Sea rescue helicopter rotor aerodynamic force simulation method and system

Abstract

The invention relates to the technical field of helicopter aerodynamic force simulation, and discloses a sea rescue helicopter rotor aerodynamic force simulation method and system. The method comprises the following steps: acquiring a rotor wing downwash airflow historical speed data set, a historical sea surface wave data set and a historical aerodynamic pressure data set monitored within a preset historical time range; executing a dynamic volatility analysis process on the three types of historical data sets to generate a speed volatility index, a sea surface wave volatility index and an aerodynamic pressure volatility index; taking the three types of volatility indexes as guide parameters, performing adaptive search operation in a rotor aerodynamic force simulation parameter database, and determining an optimal simulation time interval; and performing numerical calculation simulation on pneumatic coupling between the rotor wing and the sea surface according to the optimal simulation time interval to generate a simulation data sequence, performing feature extraction and classification on the simulation data sequence by using an aerodynamic force recognition model, and outputting a rotor wing aerodynamic force simulation result.

Description

Technical Field

[0001] This invention relates to the field of helicopter aerodynamic simulation technology, specifically to a method and system for simulating the aerodynamics of a marine rescue helicopter rotor. Background Technology

[0002] In maritime rescue scenarios, the aerodynamic characteristics of helicopter rotors directly affect flight stability and the safety of rescue operations. Simulation calculations must comprehensively consider the coupled effects of multiple factors, including rotor downwash, sea waves, and aerodynamic pressure. Currently, traditional rotor aerodynamic simulation methods mostly rely on numerical calculations at fixed time intervals, failing to fully incorporate the dynamic changes in actual monitoring data. This leads to discrepancies between simulation results and the real aerodynamic conditions in complex maritime environments.

[0003] In the data acquisition phase, existing technologies often employ single sensors or small-scale sensor deployments, making it difficult to comprehensively capture a complete set of data on rotor downwash airflow velocity, sea surface waves, and aerodynamic pressure within a preset historical time range. This easily leads to data gaps or insufficient representativeness of local data, thus affecting the accuracy of subsequent simulation analysis. Furthermore, when processing the acquired historical data, most methods only perform simple statistical analysis without delving into the dynamic fluctuations of the data. This fails to effectively extract key indicators reflecting the coupling relationship between the environment and aerodynamics, resulting in a lack of scientific basis for setting simulation parameters.

[0004] Regarding the determination of simulation parameters, traditional methods rely on experience to set simulation time intervals, lacking a correlation mechanism with data volatility indicators, making it difficult to adaptively adjust parameters according to dynamic changes in the marine environment. When sea waves are violent, rotor downwash airflow is unstable, or aerodynamic pressure fluctuates significantly, fixed time intervals may lead to decreased simulation accuracy. Either the intervals are too long, missing crucial aerodynamic details, or too short, increasing computational redundancy and reducing simulation efficiency. Furthermore, in the aerodynamic coupling numerical calculation and result processing stages, some methods oversimplify the simulation of the aerodynamic coupling between the rotor and the sea surface, and their methods for feature extraction and classification of simulation data sequences are simplistic, failing to accurately reflect the rotor aerodynamic state under different environmental conditions. Ultimately, this affects the guiding value of the simulation results for actual rescue operations.

[0005] The aforementioned shortcomings of existing technologies mean that the aerodynamic simulation of the rotor of maritime rescue helicopters cannot balance accuracy and efficiency, making it difficult to meet the actual needs of flight safety and rescue operations in complex maritime environments. There is an urgent need for a simulation method that can integrate multi-source monitoring data, correlate dynamic fluctuation characteristics, and adaptively determine simulation parameters. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for simulating the aerodynamics of a marine rescue helicopter rotor, so as to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides a method for simulating the aerodynamics of a marine rescue helicopter rotor, the method comprising: The system collects historical data sets of rotor downwash airflow velocity, sea surface wave, and aerodynamic pressure within a preset historical time range by an array of sensors installed in the helicopter rotor area. A dynamic volatility analysis process is performed on the historical velocity data set, historical sea surface wave data set, and historical aerodynamic pressure data set to generate velocity volatility index, sea surface wave volatility index, and aerodynamic pressure volatility index. Using the aforementioned velocity fluctuation index, sea surface wave fluctuation index, and aerodynamic pressure fluctuation index as guiding parameters, an adaptive search operation is performed in the rotor aerodynamic simulation parameter database to determine the optimal simulation time interval. Numerical simulation of the aerodynamic coupling between the rotor and the sea surface is performed based on the optimal simulation time interval to generate a simulation data sequence. The aerodynamic identification model is then used to extract and classify the features of the simulation data sequence, and the rotor aerodynamic simulation results are output.

[0008] Preferably, the step of performing dynamic volatility analysis on the historical velocity data set, historical sea surface wave data set, and historical aerodynamic pressure data set includes: The historical velocity data set is processed by applying the empirical mode decomposition method to obtain a set of velocity eigenmode functions. Calculate the variance of each mode function in the set of intrinsic velocity modes, and use the average variance as the velocity fluctuation index; Empirical mode decomposition was performed on the historical sea surface wave data set and the historical aerodynamic pressure data set to obtain the sea surface wave volatility index and the aerodynamic pressure volatility index.

[0009] Preferably, the step of applying the empirical mode decomposition method to perform signal processing on the historical velocity dataset includes: Identify all local extrema in the historical velocity dataset and construct upper and lower envelopes using interpolation methods; Calculate the average value of the upper and lower envelopes, and subtract this average value from the original data to obtain the candidate mode functions; Repeat the above process until the mode function stopping criterion is met, and finally extract the set of velocity intrinsic mode functions.

