A method and system for generating randomized vortex-induced forces under uniform flow

Abstract

The application discloses a method and system for generating randomized vortex-induced force under uniform flow, and relates to the technical field of ship and ocean engineering, which is used for predicting the drift trajectory of a target under the interference of uniform flow. The method comprises the following steps: obtaining original data of vortex-induced force of the target in different flow rates of uniform flow; constructing a deterministic vortex-induced force calculation formula based on the original data of vortex-induced force; obtaining calculation data; decomposing the residual of the calculation data and the original data; constructing a physical mechanism driven random process model; coupling the random process model with the deterministic formula; constructing a time-course calculation formula of the randomized vortex-induced force; inputting the time-course of the randomized vortex-induced force into an underwater motion equation; predicting the underwater drift trajectory of the target through Monte Carlo simulation; obtaining a trajectory endpoint probability distribution map by generating a trajectory endpoint; and constructing a confidence region. The application improves the prediction accuracy of the underwater drift trajectory of the target, narrows the range of the confidence region, and improves the efficiency of offshore search.

Description

Technical Field

[0001] This invention relates to the field of shipbuilding and marine engineering technology, and more particularly to the field of underwater target drift trajectory prediction and eddy-induced force calculation technology, specifically to a method and system for generating randomized eddy-induced forces under uniform flow. Background Technology

[0002] The search and location of underwater targets (such as missiles, torpedoes, mines, and submersibles) is a critical task in maritime emergency response, and its core lies in the accurate prediction of the target's underwater trajectory and impact point. Numerous studies have shown that when a target is elliptical or approximately streamlined, it undergoes flow separation as it moves through ocean currents, periodically generating and shedding vortices at its tail. This exerts a periodic lateral force on the target, with a frequency related to the flow velocity—the vortex-induced force. This force is the key physical mechanism causing the target's lateral drift ("swaying"), and its accurate modeling is a bottleneck in improving the accuracy of trajectory and impact point prediction.

[0003] In existing technologies, prediction models typically employ simplified deterministic periodic force models to approximate the vortex-induced force effect, but these prediction models have the following drawbacks:

[0004] Insufficient accuracy of empirical models: Calculation models for estimating vortex-induced forces based on empirical or semi-empirical formulas often ignore the three-dimensional effects of the flow field and the detailed features of the target geometry, resulting in low prediction accuracy;

[0005] Completely deterministic models have limitations: the prediction results of vortex-induced force calculation models obtained from computational fluid dynamics (CFD) simulations under specific working conditions are represented by a single trajectory line, which cannot reflect the inherent randomness of vortex-induced force in actual physical processes, such as the random fluctuation characteristics of vortex-induced force.

[0006] Systematic methods that organically combine deterministic physical laws with random fluctuation characteristics often use deterministic formulas and white noise to fit eddy-induced forces, which cannot reproduce the non-Gaussian, non-stationary, and time-frequency correlation characteristics of random fluctuations in eddy-induced forces.

[0007] Therefore, there is an urgent need to develop a randomized eddy-induced force generation method and system that can scientifically and quantitatively integrate the deterministic laws and inherent randomness of eddy-induced forces, and is applicable to the prediction of the drift trajectory of objects in uniform flow. Summary of the Invention

[0008] The purpose of this invention is to provide a method and system for generating randomized eddy-induced forces under uniform flow, so as to solve the problem of low accuracy in randomized prediction of eddy-induced forces of underwater targets in the prior art.

[0009] To achieve the above objectives, the present invention provides a method for generating randomized eddy-induced forces under uniform flow, comprising:

[0010] S1. Based on computational fluid dynamics, an underwater drifting mechanical model of an ellipsoid is established to obtain the original data of eddy-induced force of the target object in uniform flow at different velocities, and a deterministic eddy-induced force calculation formula is constructed.

[0011] S2. Obtain deterministic vortex-induced force calculation data based on the deterministic vortex-induced force calculation formula, calculate the residual sequence between the original vortex-induced force data and the deterministic vortex-induced force calculation data, use the variational mode decomposition method to decompose the residual sequence into multiple modes, and classify the modes into three categories: low-frequency components, mid-frequency components and high-frequency components according to the center frequency of the modes;

[0012] S3. Construct physical mechanism-driven stochastic process models for each type of component, including an Ornstein-Uhlenbeck process model for low-frequency components, a fractional-order Gaussian noise model for mid-frequency components, and a non-homogeneous Poisson process model for high-frequency components.

[0013] S4. Couple the deterministic eddy-induced force calculation formula in S1 with the output of the stochastic process model corresponding to each component to construct a randomized eddy-induced force time history;

[0014] S5. Construct the underwater motion equation of the target object based on computational fluid dynamics, input the randomized eddy-induced force time history from S4 into the underwater motion equation, predict the underwater drift trajectory of the target object through Monte Carlo simulation, obtain the trajectory endpoint probability distribution map, and construct the confidence region based on the trajectory endpoint probability distribution map.

[0015] In S1, transient computational fluid dynamics simulations are performed on the target object under a series of uniform flow velocities to obtain the eddy-induced force time history data of the target object in uniform flow at different velocities. The dominant frequency of eddy shedding is determined through spectrum analysis. With flow rate The Strouhal relation is used to calculate the Strouhal number of the target object drift. :

[0016] ;

[0017] in, Indicates the characteristic length of the target object;

[0018] Construct a formula for calculating deterministic vortex-induced forces and calculate the time history of deterministic vortex-induced forces. :

[0019] ;

[0020] ;

[0021] in, Indicates fluid density, Represents the characteristic reference area of ​​the target object. Indicates the lift coefficient. The underwater drift speed of the target object This represents the incoming flow velocity of a uniform flow. This indicates the time during the underwater drift of the target object.

[0022] In S2, the center frequency is less than 0.2. The mode is a low-frequency component with a center frequency greater than or equal to 0.5. And less than or equal to 2 The mode is a mid-frequency component with a center frequency greater than 3. The modes are high-frequency components.

[0023] For the low-frequency components, an Ornstein-Uhlenbeck process model is constructed:

[0024] ;

[0025] in, Represents a random sequence. Indicates the regression rate. Indicates the diffusion coefficient. Representing the Wiener process, Indicates a time delay;

[0026] For the intermediate frequency component, a non-homogeneous Poisson process model is constructed:

[0027] ;

[0028] in, It is a time-varying intensity function. Based on strength, The modulation coefficient, Indicates phase, For velocity gradient magnitude, The attenuation coefficient is... The shedding frequency;

[0029] For high-frequency components, a fractional-order Gaussian noise model is constructed:

[0030] ;

[0031] in, Indicates the intensity of the fluctuation. Represents the gamma function. This represents the Hearst index.

[0032] In S4, an adaptive modal coupling algorithm is used to couple the deterministic vortex-induced force calculation formula in S1 with the outputs of the stochastic process models corresponding to various components in S3, generating three mechanism components, including a deterministic baseline component. Amplitude modulation random component and frequency-modulated random components :

[0033] ;

[0034] ;

[0035] ;

[0036] in, For random modulation terms, This is the equivalent velocity disturbance term;

[0037] Adaptive weighted coupling of the three mechanism components generates the initial time history of randomized eddy-induced force. :

[0038] ;

[0039] in, , Indicates the first This mechanism Indicates the first Adaptive weights for this mechanism.

