0006] (3) Imbalance between exploration and development. When dealing with ultra-large-scale discrete spaces, existing adaptive sampling algorithms are prone to getting stuck in local optima or excessively clustering sampling in local nonlinear regions (computing power collapse), resulting in a serious waste of expensive simulation computing power.

[0007] (4) Lack of effective convergence criteria. Existing technologies mostly rely on fixed number of iterations or target values ​​as stopping conditions, lack quantitative monitoring of the topological stability of the limit state surface, and make it difficult to guarantee the engineering reliability of the sampling results.

[0008] In view of this, the present invention provides an adaptive sampling method that can balance global exploration efficiency and boundary locking accuracy to solve the above problems. Summary of the Invention

[0009] The purpose of this invention is to provide an adaptive sampling accelerated simulation method for mooring systems based on a surrogate model array. By constructing a decoupled surrogate model array and combining confidence upper bound interception, cross-dimensional extreme value extraction, and spatial clustering screening in discrete space, this method significantly reduces the cost of high-fidelity simulation while ensuring accurate capture of the multidimensional asynchronous nonlinear boundaries of the mooring system. The technical solution adopted is as follows: An adaptive sampling-accelerated simulation method for mooring systems based on surrogate model arrays includes the following steps: Step 1: Construction of the basic sample set: A multidimensional discrete grid space composed of environmental parameters is constructed. Initial working condition sampling is performed, and the sampling points are input into high-fidelity simulation software to obtain the true values ​​of the simulation response of each sampling point. After preprocessing the true values ​​of the simulation response, a basic sample set is constructed using environmental parameters as input features and the preprocessed true values ​​of the simulation response as supervision labels. The supervision labels include several sub-supervision labels. Step 2: Train the agent model array: A model architecture is established to independently establish proxy models that correspond one-to-one with multiple physical response indicators. Each proxy model corresponds to a physical response indicator. Each proxy model takes environmental parameters as input and the predicted value of its corresponding physical response indicator as output, forming a decoupled proxy model array. The environmental parameters in the basic sample set are used as input features and fed into each surrogate model for forward computation to obtain the predicted values ​​of each surrogate model for the physical response index. A sub-supervisory label that matches the physical response index is used as the prediction target. The internal parameters of each surrogate model are iteratively updated by minimizing the error between the predicted value and the prediction target, so that the predicted values ​​of each physical response index gradually approach the corresponding sub-supervisory label. After training, a trained surrogate model array is obtained. Step 3: Construct a high-risk candidate set: The trained surrogate model array is used to perform forward prediction on candidate grid points in a large-scale space to obtain the predicted value of each candidate grid point on each physical response index. The predicted values ​​are statistically analyzed to obtain the predicted mean and predicted standard deviation of each candidate grid point for each physical response index. For each candidate grid point, a confidence upper limit is constructed based on the predicted mean and predicted standard deviation of each physical response index. Candidate grid points whose confidence upper limit for any physical response index exceeds the preset engineering threshold are identified as suspected high-risk samples and intercepted. The intercepted candidate grid points together constitute a high-risk candidate set. Step 4: Comprehensive risk assessment and spatial clustering screening: From the predicted mean and predicted standard deviation obtained in step 3, extract the predicted mean and predicted standard deviation of each candidate grid point in the high-risk candidate set for each physical response index, and calculate the local nonlinear perturbation of each candidate grid point for each physical response index. For each candidate grid point in the high-risk candidate set, based on the predicted mean, predicted standard deviation and local nonlinear perturbation of each physical response index, the single-dimensional score of each physical response index is obtained after normalization and weighted synthesis. Then, the maximum value of all single-dimensional scores is taken as the comprehensive risk score of the grid point. Then, spatial clustering is performed on the high-risk candidate set, and the grid point with the highest comprehensive risk score in each cluster is extracted as an adaptive sampling point and input into high-fidelity simulation software to obtain the simulation response truth value. Step 5: Sample set update and iterative convergence determination: The true values ​​of the simulation response obtained from the adaptive sampling point simulation in step 4 are preprocessed and incorporated into the basic sample set described in step 1 to form an updated basic sample set. The surrogate model array is then trained again using the updated basic sample set, and the convergence index is dynamically monitored. If convergence is achieved, the modeling dataset is output; otherwise, the process returns to step 2 to continue iterating.

[0010] Preferably, the environmental parameters in step 1 are 7-dimensional vectors, including wave height, wave direction, spectral peak period, wind speed, wind direction, flow velocity, and flow direction.

[0011] Preferably, the initial working condition sampling in step 1 uses Latin hypercube sampling to generate initial samples in a continuous space across the entire domain, and performs grid snapping processing by calculating the Euclidean distance between the sample coordinates and the discrete grid coordinates, so that the initial sample coordinates are aligned to the nearest valid discrete grid coordinates.

[0012] Preferably, step 2 includes eight physical response indicators: sway, heave, roll, pitch, bow roll, maximum cable force, and maximum anchor force. The surrogate model is a random forest regression model, with each surrogate model taking seven-dimensional environmental parameters as input and the predicted value of the corresponding single physical response indicator as output.

[0013] Preferably, in step 3, the formula for calculating the upper confidence limit is:

[0014] - Corresponding candidate grid points , No. The predicted mean of each physical response index; - Corresponding candidate grid points , No. The predictive standard deviation of each physical response index; - A constant that controls the intensity of exploration.

[0015] Preferably, step 4, which involves obtaining the single-dimensional scores of each physical response index, specifically includes: For high-risk candidate sets For each candidate grid point within the range, the predicted standard deviation calculated in step 3 is used. As an uncertainty component The predicted mean obtained from step 3 As a component of risk And calculate the local nonlinear perturbation components of each grid point on each physical response index. Normalization was performed on each to obtain , , ; A single physical response index is synthesized using preset weights. Single-dimensional score:

[0016] in, , , These are the weighting coefficients.