[0010] Preferably, the step of performing an adaptive search operation in the rotor aerodynamic simulation parameter database includes: Establish a three-dimensional parameter search space with velocity fluctuation index, sea surface wave fluctuation index, and aerodynamic pressure fluctuation index as coordinate axes; An initial set of candidate points is randomly generated in the three-dimensional parameter search space, and each candidate point corresponds to a simulation time interval parameter. The particle swarm optimization algorithm is used to iteratively update the candidate point set. Each candidate point adjusts its movement direction and step size in the search space based on its individual optimal position and the group optimal position. The fitness value of each candidate point is calculated to evaluate the merits of its corresponding simulation time interval parameter; After a preset number of iterations, the simulation time interval corresponding to the candidate point with the highest fitness value is selected as the optimal simulation time interval.

[0011] Preferably, the step of iteratively updating the candidate point set using the particle swarm optimization algorithm includes: Initialize the position and velocity of each particle in the particle swarm, where position represents the candidate simulation time interval parameter and velocity represents the direction and magnitude of parameter adjustment; Calculate the fitness value of each particle's current position, and update the individual's historical best position and the group's historical best position; The velocity of each particle is adjusted according to the velocity update formula of the particle swarm optimization algorithm. This formula takes into account the current velocity of the particle, the optimal position direction of the individual particle and the optimal position direction of the group. Adjust the position of each particle according to the updated velocity to generate a new set of candidate points; The update process is repeated until the maximum number of iterations is reached, and finally the simulation time interval corresponding to the best historical position of the group is selected as the optimal simulation time interval.

[0012] Preferably, the step of numerically simulating the aerodynamic coupling between the rotor and the sea surface includes: The Navier-Stokes equations are discretized based on the optimal simulation time interval; The discretized Navier-Stokes equations are solved on a spatiotemporal grid using the finite difference method to obtain the velocity and pressure field distributions. The velocity and pressure field distribution data from multiple time steps are integrated to form the simulation data sequence.

[0013] Preferably, the step of solving the discretized Navier-Stokes equations on a spatiotemporal grid using the finite difference method includes: Divide the area of ​​rotor action and the sea surface boundary into uniform grids; The spatial derivative is approximated using the central difference scheme, and the time derivative is approximated using the explicit time-progression scheme. Solve the system of linear algebraic equations and update the flow field variable values ​​for each grid point.

[0014] Preferably, the step of using the aerodynamic identification model to extract features and classify the simulation data sequence includes: The simulation data sequence is input into a pre-trained support vector machine model; Data is mapped to a high-dimensional space using the kernel function of a support vector machine, and the decision function value is calculated. The rotor operating state is classified according to the decision function value, and the rotor aerodynamic simulation results are generated.

[0015] Preferably, the training steps of the pre-trained support vector machine model include: Collect historical simulation data sequences and corresponding aerodynamic label data; Choose a radial basis function as the kernel function and set the penalty parameter; The support vector machine optimization problem is solved using the sequence minimum optimization algorithm to obtain the model parameters.

[0016] Preferably, the present invention also includes a marine rescue helicopter rotor aerodynamic simulation system, including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor, when executing the computer program, implements the steps of the above-described marine rescue helicopter rotor aerodynamic simulation method.

[0017] Compared with the prior art, the beneficial effects of the present invention are: In the data acquisition stage, this method uses a sensor array installed in the helicopter rotor area, which can comprehensively capture the historical speed data set of the rotor downwash airflow, the historical sea surface wave data set, and the historical aerodynamic pressure data set within a preset historical time range. Compared with the traditional single sensor or small-scale sensor layout, it can avoid the problems of missing data or insufficient representativeness of local data, and provide complete and comprehensive basic data support for subsequent simulation analysis, making the data source of simulation calculation more objective and complete.

[0018] During the data processing stage, a dynamic fluctuation analysis process is performed on historical velocity data sets, historical sea surface wave data sets, and historical aerodynamic pressure data sets to generate velocity fluctuation indices, sea surface wave fluctuation indices, and aerodynamic pressure fluctuation indices. This breaks through the limitations of traditional methods that only perform simple statistical analysis, and can deeply explore the key features behind the data that reflect the coupling relationship between the environment and aerodynamics. These indices can be directly used to guide the setting of subsequent simulation parameters, so that the simulation parameters are closely related to the dynamic changes of the actual environment, rather than relying on experience-based judgment.

[0019] In the simulation parameter determination stage, velocity fluctuation index, sea surface wave fluctuation index, and aerodynamic pressure fluctuation index are used as guiding parameters. An adaptive search operation is performed in the rotor aerodynamic simulation parameter database to determine the optimal simulation time interval, overcoming the drawbacks of the fixed time interval in traditional methods. This process can flexibly adjust the simulation time interval according to the actual fluctuations of airflow, waves, and pressure in the marine environment. It can capture key changes through reasonable time intervals when data fluctuations are severe, and avoid computational redundancy when data is relatively stable, thus achieving a balance between simulation accuracy and efficiency.

[0020] In the aerodynamic coupling numerical calculation and result processing stage, numerical calculation simulation of the aerodynamic coupling between the rotor and the sea surface is performed according to the optimal simulation time interval. This can more accurately restore the coupling effect between the two and reduce the deviation caused by traditional simplified simulation. At the same time, the aerodynamic identification model is used to extract and classify the features of the simulation data sequence, which can more comprehensively analyze the aerodynamic information in the simulation data. This makes the output rotor aerodynamic simulation results more consistent with the actual working state of the maritime rescue helicopter. It can provide more valuable reference for the formulation of helicopter flight control strategies and the planning of rescue operation routes, and help improve the safety and reliability of maritime rescue operations. Attached Figure Description

