Differential equation and neural network fused fluid dynamic system high-precision prediction method, system and device and medium

Abstract

The invention relates to a fluid dynamic system high-precision prediction method fusing a differential equation and a neural network, belongs to the technical field of fluid dynamic system prediction, and solves the problem that in the prior art, high-precision prediction of fluid dynamic system behaviors cannot be realized by purely depending on the neural network. The method comprises the following steps: analyzing dynamic behaviors of a fluid dynamic system, and constructing an object dynamic behavior simplified model in the fluid dynamic system; initializing system parameters and external excitation parameters, and carrying out numerical solution solving on the object dynamic behavior simplified model to obtain numerical solution time sequence data of object displacement and speed in a fluid dynamic system of a sampling time sequence; and constructing training data of the neural network model for predicting the dynamic behavior of the object based on the numerical solution time sequence data of the displacement and the speed and the external excitation parameters, and predicting the displacement and the speed of the object in the fluid dynamic system at the to-be-predicted time based on the trained neural network model for predicting the dynamic behavior of the object.

Description

Technical Field

[0001] The present invention relates to the technical field of fluid dynamic system prediction, and particularly to a high-precision prediction method and system for a fluid dynamic system that combines differential equations and neural networks. Background Art

[0002] With the continuous progress of science and technology, the research and application of fluid dynamic systems have achieved remarkable development. In the early days, researchers mainly relied on physical models and experimental means to understand and predict the behavior of fluid dynamic systems. These physical models are based on the basic principles of fluid mechanics and, through simplification and assumptions, construct equations describing the laws of fluid motion, such as the Navier-Stokes equation, etc. However, with the increase in the complexity of fluid dynamic systems, especially in cases involving solid-liquid interfaces, multiphase flows, and complex external excitations, the traditional physical models gradually expose their limitations and are difficult to meet the requirements of high-precision prediction and control.

[0003] To overcome the deficiencies of traditional physical models, researchers have begun to explore new modeling methods. In recent years, with the rapid development of computer technology, numerical simulation technology has gradually become an important means for studying fluid dynamic systems. Through high-performance computing, detailed numerical simulations of complex fluid dynamic systems can be carried out, thus making up for the deficiencies of physical models to a certain extent. However, numerical simulation still depends on the accuracy and applicability of physical models, and for highly nonlinear and unsteady fluid dynamic systems, its prediction accuracy still needs to be improved. Therefore, traditional physical models often have difficulty comprehensively considering the nonlinear, unsteady characteristics of fluid dynamic systems and environmental disturbances, and still have limitations in accurately describing and predicting the dynamic behavior of such fluid dynamic systems.

[0004] At the same time, the rise of artificial intelligence technology has brought new opportunities for the prediction and control of fluid dynamic systems. Especially the rapid development of deep learning technology has enabled machine learning models such as neural networks to demonstrate powerful capabilities in dealing with complex nonlinear problems. Researchers have begun to try to apply neural networks to the prediction of fluid dynamic systems, training neural networks to capture the dynamic characteristics of fluid dynamic systems and achieve high-precision prediction of the behavior of fluid dynamic systems. However, due to the lack of physical background knowledge in neural networks, its prediction results are often difficult to ensure accurate and reliable in all cases. Therefore, pure data-driven prediction methods, such as neural networks, although having strong generalization capabilities, are difficult to guarantee the accuracy and reliability of prediction results in the absence of physical background knowledge.

[0005] In summary, how to combine and improve the generalization ability of neural networks to achieve high-precision prediction and control of the behavior of fluid dynamic systems is a technical problem that urgently needs to be solved at present. Summary of the Invention

[0006] In view of the above analysis, the embodiments of the present invention aim to provide a high-precision prediction method and system for a fluid dynamic system that combines differential equations and neural networks, so as to solve the problem in the prior art that it is impossible to achieve high-precision prediction of the behavior of a fluid dynamic system solely relying on neural networks.

[0007] First, the present invention provides a high-precision prediction method for a fluid dynamic system that combines differential equations and neural networks, and the method includes:

[0008] Analyze the dynamic behavior of the fluid dynamic system to construct a simplified model of the dynamic behavior of the object in the fluid dynamic system; the simplified model of the dynamic behavior of the object is in the form of a differential equation;

[0009] According to the physical characteristics and application scenarios of the fluid dynamic system, initialize the system parameters and external excitation parameters, solve the numerical solution of the simplified model of the dynamic behavior of the object, obtain the numerical solution time series data of the displacement and velocity of the object in the fluid dynamic system at the sampling time series, and construct the training data for predicting the dynamic behavior of the object based on the numerical solution time series data of the displacement and velocity and the external excitation parameters to train the neural network model for predicting the dynamic behavior of the object;

[0010] Based on the neural network model for predicting the dynamic behavior of the object that has passed the training, predict the displacement and velocity of the object in the fluid dynamic system at the time to be predicted.

[0011] On the basis of the above method, the present invention also makes the following improvements:

[0012] Further, the simplified model of the dynamic behavior of the object in the fluid dynamic system is expressed as:

[0013]

[0014] wherein, x, respectively represent the displacement, velocity, and acceleration of the object; δ represents the perturbation parameter, f represents the friction coefficient; θ and k respectively represent the deformation coefficient and vibration coefficient of the solid state characteristics of the object; m n , γ n respectively represent the deformation coefficient of the excitation unit n and the elastic recovery time γ n , N represents the total number of excitation units; F n (x), Ξ n (t) respectively represent the excitation function related to the spatial characteristics and the excitation function related to the time characteristics of the excitation unit n; ω represents the vibration frequency.