[0017] Preferably, in step 4, spatial clustering and adaptive sampling point extraction specifically include: High-risk candidate set Perform K-Means clustering and split into One cluster; The clustering objective function is ; in To preset the parallel simulation computing power scale, For the first One cluster; For grid points; Let be the centroid vector of the cluster; In each cluster Internal extraction of comprehensive risk score The highest grid point is used as the adaptive sampling target.

[0018] Compared with the prior art, the advantages of the present invention are: (1) Achieve non-uniform redistribution of computing power and provide a higher equivalent sampling speedup ratio.

[0019] In a high-dimensional parameter space containing hundreds of millions of grid points, traditional traversal simulation is infeasible, while conventional random sampling has a low hit rate. This invention constructs a three-dimensional information gain acquisition function that integrates "cognitive uncertainty," "predicted hazard," and "local perturbation jump intensity." This mechanism enables the algorithm to proactively reduce redundant searches of linear safe zones, focusing the extremely expensive high-fidelity time-domain simulation computing power on nonlinear failure boundaries. While maintaining high boundary identification accuracy, it significantly reduces the number of simulation samples required, significantly improving the equivalent sampling speedup ratio for engineering evaluation. Furthermore, in AQWA time-domain coupled simulation verification, the results of 20 consecutive rounds of adaptive sampling show that Level III high-risk and Level IV critical failure conditions maintain a proportion close to or above 90% in most iteration rounds, indicating that this invention can concentrate high-fidelity simulation resources on dangerous boundaries and the neighborhood of critical failures. In the offline playback verification of the effective sample pool after removing critical failure samples, the present invention adopts an adaptive sampling strategy with a preset weighted comprehensive acquisition function to achieve a high-risk identification F1 value of 0.8764 and a dangerous boundary accuracy of 0.7206 within a budget of 2000 samples, and reaches F1=0.85 with 1585 samples, indicating that the present invention can reduce redundant sampling in low-risk areas and improve the efficiency of dangerous condition identification.

[0020] (2) Eliminate the blind spot of extreme value risk caused by the "asynchronous deterioration" of multidimensional response.

[0021] The multi-degree-of-freedom motion of mooring systems and the forces acting on multiple cables typically exhibit an "asynchronous" characteristic, with inconsistent deterioration rates under complex sea conditions. Traditional multi-objective weighted algorithms are prone to a "risk masking" effect, causing extreme risks in some dimensions to be obscured by the mean. This invention innovatively introduces a decoupled surrogate model array and combines it with cross-dimensional extreme value extraction logic to uniformly map physical responses of different dimensions to a normalized risk scale and force the extraction of the highest global risk score. This mechanism ensures that the algorithm has the highest priority sensitivity to any single-dimensional failure mode, such as cable breakage or motion instability, thus eliminating the underreporting of extremely dangerous conditions from the underlying mathematical logic.

[0022] (3) Overcome the local clustering defects of adaptive sampling and ensure full coverage of the boundary topology.

[0023] Traditional optimization algorithms are prone to getting stuck in local optima when approaching steep nonlinear regions, leading to excessive clustering of sampling points in a narrow space, wasting computational resources and failing to explore the complete boundary. This invention introduces a parameter space K-Means clustering dispersion mechanism. Within the high-risk candidate set, high-risk samples are forcibly divided into multiple clusters, effectively preventing malicious local clustering of sampling points. This ensures that the new round of verification samples can be evenly and widely distributed across all unknown nonlinear boundaries in the entire domain, achieving efficient topological coverage of the system's multidimensional safety boundaries.

[0024] (4) Strictly comply with engineering specifications to ensure the physical legitimacy of discrete domain optimization.

[0025] Unlike purely mathematical continuous-space optimization divorced from engineering practice, this invention is based on a discrete grid set that strictly adheres to the physical step size specifications of ships and waterborne vehicles. By aligning and sampling continuous samples to the physical discrete grid, it ensures that the final selected extreme value samples are physically legitimate and reproducible. The generated extreme value envelope results can be directly used to guide the engineering design and actual operation of mooring systems, possessing significant engineering practical value. Attached Figure Description

[0026] Figure 1 The flowchart shows the adaptive sampling accelerated simulation method for mooring systems based on surrogate model arrays.

[0027] Figure 2 This is a chart showing the percentage of risk levels for 20 consecutive rounds of adaptive sampling. Detailed Implementation

[0028] The following will describe in more detail, with reference to the schematic diagrams, a method for accelerating the adaptive sampling simulation of a mooring system based on a surrogate model array, according to the present invention. Preferred embodiments of the invention are illustrated. It should be understood that those skilled in the art can modify the invention described herein while still achieving its advantageous effects. Therefore, the following description should be understood as being of general knowledge to those skilled in the art and is not intended to limit the invention.

[0029] like Figure 1 As shown in the figure, this embodiment provides an adaptive sampling accelerated simulation method for the dynamic response of a mooring system based on a parallel agent model array. The specific execution flow is as follows.

[0030] Step 1: Construction of the basic sample set.

[0031] Step 1A: Construction of physical parameter spatial grid.

[0032] The pretension of the mooring system's cables and anchor chains was fixed at 5% of the breaking load (MBL) to lock in the initial response characteristics and reduce the dimensionality of the environmental parameter search.

[0033] This embodiment maps the environmental parameters that affect the system's forces and motion to a 7-dimensional parameter space consisting of wave height, wave direction, spectral peak period, wind speed, wind direction, flow velocity, and flow direction.

[0034] In this embodiment, the range of each parameter and the physical step size settings are shown in Table 1.

[0035] Table 1. Range of environmental parameters and physical step size settings

[0036] This constructs a 7-dimensional discrete parameter grid space.

[0037] Taking wave height as an example, within the range of 0.1m to 1.5m, there are 15 discrete values ​​with a step size of 0.1m; within the range of wave direction from 0° to 360°, there are 16 discrete values ​​with a step size of 22.5°; within the range of spectral peak period from 4s to 12s, there are 9 discrete values ​​with a step size of 1s; and so on. The product of the number of discrete values ​​in each dimension is the total number of grid points, and its theoretical combination scale can reach hundreds of millions. This grid space is used for subsequent global search.

