High-precision prediction method for dynamic behaviors of fluid system

Abstract

The invention discloses a high-precision prediction method for dynamic behaviors of a fluid system, belongs to the technical field of dynamic behavior prediction of the fluid system, and solves the problems of relatively low precision and relatively low reliability of dynamic behavior prediction of an existing fluid system. The method comprises the following steps: analyzing dynamic behaviors of a fluid system, and constructing a random differential model considering multiple physical effects in the fluid system; the random differential model comprises a friction coefficient export item and an excitation function export item of each excitation unit; based on the friction coefficient export item and the excitation function export item of each excitation unit, obtaining expressions of a drift function and a fluctuation function of the fluid system; modeling solving processes of the friction coefficient export item and the excitation function export item of each excitation unit, and constructing to obtain a corresponding neural network model; and a drift function and a fluctuation function of the fluid system are solved in combination with the constructed neural network model, so that high-precision prediction of dynamic behaviors of the fluid system is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of fluid system dynamic behavior prediction, and in particular to a high-precision prediction method for the dynamic behavior of a fluid system. Background Art

[0002] In the field of fluid mechanics, accurate prediction and control of the dynamic behavior of objects in fluid systems is crucial to improving the efficiency and reliability of engineering applications. However, traditional analysis methods have significant limitations in dealing with multiple physical parameters and their complex interactions in the interaction between fluids and solids. These physical parameters include but are not limited to the solid-state properties of objects (such as deformation coefficients and vibration coefficients), the mechanical properties of the excitation unit (such as deformation coefficients and elastic recovery time), and the friction characteristics of the fluid. The traditional processing methods have the following main shortcomings: (1) Lack of comprehensive consideration of physical parameters: Traditional methods fail to fully integrate multiple physical parameters such as fluid properties, solid-state properties of objects, and mechanical properties of excitation units, resulting in insufficient prediction accuracy of the model.

[0003] Specifically, traditional models often have difficulty in fully considering these physical parameters and their interactions, resulting in limited accuracy in predicting and controlling the dynamic behavior of fluid systems.

[0004] (2) Low system prediction and control accuracy: Due to the one-sided consideration of physical parameters, it is difficult for system prediction and control to meet high precision requirements.

[0005] Specifically, the one-sided consideration of physical parameters causes the prediction results of traditional models in complex fluid environments to deviate from the actual behavior, making it difficult to meet the application requirements of high-precision and high-reliability dynamic behavior prediction of fluid systems.

[0006] (3) Complex functions are difficult to solve analytically: Complex time-dependent functions in fluid system models, such as friction coefficient derivatives and excitation function derivatives, are difficult to solve directly due to the limitations of traditional analytical methods, which further limits the accuracy and application scope of traditional models.

[0007] (4) Insufficient calculation methods of traditional drift function and volatility function: Traditional calculation methods ignore the time correlation between the friction coefficient and the excitation function, as well as the event correlation and delay effect between the excitation functions, resulting in low prediction accuracy of the long-term behavior and volatility of the system.

[0008] Therefore, in the process of predicting the dynamic behavior of fluid systems, how to comprehensively consider the various physical parameters and their complex interactions involved in the interaction between fluids and solids, achieve high-precision prediction and control of the dynamic behavior of fluid systems, and meet the application requirements of high precision and high reliability is a technical problem that needs to be solved urgently. Summary of the invention

[0009] In view of the above analysis, an embodiment of the present invention aims to provide a high-precision prediction method for the dynamic behavior of a fluid system, so as to solve the problem of low accuracy and low reliability in the existing prediction of the dynamic behavior of a fluid system.

[0010] The present invention discloses a high-precision prediction method for the dynamic behavior of a fluid system, the method comprising: The dynamic behavior of the fluid system is analyzed, and a stochastic differential model considering the multi-physical effects in the fluid system is constructed; the stochastic differential model includes the derived terms of the friction coefficient and the derived terms of the excitation function of each excitation unit; Based on the derived term of the friction coefficient and the derived term of the excitation function of each excitation unit, the expressions of the drift function and the wave function of the fluid system are obtained; The solution process of the derived terms of the friction coefficient and the derived terms of the excitation function of each excitation unit is modeled separately to construct the corresponding neural network model; and combined with the constructed neural network model, the drift function and wave function of the fluid system are solved to achieve high-precision prediction of the dynamic behavior of the fluid system.

[0011] On the basis of the above scheme, the present invention also discloses the following contents: Further, the expression of the drift function of the fluid system is obtained based on the derived term of the friction coefficient and the derived term of the excitation function of each excitation unit, and the following is executed: All the excitation units are combined in pairs, and the two excitation units in each combination are arranged in order to obtain two ordered pairs in each combination; for each ordered pair, a temporal correlation representation model of the corresponding time characteristic related excitation function is constructed, and combined with the corresponding excitation function derived term, the time-related drift sub-term in the corresponding excitation function derived term is obtained; The time-dependent drift sub-items in the excitation function derived items of all ordered pairs are summed to obtain the sum of the time-dependent drift sub-items in all the excitation function derived items; The expression of the drift function of the fluid system is obtained based on the sum of the time-related drift sub-terms in the friction coefficient derived terms and all the excitation function derived terms.

