A data-driven based method for rapid reconstruction of fuel tank sloshing flow field response

Abstract

This invention provides a data-driven method for rapid reconstruction of the flow field response during tank sloshing. The method includes: acquiring flow field snapshot matrix data for different sloshing conditions through numerical simulation and classifying them into linear and nonlinear conditions; performing standard POD processing and weighted POD processing on the linear and nonlinear sloshing conditions respectively to construct their respective truncated common-mode bases; extracting finite measurement point response sequences and projecting them onto the corresponding truncated common-mode bases to obtain modal coefficients, constructing training and testing sets for each condition; training neural network models for each condition; for unknown conditions, acquiring their measurement point response sequences and determining their condition type, predicting and outputting modal coefficients using the corresponding neural network; and reconstructing the full flow field response using the predicted modal coefficients and the corresponding truncated common-mode bases. This invention solves the problems of high computational cost and low computational efficiency of traditional numerical methods, achieving rapid and high-precision reconstruction of the full flow field for linear and nonlinear unknown conditions.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of fluid dynamics calculation and artificial intelligence, specifically relating to a data-driven method for rapid reconstruction of the flow field response of an oil tank sloshing. Background Technology

[0002] Liquid sloshing is a prevalent problem in aerospace and transportation, particularly in large liquid storage structures such as aircraft integral fuel tanks, spacecraft propellant tanks, and ship fuel tanks. As fuel tank sizes continue to increase, the impact of liquid sloshing on the vibration characteristics and attitude stability of the overall system becomes increasingly significant, becoming a crucial factor affecting system safety and reliability. Liquid sloshing is a typical fluid-structure interaction problem, with its internal flow field exhibiting pronounced nonlinearity, strong coupling, and multimodal characteristics. Accurately predicting the transient sloshing response of the liquid within the fuel tank under different excitation conditions is of significant engineering importance for fuel tank structural safety assessment, health monitoring, and system coupled dynamics analysis.

[0003] Existing methods for analyzing liquid sloshing response mainly include theoretical analysis and numerical calculation. Theoretical analysis methods, represented by equivalent mechanical models, are widely used due to their high computational efficiency and clear modeling approach. These models typically follow principles such as equivalent total mass, equivalent moment of inertia, and equivalent natural frequency, and can be categorized into small-amplitude (linear) equivalent models and large-amplitude (nonlinear) equivalent models based on the severity of the sloshing. Small-amplitude sloshing equivalent models mainly include spring-mass models and pendulum-mass models. These models are based on linear potential flow theory and can simulate the resultant force and resultant torque response of the fluid under small-amplitude sloshing in an oil tank. Large-amplitude sloshing models include composite equivalent mechanical models, nonlinear spring-parabolic point mass models, and motion-pulsating sphere models. By introducing nonlinear restoring forces and nonlinear damping terms, they can describe the large-amplitude sloshing response of the liquid. Numerical calculation methods mainly include the Volume of Fluid (VOF) method and the Smooth Particle Dynamics (SPH) method, which can simulate the liquid sloshing response of oil tanks of arbitrary geometries under arbitrary excitations and are currently the main means of studying liquid sloshing.

[0004] However, existing methods for analyzing liquid sloshing response still have the following technical limitations: 1. Existing equivalent mechanical models for large-amplitude sloshing are highly dependent on the operating conditions and can only remain effective under certain specific nonlinear sloshing conditions, making them difficult to apply to multi-condition scenarios with different excitation amplitudes and frequencies; 2. Equivalent model methods can only obtain the overall sloshing response of the tank (such as the total resultant force and total torque), and are difficult to reflect the distributed fluid response characteristics of the tank wall or interior; 3. Traditional numerical methods involve large computational loads, making it difficult to meet the needs of rapid flow field calculation in practical engineering. Summary of the Invention

[0005] The purpose of this invention is to address the problems of low computational efficiency and the fact that existing numerical methods are only applicable to specific excitation conditions and cannot reflect distributed flow field responses. Instead, it provides a data-driven method for rapid reconstruction of the flow field response during tank sloshing. This method starts from the perspective of flow field order reduction modeling, mapping the high-dimensional flow field to a low-dimensional modal space using the weighted POD method. It also combines the nonlinear mapping capability of deep learning in neural network models to achieve rapid and accurate reconstruction from the response at finite measurement points to the full flow field response. Furthermore, this method combines the advantages of high computational efficiency of equivalent models with strong adaptability of numerical calculation results. It can effectively improve the accuracy and computational efficiency of flow field prediction under large sloshing conditions, and has good engineering application prospects. It can be widely used in fields such as tank structural health monitoring and fuel tank-external system coupled dynamic analysis.

[0006] To achieve the above objectives, the technical solution provided by this invention is:

[0007] A data-driven method for rapid reconstruction of the flow field response during tank sloshing includes the following steps:

[0008] Step 1, Acquisition of flow field snapshot matrix data and classification of operating conditions:

[0009] A numerical model of the fuel tank is established, and numerical simulation is performed within the preset sloshing motion boundary to generate multiple excitation condition samples. The flow field snapshot matrix of each sample is obtained. Based on the degree of sloshing, the samples are classified into linear sloshing conditions and nonlinear sloshing conditions. The flow field snapshot matrix of the sample is composed of the pressure data of all fluid elements in the flow field.

[0010] Step 2: Construct the optimal truncated common-mode basis for each operating condition;

[0011] For samples classified as linear sloshing conditions, an intrinsic orthogonal decomposition is performed on their flow field snapshot matrix, and the first optimal truncation rank determined by iterative optimization is used. The optimal truncation common-mode basis for the linear swaying condition. ;

[0012] For samples classified as nonlinear swaying conditions, a weighted eigenorthogonal decomposition is performed on their flow field image matrix, and the weight matrix and the second optimal truncation rank are determined by iterative optimization. The optimal truncated common-mode basis for truncating nonlinear swaying conditions. ;

[0013] Step 3: Construct training and validation sets according to different working conditions;

[0014] Extract the time-domain response sequence of a finite number of measuring point units located at preset positions on the wall of the oil tank numerical model from the flow field snapshot matrix of each sample in step 1; for each sample, according to its working condition category, project the time-domain response sequence of each measuring point unit onto the optimal truncated common mode basis of the corresponding category obtained in step 2, and calculate the modal coefficient matrix data of the sample.

[0015] The training set includes corresponding matched time-domain response sequence data and modal coefficient matrix data;

[0016] The validation set includes the corresponding matched time-domain response sequence data and modal coefficient matrix data;

[0017] Modal coefficient matrix data is used as labels;

[0018] Step 4: Construct neural network models for different working conditions and train the models;

[0019] For linear swaying and nonlinear swaying conditions, separate neural network models are constructed. The input of the neural network model is the time-domain response sequence of the measuring point unit, and the output is the modal coefficient matrix.

[0020] Under the supervision of the loss function used for training, the corresponding neural network models are trained using their respective training and validation sets. During the training process, the goal is to minimize the function value of the loss function used for training, and a mapping relationship is established from the time-domain response sequence of the measurement points to the modal coefficient matrix.

[0021] Step 5: Perform the following sub-steps for the unknown swaying condition to reconstruct the flow field:

[0022] Step 5.1: Obtain the time-domain response sequence of several measuring point units located in a predetermined position area under unknown swaying conditions; and determine the condition category of the unknown swaying conditions based on the obtained time-domain response sequence.

[0023] The operating conditions include linear sway conditions and nonlinear sway conditions;

[0024] Step 5.2: Input the time-domain response sequence of each measuring point unit in Step 5.1 into the neural network model trained in Step 4 that corresponds to the working condition category determination result, and predict the modal coefficient matrix of the working condition.

[0025] Step 5.3: Combine the predicted modal coefficient matrix with the optimal truncated common mode obtained in Step 2 that corresponds to the working condition category determination result to reconstruct the time domain response distribution of the entire flow field inside the oil tank.

[0026] Furthermore, in step 2, the optimal truncated common-mode basis for forming the linear swaying condition is truncated. The steps include:

[0027] Step a1: Construct the extended flow field snapshot matrix;

[0028] The flow field snapshot matrices of each sample obtained in step 1 are stitched together along the time dimension to obtain the extended flow field snapshot matrix of the linear swaying condition. ;

[0029] Step a2, singular value decomposition;

[0030] Extended flow field snapshot matrix for linear swaying conditions Perform singular value decomposition to obtain the corresponding decomposition matrix; where the decomposition formula is:

[0031]

[0032] In the formula, the extended flow field snapshot matrix for the linear swaying condition is... The decomposition matrix includes , and ;in, The left singular matrix representing the linear swaying condition has column vectors that are orthogonal normalized POD modes, used to characterize the main spatial distribution features of the linear flow field response. The singular value matrix representing the linear swaying condition is a diagonal matrix, where the square of each singular value is proportional to the energy contained in the corresponding mode, i.e., the squares of the singular values ​​are arranged in descending order; Let be the right singular matrix of the linear sway condition, whose column vectors form an orthogonal time base; the coefficient matrix corresponding to each order of POD mode can be obtained by multiplying the singular value matrix of the linear sway condition with the transpose of the right singular matrix of the linear sway condition. ,Right now ;

[0033] Step a3: Based on the sequence of squared singular values ​​in the singular value matrix of the linear swaying condition, determine the first optimal truncation rank through an iterative optimization method. ;

[0034] Step a4, based on the first optimal truncation rank determined in step a3. From the decomposition matrix after singular value decomposition in step a2 Extracting from the middle separately Column, from Extracting the first line and front The columns are then used to expand the flow field snapshot matrix according to each decomposition matrix. The order in which the optimal cutoff common-mode basis for the linear swaying condition is formed. .