[0038] Step 1B: Initial operating condition sampling and grid adsorption.

[0039] Initial samples (1000 in this example) are generated in a continuous space using Latin hypercube sampling. Latin hypercube sampling is a stratified sampling technique that ensures that samples are uniformly distributed across all dimensions of the parameter space, avoiding sample clustering.

[0040] Mesh snapping is performed by calculating the Euclidean distance between the sample coordinates and the grid points in the simulation parameter space grid set (existing technology), which strictly aligns the coordinates of all initial samples to the nearest valid discrete grid coordinates.

[0041] After mesh adsorption, the coordinates of all initial samples are aligned to the valid discrete mesh coordinates, and then input into AQWA high-fidelity time-domain simulation software for numerical calculation to obtain the original true data of multidimensional physical response.

[0042] Step 1C: Simulation Response Truth Preprocessing: Temporal feature extraction and nonlinear cable breakage penalty preprocessing are performed on the acquired raw ground truth data: (1) Extraction of kinematic amplitude features.

[0043] Extract motion characteristics of six degrees of freedom: sway, heave, roll, pitch, and yaw. This is used to characterize the extreme degree of motion of the mooring platform.

[0044] Among them, the sway motion quantity This represents the maximum amplitude in one direction. Right now .

[0045] The formulas for extracting the remaining 5 degrees of freedom are as follows: .

[0046] in, , , These represent the maximum, average, and minimum values ​​of the motion time series for the corresponding degrees of freedom.

[0047] For example, in a certain simulation, the maximum value of the oscillation motion time series is 1.2m, the average value is 0.3m, and the minimum value is -0.8m. , The sum of the two, 2.0m, is taken as the kinematic characteristic value of this degree of freedom in this sample.

[0048] (2) Cable breakage penalty and cutting treatment.

[0049] For dynamic samples (maximum cable force, maximum anchor force) that experience physical breakage (breakage of any cable or anchor chain), a penalty upper limit truncation is applied, introducing a nonlinear physical step characteristic:

[0050] in, This represents the true value of the original maximum tension. Minimum breaking load, The preset penalty amplification factor ( >1).

[0051] In this embodiment, a cable is set. 720000N, anchor chain The value is 4535000 N. The tension value of any cable or anchor chain in a certain sea state exceeds 100%. The fractured sample, its tension characteristic value Forced assignment times The upper limit of the penalty, the penalty amplification factor in this embodiment It is 1.1.

[0052] Through the above preprocessing, using environmental parameters as input features and the preprocessed simulation response ground truth values ​​as supervision labels, a basic dynamic response sample set is finally constructed. Each sample in this sample set contains 7-dimensional environmental parameter inputs and their corresponding 8-dimensional physical response ground truth labels (supervision labels), which are used for subsequent parallel initialization training of the model.

[0053] Among them, the data obtained after preprocessing , In step 1, it serves as a supervisory label.

[0054] Step 2: Training the parallel agent model array.

[0055] Step 2A: Model architecture establishment.

[0056] For eight key physical response indicators, namely sway, heave, pitch, roll, pitch, bow roll, maximum cable force, and maximum anchor force, an independent proxy model is established for each of them. The eight proxy models together form a parallel proxy model array.

[0057] Each proxy model takes 7-dimensional environmental parameters (wave height, wave direction, spectral peak period, wind speed, wind direction, current speed, current direction) as input and outputs the predicted value (scalar) of the corresponding single physical response index.

[0058] The architecture of the proxy model is determined before training, and the model's establishment (determining the architecture) does not depend on any data.

[0059] The meaning of "decoupling" is that each surrogate model is only responsible for predicting one physical response metric, the models do not share intermediate results, and the training data is also separate (each uses sub-supervisory labels of the corresponding dimension). This design avoids the mutual contamination of errors between different physical quantities.

[0060] Table 2. Specific meanings and unit descriptions of the 8 physical response indicators

[0061] Step 2B: Model training.

[0062] The environmental parameters in the basic sample set of Step 1 are used as input features and fed into each surrogate model for forward calculation to obtain the preliminary prediction values ​​of each surrogate model for each physical response index.

[0063] It should be noted that when the model is first established, the internal parameters are random, and the initial predicted values ​​output by the forward calculation may be far from the true values, which is normal.

[0064] Subsequently, the one-dimensional supervision label (sub-supervision label) corresponding to the physical response index of the agent model in the basic sample set described in step 1 is used as the prediction target. The error between the preliminary prediction value and the supervision label is used as a feedback signal for backpropagation. The internal parameters of each agent model are iteratively updated so that the preliminary prediction value of each physical response index gradually approaches the supervision label of the corresponding dimension.

[0065] Let's illustrate the training process with a specific example: Taking the surrogate model responsible for predicting wave length as an example, it is input with 7-dimensional sea state parameters (such as wave height 1.0m, period 6s, etc.). The model calculates a preliminary wave length prediction (e.g., 0.8m) under the current parameters. This prediction is then compared with the true wave length simulation value (e.g., 0.5m) of the same grid point in the base sample. The error is calculated (0.8m - 0.5m = error 0.3m). Based on this error, the model's internal parameters are adjusted so that the next prediction for that sample is closer to 0.5m. This process is repeated until the model's prediction error for all base samples converges to an acceptable range.

[0066] It is important to clarify the fundamental difference between training and prediction here: During the training phase, the sub-supervisory labels serve as "scoring standards." The model first provides an initial prediction based on the input environmental parameters, then compares this prediction with the true value to calculate the error, and adjusts the model's internal parameters accordingly. The true value is not input to the model throughout the process; it is only used as a comparison standard to guide model correction.

