Inertial sensor sensitive structure design method based on neural network interpolation algorithm

Abstract

The invention relates to an inertial sensor sensitive structure design method based on a neural network interpolation algorithm, and the method comprises the steps: defining geometric parameters and material parameters of an inertial sensor sensitive structure, and generating a three-dimensional geometric configuration related to the inertial sensor sensitive structure; performing finite element simulation on the three-dimensional geometric configuration to obtain a simulation result containing performance indexes; adjusting the geometric parameters and the material parameters for a plurality of times, generating a large number of simulation results, forming a simulation database, and forming a sample data set formed by input parameter combination and target performance pairing according to the simulation database; a feedforward neural network is adopted, the sample data set is input into the feedforward neural network for training, an interpolation prediction model is obtained, and the interpolation prediction model is adopted for prediction; through an innovative framework of simulation data driving, neural network modeling and closed-loop optimization, a systematic solution is provided for sensor development which is high in performance, low in cost and rapid in iteration.

Description

Technical Field

[0001] The present invention relates to the technical field of micro-electromechanical system inertial sensors, and in particular to a design method for a sensitive structure of an inertial sensor based on a neural network interpolation algorithm. Background Art

[0002] Microelectromechanical system (MEMS) inertial sensors are a key sensor used in a wide range of fields, including consumer electronics, automotive, and aerospace, for measuring physical quantities such as acceleration and angular velocity. Their core component is the sensitive structure, whose performance directly determines the sensor's accuracy, sensitivity, and reliability. The performance of the sensitive structure in a MEMS inertial sensor is a crucial factor in determining its output performance.

[0003] In the design technology of sensitive structures of inertial sensors in micro-electromechanical systems, traditional design methods mainly rely on engineers' experience or local optimization based on limited parameters, such as optimizing sensitivity by adjusting the width or length of a single beam. However, such methods have significant drawbacks: (1) Low efficiency: Due to the high parameter dimension (such as geometric parameters, material parameters, boundary conditions, etc.), manual trial and error or single parameter optimization is extremely time-consuming and difficult to cover all possible parameter combinations. For example, the optimization of a folding beam structure may require several months of simulation and experimental verification; (2) Insufficient global optimization capabilities: Traditional methods have difficulty capturing the complex nonlinear relationship between parameters and performance and are prone to falling into local optimal solutions. For example, adjusting the curvature of the beam may unexpectedly affect the resonant frequency, and empirical design makes it difficult to predict such coupling effects; (3) Strong data dependence: In actual processing, the performance of sensitive structures is easily affected by manufacturing errors (such as etching deviations), but existing methods lack the ability to systematically model processing tolerances, resulting in deviations between design results and actual product performance; (4) Poor scalability: For different application scenarios (such as high impact environments and low-frequency vibration detection), sensitive structures need to be redesigned, and traditional methods are difficult to adapt quickly, which limits the versatility of MEMS sensors.

[0004] In recent years, machine learning techniques (such as neural networks) have been explored for engineering optimization design due to their powerful nonlinear fitting capabilities. However, in the MEMS field, existing research has primarily focused on predicting the performance of simple structures (such as the stress distribution of cantilever beams), lacking a global design framework for complex and sensitive structures. Furthermore, neural network training requires large amounts of high-quality data, while obtaining experimental samples of sensitive MEMS structures is extremely expensive. Simulation data generation also faces challenges such as complex multi-physics coupling modeling and high computational resource consumption.

[0005] Therefore, there is an urgent need for an efficient design method that can combine high-precision simulation and intelligent algorithms to break through the limitations of traditional MEMS sensitive structure design and achieve a balance between global parameter optimization and accurate performance prediction. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a design method for the sensitive structure of an inertial sensor based on a neural network interpolation algorithm with high efficiency, high precision, strong optimization capability and strong scalability.

