Method, apparatus and medium for vibration prediction of a ship hull surface based on a co-kriging model

Abstract

According to example embodiments of the present disclosure, a vibration prediction method, device, medium and product for a ship surface based on a Co-Kriging model are provided. The method performs multi-fidelity fusion according to data from a real world and data from finite element simulation, and outputs a reconstructed frequency response curve. The vibration prediction method completely solves the dimension disaster problem of high-dimensional frequency response modeling, and has advantages such as significantly improved high-precision small-sample modeling capability, greatly optimized model generalization capability and multi-fidelity fusion accuracy.

Description

Technical Field

[0001] The embodiments disclosed herein generally relate to the field of information processing, and specifically to a method for predicting vibrations on a ship hull surface based on a Co-Kriging model, electronic devices, and computer-readable media. Background Technology

[0002] Ship structural vibration directly affects a ship's safety, comfort, and equipment reliability, and is one of the key performance indicators in modern ship design and in-service assessment. Currently, methods for predicting ship structural vibration and noise primarily employ numerical calculation techniques such as the finite element method, boundary element method, and statistical energy method. While these methods can achieve simulation assessment of vibration characteristics during the design phase, they still have significant limitations in engineering applications: the computational cost of detailed finite element models for harmonic response analysis across a wide frequency range and multiple operating conditions is extremely high; a single high-fidelity simulation calculation for complex structures such as double-bottom hulls can take more than 5 hours, failing to meet the real-time requirements of multi-condition global optimization and online vibration assessment for in-service ships.

[0003] Data-driven surrogate modeling offers a feasible solution to the aforementioned computational efficiency problem. Surrogate models such as Kriging and response surface methodology can reduce the time required for a single prediction to the second level while maintaining prediction accuracy, and have been gradually introduced into the field of ship structural vibration and acoustic radiation prediction. However, existing surrogate models still face two major technical bottlenecks in the scenario of predicting hull surface vibrations: First, the prediction of ship surface vibration is a high-dimensional response field modeling problem in both frequency and space. Wideband frequency response analysis involves thousands of frequency points and needs to cover the response distribution of multiple spatial measurement points. Traditional modeling methods that proceed point by point and frequency by frequency will lead to an explosion in computational load and sever the intrinsic correlation between frequency and spatial dimensions, making it impossible to effectively capture modal coupling and peak migration characteristics. Secondly, single-fidelity Kriging models are highly dependent on high-fidelity test samples, while hull structure vibration tests are costly and difficult to obtain samples. Most existing multi-fidelity models only fuse data between numerical simulation models of different accuracies, and test data is only used as external verification. There is a lack of systematic methods to use model prediction uncertainty to guide test point supplementation and realize model self-updating, and it is impossible to continuously absorb measured data to optimize model performance during the ship's navigation phase. Summary of the Invention The embodiments of this disclosure provide a method, electronic device, and computer-readable medium for predicting the vibration of a ship's hull surface based on a Co-Kriging model, thereby overcoming the shortcomings of existing technologies such as low simulation efficiency for ship vibration prediction, lack of experimental samples, and inability of the model to achieve self-updating optimization under small sample conditions.

[0005] In a first aspect of this disclosure, a vibration prediction method for a ship hull surface based on a Co-Kriging model is provided. The vibration prediction method includes: a vibration prediction method for a ship hull surface based on a Co-Kriging model, wherein the vibration prediction method includes the following steps: Based on the selected first set of excitation points Acquire response from the first stimulus point set The first high-fidelity response set of real-world incentives from all locations; The response was acquired from the second set of excitation points based on the finite element simulation model. The first low-fidelity response set of the simulation excitation at various locations; A set of frequency response curves is generated based on the first high-fidelity response set and the first low-fidelity response set, and the average spectral shape of all frequency response curves in the set is calculated. and the nth frequency response curve Relative to the average spectral shape bias , Principal component analysis was used to uniformly reduce the dimensionality of the frequency response curves. The reduced dimensionality parameters include the spectral shape basis vector. The scores of the first principal components corresponding to each frequency response curve projected onto the principal component space. and the Low-dimensional characterization of the frequency response curves mentioned above in, in, Principal component order, Based on the first principal component score with order q of the principal component. A kriging model is established, which is characterized by the following formula: in, The predicted principal component score for the predicted point. It is a mean function with constant values. To describe the covariance matrix among training samples, Let X be the input coordinates of the predicted point, and let X be the set of input coordinates between each training sample. The prediction variance for the prediction points; Constructing a Co-Kriging model: The low-fidelity response prediction value corresponding to the first low-fidelity response set is obtained based on the Kriging model. , Solve for the coefficients of the Co-Kriging model: based on low-fidelity response predictions. The first high-fidelity response value is used to calculate the coefficients of the Co-Kriging model according to the following characterization formula to establish the Co-Kriging model: in, It is the scaling factor of the Co-Kriging model. It is global bias and It is a process of smoothing residuals.