[0035] Furthermore, in step a3, the first optimal truncation rank is determined. The iterative optimization method is as follows:

[0036] Set the initial value of the cutoff rank for the linear swaying condition. ,make ;

[0037] Take the decomposition matrix of the linear swaying condition Extracting from the middle separately Column, from Extracting the first line and front The columns are then used to expand the flow field snapshot matrix according to each decomposition matrix. The order of operations is used to construct a temporary truncated common-mode basis for the linear swaying condition. ;

[0038] Temporary truncation common-mode basis based on linear swaying condition The flow field is reconstructed to obtain the reconstructed pressure values ​​of each fluid element in the flow field. The evaluation index of the reconstructed flow field is then calculated, and it is determined whether the evaluation index meets the set accuracy conditions. If it does, the initial cutoff rank of the linear oscillation condition is used. As the first optimal truncation rank If the condition is not met, the iteration terminates; if not, the truncation rank is increased by the set adjustment step size, and the truncation step and flow field reconstruction step are re-executed until the set accuracy condition is met. The final determined truncation rank is then output as the first optimal truncation rank. .

[0039] Furthermore, in step 2, the optimal truncated common-mode basis for forming the nonlinear swaying condition is truncated. The steps include:

[0040] Step b1: For each sample of the nonlinear working condition obtained in step 1, the flow field snapshot matrix is ​​stitched together along the time dimension to obtain the nonlinear extended flow field snapshot matrix. ;

[0041] Step b2, construct the weight matrix Using the weight matrix snapshot matrix of nonlinear extended flow field After weighting, the weighted nonlinear extended flow field snapshot matrix is ​​obtained. ;in, , The weight square root matrix;

[0042] Step b3, snapshot matrix of the weighted nonlinear extended flow field Perform singular value decomposition to obtain the corresponding decomposition matrix; where the decomposition formula is:

[0043]

[0044] Among them, the weighted nonlinear extended flow field snapshot matrix The decomposition matrix includes , and ;in, The left singular matrix representing the nonlinear swaying condition has column vectors that are orthogonal normalized POD modes, used to characterize the main spatial distribution features of the nonlinear flow field response. The singular value matrix representing the nonlinear swaying condition is a diagonal matrix. The square of each singular value is proportional to the energy contained in the corresponding mode, that is, the squares of the singular values ​​are arranged in descending order. Let be the right singular matrix of the nonlinear sway condition. Its column vectors form an orthogonal time base. The coefficient matrix corresponding to each order of POD mode can be obtained by multiplying the singular value matrix of the nonlinear sway condition with the transpose of the right singular matrix of the nonlinear sway condition. ,Right now ;

[0045] Step b4: Determine the second optimal truncation rank based on the sequence of squared singular values ​​in the singular value matrix of the nonlinear swaying condition. ;

[0046] Step b5, based on the second optimal truncation rank determined in step b4. The decomposition matrix of the nonlinear working case after singular value decomposition in step b3 Extracting the first column, from Extracting the first line and front The columns are then used to calculate the weighted nonlinear extended flow field snapshot matrix based on each decomposition matrix. The order in which the optimal truncated common-mode basis is formed for the nonlinear swaying condition. .

[0047] Furthermore, in step b2, the weight matrix is ​​a diagonal matrix, which is constructed through the following optimization process:

[0048] Candidate weighted region partitioning steps:

[0049] Based on the numerical model of the fuel tank, the height of the fuel tank is normalized along its height direction as follows: With preset height step size Starting from the top of the fuel tank and moving downwards, the height of the fuel tank is divided into several candidate weighted regions; each candidate weighted region corresponds to a height interval. , Based on height step Increasing step by step, , Indicates the increment number; where, Indicates the fuel tank height;

[0050] Initial weight allocation steps:

[0051] Set the candidate weighted region near the top of the tank as the initial weighted region, and assign an initial weight value greater than 1 to all fluid units in this initial weighted region, and assign an initial weight value of 1 to all fluid units in the remaining candidate weighted regions.

[0052] Regional expansion assessment steps and optimal weighted region determination steps:

[0053] Keeping the initial weight values ​​unchanged, the range of the weighted region is gradually expanded downwards, and after each expansion operation, the preset initial value of the truncated rank of the nonlinear swaying condition is maintained. If unchanged, perform the intrinsic orthogonal decomposition and flow field response reconstruction steps, perform weighted expansion, truncation common mode basis extraction, and flow field response reconstruction steps respectively, and calculate the relative error of the pressure peak value in the pre-determined local response impact region of the tank wall. Compare the change in the relative error of the pressure peak value before and after weighting, and determine whether the change in the relative error of the pressure peak value reaches the preset change threshold. If so, select the current weighted region as the optimal weighted region; otherwise, continue to perform the region expansion operation and return to perform the corresponding judgment steps until the preset change threshold of the relative error of the pressure peak value is reached.

[0054] The formula for calculating the relative error of the peak pressure in the local response impact region of the fuel tank wall is as follows:

[0055]

[0056]

[0057]

[0058] In the formula, Indicates the first The true peak pressure of each wall element (maximum peak value); Indicates the first Peak reconstructed pressure of each wall element; For the first The relative error of the peak pressure of each wall element; This represents the total number of wall elements involved in the calculation. This represents the relative error of the average pressure peak value. Froude number in nonlinear swaying The total number of operating conditions, this type of shaking is a strong non-linear shaking, and the liquid has a significant impact on the tank wall. For the first Average relative error of peak pressure of wall unit in each working condition; The average reconstruction error of the peak impact of this type of strongly nonlinear shaking wall surface;

[0059] Steps for weight optimization and weight matrix generation:

[0060] With the objective of minimizing the relative error of the peak pressure in the local response impact region of the tank wall, the weight values ​​of each fluid element in the optimal weighted region are finely adjusted to obtain the optimal weight values, thereby forming a weight matrix. .

[0061] Furthermore, the rule for determining the local response impact region of the tank wall is as follows: this region is located in the height direction of the tank numerical model, and the height range of the wall portion is between 0.7H and H, starting from the bottom.

[0062] Furthermore, the optimal weighted region is located in the height direction of the fuel tank, extending downwards from the top of the fuel tank, and the height of this region does not exceed 0.5 times the total height of the fuel tank.

[0063] Further, in step b4, the second optimal truncation rank is determined. The iterative optimization method is as follows;

[0064] Set the initial cutoff rank for the nonlinear swaying condition ,make ;

[0065] Based on the determined optimal weighting region and weight matrix, the decomposition matrix of the nonlinear swaying condition is obtained. The front of the middle Column, take The front of the middle line and front The columns are then used to calculate the weighted nonlinear extended flow field snapshot matrix based on each decomposition matrix. The order in which the temporary truncated rank of the nonlinear swaying condition is constructed is determined. ;

[0066] Temporary truncated rank based on nonlinear swaying condition The flow field is reconstructed to obtain the reconstructed pressure values ​​of each fluid element in the flow field. The evaluation index of the reconstructed flow field is then calculated, and it is determined whether the evaluation index meets the set accuracy conditions. If it does, the initial cutoff rank of the nonlinear sloshing condition is used. As the second best truncation rank The iteration terminates; if the condition is not met, the truncation rank is increased by the set adjustment step size, and the truncation step and flow field reconstruction step are re-executed until the set accuracy condition is met. The final determined truncation rank is then output as the second optimal truncation rank. .

[0067] Furthermore, in step 4, the loss function used to train the neural network model is a weighted loss function based on modal characteristic differences. During training, the weighted loss function It can apply differentiated weights to the prediction errors of different mode coefficients based on the differences in the contributions of each mode to the overall flow field response and the local impact response.

[0068] Weighted loss function The expression is:

[0069]

[0070]

[0071] in, For the first True modal coefficients of order 1; For the network prediction of the first First-order modal coefficients; For the first First-order modal weights; For the first First-order modal eigenvalues; To balance the modal energy proportion and the contribution of the impact response, ; Indicates the first First mode at the impact response evaluation location Modal amplitude at the location; Indicates the first First mode at the evaluation location The maximum contribution amplitude of the transient impact response; This represents the maximum value of the peak contribution of each mode at the impact location among all modes involved in the reconstruction.