[0012] Further, based on the derived term of the friction coefficient and the derived term of the excitation function of each excitation unit, an expression of the wave function of the fluid system is obtained, and the following is executed: For each ordered pair, the time-dependent fluctuation sub-term in the corresponding excitation function derivative is obtained; The time-dependent fluctuation sub-items in the derived items of the activation functions of all ordered pairs are summed to obtain the sum of the time-dependent fluctuation sub-items in the derived items of all activation functions; The sum of the time-dependent wave sub-terms in all the excitation function derivatives gives the expression of the wave function of the fluid system.

[0013] Furthermore, the solution process of the derived terms of the friction coefficient is modeled separately and executed: According to the independent variables of the friction coefficient derived items, multiple groups of independent variables and their corresponding values ​​of the friction coefficient derived items are obtained to construct a training set of the friction coefficient derived items; The training set of the friction coefficient derived items is used to train the neural network model for predicting the friction coefficient derived items, and a trained neural network model for predicting the friction coefficient derived items is obtained.

[0014] Furthermore, the solution process of the derived term of the excitation function of each excitation unit is modeled separately and executed: For each excitation unit, the independent variables of the excitation function derived items of the corresponding excitation unit are determined respectively, multiple sets of independent variables and their corresponding excitation function derived items are obtained, and a training set of the corresponding excitation function derived items is constructed; The neural network model for predicting the derived items of the corresponding activation function is trained using the training set of the derived items of the corresponding activation function to obtain a trained neural network model for predicting the derived items of the corresponding activation function.

[0015] Furthermore, the constructed neural network model is combined to solve the drift function and fluctuation function of the fluid system, and the high-precision prediction of the dynamic behavior of the fluid system is achieved. The trained neural network model is used to predict the values ​​of the derived terms of the friction coefficient at different times and delay times required for the expression of the drift function of the fluid system, the derived terms of the excitation function of each excitation unit, and the values ​​of the excitation function related to the time characteristics, and the expressions of the drift function of the fluid system are brought into the solution to obtain the drift function of the fluid system; Using the trained neural network model, the derived items of the excitation functions of each excitation unit at different times and delay times required to obtain the expression of the wave function of the fluid system and the values ​​of the excitation functions related to the time characteristics are predicted, and the expression of the wave function of the fluid system is substituted into the expression of the wave function of the fluid system to solve and obtain the wave function of the fluid system; High-precision prediction of the dynamic behavior of the fluid system can be achieved through the drift function and fluctuation function of the fluid system.

[0016] Furthermore, the friction coefficient is derived It is expressed as: (1) in, Indicates time; , , They represent the amplitude function, phase function and offset constant of the displacement of the fluid system respectively; represents angular velocity; represents the friction coefficient of the fluid, , They represent the deformation coefficient and vibration coefficient of the object respectively; Indicates the system frequency; represents the deformation coefficient ratio factor; , Respectively represent the excitation unit Deformation coefficient and elastic recovery time.

[0017] Furthermore, the incentive unit The activation function derived term It is expressed as: (2) in, Indicates The spatial characteristic-related activation function of each activation unit.

[0018] Furthermore, in the process of obtaining the expression of the drift function of the fluid system, the time-related drift sub-item in the corresponding excitation function derived term is obtained by the following method: In each ordered pair, the first excitation unit is denoted as , the second excitation unit is denoted as , define the excitation unit , The time-dependent activation function , ; Constructing incentive units , The time-dependent activation function , Modeling correlation in time ,in, Indicates time delay; The corresponding time-dependent drift component of the derived activation function is: (3) The sum of the time-related drift sub-terms in all the excitation function derivatives is denoted as ; Drift Function of Fluid Systems The expression is expressed as: (4) in, Indicates the time period, Represents the influence and scaling factor of the drift function.

[0019] Furthermore, in the process of obtaining the expression of the wave function of the fluid system, execute: For each ordered pair, the time-dependent fluctuation sub-item in the corresponding excitation function derivative is obtained, which is expressed as: (5) The sum of the time-related fluctuation sub-terms in all the excitation function derivatives is denoted as ; Wave Function of Fluid System The expression is expressed as: (6).

[0020] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: First, the high-precision prediction method for the dynamic behavior of a fluid system proposed in the present invention, by comprehensively considering multi-physical effects and utilizing artificial intelligence neural network technology, can achieve high-precision prediction and control of the dynamic behavior of objects in a fluid system, meet the application requirements of high precision and high reliability, and effectively solve the problem of low accuracy and low reliability in the prediction of the dynamic behavior of existing fluid systems.

[0021] Second, the present invention also proposes a method for constructing a multi-physical effect stochastic differential model, which comprehensively considers key factors such as the solid-state properties of the object, the mechanical properties of the excitation unit, and the fluid friction coefficient, and realizes the accurate prediction and control of the displacement of the fluid system over time. On this basis, a drift function calculation method considering the time correlation of the friction coefficient and the excitation function, and a wave function calculation method considering the event correlation and delay effect between the excitation functions are proposed, which significantly improves the prediction accuracy of the long-term behavior and volatility of the system.

