A high-precision prediction method for the dynamic behavior of a fluid system

Abstract

The present invention discloses a high-precision prediction method for the dynamic behavior of a fluid system, belonging to the technical field of prediction of the dynamic behavior of a fluid system, and solving the problems of low prediction accuracy and low reliability of the existing prediction of the dynamic behavior of a fluid system. The method includes: analyzing the dynamic behavior of the fluid system and constructing a stochastic differential model considering multiple physical effects in the fluid system; the stochastic differential model includes a friction coefficient derivative term and an excitation function derivative term of each excitation unit; based on the friction coefficient derivative term and the excitation function derivative term of each excitation unit, obtaining expressions of the drift function and the fluctuation function of the fluid system; respectively modeling the solution processes of the friction coefficient derivative term and the excitation function derivative term of each excitation unit to construct corresponding neural network models; and combining the constructed neural network models to solve the drift function and the fluctuation function of the fluid system, so as to achieve high-precision prediction of the dynamic behavior of the fluid system.

Description

Technical Field

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

[0002] In the field of fluid mechanics, accurately predicting and controlling the dynamic behavior of objects in fluid systems is crucial for improving the efficiency and reliability of engineering applications. However, traditional analytical methods have significant limitations in dealing with multiple physical parameters and their complex interactions during the fluid-solid interaction process. These physical parameters include, but are not limited to, the solid-state characteristics of objects (such as deformation coefficients, vibration coefficients), the mechanical characteristics of excitation units (such as deformation coefficients, elastic recovery times), and the friction characteristics of fluids, etc. The traditional processing methods mainly have the following deficiencies:

[0003] (1) Lack of comprehensive consideration of physical parameters: Traditional methods fail to fully integrate multiple physical parameters such as fluid characteristics, object solid-state characteristics, and excitation unit mechanical characteristics, resulting in insufficient prediction accuracy of the model.

[0004] Specifically, traditional models often have difficulty comprehensively considering these physical parameters and their interactions, leading to limited prediction and control accuracy of the dynamic behavior of fluid systems.

[0005] (2) Low system prediction and control accuracy: Due to the one-sided consideration of physical parameters, it is difficult for the system to meet the high-precision requirements for prediction and control.

[0006] Specifically, the one-sided consideration of physical parameters causes the prediction results of traditional models to deviate from the actual behavior in complex fluid environments, making it difficult to meet the application requirements of high precision and high reliability for the prediction of the dynamic behavior of fluid systems.

[0007] (3) Difficulty in analytically solving complex functions: Complex time-related functions in fluid system models, such as friction coefficient derivative terms, excitation function derivative terms, etc., are difficult to directly solve due to the limitations of traditional analytical methods, further restricting the accuracy and application scope of traditional models.

[0008] (4) Deficiencies in traditional drift function and fluctuation function calculation methods: Traditional calculation methods ignore the time correlation of friction coefficients and excitation functions, as well as the event correlation and delay effects between excitation functions, resulting in low prediction accuracy of the long-term behavior and volatility of the system.

[0009] Therefore, in the process of predicting the dynamic behavior of fluid systems, how to comprehensively consider multiple physical parameters and their complex interactions involved in the fluid-solid interaction process, 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 urgently needs to be solved at present. Summary of the Invention

[0010] In view of the above analysis, embodiments of the present invention aim to provide a high-precision prediction method for the dynamic behavior of a fluid system to solve the problems of low prediction accuracy and low reliability of the dynamic behavior of existing fluid systems.

[0011] The present invention discloses a high-precision prediction method for the dynamic behavior of a fluid system, and the method includes:

[0012] Analyze the dynamic behavior of the fluid system and construct a stochastic differential model considering multiple physical effects in the fluid system; the stochastic differential model includes a friction coefficient derivative term and an excitation function derivative term of each excitation unit;

[0013] Based on the friction coefficient derivative term and the excitation function derivative term of each excitation unit, obtain the expressions of the drift function and the fluctuation function of the fluid system;

[0014] Model the solution processes of the friction coefficient derivative term and the excitation function derivative term of each excitation unit respectively to construct corresponding neural network models; and combine the constructed neural network models to solve the drift function and the fluctuation function of the fluid system to achieve high-precision prediction of the dynamic behavior of the fluid system.