[0072] Furthermore, in step 5.3, the reconstruction formula for the time-domain response distribution of the entire flow field is:

[0073]

[0074]

[0075]

[0076]

[0077] In the formula, Represents the coordinates of any spatial location within the entire flow field region; The reconstructed full flow field time-domain response; This represents the modal coefficient matrix predicted by the neural network model. Indicates the first At that moment, the first The modal coefficient values ​​corresponding to the first POD mode; For the truncation rank, in the linear swaying condition, its value is the first optimal truncation rank. In nonlinear swaying conditions, its value is the second optimal truncation rank. ; This is the optimal truncated common-mode basis matrix. In the linear swaying condition, it represents the optimal truncated common-mode basis for the linear swaying condition. In nonlinear swaying conditions, it represents the optimal truncated common-mode basis for nonlinear swaying conditions. ; Indicates the first Spatial distribution vector of the first-order POD mode; Indicates the first Spatial distribution vector of the first-order POD mode; Indicates the first The first POD mode is in the first order. The center position of each fluid unit The component at the location; This represents the spatial dimension, i.e., the number of fluid elements within each flow field. Each POD mode is a... The vector.

[0078] The advantages of this invention are:

[0079] This invention fundamentally overcomes the shortcomings of traditional large-amplitude sway equivalent mechanical models in terms of poor adaptability to different working conditions by constructing a weighted reduced-order model for different working conditions and building and training a neural network model. It achieves rapid and high-precision reconstruction of the full-field dynamic response under various working conditions. Specific advantages include:

[0080] This invention, through Latin hypercube sampling and case-specific processing, exhibits significant universality within a pre-defined sway boundary. It can obtain relatively accurate flow field reconstruction results under arbitrary combinations of excitation amplitude and frequency, with a determination coefficient reaching R² ≥ 0.9 and a standardized mean absolute error (NMAE) ≤ 0.2. Furthermore, utilizing the characteristics of truncated common-mode bases, it can reconstruct the time-domain response at any location within the flow field using a finite number of measurement points, providing comprehensive and effective supporting data for tank structure analysis and health monitoring.

[0081] To address the problem that existing equivalent mechanical models cannot obtain distributed flow field response characteristics, this invention introduces a weighted common-mode basis (POD) method. This method identifies high-impact-sensitive regions through weighted region expansion and evaluation, then determines the optimal weight values ​​through weight fine-tuning, thus obtaining the optimal weight matrix. Finally, the optimal truncation rank is determined based on the standardized mean absolute error and coefficient of determination. The resulting optimal truncation common-mode basis (POD mode basis) exhibits strong reconstruction capabilities during flow field reconstruction, significantly improving the reconstruction accuracy of local impact responses in nonlinear sloshing flow fields.

[0082] To address the issues of high computational cost and difficulty in achieving rapid analysis using traditional numerical flow analysis (CFD) methods, this invention establishes a predictive proxy model for tank sloshing response under different operating conditions using a neural network. This shifts the computational burden to the offline training phase of the neural network. In online applications, only the time-domain response data from the measurement points needs to be input into the corresponding neural network, which then predicts and outputs the corresponding modal coefficients. Experimental results show that the complete prediction and reconstruction process takes only 0.25 seconds, significantly improving the efficiency of full flow field reconstruction under unknown sloshing conditions and meeting the rapid computation and analysis needs for engineering design optimization, online health monitoring, and diagnosis.

[0083] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0084] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0085] Figure 1 This is a flowchart of the data-driven oil tank sloshing flow field response reconstruction method of the present invention;

[0086] Figure 2 This is a schematic diagram of the numerical analysis model of the rectangular liquid-filled oil tank in an embodiment of the present invention;

[0087] Figure 3 This is a diagram of the Latin hypercube sampling results in an embodiment of the present invention;

[0088] Figure 4 This is a schematic diagram of the reconstruction effect of the weighted POD method and the standard POD method in the embodiment of the present invention; wherein, (a), (b), and (c) are comparison diagrams of the pressure time domain response of the three selected sampling points under working condition 1, respectively; (d), (e), and (f) are comparison diagrams of the pressure time domain response of the three selected sampling points under working condition 2, respectively.

[0089] Figure 5 These are the standardized mean absolute error (NMAE) and coefficient of determination (R) calculated under linear and nonlinear swaying conditions in embodiments of the present invention.2 The results are shown in the figure; where (a) is a schematic diagram of the standardized mean absolute error (NMAE) as a function of the truncated rank for the linear swaying and nonlinear swaying conditions, and (b) is the coefficient of determination for the linear swaying and nonlinear swaying conditions. Schematic diagram showing the change in rank with truncation;

[0090] Figure 6 This is a schematic diagram of the structure of the neural network model constructed in an embodiment of the present invention;

[0091] Figure 7 This is a schematic diagram showing the distribution of the verification set and test set operating conditions as determined in this embodiment of the invention;

[0092] Figure 8 This is a schematic diagram showing the distribution of each verification point in the linear shaking condition in an embodiment of the present invention;

[0093] Figure 9 This is a diagram showing the flow field reconstruction result under the linear swaying condition in an embodiment of the present invention;

[0094] Figure 10 This is a schematic diagram of the distribution of verification points in the nonlinear swaying condition in an embodiment of the present invention;

[0095] Figure 11 This is a diagram showing the reconstructed flow field under nonlinear sloshing in an embodiment of the present invention. Detailed Implementation

[0096] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0097] Reference Figure 1 This invention proposes a data-driven method for reconstructing the response of a liquid sloshing flow field. Based on traditional numerical calculations and equivalent model analysis of the flow field, it introduces a hybrid modeling mechanism combining flow field order reduction modeling and deep learning. The core idea of ​​this method is to reduce the order of flow field snapshot data under typical excitation conditions, extract the dominant sloshing flow field modal features, and use a deep neural network to establish a nonlinear mapping relationship between the measurement point response and the flow field modal coefficients. This allows for rapid reconstruction of the entire field fluid pressure distribution under limited measurement point input. The specific implementation process includes the following four core steps:

[0098] Step 1: Acquisition of flow field snapshot matrix data and classification of operating conditions.

[0099] First, a numerical calculation model of the filled oil tank is established, and the sloshing motion boundary is set (the sloshing motion boundary includes the excitation amplitude and excitation frequency range, and this sloshing motion boundary is used to simulate the sloshing conditions that may occur in the actual oil tank under the operating state).

[0100] Secondly, a certain number of samples were generated within the defined sloshing motion boundary using the Latin hypercube sampling method. A numerical calculation model was then used to perform batch calculations on these samples, yielding corresponding numerical results, including the pressure calculation results and liquid surface morphology for all units at each time step under each operating condition. Next, the samples were classified according to the boundary conditions (sloshing angle and sloshing frequency) of the tank sloshing condition to determine the sloshing condition type corresponding to each sample.

[0101] Specifically, the embodiments of the present invention employ a dimensionless number commonly used in fluid mechanics: the Froude number. The shaking samples are classified. The calculation formula is defined as follows:

[0102] (1)

[0103] in, The characteristic rotation radius is 0.5 times the length of the numerical model of the fuel tank in this invention; The angular frequency of the wobbling rotation is related to the wobbling frequency. The relationship is ; This represents the maximum angular amplitude of the swaying rotation, expressed in radians. Its conversion to degrees is as follows: ,in The angle of sway is expressed in degrees. This refers to gravitational acceleration. In this embodiment of the invention, [the following is a description of the process]. The samples are considered linear oscillations, while the rest are considered nonlinear oscillations.

[0104] Subsequently, based on the classification results, the pressure time-domain response of all fluid units in each sample is extracted to form the flow field snapshot matrix of that sample. ,in, Indicates the first The flow field snapshot matrix of a sample. The physical quantities of the snapshots referred to in this invention are all pressures, that is, the flow field snapshot matrix of a sample is composed of the pressures of all fluid elements in the flow field.

[0105] Step 2: Construct common mode bases for different operating conditions.

[0106] (1) For the flow field snapshot matrix under linear sloshing conditions, perform intrinsic orthogonal decomposition (standard POD method) to obtain its optimal truncated common-mode basis. The specific process is as follows:

[0107] Step a1: Construct the extended flow field snapshot matrix: The flow field snapshot matrix of the linear swaying condition sample obtained in Step 1 is stitched together along the time dimension to obtain the extended flow field snapshot matrix of the linear swaying condition. .

[0108] Step a2: Singular Value Decomposition: Extended Flow Field Snapshot Matrix for Linear Sloshing Conditions Perform singular value decomposition to obtain the decomposition matrix; the decomposition formula is:

[0109] (2)

[0110] in, The left singular matrix representing the linear swaying condition has column vectors that are orthogonal normalized POD modes, used to characterize the main spatial distribution features of the linear flow field response. The singular value matrix representing the linear swaying condition is a diagonal matrix, where the square of each singular value is proportional to the energy contained in the corresponding mode, i.e., the squares of the singular values ​​are arranged in descending order; Let be the right singular matrix of the linear sway condition, whose column vectors form an orthogonal time base. The coefficient matrix corresponding to each order of POD mode can be obtained by multiplying the singular value matrix of the linear sway condition with the transpose of the right singular matrix of the linear sway condition. ,Right now .