[0022] Third, the present invention also utilizes neural networks and numerical integration methods to achieve efficient and accurate approximation of complex time-dependent functions (such as friction coefficient derivatives, excitation function derivatives, etc.), overcoming the limitations of traditional analytical methods.

[0023] Fourth, the fluid system model proposed in the present invention has high precision and universality. The model is not only suitable for analyzing the dynamic behavior of objects in fluids or at the interface between fluids and solids, but also has high universality and flexibility and can adapt to the needs of different application scenarios.

[0024] In the present invention, the above-mentioned technical solutions can also be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can become obvious from the description, or can be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The accompanying drawings are only used for the purpose of illustrating specific embodiments and are not to be considered as limiting the present invention. In the entire drawings, the same reference symbols represent the same components; Figure 1 A flowchart of a method for high-precision prediction of dynamic behavior of a fluid system provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0026] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.

[0027] A specific embodiment of the present invention discloses a high-precision prediction method for the dynamic behavior of a fluid system. The flowchart of the method is as follows: Figure 1 The specific instructions are as follows.

[0028] Step S1: Analyze the dynamic behavior of the fluid system and construct a stochastic differential model that considers multiple physical effects in the fluid system; the stochastic differential model includes a friction coefficient derived term and an excitation function derived term of each excitation unit.

[0029] A fluid system is a system consisting of fluids (liquids or gases) and containers or pipes containing the fluids, which are used to transport, control, and distribute the fluids. By analyzing the dynamic behavior of the fluid system, the parameters involved in the multi-physics effects of the fluid system can be determined, as described below.

[0030] Object perturbation parameters : , which is used to describe the degree of interference of the outside world on objects in the fluid system.

[0031] Deformation coefficient of the object and vibration coefficient : It can reflect the deformation and vibration characteristics of an object when it is subjected to force.

[0032] Excitation unit ( ) deformation coefficient and elastic recovery time , to describe its mechanical response characteristics, Indicates the total number of excitation units. In a fluid system, an excitation unit refers to a component or device that can generate an excitation effect, provide energy or signal to the fluid system, and thus cause a system response. Exemplarily, there can be many types of excitation units for a fluid 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, etc.), heating excitation units (such as heaters, coolers, etc.), fluid power excitation units (such as nozzles, turbines, etc.), and external force excitation units (such as vibration tables, gravity, etc.).

[0033] Spatial feature dependent activation function : It represents the external force or field that acts on the object in space, which is related to The excitation unit is associated.

[0034] Time-dependent activation function : describes the external stimulus that changes over time, similar to The excitation unit is associated.

[0035] System frequency , which is used to describe the fundamental frequency of the fluid system vibration.

[0036] Angular velocity , which is used to represent the angular velocity of the fluid element.

[0037] Deformation coefficient ratio factor In fluid mechanics, the deformation coefficient ratio factor is often used to describe the deformation characteristics of a fluid element. Specifically, it is a dimensionless parameter that quantifies the degree to which the shape of a fluid element changes during the flow process. This ratio factor can help us understand the deformation behavior of the fluid, especially under complex flow conditions such as vortex, shear flow, etc.

[0038] Friction coefficient of the fluid , which is used to describe the friction coefficient of a fluid system in the liquid state or solid-liquid interface area to take into account the influence of the fluid on the movement of the object.

[0039] As a common fluid system, hydraulic control system is a device that uses the pressure and flow of fluid (usually hydraulic oil) to control the movement of mechanical parts. Hydraulic control system usually includes components such as hydraulic pump, hydraulic valve, actuator (such as hydraulic cylinder or hydraulic motor) and oil tank. By adjusting the opening of hydraulic valve and the displacement of pump, the speed and force of actuator can be precisely controlled. In hydraulic control system, the solid-state characteristics of objects are reflected in: In hydraulic control system, the deformation coefficient and vibration coefficient of actuator (such as piston and cylinder of hydraulic cylinder) have an important influence on the accuracy and stability of the system. In hydraulic control system, the excitation unit can be: hydraulic pump and hydraulic valve and other components, whose 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 rapid response and precise control of hydraulic valve are crucial to the performance of the system. In hydraulic control system, the friction characteristics of fluid are reflected in: When the fluid in hydraulic control system flows in pipes, valves and actuators, friction loss will be generated. These losses are related to the viscosity, flow rate and pipe shape of the fluid. Optimizing pipe design and using low viscosity fluid can reduce friction loss and improve system efficiency.