[0021] Figure 1 This is a schematic diagram illustrating the working principle of the aerodynamic simulation method for the rotor of a maritime rescue helicopter described in this invention. Figure 2 A flowchart of the steps in the dynamic volatility analysis process; Figure 3 A flowchart for processing historical velocity datasets using empirical mode decomposition. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] Please see Figure 1This invention provides a method and system for simulating the aerodynamics of a helicopter rotor in maritime rescue operations. The method achieves accurate simulation of rotor aerodynamics by integrating sensor data acquisition, dynamic fluctuation analysis, adaptive parameter search, and high-precision numerical simulation. During implementation, a sensor array installed in the helicopter rotor area continuously monitors the rotor downwash velocity, sea wave state, and aerodynamic pressure parameters, collecting historical velocity, sea wave, and aerodynamic pressure data sets within a preset historical time range. The dynamic fluctuation analysis process processes these historical data sets to generate quantified velocity fluctuation indices, sea wave fluctuation indices, and aerodynamic pressure fluctuation indices. These fluctuation indices are input as guiding parameters into the rotor aerodynamic simulation parameter database, and an optimal simulation time interval is matched through an adaptive search operation. The optimal simulation time interval is used to control the numerical calculation simulation process of the aerodynamic coupling between the rotor and the sea surface, generating a high-resolution simulation data sequence. An aerodynamic identification model extracts and classifies the features of the simulation data sequence, outputting aerodynamic simulation results reflecting the actual operating state of the rotor. The entire process ensures a high degree of consistency between the simulation environment and real maritime rescue conditions.

[0024] Example 1: See Figure 2 In the dynamic fluctuation analysis process of the aerodynamic simulation method for the rotor of a maritime rescue helicopter, the Empirical Mode Decomposition (EMD) method is applied to process the historical velocity dataset. EMD is an adaptive signal processing technique suitable for analyzing non-stationary and nonlinear data sequences. The historical velocity dataset originates from long-term monitoring records of the rotor region sensor array, and the data sequence includes timestamps and corresponding three-dimensional velocity component values. The EMD method progressively filters out complex fluctuation patterns in the historical velocity dataset. The decomposition process starts from the inherent time-scale characteristics of the data itself, identifying hidden oscillation modes within the data. The signal processing aims to decompose the historical velocity dataset into a finite number of intrinsic mode functions (IMFs). Each IMF must satisfy two basic conditions: the number of extreme points and the number of zero-crossing points are equal or at most differ by one across the entire data range; and the local mean of the upper envelope defined by local maxima and the lower envelope defined by local minima is zero.

[0025] The first step in processing historical velocity datasets using the Empirical Mode Decomposition (EMD) method is to identify all local extrema, including local maxima and local minima. The algorithm iterates through each data point in the historical velocity dataset, comparing its value with that of its neighbors. Data points with values ​​greater than all their immediate neighbors are marked as local maxima, and those with values ​​less than their immediate neighbors are marked as local minima. All identified local maxima are connected using cubic spline interpolation to form an upper envelope, ensuring its smoothness and continuity. All identified local minima are connected using the same cubic spline interpolation method to form a lower envelope. The upper and lower envelopes constitute the instantaneous amplitude boundaries of the historical velocity dataset.

[0026] The upper and lower envelopes are calculated to their average values ​​at each time point, and the sequence of average values ​​constitutes the instantaneous average trend line of the data. This instantaneous average trend line is subtracted from the original historical velocity data set, and the resulting residual signal is called the candidate mode function (EMF). The candidate EMF needs to be tested to see if it meets the definition conditions of an intrinsic mode function (IMF). The testing process evaluates the difference between the number of extrema and the number of zero-crossings of the candidate EMF. If the difference is greater than one, the candidate EMF is considered to not meet the conditions and requires further processing. Candidate EMFs that do not meet the conditions are used as new input data to repeat the extrema identification and envelope construction process. This iterative screening process continues until the residual signal meets the IMF conditions. Candidate EMFs that meet the conditions are recorded as a velocity IMF and separated from the original data. The velocity IMF is subtracted from the original historical velocity data set to obtain the remaining components. The remaining components are used as new input data to repeat the entire empirical mode decomposition process, sequentially extracting multiple velocity IMFs arranged from high to low frequency. Finally, the empirical mode decomposition process terminates when the remaining components become monotonic functions or contain no more than one extreme point. The historical velocity dataset is completely decomposed into a set of velocity eigenmode functions and a residual trend term. The set of velocity eigenmode functions contains all the fluctuation information from high frequency to low frequency in the historical velocity dataset.

[0027] The variance of each mode function in the velocity intrinsic mode function set is calculated. The variance characterizes the energy distribution intensity of each intrinsic mode function. Variance calculation is based on the deviation of each intrinsic mode function's data point from its mean; a larger variance indicates stronger fluctuation energy in that mode function. The arithmetic mean of the variances of all modes in the velocity intrinsic mode function set is calculated, and this mean is used as a velocity volatility index. The velocity volatility index comprehensively reflects the average energy level of multi-scale fluctuations in the historical velocity data set; a higher index value indicates more severe velocity fluctuations in the rotor downwash airflow.

[0028] Historical sea surface wave datasets are processed using the same empirical mode decomposition (EMD) procedure. These datasets typically contain parameters such as wave height, wave period, and wave direction. The EMD method is applied to these datasets to identify local extrema and construct upper and lower envelopes. A sieving process generates a set of intrinsic mode functions (EMFs) for sea surface waves, and the variance of each EMF is calculated. The average variance of the EMF set is used as an index of sea surface wave volatility, quantifying the multi-scale wave characteristics of sea surface wave states.

[0029] The historical aerodynamic pressure dataset, derived from pressure sensor measurements, is used to obtain the set of intrinsic mode functions (EMFs) of aerodynamic pressure through empirical mode decomposition. The average variance of the EMF set serves as an aerodynamic pressure volatility index, reflecting the intensity of rotor aerodynamic pressure fluctuations. The dynamic volatility analysis process uses EMF to decompose the original historical data into fluctuation components at different time scales. The volatility index extracts the essential fluctuation characteristics of the data based on the component energy. Velocity volatility, sea surface wave volatility, and aerodynamic pressure volatility indices provide quantitative input parameters for subsequent adaptive search operations.