[0067] Each surrogate model is trained using only its corresponding one-dimensional supervision label (sub-supervision label). For example, surrogate model one (swell) uses only the swell ground truth, surrogate model two (swell) uses only the swell ground truth, and so on. The eight models are trained independently without interfering with each other.

[0068] After training is complete, a trained agent model array is obtained, which can be used in subsequent steps.

[0069] Step 3: High-risk interception with confidence limit.

[0070] Step 3A: Large-scale sea state prediction and assessment across the entire area.

[0071] Input the large-scale spatial candidate grid points (500,000 in this embodiment) into the surrogate model array trained in step 2 for forward prediction.

[0072] Specifically, for any candidate grid point, i.e. a set of 7-dimensional environmental parameters (such as wave height 1.0m, wave direction 45°, spectral peak period 6s, wind speed 10m / s, wind direction 90°, flow velocity 0.5m / s, and flow direction 180°), this set of parameters needs to be input into all 8 surrogate models in parallel. Each surrogate model performs forward calculation independently and outputs the predicted value of the grid point on the physical response index it is responsible for.

[0073] Thus, a grid point can be computed in parallel by eight surrogate models to obtain predicted values ​​for eight physical response indices.

[0074] It should be noted that ensemble learning models such as random forests contain multiple base learners (e.g., multiple decision trees). During forward prediction, each base learner outputs a prediction response value. All prediction response values ​​are aggregated to obtain the prediction value of the surrogate model.

[0075] That is, when the 7-dimensional environmental parameters of a grid point are input into a surrogate model (random forest), the internal parameters of that model... Each decision tree performs a forward computation independently, and each tree outputs a predicted value. .

[0076] All predicted response values The predicted value of the surrogate model is obtained after aggregation. That is, the output of a surrogate model is a predicted value.

[0077] Based on the ensemble learning mechanism within each surrogate model, multiple predicted values ​​for each physical response index are statistically analyzed to obtain the average predicted value of each candidate grid point for each physical response index. and the predicted standard deviation .

[0078]

[0079]

[0080] For the first The mean of each physical response index characterizing the predicted hazard level is called the predicted mean. For the first The standard deviation of a physical response index, which characterizes cognitive uncertainty, is called the prediction standard deviation. The input candidate grid points (7-dimensional environmental parameters); Index of physical response indicators ( ); The number of base learners; For the first Each base learner for grid points The predicted response value.

[0081] The physical meaning of the predicted mean and predicted standard deviation: Forecast Mean This reflects the surrogate model's "average judgment" of that grid point. The higher the value, the higher the predicted level of danger.

[0082] Predicted standard deviation This reflects the degree of disagreement among the base learners regarding the prediction. The larger the standard deviation, the greater the difference in prediction results among the base learners.

[0083] Both are indispensable: the mean is used to "explore known dangers," while the standard deviation is used to "explore unknown blind spots."

[0084] Step 3B: High-risk determination based on upper confidence limit (UCB).

[0085] Calculate the candidate grid point at the th Confidence upper limit on each physical response metric The formula is as follows:

[0086] This is a constant used to control the exploration intensity. In this embodiment, the exploration intensity constant is controlled. The value is 2.

[0087] The design logic of the confidence upper limit: It also incorporates "known dangers" ( ) and "unknown blind spots" ( When the predicted mean of a grid point is high, the UCB is naturally high (focusing on known dangers); when the predicted standard deviation of a grid point is large, the UCB will also be increased (forcefully exploring blind spots). This design allows the algorithm to both use existing knowledge to lock in known high-risk areas and actively explore unknown areas that the model has not yet fully learned.

[0088] When any candidate grid point any dimension upper confidence limit Greater than the preset engineering specification threshold If a sample is identified as a suspected high-risk sample, it will be intercepted, thus constructing a global high-risk candidate set. Its mathematical set definition is as follows:

[0089] in, For the first The physical legal threshold corresponding to the physical response index. In this embodiment, the physical legal thresholds for each output dimension are set as follows: In this embodiment, the physical legal red line threshold settings for each physical response index are shown in Table 3.

[0090] Table 3 Physical legal thresholds for each physical response index

[0091] The essence of "interception" in step 3 is that the target of interception is the candidate grid point itself (i.e., a specific combination of sea state parameters), rather than an isolated value. As long as any physical response index of the grid point exceeds the standard, the entire grid point (the complete combination of 7-dimensional environmental parameters) is intercepted as a whole and sent to the high-risk candidate set.

[0092] Step 4: Comprehensive risk assessment and spatial clustering screening.

[0093] For the high-risk candidate set obtained in step 3 To accurately select the very few grid points with the greatest simulation value from the set, and to ensure that these points are evenly distributed in the parameter space, this step sequentially performs two major stages: "point-by-point comprehensive scoring" and "set clustering screening".

[0094] Step 4A, Point-by-point comprehensive risk assessment (Object: Each candidate grid point ).

[0095] From the prediction results obtained in step 3 (including one predicted mean and one predicted standard deviation for all candidate grid points), extract the predicted mean for each candidate grid point in the high-risk candidate set for each physical response index. With the predicted standard deviation And calculate the local nonlinear perturbation of each grid point on each physical response index. .

[0096] Local nonlinear perturbation is achieved by comparing adjacent grid points. With current grid point The difference between the predicted and actual responses is used as a metric, i.e., calculating... This reflects the intensity of the nonlinear jump in the response of the region. The more dramatic the jump, the closer the region is to the nonlinear failure boundary, and the more worthy it is of sampling and verification.

[0097] To achieve equivalent evaluation of physical responses with different dimensions under a unified risk scale and to eliminate feature masking caused by asynchronous deterioration, the following measures are taken: Each candidate grid point within The following scoring calculations will be performed for all: First, for each physical response index of this grid point (Total of 8), extract their uncertainty components. Risk level components and local nonlinear perturbation components And perform normalization:

[0098]

[0099]

[0100] in, = ; = ; = .