[0015] Further, the initializing the system parameters and external excitation parameters according to the physical characteristics and application scenarios of the fluid dynamic system is performed as follows:

[0016] Initialize the system parameters according to the physical characteristics of the fluid dynamic system;

[0017] The system parameters include: the initial position, velocity, vibration frequency, perturbation parameter, friction coefficient, deformation coefficient and elastic recovery time of each excitation unit, the deformation coefficient and vibration coefficient of the solid state characteristics of the object;

[0018] Initialize the external excitation parameters according to the application scenario of the fluid dynamic system;

[0019] The external excitation parameters include the excitation function related to the spatial characteristics and the excitation function related to the time characteristics of each excitation unit.

[0020] Furthermore, for solving the numerical solution of the simplified model of the dynamic behavior of the object, execute:

[0021] Apply the system parameters and the external excitation parameters to the simplified model of the dynamic behavior of the object, and perform iterative numerical solution of the simplified model of the dynamic behavior of the object to obtain the numerical solution time series data of the displacement and velocity of the object in the fluid dynamic system at the sampling time series.

[0022] Furthermore, for constructing the training data for predicting the dynamic behavior of the object based on the numerical solution time series data of the displacement and velocity and the external excitation parameters, execute:

[0023] Take each sampling time in the sampling time series and the value of the excitation function related to the time characteristics at the corresponding sampling time as the input of a group of samples respectively, and take the numerical solutions of the displacement and velocity of the object in the fluid dynamic system at the corresponding sampling time obtained by solving as the labels of the corresponding samples, and combine all the samples to construct the training data for predicting the dynamic behavior of the object.

[0024] Furthermore, for training the neural network model for predicting the dynamic behavior of the object, execute:

[0025] Take the input of the sample as the input of the neural network model, take the label of the corresponding sample as the output of the neural network model, and train the parameters of the neural network model to obtain a trained neural network model for predicting the dynamic behavior of the object.

[0026] Furthermore, for predicting the displacement and velocity of the object in the fluid dynamic system at the time to be predicted, execute:

[0027] Take the time to be predicted and the value of the excitation function related to the time characteristics as the input of the neural network model, and output the displacement and velocity of the object in the fluid dynamic system at the time to be predicted by the neural network model.

[0028] Second, the present invention provides a high-precision prediction system for a fluid dynamic system integrating differential equations and neural networks, and the system includes:

[0029] A fluid dynamic system model construction module, which is used to analyze the dynamic behavior of a fluid dynamic system and construct a simplified model of the dynamic behavior of an object in the fluid dynamic system; the simplified model of the dynamic behavior of the object is in the form of a differential equation;

[0030] A neural network model training module, which is used to initialize system parameters and external excitation parameters according to the physical characteristics and application scenarios of the fluid dynamic system, solve the numerical solution of the simplified model of the dynamic behavior of the object, obtain the numerical solution time series data of the displacement and velocity of the object in the fluid dynamic system at the sampling time series, and construct training data for predicting the dynamic behavior of the object based on the numerical solution time series data of the displacement and velocity and the external excitation parameters, so as to train a neural network model for predicting the dynamic behavior of the object;

[0031] A high-precision dynamic behavior prediction module, which is used to predict the displacement and velocity of the object in the fluid dynamic system at the time to be predicted based on the neural network model for predicting the dynamic behavior of the object that has passed the training.

[0032] Third, the present invention provides an electronic device, including:

[0033] A processor; and

[0034] A memory, on which executable code is stored. When the executable code is executed by the processor, the processor is enabled to execute the high-precision prediction method for a fluid dynamic system that integrates a differential equation and a neural network as described above.

[0035] Fourth, the present invention provides a computer-readable storage medium, on which executable code is stored. When the executable code is executed by a processor of an electronic device, the processor is enabled to execute the high-precision prediction method for a fluid dynamic system that integrates a differential equation and a neural network as described above.

[0036] Compared with the prior art, the present invention can at least achieve one of the following beneficial effects:

[0037] The high-precision prediction method and system for a fluid dynamic system that integrates a differential equation and a neural network provided by the present invention have the following advantages:

[0038] (1) By introducing technical means such as the characteristic coefficient of the comprehensive solid-liquid properties and the approximation processing of small terms in the steady state, the solution difficulty can be reduced while maintaining the accuracy of the physical model.

[0039] Specifically, for the solid-liquid interface and multiphase flow systems, the present invention innovatively introduces the characteristic coefficient (ν) of the comprehensive solid-liquid properties, and deeply models it through the convolution function model, refining the dynamic response characteristics of objects in complex environments and improving the prediction accuracy of the model. To reduce the computational complexity and improve the real-time performance, the present invention proposes to omit the approximate small terms in the complex model equation under time-steady state in the steady state, constructing a more concise and high-precision simplified model equation, significantly improving the computational efficiency.