[0007] The technical solution adopted by the present invention is a method for designing a sensitive structure of an inertial sensor based on a neural network interpolation algorithm, which includes the following steps: S1. Define the geometric parameters and material parameters of the sensitive structure of the inertial sensor; S2. generating a three-dimensional geometric configuration of the sensitive structure of the inertial sensor based on the geometric parameters and material parameters; S3. Importing the three-dimensional geometric configuration into finite element simulation software, setting boundary conditions and physical fields, performing finite element static response simulation and dynamic response simulation, and obtaining simulation results including performance indicators; S4, adjusting the geometric parameters and material parameters several times, performing simulations several times according to steps S2 to S3 to obtain a large number of simulation results, and forming a simulation database; S5. Encoding an input parameter combination in a simulation database into a multidimensional feature vector, wherein the input parameter combination includes geometric parameters, material parameters, boundary conditions, and physical fields; using a performance indicator in the simulation database corresponding to the input parameter combination as a target performance, thereby forming a sample data set consisting of paired input parameter combinations and target performance; S6. Using a feedforward neural network, inputting the sample data set into the feedforward neural network for training, and obtaining an interpolation prediction model capable of mapping the relationship between “input parameters and target performance” through training; S7. Input the preset parameter combination into the interpolation prediction model, and the interpolation prediction model performs interpolation operation to output the optimal target performance.

[0008] The beneficial effects of the present invention are as follows: the present invention generates a massive sample database through parametric modeling and automated simulation, and combines the feedforward neural network interpolation algorithm to quickly map the "input parameter-target performance" relationship, which can quickly traverse the high-dimensional parameter space and screen the global optimal solution; the present invention trains massive simulation data through a feedforward neural network, which can accurately fit nonlinear relationships and has high prediction accuracy; the present invention replaces experimental samples with high-precision multi-physics field simulation data, and the cost of a single simulation is only 1 / 10 of that of a physical experiment. The present invention forms a closed-loop design process without the need for manual intervention, and can adapt to different MEMS sensors by adjusting parameter definitions; traditional design methods are difficult to iterate after solidification, but the present invention uses the innovative framework of "simulation data driven + neural network modeling + closed-loop optimization" to continuously add new simulation data to the database and update the model to achieve self-optimization.

[0009] Preferably, the specific process of step S2 includes the following steps: S2.1. Use 3D modeling software to construct the various components of the sensitive structure based on the defined geometric parameters; S2.2. Combine, stretch, and rotate the components of the constructed sensitive structure, ensuring that the size and position of each component are consistent with the defined geometric parameters to form a complete three-dimensional geometric configuration; S2.3. Assign the defined material parameters to the complete three-dimensional geometric configuration to obtain a constructed three-dimensional geometric configuration.

[0010] Preferably, the specific process of step S3 includes the following steps: S3.1. Exporting the constructed three-dimensional geometric configuration into a file format supported by the finite element simulation software, and then importing it into the finite element simulation software; S3.2. Set boundary conditions and physical fields. For static response simulation, the boundary conditions include fixed constraints and load application; for dynamic response simulation, the boundary conditions include fixed constraints, load application, initial velocity, and initial displacement; the physical fields include mechanical fields and electric fields. S3.3. Perform static response simulation and dynamic response simulation in finite element simulation software. Static response simulation is used to analyze the mechanical and electrical properties of sensitive structures under static loads, while dynamic response simulation is used to analyze the performance of sensitive structures under dynamic loads. S3.4. After the simulation is completed, obtain the simulation results including performance indicators from the simulation software.

[0011] Preferably, in step S6, the feedforward neural network includes an input layer, a hidden layer and an output layer; the number of neurons in the input layer is equal to the dimension of the multidimensional feature vector, that is, the number of elements of the feature vector after the input parameter combination is encoded; the number of neurons in the output layer is equal to the dimension of the target performance; the number of hidden layers and the number of neurons are obtained by dynamic adjustment.

