Underwater hull pump-jet propeller unsteady force prediction method and system

Abstract

The invention discloses an unsteady force prediction method and system for an underwater hull pump-jet propeller. The method comprises the following steps: acquiring transient speed data or simulation data of an inlet section of the pump-jet propeller in real time through a sparse speed sensor array fixedly deployed at a key position of a wake flow field of a hull; then, inputting the sparse observation data into a pre-trained GappyPOD flow field reduced order, reconstructing a global axial velocity field of the inlet section of the pump-jet propeller in real time, and synchronously extracting a time coefficient of a dominant POD mode corresponding to the velocity field; further, the time coefficient is used as an input feature, a trained TGPR model is called to execute forward reasoning calculation, an unsteady force prediction value of the pump-jet propeller at the future moment and a corresponding prediction uncertainty confidence interval are directly output, and compared with full-size unsteady CFD simulation, the calculation efficiency is improved by more than three orders of magnitude, and the calculation efficiency is improved by more than three orders of magnitude. Therefore, the engineering real-time evaluation requirement is met.

Description

Technical Field

[0001] This invention relates to the field of underwater vehicle propulsion system performance prediction and hydromechanical condition monitoring technology, specifically to a method and system for predicting unsteady forces in pump-jet propulsion systems based on sparse intrinsic orthogonal decomposition and time-delay Gaussian process regression. This method is applicable to the rapid and accurate online prediction and performance evaluation of unsteady hydrodynamic forces generated by pump-jet propulsion systems in complex, non-uniform inflows, under conditions where only sparse observation data of the wake field of the hull can be obtained. Background Technology

[0002] Accurate prediction of unsteady forces in pump-jet propulsion systems operating in non-uniform wakes is crucial for propulsion performance, structural safety, and noise control. Currently, high-precision predictions mainly rely on physical model experiments or full-scale computational fluid dynamics simulations. The former is costly and time-consuming, while the latter, although providing detailed flow field information, consumes enormous computational resources and is extremely time-consuming, especially for unsteady simulations of integrated submarine-pump-jet configurations, making it difficult to meet the needs of design iteration and real-time condition assessment. In recent years, although some studies have attempted to use data-driven models (such as convolutional neural networks and long short-term memory networks) as surrogate models for computational fluid dynamics (CFD) to improve efficiency, these methods typically heavily rely on globally complete flow field data as input, which is seriously inconsistent with the reality of "sparse observation" in actual engineering, where only a small number of sensors are deployed at key locations. Existing technologies lack a robust framework that can effectively reconstruct global flow field dynamics from sparse, local observation data and accurately map them to unsteady force responses. They also suffer from bottlenecks such as strong dependence on high-dimensional inputs and insufficient modeling of spatiotemporal flow-force coupling mechanisms, which restricts their application in engineering practice. Summary of the Invention

[0003] In view of the shortcomings of existing technologies, this invention provides a method and system for predicting unsteady forces in underwater hull pump-jet propulsion systems. It overcomes the dual limitations of low computational efficiency and heavy reliance on global flow field information in traditional high-fidelity simulations, achieving efficient and reliable prediction of unsteady forces under sparse observation conditions.

[0004] The technical means employed in this invention are as follows: A method for predicting unsteady forces in underwater hull pump-jet propulsion systems includes the following steps: S1. Construct a unified three-dimensional fluid computation domain that includes the hull and the pump-jet propulsion, and establish an integrated unsteady flow field numerical calculation model. Use numerical methods to solve the flow field under the interaction between the hull wake and the pump-jet propulsion, and obtain three-dimensional unsteady flow field data and corresponding pump-jet propulsion unsteady force time series data under the design speed-rated speed conditions. S2. The obtained unsteady flow field data is masked, and the masked unsteady flow field data is processed by the sparse intrinsic orthogonal decomposition method to extract the main flow modes and their time coefficients. The mapping relationship between the time coefficients and the unsteady force of the pump-jet propulsion is fitted and trained by time-delay Gaussian process regression to obtain a surrogate model that can characterize the characteristics of the submarine-propulsion coupled flow and the unsteady force response. S3. In practical application scenarios, data from observation points in the wake velocity field of the hull are collected. The global flow field is reconstructed and time coefficients are identified using the sparse intrinsic orthogonal decomposition method. The identified time coefficients are then input into a trained surrogate model to predict the unsteady forces of the pump-jet propulsion system.