[0040] The torque converter in the hydraulic transmission system, as a common fluid system, is a device that uses the kinetic energy of fluid (usually oil) to transmit torque and adjust the speed. The torque converter is mainly composed of a pump wheel, a turbine wheel and a guide wheel, and these components usually have complex blade shapes to optimize fluid dynamics. In the torque converter, the fluid is accelerated by the pump wheel and then transferred to the turbine to drive the turbine to rotate; the guide wheel is used to adjust the fluid flow field to improve efficiency. In the torque converter, the solid-state properties of the object are reflected in: 1) Deformation coefficient: The pump wheel, turbine wheel and guide wheel in the torque converter may undergo slight deformation due to fluid pressure and centrifugal force when rotating at high speed. 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 by optimizing the design and using shock-absorbing materials. In a torque converter, the mechanical properties of the excitation unit are reflected in: 1) Deformation coefficient: In a torque converter, the torsional stiffness (i.e., deformation coefficient) of the input and output shafts has an important influence 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 certain elastic seals in the system may have elastic recovery characteristics. These characteristics need to be considered in transient response and stability analysis. In a torque converter, the friction characteristics of the fluid are reflected in: When the fluid in the torque converter flows between the pump wheel, turbine and guide wheel, friction losses are generated. These losses are related to the viscosity, flow rate and blade shape of the fluid. Optimizing blade design and using low-viscosity fluids can reduce friction losses.

[0041] In this embodiment, by analyzing the dynamic behavior of the fluid system and comprehensively considering factors such as the solid-state characteristics of the fluid system, the friction characteristics of the fluid, the time correlation of the excitation function and the delay effect, the long-term behavior and volatility of the fluid 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 the hydraulic oil.

[0042] The following is a detailed description of the stochastic differential model considering multiple physical effects in the fluid system constructed in this embodiment. In the constructed stochastic differential model, by combining key factors such as object disturbance parameters, solid-state characteristics, excitation unit characteristics and fluid friction coefficient, accurate prediction and control of the displacement of the fluid system over time can be achieved, which is suitable for analyzing the dynamic behavior of objects in the fluid or at the interface between the fluid and the solid. Preferably, in this embodiment, the constructed stochastic differential model considering multiple physical effects of the fluid system includes a friction coefficient derivative and an excitation function derivative.

[0043] Modeling the displacement of the fluid system: The displacement of the fluid system is modeled as a cosine function whose amplitude varies with time and is given by the amplitude function Description: Phase changes with time, given by the phase function Description; also introduces the offset constant To consider the initial position. Preferably, in this embodiment, the following method is used to implement the construction of the stochastic differential model. First, derive The stochastic differential equation model of , which contains two key derived terms: the friction coefficient derived term and the excitation function derived terms of each excitation unit; among which, the excitation unit The derived term of the activation function is expressed as .

[0044] Friction coefficient derivative The calculation takes into account the friction coefficient , vibration coefficient , characteristics of the excitation unit ( , ) and system frequency The influence of fluid friction on system displacement is accurately calculated through complex mathematical expressions. It is expressed as: (1) in, Indicates time.

[0045] Excitation unit The activation function derived term According to the mechanical characteristics of the excitation unit and the system displacement , System Phase It is calculated by the above equations, which reflects the contribution of the excitation unit to the system displacement. The activation function derived term It is expressed as: (2) in, Indicates The spatial characteristic-related excitation function of each excitation unit may be determined by the actual application scenario; the spatial characteristic-related excitation function describes the change law of the external force or excitation over time. It can be a periodic force, a random force, or any other form of external action. Represents the displacement of the fluid system.

[0046] Step S2: Based on the derived term of the friction coefficient and the derived term of the excitation function of each excitation unit, the expressions of the drift function and the wave function of the fluid system are obtained.

[0047] In the dynamic behavior analysis process of the fluid system, the drift function is an important function that describes the slow change of the state of the fluid system over time. However, the traditional representation of the drift function often ignores the time correlation between the friction coefficient and the excitation function, resulting in limited model prediction accuracy. In order to solve the above problem, this embodiment adopts a method for calculating the drift function that considers the time correlation between the friction coefficient and the excitation function. This method comprehensively considers the time-related drift sub-items in the friction coefficient derived term and the excitation function derived term, so that the long-term behavior characteristics of the fluid system under different excitation conditions can be more accurately described. The specific process is described as follows.

[0048] Step S21: Based on the derived term of the friction coefficient and the derived term of the excitation function of each excitation unit, an expression of the drift function of the fluid system is obtained.

[0049] Step S211: combine all the excitation units in pairs, and arrange the two excitation units in each combination in order to obtain two ordered pairs in each combination; for each ordered pair, construct a temporal correlation characterization model of the corresponding time characteristic related excitation function, and combine the corresponding excitation function derived items to obtain the time-related drift sub-items in the corresponding excitation function derived items.

[0050] In this step, the following operations are specifically performed.

[0051] Step S2111: In each ordered pair, the first excitation unit is recorded as , the second excitation unit is denoted as , define the excitation unit , The time-dependent activation function , .

[0052] Step S2112: Constructing an excitation unit , The time-dependent activation function , Modeling correlation in time ,in, Indicates time delay.

[0053] The correlation characterization model describes the expected value of the product of different temporal characteristic related activation functions at different time points, reflecting the temporal correlation between them.

[0054] Step S2113: Using the correlation characterization model constructed in step S2112, combined with , calculate the integral and obtain the time-dependent drift sub-item in the corresponding excitation function derivative: (3) Step S212: sum the time-related drift sub-items in the excitation function derived items of all ordered pairs to obtain the sum of the time-related drift sub-items in all excitation function derived items, recorded as .