[0012] Preferably, in step S6, the specific process of inputting the sample data set into the feedforward neural network for training includes the following steps: S6.1. normalizing the sample data set; S6.2. Input the sample dataset into the feedforward neural network. The multidimensional feature vectors in the training set enter the input layer of the feedforward neural network and are then progressively transferred through the hidden layers to the output layer. In each layer, the input to a neuron is the weighted sum of the outputs of all neurons in the previous layer plus a bias, followed by a nonlinear transformation using an activation function. S6.3. After a series of forward propagation calculations, the predicted output value of the output layer is obtained. ; S6.4. Use the mean square error loss function to measure the predicted result value and the target value The difference between them is used to update the weights of the feedforward neural network through back propagation to obtain an interpolation prediction model that can map the "input parameter-target performance" relationship. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 This is a flow chart of the method for designing a sensitive structure of an inertial sensor based on a neural network interpolation algorithm according to the present invention; Figure 2 : is a network structure diagram of the feedforward neural network in the present invention; Figure 3 The structure diagram of the micro-electromechanical system accelerometer sensitive structure designed by the method of the present invention is shown in FIG. Figure 3 (a) is a top view of the crab leg beam-mass block elastic structure. Figure 3 (b) in the middle is the crab leg beam isolation diagram. Figure 3 (c) is a top view of the folded beam-mass block elastic structure. Figure 3 (d) in the middle is the diagram of the folded beam isolation body. Figure 3 Middle (e) is the top view of the serpentine beam-mass block elastic structure. Figure 3 Middle (f) is the diagram of the serpentine beam isolation body. DETAILED DESCRIPTION

[0014] The invention will be further described below with reference to the accompanying drawings and in combination with specific implementations, so that those skilled in the art can implement the invention with reference to the description. The protection scope of the invention is not limited to the specific implementations.

[0015] It should be understood by those skilled in the art that, in the disclosure of the present invention, the terms "longitudinal", "transverse", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like to indicate orientations or positional relationships are based on the orientations or positional relationships shown in the accompanying drawings, which are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the above terms should not be understood as limiting the present invention.

[0016] Furthermore, the terms “first,” “second,” “third,” etc., are merely used for distinguishing descriptions and are not to be understood as indicating or implying relative importance.

[0017] In the description of the embodiments of the present application, it should be noted that, unless otherwise specified and limited, the terms "set", "install", "connect", and "connect" should be understood in a broad sense, for example, they can be fixed connections or detachable connections. The terms "connected" and "integrated" may be mechanically or electrically connected, directly or indirectly through an intermediate medium, or may be internally connected between two components. A person skilled in the art will understand the specific meanings of the above terms in this application.

[0018] The present invention relates to a method for designing a sensitive structure of an inertial sensor based on a neural network interpolation algorithm, the method comprising the following steps: Step 1: Define the geometric parameters and material parameters of the inertial sensor sensitive structure; Regarding geometric parameters, in the sensitive structure of an inertial sensor, the geometric parameters of the sensitive structure of the inertial sensor are key elements that describe its shape and size. For a common cantilever beam sensitive structure, the geometric parameters may include the length, width, and thickness of the beam, as well as the length, width, and height of the mass. For example, in the sensitive structure of a microelectromechanical system (MEMS) accelerometer, the length of the beam may affect its sensitivity. The longer the length, the greater the deformation of the beam under the same external force, and the more obvious the change in the output electrical signal.

[0019] For some complex sensitive structures, such as those with folded beams or comb-tooth structures, it is also necessary to define parameters such as the folding method of the beam, the number of comb teeth, and the spacing. The precise setting of these parameters is crucial for accurately simulating and optimizing the performance of sensitive structures. Regarding material parameters, they determine the physical properties of sensitive structures. The main material parameters include the elastic modulus, Poisson's ratio, density, etc. The elastic modulus reflects the material's ability to resist elastic deformation. In sensitive structures, different elastic moduli will lead to different degrees of deformation when the structure is subjected to force. For example, using a material with a larger elastic modulus will result in a relatively smaller deformation of the beam under the same external force.

[0020] Poisson's ratio describes the ratio of the absolute value of the lateral normal strain to the axial normal strain when a material is subjected to unidirectional tension or compression. It affects the material's lateral deformation under load. Density is related to the mass of the structure. For applications that require consideration of inertial forces, such as accelerometers, material density can affect the structure's dynamic response characteristics.

[0021] Step 2: generating a three-dimensional geometric configuration of the sensitive structure of the inertial sensor based on the geometric parameters and material parameters; During implementation, professional 3D modeling software, such as SolidWorks and ANSYS Design Modeler, can be used for 3D modeling. First, based on the defined geometric parameters, the software's basic graphic drawing tools (such as lines, rectangles, and circles) are used to construct the various components of the sensitive structure. For example, for a cantilever beam structure, the basic shapes of the beam and mass can be drawn first. Then, these basic shapes can be combined, stretched, and rotated to form a complete 3D geometric configuration. During the construction process, the dimensions and positional relationships of each component must be consistent with the defined geometric parameters. Finally, the defined material parameters are assigned to the constructed 3D geometry to accurately simulate the material's physical properties in subsequent finite element simulations.