[0005] Furthermore, numerical methods are used to solve for the three-dimensional unsteady flow field data under the interaction between the hull wake and the pump-jet propulsion system, including: Organizing unsteady flow field data into dimensions is matrix ,in The number of spatial grid nodes divided for the inlet section of the pump-jet propulsion inlet region. The total number of time steps for the extracted data, wherein the unsteady force comprises... scalar sequence at time points .

[0006] Furthermore, the obtained three-dimensional unsteady flow field data is masked, including: Obtain a set of observation points and a preset radial position fraction, and further obtain the number of observation points based on the set of observation points; wherein, the radial position fraction is used to describe the relative radial position of the observation points; A binary mask vector is constructed based on the radial position fraction and the number of observation points to describe the availability of spatial node data; the position corresponding to the observation point is set to 1, and the other positions are set to 0; The sparse target flow field is obtained by element-wise multiplying the binary mask vector with the three-dimensional unsteady flow field data.

[0007] Furthermore, the main flow modes and their time coefficients are extracted using the sparse intrinsic orthogonal decomposition method, including: POD decomposition of three-dimensional unsteady flow field data is performed according to the following formula:

[0008] in, This represents a snapshot matrix of a three-dimensional unsteady flow field. express eigenvector set, , Let represent the j-th eigenvector. The larger the eigenvector value, the more important the corresponding mode. , , The number of spatial grid nodes divided for the inlet section of the pump-jet propulsion inlet region. The total number of time steps for the extracted data. This represents the sparse eigenorthogonal decomposition flow mode matrix. Let j represent the j-th mode, and:

[0009] The time coefficient for each mode is obtained using the following formula:

[0010] in, This represents the time coefficient corresponding to the j-th mode. This represents the time coefficient corresponding to the j-th mode at the t-th time step.

[0011] Furthermore, the extraction of the main flow modes and their time coefficients through the sparse intrinsic orthogonal decomposition method also includes: [further details on extraction methods would follow here]. A linear set of low-order eigenorthogonal bases represents a snapshot of a three-dimensional unsteady flow field according to the following formula:

[0012] in This represents the POD mode after processing with the mask matrix. This represents the corresponding time coefficient.

[0013] Furthermore, the extraction of the main flow modes and their time coefficients through the sparse intrinsic orthogonal decomposition method also includes: The time coefficients of the sparse transient field are obtained by matrix fitting using the least squares method.

[0014] in, Indicates the time coefficient.

[0015] Furthermore, the mapping relationship between the time coefficient and the unsteady force of the pump-jet propulsion system is fitted and trained using a time-delay Gaussian process regression, including: Time coefficient after dimensionality reduction of POD Rearranged as Thus, the following regression model is constructed using a Gaussian process:

[0016] Among the noise Follows Gaussian distribution ,and Indicates the noise variance; Regression mapping Following the generalized distribution prior:

[0017] in It is a mean function, initialized to 0; It is a kernel function used to measure the correlation between two samples. It is a Gaussian process function; Given training data The prior probability distribution satisfies:

[0018] in This represents the hyperparameters of the model. This represents the covariance matrix composed of kernel functions. When the observations contain noise, the likelihood distribution is expressed as:

[0019] The marginal likelihood distribution is represented as:

[0020] The model hyperparameters are optimized by maximizing the marginal likelihood function, and they exhibit the following joint distribution:

[0021] in This represents the model's predicted value. , ,and This represents the input of the test set samples; Final posterior Gaussian distribution The mean and variance can be expressed as:

[0022]

[0023] in, Represents a unit array.

[0024] Furthermore, before inputting the identified time coefficients into the trained surrogate model, a Z-score processing method for global-local time normalization of the time coefficients is included.