[0101] Uncertainty components The predicted standard deviation calculated from step 3 This reflects the size of the cognitive blind spot of the model in that region; Risk Components The predicted mean obtained from step 3 This reflects the predicted level of danger in the area; Local nonlinear perturbation components The difference in predicted values ​​between adjacent grid points is used to measure and reflect the intensity of nonlinear jumps in the region's response.

[0102] Secondly, the grid points are synthesized using preset weights. In a single physical response index The overall information gain score :

[0103] in, For the first The score of the dimensional collection function. , , These are the weighting coefficients for each feature. In this embodiment, , , .

[0104] Finally, to address the issue of asynchronous deterioration of multidimensional responses, the maximum score of all physical response indicators for that grid point is taken as its final comprehensive hazard score. This step refers to cross-dimensional asynchronous max pooling, which corresponds to... Figure 1 "Asynchronous max-pooling" in the context of this.

[0105]

[0106] The significance of asynchronous max pooling: The eight physical response indicators of a mooring system deteriorate at inconsistent rates under different sea states. For example, in one sea state, the mooring tension may be close to breakage but the motion amplitude may still be acceptable, while in another sea state, the roll may be excessive but the mooring tension may still be safe. If a weighted average is used, the two risks will "dilute" each other, leading to missed detections. Taking the maximum value means that as long as one physical response indicator scores high, that grid point will receive a high score, ensuring that any single-dimensional physical failure risk can be prioritized for identification by the system.

[0107] At this point, the high-risk candidate set... Each grid point in Each was assigned a unique overall risk score. A higher score indicates a greater overall simulation value for that point.

[0108] Step 4B: Clustering and Extreme Value Extraction (Target: the entire high-risk candidate set) ).

[0109] After completing the All grid points After scoring, to avoid excessive clustering of sampling points in local nonlinear regions, which would lead to wasted computing power, the entire set... Perform K-Means spatial clustering, forcibly splitting it into 7-dimensional parameter space. Spatial clusters ( (Equal to the preset parallel simulation computing power scale). The objective function of cluster optimization is to minimize the sum of Euclidean distances within clusters:

[0110] in, K is the preset parallel simulation computing power scale (i.e., the number of clusters); in this embodiment, K is set to 200.

[0111] For the first Spatial clusters; Let be the centroid vector of the cluster; For grid points The squared Euclidean distance to the centroid vector. The centroid vector is the "virtual center point" obtained by averaging the seven coordinates of all grid points within the cluster.

[0112] The purpose of clustering: High-risk points often concentrate near a few steep boundaries. Without intervention, all 200 sampling points might be crammed into a small corner (computing power collapse). K-Means clustering forcibly divides these points into 200 clusters based on spatial distance, ensuring that the sampling points cover different boundary areas.

[0113] After clustering is completed, in each cluster Internally, extract the overall risk score. The highest single grid point is used as the representative extreme value sample for this cluster. :

[0114] Ultimately, from Extract from each cluster Two high-value adaptive samples (200 in this embodiment) are input into high-fidelity simulation software (AQWA) for time-domain verification to obtain the true values ​​of the simulation response.

[0115] The complete logic of step 4 is as follows: First, score each point in the high-risk candidate set; then, cluster the entire set; finally, select the champion with the highest score from each group. Both "scoring" and "clustering" operate on the high-risk candidate set, but their granularity differs. Scoring is a point-by-point operation (assigning a score to each point), while clustering is a global operation (grouping the entire set according to spatial distance). Mathematically, these two operations are not contradictory and constitute a complete pipeline from "evaluation" to "selection."

[0116] Step 5: Sample set update and iterative convergence determination.

[0117] 1. Sample set update.

[0118] The true values ​​of the simulation response obtained from the adaptive sampling point simulation in step 4 are preprocessed in the same way as in step 1 and then incorporated into the dynamic response basic sample set described in step 1 to form an updated basic sample set.

[0119] It is important to explain here the necessity of "merging" rather than "replacing": If the model is retrained with only the 200 newly added sampling points and the initial 1000 samples are discarded, the model will quickly forget its knowledge of the safe regions that occupy most of the parameter space because the newly added samples are only densely distributed near the nonlinear failure boundary (accounting for a very small proportion of the total parameter space). This will lead to a large number of false positives in the full-domain scan of step 3 in subsequent iterations, meaning that the model will incorrectly mark a large number of safe regions as high-risk.

[0120] Conversely, if new data is not incorporated and the old model is used for another scan, the model parameters will not be updated at all. The high-risk candidate set obtained in step 3 will highly overlap with the previous round, and step 4 will select the exact same high-risk points. The algorithm will fall into invalid iteration and will never converge.

[0121] Therefore, this step updates the model by merging old and new samples, allowing the model to continuously absorb real response information from the boundary region while maintaining global baseline awareness, and gradually approach the real topological form of the limit state surface.

[0122] Regarding the mathematical completeness of the "merging": The adaptive sampling points selected in step 4 are all new grid points screened from the high-risk candidate set in step 3, while the initial sampling points (1000) are randomly distributed across the entire domain using Latin hypercube sampling. In a grid space of hundreds of millions, the probability of two batches of points overlapping in parameter space is extremely low. Therefore, after merging, each grid point corresponds to only one set of true values ​​for the simulation response, and there is no conflict of the same grid point corresponding to multiple sets of true values. Even if a very small number of repetitions occur (theoretically, the probability is close to zero), since the simulation response corresponding to the same physical state is objectively determined, the results of the two calculations will inevitably be consistent, and can be directly overwritten or averaged without affecting the integrity of the sample set.

[0123] 2. Iterative training of the model.

[0124] The updated base sample set is cyclically fed back into step 2, and the parallel expert agent model array is retrained using the updated base sample set. During retraining, an incremental training method is adopted: the model structure and trained model parameters from the previous round of model array are inherited, and the updated base sample set is used as incremental data to update the model parameters (instead of retraining from scratch). This design fully utilizes the knowledge of the existing model and avoids the waste of computational power in redundant calculations.

[0125] 3. Dynamic monitoring of multidimensional convergence indicators.