[0111] The singular value decomposition step decomposes the original flow field data into mutually orthogonal spatial modes and corresponding mode coefficients through mathematical transformation, wherein the magnitude of the singular value square represents the degree of contribution of each mode to the variability of the original data.

[0112] Step a3: Determine the optimal cutoff rank of the linear swaying condition based on the sequence of squared singular values ​​in the singular value matrix of the linear swaying condition. .

[0113] truncated rank Indicates taking the first Rank mode, truncated rank The smaller the value, the larger the error in flow field reconstruction, and the easier it is for the neural network to predict. To balance the accuracy of flow field reconstruction and the prediction accuracy of the neural network, this invention uses the following iterative optimization method to determine the optimal cutoff rank. The specific method is as follows:

[0114] First, set the initial value of the cutoff rank for the linear swaying condition. , that is to say (In this embodiment, it is set) ), take the first part of the decomposition matrix of the linear swaying condition. The column constitutes a temporary truncated common-mode basis. Based on temporary truncated common-mode basis The flow field is reconstructed to obtain the reconstructed pressure values ​​of each fluid element in the flow field. The evaluation index of the reconstructed flow field is then calculated, and it is determined whether the evaluation index meets the set accuracy conditions. If it does, the initial cutoff rank is taken. As the optimal truncated rank If the condition is not met, the iteration terminates; if not, the value of the truncation rank is increased according to the set adjustment step size (the adjustment step size is set to 1 in this embodiment), and the truncation and flow field reconstruction steps are re-executed until the set accuracy condition is met, and the final determined truncation rank is output as the optimal truncation rank.

[0115] This invention uses the standardized mean absolute error (NMAE) and the coefficient of determination. The evaluation index of the reconstructed flow field is calculated using the following formula:

[0116] (3)

[0117] (4)

[0118] (5)

[0119] in, Representing the The reconstructed value of each fluid unit represents the value before use. The flow field reconstructed from the first-order POD mode. Pressure value of each fluid unit; Representing the The reference value for the nth fluid element represents the value obtained by calculating the nth fluid element in the flow field using CFD (Computational Fluid Dynamics) methods. Pressure value of each fluid unit; Indicates the first The average absolute error of each fluid unit; This represents the total number of time steps for the fluid unit. This is the average absolute pressure of the fluid unit; This represents the average value of the reference signal, which is the average pressure of all fluid elements in the original flow field. The number of fluid units.

[0120] The accuracy conditions set for linear operating conditions in this embodiment of the invention are as follows: and and satisfy The smaller the standardized mean absolute error (NMAE), the higher the reconstruction accuracy of the modal basis; the coefficient of determination... The larger the value, the higher the reconstruction accuracy of the modal basis.

[0121] Step a4, based on the optimal cutoff rank of the linear swaying condition determined in step a3. From the decomposition matrix after singular value decomposition in step a2 Extracting from the middle separately Column, from Extracting the first line and front The columns are then used to expand the flow field snapshot matrix according to each decomposition matrix. The order in which the optimal cutoff common-mode basis for the linear swaying condition is formed. .

[0122] (2) For the flow field snapshot matrix of the nonlinear sloshing condition, perform the weighted intrinsic orthogonal decomposition (weighted POD method) step to obtain the optimal truncated common mode basis of the nonlinear sloshing condition. The specific process is as follows:

[0123] Step b1: The flow field snapshot matrix of the nonlinear working condition sample obtained in Step 1 is stitched together along the time dimension to obtain the nonlinear extended flow field snapshot matrix. .

[0124] Step b2: Construct the weight matrix Using the weight matrix to perform snapshots of the nonlinear extended flow field After weighting, the weighted nonlinear extended flow field snapshot matrix is ​​obtained. ;in, , This is the square root matrix of the weights.

[0125] In this embodiment of the invention, the weight matrix used This is a diagonal matrix, and its diagonal elements reflect the relative importance of different spatial units in the reduced-order modeling of the liquid sloshing flow field. Weight matrix The construction of the weighting matrix is ​​based on the spatial energy distribution characteristics and nonlinear impact response properties of the flow field response along the tank height direction. It assigns larger weights to spatial regions with low modal energy proportions but significant influence on local impact responses in the traditional orthogonal decomposition process (which directly performs singular value decomposition on the extended snapshot matrix without weighting) during nonlinear sloshing, and smaller weights to spatial regions with high modal energy proportions and relatively smooth response changes. The following optimization method was used to obtain:

[0126] Step s2.2.1: Candidate weighted region division.

[0127] First, based on the numerical model of the fuel tank, the computational domain of the flow field is divided into hierarchical parts along the height of the fuel tank, and the height direction of the fuel tank is normalized to... and at a preset height step size Divide the fuel tank height into several candidate weighted regions from the top downwards, with each candidate weighted region corresponding to a height interval. , Based on height step Increasing step by step, , Indicates the increment count. Height step size. The value is determined based on the fuel tank's geometry and flow field resolution, and can range from 0.05 to 0.1 times the total height of the fuel tank. In this embodiment of the invention, it is taken as 0.1 times the total height of the fuel tank, i.e. .

[0128] Step s2.2.2: Initial weight allocation.

[0129] In the initial stage, a candidate weighting region near the top of the oil tank is selected as the initial weighting region, and all fluid elements within this initial weighting region are assigned a uniform initial weight value. The initial weight value of all fluid elements in the remaining candidate weighted regions is assigned to 1.0; where the initial weight value is... For integers greater than 1, this embodiment sets... It is version 2.0.

[0130] Step S2.2.3: Determine the final weighted area through regional expansion and evaluation.

[0131] As the weighted region expands downwards, the improvement in relative error gradually decreases and tends to stabilize, and further expanding the weighted region has limited effect on improving the accuracy of flow field reconstruction. Therefore, in this embodiment of the invention, while keeping the initial weight values ​​constant, the weights are adjusted according to the height step size. The weighted region is gradually expanded downwards, and the initial cutoff rank of the preset nonlinear sway condition is maintained after each expansion operation. (In this embodiment) The process remains unchanged, but the standard POD method and flow field response reconstruction steps are executed respectively. Weighted expansion, truncated common-mode basis extraction, and flow field response reconstruction steps are performed. The relative error of the peak pressure in the pre-determined local response impact region of the tank wall is calculated. The change in the relative error of the peak pressure before and after weighting is compared to determine whether the change in the relative error of the peak pressure reaches a preset threshold. If so, the current weighted region is selected as the optimal weighted region; otherwise, the region expansion operation continues and the corresponding judgment step is returned until the preset threshold for the change in the relative error of the peak pressure is reached (a threshold is set in this embodiment). The rule for determining the local response impact region of the tank wall is as follows: this region is located in the height direction of the tank numerical model, and is the part of the wall with a height range between 0.7H and H, starting from the bottom.

[0132] Through the optimization steps described above, the optimal weighted region can be obtained. Experience shows that this optimal weighted region is located in the height direction of the fuel tank, extending downwards from the top of the fuel tank, and the height of this region does not exceed 0.5 times the total height of the fuel tank.

[0133] Step S2.2.4: Weight value optimization and weight matrix generation.

[0134] After determining the optimal weighted region through the weighted region optimization process, the weight values ​​of each fluid element within this optimal weighted region need to be finely adjusted with the goal of minimizing the relative error of the peak pressure in the local response impact region of the tank wall. This yields the optimal weight values, which in turn generate the weight matrix. This invention, by introducing the aforementioned weight matrix, compensates for the inadequacy of the standard intrinsic orthogonal decomposition method (standard POD method) in characterizing low-energy but highly impact-sensitive regions during the order-reduction modeling process. This enhances the reconstruction capability of the common-mode basis and improves the reconstruction accuracy of the local impact response of the flow field under nonlinear sloshing conditions. The magnitude of the weight values ​​and the range of the weighted region can be adjusted according to the changes in the overall flow field reconstruction error and the local impact peak response error under different weight configurations, to adapt to the reconstruction requirements of the liquid sloshing response under different filling heights and excitation conditions.

[0135] This invention provides a method for fine-tuning the magnitude of weight values:

[0136] After determining the optimal weighting region, within the given range of reference weight values... ( and These are the lower and upper limits of the reference weight range, respectively. In this embodiment, the given reference weight range is [2, 100]. There is a negative correlation between the weight value and the relative error of the peak pressure on the tank wall; that is, within a certain range, the larger the weight value, the smaller the relative error of the peak pressure on the tank wall. While maintaining the initial truncation rank, the weight value is adjusted step by step, for example, according to the step size. The pressure is increased incrementally. After each increment, the flow field is reconstructed, and the peak wall pressure response error (i.e., the relative error of the peak wall pressure) is calculated. By comparing the changing trends of the peak wall pressure response error under adjacent weight values, a condition is considered met when the change between two adjacent peak wall pressure response errors is less than 5%. When the increment stops, the current weight value becomes the final weight value after adjustment.