[0015] On the basis of the above solution, the present invention also discloses the following:

[0016] Further, for obtaining the expression of the drift function of the fluid system based on the friction coefficient derivative term and the excitation function derivative term of each excitation unit, perform:

[0017] Combine all the excitation units in pairs, and arrange the two excitation units in each pair in an orderly manner to obtain two ordered pairs in each pair; for each ordered pair, construct a correlation characterization model of the time characteristics of the corresponding excitation function related to time, and combine the corresponding excitation function derivative term to obtain the drift sub-item related to time in the corresponding excitation function derivative term;

[0018] Sum up the drift sub-items related to time in the excitation function derivative terms of all ordered pairs to obtain the sum of the drift sub-items related to time in all excitation function derivative terms;

[0019] According to the friction coefficient derivative term and the sum of the drift sub-items related to time in all excitation function derivative terms, obtain the expression of the drift function of the fluid system.

[0020] Further, for obtaining the expression of the fluctuation function of the fluid system based on the friction coefficient derivative term and the excitation function derivative term of each excitation unit, perform:

[0021] For each ordered pair, obtain the fluctuation sub-item related to time in the corresponding excitation function derivative term;

[0022] Sum the time-related fluctuation sub-items in the derivative terms of the excitation functions for all ordered pairs to obtain the sum of the time-related fluctuation sub-items in all derivative terms of the excitation functions;

[0023] The sum of the time-related fluctuation sub-items in all derivative terms of the excitation functions gives the expression of the fluctuation function of the fluid system.

[0024] Furthermore, model the solution processes of the derivative terms of the friction coefficient separately and perform:

[0025] According to the independent variables of the derivative terms of the friction coefficient, obtain multiple sets of independent variables and their corresponding values of the derivative terms of the friction coefficient, and construct a training set for the derivative terms of the friction coefficient;

[0026] Use the training set of the derivative terms of the friction coefficient to train the neural network model for predicting the derivative terms of the friction coefficient, and obtain a neural network model for predicting the derivative terms of the friction coefficient that has passed the training.

[0027] Furthermore, model the solution processes of the derivative terms of the excitation functions of each excitation unit separately and perform:

[0028] For each excitation unit, determine the independent variables of the derivative terms of the excitation function of the corresponding excitation unit separately, obtain multiple sets of independent variables and their corresponding values of the derivative terms of the excitation function, and construct a training set for the derivative terms of the corresponding excitation function;

[0029] Use the training set of the derivative terms of the corresponding excitation function to train the neural network model for predicting the derivative terms of the corresponding excitation function, and obtain a neural network model for predicting the derivative terms of the corresponding excitation function that has passed the training.

[0030] Furthermore, in combination with the constructed neural network model, solve the drift function and the fluctuation function of the fluid system to achieve high-precision prediction of the dynamic behavior of the fluid system, and perform:

[0031] Use the neural network model that has passed the training to predict the values of the derivative terms of the friction coefficient at different times and delay times required for the expression of the drift function of the fluid system, the derivative terms of the excitation functions of each excitation unit, and the values of the time-characteristic related excitation functions, substitute them into the expression of the drift function of the fluid system, and solve to obtain the drift function of the fluid system;

[0032] Use the neural network model that has passed the training to predict the values of the derivative terms of the excitation functions of each excitation unit and the time-characteristic related excitation functions at different times and delay times required for the expression of the fluctuation function of the fluid system, substitute them into the expression of the fluctuation function of the fluid system, and solve to obtain the fluctuation function of the fluid system;

[0033] High-precision prediction of the dynamic behavior of a fluid system is achieved through the drift function and the fluctuation function of the fluid system.