[0030] The implementation of Empirical Mode Decomposition (EMD) methods requires consideration of boundary effect handling. Boundary effect refers to the envelope distortion caused by insufficient information about extreme points at the endpoints of a data sequence. Boundary effect handling methods include characteristic wave extension and mirror extension. Characteristic wave extension extends data points outward based on waveform characteristics near the endpoints of the data sequence. Mirror extension symmetrically extends the data sequence in a mirror image before identifying extreme points and constructing the envelope; the extended portion is removed after obtaining the envelope. Boundary effect handling reduces envelope oscillations at the endpoints, improving the accuracy and reliability of Empirical Mode Decomposition results.

[0031] Historical velocity, sea wave, and aerodynamic pressure datasets require preprocessing before Empirical Mode Decomposition (EMD). Preprocessing includes outlier removal and signal filtering. Outlier removal uses statistical methods to identify and correct measurement error points that significantly deviate from the normal range, while signal filtering eliminates the influence of high-frequency noise on the EMD results. The preprocessed data sequences are then input into the EMD algorithm to ensure that the generated intrinsic mode functions (IMFs) for velocity, sea wave, and aerodynamic pressure accurately reflect the wave characteristics of the physical processes. The dynamic volatility analysis process effectively separates random fluctuations and deterministic trends in the data using EMD, and volatility indices serve as a comprehensive measure of data volatility to guide simulation parameter optimization.

[0032] Example 2: See Figure 3 The complete process of applying Empirical Mode Decomposition (EMD) to signal processing of historical velocity datasets is based on the principle of adaptive data decomposition. The historical velocity dataset, as the input signal, is progressively decomposed into a series of intrinsic mode functions (EMFs). Signal processing begins with the identification of local extrema in the historical velocity dataset, including local maxima and local minima. The algorithm scans each data point in the historical velocity dataset, comparing its value with the values ​​of its preceding and following data points. When a data point's value is greater than both its preceding and following values, it is marked as a local maximum. When a data point's value is less than both its preceding and following values, it is marked as a local minimum. Boundary data points are processed using a mirror expansion method, which copies the historical velocity dataset in reverse to both ends of the data sequence. The expanded data sequence is then used for extrema identification, and the extrema records in the expanded portion are removed after identification.

[0033] All identified local maxima are used as interpolation nodes and input into a cubic spline interpolation algorithm. This algorithm generates a smooth curve passing through all local maxima. This smooth curve forms the upper envelope of the historical velocity data set, representing the upper boundary fluctuation characteristics of the data. All identified local minima are also processed using the cubic spline interpolation algorithm to generate a lower envelope passing through all local minima. Both the upper and lower envelopes must be defined within the entire domain of the data sequence, and the envelope construction process ensures the continuity of the curve's second derivative. Overshoot may occur during interpolation, which refers to non-physical oscillations in the envelope near the endpoints of the data sequence. Overshoot is suppressed by adjusting boundary conditions and interpolation parameters to ensure that the envelope closely matches the actual fluctuation range of the data.

[0034] The average values ​​of the upper and lower envelopes at each time point are calculated, and the sequence of average values ​​constitutes the instantaneous average trend line of the data. The calculation process iterates through each time point of the historical velocity data set, reading the values ​​of the upper and lower envelopes at that time point. The two values ​​are added together and divided by two to obtain the average value. The average values ​​of all time points form a new data sequence. The instantaneous average trend line reflects the local average characteristics of the historical velocity data set, and the trend line contains the long-term variation patterns of the data. Subtracting the instantaneous average trend line from the original historical velocity data set yields the residual signal; the subtraction operation is performed point-by-point. The residual signal is called the candidate mode function, which contains the high-frequency fluctuation components of the historical velocity data set.

[0035] Candidate mode functions need to be tested to see if they meet the definition conditions of intrinsic mode functions. The definition conditions require that the number of extrema of the candidate mode function is equal to or at most differs by one from the number of zero-crossings. The testing process involves counting the total number of extrema and zero-crossings of the candidate mode function. The number of extrema includes the number of local maxima and local minima. The number of zero-crossings refers to the number of times the candidate mode function crosses the zero level line. An appropriate threshold is set during the statistical process to avoid false zero-crossings caused by noise. When the difference between the number of extrema and the number of zero-crossings does not exceed one, the candidate mode function is considered to meet the intrinsic mode function conditions. Candidate mode functions that meet the conditions are recorded as a velocity intrinsic mode function and separated from the original data.

[0036] When a candidate mode function does not meet the intrinsic mode function condition, the candidate mode function is used as new input data to repeat the extreme point identification and envelope construction process. The iterative screening process continues, and each iteration generates a new candidate mode function. The iteration stopping criteria include the standard deviation criterion and the extreme point number criterion. The standard deviation criterion calculates the ratio of the standard deviation of the current candidate mode function to that of the previous candidate mode function. The iteration stops when the standard deviation ratio is lower than a preset threshold. The extreme point number criterion checks whether the number of extreme points of the candidate mode function is less than three. The iteration process terminates when either stopping criterion is met, and the final candidate mode function is accepted as the velocity intrinsic mode function.

[0037] After separating the first velocity eigenmode function (EMF) from the original historical velocity dataset, the remaining data components serve as new input for the empirical mode decomposition (EMD) process. These remaining data components contain lower-frequency fluctuations, and the same extreme point identification, envelope construction, and sieving procedures are applied to them. The process sequentially extracts the second and third velocity EEMFs until the remaining data components become monotonic functions or contain no more than one extreme point. The complete velocity EEMF set comprises multiple EEMFs arranged in descending frequency order, each representing a fluctuation pattern at a specific time scale within the historical velocity dataset. The EEMD method adaptively separates different fluctuation components in the historical velocity dataset; the decomposition result is entirely determined by the characteristics of the data itself and does not depend on pre-defined basis functions.