[0137] The formula for calculating the relative error of the peak pressure in the local response impact region of the fuel tank wall is as follows:

[0138] (6)

[0139] (7)

[0140] (8)

[0141] In the formula, Indicates the first The true peak pressure of each wall element (maximum peak value); Indicates the first Peak reconstructed pressure of each wall element; For the first The relative error of the peak pressure of each wall element; This represents the total number of wall elements involved in the calculation. This represents the relative error of the average pressure peak value. Froude number in nonlinear swaying The total number of operating conditions, this type of shaking is a strong non-linear shaking, and the liquid has a significant impact on the tank wall. For the first Average relative error of peak pressure of wall unit in each working condition; This represents the average reconstruction error of the impact peak value of this type of strongly nonlinear shaking wall.

[0142] Step S2.2.5, based on the determined weight matrix For the extended flow field snapshot matrix A weighted transformation is performed to obtain the weighted nonlinear extended flow field snapshot matrix. ,in In the formula This is the square root matrix of the weights.

[0143] Step b3, Singular Value Decomposition: Snapshot matrix of the weighted nonlinear extended flow field Singular value decomposition is performed to obtain a nonlinear decomposition matrix; the decomposition formula is:

[0144] (9)

[0145] in, The left singular matrix representing the nonlinear swaying condition has column vectors that are orthogonal normalized POD modes, used to characterize the main spatial distribution features of the nonlinear flow field response. The singular value matrix representing the nonlinear swaying condition is a diagonal matrix. The square of each singular value is proportional to the energy contained in the corresponding mode, that is, the squares of the singular values ​​are arranged in descending order. Let be the right singular matrix of the nonlinear sway condition. Its column vectors form an orthogonal time base. The coefficient matrix corresponding to each order of POD mode can be obtained by multiplying the singular value matrix of the nonlinear sway condition with the transpose of the right singular matrix of the nonlinear sway condition. .

[0146] Step b4: Determine the optimal cutoff rank of the nonlinear swaying based on the sequence of squared singular values ​​in the singular value matrix of the nonlinear swaying condition. .

[0147] The method for determining the optimal cutoff rank for the nonlinear swaying condition is similar to step a3. First, the initial cutoff rank for the nonlinear swaying condition is set. , that is to say (In this embodiment, it is set to) Based on the determined optimal weighting region and weight matrix, the decomposition matrix of the nonlinear swaying condition is obtained. The front of the middle Column, take The front of the middle line and front The columns are arranged according to the weighted nonlinear extended flow field snapshot matrix. The order in which they form a temporary truncated rank Based on temporary truncated common-mode basis The flow field is reconstructed to obtain the reconstructed pressure values ​​of each fluid element in the flow field. The evaluation index of the reconstructed flow field is then calculated, and it is determined whether the evaluation index meets the set accuracy conditions. If it does, the initial cutoff rank is taken. As the optimal truncated rank The iteration terminates; if the condition is not met, the truncation rank is increased by the set adjustment step size (set to 1 in this embodiment), and the truncation and flow field reconstruction steps are repeated until the set accuracy condition is met. The final determined truncation rank is then output as the optimal truncation rank for the nonlinear sloshing condition. .

[0148] Similarly, the corresponding evaluation indexes are calculated using formulas (6)-(8). In this invention, the accuracy conditions set for nonlinear linear working conditions are as follows: and And it satisfies the relative error of the peak pressure in the local impact area of ​​the fuel tank wall. .

[0149] Step b5, based on the optimal cutoff rank of the nonlinear swaying condition determined in step b4. The decomposition matrix of the nonlinear working case after singular value decomposition in step b3 Extracting the first column, from Extracting the first line and front The columns are arranged according to the weighted nonlinear extended flow field snapshot matrix. The order in which the optimal truncated common-mode basis is formed for the nonlinear swaying condition. .

[0150] Step 3: Construct training and validation sets according to different working conditions.

[0151] Based on the singular value decomposition formula and the obtained optimal truncated common-mode basis in step 2, it can be seen that by obtaining the flow field snapshot matrices of different samples in step 1... Projecting onto the corresponding optimal truncated common-mode basis yields the corresponding modal coefficients:

[0152] (10)

[0153] in, Representing the The modal coefficient matrix corresponding to each sample For the first The number of columns in the modality coefficient matrix corresponding to each sample, which is also the sample snapshot matrix. The number of columns; The truncated rank is The transpose of the common-mode basis matrix.

[0154] Based on the principle of formula (10), firstly, in the numerical model of the oil tank in step 1, select the centerlines of two opposite walls along the thickness direction of the oil tank, and then select the points equidistant from the bottom to the top of the oil tank. A total of fluid units, ( ( ) fluid elements, from the flow field snapshot matrix obtained in step 1 Extract this The time-domain response sequences of each fluid element form a matrix used as input data for the neural network. ; to matrix Projecting these parameters onto the corresponding optimal truncated mode basis obtained in step 2 yields the corresponding mode coefficient matrix. This serves as the output data for training the neural network model.

[0155] According to the above method, for each sample, based on its operating condition category, the time-domain response sequence of each measuring point is projected onto the optimal truncated common-mode basis of the corresponding category obtained in step 2, and the modal coefficient matrix data of that sample is calculated. Based on the calculated data, the time-domain response sequence data is used as the input data for subsequent model training and prediction, and the modal coefficient matrix data is used as the output data. Furthermore, during model training, the modal coefficient matrix data serves as the label. In other words, both the constructed training set and validation set include corresponding matched time-domain response sequence data and modal coefficient matrix data.

[0156] Step 4: Construct neural network models for different working conditions and train the models.

[0157] Neural network model construction:

[0158] For both linear and nonlinear swaying conditions, corresponding neural network models are established. In this embodiment of the invention, a multi-layer Bi-LSTM neural network model is preferably used. Figure 6 As shown, the model structure contains an input layer with dimensions of . *1, where The number of measurement points is typically selected as [20, 40]. Two or three Bi-LSTM layers (each containing 256 neurons) are used. A Dropout layer is added after each Bi-LSTM layer, with a Dropout ratio typically between 0.1 and 0.4. After the Dropout layer, three or four fully connected layers are connected. The number of neurons in the fully connected layers is set to 128-64-γ (three fully connected layers) or 256-128-64-γ (four fully connected layers). The last fully connected layer is used to output the coefficients corresponding to each modality. A matrix is ​​formed by the time-domain response sequences of each measurement point. After being input into the established neural network input layer, the data undergoes a series of mappings, and finally the regression layer outputs the corresponding mode coefficient matrix. .

[0159] The inventors of this application, while studying the characteristics of the liquid sloshing flow field in an oil tank, discovered that the contributions of each mode to the flow field response differ significantly under different sloshing conditions. Lower-order modes typically dominate the overall evolution of the flow field, while some higher-order modes, although accounting for a smaller proportion of energy, have a significant impact on local flow field abrupt changes and liquid impact response under nonlinear sloshing conditions.

[0160] To address the aforementioned flow field characteristics, if a traditional mean squared error loss function is used to uniformly evaluate the prediction errors of each modal coefficient during neural network training, it becomes difficult to simultaneously ensure both the overall flow field reconstruction accuracy and the accuracy of peak response reconstruction at key locations. Therefore, this invention introduces a weighted loss function based on modal characteristic differences during neural network model construction. This weighted loss function applies differentiated weights to the prediction errors of different modal coefficients based on the differences in the contributions of each mode to the overall flow field response and local impact response during model training, thus balancing the overall flow field response and local impact characteristics. Weighted Loss Function The format is as follows:

[0161] (11)

[0162] (12)

[0163] in, For the first True modal coefficients of order 1; For the network prediction of the first First-order modal coefficients; For the first First-order modal weights; For the first First-order modal eigenvalues; To balance the modal energy proportion and the contribution of the impact response, ; Indicates the first First mode at the impact response evaluation location Modal amplitude at the location; Indicates the first First mode at the evaluation location The maximum contribution amplitude of the transient impact response; This represents the maximum value of the peak contribution of each mode at the impact location among all modes involved in the reconstruction.

[0164] In this step, the weighted loss function determined above... Under the supervision of the respective training and validation sets, the corresponding neural network models are trained, with the goal of minimizing the function value of the weighted loss function, and a mapping relationship from the time-domain response sequence of the measurement points to the modal coefficient matrix is ​​established.

[0165] Step 5: Perform the following sub-steps for the unknown swaying condition to reconstruct the flow field:

[0166] Step 5.1: Obtain the time-domain response sequence of several measuring point units located in the predetermined position area under the unknown swaying condition; and based on the obtained time-domain response sequence, determine whether the condition belongs to a linear swaying condition or a nonlinear swaying condition.

[0167] In practical engineering applications, the linear or nonlinear operating conditions of liquid sloshing are often difficult to determine in advance, and the characteristics of these conditions directly affect the applicability of subsequent modeling and analysis methods. Therefore, this invention introduces an automatic operating condition discrimination method based on wall pressure response to identify the type of liquid sloshing operating condition without prior information.