[0034] Furthermore, the friction coefficient derivative term is expressed as:

[0035] (1)

[0036] where represents time; , , respectively represent the amplitude function, phase function, and offset constant of the displacement of the fluid system; represents the angular velocity; represents the friction coefficient of the fluid, , respectively represent the deformation coefficient and vibration coefficient of the object; represents the system frequency; represents the deformation coefficient ratio factor; , respectively represent the deformation coefficient and elastic recovery time of the excitation unit

[0037] Furthermore, the excitation function derivative term of the excitation unit is expressed as:

[0038] (2)

[0039] where represents the excitation function related to the spatial characteristics of the th excitation unit.

[0040] Furthermore, in the process of obtaining the expression of the drift function of the fluid system, the drift sub-item related to time in the corresponding excitation function derivative term is obtained through the following method:

[0041] In each ordered pair, the first excitation unit is denoted as , and the second excitation unit is denoted as . Define the excitation functions , related to the time characteristics of the excitation units , ;

[0042] Construct the correlation characterization model , of the excitation functions , related to the time characteristics of the excitation units in terms of their correlation in time, where Indicates a time delay;

[0043] The time - related drift component in the corresponding excitation function derivative term:

[0044] (3)

[0045] Denote the sum of the time - related drift components in all excitation function derivative terms as ;

[0046] The drift function of the fluid system is expressed as:

[0047] (4)

[0048] where, represents the time period, represents the influence and scaling factor of the drift function.

[0049] Furthermore, in the process of obtaining the expression of the fluctuation function of the fluid system, execute:

[0050] For each ordered pair, obtain the time - related fluctuation component in the corresponding excitation function derivative term, which is expressed as:

[0051] (5)

[0052] Denote the sum of the time - related fluctuation components in all excitation function derivative terms as ;

[0053] The fluctuation function of the fluid system is expressed as:

[0054] (6).

[0055] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0056] First, the high - precision prediction method for the dynamic behavior of the fluid system proposed by the present invention, by comprehensively considering multi - physical effects and using artificial intelligence neural network technology, can achieve high - precision prediction and control of the dynamic behavior of objects in the fluid system, meet the application requirements of high precision and high reliability, and well solve the problems of low prediction accuracy and low reliability of the dynamic behavior of existing fluid systems.

[0057] Second, the present invention also proposes a method for constructing a multi-physical effect stochastic differential model, comprehensively considering key factors such as the solid state characteristics of the object, the mechanical characteristics of the excitation unit, and the fluid friction coefficient, etc., realizing the accurate prediction and control of the displacement of the fluid system over time. On this basis, a calculation method for the drift function considering the friction coefficient and the time correlation of the excitation function, and a calculation method for the fluctuation function considering the event correlation and delay effect between the excitation functions are proposed, significantly improving the prediction accuracy of the long-term behavior and volatility of the system.

[0058] Third, the present invention also uses neural networks and numerical integration methods to achieve efficient and accurate approximation of complex time-dependent functions (such as friction coefficient derivative terms, excitation function derivative terms, etc.), overcoming the limitations of traditional analytical methods.

[0059] Fourth, the high precision and universality of the fluid system model proposed by the present invention. This model is not only applicable to analyzing the dynamic behavior of objects in fluids or at the fluid-solid interface, but also has high universality and flexibility, and can adapt to the requirements of different application scenarios.

[0060] 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 through the content specifically pointed out in the specification and the drawings. Description of the Drawings

[0061] The drawings are only for the purpose of showing specific embodiments and are not considered as a limitation of the present invention. Throughout the drawings, the same reference signs represent the same components;

[0062] Figure 1 It is a flowchart of a high-precision prediction method for the dynamic behavior of a fluid system provided by an embodiment of the present invention. Detailed Embodiments

[0063] The following will specifically describe the preferred embodiments of the present invention with reference to the drawings, where the 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.

[0064] A specific embodiment of the present invention discloses a high-precision prediction method for the dynamic behavior of a fluid system, and the flowchart of this method is as Figure 1 shown and is specifically described as follows.

[0065] 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.

[0066] 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.

[0067] Object perturbation parameters : , which is used to describe the degree of interference of the outside world on objects in the fluid system.

[0068] 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.

[0069] 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.).

[0070] Spatial feature dependent activation function : It represents the external force or field acting on the object in space, which is related to The excitation unit is associated.

[0071] Time-dependent activation function : describes the external stimulus that changes over time, similar to The excitation units are associated.