[0040] (2) The present invention proposes a comprehensive prediction method combining a kinetic model and a neural network, which not only retains the accuracy of the physical model but also exerts the generalization ability of the neural network. By accurately describing the physical behavior of the system through the kinetic model and combining the neural network to learn complex non-linear relationships, high-precision prediction of the behavior of the fluid dynamic system is achieved. That is, by utilizing the powerful learning ability of the neural network, the accuracy and reliability of the prediction results are improved. This method not only enriches the theoretical system of fluid dynamic system prediction and control but also provides new ideas and technical support for the research and application in related fields.

[0041] (3) Design of dynamic system prediction and control strategies: Combining the above innovation points, the present invention not only realizes high-precision prediction of the displacement and velocity of the fluid dynamic system but also provides strong data support and control strategy design for engineering design, material science, etc. in related fields. By fully combining the accuracy of the differential equation model and the generalization ability of the neural network, prediction based on the differential equation model and the neural network is achieved.

[0042] In the present invention, the above technical solutions can also be combined with each other to achieve more preferred combination schemes. Other features and advantages of the present invention will be described in the subsequent specification, and some advantages can be made obvious from the specification or understood by implementing the present invention. The objectives and other advantages of the present invention can be realized and obtained from the content specifically pointed out in the specification and the drawings. Description of the Drawings

[0043] The drawings are only for the purpose of showing specific embodiments and are not considered as a limitation to the present invention. Throughout the drawings, the same reference signs represent the same components;

[0044] Figure 1 It is a flowchart of the high-precision prediction method for the fluid dynamic system integrating differential equations and neural networks provided in Embodiment 1 of the present invention;

[0045] Figure 2 It is a schematic structural diagram of the high-precision prediction system for the fluid dynamic system integrating differential equations and neural networks provided in Embodiment 2 of the present invention;

[0046] Figure 3Schematic diagram of the electronic device provided in Embodiment 3 of the present invention. Detailed implementation manners

[0047] The following will specifically describe the preferred embodiments of the present invention with reference to the accompanying drawings. The accompanying drawings form a part of this application and are used together with the embodiments of the present invention to explain the principles of the present invention, rather than to limit the scope of the present invention.

[0048] A specific Embodiment 1 of the present invention discloses a high-precision prediction method for a fluid dynamic system integrating differential equations and neural networks. The flowchart of this method is as Figure 1 shown.

[0049] Step S1: Analyze the dynamic behavior of the fluid dynamic system and construct a simplified model of the dynamic behavior of the object in the fluid dynamic system.

[0050] This embodiment proposes a model and its solution method for accurately simulating the dynamic behavior of an object in a fluid dynamic system in a complex environment (including liquid, liquid-solid interface, and solid characteristics). This model comprehensively considers the displacement, velocity, perturbation, friction, deformation, comprehensive property characteristics, vibration, and spatial and temporal characteristics of external excitation of the object. By constructing a refined dynamic equation, high-precision prediction and control of the object's dynamic behavior are achieved. The specific description is as follows.

[0051] (1) Parameter definition and setting

[0052] A fluid dynamic system refers to a system composed of a fluid (liquid or gas) and a container or pipeline containing the fluid, used for transporting, controlling, and distributing the fluid. By analyzing the dynamic behavior of the fluid dynamic system, the parameters involved in the multi-physical effects of the fluid dynamic system can be determined. The specific description is as follows.

[0053] Object displacement x: Represents the change in the position of the object in space and is a function of time.

[0054] Object velocity Describes how fast the position of the object changes with time and is the derivative of displacement with respect to time.

[0055] Perturbation parameter δ>0: Reflects the intensity of random or periodic interference generated by the environment or within the system on the object's movement.

[0056] Friction coefficient f: Characterizes the ratio of the frictional force to the normal force when the object moves in the liquid or liquid-solid interface region and affects the change in the object's movement speed.

[0057] Deformation coefficient θ: Reflects the ability of the object to resist deformation under solid characteristics and is one of the inherent properties of the object.

[0058] Vibration coefficient k: The vibration characteristics related to the solid state of an object, which describes the ease of vibration of the object when subjected to an external force.

[0059] Solid-liquid comprehensive property characteristic coefficient v: A parameter that comprehensively reflects the solid and liquid characteristics of an object, affecting the overall response of the object in a complex environment. It can be constructed as a comprehensive parameter by integrating various physical properties (such as density, thermal conductivity, viscosity, elastic modulus, etc.) of the object in the solid and liquid states to describe the overall response of the object in a complex environment.

[0060] Excitation function:

[0061] Spatial characteristic-related excitation function F n (x): Represents the external force or field acting on the object at a spatial position. n represents the number of the excitation unit, and there are a total of N excitation units.

[0062] Time characteristic-related excitation function Ξ n (t): Describes the external excitation that changes with time and is also associated with the excitation unit n.

[0063] Deformation coefficient m of the excitation unit (n = 1 to N) n and elastic recovery time γ n , to describe its mechanical response characteristics. N represents the total number of excitation units.

[0064] In a fluid dynamic system, an excitation unit refers to a component or device that can generate an excitation effect, provide energy or a signal for the fluid dynamic system, and thus cause a system response. Exemplarily, there can be various types of excitation units in a fluid dynamic system. The following are some common types: mechanical excitation units (such as pumps, fans, and compressors), electromagnetic excitation units (such as solenoid valves, fluid power pumps), heating excitation units (such as heaters, coolers), fluid power excitation units (such as nozzles, turbines), external force excitation units (such as vibration tables, gravity).