[0006] Reconstructing the target frequency response curve to predict the vibration mode at a new prediction point: After solving for the new excitation point and the new response value at the new excitation point based on the Co-Kriging model, the second principal component score of the reconstructed target frequency response curve is calculated based on the new excitation point, the new response value, and the following formula. To reconstruct the target frequency response curve: in, The reconstructed representation of the first The target frequency response curve.

[0007] In a second aspect of this disclosure, an electronic device is provided, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the method according to the first aspect of this disclosure.

[0008] In a third aspect of this disclosure, a non-transitory computer-readable storage medium storing computer instructions is provided, characterized in that the computer instructions are used to cause a computer to perform the method described according to a first aspect of this disclosure.

[0009] The summary section is provided to present the chosen concepts in a simplified form, which will be further described in the detailed description below. The summary section is not intended to identify key or essential features of this disclosure, nor is it intended to limit the scope of this disclosure. Attached Figure Description

[0010] The above and other objects, features and advantages of this disclosure will become more apparent from the accompanying drawings, in which like reference numerals generally denote like parts.

[0011] Figure 1A schematic diagram of an example environment according to an embodiment of the present disclosure is shown; Figure 2 A schematic diagram of a vibration prediction method for a ship hull surface based on a Co-Kriging model according to an embodiment of the present disclosure is shown. Figure 3 A schematic diagram of a physical hull model shown from the hull perspective, according to an embodiment of the present disclosure, is illustrated. Figure 4 A schematic diagram illustrating the construction of a Co-Kriging model according to an embodiment of the present disclosure is shown; Figure 5 A schematic diagram of the first step (adaptive point supplementation at the global level) of modifying the Co-Kriging model according to an embodiment of the present disclosure is shown. Figure 6 A schematic diagram of adaptive point compensation based on a global level according to an embodiment of the present disclosure is shown; Figure 7 A schematic diagram of the second step (adaptive point supplementation at the local level) of the modified Co-Kriging model according to an embodiment of the present disclosure is shown. Figure 8 A schematic diagram is shown illustrating the solution of the length scale of the excitation plane and the length scale of the response plane according to an embodiment of the present disclosure; Figure 9 A schematic diagram illustrating the confirmation of a second set of excitation points according to an embodiment of the present disclosure is shown; Figure 10 A block diagram schematically illustrates an electronic device suitable for implementing embodiments of the present disclosure.

[0012] In the various figures, the same or corresponding reference numerals indicate the same or corresponding parts. Detailed Implementation

[0013] Preferred embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While preferred embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that the present disclosure will be thorough and complete, and will fully convey the scope of the present disclosure to those skilled in the art.

[0014] As mentioned above, traditional methods suffer from high computational costs, applicability to vibration prediction at only a single fidelity level, limited experimental samples, and incoherent model steps. In ship vibration analysis, finite element models can provide structural responses over a wide range at low cost, but inevitably contain errors such as geometric simplification and idealized boundary conditions, thus being considered low-fidelity data. Physical experiments, on the other hand, can more accurately reflect the actual structure and boundary conditions, but are costly and have limited sample sizes, thus being considered high-fidelity data. Relying solely on any single fidelity information results in either insufficient accuracy or an inadequate sample size. To balance accuracy and stability within limited experimental and simulation costs, a modeling framework capable of systematically integrating multi-fidelity data is needed.

[0015] To address the aforementioned problems or other issues not mentioned, this disclosure provides a method for predicting vibrations on a ship's hull surface based on the Co-Kriging model. This vibration prediction method includes the following steps: Based on the selected first set of excitation points Acquire response from the first stimulus set The first high-fidelity response set of real-world incentives from all locations; The response was acquired from the second set of excitation points based on the finite element simulation model. The first low-fidelity response set of the simulation excitation at various locations; A set of frequency response curves is generated based on the first high-fidelity response set and the first low-fidelity response set, and the average spectral shape of all frequency response curves in the set is solved. and the nth frequency response curve Relative to the average spectral shape bias , Principal component analysis was used to uniformly reduce the dimensionality of the frequency response curves. The reduced dimensionality parameters include the spectral shape basis vector. The scores of the first principal components corresponding to each frequency response curve projected onto the principal component space. and the Low-dimensional characterization of frequency response curves in, in, Principal component order, The first principal component score is based on the order q of the principal components. The kriging model is established and represented by the following formula: in, The predicted principal component score for the predicted point. It is a mean function with constant values. To describe the covariance matrix among training samples, Let X be the input coordinates of the predicted point, and let X be the set of input coordinates between each training sample. The prediction variance for the prediction points; Constructing a Co-Kriging model: The low-fidelity response predictions corresponding to the first low-fidelity response set are obtained based on the Kriging model. , Solving for the coefficients of the Co-Kriging model: based on low-fidelity response predictions The first high-fidelity response value is used to calculate the coefficients of the Co-Kriging model using the following characterization formula to establish the Co-Kriging model: in, It is the scaling factor of the Co-Kriging model. It is global bias and It is a process of smoothing residuals.

