Method for evaluating reliability of underwater movement process of vertically-launched rigid body

Abstract

The invention provides a definite reliability assessment method for an underwater movement process of a vertically-launched rigid body. The method comprises the steps that factors influencing the underwater movement process of the rigid body and key performance parameters influencing the reliability are determined; carrying out regional modeling; determining a feasible spatial domain of environmental factors and emission parameters, and determining experimental points by adopting a Latin hypercube sampling method; the pitch angle deflection and the maximum bending moment corresponding to the experimental point are obtained through finite element simulation software; constructing an underwater motion multi-agent model by taking a simulation result as a sample point; according to the launching position and area modeling, determining an environment factor range; the uncertainty of environmental factors is quantified; a Monte Carlo method is adopted to transmit the uncertainty of environmental factors, and the reliability of pitch angle deflection and the maximum bending moment is obtained. According to the method, environmental factors and emission parameters are comprehensively considered, the uncertainty is quantified through the underwater motion multi-agent model, and a theoretical basis is provided for definite reliability research.

Description

Technical Field

[0001] The present invention relates to the technical field of reliability assessment, and in particular to a method for assessing the reliability of a vertically launched rigid body underwater motion process. Background Art

[0002] Underwater rigid bodies (such as underwater robots, unmanned submersibles, and projectiles) are widely used in various fields, especially in underwater detection, exploration, rescue, and environmental monitoring. They often need to traverse complex ocean environments and complete the process of moving from underwater to underwater. Therefore, how to accurately evaluate the reliability of these rigid bodies during underwater motion has become a core research issue.

[0003] During underwater motion, a rigid body will be affected by a variety of internal and external factors, mainly including the influence of marine environmental factors and initial motion parameters. The underwater environment is highly uncertain, including factors such as water currents, waves, and tides, which will affect the stability and reliability of the moving object. In addition, during underwater motion, the speed and posture of the object are affected by the complex interactions of ocean fluid mechanics. During the underwater motion of a rigid body, especially when the initial posture of the object is vertically upward and includes the process of emerging from the water, the motion process will experience a series of complex physical phenomena involving the interaction between the object and the water body, such as water flow resistance, buoyancy changes, etc. These factors will directly affect the motion state of the rigid body. During the process of emerging from the water, the motion state of the rigid body object will also be disturbed by a variety of factors, including the initial velocity of the object, fluctuations in the marine environment, and underwater launch depth. At the same time, the rigid body also has a limited number of systematic tests during underwater motion, and there is a small sample problem, which makes the reliability modeling and evaluation uncertain. The above characteristics put forward higher requirements for the reliability evaluation of the underwater motion process of rigid bodies.

[0004] However, current reliability assessments for underwater rigid bodies often focus on the influence of a single environmental factor. For rigid body underwater motion involving vertical motion, existing assessment methods often overlook the combined effects of multiple factors in complex underwater environments, such as initial vertical velocity, launch depth, and initial horizontal velocity. The interaction of these factors often creates significant uncertainty in the reliability of the motion process, making it difficult to predict and assess the reliability of rigid body underwater motion. The complex ocean environment and complex cross-media motion processes lead to high uncertainty in underwater motion. As external variables, ocean environmental factors such as waves and currents have a certain degree of dispersion, which leads to random uncertainty in the reliability of underwater motion processes. Therefore, uncertainty quantification is a key issue that needs to be addressed in the reliability assessment of rigid body underwater motion processes. Summary of the Invention

[0005] In order to address the deficiencies of the above-mentioned prior art, the present invention provides a method for confident reliability assessment of the underwater motion process of a vertically launched rigid body. After comprehensively considering the influence of marine environmental factors and initial state on the motion performance, the method constructs a reliability model of the underwater motion process and quantifies its uncertainty, thereby solving the reliability modeling and optimization problems of the underwater motion process and improving the accuracy of the reliability assessment of the underwater motion process of the rigid body.

[0006] The present invention discloses a method for assessing the assured reliability of a vertically launched rigid body during underwater motion. Based on a logical system for solving problems with assured reliability, the method employs steps such as constructing a performance model, quantifying uncertainty, and constructing margin equations and metric equations. Specifically, the method includes the following steps:

[0007] S1: Determine the factors that affect the underwater motion process of rigid bodies and the key performance parameters that affect reliability;

[0008] Determine the environmental factors and launch parameters that affect the underwater motion of the rigid body. Environmental factors include significant wave height A, wind speed v wind and ocean current velocity v ocean , environmental factors are expressed as Y = {A,v wind ,v ocean}; The launch parameters include horizontal speed v os , vertical speed v ls and launch depth h, the launch parameters are expressed as X = {h,v ls ,v os The key performance parameters affecting reliability are determined to be the pitch angle deflection of the rigid body at the time of emergence and the maximum bending moment of the rigid body during underwater movement.

[0009] S2: Conduct regional modeling;

[0010] S3: Determine the feasible space domain of environmental factors and emission parameters, and use the Latin hypercube sampling method to determine N experimental points;

[0011] S4: Based on the determined N experimental points, the pitch angle deflection and maximum bending moment corresponding to the N experimental points are obtained by finite element simulation software;

[0012] S5: Using the results of N simulations as sample points, a multi-agent model of underwater motion is constructed, and the agent model is used as a performance model;

[0013] The underwater motion multi-agent model assigns weight factors according to the accuracy of each agent model; it is constructed by linearly weighted combination of multiple agent models;

[0014] S6: Determine the scope of environmental factors based on the launch location and area modeling;

[0015] S7: Quantifying the uncertainty of environmental factors during the underwater motion of rigid bodies.

[0016] S8: The Monte Carlo method is used to transfer the uncertainty of environmental factors in S7, and the margin equation and measurement equation are constructed to obtain the reliability of pitch angle deflection and maximum bending moment, which are used to evaluate the reliability of the rigid body underwater motion process.

[0017] Preferably, S5 uses the results of N simulations as sample points to construct an underwater motion multi-agent model as follows:

[0018] The underwater motion multi-agent model is constructed by linearly weighted combination of multiple agent models, and the weight factor is assigned according to the accuracy of each model. The expression is:

[0019]

[0020] Where F(X,Y) represents the underwater motion performance model, P is the number of proxy models, and f j (X,Y) represents the jth surrogate model, ω j Respectively represent their corresponding weight factors, and the weight factors need to satisfy the condition that they add up to 1;

[0021] Preferably, the weight factors of each proxy model are:

[0022]

[0023] Where, E j represents the global error of the j-th surrogate model, ω i It represents the weight factor corresponding to the i-th model, and the root mean square error is used as the global error of the proxy model. The cross-validation method is used to obtain the root mean square error.