[0065] As a common fluid dynamic system, a hydraulic control system is a device that uses the pressure and flow rate of a fluid (usually hydraulic oil) to control the movement of mechanical components. A hydraulic control system typically includes components such as a hydraulic pump, hydraulic valves, actuators (such as hydraulic cylinders or hydraulic motors), and a fuel tank. By adjusting the opening of the hydraulic valves and the displacement of the pump, the speed and force of the actuator can be precisely controlled. In a hydraulic control system, the solid-state characteristics of an object are reflected in that: in a hydraulic control system, the deformation coefficient and vibration coefficient of the actuator (such as the piston and cylinder block of a hydraulic cylinder) have an important impact on the accuracy and stability of the system. In a hydraulic control system, the excitation unit can be components such as hydraulic pumps and hydraulic valves, and their mechanical characteristics (such as deformation coefficient and elastic recovery time) need to be considered in the transient response and stability analysis of the system. In particular, the fast response and precise control of hydraulic valves are crucial for the performance of the system. In a hydraulic control system, the friction characteristics of the fluid are reflected in that: the fluid in a hydraulic control system generates frictional losses when flowing through pipes, valves, and actuators. These losses are related to the viscosity of the fluid, the flow velocity, and the shape of the pipes. Optimizing the pipe design and using low-viscosity fluids can reduce frictional losses and improve system efficiency.

[0066] The torque converter in the hydrodynamic transmission system, as a common fluid dynamic system, is a device that utilizes the kinetic energy of a fluid (usually oil) to transfer torque and regulate rotational speed. The torque converter mainly consists of an impeller, a turbine, and a stator. These components usually have complex blade shapes to optimize hydrodynamic performance. In the torque converter, the fluid is accelerated by the impeller and then transmitted to the turbine, driving the turbine to rotate. The stator is used to regulate the fluid flow field to improve efficiency. In the torque converter, the solid-state characteristics of an object are reflected in: 1) Deformation coefficient: The impeller, turbine, and stator in the torque converter may undergo minor deformations due to fluid pressure and centrifugal force during high-speed rotation. This deformation can be minimized through advanced materials science and manufacturing processes, but it is still a factor that needs to be considered in system design. 2) Vibration coefficient: Due to the instability of fluid dynamics and the interaction of mechanical components, the torque converter may generate vibrations. These vibrations can be reduced through optimized design and the use of damping materials. In the torque converter, the mechanical characteristics of the excitation unit are reflected in: 1) Deformation coefficient: In the torque converter, the torsional stiffness (i.e., the deformation coefficient) of the input shaft and output shaft has an important impact on the performance of the system. They need to be able to withstand the transmitted torque and maintain a certain rigidity. 2) Elastic recovery time: Although the torque converter itself is not an elastic element, the fluid and some elastic seals in the system may have elastic recovery characteristics. These characteristics need to be considered in transient response and stability analysis. In the torque converter, the friction characteristics of the fluid are reflected in: The fluid in the torque converter generates frictional losses when flowing between the impeller, turbine, and stator. These losses are related to the viscosity of the fluid, the flow velocity, and the blade shape. Optimizing the blade design and using low-viscosity fluid can reduce frictional losses.

[0067] In this embodiment, by analyzing the dynamic behavior of the fluid dynamic system and comprehensively considering factors such as the solid-state characteristics of the fluid dynamic system, the friction characteristics of the fluid, the time correlation and delay effect of the excitation function, the long-term behavior and volatility of the fluid dynamic system can be accurately predicted. For example, in a hydraulic control system, the design and control strategy of the system can be optimized by analyzing the flow characteristics of hydraulic oil.

[0068] (2) Model establishment

[0069] The mathematical model proposed in this embodiment is based on the principles of dynamics and constructs a dynamic behavior model of an object in the fluid dynamic system in combination with the parameters defined above. It is in the form of a second-order nonlinear differential equation, expressed as:

[0070]

[0071] Among them, the left side of the equation reflects the dynamic characteristics of the object itself, including the acceleration and the damping term related to the velocity ( The static deformation term θ and the term (δ·k·v) jointly affected by the perturbation and vibration characteristics. The right side of the equation represents the comprehensive influence of the external excitation on the object's motion, which is weighted by the product of the excitation function related to the spatial and temporal characteristics and the square root of the perturbation parameter to reflect the interaction between different excitation sources and the modulation of the excitation effect by the perturbation.

[0072] According to the differential principle, the following steps can be used to solve the above complex differential equation:

[0073] Step 1: Parameter initialization: Determine the initial values or ranges of all parameters according to the specific application scenario.

[0074] Step 2: Numerical method selection: Adopt numerical differential methods such as the Runge - Kutta method and the Adams method to discretize the continuous time domain and gradually solve the displacement and velocity of the object in an iterative manner.

[0075] Step 3: Excitation function processing: For each excitation unit, calculate the excitation value at the current moment according to the given excitation function related to the spatial and temporal characteristics.

[0076] Step 4: Iterative calculation: Within each time step, calculate the acceleration according to the current displacement, velocity, and external excitation, and then update the velocity and displacement.

[0077] Step 5: Convergence check: Judge whether the difference between the results of two consecutive iterations (that is, the difference between the velocities of two consecutive iterations and the difference between the two displacements) is less than the preset threshold to evaluate the stability and convergence of the solution.