[0040] Using a phase synchronization and hold algorithm Reconstruction is performed, including extracting the phase skeleton of the deterministic reference components and calculating the deterministic reference phase:

[0041] ;

[0042] in, express Deterministic reference phase at time, Represents the Hilbert transform. This indicates the phase angle calculation;

[0043] Generate random phase perturbation :

[0044] ;

[0045] in, Indicates a colored noise process;

[0046] Phase synthesis is performed on the deterministic reference phase and the random phase perturbation to obtain the synthesized phase. Based on synthetic phase pairs Reconstruct the time history of the randomized eddy-induced force. :

[0047] ;

[0048] in, This is a randomized amplitude.

[0049] In S5, the underwater motion equation of the target object is constructed based on computational fluid dynamics. The time history of randomized eddy-induced force is used as a time-varying excitation source and input into the underwater motion equation of the target object. By setting multiple independent random seeds, Monte Carlo simulation is used to fit the underwater drift trajectory of the target object corresponding to each independent random seed, and the trajectory endpoints of the underwater drift trajectory of the target object corresponding to each independent random seed are obtained. A discrete set of endpoint positions is constructed. A data-driven adaptive kernel density estimation method is used to construct a continuous two-dimensional probability density function based on the set of endpoint positions, transforming the discrete set of trajectory endpoints into a continuous and visualized probability distribution map of trajectory endpoints.

[0050] Using the equal probability density contour method, based on the two-dimensional probability density function, a closed curve is constructed in the set of trajectory endpoints to generate a multi-level confidence region for the same center point, including the core search region, the key search region, and the outer edge screening region. The confidence level of the core search region is 50% to 70%, the confidence level of the key search region is 90% to 95%, and the confidence level of the outer edge screening region is 99%.

[0051] To achieve the above objectives, the present invention also provides a system for generating randomized eddy forces under uniform flow, using the aforementioned method for generating randomized eddy forces under uniform flow, comprising:

[0052] The CFD calculation and deterministic modeling module is used to simulate the drift of a target object in a uniform flow at different velocities based on computational fluid dynamics, obtain the original data of vortex-induced forces of the target object in a uniform flow at different velocities, and construct a deterministic vortex-induced force calculation formula based on the original data of vortex-induced forces.

[0053] The signal decomposition and feature extraction module is used to calculate the residual sequence between the original vortex-induced force data and the deterministic vortex-induced force calculation data, and to perform variational mode decomposition and feature quantization on the residual sequence.

[0054] The stochastic process modeling module is used to construct and calibrate stochastic process models corresponding to various components;

[0055] The eddy force synthesis module is used to couple the deterministic eddy force calculation formula with the output of the stochastic process model corresponding to various components to generate a randomized eddy force time history.

[0056] The Monte Carlo simulation module is used to perform large-scale trajectory prediction simulations;

[0057] The probability analysis and visualization module is used to obtain the trajectory endpoint, generate a probability distribution map of the trajectory endpoint, and construct a confidence region in the probability distribution map of the trajectory endpoint.

[0058] Compared with the prior art, the present invention has the following advantages:

[0059] This invention quantifies the uncertainty of vortex-induced force generation under uniform flow disturbance, and for the first time constructs a randomized vortex-induced force calculation formula under uniform flow disturbance and builds a vortex-induced force calculation model based on the randomized vortex-induced force calculation formula to generate vortex-induced force under uniform flow disturbance.

[0060] Compared to traditional computational fluid dynamics (CFD) calculation models, the randomized eddy-induced force generation method provided by this invention is highly consistent with high-precision CFD benchmark data in key statistical and time-frequency characteristics such as mean, standard deviation, skewness, kurtosis, dominant frequency and overall spectral structure (correlation coefficient 0.94), but the calculation speed is improved by more than 340,000 times, providing near real-time dynamic trajectory prediction and updating capabilities for time-sensitive tasks such as maritime emergency search.

[0061] Compared to traditional deterministic models, the randomized eddy-induced force generation method provided by this invention not only reduces the area of ​​the confidence region, but also makes the shape of the confidence region closer to the ideal shape, greatly reducing the search range at sea and improving the deployment efficiency of search forces. Attached Figure Description

[0062] Figure 1 A flowchart illustrating the workflow of the randomized vortex-induced force generation method and system provided by this invention in practical applications;

[0063] Figure 2 The vorticity distribution diagram of the elliptic at t=0.4s provided for this invention;

[0064] Figure 3 The vorticity distribution diagram of the elliptic at t=0.8s provided for this invention;

[0065] Figure 4 The vorticity distribution diagram of the elliptic at t=1.2s provided for this invention;

[0066] Figure 5 The vorticity distribution diagram of the elliptic at t=1.4s provided for this invention;

[0067] Figure 6 The vorticity distribution diagram of the elliptic at t=1.6s provided for this invention;

[0068] Figure 7The vorticity distribution diagram of the elliptic at t=1.9s provided for this invention;

[0069] Figure 8 The deterministic vortex-induced force time-history diagrams in the X direction under different flow velocities provided by this invention;

[0070] Figure 9 The present invention provides a deterministic vortex-induced force time-history diagram in the Y direction under different flow velocities. Detailed Implementation

[0071] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0072] A method for generating randomized eddy-induced forces under uniform flow conditions includes:

[0073] S1. Based on computational fluid dynamics, an underwater drifting mechanical model of an ellipsoid is established to obtain the original data of eddy-induced force of the target object in uniform flow at different velocities, and a deterministic eddy-induced force calculation formula is constructed.

[0074] S2. Obtain deterministic vortex-induced force calculation data based on the deterministic vortex-induced force calculation formula, calculate the residual sequence between the original vortex-induced force data and the deterministic vortex-induced force calculation data, use the variational mode decomposition method to decompose the residual sequence into multiple modes, and classify the modes into three categories: low-frequency components, mid-frequency components and high-frequency components according to the center frequency of the modes;

[0075] S3. Construct physical mechanism-driven stochastic process models for each type of component, including an Ornstein-Uhlenbeck process model for low-frequency components, a fractional-order Gaussian noise model for mid-frequency components, and a non-homogeneous Poisson process model for high-frequency components.

[0076] S4. Couple the deterministic eddy-induced force calculation formula in S1 with the output of the stochastic process model corresponding to each component to construct a randomized eddy-induced force time history;

[0077] S5. Construct the underwater motion equation of the target object based on computational fluid dynamics, input the randomized eddy-induced force time history from S4 into the underwater motion equation, predict the underwater drift trajectory of the target object through Monte Carlo simulation, obtain the trajectory endpoint probability distribution map, and construct the confidence region based on the trajectory endpoint probability distribution map.