[0024] Preferably, the underwater motion multi-agent model is composed of a Gaussian process regression model, a radial basis function model, and a support vector regression model, with a total of 6-dimensional inputs, including three-dimensional environmental factors and three-dimensional launch parameters. The three-dimensional environmental factors are significant wave height, wind speed, and ocean current velocity, and the three-dimensional launch parameters are horizontal velocity v os , vertical speed v ls and launch depth h, with a total of two-dimensional outputs, namely pitch angle deflection and maximum bending moment.

[0025] Preferably, S2 performs regional modeling specifically as follows: regional modeling is achieved by clustering environmental factors, the environmental factors are obtained through ocean hydrological data, and the obtained ocean hydrological data is preprocessed and then the ST-DBSCAN algorithm is used to cluster the environmental factors.

[0026] Preferably, the models enabled in the finite element simulation include a multiphase flow model, a turbulence model, an overlapping grid, a DFBI method, a VOF multiphase flow model and a gravity model.

[0027] Preferably, S7 quantifies the uncertainty of environmental factors in the water area during the underwater movement of a rigid body as follows: after statistically analyzing the data of effective wave height, wind speed and ocean current velocity based on the environmental factors of a specified ocean area and time period, a frequency distribution or probability density function of effective wave height, wind speed and ocean current velocity is constructed, the probability density function of effective wave height is described by Rayleigh distribution, the probability density function of wind speed is described by Weibull distribution or normal distribution, and the probability density function of ocean current velocity is described by Weibull distribution, lognormal distribution or gamma distribution.

[0028] Preferably, S8 uses the Monte Carlo method to transfer the uncertainty of the environmental factors in S7, constructs the margin equation and the metric equation, and obtains the reliability of the pitch angle deflection and the maximum bending moment, which are used to evaluate the reliability of the rigid body underwater motion process, specifically:

[0029] According to the target values ​​of the pitch angle deflection and the maximum bending moment of the rigid body during underwater motion, the margin equation and measurement equation of the pitch angle deflection and the maximum bending moment are constructed.

[0030] According to the requirements of the Monte Carlo method, the probability density function of the environmental factors in S7 is sampled to obtain the environmental factors, and the sampled environmental factors and the launch parameters are combined to generate the input data set of the underwater motion multi-agent model.

[0031] Input the input data set into the underwater motion multi-agent model to obtain the predicted result data set of the rigid body's pitch angle deflection at the time of exiting the water and the maximum bending moment of the rigid body during underwater motion;

[0032] According to the prediction result data set, the probability density functions of the pitch angle deflection of the rigid body at the moment of emergence and the maximum bending moment of the rigid body during underwater movement are obtained.

[0033] According to the probability density functions of the pitch angle deflection and the maximum bending moment, as well as the target pitch angle deflection and the target maximum bending moment, combined with the measurement equations of the pitch angle deflection and the maximum bending moment, the reliability of the target pitch angle deflection and the target maximum bending moment is obtained.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] 1. Based on the theory of certainty reliability, the present invention comprehensively considers the complex influences of water environment factors and launch strategy parameters, constructs a reliability model for the underwater motion process, and quantitatively analyzes the uncertainty of the motion process. Compared with traditional theoretical research, the present invention has a wider applicability, and can simultaneously consider the multi-factor coupling of the marine environment and the initial state of the rigid body, avoiding the one-sided analysis of a single factor in traditional methods, thereby providing a more comprehensive theoretical basis for the reliability research of the underwater motion process of the rigid body. Compared with experimental research, the present invention significantly reduces the experimental cost and cycle by establishing a simulation model, avoids the problem of difficult reproduction of complex sea conditions in the experiment, and can more efficiently explore the influence of the initial state of the rigid body on reliability.

[0036] 2. The underwater motion performance model of this invention utilizes a multi-proxy model approach. By fusing the prediction results of multiple proxy models, this diversity can be effectively utilized to offset the shortcomings of a single model, integrating the strengths of different models and reducing the uncertainty of the performance model during underwater motion of a rigid body. The weighted combination of the prediction means and uncertainties (variances) provided by each model can better reflect the overall trends of the data while reducing the potential for overly pessimistic or optimistic predictions from individual models.

[0037] 3. In addition, the confidence reliability modeling method proposed in the present invention can provide a scientific basis for the optimization of launch strategies in the underwater rigid body launch process, and provide methodological support for the design of launch schemes under different scenarios and reliability requirements. It has important engineering application value for improving the reliability of the underwater rigid body launch process. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Flowchart of a method for evaluating the reliability of a vertically launched rigid body underwater motion process according to the present invention;

[0039] FIG2( a ) shows the wind field distribution in the Bohai Sea region according to an embodiment of the present invention;

[0040] FIG2( b ) is a clustering result of wind farms in the Bohai Sea region according to an embodiment of the present invention;

[0041] FIG3( a ) is a diagram showing the significant wave height field distribution in the Bohai Sea region according to an embodiment of the present invention;

[0042] FIG3( b ) is a clustering result of significant wave height in the Bohai Sea region according to an embodiment of the present invention;

[0043] FIG4( a ) is a diagram showing the distribution of ocean current velocity in the Bohai Sea region according to an embodiment of the present invention;

[0044] FIG4( b ) is a clustering result of ocean current velocity in the Bohai Sea region according to an embodiment of the present invention;

[0045] FIG5( a ) is a schematic diagram of Latin hypercube sampling results of environmental factors according to an embodiment of the present invention;

[0046] FIG5( b ) is a schematic diagram of a Latin hypercube sampling result of a transmission parameter according to an embodiment of the present invention;

[0047] FIG6( a ) is an example of underwater rigid body modeling parameters according to an embodiment of the present invention;

[0048] FIG6( b ) is an example of water area modeling according to an embodiment of the present invention;

[0049] FIG7( a ) is an example of overlapping grids according to an embodiment of the present invention;

[0050] FIG7( b ) is an example of a wave diagram according to an embodiment of the present invention;

[0051] Figure 8 is a schematic diagram of the posture of an underwater rigid body at different times during a certain simulation according to an embodiment of the present invention;

[0052] FIG9( a ) is a pitch angle deflection response surface related to ocean current velocity and launch depth according to an embodiment of the present invention;

[0053] FIG9( b ) is a pitch angle deflection response surface related to wind speed and horizontal speed according to an embodiment of the present invention;

[0054] FIG9( c ) is a pitch angle deflection response surface related to significant wave height and vertical velocity according to an embodiment of the present invention;

[0055] FIG9( d ) is a maximum bending moment response surface related to ocean current velocity and launch depth according to an embodiment of the present invention;

[0056] FIG9( e ) is a maximum bending moment response surface related to wind speed and horizontal speed according to an embodiment of the present invention;