[0078] Step 6: Result output: Output the dynamic characteristic parameters such as the displacement and velocity of the object at different time points for further analysis or control strategy design.

[0079] In the specific implementation process, considering that in the process of solving the numerical solution of the above steps, parameters such as v are set to a series of empirical values through simulation; the speed of obtaining the numerical solution is slow, and the understanding of the problem mechanism is insufficient, and the optimization space is limited. To solve the above problems, this embodiment creatively proposes the following method for modeling the solid - liquid comprehensive property characteristic coefficient and describing the dynamic response characteristics. Preferably, in this embodiment, the solid - liquid comprehensive property characteristic coefficient v is deeply modeled and refined, especially by introducing a convolution function model to accurately describe the dynamic response characteristics of the object in a complex environment. This method not only considers the basic physical properties of the object but also integrates the deformation characteristics of the excitation unit, the elastic recovery time, and the response of the vibration model, thus realizing a comprehensive characterization of the characteristic coefficient v.

[0080] (1) Convolution function model of the solid - liquid comprehensive property characteristic coefficient v

[0081] The convolution function model of the solid-liquid comprehensive property characteristic coefficient v aims to finely describe the comprehensive properties of an object through mathematical tools. This convolution function model combines the deformation coefficient m of the excitation unit n and the elastic recovery time γ n , and through the method of convolution integral, closely links the dynamic behavior of the object with the spatio-temporal characteristics of the external environmental excitation.

[0082] The deformation coefficient m of the excitation unit n : It characterizes the influence of the nth excitation unit on the deformation ability of the object and is one of the important parameters in the model.

[0083] The elastic recovery time γ of the excitation unit n : It reflects the time required for the nth excitation unit to return to its original state after being subjected to an external force and is a key parameter for describing the elastic characteristics of the object.

[0084] The convolution integral term h(τ) characterizing the recovery characteristics: According to formula (2), the function characterizing the recovery characteristics of the object is obtained:

[0085]

[0086] The response function x(t - τ) of the vibration model: It describes the displacement response of the object under the action of vibration, considering the initial displacement x, velocity of the object and the influence of the vibration frequency ω, where τ represents the time delay. The specific expression is:

[0087]

[0088] To solve the convolution function model of the solid-liquid comprehensive property characteristic coefficient ν, the above two functions (2) and (3) are combined through convolution integral to obtain the expression of the characteristic coefficient ν. This expression details the dynamic behavior of the object in a complex environment, and the specific calculation process is as follows:

[0089]

[0090] Substitute the expressions of h(τ) and x(t - τ) into the above formula. After integral operation and algebraic simplification, the convolution function model of the solid-liquid comprehensive property characteristic coefficient v is finally obtained:

[0091]

[0092] In the specific implementation process, the convolution function model of the solid-liquid comprehensive property characteristic coefficient v can be solved according to the following steps:

[0093] The first step: Parameter initialization: According to the specific application scenario, determine the initial displacement x, velocity The vibration frequency ω, and the deformation coefficient m of each excitation unit n and the elastic recovery time γ n .

[0094] Step 2: Calculate the convolution integral term h(τ): Calculate the convolution integral term h(τ) that characterizes the recovery characteristics according to the formula.

[0095] Step 3: Construct the vibration response function x(t - τ): Construct the response function of the vibration model according to the vibration frequency ω and the current state (displacement, velocity) of the object.

[0096] Step 4: Calculate the characteristic coefficient ν: Substitute h(τ) and x(t - τ) into the convolution function model, and calculate the characteristic coefficient ν through numerical integration or analytical methods.

[0097] Result analysis and application: According to the calculated characteristic coefficient ν, analyze the dynamic response characteristics of the object, and apply them to engineering design, materials science, biomechanics and other aspects in related fields.

[0098] The equations of the above two models contain a large number of parameters and complex mathematical expressions. This embodiment provides a method that can not only accurately describe the dynamic behavior of the system, but also simplify the calculation amount and improve the calculation real-time performance. By performing an approximation small term omission process on the original complex model equation under time steady state, a more concise and high-precision system dynamic description method is obtained.

[0099] First, based on the time steady state characteristics of the system, substitute Equation (5) into Equation (1), analyze the original complex model equation, and identify and omit the approximation small terms that can be ignored on the long time scale. These small terms are usually caused by small vibrations inside the system or weak external perturbations, and have little impact on the overall dynamic behavior of the system. Specifically: Analyze each term of the original model equation item by item to identify all terms related to time; According to the steady state characteristics of the system, judge the change trend of each term on the long time scale; Mark those terms that tend to zero or change very little with time as approximation small terms; Omit these approximation small terms to simplify the equation form. These terms are usually caused by small vibrations inside the system or weak external perturbations, and have little impact on the overall dynamic behavior of the system. By omitting these terms, the equation form can be simplified and the calculation efficiency can be improved. After omitting the approximation small terms, reorganize the equation to obtain the simplified model equation (*) formula, that is, the simplified model of the dynamic behavior of the object in the fluid dynamic system:

[0100]

[0101] Based on the above parameters and activation functions, a differential equation model of the system is constructed, which is a simplified model of the dynamic behavior of objects in a fluid dynamic system. This model describes the relationship between the displacement and velocity of the system over time. To handle complex non-linear relationships, numerical solution methods can be used to solve the differential equation.