[0078] In S1, an underwater drifting motion mechanical model of the target object is established based on the computational fluid dynamics (CFD) method. Transient CFD simulations are performed on the target object under a series of uniform flow velocities to obtain eddy-induced force time history data of the target object in uniform flow at different velocities. The dominant frequency of eddy shedding is determined through spectral analysis. With flow rate The Strouhal relation is used to calculate the Strouhal number of the target object drift. :

[0079] ;

[0080] in, Indicates the characteristic length of the target object;

[0081] Construct a formula for calculating deterministic vortex-induced forces and calculate the time history of deterministic vortex-induced forces. :

[0082] ;

[0083] ;

[0084] in, Indicates fluid density, The characteristic reference area of ​​the target object is usually taken as the area of ​​the cross-section facing the flow. This represents the lift coefficient, which is related to the velocity of the uniform flow. The underwater drift speed of the target object This represents the incoming flow velocity of a uniform flow. Indicates the time during the underwater drift of the target object. It can reflect the periodic variation law of vortex-induced force.

[0085] The deterministic calculation formula can reflect the eddy-induced force of the target object in still water. Its core ability to solve the eddy-induced force under uniform flow disturbance lies in the lift coefficient, which is obtained by statistically analyzing the target object.

[0086] In conducting numerical simulations of underwater drift of an ellipsoid under a series of uniform flow velocities, it is crucial to ensure that the computational fluid dynamics (CFD) simulation time is sufficiently long, including at least 20 vortex shedding cycles, to obtain a fully developed flow field and stable statistical vortex-induced force (VEF) data. The series of uniform flow velocities are 0.0 m / s, 0.05 m / s, 0.1 m / s, 0.15 m / s, 0.2 m / s, 0.25 m / s, 0.3 m / s, 0.35 m / s, 0.4 m / s, 0.45 m / s, and 0.5 m / s, with each velocity corresponding to a specific simulation condition. VEF time history data is extracted from the transient CFD simulation results and used as the raw vortex-induced force data. Spectral analysis is then performed on the raw vortex-induced force data to determine the dominant vortex shedding frequency. With flow rate The Strouhal relation is used to calculate the Strouhal number of an elliptic body within a specific Reynolds number range. This study analyzes the nonlinear relationship between vortex-induced force amplitude and flow velocity. Based on the analysis results, a deterministic vortex-induced force calculation formula applicable to ellipsoids is constructed using a multi-field linear regression method. The deterministic vortex-induced force calculation time histories for uniform flow conditions at different flow velocities are then calculated using this formula, yielding deterministic vortex-induced force calculation data.

[0087] In S2, the residual sequence between the original data of vortex-induced force calculation and the deterministic vortex-induced force calculation data is used. The residual sequence is refined by using a variational mode decomposition coupled with Hilbert transform. The residual sequence is decomposed into multiple intrinsic mode functions, each of which is a mode. The intrinsic mode functions are classified according to their center frequencies into three scales: low-frequency components, mid-frequency components, and high-frequency components. The low-frequency components represent environmental fluctuation components, the mid-frequency components represent eddy shedding random modulation components, and the high-frequency components represent microscale turbulent fluctuation components.

[0088] ;

[0089] Where K represents the total number of intrinsic mode functions after decomposition. Indicates the first One eigenmode function This represents the residual term.

[0090] The modal classification is based on a center frequency less than 0.2. The mode is a low-frequency component with a center frequency greater than or equal to 0.5. And less than or equal to 2 The mode is a mid-frequency component with a center frequency greater than 3. The modes are high-frequency components.

[0091] In S3, the random characteristics of each scale component are systematically quantified, including time-varying evolution analysis of probability distribution characteristics, characterization of time-frequency structure, and flow-state dependence analysis of higher-order statistical moments.

[0092] The probability density function for each time window is calculated using the sliding window technique, with a time window length of [value missing]. =10 / Constructing a time-varying distribution distance function Analyze the time-varying evolution of probability distribution characteristics;

[0093] ;

[0094] in, for The probability density function of the time window at time step 1. For reference to Gaussian distribution, Indicates signal amplitude; through analysis The evolutionary pattern reveals the dynamic characteristics of the non-stationarity of random fluctuations.

[0095] A parameterized model of the time-varying autocorrelation function is constructed through two-dimensional interpolation and surface fitting. This enables the characterization of the time-frequency structure;

[0096] ;

[0097] in, Represents the expectation operator. Indicates time delay, via The non-stationary characteristics of the time-frequency structure are analyzed, and the dynamic changes of the correlation time with the flow state are analyzed.

[0098] Taking the fourth-order statistical moments as an example, the skewness is calculated by analyzing the functional relationship between the fourth-order statistical moments and flow parameters. and peak Analyze the flow-state dependence of higher-order statistical moments;

[0099] ;

[0100] ;

[0101] in, This represents the skewness calculation function. Represents the peak value calculation function. express The Reynolds number at time 10:00. This represents the pressure gradient.

[0102] For each type of component, a physical mechanism-driven stochastic process model is constructed. For the low-frequency environmental fluctuation component, an Ornstein-Uhlenbeck process model is constructed.

[0103] ;

[0104] in, Represents a random sequence. Indicates the regression rate. Indicates the diffusion coefficient. Representing the Wiener process, Indicates a time delay.

[0105] For the mid-frequency vortex shedding modulation component, an event-driven non-homogeneous Poisson process model is constructed based on the stochastic occurrence mechanism of simulated vortex shedding events:

[0106] ;

[0107] in, It is a time-varying intensity function. Based on strength, The modulation coefficient, Indicates phase, For velocity gradient magnitude, The attenuation coefficient is... This represents the shedding frequency.

[0108] For high-frequency microscale turbulent fluctuation components, based on the continuous fluctuations caused by micro-perturbations in the simulated flow field, a continuous fluctuation type fractional Gaussian noise model is constructed using non-stationary fractional Gaussian noise:

[0109] ;

[0110] in, Indicates the intensity of the fluctuation. Represents the gamma function. This represents the Hearst index.

[0111] Physical constraint modulation functions are introduced, including energy constraint modulation, phase coupling constraint, and amplitude-frequency joint constraint, to ensure that the stochastic process model strictly follows the laws of fluid dynamics.

[0112] The energy spectral density of the constructed stochastic process model satisfies ;

[0113] in, For reference energy, Indicates the center frequency of the mode. For the integral scale frequency, It is a low-frequency index. The minimum vortex scale frequency.

[0114] The phase relationship between different frequency components of the constructed stochastic process model must satisfy... ;

[0115] in, Indicates the first One frequency component, Indicates the first One frequency component, For frequency The instantaneous phase of the component, For frequency The instantaneous phase of the component, For deterministic phase difference, This indicates random phase fluctuations.

[0116] The joint probability distribution of the magnitude and frequency of the constructed stochastic process model satisfies ;

[0117] in, To express the conditions, a generalized Pareto distribution is used. To represent the marginal distribution, a gamma distribution is used.