[0025] This invention also discloses an unsteady force prediction system for underwater hull pump-jet propulsion, used to implement the above method, comprising: The data acquisition unit is used to construct an integrated numerical calculation model of the hull and the pump-jet propulsion. It uses numerical methods to solve the flow field under the interaction between the wake of the hull and the pump-jet propulsion, and obtains three-dimensional unsteady flow field data and corresponding pump-jet propulsion unsteady force time series data under typical working conditions. The model building unit is used to mask the obtained three-dimensional unsteady flow field data and extract the main flow modes and their time coefficients through the sparse intrinsic orthogonal decomposition method. The mapping relationship between the time coefficients and the unsteady force of the pump-jet propulsion is fitted and trained through time-delay Gaussian process regression to obtain a surrogate model that can characterize the coupled flow characteristics and unsteady force response of the submarine and the propulsion. The prediction unit is used to collect observation point data in the wake velocity field of the hull in practical application scenarios, reconstruct the flow state of the entire field and identify the time coefficient using the sparse intrinsic orthogonal decomposition method, and input the identified time coefficient into the trained surrogate model to achieve the prediction of the unsteady force of the pump-jet propulsion.

[0026] Compared with the prior art, the present invention has the following advantages: This invention combines sparse intrinsic orthogonal decomposition with time-delay Gaussian process regression to achieve high-precision prediction of unsteady forces in pump-jet propulsion systems under sparse observation conditions, reducing dependence on global flow field information. Furthermore, the sparse intrinsic orthogonal decomposition effectively utilizes the low-dimensional characteristics of the flow, robustly recovering the dominant flow structure from sparse data, providing physically meaningful low-dimensional input features for subsequent force prediction.

[0027] This invention introduces a time delay embedding mechanism to explicitly model the dynamic hysteresis effect between flow field evolution and force response, thereby improving the accuracy of unsteady force time series prediction.

[0028] The Gaussian process regression framework in this invention not only provides point predictions but also estimates of prediction uncertainties, enhancing the reliability and interpretability of the model in practical applications. The method of this invention is computationally efficient; once the model is trained, it can achieve near real-time prediction of unsteady forces, providing a powerful tool for thruster condition monitoring, rapid performance evaluation, and active control. Attached Figure Description

[0029] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0030] Figure 1This is a flowchart illustrating the fast prediction process for unsteady forces based on sparse observations and the GappyPOD-TGPR model in an embodiment of the present invention.

[0031] Figure 2 This is a schematic diagram of the integrated pump-jet propulsion system coupled to the hull in an embodiment of the present invention.

[0032] Figure 3 This is a schematic diagram illustrating the definition of sparse observation points at the thruster inlet section in an embodiment of the present invention.

[0033] Figure 4 In this embodiment of the invention, the velocity field reconstructed by GappyPOD-TGPR based on sparse observations and the predicted unsteady force of the thruster are presented. Detailed Implementation

[0034] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0035] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0036] like Figure 1 As shown, this invention provides a method for predicting unsteady forces in underwater hull pump-jet propulsion systems. Figure 1 As shown, both the S1 data generation step and the S2 model training step are offline processes, and the specific process is as follows.

[0037] First, a simulation template is constructed. In this embodiment, the template selected is as follows: Figure 2The integrated propulsion model shown is designed to match the propulsion system. By removing the stern cover from the original standard Suboff model, the overall length is appropriately reduced to 4.207m, and the maximum diameter is 0.508m. The pump-jet propulsion system employs a pre-swirling stator structure with 13 blades on the stator and 9 blades on the rotor. The rotor diameter and blade tip clearance are set to 0.177m and 0.001m, respectively, and the rotational speed is set to 1200 rad / min. For accurate numerical simulation, this embodiment divides the computational domain into three parts: the rotor domain, the internal flow domain of the propulsion system, and the external open water domain. The overall mesh size is on the order of 10^36. For the unsteady simulation of the integrated propulsion system, a sliding mesh method is used to simulate rotation in the rotor region. A turbulence model was used, and the SIMPLEC algorithm was employed to decouple the velocity and pressure fields, preserving second-order accuracy in both time and space solutions. To obtain a precession velocity of 0.38, the inflow velocity was set to 1.346 m / s. After convergence, data was extracted every 1° of rotor rotation, covering two full rotations within 0.1 seconds. This data will be used to train subsequent machine learning models.

[0038] The extracted data mainly includes the internal velocity field of the pump-jet propulsion system and the total axial force acting on the propulsion system. The time coefficients obtained from the solution are then used as input to a Gaussian process model, and the total axial force is used as the output of the Gaussian process model. The CFD velocity field snapshots are organized into a matrix containing 2213 spatial nodes and 720 time nodes, while the unsteady force data are presented as a one-dimensional vector containing 720 time nodes. Due to the relatively low advance coefficient, the suction effect generated by the rotor is stronger than the non-uniform inflow effect caused by the control surfaces; therefore, the velocity field at the propulsion inlet clearly reflects the stator profile.