[0038] Signal processing for historical sea surface wave and aerodynamic pressure datasets employs the same empirical mode decomposition (EMD) method. Extremum point identification in the sea surface wave data considers the periodicity of the wave height time series. Envelope construction for the aerodynamic pressure data considers the instantaneous pressure fluctuation range, and the signal processing ensures consistent decomposition criteria across the three datasets. The advantages of EMD in handling non-stationary signals are fully demonstrated in the aerodynamic simulation of the rotor of a maritime rescue helicopter, as the method adapts to the complex variations in rotor downwash velocity. The signal processing result is a set of intrinsic mode functions (EMFs), which provides the input basis for subsequent wave behavior index calculations. The entire signal processing flow extracts the inherent vibration modes of the data through an iterative sieving mechanism, and mode decomposition creates the necessary conditions for multi-scale wave analysis. The non-stationarity of marine environmental data is effectively addressed through EMD, providing an accurate description of wave characteristics for aerodynamic simulation.

[0039] Example 3: An adaptive search operation is performed in the rotor aerodynamic simulation parameter database to determine the optimal simulation time interval. The adaptive search operation constructs a parameter search space based on velocity fluctuation index, sea surface wave fluctuation index, and aerodynamic pressure fluctuation index. These three indices define a three-dimensional parameter search space as three mutually orthogonal coordinate axes, with each point in the three-dimensional parameter search space corresponding to a candidate simulation time interval parameter value. The adaptive search operation employs a particle swarm optimization (PSO) algorithm to perform intelligent search within the three-dimensional parameter search space. The PSO algorithm simulates the social behavior of flocks of birds or schools of fish to achieve collective optimization. In the initialization phase of the PSO algorithm, a group of particles is randomly generated to form an initial population. The position vector of each particle represents the coordinates of a candidate simulation time interval parameter in the three-dimensional parameter search space. The three components of the position vector correspond to the scaling values ​​of the velocity fluctuation index, sea surface wave fluctuation index, and aerodynamic pressure fluctuation index, respectively. The scaling process maps fluctuation indices with different dimensions to a unified numerical range.

[0040] The Particle Swarm Optimization (PSO) algorithm assigns a velocity vector to each particle to control its direction and step size in the search space. The velocity vectors are initialized to small, random values. Each particle's position in the three-dimensional parameter search space corresponds to a simulation time interval parameter, which is evaluated using a fitness function. The fitness function calculates the fitting accuracy of the simulation time interval parameter on historical data; fitting accuracy is quantified by comparing the differences between numerical simulation results and measured data. A higher fitness value indicates a better match between the simulation time interval parameter and the current volatility index. The PSO algorithm iteratively updates particle positions to find the optimal solution with the highest fitness value.

[0041] The core update mechanism of the Particle Swarm Optimization (PSO) algorithm guides particle movement based on individual and swarm experience. Each particle records its individual best position and swarm best position. The individual best position records the position of the particle with the highest fitness value achieved in each iteration, while the swarm best position records the position of the highest fitness value achieved by all particles in the entire swarm. The particle velocity update formula combines the particle's current velocity, the guidance from the individual best position, and the guidance from the swarm best position. The velocity update formula is expressed as:

[0042] in, This represents the velocity component of the i-th particle in the d-th dimension during the (k+1)-th iteration. This represents the velocity component of the i-th particle in the d-th dimension during the k-th iteration. Indicates the inertia weighting coefficient. Represents individual learning factors. Represents the group learning factor. and It is a random number in the range [0,1]. This represents the historical best position of the i-th particle in the d-th dimension up to the k-th iteration. This represents the current position of the i-th particle in the d-th dimension at the k-th iteration. This represents the historical best position of the entire population in the d-th dimension up to the k-th iteration.

[0043] Inertia weight coefficient The degree to which the current velocity of a particle affects the velocity of the next generation is controlled; a larger inertial weight coefficient is beneficial for global exploration, while a smaller inertial weight coefficient is beneficial for fine-grained local search. Individual learning factor. Adjusting the step size of a particle's movement towards its individual historical best position, the group learning factor. Adjust the step size for particles to move towards the group's historical best position. (Random number) and To introduce randomness into the update process, the algorithm is prevented from getting trapped in local optima too early.

[0044] Particle position updates are based on adjustments made to the updated velocity vector, with the position update formula adding the velocity vector to the current position. The new position needs to be checked to see if it exceeds the boundary of the 3D parameter search space; out-of-bounds positions are either pulled back to the boundary or handled with periodic boundary conditions. After each iteration, the fitness value of each particle's new position is recalculated, updating the individual's best historical position and the population's best historical position records. The iterative process is repeated until the preset maximum number of iterations is reached or a convergence condition is met. The convergence condition is typically that the population's best historical position has not significantly improved over multiple consecutive iterations.

[0045] The Particle Swarm Optimization (PSO) algorithm ultimately outputs the simulation time interval corresponding to the swarm's historical best position as the optimal simulation time interval, balancing computational accuracy and efficiency. The adaptive search operation explores the high-dimensional parameter space through swarm intelligence, avoiding getting trapped in local optima. The parameters of the PSO algorithm include population size, maximum number of iterations, inertia weight coefficient, individual learning factor, and swarm learning factor. These parameters affect the algorithm's search performance and convergence speed. The population size determines the number of particles participating in the search; a larger population size increases search diversity but also increases computational cost. The maximum number of iterations controls the algorithm's termination condition, and the inertia weight coefficient can employ a linearly decreasing strategy to enhance search performance.

[0046] The ratio of individual learning factors to group learning factors influences the relative importance of individual and group experiences; a typical setting is to keep the individual and group learning factors equal. A uniformly distributed random number generator is used to ensure the randomness and exploratory capability of the search process. The fitness function is designed considering the impact of the simulation time interval parameter on the accuracy of the numerical simulation; the fitness function value is obtained by calculating the average fitting error over multiple historical time periods. A smaller average fitting error corresponds to a higher fitness value, and the optimal simulation time interval parameter ensures the best match between the numerical simulation results and the measured data.