[0016] Reconstructing the target frequency response curve to predict the vibration mode at a new prediction point: After solving for the new excitation point and the new response value at the new excitation point based on the Co-Kriging model, the second principal component score of the reconstructed target frequency response curve is calculated based on the new excitation point, the new response value, and the following formula. To reconstruct the target frequency response curve: in, The reconstructed representation of the first The target frequency response curve.

[0017] Therefore, by using principal component analysis (PCA), complex frequency response data in high-dimensional space is mapped to independent principal component spaces through orthogonal transformation. The first few principal components (q-order) typically reflect the main frequency domain variation characteristics formed by several dominant modes and their couplings. By characterizing the complex data in the original high-dimensional space through the first few principal components, the dimensionality of the data is reduced, thus alleviating the workload. In addition, high-fidelity real experimental data and low-fidelity simulation data are fused into the data to establish a multi-fidelity fusion Co-Kriging model. On the one hand, this solves the various problems existing in previous models that used a single fidelity as the data source. On the other hand, it enables high-precision and rapid prediction of dual high-dimensional frequency response fields under the constraint of small samples in the real world.

[0018] The following is a detailed explanation with reference to the accompanying drawings.

[0019] Figure 1 A schematic diagram of an example environment 100 according to an embodiment of the present disclosure is shown. (As...) Figure 1 As shown, the example environment 100 includes a computing device 110, a first high-fidelity response set 120 in response to real stimuli at each of the first stimulus point set, and a response set to a second stimulus point set. The simulation excitation at various locations generates a first low-fidelity response set 130 and a reconstructed frequency response curve 140. The computing device 110 performs multi-fidelity fusion based on data from the real world and data from the finite element simulation, and outputs the reconstructed frequency response curve 140. The user can predict the vibration mode of the hull surface after being subjected to a set excitation based on the reconstructed frequency response curve 140.

[0020] The computing device 110 may include, but is not limited to, personal computers, personal digital assistants, wearable devices, tablet computers, smartphones, etc.

[0021] Figure 2 A schematic diagram illustrating an example of a vibration prediction method 200 for a hull surface based on a Co-Kriging model according to an embodiment of the present disclosure is shown. Figure 2 In the middle, each action, for example, can be generated by... Figure 1 The computing device shown performs the operation. It should be understood that method 200 may also include additional actions not shown and / or the actions shown may be omitted, and the scope of this disclosure is not limited in this respect.

[0022] At box 202, computing device 110 is based on the selected first set of excitation points. Acquire response from the first stimulus set The first high-fidelity response set of real-world incentives from all over the world: 120.

[0023] Combination Figure 1 , 3 Understanding, among them Figure 3 The hull is shown from its bottom. In this example, the first high-fidelity response set 120 is based on... Figure 1 , 3 Data collected from the double-bottom rigid structure shown. Figure 1 , 3 The physical model shown is the most conventional structure of a ship hull. It should be understood that this disclosure is only used as an example of a double-bottom rigid structure, but the range of hull forms is not limited to this. It can also be other hull structures with higher rigidity requirements (such as special ships) or hull structures of small ships with lower rigidity (such as motorboats).

[0024] See Figure 1In this example, the hull is suspended from the test frame by elastic rope 4, and the applied real excitation is applied to the hull surface by exciter 1 through push rod 2. Here, to collect the excitation applied by exciter 1 at the same frequency, a force sensor 3 capable of collecting excitation data is connected in series between push rod 2 and the hull. The response data corresponding to the excitation is transmitted through… Figure 3 As shown, the acceleration sensor 5 is located on the hull surface and collects data. Considering the error caused by boundary effect proxies, both the excitation points and response data are arranged with the data recessed from the hull boundary. In this example, the response data collection points use 3... 3. Layout. It is understandable that, depending on the ship's size and accuracy requirements, the data collection points for the response can be set in other forms.

[0025] It should be understood that this disclosure uses only a double-bottom rigid structure as an example, but the range of hull forms is not limited to this. It can also be other hull structures with higher rigidity requirements (e.g., special vessels), or hull structures of smaller vessels with lower rigidity (e.g., motorboats). A real excitation is applied to the hull surface of the target vessel.

[0026] At frame 204, computing device 110 acquires the response from the second set of excitation points based on a finite element simulation model. The first low-fidelity response set of the simulation excitation at various locations.