[0102] The prediction of the displacement and velocity of a dynamic system based on the above simplified model of the dynamic behavior of objects is a key issue in engineering practice. Traditional prediction methods often rely on accurate mathematical models, but in the face of complex systems, these models may be difficult to establish or solve. At the same time, pure data-driven methods such as neural networks, although having strong generalization ability, may be difficult to ensure the accuracy of prediction in the absence of physical background knowledge. To solve this problem, this embodiment presents a prediction method based on a differential equation model and neural network prediction, which is applicable to the prediction of the displacement and velocity of complex dynamic systems. This method combines the accuracy of the differential equation model and the generalization ability of the neural network to achieve efficient prediction of the dynamic behavior of the system.

[0103] Step S2: According to the physical characteristics and application scenarios of the fluid dynamic system, initialize the system parameters and external excitation parameters, solve the numerical solution of the simplified model of the dynamic behavior of the object, obtain the numerical solution time series data of the displacement and velocity of the object in the fluid dynamic system at the sampling time series, and construct the training data for the prediction of the dynamic behavior of the object based on the numerical solution time series data of the displacement and velocity and the external excitation parameters to train the neural network model for the prediction of the dynamic behavior of the object.

[0104] Step S21: Initialize the system parameters according to the physical characteristics of the fluid dynamic system; including: the initial position x of the object, the velocity vibration frequency ω, perturbation parameter δ, friction coefficient f, the deformation coefficient and elastic recovery time of each excitation unit, the deformation coefficient θ and vibration coefficient k of the solid state characteristics of the object;

[0105] Step S22: Initialize the external excitation parameters according to the application scenario of the fluid dynamic system, including the excitation functions related to the spatial characteristics and the excitation functions related to the time characteristics of each excitation unit, which are used to simulate the influence of external excitation on the fluid dynamic system;

[0106] Specifically, according to the application scenario, each excitation unit of the fluid dynamic system can be determined, and according to the characteristics of each excitation unit, the corresponding excitation functions related to the spatial characteristics and the excitation functions related to the time characteristics can be determined respectively; the excitation functions related to the spatial characteristics are used to describe the distribution of the excitation in space, and the excitation functions related to the time characteristics are used to describe the change of the excitation over time. Multiplying the two can describe the spatio-temporal change of this excitation unit.

[0107] Step S23: Apply the system parameters and external excitation parameters to the simplified model of the object's dynamic behavior, and perform iterative numerical solution for the simplified model of the object's dynamic behavior to obtain the numerical solution time series data of the object's displacement and velocity in the fluid dynamic system at the sampling time series.

[0108] Preferably, use a numerical solution method (such as the Runge-Kutta method) to perform iterative numerical solution for the simplified model of the object's dynamic behavior.

[0109] In the specific implementation process, an appropriate numerical differentiation method can be selected, such as the fourth-order Runge-Kutta method, for discretizing the time domain and iteratively solving the differential equation. Define the time step Δt and initialize the time t = 0.

[0110] For each excitation unit n (n = 1, 2, …, N), calculate the excitation F n (x(t)) related to the spatial characteristics and the excitation Ξ n (t) related to the time characteristics at the current time t. Then, calculate the combined excitation effect:

[0111]

[0112] Within each time step Δt, perform iterative calculations according to the following steps:

[0113] Calculate the current acceleration:

[0114] According to the dynamics equation:

[0115]

[0116] Calculate the acceleration a(t) at the current time.

[0117] Update the velocity:

[0118] Use a numerical integration method (such as the intermediate step in the Runge-Kutta method) to update the velocity v(t + Δt):

[0119] v(t + Δt) = v(t) + Δt · a(t)

[0120] Update the displacement:

[0121] According to the updated velocity, calculate the new displacement x(t + Δt):

[0122] x(t + Δt) = x(t) + Δt · v(t + Δt)

[0123] Time stepping:

[0124] Update the time t = t + Δt.

[0125] After each time step, a convergence check is performed to determine whether the difference between the current iteration result and the result of the previous time step is less than a preset threshold ∈. Specifically, it can be done by comparing the relative change in displacement or velocity:

[0126] Judge whether both and

[0127] If the convergence condition is satisfied, the current solution is considered stable and the calculation for the next time step continues; otherwise, the time step Δt is reduced or the numerical method is adjusted and the iterative calculation is performed again.

[0128] After the iterative calculation is completed, the dynamic characteristic parameters such as the displacement x(t_i) and velocity v(t_i) of the object at different time points t_i are output. These results can be stored in a data structure (such as an array or a file) for subsequent analysis or control strategy design.

[0129] Step S24: Use each sampling time in the sampling time series and the values of the excitation functions related to the time characteristics at the corresponding sampling time as the inputs of a set of samples, and use the numerical solutions of the object displacement and velocity in the fluid dynamic system at the corresponding sampling time obtained by solving as the labels of the corresponding samples. Combine all the samples to construct the training data for predicting the dynamic behavior of the object.

[0130] Step S25: Train a neural network model for predicting the dynamic behavior of the object based on the training data.

[0131] Use the input of the sample as the input of the neural network model, and use the label of the corresponding sample as the output of the neural network model. Train the parameters of the neural network model to obtain a trained neural network model for predicting the dynamic behavior of the object.