[0047] The particle swarm optimization (PSO) algorithm exhibits self-organizing characteristics in its search process within a three-dimensional parameter search space. Particles collaboratively explore the parameter space through information sharing and mutual influence. Initially, particles are dispersed throughout the search space, extensively exploring potential solution regions. As iterations progress, particles gradually cluster towards regions with high fitness values. The swarm's historical optimal position guides the entire particle swarm towards the global optimum, while the individual historical optimal positions maintain population diversity and prevent premature convergence. The adaptive search operation can adapt to the volatile characteristics of different sea states, finding the most suitable simulation time interval parameter for each specific environmental condition. The optimal simulation time interval parameter ensures that subsequent numerical simulations improve computational efficiency while maintaining accuracy, meeting the real-time requirements of aerodynamic simulation of the rotor of a maritime rescue helicopter. The parallel nature of the PSO algorithm makes it suitable for implementation in a distributed computing environment, accelerating the computation process of the adaptive search operation.

[0048] Example 4: Numerical simulation of aerodynamic coupling between a rotor and the sea surface based on the optimal simulation time interval. The numerical simulation process is based on the fundamental governing equations of fluid mechanics. The Navier-Stokes equations describe the motion of a viscous incompressible fluid, including mass and momentum conservation equations. The optimal simulation time interval is used as the time discretization step size. Spatial discretization uses a mesh generation method to transform the continuous computational domain into a set of discrete nodes. The discretized Navier-Stokes equations are transformed into a system of algebraic equations, which are solved to obtain the flow field variable values ​​at each mesh node. The finite difference method is applied to the spatiotemporal mesh to solve the discrete equations, covering the rotor rotation region and the sea surface boundary region. Mesh generation generates a uniformly distributed array of mesh points, with each mesh point storing three velocity components and a pressure value. The central difference scheme approximates the spatial derivative term in the Navier-Stokes equations, and the central difference scheme has second-order accuracy, reducing numerical dissipation errors. The explicit time-progression scheme handles the time derivative term, calculating the updated value for the next time step based on the flow field value at the current time step. Each time step requires solving a large system of sparse linear algebraic equations, which are solved numerically using an iterative method. Flow field data from multiple consecutive time steps are combined in chronological order to form a simulation data sequence, which fully records the dynamic process of flow field evolution.

[0049] The discretization process of the Navier-Stokes equations involves the separation of time and spatial terms. The time term discretization uses the optimal simulation time interval as the time step. Spatial derivative discretization employs the finite difference method, which approximates derivative calculations using a linear combination of grid node values. A uniform grid covers the entire fluid computational domain, including the rotor's influence area and the sea surface's influence area. Grid nodes are arranged at equal intervals in three-dimensional space, with the grid spacing determined based on the rotor size and computational accuracy requirements. Boundary nodes specifically handle sea surface wave boundary conditions, which are dynamically adjusted based on historical sea surface wave data. Discrete equations are established on each grid node, containing a weighted combination of values ​​from adjacent nodes. The weighting coefficients are determined by the difference scheme and grid spacing; the accuracy of the difference scheme affects the accuracy of the numerical solution.

[0050] The finite difference method (FDM) employs a step-by-step computation strategy to solve the discretized Navier-Stokes equations on a spatiotemporal grid, with the velocity and pressure fields solved alternately using a coupled algorithm. The mass conservation equation, after discretization, forms the pressure Poisson equation, which ensures the velocity field satisfies the incompressibility condition. The momentum conservation equation is discretized into transport equations with three velocity components, including convection and diffusion terms. The convection term is discretized using a central difference scheme, which avoids numerical dissipation and maintains energy conservation. The diffusion term is discretized using a second-order accurate difference scheme, which accurately captures viscous effects. Time progression uses an explicit Euler scheme, which is simple to implement but requires stability conditions. These stability conditions require a specific relationship between the time step and the grid spacing, and the optimal simulation time interval must satisfy these stability constraints.

[0051] The Gauss-Seidel iterative method is used to solve the linear algebraic equations. This method updates the grid node values ​​one by one. The updated value of each node is immediately used to calculate the values ​​of its neighboring nodes, and the iteration continues until the solution vector converges. The convergence criterion is based on the difference norm between two adjacent iterations; iteration stops when the difference norm is less than a preset threshold. Solving the pressure Poisson equation requires special handling. After discretization, the pressure Poisson equation forms a symmetric positive definite linear system. The conjugate gradient method is suitable for solving the pressure Poisson equation, utilizing gradient information to accelerate convergence. The flow field solution at each time step includes two stages: velocity prediction and pressure correction. In the velocity prediction stage, the pressure gradient is ignored when calculating the intermediate velocity field. In the pressure correction stage, the pressure Poisson equation is solved to obtain the pressure field, which is used to correct the velocity field to satisfy mass conservation.

[0052] The processing of sea surface wave boundaries employs dynamic meshing technology, which adjusts the positions of boundary nodes based on wave equations. These wave equations are derived from historical sea surface wave data sets, describing the temporal and spatial variations in wave elevation. Boundary node positions are dynamically updated over time, while the mesh topology remains constant. Dynamic meshing requires specialized interpolation methods to maintain computational accuracy, transmitting boundary information to internal mesh nodes. The rotor blade region utilizes a rotating mesh, exchanging data with the stationary mesh at the interface. This interface data exchange employs a conserved interpolation method, ensuring flux continuity.

[0053] The generation of the simulation data sequence requires integrating flow field data from multiple time steps, with each time step outputting the flow field variable values ​​for all grid nodes. Data storage employs a hierarchical format, organizing the flow field data by time step. The flow field data includes velocity vector fields and pressure scalar fields, and the data sequence provides complete information for subsequent feature extraction. The numerical characteristics of the finite difference method are reflected through the difference template, which determines the accuracy and stability of the discrete equations. Refer to Table 1 to see the coefficient distribution of the central difference template in three-dimensional space.