[0057] FIG9( f ) is a maximum bending moment response surface related to significant wave height and vertical velocity according to an embodiment of the present invention;

[0058] Figure 10 is a wind speed distribution fitting diagram in the area of ​​(118°E, 39.8°N) generated according to an embodiment of the present invention;

[0059] Figure 11 is a fitting diagram of significant wave height distribution in the area (118°E, 39.8°N) generated according to an embodiment of the present invention;

[0060] Figure 12 is a fitting diagram of the ocean current velocity distribution in the area of ​​(118°E, 39.8°N) generated according to an embodiment of the present invention;

[0061] FIG13( a ) is a diagram showing the reliability evaluation results of the pitch angle deflection under certain transmission parameters according to an embodiment of the present invention;

[0062] FIG13( b ) is a diagram showing the reliability evaluation results of the maximum bending moment under certain launch parameters according to an embodiment of the present invention. DETAILED DESCRIPTION

[0063] The exemplary embodiments, features and aspects of the present invention will be described in detail below with reference to the accompanying drawings. Although various parameter values ​​and aspects of the embodiments are shown in the embodiments, unless otherwise specified, the evaluation process does not necessarily need to be completed with exactly the same parameters and aspects.

[0064] In the following, a rigid body is used as a cannonball, and it is fired in the Bohai Sea area as an example. The reliability evaluation method of the underwater motion process of a vertically launched rigid body of the present invention is used to evaluate the reliability of the underwater motion process of the cannonball. Figure 1 The following steps are shown:

[0065] S1: Determine the factors that affect the underwater motion of rigid bodies and the key performance parameters that affect reliability

[0066] The external factors that affect the underwater motion of rigid bodies are mainly environmental factors of the water area, including effective wave height A, wind speed v wind and ocean current velocity v ocean , environmental factors are expressed as Y = {A,v wind ,v ocean}; It is determined that the internal factors affecting the underwater motion of the rigid body are mainly the launch parameters, including the horizontal velocity v os , vertical speed v ls and launch depth h, the launch parameters are expressed as X = {h,v ls ,v os Environmental factors can be obtained by spatiotemporal clustering of ocean hydrological data at different locations and times, and the launch parameters determine the initial state of the rigid body.

[0067] The key performance parameters affecting reliability are determined to be the pitch angle deflection of the rigid body at the moment of emergence from the water and the maximum bending moment of the rigid body during underwater movement. The pitch angle deflection is the key performance parameter describing the posture of the rigid body, and the maximum bending moment is the key performance parameter describing the load of the rigid body.

[0068] The specific reasons for selecting the above variables as environmental factors, emission parameters and key performance parameters are as follows:

[0069] Wave height affects the amplitude of wave forces, which in turn has a direct impact on the pitch and deflection of a rigid body. Therefore, effective wave height is selected as one of the environmental factors affecting the underwater motion of a rigid body. The influence of wind on a rigid body is primarily reflected in the phase from the head of the body out of the water to the complete out of the water, primarily due to the influence of wind direction and speed. However, the influence of wind direction on the rigid body can be reduced by adjusting the launcher's direction during launch. However, when the underwater rigid body is mostly in the air, the main environmental force changes from hydrodynamics to aerodynamics. Wind speed is a significant factor influencing aerodynamics, resulting in significant changes in pitch and deflection. Therefore, wind speed is selected as one of the environmental factors affecting the underwater motion of a rigid body. The influence of ocean currents on the underwater motion and out of the water phase of a rigid body can be considered as adding a constant interference in a certain direction. Therefore, ocean current velocity is also considered as one of the environmental factors affecting the underwater motion of a rigid body.

[0070] Different initial states of a rigid body affect the pitch deflection and maximum bending moment of an underwater rigid body. The initial state of the rigid body is determined by the launch parameters. The launcher is usually not stationary, so the rigid body will carry the launcher's horizontal velocity component after being released from the launcher, making the rigid body's initial trajectory non-vertical and having a lateral offset. The launch depth also greatly affects the rigid body's motion process. At a shallow launch depth, the rigid body can escape the water surface faster, but it is more susceptible to the effects of waves. At a deeper launch depth, the rigid body must overcome more water resistance, which may result in excessive pitch deflection or even failure to emerge from the water. The initial velocity of the rigid body after leaving the launcher affects the rigid body's motion time in the water. Since water resistance is highly correlated with the rigid body's velocity, an excessively high initial velocity may damage the rigid body's structure. Therefore, the launch depth, the vertical velocity at launch, and the horizontal velocity of the launcher are selected to describe the launch parameters.

[0071] A key factor affecting the reliability of a rigid body's underwater motion is its posture at the moment of emerging from the water. The roll angle, pitch angle, and heading angle are usually used to describe the complete posture of the rigid body. Since the present invention only considers that the rigid body is launched vertically from the launcher, it is believed that its initial motion direction is perpendicular to the water surface. Therefore, the heading angle is not considered when it is in the water; and the rigid body can control the roll angle through a rudder or a balance wing to keep itself in a stable posture, so the roll angle does not need to be considered. However, the deflection of the pitch angle (that is, the degree of deviation between the actual pitch angle at the moment of emerging from the water and the ideal vertical reference) directly determines the initial flight posture and trajectory evolution of the rigid body after entering the air environment. If the pitch angle deflection exceeds the threshold, it may cause an imbalance in the distribution of aerodynamic loads, causing trajectory deviation or even instability. Therefore, the present invention ultimately selects pitch angle deflection as one of the key performance parameters affecting reliability. In addition, the maximum load on a rigid body during underwater movement may cause deformation or damage to its structure. Stress concentration under high load will cause fatigue failure of the rigid body's material, affecting the reliability of the rigid body during underwater movement. The maximum load on a rigid body can be described by the maximum bending moment, so the maximum bending moment is also regarded as one of the key performance parameters affecting reliability.

[0072] S2: Perform regional modeling

[0073] Regional modeling is achieved by clustering environmental factors. This clustering divides the region into several sub-regions. The environmental factors in each sub-region are similar, forming an environmental model for each sub-region, preparing for subsequent finite element simulation and quantification of environmental factor uncertainties.

[0074] Environmental factors are derived from oceanographic data, but using this data directly results in high computational complexity and makes it difficult to capture key environmental patterns. Regional modeling allows for intuitive understanding of the differences in environmental factors across subregions, allowing for the identification of environmental patterns within each subregion. For example, based on wind speed and significant wave height, subregions with environmental characteristics such as "low wind speed-low wave height" and "high wind speed-high wave height" can be identified, simplifying finite element simulations. Furthermore, clustering allows for understanding the range of environmental factors within each subregion, simplifying the quantification of environmental uncertainty.