[0132] Specifically, during the process of training the neural network model for predicting the dynamic behavior of the object, a suitable neural network model can be constructed according to the characteristics of the training data, and the appropriate number of hidden layers and neurons can be set. Then, use the training data to train the neural network model, and minimize the prediction error by adjusting the network weights and biases. In addition, during the training process, training parameters such as the maximum number of iterations and the minimum performance gradient can be configured to optimize the training effect.

[0133] After training is completed, the trained neural network can be used to predict the test data. The prediction results include the displacement and velocity of the system at future time points. To evaluate the accuracy of the prediction, the performance of the neural network is evaluated by calculating the error (such as the mean square error, absolute error, etc.) between the predicted value and the actual value.

[0134] Step S3: Based on the neural network model for predicting the dynamic behavior of an object that has passed the training, predict the displacement and velocity of the object in the fluid dynamic system at the time to be predicted.

[0135] Specifically, take the time to be predicted and the values of the excitation functions related to its time characteristics as the input of the neural network model, and the neural network model outputs the displacement and velocity of the object in the fluid dynamic system at the time to be predicted.

[0136] Specific embodiment 2 of the present invention provides a high-precision prediction system for a fluid dynamic system that integrates differential equations and neural networks. The structural schematic diagram is as Figure 2 shown. This system includes:

[0137] A fluid dynamic system model construction module, which is used to analyze the dynamic behavior of the fluid dynamic system and construct a simplified model of the dynamic behavior of the object in the fluid dynamic system; the simplified model of the dynamic behavior of the object is in the form of a differential equation.

[0138] A neural network model training module, which is used to initialize the system parameters and external excitation parameters according to the physical characteristics and application scenarios of the fluid dynamic system, solve the numerical solution of the simplified model of the dynamic behavior of the object, obtain the numerical solution time series data of the displacement and velocity of the object in the fluid dynamic system at the sampling time series, and construct the training data for predicting the dynamic behavior of the object to train the neural network model for predicting the dynamic behavior of the object.

[0139] A high-precision prediction module for dynamic behavior, which is used to predict the displacement and velocity of the object in the fluid dynamic system at the time to be predicted based on the neural network model for predicting the dynamic behavior of the object that has passed the training.

[0140] Regarding the system in the above embodiments, the specific ways in which each module performs operations have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0141] Figure 3 This is the structural schematic diagram of the electronic device provided by the embodiment of the present invention. Refer to Figure 3 . The electronic device includes a memory and a processor.

[0142] The processor can be a Central Processing Unit (CPU), or it can also be other general-purpose processors, Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor, or the processor can also be any conventional processor, etc.

[0143] The memory can include various types of storage units, such as system memory, read-only memory (ROM), and permanent storage devices. Among them, the ROM can store static data or instructions required by the processor or other modules of the computer. The permanent storage device can be a read-write storage device. The permanent storage device can be a non-volatile storage device that does not lose the stored instructions and data even when the computer is powered off. In some embodiments, the permanent storage device uses a mass storage device (such as a magnetic or optical disk, flash memory) as the permanent storage device. In some other embodiments, the permanent storage device can be a removable storage device (such as a floppy disk, optical drive). The system memory can be a read-write storage device or a volatile read-write storage device, such as dynamic random access memory. The system memory can store some or all of the instructions and data required by the processor during operation. In addition, the memory can include any combination of computer-readable storage media, including various types of semiconductor storage chips (such as DRAM, SRAM, SDRAM, flash memory, programmable read-only memory), and magnetic disks and / or optical disks can also be used. In some embodiments, the memory can include a removable storage device that is readable and / or writable, such as a compact disc (CD), read-only digital versatile disc (such as DVD-ROM, dual-layer DVD-ROM), read-only Blu-ray disc, ultra-dense disc, flash memory card (such as SD card, min SD card, Micro-SD card, etc.), magnetic floppy disk, etc. The computer-readable storage medium does not include carrier waves and instantaneous electronic signals transmitted wirelessly or wired.

[0144] An executable code is stored on the memory. When the executable code is processed by the processor, it can cause the processor to execute some or all of the methods described above.

[0145] In addition, the method according to the present application can also be implemented as a computer program or a computer program product, which includes computer program code instructions for performing some or all of the steps of the above method of the present application.

[0146] Alternatively, the present application can also be implemented as a computer-readable storage medium (or a non-transitory machine-readable storage medium or a machine-readable storage medium) having executable code (or a computer program or computer instruction code) stored thereon. When the executable code (or the computer program or the computer instruction code) is executed by a processor of an electronic device (or a server, etc.), the processor is caused to execute some or all of the steps of the above-described method according to the present application.

[0147] Those skilled in the art can understand that all or part of the process of implementing the above-described embodiment method can be completed by instructing relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium. Among them, the computer-readable storage medium is a magnetic disk, an optical disk, a read-only memory, or a random access memory, etc.

[0148] As described above, the above are only the preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention.