[0072] System frequency , which is used to describe the fundamental frequency of the fluid system vibration.

[0073] Angular velocity , which is used to represent the angular velocity of the fluid element.

[0074] Deformation coefficient ratio factor , in fluid mechanics, the deformation coefficient ratio factor is usually used to describe the deformation characteristics of fluid elements. Specifically, it is a dimensionless parameter used to quantify the degree of shape change of fluid elements during flow. This ratio factor helps us understand the deformation behavior of fluids, especially under complex flow conditions such as vortices and shear flows.

[0075] Friction coefficient of fluid , which is used to describe the friction coefficient of a fluid system in the liquid state or at the liquid-solid interface region, to consider the influence of the fluid on the motion of an object.

[0076] As a common fluid system, a hydraulic control system is a device that uses the pressure and flow rate of a fluid (usually hydraulic oil) to control the motion 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: 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 units 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: 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.

[0077] The torque converter in the hydrodynamic transmission system, as a common fluid system, is a device that uses the kinetic energy of a fluid (usually oil) to transmit torque and adjust the rotational speed. The torque converter mainly consists of a pump 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 pump impeller and then transmitted to the turbine, thus driving the turbine to rotate; the stator is used to adjust 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 pump 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 the 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 friction losses when flowing between the pump 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 friction losses.

[0078] 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 and delay effect of the excitation function, 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 hydraulic oil.

[0079] Next, the specific description of the stochastic differential model considering multiple physical effects in the fluid system constructed in this embodiment is as follows. In the constructed stochastic differential model, by combining key factors such as object perturbation parameters, solid-state characteristics, excitation unit characteristics, and fluid friction coefficients, accurate prediction and control of the displacement change of the fluid system over time can be achieved, which is applicable to analyzing the dynamic behavior of objects in the fluid or at the fluid-solid interface. Preferably, in this embodiment, the constructed stochastic differential model considering multiple physical effects in the fluid system includes a friction coefficient derivation term and an excitation function derivation term.

[0080] Modeling the displacement of a fluid system: The displacement of the fluid system is modeled as a cosine function, whose amplitude varies with time and is described by an amplitude function ; the phase varies with time and is described by a phase function ; meanwhile, an offset constant is introduced to account for the initial position. Preferably, in this embodiment, the construction of the stochastic differential model is implemented in the following manner. First, a stochastic differential equation model for is derived, which includes two key derived terms: the friction coefficient derived term and the excitation function derived term of each excitation unit; among them, the excitation function derived term of the excitation unit is expressed as .

[0081] The friction coefficient derived term takes into account the comprehensive effects of the friction coefficient , the vibration coefficient , the characteristics of the excitation unit ( , ) and the system frequency , and accurately calculates the influence of fluid friction on the system displacement through a complex mathematical expression. The friction coefficient derived term is expressed as:

[0082] (1)

[0083] where represents time.

[0084] The excitation function derived term of the excitation unit is calculated based on the mechanical characteristics of the excitation unit, the system displacement , the system phase , etc., and reflects the contribution of the excitation unit to the system displacement. The excitation function derived term of the excitation unit is expressed as:

[0085] (2)

[0086] where represents the excitation function related to the spatial characteristics of the th excitation unit, and its specific form may be determined by the actual application scenario; the excitation function related to the spatial characteristics describes the variation law of the external force or excitation with time. It can be a periodic force, a random force, or any other form of external action. represents the displacement of the fluid system.

[0087] Step S2: Based on the derived terms of the friction coefficient and the derived terms of the excitation functions of each excitation unit, obtain the expressions of the drift function and the fluctuation function of the fluid system.

[0088] In the process of analyzing the dynamic behavior 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. To solve the above problems, in this embodiment, a calculation method of the drift function considering the time correlation between the friction coefficient and the excitation function is adopted. This method comprehensively considers the drift sub-items related to time in the derived terms of the friction coefficient and the derived terms of the excitation function, so as to be able to more accurately describe the long-term behavior characteristics of the fluid system under different excitation conditions. The specific process is described as follows.