[0075] Ocean hydrological data has obvious spatiotemporal characteristics and strong spatiotemporal correlation, and belongs to spatiotemporal data. Spatiotemporal data refers to data that contains both time information and spatial information at a specific time and place, and has the characteristics of multidimensionality, multi-scale, massiveness and dynamic correlation. The data sources used in the present invention are: ERA5h and global ocean physical ensemble reanalysis data. The acquired ocean hydrological data are preprocessed, and the main task of the preprocessing is to eliminate and repair missing data, and then the ST-DBSCAN algorithm (Space-Time Density-Based Spatial Clustering of Applications with Noise) is used to realize the clustering of environmental factors. The regional modeling in the present invention includes the clustering of effective wave height, wind speed and ocean current velocity in the specified area.

[0076] Taking the firing of artillery shells in the Bohai Sea as an example, the clustering method is used to obtain the effective wave height A and wind speed v in the current time period. wind and ocean current velocity v ocean . In this embodiment, the database uses ERA5 and global ocean physical ensemble reanalysis data. The ERA5 dataset provides high temporal and spatial resolution global meteorological and climate data from 1950 to the present by combining observational data with numerical weather prediction models, with a spatial resolution of 31 kilometers (about 0.25°×0.25°) and a temporal resolution of every hour. Global Ocean Physical Ensemble Reanalysis Data (Global_SMULTIYEAR-PHY-INs_001_031), developed by the European Copernicus Marine Agency, is used to provide a high-quality three-dimensional grid description of the physical state of the global ocean. This dataset combines numerical models with satellite and in-situ observation data, and generates estimates of variables such as monthly average temperature, salinity, ocean currents, and sea ice since 1993 through data assimilation techniques.

[0077] Download the wind speed and significant wave height datasets for the Bohai Sea region from 2010 to 2020 using the API from the ERA5 dataset official website. The significant wave height dataset has a temporal resolution of one hour and a spatial resolution of 0.5°×0.5°. The wind speed dataset in the ERA5 dataset has a temporal resolution of one hour and a vector u of the east-west wind speed at a height of 10 meters. 10 and the north-south wind speed v at a height of 10 meters 10 The spatial resolution is 0.25°×0.25°, and the wind speed at a height of 10 meters is:

[0078]

[0079] Wind speeds in the Bohai Sea region for January were regionalized using the spatiotemporal clustering ST-DBSCAN algorithm. Figure 2(a) below shows the wind field distribution in the Bohai Sea region, while Figure 2(b) shows the wind speed clustering results. The clustering results divide the Bohai Sea data into five categories, which generally align with the wind field distribution, demonstrating the effectiveness of the algorithm.

[0080] The ERA5 dataset shows significant wave heights in the Bohai Sea region concentrated between longitudes 117°E-140°E and latitudes 30°N-41°N. Using the spatiotemporal clustering ST-DBSCAN algorithm, the significant wave height field distribution and clustering results are shown in Figures 3(a) and 3(b). The clustering results for significant wave heights in the Bohai Sea region contain some noise points. This is primarily due to the relatively limited significant wave height data for the Bohai Sea region in the ERA5 dataset, the high number of regions far from the coast, and the high wind speeds in January. Deep sea areas far from the coast lack the barrier effect of coastal topography, resulting in large fluctuations.

[0081] A dataset of ocean current velocities for the Bohai Sea region with a launch depth of 0-50 m from 2011 to 2020 was downloaded in batches using the Global Ocean Physics Ensemble Reanalysis Data API. The dataset has a spatial resolution of 0.25° × 0.25° and a daily temporal resolution. Using the spatiotemporal clustering ST-DBSCAN algorithm, the velocity data at launch depth 0 were used to divide the region into regions. The distribution of the current velocity field and the clustering results are shown in Figures 4(a) and 4(b). Based on the clustering results, the ocean region has only one cluster (other regions have no data and the colors have no practical meaning). Statistical analysis of the ocean current data in the dataset reveals a relatively concentrated distribution of current velocities, with most data points ranging from 0.007 m / s to 0.5 m / s, and a standard deviation of 0.087 m / s. This indicates that the data are mostly distributed around a mean value of 0.154 m / s, with little variance and an overly uniform distribution. Therefore, the ocean currents in the Bohai Sea can be described by a single distribution, and the clustering results are consistent with the actual situation.

[0082] S3: Determine the feasible space domain of environmental factors and emission parameters, and use the Latin hypercube sampling method to determine N experimental points;

[0083] According to the collected actual data and existing numerical simulation cases, the value ranges of environmental factors are determined as follows: significant wave height A: [0.1m, 2m], wind speed value range v wind :[0m / s,13.8m / s], ocean current velocity v ocean :[0m / s,5m / s]; the range of launch parameters is: launch depth h:[10m,30m]; vertical speed v ls :[15m / s,25m / s]; horizontal speed v os:[0.5144m / s,3.08664m / s].

[0084] Wind speed and significant wave height are important indicators of different sea state levels, and there is obviously a certain correlation between the two. In this patent, the PM (Pierson-Moskowitz) spectrum is used to constrain the relationship between wind speed and significant wave height. The relationship between significant wave height and wind speed can be expressed as:

[0085]

[0086] Here, c1 is a constant that can be determined empirically.

[0087] At the same time, certain restrictions are placed on the launch depth and vertical speed, and a simple linear relationship limit is set for the vertical speed and launch depth to avoid the situation where the aircraft cannot get out of the water.

[0088] The present invention uses Latin Hypercube Sampling (LHS) to achieve effective coverage of the sampling space with minimal computational effort. In this embodiment, the results of the LHS sampling of environmental factors are shown in Figure 5(a), and the results of the LHS sampling of transmission parameters are shown in Figure 5(b).

[0089] According to the sampling results, N experimental points are determined, where N is a positive integer. In this embodiment, 70 experimental points are selected for finite element simulation.

[0090] S4: Based on the determined N experimental points, the pitch angle deflection and maximum bending moment are obtained through finite element simulation software

[0091] Based on the determined experimental points, the environmental factors and launch parameters for each experimental point are input into the finite element simulation software. After each finite element simulation, the pitch angle deflection of the rigid body when it is completely out of the water, as well as the maximum bending moment experienced by the rigid body throughout the entire process, are recorded. Models enabled in the finite element simulation may include multiphase flow models, turbulence models, overset meshes and DFBI methods, VOF multiphase flow models, gravity, and more. The finite element simulation software can be implemented using existing software such as STAR-CCM and COMSOL Multiphysics.

[0092] Assume that the diameter of a certain type of shell is d = 200 mm and the length is l total =1m, mass m missile= 36 kg. Since a blunter head shape reduces drag when a rigid body moves underwater, a blunter head shape was used for modeling. An overlapping region was created around it to prepare for subsequent overlapping meshing. The parameters for the rigid body and overlapping region are shown in Figure 6(a). The rigid body and overlapping region were imported into finite element simulation software, and a water model was created based on the launch depth. Figure 6(b) shows the water modeling for a launch depth of 10 m.