[0027] against Figure 1 , 3 The solid hull model shown can be generated as a finite element model by computing device 110 or any other device that supports finite element model creation. In this example, it was drawn using the 3D modeling software UG and then imported into ANSYS Workbench. The model uses free boundary conditions to simulate the structural dynamics under actual suspension conditions. Four-node shell elements were selected for mesh generation to ensure good accuracy and computational efficiency. After mesh convergence analysis, the final element size was controlled at around 5mm, with a total of 12597 elements, which can well reflect the dynamic characteristics of each frequency band.

[0028] At box 206, computing device 110 generates a set of frequency response curves based on the first high-fidelity response set and the first low-fidelity response set, and solves for the average spectral shape of all frequency response curves in the set. and the nth frequency response curve Relative to the average spectral shape bias Average spectral shape Bias This can be confirmed using the following formulas: At box 208, computing device 110 performs a uniform dimensionality reduction on the frequency response curve set based on principal component analysis (PCA). The dimensionality-reduced characterization parameters include the spectral shape basis vectors. The scores of the first principal components corresponding to each frequency response curve projected onto the principal component space. and the Low-dimensional characterization of frequency response curves in, in, The order of the principal components.

[0029] Principal Component Analysis (PCA) is a conventional dimensionality reduction method, which will not be elaborated upon here. The contribution of this disclosure in this step lies in uniformly reducing the dimensionality of high-fidelity and low-fidelity correlation data, and then placing them within the same principal component space for unified representation.

[0030] At box 210, computing device 110 calculates the first principal component score based on the order q of the principal component. The kriging model is established and represented by the following formula: in, The predicted principal component score for the predicted point. It is a mean function with constant values. To describe the covariance matrix among training samples, Let X be the input coordinates of the predicted point, and let X be the set of input coordinates between each training sample. This represents the prediction variance for the predicted points.

[0031] The Kriging model is the first-layer model, which takes the excitation location and response measurement points as inputs and the principal component scores of the simulated frequency response as outputs. It establishes a low-fidelity Kriging proxy to characterize the main vibration trend of the structure throughout the excitation-response domain. For the k-th principal component, the output of the first-layer model is the corresponding low-fidelity response prediction value (i.e., the low-fidelity principal component score prediction value).

[0032] At box 212, computing device 110 constructs a Co-Kriging model. The process of constructing the Co-Kriging model at box 212 can be found in [reference needed]. Figure 3 The process shown is as follows: At box 410, computing device 110 solves for the low-fidelity response prediction value corresponding to the first low-fidelity response set based on the aforementioned Kriging model. That is, the principal component scores of the simulated frequency response (i.e., low-fidelity frequency response) are obtained through the constructed Kriging model.

[0033] At box 420, computing device 110 solves for the scaling factor of the Co-Kriging model. , is global bias Smoothing residual process The Co-Kriging model uses the formula... Characterization. Scaling factor. , is global bias Smoothing residual process These coefficients are based on low-fidelity response prediction values. First high-fidelity response value Several sets of data were obtained.

[0034] The Co-Kriging model is the second-layer model constructed in this disclosure. The scaling factor of the Co-Kriging model... Used to correct for differences in overall amplitude or energy scale between low-fidelity simulations and high-fidelity experiments, global bias Residual Gaussian process used to correct baseline offset This is used to characterize the local differences between low-fidelity and high-fidelity predictions under different excitation and response locations that are not uniformly scaled. Since this disclosure models within the principal component space, the scaling factors correspond to the overall scaling parameters on each principal component, rather than scaling functions that vary individually per frequency point or per measurement point. For the scaling factors and bias coefficients in the second-layer model, a weighted least squares fitting method is used, calculated based on the correspondence between the high-fidelity samples and the first-layer low-fidelity prediction results; on this basis, a residual Gaussian process model is then established for the remaining error.

[0035] During model training, a corresponding two-layer model is built for each retained principal component to obtain the low-fidelity surrogate, residual correction term, and corresponding scaling and bias parameters for that principal component. In other words, this invention adopts a "modeling one principal component at a time" approach to decompose the original high-dimensional frequency response problem into several low-dimensional scalar response multi-fidelity modeling subproblems. In the code implementation, a first-layer Kriging model and a second-layer residual Gaussian process model are trained for each principal component, and the corresponding scaling coefficients and bias parameters are estimated.

[0036] Back Figure 2After constructing the Co-Kriging model, at box 214, the computing device 110 reconstructs the target frequency response curve to predict the vibration mode at the new prediction point. Specifically, the computing device 110 first obtains the new response value corresponding to the new excitation point based on the Co-Kriging model obtained at box 320. Then, based on the new excitation point, the new response value, and according to equation... Confirm the score of the second principal component At this point, the reconstructed [number]th [item] can be obtained. The target frequency response curve, i.e. .