[0118] In S4, an adaptive modal coupling algorithm is used to couple the deterministic vortex-induced force calculation formula in S1 with the outputs of the stochastic process models corresponding to various components in S3, generating three mechanism components, including a deterministic baseline component. Amplitude modulation random component and frequency-modulated random components :

[0119] ;

[0120] ;

[0121] ;

[0122] in, For random modulation terms, The equivalent velocity disturbance term is represented by the deterministic reference component, which is calculated using the deterministic vortex-induced force calculation formula constructed by S1. It exhibits no randomness and reflects the average flow effect. The amplitude-modulated random component is superimposed on the deterministic reference component by superimposing amplitude-random fluctuations. For random modulation terms, reflecting the random process of amplitude modulation, when A value greater than zero indicates that the vortex shedding in the current state is relatively strong. When the value is less than zero, it indicates that the vortex shedding in the current state is relatively weak. The frequency modulation random component is frequency modulated based on the deterministic reference component through equivalent velocity perturbation. This is the equivalent velocity disturbance term, reflecting the virtual velocity disturbance.

[0123] Adaptive weighted coupling of the three mechanism components generates the initial time history of randomized eddy-induced force. This achieves the organic coupling of deterministic and random components:

[0124] ;

[0125] in, , Indicates the first This mechanism Indicates the first Adaptive weights for this mechanism.

[0126] To ensure that the correct physical phase relationship is maintained during randomization, a phase synchronization preservation algorithm is used. Reconstruction is performed, including extracting the phase skeleton of the deterministic reference components and calculating the deterministic reference phase:

[0127] ;

[0128] in, express Deterministic reference phase at time, Represents the Hilbert transform. This indicates the phase angle calculation;

[0129] Generate random phase perturbation :

[0130] ;

[0131] in, Indicates a colored noise process;

[0132] Phase synthesis is performed on the deterministic reference phase and the random phase perturbation to obtain the synthesized phase. The synthesized phase is the final phase, based on the synthesized phase pair. Reconstruct the time history of the randomized eddy-induced force. :

[0133] ;

[0134] ;

[0135] in, This is a randomized amplitude.

[0136] By deeply integrating the randomized eddy-induced force model with the dynamics of underwater target motion, a systematic engineering solution based on large-scale probabilistic simulation is constructed, which can accurately predict the drift trajectory and final landing point probability distribution of underwater targets.

[0137] In S5, the underwater motion equation of the target object is constructed based on computational fluid dynamics. The time history of randomized eddy-induced force is used as a time-varying excitation source and input into the underwater motion equation of the target object. By setting multiple independent random seeds, Monte Carlo simulation is used to fit the underwater drift trajectory of the target object corresponding to each independent random seed, and the trajectory endpoints of the underwater drift trajectory of the target object corresponding to each independent random seed are obtained. A discrete set of endpoint positions is constructed. A data-driven adaptive kernel density estimation method is used to construct a continuous two-dimensional probability density function based on the set of endpoint positions, transforming the discrete set of trajectory endpoints into a continuous and visualized probability distribution map.

[0138] Using the equal probability density contour method, based on the two-dimensional probability density function, a closed curve is constructed in the set of trajectory endpoints to generate a multi-level confidence region for the same center point, including the core search region, the key search region, and the outer edge screening region. The confidence level of the core search region is 50% to 70%, the confidence level of the key search region is 90% to 95%, and the confidence level of the outer edge screening region is 99%.

[0139] The underwater motion equations of the target object, constructed based on computational fluid dynamics, are the underwater six-degree-of-freedom motion equations of the target object, which incorporate randomized eddy-induced forces. As a key time-varying excitation source, the underwater six-degree-of-freedom motion equations embedded in the target object comprehensively consider hydrostatics (buoyancy, gravity), hydrodynamics (viscous drag, added mass force, possible hydrodynamic derivatives), the Earth's rotation effect (Coriolis force), and ocean currents. Each independent Monte Carlo simulation generates a unique eddy-induced force time history by assigning a new seed to the stochastic process, thereby driving the target object to produce a possible three-dimensional motion trajectory in the virtual ocean environment. To ensure a balance between simulation efficiency and accuracy, parallel computing technology allows for the simultaneous execution of hundreds to thousands of such simulations, efficiently exploring the vast trajectory space caused by the stochasticity of eddy-induced forces.

[0140] A system for generating randomized eddy forces under uniform flow, using the aforementioned method for generating randomized eddy forces under uniform flow, includes:

[0141] The CFD calculation and deterministic modeling module is used to simulate the drift of a target object in a uniform flow at different velocities based on computational fluid dynamics, obtain the original data of vortex-induced forces of the target object in a uniform flow at different velocities, and construct a deterministic vortex-induced force calculation formula based on the original data of vortex-induced forces.

[0142] The signal decomposition and feature extraction module is used to calculate the residual sequence between the original vortex-induced force data and the deterministic vortex-induced force calculation data, and to perform variational mode decomposition and feature quantization on the residual sequence.

[0143] The stochastic process modeling module is used to construct and calibrate stochastic process models corresponding to various components;

[0144] The eddy force synthesis module is used to couple the deterministic eddy force calculation formula with the output of the stochastic process model corresponding to various components to generate a randomized eddy force time history.

[0145] The Monte Carlo simulation module is used to perform large-scale trajectory prediction simulations;

[0146] The probability analysis and visualization module is used to obtain the trajectory endpoint, generate a probability distribution map of the trajectory endpoint, and construct a confidence region in the probability distribution map of the trajectory endpoint.

[0147] The essence of the Monte Carlo framework is to quantify and propagate uncertainty. A randomized eddy-induced force generation system built upon the Monte Carlo framework not only considers the randomness of eddy-induced forces but also incorporates uncertainties from other sources, such as errors in the target's initial water entry state (position, velocity, attitude) and fluctuations in environmental parameters (e.g., seawater density profile), depending on the quality of the actual data. By employing a Latin hypercube sampling strategy, the system can more efficiently and uniformly cover the multidimensional uncertainty space with fewer simulations, ensuring the robustness and reliability of the probabilistic statistical results. In-depth variance and sensitivity analyses of the simulation results can identify key uncertainty factors affecting the dispersion of landing points, providing deeper insights into the allocation of search resources.

[0148] By fitting the underwater drift trajectory of the target object corresponding to each independent random seed using Monte Carlo simulation, a trajectory cluster is constructed. The system automatically analyzes the statistical characteristics of this trajectory cluster, such as: the average trajectory path, the amplitude and periodic distribution of lateral drift (sway), the range of settling velocity variation, and possible periodic "zigzag" motion patterns. These statistical characteristics not only verify the physical rationality of the randomized force model (such as its consistency with classical eddy-induced vibration phenomena), but also provide an intuitive basis for understanding the macroscopic motion behavior of the target underwater.

[0149] The probability analysis and visualization module transforms the discrete set of trajectory endpoints into a continuous, visualized probability field, thereby defining a scientifically reliable search area. Based on the probability density function system, it can accurately calculate confidence regions at any specified confidence level (e.g., 90%, 95%, 99%). Typically, the equal probability density contour method is used to find a closed curve such that the probability integral of the region within the curve reaches the preset confidence level, generating multi-level "concentric" confidence regions, for example:

[0150] Core search area (50-70% confidence): This is the smallest area, and high-precision search equipment (such as side-scan sonar and underwater robots) should be deployed first.

[0151] Key search area (90-95% confidence level): A moderately sized area where the main search forces are deployed.

[0152] Outer screening area (99% confidence): Largest area, used for rapid exclusion or wide-area scanning.