[0126] During the iterative update of the adaptive sampling method, the following dynamic metrics are monitored and tracked in real time: (1) Maximum normalized uncertainty in the whole space :

[0127] in, - Grid points; -Physical response indicators; This metric reflects the model's maximum cognitive uncertainty across the entire parameter space. When this value continuously decreases and tends to stabilize, it indicates that the model's understanding of the entire domain has become sufficient.

[0128] (2) Nonlinear jump intensity :

[0129] This index reflects the average comprehensive risk score of grid points within the high-risk candidate set, characterizing the severity of nonlinear transitions at the boundary.

[0130] (3) Change rate of high-risk candidate set volume :

[0131] in, This represents the number of grid cells in the high-risk candidate set for the current round. This represents the number from the previous round. When the size of the high-risk candidate set stabilizes, it indicates that the boundary topology has been largely fixed.

[0132] (4) Limit state topological coincidence :

[0133] in, and These are the sets of high-risk candidates intercepted in the current round and the previous round, respectively.

[0134] Intersection over Union (IUCN) is a commonly used overlap metric in computer vision. This invention introduces it into the convergence criterion of adaptive sampling in mooring systems to quantify the degree of spatial topological overlap of high-risk candidate sets between two consecutive iterations. The closer the value is to 1, the more consistent the high-risk areas are between the two rounds of interception, and the more stable the extreme state surface is.

[0135] 4. Convergence criterion: When topological overlap The indicator consistently reaches the preset engineering threshold limit for multiple consecutive rounds (in this embodiment). (that is), and various dynamic tracking indicators ( , , When the state becomes stable, the limit state surface is determined to have successfully achieved topological freezing, the adaptive sampling process terminates, and the final basic sample set is solidified and output as the modeling dataset.

[0136] If the above convergence criteria are not met, the loop returns to step 2 to continue iterating until the convergence condition is met.

[0137] To verify the engineering applicability of the method of the present invention, this embodiment performs process verification and offline playback effectiveness verification based on the AQWA time-domain coupled simulation results.

[0138] First, the process verification of the adaptive sampling output results for 20 consecutive rounds was performed. Each round of sampling included 7-dimensional environmental parameter inputs and corresponding dynamic response simulation results. The 7-dimensional environmental parameters included wave height, wave direction, spectral peak period, wind speed, wind direction, current speed, and current direction. The dynamic response simulation results included ship motion response, cable stress response, and anchor chain stress response.

[0139] When classifying risk levels, the amplitude of motion for sway, heave, roll, pitch, and bow is the difference between the maximum and minimum values ​​of the corresponding time series. For sway, the maximum amplitude in one direction relative to the reference position in the corresponding time series is used. If the sway response time series is zeroed out at the initial equilibrium position, the sway amplitude is the larger of the absolute values ​​of the maximum and minimum values ​​of the sway time series. For cable stress, the maximum stress value of each cable is used, and for anchor chain stress, the maximum stress value of the left and right anchor chains is used. The minimum breaking load of the cables is 720,000 N, and the minimum breaking load of the anchor chains is 4,535,000 N. The larger of the ratio of the maximum cable stress to the minimum breaking load of the cables and the ratio of the maximum anchor chain stress to the minimum breaking load of the anchor chains is taken as the stress percentage. If none of the six motion responses of the vessel exceed the corresponding limit and the force ratio is no greater than 50%, it is classified as Level I, low risk. If any motion response exceeds the corresponding limit and the force ratio is no greater than 50%, or if none of the six motion responses exceed the corresponding limit but the force ratio is greater than 50% but not greater than 80%, it is classified as Level II, medium risk. If any motion response exceeds the corresponding limit and the force ratio is greater than 50% but not greater than 80%, or if the force ratio is greater than 80% but less than 100%, it is classified as Level III, high risk. If the force on any cable or anchor chain reaches or exceeds the corresponding minimum breaking load, it is classified as Level IV, critical failure. The risk level classification is shown in Table 4.

[0140] Table 4 Risk Level Classification Table

[0141] like Figure 2 As shown, during 20 consecutive rounds of adaptive sampling, the proportion of Level III high-risk and Level IV critical failure conditions remained close to or above 90% in most iterations. This result indicates that the present invention does not perform indiscriminate sampling in the parameter space, but rather continuously allocates the limited high-fidelity simulation budget to high-risk conditions and the neighborhood of critical failures through high-risk candidate set interception, comprehensive risk scoring, and spatial clustering screening. Since Level IV critical failure conditions are the most dangerous conditions that need to be identified and avoided in engineering, the above enrichment phenomenon proves that the present invention has a strong ability to discover dangerous areas and has engineering verification value.

[0142] In the offline playback validity verification, a high-fidelity simulation sample set was first formed based on approximately 4,000 sets of working conditions sampled in the first round of random sampling and approximately 4,000 sets of working conditions sampled in subsequent adaptive iterations. To avoid excessive interference from critical failure samples in the identification of the boundary between Level II medium risk and Level III high risk, approximately 1,600 sets of critical failure samples with any cable stress or anchor chain stress exceeding 100% MBL were removed, resulting in approximately 6,400 valid samples. In this embodiment, 6,402 of these valid samples were used as the offline playback sample pool to verify the hazard boundary identification capability and sample efficiency of the present invention within the range of valid working conditions without failure.

[0143] Each valid sample includes 7-dimensional environmental parameter inputs and 16-dimensional underlying dynamic response outputs. The 16-dimensional underlying dynamic response outputs include 6-dimensional ship motion response and 10-dimensional cable / anchor chain force response. These 16-dimensional underlying dynamic responses do not contradict the 8 physical response indices in Example 1: the 6-dimensional ship motion response corresponds to pitch, sway, heave, roll, pitch, and bow roll; the 10-dimensional cable / anchor chain force response can further extract the maximum cable force and maximum anchor force, thus corresponding to the maximum cable force and maximum anchor force in Example 1. Therefore, the underlying simulation data used for offline playback verification can be mapped to form the 8 physical response indices described in Example 1.