[0037] For any potential excitations, the testers or designers can predict the corresponding vibration modes based on the reconstructed target frequency response curve.

[0038] The principal component order q can be validated by incrementally setting candidate principal component orders from small to large. In some examples, computing device 110 can select 2 as the initial value of the candidate principal component order, build Kriging models for different candidate values ​​in an incremental manner, and solve for the root mean square error (RMSE) based on the validation set. The candidate value when the RMSE is minimized is defined as the principal component order, where the validation set is taken from the first high-fidelity response set.

[0039] In such Figure 1 , 3 In the hull shown, the minimum root mean square error is obtained when the principal component order q is set to 4. It can be understood that different principal component orders, such as 3 or 5, may be obtained when building different hull models using the above method.

[0040] After constructing the initial model of the reconstructed frequency response curve, this disclosure introduces a self-updating mechanism based on active learning to achieve low-cost and high-efficiency model optimization. Here, this disclosure performs active learning through global and local level searches to find new experimental / simulation points that need to be added. The Co-Kriging model and subsequent reconstructed frequency response curves are updated using a strategy of "fixed PCA base - small-step recalibration of Co-Kriging model parameters," aiming to improve the accuracy of the reconstructed frequency response curves.

[0041] At the global level, it can be achieved through Figure 5 The process shown is to find new test points (i.e., points verified with actual test data), supplement the first set of excitation points and the first set of high-fidelity responses, and use these data to revise the Co-Kriging model.

[0042] At frame 510, computing device 110 generates a set of candidate complement points within the candidate region based on the model dimensions of the hull. This set of candidate complement points is consistent with the first set of excitation points. Second set of incentive points There is no overlap.

[0043] At frame 520, computing device 110 iteratively searches for the overall posterior variance of the candidate complement set at predetermined step sizes. The overall posterior variance is calculated using the following formula: .in, The predicted variance on the k-th principal component obtained according to the Kriging model is... It is the prediction variance of the smoothed residual Gaussian process corresponding to the k-th principal component obtained from the Co-Kriging model.

[0044] At box 530, after the computing device 110 selects the target complement set to supplement the first high-fidelity response set, it returns to the step of solving the coefficients of the Co-Kriging model in box 320 above. Here, the corresponding total posterior prediction variances in the candidate complement set are sorted from largest to smallest, and the points ranked A positions above are selected as points in the aforementioned target candidate set, where A is a preset integer. A can be any number between 1 and 1000, such as 3, 5, or 100, and can be set after comprehensively considering factors such as accuracy and model size.

[0045] Given that this disclosure employs a two-layer, multi-fidelity structure, the uncertainty in the aforementioned global point-addition active learning does not originate solely from a single model, but rather comprehensively considers the uncertainty of the low-fidelity layer and the uncertainty of the high-low fidelity difference correction layer. The resulting overall posterior uncertainty simultaneously reflects: on the one hand, whether the low-fidelity simulation samples adequately cover the global trend; and on the other hand, whether the high-fidelity experimental samples adequately correct local deviations. Therefore, the selected supplementary points can not only fill large-scale sample gaps but also provide targeted corrections for areas with significant discrepancies between simulation and experiment.

[0046] against Figure 1 , 3 The model shown, based on the initially constructed two-layer Co-Kriging model, calculates the distribution of the overall posterior variance at each coordinate point of the virtual scan grid, and thus obtains... Figure 6 The three global-level supplementary points are shown (marked with red triangles).

[0047] At the local level, it can be achieved through Figure 7 The process shown is to find new simulation points, supplement the second set of excitation points and the first set of low-fidelity responses, and use these data to revise the Co-Kriging model.

[0048] At box 710, computing device 110 obtains the corresponding first set of excitation points based on the Co-Kriging model. The high-fidelity predicted response set at each excitation point; At frame 720, computing device 110 compares the corresponding response values ​​of each group in the high-fidelity predicted response set and the first high-fidelity response set one by one. When the difference between the corresponding response values ​​reaches the maximum value, the corresponding distortion point is recorded.

[0049] At frame 730, the computing device 110 supplements the set of excitation points within a predetermined interval of the distortion points with a third set of excitation points consisting of at least three excitation points located in different orientations, and acquires a third low-fidelity response set based on the response at the third set of excitation points using a finite element simulation model. Researchers can set the value of the predetermined interval as needed, for example, it can be set to any value such as 10mm or 15mm.

[0050] At frame 740, computing device 110 projects the third excitation point set and the third low-fidelity response set onto the second excitation point set, respectively, while keeping the principal component order q fixed. After obtaining the first low-fidelity response set, return to the step of generating a set of frequency response curves based on the first high-fidelity response set and the first low-fidelity response set.