[0153] By optimizing the algorithm, the area of ​​the defined region can be minimized or the boundary can be made smoothest while meeting the confidence level, thereby further improving the efficiency of the search operation.

[0154] Through probability analysis and visualization modules, the system can not only provide the final static landing point distribution but also demonstrate the dynamic evolution of the probability distribution during the target's underwater drift. By analyzing the target's position distribution at different simulation times (such as 1 hour, 6 hours, and 12 hours after entry into the water), time-varying animations of probability cloud maps can be generated. This helps in understanding the target's drift patterns and dynamically adjusting subsequent search strategies based on areas that have not been successfully searched during the search operation.

[0155] Example: Randomized eddy-induced force generation and drift trajectory prediction of an ellipsoid with a length-to-diameter ratio of 3:1 under uniform flow;

[0156] 1. Experimental Preparation; In this embodiment, an ellipsoid with a major axis of 3 meters, a minor axis of 1 meter, and a mass of 850 kg is used as the target object. The drift process of the ellipsoid in a uniform ocean current is simulated based on computational fluid dynamics. The seawater density is 1025 kg / m³, and the kinematic viscosity is 1.05 × 10⁻⁻⁻⁻⁶. 6 m 2 With a flow rate of V = 1.5 m / s and a water temperature of 20℃, the main consideration in a series of uniform flow velocities is the flow velocity V = 1.5 m / s.

[0157] 2. Construction of the formula for calculating deterministic vortex-induced force;

[0158] The Star-CCM+ software was used to perform transient computational fluid dynamics simulation of the target object and calculate high-precision eddy-induced forces. A three-dimensional computational model based on computational fluid dynamics (CFD) was constructed in the Star-CCM+ software, which is equivalent to simulating the underwater drifting mechanics of an ellipsoid. The following simulation parameters were set in the model.

[0159] The computational domain size is set to 60m × 30m × 30m (flow direction × horizontal × vertical).

[0160] The mesh generation is set to a structured hexahedral mesh with finer mesh near the walls, and the total number of meshes is 8.5 million.

[0161] The turbulence model was set to Large Eddy Simulation (LES) and WALE subgrid model.

[0162] The boundary conditions are set as follows: the inlet condition is the velocity of a uniform flow under the corresponding working condition, the outlet condition is a pressure outlet, and there is no slippage on the wall (the fluid velocity at the wall is the same as the wall velocity). Natural boundary conditions are set through the inlet velocity and the outlet pressure to form a closed flow domain.

[0163] The time step is set to 0.001s, and the total calculation time is 60s, ensuring that more than 20 vortex shedding cycles are included.

[0164] With a sampling interval of 0.001s, the time history data (force signal) of the transverse force is extracted from the CFD calculation results. The extracted time history data is subjected to bandpass filtering from 0.1 Hz to 10 Hz and outlier detection and correction. The relevant frequency band of vortex-induced force is retained to obtain CFD data of ellipsoid in uniform flow at different flow velocities. This is equivalent to the original data of vortex-induced force and is expressed as vortex-induced force signal.

[0165] Spectral analysis was performed on CFD data for a series of flow velocity conditions (0.0 m / s, 0.05 m / s, 0.1 m / s, 0.15 m / s, 0.2 m / s, 0.25 m / s, 0.3 m / s, 0.35 m / s, 0.4 m / s, 0.45 m / s, and 0.5 m / s) to extract the dominant vortex shedding frequency under each condition. And, calculate the Strauhal number of the elliptic body within a specific Reynolds number range. Through nonlinear analysis, a deterministic formula for calculating the vortex-induced force applicable to this ellipsoid is obtained:

[0166] ;

[0167] in, For fluid density, , This indicates the underwater drift velocity of the ellipsoid. As a characteristic reference area for the target object, the flow-facing area of ​​an ellipsoid is selected. The characteristic length of an elliptic is represented by its minor axis. The inflow velocity is the velocity of the uniform flow.

[0168] Lift coefficient Closely related to the uniform flow velocity, a correspondence between the lift coefficient and the uniform flow velocity is established through detailed calculations, and the lift coefficient is... Substituting into the deterministic vortex-induced force calculation formula, we obtain a deterministic vortex-induced force calculation formula that can calculate arbitrarily uniform flow disturbances: The formula was verified under the condition of flow velocity V=1.5m / s. The average amplitude relative error between the formula calculation value and the CFD result was 2.3%, the main frequency relative error was 1.7%, and the phase cumulative error (10 cycles) was 4.2%.

[0169] 3. Random fluctuation characteristic analysis;

[0170] Calculate CFD data Calculation data with deterministic vortex-induced force calculation formula residual sequence , the residual sequence The residual sequence has a length of 60,000 points (sampling time is 60s, sampling rate is 1000Hz). Variational mode decomposition (VMD) is performed on the residual sequence with the following parameters: number of modes K=5, penalty parameter α=2000, convergence tolerance tol=1×10⁻ 7 The initialization method is to uniformly distribute the center frequency.

[0171] Five intrinsic mode functions (IMF1(t) to IMF5(t) and a residual term r(t) are obtained through variational mode decomposition. The center frequencies of each intrinsic mode function are 0.32Hz, 0.75Hz, 1.50Hz, 2.98Hz, and 6.21Hz, respectively.

[0172] Based on center frequency and vortex shedding main frequency Based on the relationship of 0.297Hz, the modal IMF is divided into three categories:

[0173] Category 1 (Low-frequency environmental fluctuations): IMF1(t), <0.2 This represents the slow-varying disturbance of the flow environment, contributing 8.2% to the variance;

[0174] Type II (vortex shedding modulation components): IMF2(t), IMF3(t), 0.5 ≤ ≤2 This represents the unsteady modulation inherent in the vortex shedding process itself, contributing 57.7% to the combined variance.

[0175] The third category (microscale turbulent fluctuations): IMF4(t), IMF5(t), >3 This represents random fluctuations caused by small-scale turbulence, contributing 34.1% to the pooled variance.

[0176] For each intrinsic mode function, a Hilbert transform is performed to extract instantaneous amplitude, instantaneous phase, and instantaneous frequency. Three types of statistical features are calculated: amplitude distribution, frequency stability, and time correlation. The statistical feature calculations for amplitude distribution include mean calculation, standard deviation calculation, skewness calculation, and kurtosis calculation. The statistical feature calculation for frequency stability is the standard deviation of instantaneous frequency. The statistical feature calculation for time correlation is the decay time constant of the autocorrelation function.

[0177] 4. Stochastic process modeling and parameter calibration;

[0178] For the three types of modal IMFs, stochastic process models are established respectively. For the eddy shedding modulation component (intermediate frequency IMF), an event-driven model—a non-homogeneous Poisson process—is adopted. ,in, The base strength is the average event rate. =0.75Hz, =0.3 is the modulation coefficient, which is equivalent to the modulation depth. =0.25Hz is the dropout frequency, which is equivalent to the modulation frequency.

[0179] For microscale turbulent fluctuations (high-frequency IMF), a continuous wave-type model with fractional-order Gaussian noise is adopted. Where H = 0.72 is the Hurst exponent. =0.18 represents the fluctuation intensity. For the differentiation of the Wiener process.