[0168] In this embodiment of the invention, for unknown shaking conditions, the data arranged on the side wall of the fuel tank is obtained. The pressure time-domain response signals of each measuring point (i.e., fluid element) are used to construct a flow field snapshot matrix from the time-domain pressure responses acquired at these measuring points during a complete excitation process. Let... The time-domain pressure signal at each measuring point is:

[0169] (13)

[0170] in, Number of sampling times; The meaning is the pressure value at the first measuring point at time T. A sliding time window analysis method is introduced along the time dimension to analyze the pressure signal, with the time window length set as . (The value is generally [50, 100], and 50 is preferred in this real-time example), then the first... The pressure submatrix corresponding to each sliding window It can be represented as:

[0171] (14)

[0172] in, This represents the total number of sliding windows. .

[0173] To quantitatively characterize the intensity of liquid sloshing within each time window, a window energy index is introduced. For the first... The first time window, the first The pressure time series corresponding to each measuring point is denoted as . The total energy within that time window is defined as:

[0174] (15)

[0175] in, Indicates variance operation; Under the sliding time window, the first Pressure time series at each measuring point; energy series for all sliding windows. Then, sort them in descending order and select the ones with the highest energy. A high-energy time window (the maximum number of windows is generally [3,5], and in this embodiment, a value of 4 is preferred). Furthermore, to characterize the degree of energy concentration over time, an energy concentration index is defined. :

[0176] (16)

[0177] in This indicates the order after sorting by energy level. Maximum window energy.

[0178] This indicator essentially reflects the proportion of high-energy time periods in the pressure response relative to the overall response. When liquid sloshing is under nonlinear sloshing conditions, the pressure response typically exhibits obvious intermittent impacts and energy surges, corresponding to... The value is relatively large; however, under linear swaying conditions, the pressure fluctuation is relatively stable, and the energy distribution within the window is more uniform. The value is relatively small. In this invention, when... If the oscillation is non-linear, it is considered non-linear; otherwise, it is considered linear.

[0179] Step 5.2: Input the pressure time-domain response sequence of each measuring point unit in Step 5.1 into the neural network model trained in Step 4 that corresponds to the working condition category determination result, and predict the modal coefficient matrix of the working condition.

[0180] After classification, the aforementioned The time-domain pressure data from each measuring point can be used as input data for the corresponding neural network model to obtain the modal coefficient matrix predicted by the network. .

[0181] Step 5.3, convert the modal coefficient matrix predicted by the network. The optimal truncated common-mode basis obtained in step 2, which corresponds to the operating condition category determination result, is combined to reconstruct the time-domain response distribution of the entire flow field within the tank. The reconstruction formula is as follows:

[0182] (17)

[0183] (18)

[0184] (19)

[0185] (20)

[0186] In the formula, Represents the coordinates of any spatial location within the entire flow field region; The reconstructed full flow field time-domain response; This represents the modal coefficient matrix of the network prediction. Indicates the first At that moment, the first The modal coefficient values ​​corresponding to the first POD mode; For the cutoff rank, in the linear swaying condition, its value is the optimal cutoff rank. In nonlinear swaying conditions, its value is the optimal truncated rank. ; The optimal truncated common-mode basis matrix, in the linear swaying condition, is the optimal truncated common-mode basis obtained in step 2. In the nonlinear swaying condition, it is the optimal truncated common-mode basis obtained in step 2. ; Indicates the first Spatial distribution vector of the first-order POD mode; Indicates the first Spatial distribution vector of the first-order POD mode; Indicates the first The first POD mode is in the first order. The center position of each fluid unit The component at the location; This represents the spatial dimension, i.e., the number of fluid elements within each flow field. Each POD mode is a... The vector.

[0187] To illustrate the feasibility of the flow field reconstruction method of the present invention and the reliability of the reconstruction results, a detailed explanation is provided below using specific examples.

[0188] Example 1, referring to Figures 2-11 .

[0189] Example 1 focuses on a rectangular liquid-filled oil tank model, which rotates sinusoidally at a constant frequency around its base axis. The model has a length of 0.9m, a thickness of 0.031m, a height of 0.51m, and a liquid filling height of 0.093m. This example uses the VOF method to establish a numerical simulation model of this rectangular liquid-filled oil tank, as follows... Figure 2 As shown.

[0190] Based on step 1 above, the swaying motion boundary of the numerical model of the rectangular liquid-filled oil tank is set, and several sample points are generated using the Latin hypercube sampling method. Simulation calculations are performed in batches according to the sample conditions to obtain the flow field snapshot matrix for each sample. The samples are then classified based on the calculation results, such as... Figure 3 As shown.

[0191] Based on step 2 above, extended flow field snapshot matrices are constructed for sample points under both linear and nonlinear sloshing conditions. The initial cutoff rank for linear sloshing is set to 10, and the initial cutoff rank for nonlinear sloshing is set to 20. In the nonlinear sloshing condition, with an initial weight value of 2.0 assigned to all fluid elements within the initial weighted region and an initial weight value of 1.0 assigned to fluid elements in other candidate weighted regions, the weighted region is gradually expanded. When the region expands to more than 0.357m above the tank height, the Froude number... The strongly nonlinear operating condition has satisfied the peak response reconstruction error of the oil tank wall pressure. Therefore, the optimal weighted region is determined to be the area above 0.357m in the height direction of the fuel tank. After determining the optimal weighted region, the weight value is gradually increased according to the method in step 2. When the weight value increases to 35, the peak pressure response reconstruction error of the fuel tank wall is... The specific value is Therefore, the final weight value is determined to be 35. According to the singular value decomposition formula shown in step 2, singular value decomposition is performed on the weighted extended flow field snapshot matrix to obtain the decomposition matrix.

[0192] by Figure 3Taking the pressure time-domain response of three measuring points at heights of 0.396m (sampling point 1), 0.451m (sampling point 2), and 0.506m (sampling point 3) on the left wall centerline of the fuel tank in the sample (7.96°, 0.65Hz and 11.19°, 0.73Hz respectively) as an example, the effects of the weighted POD method and the standard POD method in flow field reconstruction are compared. Figure 4 As shown, (a), (b), and (c) are comparison diagrams of the pressure time-domain response of the three sampling points under operating condition 1, and (d), (e), and (f) are comparison diagrams of the pressure time-domain response of the three sampling points under operating condition 2. The blue line represents the result obtained by the CFD method, the green dashed line represents the result obtained by the standard POD method, and the red dashed line represents the result obtained by the weighted POD method (WPOD) of this invention. The comparison results show that the weighted POD method proposed in this invention has a significant advantage in terms of flow field reconstruction accuracy. Using the evaluation formula shown in step 2, the standardized mean absolute error NMAE and the coefficient of determination R are calculated. 2 The value, the result is as follows Figure 5 As shown, (a) is a schematic diagram of the standardized mean absolute error (NMAE) as a function of the truncated rank for the linear swaying and nonlinear operating conditions, and (b) is the coefficient of determination (R) for the linear swaying and nonlinear operating conditions. 2 Schematic diagram showing the change in rank with truncation.

[0193] For linear oscillation conditions, the truncated rank... When increased to 16, the condition is satisfied. And the standardized mean absolute error satisfies And the coefficient of determination Therefore, the truncation rank for linear operating conditions is determined to be 16. For nonlinear swaying, within the given weighted region, the optimal rank is selected according to step 2. hour, The nonlinear operating condition has satisfied the relative error of the peak pressure in the local impact region of the wall. And the average reconstruction accuracy across the entire field meets the requirements. , Therefore, the optimal truncation rank for the nonlinear condition is 34.

[0194] The optimal cutoff rank for the linear swaying condition in this example. The optimal cutoff rank for the nonlinear swaying condition is determined to be 16. The value is determined to be 34.

[0195] According to step 3 above, 20 fluid element response sequences are extracted from the two opposing wall midlines along the thickness direction of the oil tank numerical model, and the corresponding modal coefficients are calculated according to formula (10) in step 3 above to form a training set. Then, a Bi-LSTM neural network is constructed for both linear and nonlinear swaying conditions. Among them, for the neural network model of the linear swaying condition, its loss function contains The value is 0.7, and the dropout ratios after the Bi-LSTM layer are 0.3 and 0.2, respectively. The shock response evaluation location... Take a fluid element at a height of 0.396m on the centerline of the left wall of the model; for the neural network model under nonlinear swaying conditions, its loss function contains With a value of 0.5, the Dropout ratios after the Bi-LSTM layer are 0.35 and 0.25, respectively, for shock response evaluation. The fluid element is located at a height of 0.506m on the central axis of the left wall of the model. The neural network model constructed in this example has two Bi-LSTM layers and three fully connected layers, each containing 128, 64, and... One neuron.