Claims

1. A high-precision prediction method for fluid dynamic systems integrating differential equations and neural networks, characterized in that: The method comprises: Analyze the dynamic behavior of the fluid dynamic system and construct a simplified model of the dynamic behavior of the object in the fluid dynamic system; the simplified model of the dynamic behavior of the object is in the form of a differential equation; Initialize system parameters and external excitation parameters according to the physical characteristics and application scenarios of the fluid dynamic system, perform numerical solution on the simplified model of the dynamic behavior of the object, obtain numerical solution time series data of displacement and velocity of the object in the fluid dynamic system of the sampling time series, construct training data for predicting the dynamic behavior of the object based on the numerical solution time series data of displacement and velocity and the external excitation parameters, so as to train the neural network model for predicting the dynamic behavior of the object; Based on the trained neural network model for predicting the dynamic behavior of objects, the displacement and velocity of objects in the fluid dynamic system at the time to be predicted are predicted.

2. The high-precision prediction method for fluid dynamics system integrating differential equations and neural networks according to claim 1 is characterized in that: The simplified model of the dynamic behavior of objects in a fluid dynamic system is expressed as: Among them, x, They represent the displacement, velocity and acceleration of the object respectively; δ represents the disturbance parameter, f represents the friction coefficient; θ and k represent the deformation coefficient and vibration coefficient of the solid-state characteristics of the object respectively; m n , γ n They represent the deformation coefficient and elastic recovery time γ of the excitation unit n respectively. n , N represents the total number of excitation units; F n (x),Ξ n (t) represent the spatial characteristic related excitation function and the temporal characteristic related excitation function of the excitation unit n respectively; ω represents the vibration frequency.

3. The high-precision prediction method for fluid dynamic systems integrating differential equations and neural networks according to claim 2 is characterized in that: According to the physical characteristics and application scenarios of the fluid dynamic system, the system parameters and external excitation parameters are initialized and executed: Initialize system parameters according to the physical characteristics of the fluid dynamic system; The system parameters include: the initial position, velocity, vibration frequency, disturbance parameter, friction coefficient, deformation coefficient and elastic recovery time of each excitation unit, deformation coefficient and vibration coefficient of the solid state characteristics of the object; Initialize external excitation parameters according to the application scenario of the fluid dynamic system; The external excitation parameters include an excitation function related to spatial characteristics and an excitation function related to temporal characteristics of each excitation unit.

4. The high-precision prediction method for fluid dynamics system integrating differential equations and neural networks according to claim 3 is characterized in that: The simplified model of the dynamic behavior of the object is numerically solved by executing: The system parameters and external excitation parameters are applied to a simplified model of the object's dynamic behavior, and the simplified model of the object's dynamic behavior is iteratively numerically solved to obtain numerical solution time series data of the displacement and velocity of the object in the fluid dynamic system in a sampling time series.

5. The high-precision prediction method for fluid dynamics system integrating differential equations and neural networks according to claim 4 is characterized in that: The training data for predicting the dynamic behavior of an object is constructed based on the numerical solution time series data of displacement and velocity and external excitation parameters, and the following is executed: Each sampling time in the sampling time series and the value of the time characteristic related excitation function of the corresponding sampling time are taken as the input of a group of samples, and the numerical solutions of the displacement and velocity of the object in the fluid dynamic system at the corresponding sampling time are taken as the labels of the corresponding samples. All samples are combined to construct the training data for predicting the dynamic behavior of the object.

6. The high-precision prediction method for fluid dynamics system integrating differential equations and neural networks according to claim 5 is characterized in that: The neural network model for training object dynamic behavior prediction executes: The input of the sample is used as the input of the neural network model, the label of the corresponding sample is used as the output of the neural network model, the parameters of the neural network model are trained, and a neural network model for predicting the dynamic behavior of the object that has passed the training is obtained.

7. The high-precision prediction method for fluid dynamics system integrating differential equations and neural networks according to claim 6 is characterized in that: The prediction of the displacement and velocity of an object in a fluid dynamic system at a time to be predicted is performed by: The value of the activation function related to the time to be predicted and its time characteristics is used as the input of the neural network model, and the neural network model outputs the displacement and velocity of the object in the fluid dynamic system at the time to be predicted.

8. A high-precision prediction system for fluid dynamic systems that integrates differential equations and neural networks, characterized in that: The system comprises: A fluid dynamic system model building module is used to analyze the dynamic behavior of the fluid dynamic system and build a simplified model of the dynamic behavior of the object in the fluid dynamic system; the simplified model of the dynamic behavior of the object is in the form of a differential equation; A neural network model training module is used to initialize system parameters and external excitation parameters according to the physical characteristics and application scenarios of the fluid dynamic system, numerically solve the simplified model of the object's dynamic behavior, obtain the numerical solution time series data of the displacement and velocity of the object in the fluid dynamic system of the sampling time series, and construct training data for object dynamic behavior prediction based on the numerical solution time series data of the displacement and velocity and the external excitation parameters to train the neural network model for object dynamic behavior prediction; The dynamic behavior high-precision prediction module is used to predict the displacement and velocity of objects in the fluid dynamic system at the time to be predicted based on the trained neural network model for predicting the dynamic behavior of objects.

9. An electronic device, characterized in that: include: processor; as well as A memory having executable codes stored thereon, which, when executed by the processor, causes the processor to execute a high-precision prediction method for a fluid dynamic system integrating differential equations and neural networks as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: Executable codes are stored thereon, and when the executable codes are executed by a processor of an electronic device, the processor is caused to execute a high-precision prediction method for a fluid dynamic system integrating differential equations and neural networks as described in any one of claims 1 to 7.

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