[0180] For environmental fluctuations (low-frequency IMF), the Ornstein-Uhlenbeck process is adopted. ,in, =0.05s -1 For the regression rate, =0.08 is the diffusion coefficient.

[0181] Model parameters, including Poisson process parameters, fractional-order parameters, and OU process parameters, are extracted from the IMF decomposed by CFD. The Poisson process parameters are determined by fitting statistical histograms of event intervals. and The Hurst exponent H (fractional-order parameter) was estimated using rescaled range analysis (R / S analysis), and the regression rate was determined by fitting the autocorrelation function with exponential decay. .

[0182] The calibrated parameters ensure that the error between the random sequence generated by the model and the statistical characteristics (mean, variance, skewness, kurtosis, power spectral density, etc.) of the corresponding IMF is less than 5%.

[0183] 5. Synthesis of randomized eddy-induced forces;

[0184] Randomized eddy-induced forces are synthesized using three mechanisms through an adaptive modal coupling algorithm.

[0185] Mechanism 1 (Deterministic Benchmark) Mechanism 2 (Amplitude Modulation) ,in, For random modulation terms; Mechanism 3 (frequency modulation) ,in, To achieve an equivalent velocity perturbation, the three mechanisms are dynamically fused using a time-varying weighting function, and finally synthesized. .

[0186] To ensure the correct physical phase relationship is maintained during randomization, a Phase Synchronization Preservation (PSP) algorithm is developed. Step 1 extracts the phase skeleton of the deterministic components and calculates the deterministic reference phase. ,in, For Hilbert transform, To take the complex phase angle.

[0187] Step 2: Generate random phase perturbations that satisfy the constraints. ,in, , The intensity of time-varying frequency fluctuations is related to local flow instability.

[0188] Step 3: Perform phase synthesis on the deterministic reference phase and the random phase perturbation to synthesize the final phase. Based on synthetic phase reconstruction signal ,in, To randomize the amplitude, For the final synthesized phase, For deterministic reference phase, Random phase perturbation.

[0189] 6. Generation of probability dropout distribution and determination of confidence region;

[0190] Five hundred independent random seeds are set up, and an independent randomized eddy-induced force time history is generated for each seed. The randomized eddy-induced force time history is then input into the six-degree-of-freedom rigid body motion equation for numerical solution, resulting in an underwater drift trajectory of an ellipsoid. A total of 500 underwater drift trajectories are obtained, each corresponding to a trajectory endpoint, which is equivalent to the final landing point of the ellipsoid. An adaptive kernel density estimation method was used to analyze 500 landing points. Perform probability density estimation ;

[0191] ;

[0192] Among them, bandwidth function Inversely proportional to local point density, a smaller bandwidth (fine resolution) is used in high-density regions, and a larger bandwidth (smoothing estimation) is used in low-density regions.

[0193] Using the equal probability density contour method, a two-dimensional probability density distribution map is constructed based on probability density estimation. The probability density values ​​are sorted from high to low and the probabilities are accumulated until a specified confidence level is reached. The contour lines corresponding to the density values ​​are used as the boundaries of the confidence regions. Multi-level concentric confidence regions are calculated for each confidence level, including the core search area (confidence level of 50% to 70%), the key search area (confidence level of 90% to 95%), and the outer screening area (confidence level of 99%).

[0194] When generating the search priority map, the probability density distribution of target existence is integrated with marine environmental data, and a comprehensive scoring formula is used. Calculate the priority score for each position, where, There is a probability that the target exists. It takes into account comprehensive environmental accessibility factors (considering water depth, bottom sediment, obstacles, etc.). As a search efficiency factor, the weights of the three factors are set as follows: : : =0.6:0.3:0.1, achieving a balance between probability guidance, practical feasibility, and search efficiency, ultimately forming a priority spatial distribution map to guide the optimized deployment of search resources.

[0195] 7. Effectiveness verification and accuracy evaluation;

[0196] The randomized eddy force calculation data of the target object was obtained based on the constructed randomized eddy force time history calculation formula. The data was compared with the high-fidelity original CFD data in multiple indicators. The calculation model was verified based on statistical characteristics and frequency domain characteristics. The verification results are shown in Table 1.

[0197] Table 1. Comparison of randomized vortex-induced force calculation data with original CFD data;

[0198] ;

[0199] As shown in Table 1, the mean value reflects the overall shift of the vortex-induced force. The CFD data is -0.12, and the calculated data is -0.11, with a relative error of 8.3%, indicating that the vortex-induced force calculation model is close to the actual situation in mean estimation. The standard deviation characterizes the fluctuation range of the force. The CFD data is 3.21, and the calculated value is 3.18, with a relative error of 0.9%, indicating that the vortex-induced force calculation model can accurately capture the degree of variation of the vortex-induced force. The skewness is used to analyze the symmetry of the vortex-induced force distribution. The CFD value is 0.15, and the calculated value is 0.13, with a relative error of 13.3%, indicating that the vortex-induced force... The computational model exhibits a symmetrical distribution consistent with reality. Kurtosis, reflecting the tail characteristics of the vortex-induced force distribution, is 3.45 in CFD and 3.38 in computation, with a relative error of 2.0%, indicating a good match for extreme values. The dominant frequency reflects the predominant fluctuation frequency of the vortex-induced force, with 0.297Hz in CFD and 0.295Hz in computation, with a relative error of 0.7%, demonstrating high accuracy of the vortex-induced force computational model in its core frequency domain characteristics. The spectral correlation coefficient of the computational data is 0.94, further confirming a high degree of consistency between the computational data and the CFD data in their overall spectral structure. In summary, the vortex-induced force computational model constructed in this invention exhibits extremely small errors (all below 2%) in key indicators such as standard deviation, kurtosis, and dominant frequency. While the average and skewness errors are slightly larger, they remain within acceptable limits. Furthermore, it demonstrates excellent spectral correlation and can reliably simulate the randomized vortex-induced force time-history characteristics of the target object.

[0200] Based on the statistical results of 100 high-precision CFD direct simulations, a comparative analysis was conducted on the computational models of the traditional deterministic model and the randomized eddy force generation method provided by this invention. The prediction accuracy of the randomized eddy force generation method provided by this invention for the underwater drift trajectory and trajectory endpoint of the target object was evaluated. The evaluation results are shown in Table 2. The eddy force calculation efficiency of the randomized eddy force generation method provided by this invention and the traditional CFD method was compared and analyzed. The efficiency analysis results are shown in Table 3.