[0196] Six sample points (i.e., six operating conditions) are randomly generated within the boundary of the swaying motion, such as... Figure 7 As shown in step 3 above, a test set and a validation set are constructed, and network training is carried out. After network training is completed, the energy concentration index of the responses of 20 fluid elements in the test set is calculated according to step 4 above. The calculated values ​​for operating conditions TP1-TP6 are 7.08, 4.95, 3.82, 11.55, 11.63, and 13.59, respectively.

[0197] After classification, the time-domain response data of 20 fluid units are input into the corresponding neural network model to obtain the predicted modal coefficient matrix. The full flow field response can be reconstructed according to formulas (17)-(20) in step 5 above.

[0198] This example verifies the accuracy of the reconstruction results of the method of the present invention by calculating the modal contribution of each fluid element. Specifically, it selects from the entire flow field elements... The representative fluid unit is calculated according to the following formula. Modal contribution of each fluid element:

[0199] (twenty one)

[0200] in, For the first The fluid unit in the first The coefficients of the first mode, The larger the value, the more significant the contribution of the fluid element to the overall dominant mode.

[0201] In the test set, the contribution of all fluid elements in the flow field was calculated using the above formula, and six representative fluid elements were selected within the thickness-direction symmetry plane (to ensure sufficient dispersion of the selected fluid element locations, the distance between each fluid element in this example was set to be no less than 0.15m). The selection results for the linear sloshing and nonlinear sloshing conditions are as follows: Figure 8 and Figure 10 As shown, the corresponding flow field temporal reconstruction results are as follows: Figure 9 and Figure 11 As shown.

[0202] Among them, reference Figure 8 The coordinates of the six representative elements #1 to #6 selected under the linear swaying condition are as follows: #1 (0.0175, 0.0155, 0.0274), #2 (0.4475, 0.0155, 0.0174), #3 (0.8875, 0.0155, 0.1270), #4 (0.0175, 0.0155, 0.2266), #5 (0.4475, 0.0155, 0.2017), and #6 (0.8875, 0.0155, 0.4806). (Refer to...) Figure 10 The coordinates of the six representative elements #1 to #6 selected under nonlinear swaying conditions are #1 (0.0125, 0.0155, 0.0174), #2 (0.4475, 0.0155, 0.0174), #3 (0.0125, 0.0155, 0.1718), #4 (0.4475, 0.0155, 0.1917), #5 (0.8875, 0.0155, 0.2216), and #6 (0.8875, 0.0155, 0.4806)), all in meters.

[0203] Depend on Figure 9 and Figure 11 It can be seen that the method of the present invention can reconstruct the pressure time-domain response of a fluid element under unknown sloshing conditions very well (CFD represents the numerical model calculation result, and ROM represents the reconstruction result of the method of the present invention). In order to comprehensively evaluate the reconstruction effect of the flow field, this example calculates the standardized mean absolute error (NMAE) and the coefficient of determination of all fluid elements under the test set conditions. The values ​​are shown in Table 1.

[0204] Table 1 Test Set Condition Reconstruction Results

[0205]

[0206] As shown in Table 1, the method of the present invention can reconstruct the pressure response of the entire flow field well based on finite response measurement points. Under linear swaying conditions, its coefficient of determination is [missing information]. Mean absolute error It can maintain high reconstruction accuracy even under nonlinear swaying conditions, and its coefficient of determination is... Mean absolute error For the strongly nonlinear condition TP6, the relative error of the peak pressure in the local impact region of the wall is 19.51%, proving the effectiveness of the method of the present invention. Furthermore, after completing network training, the total time for modal coefficient prediction and flow field reconstruction is only 0.25s, demonstrating significant reconstruction efficiency and proving that the scheme of the present invention can meet the needs of rapid calculation and analysis in engineering applications.

[0207] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A data-driven method for rapid reconstruction of the flow field response of a fuel tank sloshing, characterized in that, Includes the following steps: Step 1, Acquisition of flow field snapshot matrix data and classification of operating conditions: A numerical model of the fuel tank is established, and numerical simulation is performed within the preset swaying motion boundary to generate multiple excitation condition samples and obtain the flow field snapshot matrix of each sample. Based on the degree of swaying, the samples are classified into linear swaying conditions and nonlinear swaying conditions; the flow field snapshot matrix of the samples is composed of the pressure data of all fluid elements in the flow field; Step 2: Construct the optimal truncated common-mode basis for each operating condition; For samples classified as linear sloshing conditions, an intrinsic orthogonal decomposition is performed on their flow field snapshot matrix, and the first optimal truncation rank determined by iterative optimization is used. The optimal truncated common-mode basis for forming linear swaying conditions. ; For samples classified as nonlinear swaying conditions, a weighted eigenorthogonal decomposition is performed on their flow field image matrix, and the weight matrix and the second optimal truncation rank are determined by iterative optimization. The optimal truncated common-mode basis for forming nonlinear swaying conditions. ; Step 3: Construct training and validation sets according to different working conditions; Extract the time-domain response sequence of a finite number of measuring point units located at preset positions on the wall of the oil tank numerical model from the flow field snapshot matrix of each sample in step 1; for each sample, according to its working condition category, project the time-domain response sequence of each measuring point unit onto the optimal truncated common mode basis of the corresponding category obtained in step 2, and calculate the modal coefficient matrix data of the sample. The training set includes corresponding matched time-domain response sequence data and modal coefficient matrix data; The validation set includes the corresponding matched time-domain response sequence data and modal coefficient matrix data; Modal coefficient matrix data is used as labels; Step 4: Construct neural network models for different working conditions and train the models; For linear swaying and nonlinear swaying conditions, separate neural network models are constructed. The input of the neural network model is the time-domain response sequence of the measuring point unit, and the output is the modal coefficient matrix. Under the supervision of the loss function used for training, the corresponding neural network models are trained using their respective training and validation sets; During training, with the goal of minimizing the function value of the loss function used for training, a mapping relationship is established from the time-domain response sequence of the measurement points to the modal coefficient matrix. Step 5: Perform the following sub-steps for the unknown swaying condition to reconstruct the flow field: Step 5.1: Obtain the time-domain response sequence of several measuring point units located in a predetermined position area under unknown swaying conditions; and determine the condition category of the unknown swaying conditions based on the obtained time-domain response sequence. The operating condition categories include linear swaying conditions and nonlinear swaying conditions; Step 5.2: Input the time-domain response sequence of each measuring point unit in Step 5.1 into the neural network model trained in Step 4 that corresponds to the working condition category determination result, and predict the modal coefficient matrix of the working condition. Step 5.3: Combine the predicted modal coefficient matrix with the optimal truncated common mode obtained in Step 2 that corresponds to the working condition category determination result to reconstruct the time domain response distribution of the entire flow field inside the oil tank.

2. The data-driven method for rapid reconstruction of the flow field response of a tank sloshing as described in claim 1, characterized in that, In step 2, the optimal truncated common-mode basis for forming the linear swaying condition is truncated. The steps include: Step a1: Construct the extended flow field snapshot matrix; The flow field snapshot matrices of each sample obtained in step 1 are stitched together along the time dimension to obtain the extended flow field snapshot matrix of the linear swaying condition. ; Step a2, singular value decomposition; Extended flow field snapshot matrix for linear swaying conditions Perform singular value decomposition to obtain the corresponding decomposition matrix; where the decomposition formula is: In the formula, the extended flow field snapshot matrix for the linear swaying condition is... The decomposition matrix includes , and ;in, The left singular matrix representing the linear swaying condition has column vectors that are orthogonal normalized POD modes, used to characterize the main spatial distribution features of the linear flow field response. The singular value matrix representing the linear swaying condition is a diagonal matrix, where the square of each singular value is proportional to the energy contained in the corresponding mode, i.e., the squares of the singular values ​​are arranged in descending order; Let be the right singular matrix of the linear sway condition, whose column vectors form an orthogonal time base; the coefficient matrix corresponding to each order of POD mode can be obtained by multiplying the singular value matrix of the linear sway condition with the transpose of the right singular matrix of the linear sway condition. ,Right now ; Step a3: Based on the sequence of squared singular values ​​in the singular value matrix of the linear swaying condition, determine the first optimal truncation rank through an iterative optimization method. ; Step a4, based on the first optimal truncation rank determined in step a3. From the decomposition matrix after singular value decomposition in step a2 Extracting from the middle separately Column, from Extracting the first line and front The columns are then used to expand the flow field snapshot matrix according to each decomposition matrix. The order in which the optimal cutoff common-mode basis for the linear swaying condition is formed. .

3. The data-driven rapid reconstruction method for the flow field response of a tank sloshing as described in claim 2, characterized in that, In step a3, the first optimal truncation rank is determined. The iterative optimization method is as follows: Set the initial value of the cutoff rank for the linear swaying condition. ,make ; Take the decomposition matrix of the linear swaying condition Extracting from the middle separately Column, from Extracting the first line and front The columns are then used to expand the flow field snapshot matrix according to each decomposition matrix. The order of operations is used to construct a temporary truncated common-mode basis for the linear swaying condition. ; Temporary truncated common-mode basis based on the linear swaying condition The flow field is reconstructed to obtain the reconstructed pressure values ​​of each fluid element in the flow field. The evaluation index of the reconstructed flow field is then calculated, and it is determined whether the evaluation index meets the set accuracy conditions. If it does, the initial cutoff rank of the linear oscillation condition is used. As the first optimal truncation rank If the condition is not met, the iteration terminates; if not, the truncation rank is increased by the set adjustment step size, and the truncation step and flow field reconstruction step are re-executed until the set accuracy condition is met. The final determined truncation rank is then output as the first optimal truncation rank. .