[0089] Step S21: Based on the derived terms of the friction coefficient and the derived terms of the excitation functions of each excitation unit, obtain the expression of the drift function of the fluid system.

[0090] Step S211: Combine all the excitation units in pairs, and arrange the two excitation units in each pair in an orderly manner to obtain two ordered pairs in each pair; for each ordered pair, construct a correlation characterization model of the time characteristics-related excitation function in time, and combine the corresponding derived terms of the excitation function to obtain the drift sub-items related to time in the corresponding derived terms of the excitation function.

[0091] In this step, the following operations are specifically performed.

[0092] Step S2111: In each ordered pair, denote the first excitation unit as , and the second excitation unit as , and define the time characteristics-related excitation functions , of the excitation units. , .

[0093] Step S2112: Construct a correlation characterization model , of the time characteristics-related excitation functions , in time, where , and represents the time delay.

[0094] The correlation characterization model describes the expected value of the product of different time characteristics-related excitation functions at different time points, reflecting the time correlation between them.

[0095] Step S2113: Using the correlation characterization model constructed in Step S2112, combine , calculate the integral to obtain the time-related drift sub-item in the corresponding excitation function derivative term:

[0096] (3)

[0097] Step S212: Sum up the time-related drift sub-items in the excitation function derivative terms of all ordered pairs to obtain the sum of the time-related drift sub-items in all excitation function derivative terms, denoted as .

[0098] Step S213: Based on the friction coefficient derivative term and the sum of the time-related drift sub-items in all excitation function derivative terms, obtain the expression of the drift function of the fluid system.

[0099] The drift function of the fluid system is expressed as:

[0100] (4)

[0101] where represents the time period, represents the influence and scaling factor of the drift function.

[0102] Step S22: Based on the excitation function derivative terms of each excitation unit, obtain the expression of the fluctuation function of the fluid system.

[0103] In the process of analyzing the dynamic behavior of the fluid system in this embodiment, the fluctuation function is a key function for measuring the degree of fluctuation of the state variables of the fluid system over time. The traditional expression of the fluctuation function often ignores the time correlation and delay effect between excitation functions, resulting in inaccurate calculation results. Therefore, this embodiment proposes a new expression of the fluctuation function, which can more comprehensively consider the time correlation and delay effect between excitation functions, improve the accuracy of the fluctuation function, and provide an important basis for system stability analysis and control strategy design. The specific steps are as follows.

[0104] Step S221: For each ordered pair, obtain the time-related fluctuation sub-item in the corresponding excitation function derivative term, expressed as:

[0105] (5)

[0106] Step S222: Sum up the time-related fluctuation sub-items in the excitation function derivative terms of all ordered pairs to obtain the sum of the time-related fluctuation sub-items in all excitation function derivative terms, denoted as .

[0107] Step S223: Sum the time-related fluctuation components in all the derivative terms of the activation functions to obtain the expression of the fluctuation function of the fluid system.

[0108] The fluctuation function of the fluid system The expression is represented as:

[0109] (6)

[0110] This fluctuation function reflects the state variables of the fluid system changing with time and the degree of fluctuation.

[0111] Step S3: Model the solution processes of the derivative term of the friction coefficient and the derivative terms of the activation functions of each excitation unit respectively to construct the corresponding neural network models; and combine the constructed neural network models to solve the drift function and the fluctuation function of the fluid system, so as to achieve high-precision prediction of the dynamic behavior of the fluid system.

[0112] 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 directly solve analytically, and their characteristics change significantly with time, making it difficult for traditional methods to accurately approximate and calculate. Therefore, an efficient and accurate method is needed to handle such problems. This embodiment proposes a method using neural networks and numerical integration to achieve the approximation of complex functions and the calculation of the drift function through the following steps.

[0113] Step S31: According to formula (1), determine the independent variables of the derivative term of the friction coefficient (including at least time ), obtain multiple sets of independent variables and their corresponding values of the derivative term of the friction coefficient, and construct the training set of the derivative term of the friction coefficient; use the training set of the derivative term of the friction coefficient to train the neural network model for predicting the derivative term of the friction coefficient to obtain the neural network model for predicting the derivative term of the friction coefficient that passes the training.