[0201] Table 2 Comparison of the prediction accuracy evaluation results of underwater drift trajectory of target objects;

[0202] ;

[0203] As shown in Table 2, the randomized eddy force generation method provided by this invention significantly outperforms the traditional model in three key indicators: confidence region area, region aspect ratio, and probability of including the true location. The 95% confidence region area is reduced from 15.6 km² in the traditional model to 7.3 km², a reduction of 53.2%, indicating a significant decrease in the spatial uncertainty of the predicted trajectory and more accurate positioning. The region aspect ratio is improved from 1.8 to 1.2, an improvement of 33.3%. The confidence region constructed by the randomized eddy force generation method provided by this invention is closer to a circle (ideal value of 1), indicating a more balanced shape of the confidence region and a more uniform distribution of uncertainty in all directions. The probability of including the true location is increased from 62% to 94%, improving the prediction accuracy of the true location by 32%. Moreover, the prediction accuracy of this invention is close to 1, demonstrating higher reliability and statistical coverage. In summary, the randomized eddy force generation method provided by this invention can significantly reduce the confidence region, optimize the region shape, and significantly improve the probability of including the true location, greatly improving the prediction accuracy of the underwater drift trajectory of the target object.

[0204] Table 3 Comparison of model computational efficiency;

[0205] ;

[0206] As shown in Table 3, in a single vortex-induced force generation task, the traditional CFD method takes up to 48 hours, while the vortex-induced force generation method provided by this invention only takes 0.5 seconds. Compared with the traditional CFD method, the computational efficiency (speed-up ratio) of the calculation method provided by this invention is as high as 345,600 times, making the calculation process that originally required several days almost instantaneous, suitable for engineering applications. For 500 Monte Carlo simulations requiring large-scale uncertainty analysis, the theoretical calculation time of the traditional CFD method is as long as 24,000 hours (approximately 2.74 years), while the vortex-induced force generation method provided by this invention only takes 250 seconds (approximately 4.2 minutes), with a speed-up ratio of 345,600 times. This transforms what was originally an infeasible long-term simulation into a routine analysis that can be completed in minutes. In the critical application scenario of real-time prediction and updating, traditional CFD methods are completely impractical due to excessive computation time. However, the eddy-induced force generation method provided by this invention can complete the update within 5 minutes, realizing dynamic and near real-time prediction and updating of target trajectories (such as landing points at sea) for the first time, providing crucial decision support capabilities for time-sensitive tasks such as emergency response and maritime search and rescue.

[0207] like Figure 1 As shown, when applying the randomized vortex-induced force generation method and system provided by this invention, a database is first constructed through high-precision CFD numerical simulation to extract vortex-induced force characteristics and conduct parametric analysis, thereby establishing a deterministic vortex-induced force calculation formula. Subsequently, the random fluctuation characteristics of vortex-induced force are deeply analyzed and quantified, and a hybrid stochastic process model driven by physical mechanisms is constructed to form a high-fidelity synthesis technology for randomized vortex-induced force. Finally, the results are applied to engineering practice, generating intelligent probability landing point distribution and confidence region through a high-precision Monte Carlo trajectory prediction system, and providing intelligent decision support for tasks such as emergency search and rescue by combining multi-source information fusion technology, thus completing a closed-loop technology chain from theory to application.

[0208] Figures 2 to 7The diagrams show the vorticity distribution of the ellipsoid during its underwater drift at 0.4s, 0.8s, 1.2s, 1.4s, 1.6s, and 1.9s, illustrating the dynamic process of wake evolution and vortex shedding during the ellipsoid's motion in a viscous fluid. Blue represents negative vorticity, red represents positive vorticity, and green, yellow, and orange represent transitional vorticities of different magnitudes. From 0.4s to 0.8s, the ellipsoid has just entered the fluid, and a distinct high vorticity region forms at its lower end, resulting in a relatively short wake. From 0.8s to 1.6s, as the ellipsoid descends, the wake lengthens significantly. At t=1.4s, the wake begins to bend and twist, with alternating structures of positive and negative vorticity appearing on both sides (red and blue separating). From 1.6s to 1.9s, the wake vortex enters its mature stage, the colors of the vorticity concentration region become more distinct, the vortex street structure of the wake is fully formed, and positive and negative vortex pairs shed alternately, exhibiting a periodic "vortex shedding" phenomenon.

[0209] Figure 8 It presented five different incoming flow velocities within a range of 0 to 2.0 seconds. The dynamic response of the target object to the vortex-induced force in the X direction under the action of (0.0 m / s, 0.05 m / s, 0.1 m / s, 0.15 m / s, 0.2 m / s) is shown. The stationary fluid (black curve) serves as the control group. In the initial time (0~0.5 s), the vortex-induced force in the stationary fluid remains stable near 0. However, as the incoming flow velocity increases from 0.05 m / s to 0.2 m / s, the curves at each velocity show obvious initial positive force peaks, with the peak value increasing as the velocity increases. At a flow rate of 0.2 m / s, the peak force reaches approximately 0.042 N, after which the force values ​​at all flow velocities rapidly decay and converge to zero. In the intermediate stage (0.5–1.0 s), the vortex-induced force at all flow velocities enters a negative fluctuation range, oscillating slightly between 0 and -0.005 N. The most significant negative shift is at 0.15 m / s; in the later stage (1.0~2.0 s), the vortex-induced force recovers from the negative range and exhibits periodic oscillation characteristics, reaching a peak around 1.5 s. The curve with a velocity of 0.15 m / s shows a clear negative trough, while =0.05m / s and The curve with a velocity of 0.2 m / s shows a peak in the positive direction. At 2.0 s, the vortex-induced force converges to zero again at all flow velocities, reflecting that the amplitude of the vortex-induced force is positively correlated with the incoming flow velocity, and its periodic fluctuations originate from the coupling effect of vortex shedding and structural vibration.

[0210] Figure 9 It presented five different incoming flow velocities within a range of 0 to 2.0 seconds. The dynamic response process of the target object under the influence of vortex-induced force in the Y direction at speeds of 0.0 m / s, 0.05 m / s, 0.1 m / s, 0.15 m / s, and 0.2 m / s. The stationary fluid (black curve) serves as the control group. In the initial 0 to 0.5 seconds, the vortex-induced force curves corresponding to all velocities exhibit random fluctuations with small amplitudes near the zero value. This indicates that the flow field has not yet fully developed, the vortex shedding phenomenon has not yet stabilized, and the target object is only subjected to weak flow field disturbances. From 0.5 seconds onwards, as the vortex target object gradually forms and detaches in the flow field, the fluctuation amplitude of each curve begins to increase significantly, and the curves for different flow velocities gradually separate, showing that the influence of outflow velocity on vortex-induced force begins to appear. After 1.0 second, the differences are further amplified. The static flow field (black curve) remains within a small fluctuation range of ±0.02N, reflecting the system's own weak noise. The amplitude at low flow velocity (red curve) is approximately ±0.03N, initially showing the excitation effect of vortex-induced force. The amplitude at medium flow velocity (blue curve) increases to close to ±0.04N, and the fluctuation frequency also increases. When the incoming flow velocity is 0.15m / s (pink curve), the amplitude reaches the maximum value among the series of flow velocity conditions, with the positive peak exceeding 0.04N and the negative peak approaching −0.03N. This significant enhancement of vortex-induced force response indicates that the flow velocity may be in the locked range of vortex-induced vibration of the target object. At this time, the vortex shedding frequency is close to the natural frequency of the target object, triggering a resonance effect. At higher flow velocities (green curve), although the amplitude decreases, the fluctuation frequency is still the highest among all curves, reflecting the high-frequency characteristics of vortex shedding at high flow velocities. Overall, the amplitude and frequency of vortex-induced force both show an upward trend with the increase of the incoming flow velocity, and the peak value of the vortex-induced force response appears when the incoming flow velocity is 0.15 m / s. The whole process clearly shows the stage evolution of vortex-induced force from "start-up-development-violent fluctuation", which also corresponds to the complete physical process of vortex shedding in the flow field from formation, stabilization to resonance.