4. The data-driven method for rapid reconstruction of the flow field response of a tank sloshing as described in claim 1, characterized in that, In step 2, the optimal truncated common-mode basis for forming the nonlinear swaying condition is truncated. The steps include: Step b1: For each sample of the nonlinear working condition obtained in step 1, the flow field snapshot matrix is ​​stitched together along the time dimension to obtain the nonlinear extended flow field snapshot matrix. ; Step b2, construct the weight matrix Using the weight matrix snapshot matrix of nonlinear extended flow field After weighting, the weighted nonlinear extended flow field snapshot matrix is ​​obtained. ;in, , The weight square root matrix; Step b3, snapshot matrix of the weighted nonlinear extended flow field Perform singular value decomposition to obtain the corresponding decomposition matrix; where the decomposition formula is: Among them, the weighted nonlinear extended flow field snapshot matrix The decomposition matrix includes , and ;in, The left singular matrix representing the nonlinear swaying condition has column vectors that are orthogonal normalized POD modes, used to characterize the main spatial distribution features of the nonlinear flow field response. The singular value matrix representing the nonlinear swaying condition is a diagonal matrix. The square of each singular value is proportional to the energy contained in the corresponding mode, that is, the squares of the singular values ​​are arranged in descending order. Let be the right singular matrix of the nonlinear sway condition. Its column vectors form an orthogonal time base. The coefficient matrix corresponding to each order of POD mode can be obtained by multiplying the singular value matrix of the nonlinear sway condition with the transpose of the right singular matrix of the nonlinear sway condition. ,Right now ; Step b4: Determine the second optimal truncation rank based on the sequence of squared singular values ​​in the singular value matrix of the nonlinear swaying condition. ; Step b5, based on the second optimal truncation rank determined in step b4. The decomposition matrix of the nonlinear working case after singular value decomposition in step b3 Extracting the first column, from Extracting the first line and front The columns are then used to calculate the weighted nonlinear extended flow field snapshot matrix based on each decomposition matrix. The order in which the optimal truncated common-mode basis is formed for the nonlinear swaying condition. .

5. The data-driven method for rapid reconstruction of the flow field response of a tank sloshing as described in claim 4, characterized in that, In step b2, the weight matrix is ​​a diagonal matrix, and its construction is achieved through the following optimization process: Candidate weighted region partitioning steps: Based on the numerical model of the fuel tank, the height of the fuel tank is normalized along its height direction as follows: With preset height step size Starting from the top of the fuel tank and moving downwards, the height of the fuel tank is divided into several candidate weighted regions; each candidate weighted region corresponds to a height interval. , Based on height step Increasing step by step, , Indicates the increment number; where, Indicates the fuel tank height; Initial weight allocation steps: Set the candidate weighted region near the top of the tank as the initial weighted region, and assign an initial weight value greater than 1 to all fluid units in this initial weighted region, and assign an initial weight value of 1 to all fluid units in the remaining candidate weighted regions. Regional expansion assessment steps and optimal weighted region determination steps: Keeping the initial weight values ​​unchanged, the range of the weighted region is gradually expanded downwards, and after each expansion operation, the preset initial value of the truncated rank of the nonlinear swaying condition is maintained. If unchanged, perform the intrinsic orthogonal decomposition and flow field response reconstruction steps, perform weighted expansion, truncation common mode basis extraction, and flow field response reconstruction steps respectively, and calculate the relative error of the pressure peak value in the pre-determined local response impact region of the tank wall. Compare the change in the relative error of the pressure peak value before and after weighting, and determine whether the change in the relative error of the pressure peak value reaches the preset change threshold. If so, select the current weighted region as the optimal weighted region; otherwise, continue to perform the region expansion operation and return to perform the corresponding judgment steps until the preset change threshold of the relative error of the pressure peak value is reached. The formula for calculating the relative error of the peak pressure in the local response impact region of the fuel tank wall is as follows: In the formula, Indicates the first The true peak pressure of each wall element (maximum peak value); Indicates the first Peak reconstructed pressure of each wall element; For the first The relative error of the peak pressure of each wall element; This represents the total number of wall elements involved in the calculation. This represents the relative error of the average pressure peak value. Froude number in nonlinear swaying The total number of operating conditions, this type of shaking is a strong non-linear shaking, and the liquid has a significant impact on the tank wall. For the first Average relative error of peak pressure of wall unit in each working condition; The average reconstruction error of the peak impact of this type of strongly nonlinear shaking wall surface; Steps for weight optimization and weight matrix generation: With the goal of minimizing the relative error of the peak pressure in the local response impact region of the tank wall, the weight values ​​of each fluid unit in the optimal weighted region are finely adjusted to obtain the optimal weight values, thereby forming a weight matrix. .

6. The data-driven rapid reconstruction method for the flow field response of a tank sloshing as described in claim 5, characterized in that, The rule for determining the local response impact area of ​​the tank wall is as follows: the area is located in the height direction of the tank numerical model, and the height range of the wall portion is between 0.7H and H, starting from the bottom.

7. The data-driven method for rapid reconstruction of the flow field response of a tank sloshing as described in claim 5, characterized in that, The optimal weighted region is located in the height direction of the fuel tank, extending downwards from the top of the fuel tank, and the height of this region does not exceed 0.5 times the total height of the fuel tank.

8. The data-driven method for rapid reconstruction of the flow field response of a tank sloshing as described in claim 5, characterized in that, In step b4, the second optimal truncation rank is determined. The iterative optimization method is as follows; Set the initial cutoff rank for the nonlinear swaying condition ,make ; Based on the determined optimal weighting region and weight matrix, the decomposition matrix of the nonlinear swaying condition is obtained. The front of the middle Column, take The front of the middle line and front The columns are then used to calculate the weighted nonlinear extended flow field snapshot matrix based on each decomposition matrix. The order in which the temporary truncated rank of the nonlinear swaying condition is constructed is determined. ; Based on the temporary truncated rank of the nonlinear swaying condition The flow field is reconstructed to obtain the reconstructed pressure values ​​of each fluid element in the flow field. The evaluation index of the reconstructed flow field is then calculated, and it is determined whether the evaluation index meets the set accuracy conditions. If it does, the initial cutoff rank of the nonlinear sloshing condition is used. As the second best truncation rank The iteration terminates; if the condition is not met, the truncation rank is increased by the set adjustment step size, and the truncation step and flow field reconstruction step are re-executed until the set accuracy condition is met. The final determined truncation rank is then output as the second optimal truncation rank. .

9. The data-driven method for rapid reconstruction of the flow field response of a fuel tank sloshing as described in claim 1, characterized in that, In step 4, the loss function used to train the neural network model is a weighted loss function based on modal characteristic differences. During training, the weighted loss function It can apply differentiated weights to the prediction errors of different mode coefficients based on the differences in the contributions of each mode to the overall flow field response and the local impact response. The weighted loss function The expression is: in, For the first True modal coefficients of order 1; For the network prediction of the first First-order modal coefficients; For the first First-order modal weights; For the first First-order modal eigenvalues; To balance the modal energy proportion and the contribution of the impact response, ; Indicates the first First mode at the impact response evaluation location Modal amplitude at the location; Indicates the first First mode at the evaluation location The maximum contribution amplitude of the transient impact response; This represents the maximum value of the peak contribution of each mode at the impact location among all modes involved in the reconstruction.

10. The data-driven method for rapid reconstruction of the flow field response of a tank sloshing as described in claim 9, characterized in that, In step 5.3, the reconstruction formula for the time-domain response distribution of the entire flow field is: In the formula, Represents the coordinates of any spatial location within the entire flow field region; The reconstructed full flow field time-domain response; This represents the modal coefficient matrix predicted by the neural network model. Indicates the first At that moment, the first The modal coefficient values ​​corresponding to the first POD mode; For the truncation rank, in the linear swaying condition, its value is the first optimal truncation rank. ; In nonlinear swaying conditions, its value is the second optimal truncation rank. ; This is the optimal truncated common-mode basis matrix. In the linear swaying condition, it represents the optimal truncated common-mode basis for the linear swaying condition. In nonlinear swaying conditions, it represents the optimal truncated common-mode basis for nonlinear swaying conditions. ; Indicates the first Spatial distribution vector of the first-order POD mode; Indicates the first Spatial distribution vector of the first-order POD mode; Indicates the first The first POD mode is in the first order. The center position of each fluid unit The component at the location; This represents the spatial dimension, i.e., the number of fluid elements within each flow field. Each POD mode is a... The vector.

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