[0055] Step S213: Obtain an expression for the drift function of the fluid system based on the friction coefficient derived term and the sum of the time-related drift sub-terms in all excitation function derived terms.

[0056] Drift Function of Fluid Systems The expression is expressed as: (4) in, Indicates the time period, Represents the influence and scaling factor of the drift function.

[0057] Step S22: Based on the derived terms of the excitation function of each excitation unit, an expression of the wave function of the fluid system is obtained.

[0058] In the dynamic behavior analysis process of the fluid system of this embodiment, the wave function is a key function to measure the degree of fluctuation of the state variables of the fluid system over time. The traditional expression of the wave function often ignores the time correlation and delay effect between the excitation functions, resulting in inaccurate calculation results. Therefore, this embodiment proposes a new expression of the wave function, which can more comprehensively consider the time correlation and delay effect between the excitation functions, improve the accuracy of the wave function, and provide an important basis for system stability analysis and control strategy design. The specific steps are as follows.

[0059] Step S221: For each ordered pair, obtain the time-related fluctuation sub-item in the corresponding excitation function derived term, expressed as: (5) Step S222: Sum the time-related fluctuation sub-items in the derived items of the activation function of all ordered pairs to obtain the sum of the time-related fluctuation sub-items in the derived items of all activation functions, which is recorded as .

[0060] Step S223: The sum of the time-related fluctuation sub-items in all the excitation function derived items is obtained to obtain the expression of the fluctuation function of the fluid system.

[0061] Wave Function of Fluid System The expression is expressed as: (6) The wave function reflects the state variables of the fluid system. Over time The degree of fluctuation of the change.

[0062] Step S3: Model the solution process of the derived terms of the friction coefficient and the derived terms of the excitation function of each excitation unit respectively, and construct the corresponding neural network model; and combine the constructed neural network model to solve the drift function and fluctuation function of the fluid system to achieve high-precision prediction of the dynamic behavior of the fluid system.

[0063] In the calculation process of the fluid system model involved in this embodiment, it is necessary to process complex time-related functions, such as , , Etc., and combinations of these functions. These functions are often difficult to solve directly analytically, and their characteristics change significantly over time, making it difficult for traditional methods to accurately approximate and calculate them. Therefore, efficient and accurate methods are needed to deal with such problems. This embodiment proposes a method using a neural network and numerical integration to implement the approximation of complex functions and the calculation of drift functions through the following steps.

[0064] Step S31: According to formula (1), determine the independent variables of the friction coefficient derivative (including at least time ), obtain the values ​​of multiple groups of independent variables and their corresponding friction coefficient derived items, and construct a training set of friction coefficient derived items; use the training set of friction coefficient derived items to train the neural network model for predicting friction coefficient derived items, and obtain a trained neural network model for predicting friction coefficient derived items.

[0065] Define or generate data sets for training neural networks. These data sets include a series of time points and related physical parameters. The specific steps are as follows: Determine the time range and time points , generating a time point vector ; Get the training data sets X_train and Y_train, where X_train contains input features (such as , and other physical parameters, etc.), Y_train contains the corresponding output values ​​(the corresponding ).

[0066] In this embodiment, the friction coefficient is used to train the derived term The process of obtaining the dataset is as follows.

[0067] 1) Determine the basic parameters. First, clarify the basic parameters in the system, including the object disturbance parameters , deformation coefficient of solid state characteristics and vibration coefficient , No. The deformation coefficient of the excitation unit and elastic recovery time ( ), set frequency parameters , friction coefficient of liquid or solid-liquid interface , and the deformation coefficient ratio factor .

[0068] 2) Calculate the molecular part. According to formula (1), calculate the friction coefficient derivative This includes calculating , , , and the summation In the summation, for the incentive units, calculate their contribution , and divided by After normalization, the contributions of all excitation units are added together and Add.

[0069] 3) Calculate the denominator. Next, calculate the friction coefficient derivative This includes calculating And the summation Similarly, for each excitation unit , calculate its contribution , and divided by Normalize, then add up the contributions of all excitation units and get Minus Times this sum.

[0070] 4) Calculate the derived terms of the friction coefficient Finally, divide the numerator obtained in step 2) by the denominator obtained in step 3) to obtain the friction coefficient derivative The value of .

[0071] For the friction coefficient derivative to be approximated, a feedforward network with an appropriate number of hidden layer neurons is created. The neural network model for predicting the friction coefficient derivative is trained using the training set of the friction coefficient derivative to obtain a trained neural network model for predicting the friction coefficient derivative.

[0072] Step S32: For each excitation unit, determine the independent variables (including at least time ), obtain multiple groups of independent variables and their corresponding values ​​of the derived items of the activation function, and construct a training set of the derived items of the corresponding activation function; use the training set of the derived items of the corresponding activation function to train the neural network model for predicting the derived items of the corresponding activation function, and obtain a trained neural network model for predicting the derived items of the corresponding activation function.