[0093] When the projectile is underwater, the surrounding mesh is densified using a prismatic layer. The mesh is also densified for the water surface and the portion of the mesh where the rigid body moves underwater. The resulting mesh is shown in Figure 7(a). Environmental factors that affect the underwater motion of a rigid body include significant wave height, so a fifth-order wave is selected for the VOF wave. The resulting wave surface is shown in Figure 7(b).

[0094] In the simulation software, select the settings of 3D model, implicit unsteady state, multiphase flow, volume of fluid (VOF), turbulence, VOF wave, and gravity to simulate. Figure 8 The environmental factors are shown as significant wave height A = 1m, wind speed v wind =5m / s, ocean current velocity v ocean =5m / s, launch depth h=10m, vertical speed v ls =20m / s, horizontal speed v os =3 knots, the posture of the rigid body at different synchronous frequencies during the simulation process.

[0095] S5: Using the results of N simulations as sample points, construct a multi-agent model for underwater motion and use the agent model as a performance model.

[0096] The underwater motion multi-agent model has a total of 6-dimensional inputs, including 3D environmental factors and 3D launch parameters. The 3D environmental factors are significant wave height, wind speed and ocean current velocity, and the 3D launch parameters are horizontal velocity v os , vertical speed v ls and launch depth h, with a total of two-dimensional outputs, namely pitch angle deflection and maximum bending moment.

[0097] Since each time a finite element simulation software is used to simulate the underwater motion process of a rigid body to obtain the pitch angle deflection and maximum bending moment, it takes a lot of computing time. Therefore, this patent constructs a proxy model and uses the proxy model as a performance model to approximately simulate the input and output responses of the rigid body underwater motion process, thereby replacing the time-consuming simulation model. According to the characteristics of the rigid body underwater motion process with high data point dimension, strong nonlinearity and few sample points, the underwater motion multi-proxy model of the present invention selects Gaussian process regression, radial basis function network and support vector machine methods for modeling, specifically:

[0098] S51: Building a Gaussian Process Regression (GPR) Model

[0099] Gaussian process regression (GPR) is a method that uses Gaussian process to perform regression analysis on data. Its core idea is to use the Gaussian process model to predict the output of unknown points based on existing training data. Assume that the training data set consists of n pairs of input-output {(x i ,y(x i )), i=1,2,…,n}, and there is noise ε, then the Gaussian process regression model is as follows:

[0100]

[0101] in, The mean is 0 and the variance is The normally distributed noise term is is the true value of the output, m(x) is the mean function, k(x,x′) is the covariance function (also called the kernel function), and GP() is the Gaussian process.

[0102] Gaussian process regression can be used to process small amounts of data and performs well on small data sets because it is a Bayesian method that can make inferences based on the joint distribution of prior information and observed data. It can be used for nonlinear modeling. By selecting a suitable kernel function (such as the RBF kernel), GPR can effectively handle nonlinear relationships. In addition, GPR can be used for uncertainty estimation, providing not only predicted values ​​but also predicted uncertainties, which is obviously particularly important in high-dimensional problems.

[0103] The basic steps of constructing the GPR model of the present invention are as follows:

[0104] (1) Import n sample data with 6-dimensional input and 2-dimensional output and perform normalization as training data;

[0105] (2) Using the product of the constant kernel and the RBF kernel (radial basis function kernel) as the kernel function of Gaussian process regression;

[0106] (3) Establish a Gaussian process regression model, set the number of restart optimizations and the noise variance;

[0107] (4) Use the standardized training data to train and fit the Gaussian process regression model;

[0108] (5) Standardize the new data and use the trained model to make predictions, return the predicted value and standard deviation, and finally reverse the normalization to restore the predicted result;

[0109] (6) Calculate the mean square error of the Gaussian process regression model on the training data and evaluate the model performance.

[0110] S52: Building a Radial Basis Function (RBF) Model

[0111] The RBF model has relatively few parameters and is less prone to overfitting, so it performs well on small data sets. By selecting appropriate radial basis functions and parameters, high fitting accuracy can be achieved on small data sets. However, in actual modeling, it should be noted that the performance of the RBF model is sensitive to the choice of radial basis functions and parameters (such as center position and width), requiring appropriate parameter tuning.

[0112] Assuming that the number of sample points is n, the expression of the RBF proxy model can be written as:

[0113]

[0114] in, and δ i is the weight coefficient, φ(r i ) is the radial function, r i =||xx i || is the Euclidean distance between the test point and the sample point, where x is the test point, x j is the sample point.

[0115] The present invention adopts the following steps to construct the radial basis function model using the regression method:

[0116] (1) Import n sample data with 6-dimensional input and 2-dimensional output and perform normalization as training data;

[0117] (2) Selecting an RBF kernel function (such as a Gaussian function) and defining the kernel function parameters, including bandwidth parameter, length scale, signal variance, anisotropy parameter, and other core parameters; using the Kernel Ridge Regression algorithm to construct a radial basis function model using the radial basis function as the kernel function;

[0118] (3) Use the standardized training data to train and fit the radial basis function model;

[0119] (4) Standardize the new data and use the trained radial basis function model to make predictions, return the predicted value and standard deviation, and finally reverse the normalization to restore the predicted result;

[0120] (5) Calculate the mean square error of the radial basis function model on the training data and evaluate the model performance.

[0121] S53: Building a Support Vector Regression (SVR) Model

[0122] The Support Vector Regression (SVR) model is a method that applies an extended support vector machine to regression problems. SVR has the ability to handle high-dimensional data and nonlinear relationships, and can avoid overfitting through the principle of structured risk minimization.

[0123] The objective function of SVR can be expressed as

[0124]

[0125] The constraints are

[0126]

[0127] Among them, w is the weight vector; b is the bias; ò is the width of the insensitive interval; ξ i and is a slack variable, which indicates the allowed deviation; C is a regularization parameter used to control the trade-off between model complexity and training error, and n is the number of sample points.

[0128] The basic steps of constructing a surrogate model algorithm using support vector regression are as follows:

[0129] (1) Import n sample data with 6-dimensional input and 2-dimensional output and perform normalization as training data;

[0130] (2) Select an appropriate kernel function (such as RBF kernel) and define the parameters of the SVR model, including the regularization parameter and the interval band width;

[0131] (3) Use the training data to train and fit two SVR models separately; because two outputs are required, two SVR models are used to output them separately.

[0132] (4) Standardize the new data and use the two trained SVR models to make predictions, return the predicted value and standard deviation, and finally reverse the normalization to restore the predicted results;

[0133] (5) Calculate the mean square error of the SVR model on the training data and evaluate the model performance.