[0039] Specifically, in step S1 of this application, a pump-jet propulsion unit is installed at the stern of the submarine model. The non-uniform inflow is provided by the wake field generated by the hull and appendages, and the inlet section is located in the inlet region of the pump-jet propulsion unit. The unsteady flow field data is organized in a dimension of [dimension missing]. matrix ,in The number of spatial grid nodes divided by the entrance section. The total number of time steps for the extracted data, wherein the unsteady force comprises... scalar sequence at time points .

[0040] Secondly, a surrogate model is constructed to simulate the actual conditions of sparse observations. For example... Figure 3 As shown, the thruster inlet observation point layout is based on radial position fractions. With the number of sampling points Perform parameterization. This represents the angular spacing between adjacent observation points in the circumferential direction. In the baseline scene, this is achieved by selecting points that are uniformly distributed circumferentially and radially... of Each observation point corresponds to a snapshot of the masked velocity field and its corresponding POD mode. The training and test sets are evenly divided in a 1:1 ratio along the time dimension for model development and validation.

[0041] In the dimensionality reduction and flow field reconstruction process based on GappyPOD, the inlet section in the training set is... Transient data of axial velocity at discrete time scales are integrated into a data matrix. The rank-valued component was then extracted using the POD method. The main space mode, which captures 99% of the accumulated eigenvalue energy. Training snapshot processed by masking. and its corresponding mask space modes The time coefficients are solved using the least squares method within the GappyPOD framework. By Projected to global space mode The complete velocity field is reconstructed using the inverse POD.

[0042] Building upon the previous stage, for the task of predicting unsteady forces, the delay window size is set to... This involves integrating latency handling mechanisms into the TGPR framework to explicitly incorporate time correlations. Compared to processing each timestamp independently, the original training set... (Mask time coefficients derived from GappyPOD) and the corresponding unsteady force of the thruster The components are reorganized and normalized into delayed input-output sequences. This reconstruction process reshapes the time evolution coefficients to a size of The matrix is ​​then used to reshape the corresponding unsteady forces into a matrix of size . The matrix enables the model to learn dynamic patterns across multiple time series. In the baseline configuration used in this study, the delayed embedding step size is set to... During the training phase, the TGPR model learns from the mask time coefficients. to unsteady forces The mapping relationship is established. By maximizing the marginal likelihood of the data through gradient-based optimization, the TGPR model is trained, thereby automatically calibrating hyperparameters and completing the mapping from time coefficients to unsteady forces, preparing for subsequent inference.

[0043] Specifically, in S2 of this application, the flow field data masking process is based on radial position fractions. With the number of observation points Parameterization is performed. Indicates the relative radial position, applied to the local hull radius at the corresponding cross-section. smaller Larger values ​​correspond to the area near the hull, while larger values ​​correspond to the area near the duct; additionally... This represents the angular distance between adjacent observation points in the circumferential direction. This is achieved through a binary mask vector. This indicates the availability of spatial node data, and the set of observation points. Within Setting it to 1 indicates that data is available, the rest... This indicates missing data. The sparse target flow field can then be represented as the element-wise product of the mask vector and the original flow field:

[0044] According to the method of claim 1, the feature is that the GappyPOD method described in step S2 for extracting the main flow modes and their time coefficients includes processing the original flow field snapshot matrix. Perform POD decomposition:

[0045] in express eigenvector set, , , and Corresponding to the first There are eigenvalues ​​and eigenvectors. The POD flow mode describing spatial characteristics is then defined as:

[0046] The time coefficient for each mode is:

[0047] The contribution of each mode to the original snapshot can be expressed as a ratio of its eigenvalues. Measurement. Based on this, a truncated [measurement] is established. Rank POD model (where ),pass The original snapshot can be represented by a linear combination of several low-order POD bases:

[0048] The sparse observed flow field obtained by the mask in claim 3 can be rewritten as follows:

[0049] in Indicates passing through the mask matrix The processed POD mode, For the corresponding time coefficients, the complete transient field (containing full flow field information) and the sparse transient field constructed based on the mask matrix are assumed to have the same time evolution form in the low-dimensional space, thereby ensuring their evolution coefficients. and They are similar.