[0051] At box 740, preferably, the third high-fidelity response set is assigned a weight of less than 0.8 and greater than 0.3 before being projected onto the principal component space. For example, the weight can be set to 0.5. It should be noted that this weight is not arbitrarily set empirically, but is determined based on preliminary trial results: when the weight is 1, although the local error is further reduced, the global error increases slightly. Considering both the local correction effect and the global generalization ability, for... Figure 1 , 3 The weight of the ship hull model was ultimately determined to be 0.5 using the method described above. Setting a low weight is to prevent these local simulation samples targeting specific stimulus points from excessively affecting the generalization ability of the global model.

[0052] It is understandable that, in addition to global experimental point supplementation, the relevant steps of the local-level point supplementation method disclosed herein, combined with the results of local error analysis, supplement low-cost simulation samples in local regions with high initial model errors to enhance the ability of the first-layer low-fidelity model to express local response features. Unlike high-fidelity experimental point supplementation, local simulation point supplementation uses lower weights in model training to avoid local samples excessively affecting the overall generalization ability of the model. Thus, this study forms a joint update mechanism of "global high-fidelity point supplementation + local low-fidelity point supplementation": the former focuses on reducing global uncertainty, while the latter focuses on correcting local high-error regions.

[0053] The covariance matrix is ​​determined by the RBF product kernel of the excitation and response coordinates. In the first-level Gaussian process model, the choice of kernel function determines how the model interprets the similarity of the input space (excitation and response coordinates), thus directly affecting its ability to capture the main trend of the vibration response. Therefore, this disclosure attempts to verify reliability using kernel functions such as the RBF product kernel, Matérn-3 / 2, Matérn-5 / 2, a single RBF kernel, and RQ. The total vibration level error OL ( That is, predicting the total vibration level Compared with the actual total vibration level The evaluation criteria included the absolute difference and the coefficient of determination R². The total vibration level error OL of the RBF product kernel, the single RBF kernel, the Matérn-3 / 2, the Matérn-5 / 2, and the RQ kernel were 2.24, 2.63, 2.53, 2.61, and 2.59 dB, respectively. Furthermore, the coefficients of determination R² for each of these kernel functions were 0.91, 0.89, 0.89, 0.89, and 0.89, respectively. It can be seen that the RBF product kernel function has the highest coefficient of determination R² (0.91) and the lowest total vibration level error OL (2.24 dB). Therefore, the RBF product kernel was ultimately selected as the kernel function for determining the covariance matrix.

[0054] The RBF product kernel for determining the covariance matrix is ​​determined by the RBF product kernel of the excitation coordinates and the response coordinates. This RBF kernel is obtained using the following formula: .in, and These represent the known stimulus input samples and the stimulus points to be predicted, respectively. and These represent the known vibration response and the vibration response to be predicted, respectively. and These are the length scales of the excitation plane and the response plane, respectively. The known excitation input samples consist of the first set of excitation points. Second set of incentive points It is determined that the known vibration response is determined by a set of frequency response curves.

[0055] In fact, according to the inventors' analysis, a single RBF kernel or Matérn kernel treats the excitation and response coordinates as a mixed high-dimensional input, failing to explicitly distinguish the differences in spatial correlation between the two types. The product kernel, by decoupling the correlation between the excitation and response spaces, more closely aligns with the engineering understanding that frequency response curves are only highly similar when excitation and response points are close. This structure allows the model to learn the spatial propagation laws of vibration response more efficiently and accurately from a limited sample. In summary, the covariance structure based on the product kernel (with hyperparameters determined by Bayesian optimization) is more suitable for describing the vibration transmission characteristics of the ship's hull structure in this study and provides reliable main trend predictions for the subsequent accurate correction of the second layer.

[0056] The length of the RBF can be determined based on empirical values ​​or by calculation using a formula. The calculation method involves the following steps: First, at box 810, computing device 110 defines an objective function in the form of root mean square prediction error according to the following formula: in, This means removing the first... After the first sample, the target frequency response curve constructed using the remaining samples is used to analyze the second sample. Predicted value of the point; Next, at box 820, computing device 110 calculates the median Euclidean distance of sample points in each coordinate dimension in the excitation space and response space as an initial estimate of the feature length scale. Finally, at box 830, computing device 110 uses 0.2 to 0.3 times the initial estimate as the search range for Bayesian optimization and performs global optimization in logarithmic space to obtain the optimal solution. .