[0134] The SVR method can map data into a high-dimensional space using kernel methods to handle complex nonlinear relationships. It can also be applied to small data sets by maximizing the margin and using a small number of support vectors for modeling. By selecting appropriate kernel functions and regularization parameters, the model's generalization capabilities can be effectively controlled to avoid overfitting. Therefore, the SVR model's ability to handle high-dimensional data, its applicability to small data sets, and its advantages in controlling generalization make it well suited to the high-dimensional, nonlinear, and small-dataset characteristics of underwater motion performance models.

[0135] S54: Building a multi-agent model for underwater motion

[0136] The underwater motion multi-agent model is constructed by linearly weighted combination of multiple agent models. The weight factor is assigned according to the accuracy of each agent model. Its mathematical expression can be written as:

[0137]

[0138] Where F(X,Y) represents the underwater motion performance model, P is the number of proxy models, and f j (X,Y) represents the jth surrogate model, ω j In this embodiment, three proxy models are used, so P=3, f1(X, Y) represents the use of the GPR model, f2(X, Y) represents the use of the RBF model, and f3(X, Y) represents the use of the SVR model.

[0139] Among them, the weight factor ω in the above equation is j The following conditions need to be met:

[0140]

[0141] This paper uses root mean square error (RMS) as a global accuracy evaluation criterion to calculate weighting factors. To reduce computational complexity, a cross-validation method is used to obtain the RMS error, which is used as the global measurement error. The cross-validation method divides the sample set into a training set and a validation set. The model is trained on the training set, and the RMS error is calculated on the validation set.

[0142] The global measurement error formula of the jth model is:

[0143]

[0144] In the formula, q represents the number of samples in the validation set, represents the actual value of the pth sample in the validation set of the jth model, represents the predicted value of the p-th sample in the validation set of the j-th model.

[0145] Based on the global measurement error, the weight factor of each model is calculated using the following formula:

[0146]

[0147] Where, E j represents the global error of the j-th surrogate model, ω j Represents the weight factor corresponding to the j-th model.

[0148] The basic process of building an underwater motion performance model is as follows:

[0149] (1) Divide the overall sample data into k * subsample data sets, each subsample data set contains q samples; k * and q are both positive integers;

[0150] (2) Construct Gaussian process regression model, radial basis function model and support vector regression model according to S41-S43;

[0151] (3) Each single subsample dataset is used as a validation sample set, and the rest of the sample space sets are used as training sample sets;

[0152] (4) training Gaussian process regression model, radial basis function model and support vector regression model respectively;

[0153] (5) Repeat steps (3)-(4) k * After that, the root mean square error is obtained by taking the average;

[0154] (6) Calculate model weights based on the root mean square error;

[0155] (7) The prediction results of each model are weighted and combined according to the model weights, and the combined prediction results are output.

[0156] Using 70 experimental points obtained through Latin hypercube sampling as sample points, a finite element model was established. Using numerical simulation methods for underwater launch processes, a turbulence model, overlapping grids, DFBI, and fifth-order VOF waves were set. Using linear thrust, software was used to simulate the underwater motion of a rigid body under different environmental factors and launch parameters. The pitch angle deflection and maximum bending moment of the rigid body were calculated for each of the 70 experimental points. The algorithmic process for constructing proxy models was based on the GPR, RBF, and SVR methods. Three proxy models of the underwater motion multi-proxy model were trained based on the 70 sample points from the numerical simulation.

[0157] Based on the root mean square error and K-fold validation method, the weights of the three proxy models are calculated as follows: GPR weight is 0.2693, RBF weight is 0.3924, and SVR weight is 0.3383. The proxy model is used as the performance model of underwater motion, and the underwater motion multi-agent model is constructed using the weight-based multi-agent model. Due to the nonlinear characteristics of the underwater motion multi-agent model of pitch angle deflection and maximum bending moment during underwater vertical launch, its physical expression cannot be written directly. Here, the two performance models are visualized by drawing the response surface. The results are shown as follows: Figure 9(a)-Figure 9(f) shown.

[0158] S6: Model the launch location and area to determine the scope of environmental factors

[0159] According to the launch position of the rigid body, Y={A,v wind ,v ocean} value range.

[0160] In this embodiment, the longitude and latitude of the location where the shell is launched is (118°E, 39.8°N); in the regional modeling of S2, the environmental factor Y1 of the location is directly obtained according to the longitude and latitude (118°E, 39.8°N) = {A, v wind ,v ocean The value range of} is: significant wave height is distributed between 0.18 and 1.38 m, wind speed is distributed between 0 and 10.5 m / s, and current velocity is distributed between 0.007 m / s and 0.5 m / s.

[0161] S7: Quantify the uncertainty of environmental factors in the water during the underwater motion of a rigid body.

[0162] The purpose of deterministic quantification is to obtain the distribution of parameters with uncertainty. The present invention adopts the following process to quantify the significant wave height A, wind speed v in environmental factors wind and ocean current velocity v ocean uncertainty.

[0163] According to the environmental factors of the specified ocean area and time period, the data of significant wave height, wind speed and ocean current velocity are statistically analyzed, and the frequency distribution or probability density function of significant wave height, wind speed and ocean current velocity is constructed. Finally, the significant wave height, wind speed and ocean current velocity are fitted within the value range of the environmental factors, and an appropriate statistical model (such as Rayleigh distribution, Weibull distribution, etc.) is selected to describe the distribution characteristics and estimate the distribution parameters. Specifically,

[0164] Significant wave height is usually defined as the average height of the highest one-third of waves. Significant wave height can be described using either a Rayleigh distribution or a Weibull distribution. In this embodiment, the Rayleigh distribution is preferably used to describe the wave height data, and its probability density function (PDF) is:

[0165]

[0166] Here, c is the shape parameter.

[0167] The statistical distribution model of wind speed can adopt Weibull distribution or normal distribution. In this embodiment, the wind speed mainly adopts Weibull distribution, but for the wind speed distribution in some areas, especially in the case of medium wind speed, normal distribution can also well describe the wind speed data.

[0168] When the wind speed adopts Weibull distribution, its probability density function is:

[0169]

[0170] Where c is the shape parameter and λ is the scale parameter.

[0171] When the wind speed adopts a normal distribution, its probability density function is:

[0172]

[0173] Where μ′ represents the mean and σ′ represents the variance.

[0174] The statistical distribution model of ocean current velocity can adopt Weibull distribution, lognormal distribution or gamma distribution, etc. In this embodiment, gamma distribution is preferably used to describe ocean current velocity, and its probability density function is:

[0175]

[0176] Where c is the shape parameter and λ is the scale parameter.

