A temperature sensing method for piezoelectric active vibration suppression system in low-temperature wind tunnel tests

Abstract

A temperature sensing method for a piezoelectric active vibration suppression system in a low-temperature wind tunnel test is proposed. This method first formulates a potential measurement point layout method based on simulation results under different low-temperature wind tunnel test conditions and actual conditions, ensuring a compact layout of measurement points while guaranteeing the acquisition of key temperatures. To acquire a large amount of discrete point temperature information, a surrogate model is used to approximate the simulation process. Considering interpolation accuracy and speed, a method for laying out the discrete simulation nodes of the system is studied. A nonlinear mapping model between the measured feature matrix and the simulated node temperatures is constructed. Deep learning is used to train and solve the surrogate model, enabling rapid acquisition of a large amount of discrete point temperature information of the system, replacing finite element calculations. To achieve accurate interpolation and reconstruction of the overall temperature, local large gradient temperature interpolation methods and global smooth temperature interpolation methods are studied. A weighted fusion model for overall temperature interpolation is constructed, forming a regional three-dimensional temperature field interpolation method to ensure high-precision interpolation of the overall temperature field of the system.

Description

Technical Field

[0001] This invention belongs to the field of low-temperature wind tunnel testing and relates to a real-time temperature sensing method for an active vibration suppression system based on a surrogate model combined with spatial interpolation. Background Technology

[0002] Cryogenic wind tunnel testing can simulate full-scale Reynolds numbers and is a primary means of obtaining key aerodynamic parameters of aircraft. To ensure measurement accuracy, piezoelectric active vibration suppression systems suppress the vibration of aircraft models during wind tunnel testing. Their core principle utilizes the piezoelectric effect to output a reverse torque to reduce model vibration. As the temperature decreases, the strain capacity of the piezoelectric actuator to control output force and displacement significantly reduces. Therefore, to effectively control the operating temperature of the piezoelectric actuator and ensure the real-time response capability of the vibration suppression system, it is necessary to clarify its cooling law and instantaneous temperature information in a cryogenic wind tunnel environment to guide the active temperature control system. Considering the piezoelectric actuator's own heat transfer characteristics, operating environment, and insulation structure limitations, the lowest temperature is often distributed at the end face. However, the piezoelectric actuator is embedded in the support structure, resulting in severe obstruction and axial compression, making it impossible to directly set measurement points at the end face. This makes it difficult to monitor the lowest temperature of the piezoelectric actuator in real time, posing a challenge to maintaining the optimal output performance of the active vibration suppression system. Therefore, to improve the performance of the vibration suppression system in cryogenic environments and ensure the safety and reliability of aircraft design, researching real-time temperature sensing methods for piezoelectric active vibration suppression systems is of great significance.

[0003] In the paper "Transition detection by temperature sensitive paint at cryogenic temperatures in the European Transonic Wind tunnel (ETW)" published by Fey et al. of the German Aerospace Center at the 20th International Congress on Instrumentation in Aerospace Simulation Facilities, aiming at the problem that the non-contact measurement in the cryogenic transonic wind tunnel is affected by low temperature, resulting in the inability to monitor the surface temperature of the aircraft model and thus difficult to identify the boundary layer transition, a temperature measurement system based on the temperature sensitive paint (TSP) technology is proposed. This temperature measurement system realizes high-precision measurement of the wing surface temperature of the three-dimensional model and high-precision acquisition of the transition image within the temperature range of 115K < T < 180K. However, different from the wing, the active vibration suppression system is embedded in the support structure and the end face is blocked, making it impossible to achieve the full-field temperature perception of the system. Shen Xing et al. of Nanjing University of Aeronautics and Astronautics, in the paper "Design and Analysis of a Thermally Insulating and Heating Scheme for Piezoelectric Stack Actuators Used in the Cryogenic Environment", aiming at the need to study the temperature rise method of piezoelectric actuators in the cryogenic environment, constructed a two-dimensional theoretical heat transfer model to obtain the temperature distribution of piezoelectric actuators and verified the effectiveness of the method by finite element analysis. This method can quickly evaluate the temperature distribution of piezoelectric actuators. However, due to the deviation between the model assumption and the actual situation, there are certain errors in the calculation results, and the boundary (end face) temperature needs to be applied for correction, which is contradictory to the actual measurement requirements.