[0057] Here, the inventors would like to further clarify that, in some preferred embodiments, this application does not employ random sampling or the conventional LHS (Latin Hypercube Sampling) method to determine the second set of excitation points corresponding to the simulation. Instead, through Figure 9 The specific method shown is as follows: At frame 910, computing device 110 defines the feasible region of excitation coordinates based on the physical dimensions of the hull, by indenting the hull boundary by 8mm-12mm: At frame 920, computing device 110 generates a set of candidate points. The computing device 110 uses the minimum Euclidean distance between sample points as the objective function and generates a preset number of candidate point sets within the feasible region based on the Latin hypercube sampling method. The objective function is: , in, It is the first set of incentive points Each point within, These are the points pre-generated using the Latin hypercube sampling method.

[0058] At frame 930, computing device 110 determines the candidate point set. Does it meet the requirements? ;in, It is a pre-defined set of first stimulus points. Second set of incentive points The minimum constraint distance between all points is used to determine if the condition is met, and then the candidate point set is placed in box 940. Defined as the second set of excitation points If the result is negative, return to the candidate point set generated in box 920. The steps.

[0059] Figure 10 A block diagram schematically illustrates an electronic device 1000 suitable for implementing embodiments of the present disclosure. Device 1000 can be used to implement... Figure 1 The computing device 1000 includes a central processing unit (CPU) 1001, which can perform various appropriate actions and processes according to computer program instructions stored in read-only memory (ROM) 1002 or loaded from storage unit 1008 into random access memory (RAM) 1003. The RAM 1003 may also store various programs and data required for the operation of the device 1000. The CPU 1001, ROM 1002, and RAM 1003 are interconnected via bus 1004. An input / output (I / O) interface 1005 is also connected to bus 1004.

[0060] Multiple components in device 1000 are connected to I / O interface 1005, including: input unit 1006, such as keyboard, mouse, etc.; output unit 1007, such as various types of monitors, speakers, etc.; storage unit 1008, such as disk, optical disk, etc.; and communication unit 1009, such as network card, modem, wireless transceiver, etc. Communication unit 1009 allows device 1000 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0061] Processing unit 1001 executes the various methods and processes described above, such as methods 200 and 800. For example, in some embodiments, methods 200 and 800 may be implemented as computer software programs stored in a machine-readable medium, such as storage unit 1008. In some embodiments, part or all of the computer program may be loaded and / or installed on device 1000 via ROM 1002 and / or communication unit 1009. When the computer program is loaded into RAM 1003 and executed by CPU 1001, one or more operations of methods 200 and 800 described above may be performed. Alternatively, in other embodiments, CPU 1001 may be configured to perform one or more actions of method 100 by any other suitable means (e.g., by means of firmware).

[0062] This disclosure can be a method, apparatus, system, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for performing various aspects of this disclosure.

[0063] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example—but not limited to—electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination of the foregoing. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0064] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0065] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0066] Various aspects of this disclosure are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0067] These computer-readable program instructions can be provided to a processing unit of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processing unit of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner. Thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0068] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0069] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction, which contains one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0070] The various embodiments of this disclosure have been described above. These descriptions are exemplary and not exhaustive, and are not limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical applications, or technical improvements to the technology in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A vibration prediction method for ship hull surfaces based on the Co-Kriging model, wherein, The vibration prediction method includes the following steps: Based on the selected first set of excitation points Acquire response from the first stimulus point set The first high-fidelity response set of real-world incentives from all locations; The response was acquired from the second set of excitation points based on the finite element simulation model. The first low-fidelity response set of the simulation excitation at various locations; A set of frequency response curves is generated based on the first high-fidelity response set and the first low-fidelity response set, and the average spectral shape of all frequency response curves in the set is calculated. and the nth frequency response curve Relative to the average spectral shape bias , Principal component analysis was used to uniformly reduce the dimensionality of the frequency response curves. The reduced dimensionality parameters include the spectral shape basis vector. The scores of the first principal components corresponding to each frequency response curve projected onto the principal component space. and the Low-dimensional characterization of the frequency response curves mentioned above in, in, Principal component order, Based on the first principal component score with order q of the principal component. A kriging model is established, which is characterized by the following formula: in, The predicted principal component score for the predicted point. It is a mean function with constant values. To describe the covariance matrix among training samples, Let X be the input coordinates of the predicted point, and let X be the set of input coordinates between each training sample. The prediction variance for the prediction points; Constructing a Co-Kriging model: The low-fidelity response prediction value corresponding to the first low-fidelity response set is obtained based on the Kriging model. , Solve for the coefficients of the Co-Kriging model: based on low-fidelity response predictions. The first high-fidelity response value is used to calculate the coefficients of the Co-Kriging model according to the following characterization formula to establish the Co-Kriging model: in, It is the scaling factor of the Co-Kriging model. It is global bias and It is a process of smoothing residuals. Reconstructing the target frequency response curve to predict the vibration mode at a new prediction point: After solving for the new excitation point and the new response value at the new excitation point based on the Co-Kriging model, the second principal component score of the reconstructed target frequency response curve is calculated based on the new excitation point, the new response value, and the following formula. To reconstruct the target frequency response curve: in, The reconstructed representation of the first The target frequency response curve.