[0144] Offline playback verification employs a pooling sampling protocol. First, 20 samples are selected from the effective sample pool as the initial seed sample set, with the remaining samples forming the candidate pool. In each round, the current surrogate model predicts the unselected samples in the candidate pool, and the five samples with the highest scores are added to the training sample set based on the sampling function. After adding samples, the surrogate model is retrained, and the next iteration begins, until the total sampling reaches 2000 samples. This process simulates the adaptive sampling process of progressively selecting high-value scenarios and updating the surrogate model within a limited high-fidelity simulation budget.

[0145] To verify the effectiveness of the pre-weighted comprehensive acquisition function of this invention, three sampling strategies were set up for comparison: the first is the adaptive sampling strategy of this invention, which uses pre-weighted weights to weight and synthesize the uncertainty component, the hazard component, and the local nonlinear perturbation component, and selects new samples based on the comprehensive hazard score in each iteration; the second is a random sampling strategy, which randomly selects samples from the candidate pool in each round; and the third is a pure coverage sampling strategy, which selects samples only based on the coverage of the parameter space. Evaluation metrics include the F1 score for high-risk identification, the accuracy of the hazard boundary, the area under the learning curve (AULC), and the minimum number of samples required to achieve F1=0.85.

[0146] Explanation of evaluation indicators: The F1 score for high-risk identification is used to evaluate the surrogate model's ability to identify Level III high-risk operating conditions. In offline playback validation, Level III high-risk samples are designated as positive classes, while Level I low-risk and Level II medium-risk samples are designated as negative classes. Precision and recall are calculated based on the surrogate model's prediction results on unselected samples, and the harmonic average of these two values ​​is used to obtain the F1 score. A higher F1 score indicates that the model identifies high-risk operating conditions more accurately and completely.

[0147] The hazard boundary accuracy is used to evaluate the surrogate model's ability to locate the transition zone between Level II medium risk and Level III high risk. In this embodiment, samples with high-risk predicted probabilities close to the classification boundary are used as boundary zone samples, and the proportion of correctly classified samples in the boundary zone is statistically analyzed. The higher the hazard boundary accuracy, the more stable the model's identification of the medium-to-high risk transition boundary.

[0148] The area under the learning curve (AULC) is used to evaluate the overall efficiency of the entire sampling process. In this embodiment, a learning curve is constructed with the number of samples on the horizontal axis and the F1 score for high-risk identification on the vertical axis, and the area under the curve is calculated from the initial seed sample to a budget range of 2000 samples. The larger the AULC, the more likely the sampling strategy can maintain high recognition ability with fewer samples throughout the entire iteration process.

[0149] N@F1=0.85 is used to evaluate the minimum number of samples required to achieve target recognition accuracy, i.e., the number of samples used when the F1 value for high-risk recognition first reaches 0.85. The smaller this index, the fewer high-fidelity simulations are required for the sampling strategy to achieve the same recognition accuracy.

[0150] Table 5. Offline playback verification results of different sampling strategies

[0151] As shown in Table 5: (1) The high-risk identification F1 value of the adaptive sampling strategy of the present invention reaches 0.8764, which is about 9.8 percentage points higher than the random sampling strategy and about 10.0 percentage points higher than the pure coverage sampling strategy; the accuracy of the dangerous boundary reaches 0.7206, which is about 9.7 percentage points higher than the random sampling strategy and about 15.2 percentage points higher than the pure coverage sampling strategy.

[0152] (2) Meanwhile, the adaptive sampling strategy of this invention can achieve F1=0.85 with 1585 samples, while the random sampling strategy and the pure coverage sampling strategy did not reach this threshold within a budget of 2000 samples. This result shows that this invention can reduce the number of high-fidelity simulation samples required while achieving the target high-risk identification accuracy.

[0153] The three quantization components Cover, NonLin, and Bound used in the offline playback verification are experimental proxy expressions for the sampling target of this invention for the convenience of experimental comparison, and are not a replacement for the comprehensive risk score formula in Example 1. Example 1 still uses the predicted mean, predicted standard deviation, and local nonlinear perturbation to construct the comprehensive risk score, and each component is synthesized using preset weights.

[0154] Cover is used to characterize the spatial distance of candidate samples relative to the selected sample set and the gap in parameter spatial coverage. Its function corresponds to the cognitive uncertainty reflected by the prediction standard deviation in Example 1 and the global decentralized exploration effect achieved by spatial clustering screening. In other words, Cover is an experimental quantitative expression of the exploration value of unknown areas, used to avoid excessive concentration of sampling points in local areas.

[0155] NonLin is used to characterize the intensity of nonlinear response near candidate samples, and its function corresponds to the local nonlinear perturbation in Example 1. Example 1 characterizes the intensity of local jumps by the difference in response between adjacent grid points, while in offline playback verification, the nonlinear intensity is characterized by changes in the surrogate model response or model divergence. Both are used to improve the algorithm's sensitivity to regions of sudden changes in cable force, sudden changes in anchor chain force, and sudden changes in motion response.

[0156] Bound is used to characterize the degree to which candidate samples approach the risk boundary. Its function corresponds to the high-risk interception logic formed by the predicted mean and predicted standard deviation in Example 1. In Example 1, the predicted mean reflects the degree of danger, and the predicted standard deviation reflects the uncertainty. The two are used together by the upper confidence limit to determine whether the candidate grid point is close to the engineering threshold. Bound in offline playback verification transforms this idea into a boundary measurement of the transition area between Level II medium risk and Level III high risk.

[0157] Therefore, Cover, NonLin, and Bound are functionally mapped to the global exploration, dangerous boundary locking, and local nonlinear transition identification in this invention. This mapping is only used for index quantification and strategy comparison in offline playback verification and does not change the preset weight comprehensive scoring and iterative sampling process defined in the claims and Embodiment 1.