[0054] Table 1: Coefficients of the Three-Dimensional Central Difference Template

[0055] , , The grid spacing represents the three coordinate directions, and the truncation error term indicates the precision order of the discretization scheme. The coefficient table is used to construct the coefficient matrix of the discrete equations, which participates in solving the system of linear algebraic equations. The numerical simulation process transforms the partial differential equations into algebraic problems using the finite difference method, and solving these algebraic problems generates flow field evolution data. The simulation data sequence records the complete physical process of the interaction between the rotor downwash airflow and sea surface waves, providing the input basis for aerodynamic identification. The spatiotemporal resolution of the flow field data is determined by the optimal simulation time interval and grid spacing; the resolution setting balances computational accuracy and resource consumption. The numerical simulation results reflect the essential characteristics of aerodynamic coupling effects, and feature extraction is based on the complete flow field evolution history.

[0056] Example 5: Feature extraction and classification of simulation data sequences using an aerodynamic identification model. The aerodynamic identification model is based on a support vector machine (SVM) algorithm to construct a classification decision system. The simulation data sequence originates from the flow field data output by numerical simulation, containing velocity and pressure field distribution information at multiple time steps. The SVM model maps high-dimensional flow field data to a feature space, where the linear decision boundary corresponds to the complex classification interface of the original data space. The feature extraction process extracts discriminative statistical features from the simulation data sequence, including mean, variance, skewness, and kurtosis. Frequency domain features are extracted from the time domain data using Fast Fourier Transform (FFT), reflecting the periodic characteristics of rotor aerodynamics. The feature vectors, combined with statistical and frequency domain features, constitute the input samples for the SVM model. The dimensionality of the input samples is reduced using principal component analysis (PCA). The SVM kernel function calculates the inner product of the feature vectors in the high-dimensional space; the choice of kernel function affects the complexity and generalization ability of the classification surface. The decision function value is calculated based on a weighted average of the support vectors and the kernel function value; the sign of the decision function value determines the classification result of the rotor's operating state. The classification results output the rotor aerodynamic simulation results, and the simulation results indicate the aerodynamic performance level of the rotor under different sea conditions.

[0057] The training process of the Support Vector Machine (SVM) model utilizes historical simulation data sequences and corresponding aerodynamic label data, covering various typical operating conditions. The historical simulation data sequences are generated through numerical simulations of various sea states, including combinations of wave height, wave period, and wind speed. Aerodynamic label data originates from actual flight tests or high-precision wind tunnel experiments, and includes rotor thrust coefficient, torque coefficient, and vibration intensity level. During data preprocessing, the historical simulation data sequences are standardized to ensure that features of different physical quantities have the same scale. Feature selection algorithms remove redundant features to improve model efficiency, and feature selection is based on mutual information or chi-square tests to evaluate the correlation between features and labels. The SVM model selects radial basis functions (RBFs) as kernel functions, which map data to an infinite-dimensional feature space to achieve nonlinear separation. The kernel parameter γ controls the width of the RDF, influencing the curvature of the decision boundary. The penalty parameter C balances model complexity and training error; a larger C value reduces misclassification but may lead to overfitting.

[0058] Sequential minimization (SVM) algorithm solves the support vector machine (SVM) optimization problem by decomposing a large-scale quadratic programming problem into smaller subproblems for iterative solving. Each subproblem involves optimizing two Lagrange multipliers, which correspond to candidate SVMs from the training samples. SVM checks if the multipliers violate the KKT conditions; multipliers that violate the KKT conditions are selected for optimization. Subproblems have analytical solutions, obtained by calculating the error and kernel function values. The optimized multipliers update the decision function parameters, which include bias terms and support vector weights. SVM uses a heuristic rule to select multiplier pairs based on the principle of minimizing error. The iterative process continues until all Lagrange multipliers satisfy the KKT conditions within the tolerance error range. The trained SVM model stores the set of support vectors and their corresponding Lagrange multiplier values.

[0059] The simulation data sequence is input into a pre-trained support vector machine (SVM) model, which standardizes the input feature vectors. The standardization parameters are derived from the training phase and include the feature mean and standard deviation. A kernel function calculates the similarity between the test sample and each support vector, based on the radial basis function. The decision function value is obtained by weighted summation of the kernel function outputs, with the weights being the multipliers of the corresponding support vectors. The decision function value is then transformed into a classification label using a sign function, corresponding to the rotor operating state category. For multi-class problems, a one-to-one or one-to-many strategy is employed. The one-to-one strategy uses multiple binary classifiers to vote on the final category. The SVM model outputs rotor aerodynamic simulation results, including aerodynamic load levels and stability assessments.

[0060] The implementation of the aerodynamic identification model considers a balance between computational efficiency and accuracy. The support vector machine model employs kernel caching technology to accelerate kernel matrix calculation. An incremental learning mechanism adapts to new data patterns, updating model parameters without retraining. The feature extraction stage uses a sliding window to process simulation data sequences, with the window width synchronized to the rotor rotation period. Time-domain features include zero-crossing rate, energy entropy, and short-time energy; frequency-domain features include spectral centroid, spectral roll-off point, and band energy ratio. Feature selection is based on a recursive feature elimination method, which evaluates feature importance through iterative training. Support vector machine model parameters are optimized through cross-validation, which divides the training data into multiple mutually exclusive subsets. A grid search traverses the parameter combination space, finding the hyperparameter configuration that performs best on the validation set.

[0061] A pre-trained support vector machine (SVM) model is deployed in a real-time simulation system, and the model inference time meets the requirements of online applications. Model compression technology reduces the number of support vectors; model compression is achieved by clustering similar support vectors. Hardware acceleration utilizes GPU parallel computing to compute kernel function values, significantly improving classification speed. The aerodynamic recognition model and numerical simulation module form a closed-loop system, enabling adaptive adjustment of simulation parameters. The decision confidence of the SVM model is estimated using Platt scaling, which transforms the decision function values ​​into posterior probabilities. The probability output provides a quantitative basis for risk assessment, and the probability threshold can be adjusted to balance the false positive and false negative rates. The rotor aerodynamic simulation results guide rescue operation decisions, and the simulation results help pilots optimize flight attitude and load distribution.