[0050] According to the method of claim 1, the time coefficients of the sparse transient field calculated by the GappyPOD method in step S2 are achieved by matrix fitting using the least squares method, i.e.:

[0051] For the norms in the above equations, respectively... Taking the derivative and setting the partial derivatives to 0, we can obtain a system of linear equations:

[0052] in and operators The Hermitian inner product can be represented by the mask time coefficients obtained by solving a system of linear equations. .

[0053] Furthermore, the TGPR model in S2, which establishes a mapping relationship between the time coefficient and the unsteady force of the pump-jet propulsion system, includes a time-delay input module to reduce the time coefficient after POD dimensionality reduction. Rearranged as Thus, the following regression model is constructed using a Gaussian process:

[0054] Among the noise Follows Gaussian distribution ,and This represents the noise variance.

[0055] The method according to claim 1, characterized in that, in step S2, the regression mapping of the TGPR model with respect to claim 6... Following the generalized distribution prior:

[0056] in It is a mean function, initialized to 0; It is a kernel function used to measure the correlation between two samples, using Matern32 as the kernel function.

[0057] Given training data The prior probability distribution satisfies:

[0058] in This represents the hyperparameters of the model. This represents the covariance matrix composed of kernel functions. When the observations contain noise, the likelihood distribution is expressed as:

[0059] The marginal likelihood distribution is represented as:

[0060] Typically, model hyperparameters can be optimized by maximizing the marginal likelihood function. According to the GP property, the following joint distribution exists:

[0061] in This represents the model's predicted value. , ,and This represents the input of the test set samples.

[0062] Final posterior Gaussian distribution The mean and variance can be expressed as:

[0063]

[0064] In the time delay coefficient Before inputting the proxy model, global-local time normalization Z-score processing needs to be performed. For the original time series... Its global mean and standard deviation are defined as:

[0065]

[0066] This is then applied to the time delay vector:

[0067] In S3, the online testing phase described by a real-world scenario, it is assumed that the spatial modal structure and temporal evolution patterns identified during training remain unchanged. Masked spatial modalities are trained using masked test snapshots to estimate test temporal coefficients. These coefficients are then combined with the global spatial modalities to reconstruct the complete velocity field in the test set. Subsequently, masked temporal coefficients are calculated using sparse velocity observations via GappyPOD, and unsteady forces are directly inferred from TGPR.

[0068] To evaluate the fidelity of the reconstructed velocity field, we treat the transient observation data as an image and use the recognized peak signal-to-noise ratio (PSNR) as the evaluation metric, measured in decibels (dB). This metric is defined as follows:

[0069] in and These represent the original velocity snapshot vector and the reconstructed velocity snapshot vector at a single moment, respectively, both of which have been normalized to the interval [missing information]. , This represents the upper limit of pixel intensity and is set to 1. A higher PSNR value indicates better reconstruction quality and reflects a higher similarity between the reconstructed snapshot and the reference snapshot.

[0070] Secondly, for unsteady force prediction tasks, model performance is assessed through the coefficient of determination. An evaluation is conducted. It is defined as follows:

[0071] in , and These represent the original value, predicted value, and average value of the unsteady force of the thruster, respectively.

[0072] Figure 4 (a) shows the reconstruction results of the inlet velocity field of the pump-jet propulsion system based on sparse velocity observation data using the GappyPOD method. Figure 4 (b) The predicted axial velocity field achieves a peak-to-mean-square ratio (PSNR) exceeding 50 dB on the test set, demonstrating high reconstruction fidelity. These results show that the reduced-order model can preserve key features of the inlet flow field with high fidelity even with limited spatial observations available, highlighting the robustness and practicality of the method under sparse data conditions.