[0004] At present, the TSP non-contact measurement method and theoretical calculation method are mostly used for regional temperature perception in cryogenic wind tunnel tests. However, the existing temperature real-time monitoring methods cannot achieve high-precision measurement of the full-field temperature under the constraints of blocked areas / contact surfaces. Therefore, there is an urgent need for a full-field temperature real-time and accurate perception method that meets the actual test requirements, does not affect the output displacement of the actuator, and is not restricted by severe structural blockage. Summary of the Invention

[0005] This invention overcomes the shortcomings of existing methods and proposes a full-field temperature sensing method for an active vibration suppression system under low-temperature wind tunnel conditions. First, based on simulation results under different low-temperature wind tunnel test conditions, and combined with actual conditions, a potential measurement point layout method is formulated, and a feature point optimization method based on statistical analysis is proposed to form a compact layout of temperature sensors. Second, considering interpolation accuracy and rate, a method for the layout of discrete simulation nodes in the system is studied. The temperature state of the measurement points is characterized by the measured feature matrix, and a nonlinear mapping model between the measured feature matrix and the simulated node temperature is constructed to quickly obtain a large amount of discrete point temperature information of the system, replacing finite element calculations. Finally, considering the non-uniformity of system temperature distribution, a local large gradient temperature interpolation method and a global smooth temperature interpolation method are studied, and a weighted fusion model of full-field temperature interpolation is constructed to form a regional three-dimensional temperature field interpolation method. This method can achieve real-time and accurate sensing of the dynamic temperature of the entire active vibration suppression system, laying the foundation for subsequent development of a coordinated temperature control strategy for piezoelectric actuators in different orientations throughout the system.

[0006] The technical solution of the present invention:

[0007] A temperature sensing method for a piezoelectric active vibration damping system in a low-temperature wind tunnel test, comprising the following steps:

[0008] 1) Finite element simulation analysis was conducted based on a typical active vibration damping structure model. Through finite element simulations under different low-temperature wind tunnel test conditions, the temperature distribution patterns and sensitive areas were obtained. Considering the simulation analysis results and practical operational limitations, the most representative measurement points were selected, and the number and distribution of potential temperature sampling points were determined. Statistical analysis methods were used to optimize the selection of potential measurement points, ensuring that a small number of measured points represent the changes in the entire temperature field to the greatest extent possible. The number and distribution of measured points were also determined, forming a measurement point optimization method. Finally, a low-temperature temperature measurement test was conducted to reproduce the low-temperature wind tunnel test environment and collect measured temperature data. Details are as follows:

[0009] 1.1) Establish an active vibration damping structure model, and based on the actual working needs of low-temperature wind tunnel tests, change the test conditions such as the angle of attack and the incoming flow velocity, and carry out finite element simulations under different low-temperature wind tunnel test conditions to obtain the temperature distribution law and sensitive areas.

[0010] 1.2) Based on the simulation results, determine the regions with large temperature gradient changes, and select the most representative measurement points as potential temperature measurement points by considering factors such as the feasibility of actual operation, structural geometry, sensor size, and the impact of force position on measurement accuracy.

[0011] 1.3) Based on the simulation results in 1.1, temperature time-series data of potential measuring points under different experimental conditions are obtained. The standardized matrix X is calculated using principal component analysis (PCA). std The covariance matrix C:

[0012]

[0013] Where X is the coordinate matrix of the potential measurement points, μ is the mean, and σ is the standard deviation. Then, eigenvalue decomposition Cv is performed. i =λ i v i , where λ i It is the i-th eigenvalue, v i Is with λ i The corresponding eigenvectors. Select the component that has the greatest impact on system temperature changes, determine the number and distribution of measurement points, and complete the optimal selection of measurement point locations:

[0014] Y = X std V k (3)

[0015] Importance i =||Yi|| (4)

[0016] In the above process, V k Y is a matrix composed of the first k eigenvectors, and Y is the projected data matrix. i It is the projection vector of the i-th measurement point in the principal component space, and ||Yi|| is its Euclidean norm;

[0017] 1.4) Build a small low-temperature wind tunnel test platform to reproduce the low-temperature wind tunnel test environment, and arrange temperature sensors at the selected locations to conduct temperature measurement tests under different working conditions and complete the acquisition of temperature time series data at the measurement points.

[0018] 2) To address the need for sufficient temperature measurement points to cover the entire 3D space in online 3D temperature field reconstruction tasks, and to provide prediction results within a short timeframe, a surrogate model is proposed to approximate the simulation process and reduce computational costs. Considering both interpolation fitting accuracy and computational speed, an optimization method for the surrogate model simulation node layout is designed to ensure the optimal balance between speed and accuracy in the optimized interpolation results. An input feature matrix is ​​constructed by combining the time-domain features (first and second derivatives) and frequency-domain features (amplitude and phase) of the measured point time series data, with the simulation node temperature information at the next time step as the output to build a large dataset. A nonlinear mapping model from measured points to simulation node temperatures is constructed using deep learning methods to achieve rapid and accurate acquisition of a large amount of discrete temperature information for the active vibration damping system. The specific steps are as follows:

[0019] 2.1) Considering that accurate interpolation of the three-dimensional temperature field requires a large amount of data, a surrogate model is used to approximate the simulation results. A large number of discrete simulation nodes are selected, and the number and layout of the discrete simulation nodes are determined with interpolation speed and accuracy as optimization objectives. This forms a method for optimizing the layout of discrete simulation nodes based on the ADAM (Adaptive Moment Estimation) method.