[0177] This step selects a location in the Bohai Sea as a case study. The Bohai Sea region model has already been completed in S2. We perform statistical analysis on the datasets for sea breeze speed, current velocity, and significant wave height for this location. We construct frequency distributions and probability density functions for the three marine environmental factors and fit their distributions. Based on the characteristics of the data and past experience, we select appropriate statistical models to describe the distribution characteristics of the three environmental factors and estimate their distribution parameters.

[0178] Assume that a rigid body needs to be launched at the latitude and longitude of (118°E, 39.8°N) in January. Statistical analysis is performed on the January data for the area where this location is located. The frequency distribution and probability density functions of wind speed, significant wave height, and ocean current speed in this area are constructed and fitted, and the uncertainty of the environmental factors of this mission is quantified.

[0179] For the wind speed in this area, its frequency distribution histogram is obtained and fitted using Weibull distribution and normal distribution, as shown in Figure 10 shown.

[0180] Finally, the Weibull distribution is selected and its distribution parameters are estimated. Finally, the wind speed f in the area is wind (x) distribution expression:

[0181]

[0182] Since the amount of significant wave height data at point (118°E, 39.8°N) is very small and cannot be statistically analyzed, the significant wave height at this location is fitted using the area at longitude and latitude (119.4°E, 39.6°N). For the significant wave height in this area, the frequency distribution histogram is established by statistically analyzing the ERA5 data set, and Rayleigh distribution fitting is performed, as shown in the following example: Figure 11 shown.

[0183] Finally, the Rayleigh distribution is selected and its distribution parameters are estimated. Finally, the effective wave height f in the area is A The expression of (x) distribution is:

[0184]

[0185] For the ocean current velocity in this area, the frequency distribution histogram is established by statistically analyzing the global ocean physics ensemble reanalysis data set, and the Gamma distribution is fitted, such as Figure 12 shown.

[0186] Finally, the Gamma distribution is selected and its distribution parameters are estimated. Finally, the ocean current velocity f in the area is ocean The expression of (x) distribution is:

[0187]

[0188] S8: The Monte Carlo method is used to transfer the uncertainty of environmental factors in S7, construct margin equations and measurement equations, and obtain the reliability of the rigid body underwater motion process.

[0189] According to the target values ​​of the pitch angle deflection and the maximum bending moment of the rigid body during underwater motion, the margin equation and measurement equation of the pitch angle deflection and the maximum bending moment are constructed.

[0190] The margin equations for pitch angle deflection and maximum bending moment are expressed by m1(X,Y) and m2(X,Y) respectively.

[0191] The pitch angle deflection of the rigid body is the sight parameter, and its margin equation can be expressed as:

[0192] m1(X,Y)=min{F1(X,Y)-Y th1,L ,Y th1,U -F1(X,Y)}

[0193] The maximum bending moment of the rigid body is the minimum parameter, and its margin equation is expressed as

[0194] m2(X,Y)=Y th2 -F2(X,Y)

[0195] Among them, F1(X,Y) and F2(X,Y) represent the pitch angle deflection and maximum bending moment obtained from the underwater motion multi-agent model, respectively; Y th1,L 、Y th1,U 、Y th2 They represent the lower threshold limit of the pitch angle deflection, the upper threshold limit of the pitch angle deflection, and the upper threshold limit of the maximum bending moment, respectively, and are set according to the target pitch angle deflection and the target maximum bending moment.

[0196] The reliability measurement equations of pitch angle deflection and maximum bending moment are expressed by state reliability R1 and structural strength reliability R2.

[0197] State reliability R1 is the degree to which the pitch angle deflection margin is greater than zero:

[0198] R1=Pr{m1(X,Y)≥0}

[0199] Structural strength reliability R2 is the degree to which the maximum bending moment margin is greater than zero:

[0200] R2=Pr{m2(X,Y)≥0}.

[0201] Where m1 is the pitch angle deflection margin of the rigid body, m2 is the maximum bending moment margin of the rigid body, and Pr() is the probability measure that measures the probability of an event occurring.

[0202] The basic steps for reliability assessment of the underwater motion process of a rigid body are as follows:

[0203] (1) According to the Monte Carlo method, environmental factors are sampled from the distribution of various environmental factors;

[0204] (2) combining the sampled environmental factors with the launch parameters to generate the input dataset for the underwater motion multi-agent model;

[0205] (3) Substitute the input data set into the underwater motion multi-agent model to obtain the prediction results, and obtain the probability density functions of the pitch angle deflection and maximum bending moment based on the prediction results;

[0206] (4) The reliability of pitch angle deflection and maximum bending moment can be obtained based on the probability density function of pitch angle deflection and maximum bending moment.

[0207] Assuming that the performance threshold requirements for this projectile launch are that the target pitch angle deflection in terms of projectile attitude does not exceed 11°, and the target maximum bending moment in terms of rigid body structure strength does not exceed 3000 (N·m), then Y can be set th1,L is 0°, Y th1,U is 11° and Y th2 It is 3000 (N·m).

[0208] In this embodiment, the uncertainty of environmental factors is quantified according to the probability density function in S7. The basic steps of using the Monte Carlo method to evaluate the reliability of the underwater motion process of the projectile are as follows:

[0209] According to the requirements of the Monte Carlo method, the probability density function of the environmental factors in S7 is sampled to obtain the environmental factors, and the sampled environmental factors are combined with the parameters of this launch to generate the input data set of the underwater motion multi-agent model.

[0210] Input the input data set into the underwater motion multi-agent model to obtain the prediction result data set of the projectile's pitch angle deflection at the time of exiting the water and the projectile's maximum bending moment during underwater motion;

[0211] According to the prediction result data set, the probability density function of the pitch angle deflection of the projectile at the moment of exiting the water and the maximum bending moment of the projectile during underwater movement are obtained.