[0073] Figure 4 (c) This paper presents the prediction results of unsteady forces obtained by the TGPR method based on the low-dimensional time-domain representation obtained by GappyPOD through sparse velocity observations. The predicted unsteady forces are in good agreement with the CFD results. The value reached 0.9452. Furthermore, the double standard deviation confidence interval derived from the TGPR posterior distribution effectively captured the uncertainty, with most true values ​​falling within the confidence boundaries, indicating low prediction variance and reliable uncertainty quantification. Figure 4 In the frequency domain of (d), the predicted FFT spectrum of the unsteady force is in high agreement with the CFD results. The intensity difference at the blade passage frequency is approximately 3%, while the deviations at other minor frequencies are all around 10%. These comparative results further validate the prediction accuracy and spectral consistency of the proposed framework.

[0074] Another aspect of this invention discloses a system for predicting unsteady forces in underwater hull pump-jet propulsion, comprising: The data acquisition unit is used to construct an integrated numerical calculation model of the hull and the pump-jet propulsion. It uses numerical methods to solve the flow field under the interaction between the wake of the hull and the pump-jet propulsion, and obtains three-dimensional unsteady flow field data and corresponding pump-jet propulsion unsteady force time series data under typical working conditions. The model building unit is used to mask the obtained three-dimensional unsteady flow field data and extract the main flow modes and their time coefficients through the sparse intrinsic orthogonal decomposition method. The mapping relationship between the time coefficients and the unsteady force of the pump-jet propulsion is fitted and trained through time-delay Gaussian process regression to obtain a surrogate model that can characterize the coupled flow characteristics and unsteady force response of the submarine and the propulsion. The prediction unit is used to collect observation point data in the wake velocity field of the hull in practical application scenarios, reconstruct the flow state of the entire field and identify the time coefficient using the sparse intrinsic orthogonal decomposition method, and input the identified time coefficient into the trained surrogate model to achieve the prediction of the unsteady force of the pump-jet propulsion.

[0075] As for the embodiment of the unsteady force prediction system for an underwater hull pump-jet propulsion device of the present invention, since it corresponds to the embodiment of the unsteady force prediction method for an underwater hull pump-jet propulsion device described above, the description is relatively simple. For related similarities, please refer to the description in part of the embodiment of the unsteady force prediction method for an underwater hull pump-jet propulsion device described above, and it will not be described in detail here.

[0076] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting unsteady forces in underwater hull pump-jet propulsion systems, characterized in that, Includes the following steps: S1. Construct a unified three-dimensional fluid computation domain that includes the hull and the pump-jet propulsion, and establish an integrated unsteady flow field numerical calculation model. Use numerical methods to solve the flow field under the interaction between the hull wake and the pump-jet propulsion, and obtain three-dimensional unsteady flow field data and corresponding pump-jet propulsion unsteady force time series data under the design speed-rated speed conditions. S2. The obtained unsteady flow field data is masked, and the masked unsteady flow field data is processed by the sparse intrinsic orthogonal decomposition method to extract the main flow modes and their time coefficients. The mapping relationship between the time coefficients and the unsteady force of the pump-jet propulsion is fitted and trained by time-delay Gaussian process regression to obtain a surrogate model that can characterize the coupled flow characteristics of the submarine and the unsteady force response. S3. In practical application scenarios, data from observation points in the wake velocity field of the hull are collected. The global flow field is reconstructed and time coefficients are identified using the sparse intrinsic orthogonal decomposition method. The identified time coefficients are then input into a trained surrogate model to predict the unsteady forces of the pump-jet propulsion system.

2. The method for predicting unsteady forces in an underwater hull pump-jet propulsion system according to claim 1, characterized in that, Numerical methods were used to solve the three-dimensional unsteady flow field data under the interaction between the submarine wake and the pump-jet propulsion system, including: Organizing unsteady flow field data into dimensions is matrix ,in The number of spatial grid nodes divided for the inlet section of the pump-jet propulsion inlet region. The total number of time steps for the extracted data, wherein the unsteady force comprises... scalar sequence at time points .

3. The method for predicting unsteady forces in an underwater hull pump-jet propulsion system according to claim 1, characterized in that, The obtained three-dimensional unsteady flow field data is masked, including: Obtain a set of observation points and a preset radial position fraction, and further obtain the number of observation points based on the set of observation points; wherein, the radial position fraction is used to describe the relative radial position of the observation points; A binary mask vector is constructed based on the radial position fraction and the number of observation points to describe the availability of spatial node data; the position corresponding to the observation point is set to 1, and the other positions are set to 0; The sparse target flow field is obtained by element-wise multiplying the binary mask vector with the three-dimensional unsteady flow field data.