[0073] Define or generate data sets for training neural networks. These data sets include a series of time points, activation function samples, and related physical parameters. The specific steps are as follows: Determine the time range and time points , generating a time point vector ; Get the training data sets X_train and Y_train, where X_train contains input features (such as , and other physical parameters, etc.), Y_train contains the corresponding output values ​​(the corresponding ).

[0074] In this embodiment, the term used to train the activation function is derived The process of obtaining the dataset is as follows.

[0075] 1) Determine the basic parameters and activation function. First, clarify the derived terms of the activation function All basic parameters related to , , , (spatial characteristic related activation function, the specific form may be determined by the actual application scenario), , , , , , , as well as .

[0076] 2) Calculate the numerator. According to formula (2), calculate the derived term of the activation function: This includes calculating .

[0077] 3) Calculate the denominator. The denominator and the friction coefficient derived term The denominator of is the same, that is Note that although the denominator includes the sum of all excitation units, When the summation term is for a specific is fixed because About function.

[0078] 4) Calculate the derived term of the activation function Finally, divide the numerator obtained in step 2) by the denominator obtained in step 3) to obtain the derived term of the activation function The value of .

[0079] For the activation function to be approximated, a feedforward network with an appropriate number of hidden layer neurons is created. The training set of the activation function derivatives is used to train the neural network model for predicting the corresponding activation function derivatives, and a trained neural network model for predicting the corresponding activation function derivatives is obtained.

[0080] In this embodiment, the excitation function of each excitation unit can be determined according to the actual situation. If the form of the excitation function is relatively simple and easy to solve, it is possible to directly bring the time variable into the excitation function to obtain the corresponding excitation function value. However, in some cases, the excitation function is relatively complex and difficult to solve directly, and it is also possible to consider using a neural network model for training and solving. See step S33.

[0081] Step S33: For each excitation unit's time characteristic related excitation function, the independent variables of the excitation unit's time characteristic related excitation function (including at least time ), obtain multiple groups of independent variables and their corresponding time characteristic related activation function values, and construct a training set of the corresponding time characteristic related activation function; use the training set of the corresponding time characteristic related activation function to train the neural network model for predicting the corresponding time characteristic related activation function, and obtain a trained neural network model for predicting the corresponding time characteristic related activation function.

[0082] Step S34: Utilize the trained neural network model to predict the values ​​of the derived terms of the friction coefficient at different times and delay times required to obtain the expression of the drift function of the fluid system, the derived terms of the excitation function of each excitation unit, and the values ​​of the excitation function related to the time characteristics, substitute them into the expression of the drift function of the fluid system, and solve to obtain the drift function of the fluid system.

[0083] Specifically, the trained neural network is used for prediction, and the drift function is calculated by numerical integration. The specific steps are as follows.

[0084] Use the trained neural network model net_Bn1 for predicting the derived term of the activation function to predict the value of the derived term of the activation function at time point t to obtain the predicted value B_n1_pred of B_n1(t).

[0085] Use the trained neural network model net_Bn2 for predicting the derived term of the activation function to predict the value of the derived term of the activation function at the time point t+tau_values ​​to obtain the predicted value B_n2_pred_shifted of B_n2(t).

[0086] Use the difference method or other numerical differentiation techniques to calculate an approximation of dB_n1 / ds(t).

[0087] And use the trained neural network model to predict the time characteristics of each excitation unit related to the excitation function, , Make predictions respectively and get corresponding prediction results. And calculate the calculation results of the corresponding correlation characterization model .

[0088] For each time point t_i, the integral term integral_at_t_i is calculated using the numerical integration method. The integral term is dB_n1 / ds(t_i), and The product of The integral within the range.

[0089] The integral terms at all time points t are accumulated to obtain the integral term vector integral_term.

[0090] use The total drift function is calculated with integral_term, i.e. the drift function μ(s(t)) of the fluid system.

[0091] Through this method, the approximation accuracy of complex functions related to fluid systems and their combinations is improved, and the complex functions can be accurately approximated through the powerful nonlinear fitting ability of neural networks.

[0092] It should be noted that in the specific implementation process, it is possible to give in advance The value range of The lower limit of the range of values ​​is set to a specific, larger value to simulate the negative infinity situation. The value range of each parameter in the output formula is simulated and predicted using a neural network to obtain the drift function.

[0093] Step S35: Use the trained neural network model to predict the derived terms of the excitation functions of each excitation unit at different times and delay times required to obtain the expression of the wave function of the fluid system and the values ​​of the time-characteristic related excitation functions, substitute them into the expression of the wave function of the fluid system, and solve to obtain the wave function of the fluid system.

[0094] Preferably, this embodiment proposes a method for calculating the wave function based on time-dependent neural network approximation and numerical integration. In the process of processing the time-dependent complex functions of the wave function proposed above, and in the process of calculating specific performance indicators based on these functions, traditional analytical methods often have the disadvantages of difficult analytical solutions or high computational complexity when dealing with such problems. Therefore, a method is needed that can efficiently and accurately approximate complex functions and calculate related performance indicators. This embodiment provides a method based on time-dependent neural network approximation and numerical integration to approximate and calculate the wave function in the fluid system model, thereby improving the accuracy and efficiency in the field of fluid system modeling and analysis. Specifically, the following steps are included.