[0212] According to the probability density function of pitch angle deflection and maximum bending moment, as well as the deflection limit of target pitch angle deflection and the target maximum bending moment requirement, combined with the measurement equation of pitch angle deflection and maximum bending moment, the reliability of pitch angle deflection and maximum bending moment obtained in this launch is obtained, that is, attitude reliability and structural strength reliability. According to the Monte Carlo sampling results, the attitude reliability R1 of the projectile during underwater motion is

[0213] R1=Pr{m1(X1,Y1)≥0}=91.75%

[0214] The structural strength reliability R2 of the rigid body underwater launching process is

[0215] R2=Pr{m2(X1,Y1)≥0}=95.77%

[0216] The Monte Carlo simulation results and the pitch angle deflection reliability evaluation results of this underwater vertical launch are shown in Figure 13(a), and the maximum bending moment reliability evaluation results are shown in Figure 13(b);

[0217] The present invention provides a method for assessing the reliability of underwater rigid body missions, offering significant advantages over traditional theoretical analysis and experimental measurements. Based on the theory of assured reliability, the present invention comprehensively considers the complex influence of water environment factors and launch strategy parameters, constructs a reliability model for the underwater launch process, and quantitatively analyzes the uncertainty of the launch process. Compared with traditional theoretical research, the present invention has broader applicability, simultaneously considering the multi-factor coupling of the ocean environment and launch strategy, avoiding the one-sided analysis of a single factor in traditional methods, and thus providing a more comprehensive theoretical basis for reliability research on underwater rigid body launch processes. Compared with experimental research, the present invention significantly reduces experimental costs and time by establishing a simulation model, avoiding the difficulty of replicating complex sea conditions in experiments, and more efficiently exploring the effects of different launch strategies on reliability. Furthermore, the assured reliability modeling method proposed in the present invention can provide a scientific basis for optimizing launch strategies for underwater rigid body launch processes, providing methodological support for designing launch schemes under different scenarios and reliability requirements, and has important engineering application value for improving the reliability of underwater rigid body launch processes.

[0218] The embodiments described above are merely descriptions of preferred implementations of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present invention.

Claims

1. A method for assessing the reliability of a vertically launched rigid body underwater motion process, characterized in that: The following steps are involved: S1: Determine the factors that affect the underwater motion process of rigid bodies and the key performance parameters that affect reliability; Determine the environmental factors and launch parameters that affect the underwater motion of the rigid body. Environmental factors include significant wave height A, wind speed v wind and ocean current velocity v ocean , environmental factors are expressed as Y = {A,v wind ,v ocean }; The launch parameters include horizontal speed v os , vertical speed v ls and launch depth h, the launch parameters are expressed as X = {h,v ls ,v os The key performance parameters affecting reliability are determined to be the pitch angle deflection of the rigid body at the time of emergence and the maximum bending moment of the rigid body during underwater movement. S2: Conduct regional modeling; S3: Determine the feasible space domain of environmental factors and emission parameters, and use the Latin hypercube sampling method to determine N experimental points; S4: Based on the determined N experimental points, the pitch angle deflection and maximum bending moment corresponding to the N experimental points are obtained by finite element simulation software; S5: Using the results of N simulations as sample points, a multi-agent model of underwater motion is constructed, and the agent model is used as a performance model; The underwater motion multi-agent model assigns weight factors according to the accuracy of each agent model; it is constructed by linearly weighted combination of multiple agent models; S6: Determine the scope of environmental factors based on the launch location and area modeling; S7: Quantifying the uncertainty of environmental factors during the underwater motion of rigid bodies. S8: The Monte Carlo method is used to transfer the uncertainty of environmental factors in S7, and the margin equation and measurement equation are constructed to obtain the reliability of pitch angle deflection and maximum bending moment, which are used to evaluate the reliability of the rigid body underwater motion process.

2. The method for confident reliability assessment of a vertically launched rigid body underwater motion process according to claim 1, characterized in that: S5 uses the results of N simulations as sample points to construct a multi-agent model for underwater motion as follows: The underwater motion multi-agent model is constructed by linearly weighted combination of multiple agent models, and the weight factor is assigned according to the accuracy of each model. The expression is: Where F(X,Y) represents the underwater motion performance model, P is the number of proxy models, and f j (X,Y) represents the jth surrogate model, ω j They represent their corresponding weight factors respectively, and the weight factors need to satisfy the condition that they add up to 1.

3. The method for confident reliability assessment of a vertically launched rigid body underwater motion process according to claim 2, characterized in that: Weight factors of each proxy model: Where, E j represents the global error of the j-th surrogate model, ω i It represents the weight factor corresponding to the i-th model, and the root mean square error is used as the global error of the proxy model. The cross-validation method is used to obtain the root mean square error.

4. The method for confident reliability assessment of a vertically launched rigid body underwater motion process according to claim 1, characterized in that: The underwater motion multi-agent model consists of a Gaussian process regression model, a radial basis function model, and a support vector regression model. It has a total of 6-dimensional inputs, including three-dimensional environmental factors and three-dimensional launch parameters. The three-dimensional environmental factors are significant wave height, wind speed, and ocean current velocity, and the three-dimensional launch parameters are horizontal velocity v os , vertical speed v ls and launch depth h, with a total of two-dimensional outputs, namely pitch angle deflection and maximum bending moment.

5. The method for confident reliability assessment of a vertically launched rigid body underwater motion process according to claim 1, characterized in that: S2 performs regional modeling specifically as follows: regional modeling is achieved by clustering environmental factors, which are obtained through ocean hydrological data. After preprocessing the acquired ocean hydrological data, the ST-DBSCAN algorithm is used to cluster environmental factors.

6. The method for confident reliability assessment of a vertically launched rigid body underwater motion process according to claim 1, characterized in that: The models enabled in finite element simulation include multiphase flow model, turbulence model, overlapping grid, DFBI method, VOF multiphase flow model and gravity model.

7. The method for confident reliability assessment of a vertically launched rigid body underwater motion process according to claim 1, characterized in that: S7 quantifies the uncertainty of environmental factors in the water area during the underwater motion of a rigid body as follows: based on the environmental factors of the specified ocean area and time period, after statistically analyzing the data of significant wave height, wind speed and ocean current velocity, the frequency distribution or probability density function of significant wave height, wind speed and ocean current velocity is constructed. The Rayleigh distribution is used to describe the probability density function of significant wave height, the Weibull distribution or normal distribution is used to describe the probability density function of wind speed, and the Weibull distribution, lognormal distribution or gamma distribution is used to describe the probability density function of ocean current velocity.

8. The method for confident reliability assessment of a vertically launched rigid body underwater motion process according to claim 1, characterized in that: S8 uses the Monte Carlo method to transfer the uncertainty of environmental factors in S7 and obtain the reliability of pitch angle deflection and maximum bending moment, which are used to evaluate the reliability of the rigid body underwater motion process. Specifically: According to the requirements of the Monte Carlo method, the probability density function of the environmental factors in S7 is sampled to obtain the environmental factors, and the sampled environmental factors and the launch parameters are combined to generate the input data set of the underwater motion multi-agent model. Input the input data set into the underwater motion multi-agent model to obtain the predicted result data set of the rigid body's pitch angle deflection at the time of exiting the water and the maximum bending moment of the rigid body during underwater motion; According to the prediction result data set, the probability density functions of the pitch angle deflection of the rigid body at the moment of emergence and the maximum bending moment of the rigid body during underwater movement are obtained. According to the probability density functions of the pitch angle deflection and the maximum bending moment, as well as the target pitch angle deflection and the target maximum bending moment, the reliability of the target pitch angle deflection and the target maximum bending moment is obtained.

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