[0022] Step 3: importing the three-dimensional geometric configuration into finite element simulation software, setting boundary conditions and physical fields, performing finite element static response simulation and dynamic response simulation, and obtaining simulation results including performance indicators; In the specific implementation process, the 3D geometric configuration constructed in the 3D modeling software is exported to a file format supported by the finite element simulation software, such as STEP, IGES, etc., and then imported into the finite element simulation software (such as ANSYS, COMSOL, etc.); Boundary conditions refer to the constraints and forces on a sensitive structure in its actual working environment. For static response simulation, common boundary conditions include fixed constraints and load application. For example, in a cantilever beam sensitive structure, one end of the beam is usually fixed. This end can be set as a fixed constraint in the simulation software, limiting the displacement of this end in all directions. Then, appropriate loads such as gravity and external forces are applied according to the actual situation.

[0023] For dynamic response simulation, in addition to fixed constraints and loads, initial conditions such as initial velocity and initial displacement need to be considered. For example, when simulating the response of an accelerometer in a vibration environment, parameters such as the frequency and amplitude of the vibration need to be set;

[0024] According to the working principle and application scenario of the inertial sensor, the corresponding physical field is set. For MEMS accelerometers, the main physical fields involved are mechanical and electric fields. In the mechanical field, the mechanical response of the structure, such as stress, strain, and displacement, is simulated; in the electric field, the changes in electrical signals generated by the structure when subjected to force, such as voltage and capacitance, are simulated.

[0025] After setting the boundary conditions and physical fields, perform static response simulation and dynamic response simulation in the finite element simulation software. Static response simulation mainly analyzes the mechanical and electrical properties of the structure under static loads, while dynamic response simulation analyzes the performance of the structure under dynamic loads (such as vibration, impact, etc.);

[0026] After the simulation is completed, the simulation results including performance indicators such as maximum stress, maximum displacement, sensitivity, etc. are obtained from the simulation software. These performance indicators will be used for subsequent data analysis and optimization;

[0027] Step 4: Adjust the geometric parameters and material parameters several times, perform simulations several times according to the method of steps S2 to S3 to obtain a large number of simulation results, and form a simulation database; In the specific implementation process, orthogonal experimental design, uniform experimental design and other methods can be used to adjust the geometric parameters and material parameters. Among them, orthogonal experimental design is an efficient experimental design method, which can comprehensively examine the impact of various parameters on performance indicators with a smaller number of experiments. For example, for three geometric parameters (beam length, beam width, mass block height) and two material parameters (elastic modulus, Poisson's ratio), an orthogonal experimental table can be designed to determine several groups of different parameter combinations; or a random sampling method can be used to randomly select parameter values ​​within a certain parameter range for combination. This method can explore the parameter space more extensively, but may require more simulation times to ensure the comprehensiveness of the data;

[0028] Repeat steps S2 and S3 according to each adjusted parameter combination, that is, regenerate the three-dimensional geometric configuration, import it into the finite element simulation software to perform static response simulation and dynamic response simulation, and obtain corresponding simulation results; The input parameter combinations (including geometric parameters, material parameters, boundary conditions, and physical fields) and corresponding performance indicators obtained from each simulation are stored in a database to form a simulation database. This database will serve as a sample data set for subsequent neural network training.

[0029] Step 5: Encode the input parameter combination in the simulation database into a multidimensional feature vector, wherein the input parameter combination includes geometric parameters, material parameters, boundary conditions, and physical fields; use the performance indicators corresponding to the input parameter combination in the simulation database as target performance, and form a sample data set consisting of input parameter combinations and target performance pairs; Since the input parameter combination contains multiple types of parameters, they need to be encoded into a unified multi-dimensional feature vector. For continuous parameters, such as geometric parameters and material parameters, their numerical values ​​can be directly used as elements of the feature vector. For discrete parameters, such as boundary conditions and physical field types, the one-hot encoding method can be used to convert them into binary vectors; for example, assuming that the input parameter combination contains beam length, beam width, elastic modulus, fixed constraint type (there are two types) and physical field type (there are three types), the numerical values ​​of beam length, beam width and elastic modulus can be directly used as the first three elements of the feature vector, and then the fixed constraint type and physical field type can be one-hot encoded respectively and added to the end of the feature vector to form a multi-dimensional feature vector;

[0030] The encoded multidimensional feature vector is used as input, and the corresponding performance indicators in the simulation database are used as target performance. They are paired to form a sample data set; each sample consists of an input feature vector and a target performance value. The sample data set contains a large number of such samples for training feedforward neural networks.