[0095] (1) Define the problem and prepare data First, we need to define or generate a data set for training the neural network. Since this method deals with time-dependent functions, we can create a series of time points, activation function samples, and related physical parameters. Specifically, we set the total time T, the time step dt, and the corresponding time vector t. Then, we can generate or define the simulated B_n(t) and Functions, and their correlation functions Here, B_n(t) and It can be the output of a physical model or some random process.

[0096] (2) Creating and training a neural network For each function that needs to be approximated (such as B_n(t)), a neural network is trained separately. Neural networks can use common architectures, such as feedforward neural networks, and learn the mapping relationship between input and output through a large amount of training data. Taking B_n(t) as an example, the neural network net_Bn is trained to approximate the actual value of B_n(t). The training process uses the prepared data sets B_train_X and B_train_Y and is trained using standard neural network training algorithms.

[0097] (3) Using neural networks for prediction and numerical integration After the neural network training is completed, it is used for prediction. Specifically, the time vector t is input to the neural network net_Bn1 to obtain the predicted value B_n1_pred of B_n1(t). Then, according to the time delay The range of tau_values ​​is generated, and the prediction neural network net_Bn2 of another activation function fluctuation term is used to predict Considering the possible time boundary situation, appropriate processing is required.

[0098] To calculate the wave function , it is necessary to further perform numerical integration on the time-related terms. Specifically, construct an integral function integrand, which is composed of B_n1(t), and The product of . Additional models or data may be required for calculation if the For each time point t_i, we use the numerical integration method to calculate the integral in Integrate within the domain to obtain the fluctuation item at that time point.

[0099] (4) Calculate the total fluctuation function

[0100] After all the fluctuations at all time points have been calculated, they are combined to calculate the total fluctuation function. This process can be achieved by weighted integration of all fluctuation items on the time vector t, with the weight being the time step or other relevant weight factors. Finally, A quantitative representation of the volatility of the system over the entire time frame.

[0101] It should be noted that in the specific implementation process, it is possible to give in advance The value range of The two boundary values ​​of the range of values ​​are set to specific, larger values ​​to simulate the positive infinity and negative infinity situations. The range of values ​​of each parameter in the output formula is simulated and predicted using a neural network to obtain the fluctuation function.

[0102] This method can efficiently approximate and calculate the wave function in complex fluid system models by combining neural networks with numerical integration. Neural networks have powerful nonlinear mapping capabilities and can capture complex relationships in data; while numerical integration technology ensures the accuracy of the calculation results.

[0103] This embodiment achieves high-precision prediction of the dynamic behavior of the fluid system through the drift function and fluctuation function of the fluid system. Specifically, in this embodiment, the relationship between the drift function and the operation of the fluid system is described as follows: the drift function represents the average trend or main direction of the system displacement over time during the operation of the fluid system. It combines the influence of the friction coefficient, the excitation function, and the solid and liquid properties of the system, and reflects the average behavior of the fluid system under the combined action of external excitation and internal friction. The drift function is calculated to determine the average path or main trend of the fluid system displacement over time. By calculating the drift function, the approximate position of the fluid system at a certain moment in the future can be predicted, as well as the behavior changes of the fluid system under different excitation and friction conditions.

[0104] In this embodiment, the relationship between the wave function and the operation of the fluid system is described as follows: the wave function represents the random fluctuation or uncertainty of the displacement of the system over time in the operation of the fluid system. It reflects the randomness of the system under the combined action of external excitation and internal friction, including the time correlation and delay effect between the excitation functions. The wave function is calculated to quantify the randomness and uncertainty of the displacement of the fluid system over time. By understanding the wave function, the stability, robustness and anti-interference ability of the fluid system under different excitation and friction conditions can be evaluated.

[0105] Those skilled in the art will appreciate that all or part of the processes of the above-mentioned embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.

[0106] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A high-precision prediction method for the dynamic behavior of a fluid system, characterized in that: The method comprises: The dynamic behavior of the fluid system is analyzed, and a stochastic differential model considering the multi-physical effects in the fluid system is constructed; the stochastic differential model includes the derived terms of the friction coefficient and the derived terms of the excitation function of each excitation unit; Based on the derived term of the friction coefficient and the derived term of the excitation function of each excitation unit, the expressions of the drift function and the wave function of the fluid system are obtained; The solution process of the derived terms of the friction coefficient and the derived terms of the excitation function of each excitation unit is modeled separately to construct the corresponding neural network model; and combined with the constructed neural network model, the drift function and wave function of the fluid system are solved to achieve high-precision prediction of the dynamic behavior of the fluid system.

2. The high-precision prediction method for the dynamic behavior of a fluid system according to claim 1, characterized in that: The expression of the drift function of the fluid system is obtained based on the derived term of the friction coefficient and the derived term of the excitation function of each excitation unit, and the following is performed: all the excitation units are combined in pairs, and the two excitation units in each combination are arranged in order to obtain two ordered pairs in each combination; for each ordered pair, a temporal correlation characterization model of the corresponding time characteristic related excitation function is constructed, and combined with the corresponding excitation function derived term, the drift sub-term related to time in the corresponding excitation function derived term is obtained; The time-dependent drift sub-items in the excitation function derived items of all ordered pairs are summed to obtain the sum of the time-dependent drift sub-items in all the excitation function derived items; The expression of the drift function of the fluid system is obtained based on the sum of the time-related drift sub-terms in the friction coefficient derived terms and all the excitation function derived terms.