2. The vibration prediction method according to claim 1, wherein, 2 is selected as the initial value of the candidate value of the principal component order. The Kriging model under different candidate values ​​is constructed in an incremental manner, and the root mean square error based on the validation set is solved. The candidate value when the root mean square error is minimized is defined as the principal component order, wherein the validation set is taken from the first high-fidelity response set.

3. The vibration prediction method according to claim 1, further comprising a first step of modifying the Co-Kriging model, which includes: Based on the model dimensions of the hull, a set of candidate supplementary points is generated within the candidate region. This set of candidate supplementary points is then compared with the first set of excitation points. Second set of incentive points No intersection occurs; The overall posterior variance of the candidate complement set is found iteratively with a predetermined step size. The overall posterior variance is calculated using the following formula: in, The predicted variance on the k-th principal component obtained according to the Kriging model is... It is the prediction variance of the smoothed residual Gaussian process corresponding to the k-th principal component obtained according to the Co-Kriging model; After selecting a target complement set to supplement the first high-fidelity response set, the process returns to the step of solving the coefficients of the Co-Kriging model. In this step, the corresponding total posterior prediction variances in the candidate complement set are sorted from largest to smallest, and the points ranked A positions above the top A are selected as points in the target candidate set, where A is a preset integer.

4. The vibration prediction method according to claim 1 or 3, wherein the vibration prediction method further comprises a second step of modifying the Co-Kriging model, which includes: Based on the Co-Kriging model, the corresponding set of first excitation points is obtained. The high-fidelity predicted response set at each excitation point; Compare the response values ​​of each group in the high-fidelity predicted response set with those of the first high-fidelity response set one by one. When the difference between the corresponding response values ​​reaches the maximum value, record the corresponding distortion point. A third set of excitation points, consisting of at least three excitation points located in different orientations, is added within a predetermined interval of the distortion points. A third low-fidelity response set based on the response at the third set of excitation points is then acquired based on the finite element simulation model. By using a fixed principal component order, the third excitation point set and the third low-fidelity response set are respectively added to the second excitation point set. After the first low-fidelity response set, return to the step of generating a group of frequency response curves based on the first high-fidelity response set and the first low-fidelity response set.

5. The vibration prediction method according to claim 4, wherein, The third high-fidelity response set is projected onto the principal component space with a weight of less than 0.8 and greater than 0.

3.

6. The vibration prediction method according to claim 1, wherein the covariance matrix is ​​determined by the RBF product kernel of the excitation coordinates and the response coordinates, and the RBF product kernel is obtained by the following formula: in, and These represent the known stimulus input samples and the stimulus points to be predicted, respectively. and These represent the known vibration response and the vibration response to be predicted, respectively. and These are the length scales of the excitation plane and the response plane, respectively. The known excitation input samples are derived from the first set of excitation points. and the second set of incentive points It is confirmed that the known vibration response is determined by the set of frequency response curves.

7. The method according to claim 6, wherein the length dimension of the excitation plane is... and the length scale of the response plane Solve using the following steps: The objective function in the form of root mean square prediction error is defined by the following formula: in, This means removing the first... After the nth sample, the target frequency response curve constructed using the remaining samples is used to evaluate the nth sample. Predicted value of the point; Calculate the median Euclidean distance of sample points in each coordinate dimension in the excitation space and response space, and use it as the initial estimate of the feature length scale; Using 0.2 to 0.3 times the initial estimate as the search range for Bayesian optimization, global optimization is performed in logarithmic space to obtain the optimal solution. .

8. The vibration prediction method according to claim 1, wherein, The second set of incentive points is confirmed through the following steps. : Based on the physical dimensions of the hull, a feasible region for the excitation coordinates is defined by indenting the hull boundary by 8mm-12mm: Generate candidate point set With the objective function of maximizing the minimum Euclidean distance between sample points, a predetermined number of candidate point sets are generated within the feasible region based on the Latin hypercube sampling method. The objective function is: ， in, It is the first set of excitation points Each point within, These are the points pre-generated using the Latin hypercube sampling method; Determine the candidate point set Does it meet the following requirements: ； in, It is a preset representation of the first set of excitation points. and the second set of incentive points The minimum constraint distance between all points, If the determination is yes, then the candidate point set is... Defined as the second set of excitation points If the determination is negative, then return to the process of generating the candidate point set. The steps.

9. An electronic device, comprising: At least one processor; as well as A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the vibration prediction method according to any one of claims 1-8.

10. A non-transitory computer-readable storage medium storing computer instructions, characterized in that, The computer instructions are used to cause the computer to execute the vibration prediction method according to any one of claims 1-8.

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