[0031] Step 6: Using a feedforward neural network, input the sample data set into the feedforward neural network for training, and obtain an interpolation prediction model that can map the relationship between "input parameters and target performance" through training; In practice, a feedforward neural network typically consists of an input layer, a hidden layer, and an output layer. The number of neurons in the input layer is equal to the dimensionality of the multidimensional feature vector, that is, the number of elements in the feature vector after encoding the input parameter combinations. The number of neurons in the output layer is equal to the dimensionality of the target performance, usually 1 (if only a single performance metric is of interest).

[0032] The number of hidden layers and neurons can be adjusted based on the specific problem. Generally speaking, increasing the number of hidden layers and neurons can improve the fitting ability of the neural network, but it will also increase the training time and the risk of overfitting. The appropriate network structure can be determined through experimentation and verification.

[0033] The specific process of inputting the sample data set into the feedforward neural network for training is as follows: Normalizing the sample data set; specifically, using Z-score normalization to normalize the data by converting the data in the sample data set into a distribution with a mean of 0 and a standard deviation of 1; The sample data set is input into the feedforward neural network, and the multidimensional feature vector in the training set enters the input layer of the feedforward neural network, and then is gradually transmitted to the output layer through the hidden layer; in each layer, the input of the neuron is obtained by adding the weighted sum of the outputs of all neurons in the previous layer plus the bias, and then performing a nonlinear transformation through the activation function; for example, The input of the jth neuron in the layer is , the output is ,in, = + ; =f( );in, Indicates the The jth neuron in the layer is connected to the The weights between the i-th neurons in the layer, Indicates the The bias of the j-th neuron in the layer, Indicates the The number of neurons in the layer, f represents the activation function, and commonly used activation functions include Sigmoid function, ReLU function, etc. After a series of forward propagation calculations, the predicted output value of the output layer is obtained. ; Use the mean square error loss function to measure the predicted result value and the target value The difference between them is updated by back propagation to obtain the interpolation prediction model that can map the relationship between “input parameters and target performance”; the mean square error loss function is specifically expressed as: L= ; where N represents the number of samples.

[0034] Step 7: inputting the preset parameter combination into the interpolation prediction model, and the interpolation prediction model performs interpolation operation to output the optimal target performance; During the specific implementation process, the preset parameter combination (geometric parameters, material parameters, boundary conditions and physical fields) is normalized to make it consistent with the encoding of the sample data set during training; the preset parameter combination is input into the interpolation prediction model, and the gradient of the output layer to the input layer is calculated through the back propagation algorithm; the optimization is stopped when the set conditions are met, and the set conditions are specifically: the error between the predicted value and the target value is less than the set threshold, or the gradient amplitude is less than the set threshold, or the maximum number of iterations is reached; and the target performance that meets the conditions is output.

[0035] During the specific implementation process, the preset target performance parameters (such as sensitivity, natural frequency, maximum stress, etc.) are normalized to make them consistent with the target data range during training; if multiple performance indicators (such as sensitivity and impact resistance) need to be optimized at the same time, the multi-objective parameters need to be converted into a comprehensive objective function; the target performance is input into the interpolation prediction model, and the gradient of the output layer to the input layer is calculated by the back propagation algorithm. To ensure the physical feasibility of the parameter combination, constraints such as geometric constraints, material constraints, and process constraints need to be added during the optimization process; the optimization is stopped when the set conditions are met, and the set conditions are specifically: the error between the predicted value and the target value is less than the set threshold, or the gradient amplitude is less than the set threshold, or the maximum number of iterations is reached; if multiple input parameter combinations that meet the conditions are output, then the optimal input parameter combination is selected based on process friendliness, robustness, economy and other conditions; the finite element software is imported to simulate and output the actual performance to verify the deviation between the preset target performance and the actual performance.