[0211] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for generating randomized eddy-induced forces under uniform flow, characterized in that, include: S1. Based on computational fluid dynamics, an underwater drifting mechanical model of an ellipsoid is established to obtain the original data of eddy-induced force of the target object in uniform flow at different velocities, and a deterministic eddy-induced force calculation formula is constructed. S2. Obtain deterministic vortex-induced force calculation data based on the deterministic vortex-induced force calculation formula, calculate the residual sequence between the original vortex-induced force data and the deterministic vortex-induced force calculation data, use the variational mode decomposition method to decompose the residual sequence into multiple modes, and classify the modes into three categories: low-frequency components, mid-frequency components and high-frequency components according to the center frequency of the modes; S3. Construct physical mechanism-driven stochastic process models for each type of component, including an Ornstein-Uhlenbeck process model for low-frequency components, a fractional-order Gaussian noise model for mid-frequency components, and a non-homogeneous Poisson process model for high-frequency components. S4. Couple the deterministic eddy-induced force calculation formula in S1 with the output of the stochastic process model corresponding to each component to construct a randomized eddy-induced force time history; S5. Construct the underwater motion equation of the target object based on computational fluid dynamics, input the randomized eddy-induced force time history in S4 into the underwater motion equation, predict the underwater drift trajectory of the target object through Monte Carlo simulation, obtain the trajectory endpoint probability distribution map, and construct the confidence region based on the trajectory endpoint probability distribution map. A computational fluid dynamics (CFD) model of an ellipsoidal body floating underwater was established. Transient CFD simulations were performed on the target object under a series of uniform flow velocities to obtain time history data of eddy-induced forces in uniform flow at different velocities. The dominant frequency of eddy shedding was determined through spectral analysis. With flow rate The Strouhal relation is used to calculate the Strouhal number of the target object drift. : ； in, Indicates the characteristic length of the target object; Construct a formula for calculating deterministic vortex-induced forces and calculate the time history of deterministic vortex-induced forces. : ； ； in, Indicates fluid density, Represents the characteristic reference area of ​​the target object. Indicates the lift coefficient. The underwater drift speed of the target object This represents the incoming flow velocity of a uniform flow. Indicates the time during the underwater drift of the target object; In S4, an adaptive modal coupling algorithm is used to couple the deterministic vortex-induced force calculation formula in S1 with the outputs of the stochastic process models corresponding to various components in S3, generating three mechanism components, including a deterministic baseline component. Amplitude modulation random component and frequency-modulated random components : ； ； ； in, For random modulation terms, This is the equivalent velocity disturbance term; Adaptive weighted coupling of the three mechanism components generates the initial time history of randomized eddy-induced force. : ； in, , Indicates the first This mechanism Indicates the first Adaptive weights for this mechanism; Using a phase synchronization and hold algorithm Reconstruction is performed, including extracting the phase skeleton of the deterministic reference components and calculating the deterministic reference phase: ； in, express Deterministic reference phase at time, Represents the Hilbert transform. This indicates the phase angle calculation; Generate random phase perturbation : ； in, Indicates a colored noise process; Phase synthesis is performed on the deterministic reference phase and the random phase perturbation to obtain the synthesized phase. Based on synthetic phase pairs Reconstruct the time history of the randomized eddy-induced force. : ； in, This is a randomized amplitude.

2. The method for generating randomized eddy-induced force under uniform flow according to claim 1, characterized in that, In S2, the center frequency is less than 0.

2. The mode is a low-frequency component with a center frequency greater than or equal to 0.

5. And less than or equal to 2 The mode is a mid-frequency component with a center frequency greater than 3. The modes are high-frequency components.

3. The method for generating randomized eddy-induced force under uniform flow according to claim 2, characterized in that, For the low-frequency components, an Ornstein-Uhlenbeck process model is constructed: ； in, Represents a random sequence. Indicates the regression rate. Indicates the diffusion coefficient. Representing the Wiener process, Indicates a time delay; For the intermediate frequency component, a non-homogeneous Poisson process model is constructed: ； in, It is a time-varying intensity function. Based on strength, The modulation coefficient, Indicates phase, For velocity gradient magnitude, The attenuation coefficient is... The shedding frequency; For high-frequency components, a fractional-order Gaussian noise model is constructed: ； in, Indicates the intensity of the fluctuation. Represents the gamma function. This represents the Hearst index.

4. The method for generating randomized eddy-induced force under uniform flow according to claim 3, characterized in that, In S5, the underwater motion equation of the target object is constructed based on computational fluid dynamics. The time history of randomized eddy-induced force is used as a time-varying excitation source and input into the underwater motion equation of the target object. By setting multiple independent random seeds, Monte Carlo simulation is used to fit the underwater drift trajectory of the target object corresponding to each independent random seed, and the trajectory endpoints of the underwater drift trajectory of the target object corresponding to each independent random seed are obtained. A discrete set of endpoint positions is constructed. A data-driven adaptive kernel density estimation method is used to construct a continuous two-dimensional probability density function based on the set of endpoint positions, transforming the discrete set of trajectory endpoints into a continuous and visualized probability distribution map.

5. The method for generating randomized eddy-induced force under uniform flow according to claim 4, characterized in that, Using the equal probability density contour method, based on the two-dimensional probability density function, a closed curve is constructed in the set of trajectory endpoints to generate a multi-level confidence region for the same center point, including the core search region, the key search region, and the outer edge screening region. The confidence level of the core search region is 50% to 70%, the confidence level of the key search region is 90% to 95%, and the confidence level of the outer edge screening region is 99%.

6. A randomized eddy-induced force generation system under uniform flow, characterized in that, The method for generating randomized eddy-induced forces under uniform flow as described in any one of claims 1 to 5 includes: The CFD calculation and deterministic modeling module is used to simulate the drift of a target object in a uniform flow at different velocities based on computational fluid dynamics, obtain the original data of vortex-induced forces of the target object in a uniform flow at different velocities, and construct a deterministic vortex-induced force calculation formula based on the original data of vortex-induced forces. The signal decomposition and feature extraction module is used to calculate the residual sequence between the original vortex-induced force data and the deterministic vortex-induced force calculation data, and to perform variational mode decomposition and feature quantization on the residual sequence. The stochastic process modeling module is used to construct and calibrate stochastic process models corresponding to various components; The eddy force synthesis module is used to couple the deterministic eddy force calculation formula with the output of the stochastic process model corresponding to various components to generate a randomized eddy force time history. The Monte Carlo simulation module is used to perform large-scale trajectory prediction simulations; The probability analysis and visualization module is used to obtain the trajectory endpoint, generate a probability distribution map of the trajectory endpoint, and construct a confidence region in the probability distribution map of the trajectory endpoint.

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