[0114] Define or generate the data sets for training the neural network. These data sets include a series of time points and related physical parameters. The specific steps are as follows: Determine the time range and the number of time points , generate the time point vector ; obtain the data sets X_train and Y_train for training, where X_train contains input features (such as , and other physical parameters, etc.), and Y_train contains the corresponding output values (the corresponding to the independent variables).

[0115] In this embodiment, the process of obtaining the dataset for training the friction coefficient derivation term is as follows.

[0116] 1) Determine the basic parameters. First, clarify each basic parameter in the system, including the object perturbation parameter , the deformation coefficient of the solid state characteristics and the vibration coefficient , the deformation coefficient of the th excitation unit and the elastic recovery time ( ), set the frequency parameter , the friction coefficient in the liquid or liquid-solid interface region, and the deformation coefficient ratio factor .

[0117] 2) Calculate the numerator part. According to formula (1), calculate the numerator part of the friction coefficient derivation term . This includes calculating , , , and the summation term . In the summation term, for the th excitation unit, calculate its contribution , divide it by for normalization, then add up the contributions of all excitation units, and add it to .

[0118] 3) Calculate the denominator part. Then, calculate the denominator part of the friction coefficient derivation term . This includes calculating and the summation term . Similarly, for each excitation unit , calculate its contribution , divide it by for normalization, then add up the contributions of all excitation units, and subtract times this sum from .

[0119] 4) Calculate the friction coefficient derivation term . Finally, divide the numerator part obtained in step 2) by the denominator part obtained in step 3) to get the value of the friction coefficient derivation term .

[0120] For the friction coefficient derivative term to be approximated, a feedforward network with an appropriate number of neurons in the hidden layer is created. The neural network model for predicting the friction coefficient derivative term is trained using the training set of the friction coefficient derivative term, and a neural network model for predicting the friction coefficient derivative term that passes the training is obtained.

[0121] Step S32: For each excitation unit, respectively, according to formula (2), determine the independent variable of the excitation function derivative term of the corresponding excitation unit (including at least time ), obtain multiple sets of independent variables and their corresponding values of the excitation function derivative term, and construct the training set of the corresponding excitation function derivative term; use the training set of the corresponding excitation function derivative term to train the neural network model for predicting the corresponding excitation function derivative term, and obtain a neural network model for predicting the corresponding excitation function derivative term that passes the training.

[0122] Define or generate a data set for training the neural network. These data sets include a series of time points, excitation function samples, and related physical parameters. The specific steps are as follows: Determine the time range and the number of time points , generate a time point vector ; obtain the data sets X_train and Y_train for training, where X_train contains input features (such as , and other physical parameters, etc.), and Y_train contains the corresponding output values (the corresponding to the independent variable).

[0123] In this embodiment, the process of obtaining the data set for training the excitation function derivative term is as follows.

[0124] 1) Determine the basic parameters and the excitation function. First, clarify all the basic parameters related to the excitation function derivative term , including , , , (the excitation function related to spatial characteristics, and the specific form may be determined by the actual application scenario), , , , , , , and .

[0125] 2) Calculate the numerator part. According to formula (2), calculate the numerator part of the excitation function derivative term . This includes calculating .

[0126] 3) Calculate the denominator part. The denominator part is the same as that of the friction coefficient derivation term , that is . Note that although the denominator contains the summation over all excitation units, when calculating , this summation term is fixed for a specific because is a function of .

[0127] 4) Calculate the excitation function derivation term . Finally, divide the numerator part obtained in step 2) by the denominator part obtained in step 3) to get the value of the excitation function derivation term .

[0128] For the excitation function to be approximated, create a feedforward network with an appropriate number of hidden layer neurons. Use the training set of the excitation function derivation term to train the neural network model for predicting the corresponding excitation function derivation term, and obtain the neural network model for predicting the corresponding excitation function derivation term that passes the training.

[0129] 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 can be considered to directly substitute the time variable into the excitation function to obtain the corresponding value of the excitation function. However, in some cases, the excitation function is relatively complex and difficult to solve directly, and it can also be considered to use the neural network model for training and solution. See step S33.