Claims

1. A design method for the sensitive structure of an inertial sensor based on a neural network interpolation algorithm, characterized by: The method comprises the following steps: S1. Define the geometric parameters and material parameters of the sensitive structure of the inertial sensor; S2. generating a three-dimensional geometric configuration of the sensitive structure of the inertial sensor based on the geometric parameters and material parameters; S3. Importing the three-dimensional geometric configuration into finite element simulation software, setting boundary conditions and physical fields, performing finite element static response simulation and dynamic response simulation, and obtaining simulation results including performance indicators; S4, adjusting the geometric parameters and material parameters several times, performing simulations several times according to steps S2 to S3 to obtain a large number of simulation results, and forming a simulation database; S5. Encoding an input parameter combination in a simulation database into a multidimensional feature vector, wherein the input parameter combination includes geometric parameters, material parameters, boundary conditions, and physical fields; using a performance indicator in the simulation database corresponding to the input parameter combination as a target performance, thereby forming a sample data set consisting of paired input parameter combinations and target performance; S6. Using a feedforward neural network, inputting the sample data set into the feedforward neural network for training, and obtaining an interpolation prediction model capable of mapping the relationship between "input parameters and target performance" through training; S7. Input the preset parameter combination into the interpolation prediction model, and the interpolation prediction model performs interpolation operation to output the optimal target performance.

2. The method for designing a sensitive structure of an inertial sensor based on a neural network interpolation algorithm according to claim 1, wherein: The specific process of step S2 includes the following steps: S2.

1. Use 3D modeling software to construct the various components of the sensitive structure based on the defined geometric parameters; S2.

2. Combine, stretch, and rotate the components of the constructed sensitive structure, ensuring that the size and position of each component are consistent with the defined geometric parameters to form a complete three-dimensional geometric configuration; S2.

3. Assign the defined material parameters to the complete three-dimensional geometric configuration to obtain a constructed three-dimensional geometric configuration.

3. The method for designing a sensitive structure of an inertial sensor based on a neural network interpolation algorithm according to claim 2, wherein: The specific process of step S3 includes the following steps: S3.

1. Exporting the constructed three-dimensional geometric configuration into a file format supported by the finite element simulation software, and then importing it into the finite element simulation software; S3.

2. Setting boundary conditions and physical fields. For static response simulation, the boundary conditions include fixed constraints and load application. For dynamic response simulation, the boundary conditions include fixed constraints, load application, initial velocity, and initial displacement; the physical fields include mechanical fields and electric fields; S3.

3. Perform static response simulation and dynamic response simulation in finite element simulation software. Static response simulation is used to analyze the mechanical and electrical properties of sensitive structures under static loads, while dynamic response simulation is used to analyze the performance of sensitive structures under dynamic loads. S3.

4. After the simulation is completed, obtain the simulation results including performance indicators from the simulation software.

4. The method for designing a sensitive structure of an inertial sensor based on a neural network interpolation algorithm according to claim 3, wherein: In step S6, the feedforward neural network includes an input layer, a hidden layer and an output layer; the number of neurons in the input layer is equal to the dimension of the multidimensional feature vector, that is, the number of elements of the feature vector after the input parameter combination is encoded; the number of neurons in the output layer is equal to the dimension of the target performance; the number of hidden layers and the number of neurons are obtained by dynamic adjustment.

5. The method for designing a sensitive structure of an inertial sensor based on a neural network interpolation algorithm according to claim 4, characterized in that: In step S6, the specific process of inputting the sample data set into the feedforward neural network for training includes the following steps: S6.

1. normalizing the sample data set; S6.

2. Input the sample dataset into the feedforward neural network. The multidimensional feature vectors in the training set enter the input layer of the feedforward neural network and are then progressively transferred through the hidden layers to the output layer. In each layer, the input to a neuron is the weighted sum of the outputs of all neurons in the previous layer plus a bias, followed by a nonlinear transformation using an activation function. S6.

3. After a series of forward propagation calculations, the predicted output value of the output layer is obtained. ; S6.

4. Use the mean square error loss function to measure the predicted result value and the target value The difference between them is used to update the weights of the feedforward neural network through back propagation to obtain an interpolation prediction model that can map the "input parameter-target performance" relationship.

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