[0062] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for simulating the aerodynamics of a marine rescue helicopter rotor, characterized in that, The method includes the following steps: The system collects historical data sets of rotor downwash airflow velocity, sea surface wave, and aerodynamic pressure within a preset historical time range by an array of sensors installed in the helicopter rotor area. A dynamic volatility analysis process is performed on the historical velocity data set, historical sea surface wave data set, and historical aerodynamic pressure data set to generate velocity volatility index, sea surface wave volatility index, and aerodynamic pressure volatility index. Using the aforementioned velocity fluctuation index, sea surface wave fluctuation index, and aerodynamic pressure fluctuation index as guiding parameters, an adaptive search operation is performed in the rotor aerodynamic simulation parameter database to determine the optimal simulation time interval. Numerical simulation of the aerodynamic coupling between the rotor and the sea surface is performed based on the optimal simulation time interval to generate a simulation data sequence. The aerodynamic identification model is then used to extract and classify the features of the simulation data sequence, and the rotor aerodynamic simulation results are output.

2. The aerodynamic simulation method for the rotor of a maritime rescue helicopter as described in claim 1, characterized in that, The steps involved in performing dynamic fluctuation analysis on historical velocity datasets, historical sea surface wave datasets, and historical aerodynamic pressure datasets include: The historical velocity data set is processed by applying the empirical mode decomposition method to obtain a set of velocity eigenmode functions. Calculate the variance of each mode function in the set of intrinsic velocity modes, and use the average variance as the velocity fluctuation index; Empirical mode decomposition was performed on the historical sea surface wave data set and the historical aerodynamic pressure data set to obtain the sea surface wave volatility index and the aerodynamic pressure volatility index.

3. The aerodynamic simulation method for the rotor of a maritime rescue helicopter as described in claim 2, characterized in that, The steps for applying the empirical mode decomposition method to perform signal processing on the historical velocity dataset include: Identify all local extrema in the historical velocity dataset and construct upper and lower envelopes using interpolation methods; Calculate the average value of the upper and lower envelopes, and subtract this average value from the original data to obtain the candidate mode functions; Repeat the above process until the mode function stopping criterion is met, and finally extract the set of velocity intrinsic mode functions.

4. The aerodynamic simulation method for the rotor of a maritime rescue helicopter as described in claim 1, characterized in that, The steps for performing an adaptive search operation in the rotor aerodynamic simulation parameter database include: Establish a three-dimensional parameter search space with velocity fluctuation index, sea surface wave fluctuation index, and aerodynamic pressure fluctuation index as coordinate axes; An initial set of candidate points is randomly generated in the three-dimensional parameter search space, and each candidate point corresponds to a simulation time interval parameter. The particle swarm optimization algorithm is used to iteratively update the candidate point set. Each candidate point adjusts its movement direction and step size in the search space based on its individual optimal position and the group optimal position. The fitness value of each candidate point is calculated to evaluate the merits of its corresponding simulation time interval parameter; After a preset number of iterations, the simulation time interval corresponding to the candidate point with the highest fitness value is selected as the optimal simulation time interval.

5. The aerodynamic simulation method for the rotor of a maritime rescue helicopter as described in claim 4, characterized in that, The step of iteratively updating the candidate point set using the particle swarm optimization algorithm includes: Initialize the position and velocity of each particle in the particle swarm, where position represents the candidate simulation time interval parameter and velocity represents the direction and magnitude of parameter adjustment; Calculate the fitness value of each particle's current position, and update the individual's historical best position and the group's historical best position; The velocity of each particle is adjusted according to the velocity update formula of the particle swarm optimization algorithm. This formula takes into account the current velocity of the particle, the optimal position direction of the individual particle and the optimal position direction of the group. Adjust the position of each particle according to the updated velocity to generate a new set of candidate points; The update process is repeated until the maximum number of iterations is reached, and finally the simulation time interval corresponding to the best historical position of the group is selected as the optimal simulation time interval.

6. The aerodynamic simulation method for the rotor of a maritime rescue helicopter as described in claim 1, characterized in that, The steps for numerically simulating the aerodynamic coupling between the rotor and the sea surface include: The Navier-Stokes equations are discretized based on the optimal simulation time interval; The discretized Navier-Stokes equations are solved on a spatiotemporal grid using the finite difference method to obtain the velocity and pressure field distributions. The velocity and pressure field distribution data from multiple time steps are integrated to form the simulation data sequence.

7. The aerodynamic simulation method for the rotor of a maritime rescue helicopter as described in claim 6, characterized in that, The steps for solving the discretized Navier-Stokes equations on a spatiotemporal grid using the finite difference method include: Divide the area of ​​rotor action and the sea surface boundary into uniform grids; The spatial derivative is approximated using the central difference scheme, and the time derivative is approximated using the explicit time-progression scheme. Solve the system of linear algebraic equations and update the flow field variable values ​​for each grid point.

8. The aerodynamic simulation method for the rotor of a maritime rescue helicopter as described in claim 1, characterized in that, The steps of using the aerodynamic identification model to extract features and classify the simulation data sequence include: The simulation data sequence is input into a pre-trained support vector machine model; Data is mapped to a high-dimensional space using the kernel function of a support vector machine, and the decision function value is calculated. The rotor operating state is classified according to the decision function value, and the rotor aerodynamic simulation results are generated.

9. The aerodynamic simulation method for the rotor of a maritime rescue helicopter as described in claim 8, characterized in that, The training steps of the pre-trained support vector machine model include: Collect historical simulation data sequences and corresponding aerodynamic label data; Choose a radial basis function as the kernel function and set the penalty parameter; The support vector machine optimization problem is solved using the sequence minimum optimization algorithm to obtain the model parameters.

10. A marine rescue helicopter rotor aerodynamic simulation system, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the aerodynamic simulation method for the rotor of a maritime rescue helicopter as described in any one of claims 1 to 9.

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