[0130] Step S33: For the time-characteristic-related excitation function of each excitation unit, also for the independent variable (at least including time ) of the time-characteristic-related excitation function of the corresponding excitation unit, obtain multiple sets of independent variables and their corresponding values of the time-characteristic-related excitation function, and construct the training set of the corresponding time-characteristic-related excitation function; use the training set of the corresponding time-characteristic-related excitation function to train the neural network model for predicting the corresponding time-characteristic-related excitation function, and obtain the neural network model for predicting the corresponding time-characteristic-related excitation function that passes the training.

[0131] Step S34: Use the neural network model that passes the training to predict the numerical values of the friction coefficient derivation terms at different times and delay times required for the expression of the drift function of the fluid system, the excitation function derivation terms of each excitation unit, and the numerical values of the time-characteristic-related excitation functions, and substitute them into the expression of the drift function of the fluid system to solve for the drift function of the fluid system.

[0132] Specifically, use the trained neural network for prediction and calculate the drift function through numerical integration. The specific steps are as follows.

[0133] Use the neural network model net_Bn1 trained to predict the derived terms of the excitation function to predict the value of the derived term of the excitation function at time point t, and obtain the predicted value B_n1_pred of B_n1(t).

[0134] Use the neural network model net_Bn2 trained to predict the derived terms of the excitation function to predict the value of the derived term of the excitation function at time point t+tau_values, and obtain the predicted value B_n2_pred_shifted of B_n2(t).

[0135] Use the difference method or other numerical differentiation methods to calculate the approximate value of dB_n1 / ds(t).

[0136] And use the neural network model trained to predict the excitation functions related to the time characteristics of each excitation unit to perform corresponding 、 Predictions respectively, and obtain the corresponding prediction results. And calculate the calculation results of the corresponding correlation characterization model 。

[0137] For each time point t_i, use the numerical integration method to calculate the integral term integral_at_t_i, which is the integral of the product of dB_n1 / ds(t_i), and within the range of 。

[0138] Accumulate the integral terms for all time points t to obtain the integral term vector integral_term.

[0139] Use and integral_term to calculate the total drift function, that is, the drift function μ(s(t)) of the fluid system.

[0140] By this method, the approximation accuracy of the complex functions related to the fluid system and their combinations is improved. Through the powerful nonlinear fitting ability of the neural network, complex functions can be accurately approximated.

[0141] It should be noted that in the specific implementation process, according to the actual situation, the value range of can be given in advance, and the lower limit of the value range of is set to a specific and relatively large value to simulate the situation of negative infinity. And according to the value range of , use the neural network to simulate and predict the values of the parameters in the output formula to obtain the drift function.

[0142] Step S35: Using the neural network model that has passed the training, predict the derivative terms of the excitation functions of each excitation unit at different times and the delay time required for the expression of the fluctuation function of the fluid system and the numerical values of the time characteristic-related excitation functions, and substitute them into the expression of the fluctuation function of the fluid system to solve for the fluctuation function of the fluid system.

[0143] Preferably, this embodiment proposes a method for calculating the fluctuation function based on neural network approximation with time-dependent terms and numerical integration. In the process of processing the time-related complex functions of the above-mentioned proposed fluctuation function and calculating specific performance indicators based on these functions, traditional analytical methods often have the disadvantages that it is difficult to obtain the analytical solution or the computational complexity is too high when dealing with such problems. Therefore, a method that can efficiently and accurately approximate complex functions and calculate related performance indicators is needed. This embodiment gives a method based on neural network approximation with time-dependent terms and numerical integration to approximate and calculate the fluctuation function in the fluid system model, thereby improving the accuracy and efficiency in the related fields of fluid system modeling and analysis. The specific steps are as follows.

[0144] (1) Define the problem and prepare the data

[0145] First of all, it is necessary to define or generate a data set for training the neural network. Since this method deals with time-related functions, a series of time points, excitation function samples, and related physical parameters can be created. Specifically, set the total time T, the time step dt, and the corresponding time vector t. Subsequently, the simulated B_n(t) and functions, as well as the correlation function between them . Here, B_n(t) and can be the output based on the physical model or a certain random process.