3. The high-precision prediction method for the dynamic behavior of a fluid system according to claim 2, characterized in that: Based on the derived term of the friction coefficient and the derived term of the excitation function of each excitation unit, the expression of the wave function of the fluid system is obtained, and the following is executed: For each ordered pair, the time-dependent fluctuation sub-term in the corresponding excitation function derivative is obtained; The time-dependent fluctuation sub-items in the derived items of the activation functions of all ordered pairs are summed to obtain the sum of the time-dependent fluctuation sub-items in the derived items of all activation functions; The sum of the time-dependent wave sub-terms in all the excitation function derivatives gives the expression of the wave function of the fluid system.

4. The high-precision prediction method for the dynamic behavior of a fluid system according to claim 3, characterized in that: Model the solution process of the derived terms of the friction coefficient separately and execute: According to the independent variables of the friction coefficient derived items, multiple groups of independent variables and their corresponding values ​​of the friction coefficient derived items are obtained to construct a training set of the friction coefficient derived items; The training set of the friction coefficient derived items is used to train the neural network model for predicting the friction coefficient derived items, and a trained neural network model for predicting the friction coefficient derived items is obtained.

5. The high-precision prediction method for the dynamic behavior of a fluid system according to claim 4, characterized in that: The solution process of the derived term of the excitation function of each excitation unit is modeled separately and executed: For each excitation unit, the independent variables of the excitation function derived items of the corresponding excitation unit are determined respectively, multiple sets of independent variables and their corresponding excitation function derived items are obtained, and a training set of the corresponding excitation function derived items is constructed; The neural network model for predicting the derived items of the corresponding activation function is trained using the training set of the derived items of the corresponding activation function to obtain a trained neural network model for predicting the derived items of the corresponding activation function.

6. The high-precision prediction method for the dynamic behavior of a fluid system according to claim 5, characterized in that: Combined with the constructed neural network model, the drift function and fluctuation function of the fluid system are solved to achieve high-precision prediction of the dynamic behavior of the fluid system and execute: The trained neural network model is used to predict the values ​​of the derived terms of the friction coefficient at different times and delay times required for the expression of the drift function of the fluid system, the derived terms of the excitation function of each excitation unit, and the values ​​of the excitation function related to the time characteristics, and the expressions of the drift function of the fluid system are brought into the solution to obtain the drift function of the fluid system; Using the trained neural network model, the derived items of the excitation functions of each excitation unit at different times and delay times required to obtain the expression of the wave function of the fluid system and the values ​​of the excitation functions related to the time characteristics are predicted, and the expression of the wave function of the fluid system is substituted into the expression of the wave function of the fluid system to solve and obtain the wave function of the fluid system; High-precision prediction of the dynamic behavior of the fluid system can be achieved through the drift function and fluctuation function of the fluid system.

7. The high-precision prediction method for the dynamic behavior of a fluid system according to claim 6, characterized in that: Friction coefficient derivative It is expressed as: （1） in, Indicates time; , , They represent the amplitude function, phase function and offset constant of the displacement of the fluid system respectively; represents angular velocity; represents the friction coefficient of the fluid, , They represent the deformation coefficient and vibration coefficient of the object respectively; Indicates the system frequency; represents the deformation coefficient ratio factor; , Respectively represent the excitation unit Deformation coefficient and elastic recovery time.

8. The high-precision prediction method for the dynamic behavior of a fluid system according to claim 7, characterized in that: Excitation unit The activation function derived term It is expressed as: （2） in, Indicates The spatial characteristics of each excitation unit are related to the excitation function.

9. The high-precision prediction method for the dynamic behavior of a fluid system according to claim 8, characterized in that: In the process of obtaining the expression of the drift function of the fluid system, the time-dependent drift sub-item in the corresponding excitation function derived term is obtained in the following way: In each ordered pair, the first excitation unit is denoted as , the second excitation unit is denoted as , define the excitation unit , The time-dependent activation function , ; Constructing incentive units , The time-dependent activation function , Modeling correlation in time ,in, Indicates time delay; The corresponding time-dependent drift component of the derived activation function is: （3） The sum of the time-related drift sub-terms in all the excitation function derivatives is denoted as ; Drift Function of Fluid Systems The expression is expressed as: （4） in, Indicates the time period, Represents the influence and scaling factor of the drift function.

10. The high-precision prediction method for the dynamic behavior of a fluid system according to claim 9, characterized in that: In the process of obtaining the expression of the wave function of the fluid system, execute: For each ordered pair, the time-dependent fluctuation sub-item in the corresponding excitation function derivative is obtained, which is expressed as: （5） The sum of the time-related fluctuation sub-terms in all the excitation function derivatives is denoted as ; Wave Function of Fluid System The expression is expressed as: （6）。

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