[0158] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the present invention. Any equivalent substitutions or modifications made by those skilled in the art to the technical solutions and content disclosed in the present invention without departing from the scope of the present invention shall be deemed to have remained within the protection scope of the present invention.

Claims

1. An adaptive sampling accelerated simulation method for mooring systems based on surrogate model arrays, characterized in that, Includes the following steps: Step 1: Construction of the basic sample set: A multidimensional discrete grid space composed of environmental parameters is constructed. Initial working condition sampling is performed, and the sampling points are input into high-fidelity simulation software to obtain the true values ​​of the simulation response of each sampling point. After preprocessing the true values ​​of the simulation response, a basic sample set is constructed using environmental parameters as input features and the preprocessed true values ​​of the simulation response as supervision labels. The supervision labels include several sub-supervision labels. Step 2: Train the agent model array: A model architecture is established to independently establish proxy models that correspond one-to-one with multiple physical response indicators. Each proxy model corresponds to a physical response indicator. Each proxy model takes environmental parameters as input and the predicted value of its corresponding physical response indicator as output, forming a decoupled proxy model array. The environmental parameters in the basic sample set are used as input features and fed into each surrogate model for forward computation to obtain the predicted values ​​of each surrogate model for the physical response index. A sub-supervisory label that matches the physical response index is used as the prediction target. The internal parameters of each surrogate model are iteratively updated by minimizing the error between the predicted value and the prediction target, so that the predicted values ​​of each physical response index gradually approach the corresponding sub-supervisory label. After training, a trained surrogate model array is obtained. Step 3: Construct a high-risk candidate set: The trained surrogate model array is used to perform forward prediction on candidate grid points in a large-scale space to obtain the predicted value of each candidate grid point on each physical response index. The predicted values ​​are statistically analyzed to obtain the predicted mean and predicted standard deviation of each candidate grid point for each physical response index. For each candidate grid point, a confidence upper limit is constructed based on the predicted mean and predicted standard deviation of each physical response index. Candidate grid points whose confidence upper limit for any physical response index exceeds the preset engineering threshold are identified as suspected high-risk samples and intercepted. The intercepted candidate grid points together constitute a high-risk candidate set. Step 4: Comprehensive risk assessment and spatial clustering screening: From the predicted mean and predicted standard deviation obtained in step 3, extract the predicted mean and predicted standard deviation of each candidate grid point in the high-risk candidate set for each physical response index, and calculate the local nonlinear perturbation of each candidate grid point for each physical response index. For each candidate grid point in the high-risk candidate set, based on the predicted mean, predicted standard deviation and local nonlinear perturbation of each physical response index, the single-dimensional score of each physical response index is obtained after normalization and weighted synthesis. Then, the maximum value of all single-dimensional scores is taken as the comprehensive risk score of the grid point. Then, spatial clustering is performed on the high-risk candidate set, and the grid point with the highest comprehensive risk score in each cluster is extracted as an adaptive sampling point and input into high-fidelity simulation software to obtain the simulation response truth value. Step 5: Sample set update and iterative convergence determination: The true values ​​of the simulation response obtained from the adaptive sampling point simulation in step 4 are preprocessed and incorporated into the basic sample set described in step 1 to form an updated basic sample set. The surrogate model array is then trained again using the updated basic sample set, and the convergence index is dynamically monitored. If convergence is achieved, the modeling dataset is output; otherwise, the process returns to step 2 to continue iterating.

2. The adaptive sampling accelerated simulation method for mooring systems based on surrogate model arrays according to claim 1, characterized in that, The environmental parameters mentioned in step 1 are 7-dimensional vectors, including wave height, wave direction, spectral peak period, wind speed, wind direction, flow velocity, and flow direction.

3. The adaptive sampling accelerated simulation method for mooring systems based on surrogate model arrays according to claim 1, characterized in that, The initial working condition sampling in step 1 uses Latin hypercube sampling to generate initial samples in the global continuous space, and performs grid snapping processing by calculating the Euclidean distance between the sample coordinates and the discrete grid coordinates, so that the initial sample coordinates are aligned to the nearest valid discrete grid coordinates.

4. The adaptive sampling accelerated simulation method for mooring systems based on surrogate model arrays according to claim 1, characterized in that, Step 2 includes eight physical response indicators: sway, heave, roll, pitch, bow roll, maximum cable force, and maximum anchor force. The surrogate model is a random forest regression model, with each surrogate model taking seven-dimensional environmental parameters as input and the predicted value of the corresponding single physical response indicator as output.

5. The adaptive sampling accelerated simulation method for mooring systems based on surrogate model arrays according to claim 1, characterized in that, In step 3, the formula for calculating the upper confidence limit is: ； - Corresponding candidate grid points , No. The predicted mean of each physical response index; - Corresponding candidate grid points , No. The predictive standard deviation of each physical response index; - A constant that controls the intensity of exploration.

6. The adaptive sampling accelerated simulation method for mooring systems based on surrogate model arrays according to claim 1, characterized in that, Step 4, specifically the steps for obtaining the single-dimensional scores of each physical response index, include: For high-risk candidate sets For each candidate grid point within the range, the predicted standard deviation calculated in step 3 is used. As an uncertainty component The predicted mean obtained from step 3 As a component of risk And calculate the local nonlinear perturbation components of each grid point on each physical response index. Normalization was performed on each to obtain , , ; A single physical response index is synthesized using preset weights. Single-dimensional score: ； in, , , These are the weighting coefficients.

7. The adaptive sampling accelerated simulation method for mooring systems based on surrogate model arrays according to claim 1, characterized in that, Step 4, spatial clustering and adaptive sampling point extraction specifically includes: High-risk candidate set Perform K-Means clustering and split into One cluster; The clustering objective function is ; in To preset the scale of parallel simulation computing power, For the first One cluster; For grid points; Let be the centroid vector of the cluster; In each cluster Internal extraction of comprehensive risk score The highest grid point is used as the adaptive sampling target.

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