[0146] (2) Create and train the neural network

[0147] For each function to be approximated (such as B_n(t)), train a neural network respectively. The neural network can adopt a common architecture, such as a feedforward neural network, and learn the mapping relationship between the input and output through a large amount of training data. Taking B_n(t) as an example, train the neural network net_Bn 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 through standard neural network training algorithms.

[0148] (3) Use the neural network for prediction and numerical integration

[0149] After the neural network training is completed, it is used for prediction. Specifically, the time vector t is input into the neural network net_Bn1 to obtain the predicted value B_n1_pred of B_n1(t). Subsequently, according to the range of the time delay tau_values are generated, and the predicted neural network net_Bn2 of another excitation function fluctuation term is used to predict the value B_n2_pred_shifted. Considering possible time boundary conditions, appropriate processing is required.

[0150] To calculate the fluctuation function , it is necessary to further perform numerical integration on the time-related terms. Specifically, the integration function integrand is constructed, which is composed of the product of B_n1(t), and . Among them, may need to be calculated through additional models or data. If it has complex dependencies, another neural network can be trained to approximate it. For each time point t_i, the integrand is integrated within the domain using numerical integration methods to obtain the fluctuation sub-item at this time point.

[0151] (4) Calculate the total fluctuation function

[0152] After the fluctuation sub-items at all time points are calculated, they are integrated to calculate the total fluctuation function . This process can be achieved by weighted integration of all fluctuation sub-items on the time vector t, with the weight being the time step or other relevant weight factors. Finally, reflects the quantitative representation of the system volatility throughout the time range.

[0153] It should be noted that in the specific implementation process, according to the actual situation, the value range of can be given in advance, and the two boundary values of the value range of are set to specific and larger values to simulate the cases of positive infinity and negative infinity. And according to the value range of , the values of the parameters in the predicted output formula are simulated and predicted using a neural network to obtain the fluctuation function.

[0154] This method combines a neural network with numerical integration and can efficiently approximate and calculate the fluctuation function in a complex fluid system model. The neural network has a powerful non-linear mapping ability and can capture complex relationships in the data; while the numerical integration technology ensures the accuracy of the calculation results.

[0155] In this embodiment, high-precision prediction of the dynamic behavior of the fluid system is achieved through the drift function and the 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 the main direction of the change in the system displacement over time during the operation of the fluid system. It synthesizes the influences of the friction coefficient, the excitation function, and the solid and liquid characteristics of the system, and reflects the average behavior of the fluid system under the combined action of external excitation and internal friction. Calculating the drift function is to determine the average path or the main trend of the change in the fluid system displacement over time. By calculating the drift function, the approximate position of the fluid system at a future moment can be predicted, as well as the behavioral changes of the fluid system under different excitation and friction conditions.

[0156] In this embodiment, the relationship between the fluctuation function and the operation of the fluid system is described as follows: The fluctuation function represents the random fluctuations or uncertainties of the change in the system displacement over time during 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 effects between the excitation functions, etc. Calculating the fluctuation function is to quantify the randomness and uncertainties of the change in the fluid system displacement over time. By understanding the fluctuation function, the stability, robustness, and anti-interference ability of the fluid system under different excitation and friction conditions can be evaluated.

[0157] Those skilled in the art can understand that all or part of the processes for implementing the above embodiment methods 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.

[0158] The above is only a preferred specific embodiment 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 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; 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.

2. The high-precision prediction method for the dynamic behavior of a fluid system according to claim 1, 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.

3. The high-precision prediction method for the dynamic behavior of a fluid system according to claim 2, 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.

4. The high-precision prediction method for the dynamic behavior of a fluid system according to claim 3, 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.

5. The high-precision prediction method for the dynamic behavior of a fluid system according to claim 4, 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.

6. The high-precision prediction method for the dynamic behavior of a fluid system according to claim 5, 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.

7. The high-precision prediction method for the dynamic behavior of a fluid system according to claim 6, 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.

8. The high-precision prediction method for the dynamic behavior of a fluid system according to claim 7, 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.

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 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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