4. The method for predicting unsteady forces in an underwater hull pump-jet propulsion system according to claim 3, characterized in that, The main flow modes and their time coefficients are extracted using the sparse intrinsic orthogonal decomposition method, including: POD decomposition of three-dimensional unsteady flow field data is performed according to the following formula: in, This represents a snapshot matrix of a three-dimensional unsteady flow field. express eigenvector set, , Let represent the j-th eigenvector. The larger the eigenvector value, the more important the corresponding mode. , , The number of spatial grid nodes divided for the inlet section of the pump-jet propulsion inlet region. The total number of time steps for the extracted data. This represents the sparse eigenorthogonal decomposition flow mode matrix. Let j represent the j-th mode, and: The time coefficient for each mode is obtained using the following formula: in, This represents the time coefficient corresponding to the j-th mode. This represents the time coefficient corresponding to the j-th mode at the t-th time step.

5. The method for predicting unsteady forces in an underwater hull pump-jet propulsion system according to claim 4, characterized in that, Extracting the main flow modes and their time coefficients using the sparse intrinsic orthogonal decomposition method also includes: A linear set of low-order eigenorthogonal bases represents a snapshot of a three-dimensional unsteady flow field according to the following formula: in This represents the POD mode after processing with the mask matrix. This represents the corresponding time coefficient.

6. The method for predicting unsteady forces in an underwater hull pump-jet propulsion system according to claim 5, characterized in that, Extracting the main flow modes and their time coefficients using the sparse intrinsic orthogonal decomposition method also includes: The time coefficients of the sparse transient field are obtained by matrix fitting using the least squares method. in, Indicates the time coefficient.

7. The method for predicting unsteady forces in an underwater hull pump-jet propulsion system according to claim 1, characterized in that, The mapping relationship between the time coefficient and the unsteady force of the pump-jet propulsion system is fitted and trained using a time-delay Gaussian process regression, including: Time coefficient after dimensionality reduction of POD Rearranged as Thus, the following regression model is constructed using a Gaussian process: Among the noise Follows Gaussian distribution ,and Indicates the noise variance; Regression mapping Following the generalized distribution prior: in It is a mean function, initialized to 0; It is a kernel function used to measure the correlation between two samples. It is a Gaussian process function; Given training data The prior probability distribution satisfies: in This represents the hyperparameters of the model. This represents the covariance matrix composed of kernel functions. When the observations contain noise, the likelihood distribution is expressed as: The marginal likelihood distribution is represented as: The model hyperparameters are optimized by maximizing the marginal likelihood function, and they exhibit the following joint distribution: in This represents the model's predicted value. , ,and This represents the input of the test set samples; Final posterior Gaussian distribution The mean and variance can be expressed as: in, Represents a unit array.

8. The method for predicting unsteady forces in an underwater hull pump-jet propulsion system according to claim 1, characterized in that, Before the identified time coefficients are input into the trained surrogate model, Z-score processing is also included for global-local time normalization of the time coefficients.

9. A system for predicting unsteady forces in an underwater hull pump-jet propulsion system, used to implement the method for predicting unsteady forces in an underwater hull pump-jet propulsion system as described in any one of claims 1-8, characterized in that, include: The data acquisition unit is used to construct an integrated numerical calculation model of the hull and the pump-jet propulsion. It uses numerical methods to solve the flow field under the interaction between the wake of the hull and the pump-jet propulsion, and obtains three-dimensional unsteady flow field data and corresponding pump-jet propulsion unsteady force time series data under typical working conditions. The model building unit is used to mask the obtained three-dimensional unsteady flow field data and extract the main flow modes and their time coefficients through the sparse intrinsic orthogonal decomposition method. The mapping relationship between the time coefficients and the unsteady force of the pump-jet propulsion is fitted and trained through time-delay Gaussian process regression to obtain a surrogate model that can characterize the coupled flow characteristics and unsteady force response of the submarine and the propulsion. The prediction unit is used to collect observation point data in the wake velocity field of the hull in practical application scenarios, reconstruct the flow state of the entire field and identify the time coefficient using the sparse intrinsic orthogonal decomposition method, and input the identified time coefficient into the trained surrogate model to achieve the prediction of the unsteady force of the pump-jet propulsion.

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