[0020]

[0021]

[0022] Equation (5) is the defined mean square error (MSE) loss function, which characterizes the interpolation accuracy. The interpolation speed is proportional to the number of nodes N, where M is the number of validation points and T is the number of nodes N. j It is the actual temperature of the j-th verification point. The interpolated temperature at the j-th verification point is used to calculate the gradient of the loss function with respect to the node location. The first-order moment m is updated using the ADAM algorithm combined with equations (6) and (7). t Second moment v t Correcting deviations, updating node positions and continuously iterating and optimizing, optimizing the layout of simulation nodes, and ensuring that the interpolation results achieve the best balance between speed and accuracy;

[0023] 2.2) Collect temperature data at time t+1 of N nodes in the simulation, convert the time series data of the measured points to the frequency domain, extract the amplitude and phase of the main frequency components, combine the derivatives of the time series data to form the feature matrix of the measured points, construct the dataset and segment it (training set: validation set: test set = 6:2:2);

[0024] 2.3) Using the measured feature matrix as input and the instantaneous temperature of the simulated nodes as output, a nonlinear mapping relationship between the two is constructed based on a recurrent neural network (RNN):

[0025] h t =σ(W in x t +W h h t-1 +b h (8)

[0026] y t =softmax(W out h t +b out (9)

[0027] Where the time step is t and the input vector is x t h t Let y be the hidden state vector and y be the output vector. t W in For the input weight matrix, W h W is the hidden state weight matrix. out To output the weight matrix, b h b outThese are the bias vectors for the hidden layer and the output layer, respectively. The activation function here is σ = tanh. The model is trained using the training set, its parameters are adjusted using the validation set, and its accuracy is evaluated using the test set.

[0028] 3) The interpolation region is divided based on the temperature gradient. Regions with significant temperature changes are designated as local regions, while the remaining areas are considered global regions. A large-gradient local temperature interpolation model and a global smooth transition temperature interpolation model are constructed, and model parameters are determined through boundary conditions. A combination method for multi-region interpolation is studied, and a weighted average is used to achieve a smooth transition between interpolation results from different regions, enabling real-time and accurate reconstruction of the entire system temperature using discrete point temperature information. The specific steps are as follows:

[0029] 3.1) The interpolation region is divided based on the temperature gradient. Regions with significant temperature changes are designated as local regions, while the remaining areas are designated as global regions. For discrete simulation nodes within the local regions, a Gaussian function is selected as the basis function to construct the RBF interpolation model.

[0030]

[0031] Wherein, the basis function φ(r) = e -∈r2 ,and ε is the shape parameter, m is the number of discrete points in the region, and w i The weights are p(x,y,z), which are polynomial terms. The weights w are determined by minimizing the interpolation error. i and the polynomial p(x,y,z):

[0032]

[0033] High-precision interpolation in regions with large temperature variations is achieved using local radial basis functions (RBF).

[0034] 3.2) For three-dimensional interpolation of the global region, firstly, based on the cubic spline interpolation method, a single-dimensional cubic spline interpolation is performed. One-dimensional cubic spline interpolation is then performed in the x-direction (y and z are fixed) to obtain the cubic spline interpolation function S in the x-direction. x (x,y j ,z k ):

[0035]

[0036] Among them, coefficient The boundary condition is determined by the equality of the first and second derivatives at the connection point. Then, one-dimensional cubic spline interpolation is performed in the y-direction (with z fixed) to obtain S. y (x,y,z k ):

[0037]

[0038] in, These are the coefficients used in the interpolation process. Finally, one-dimensional cubic spline interpolation is performed in the z-direction to obtain the final three-dimensional cubic spline interpolation function S(x,y,z):

[0039]

[0040] in, The coefficient is used. Through the above interpolation process, a smooth and accurate temperature interpolation result for the entire region is obtained;

[0041] 3.3) A smooth transition between local and global interpolation results is achieved through distance-weighted averaging. For query point T(x) q ,y q ,z q The temperature interpolation result is expressed as follows:

[0042]

[0043] The beneficial effects of this invention are to provide a temperature sensing method for piezoelectric active vibration suppression systems in low-temperature wind tunnel tests, addressing the challenges of real-time temperature sensing in confined test spaces, severe structural obstruction, and unclear extreme temperature distribution in active vibration suppression systems. Compared to traditional methods that cannot measure obstructed areas and suffer from poor theoretical modeling accuracy, this invention optimizes the layout of measurement points within the confined space of a low-temperature wind tunnel active vibration suppression system. It constructs a surrogate model to simulate and acquire a large amount of discrete temperature information, accurately interpolates and fits the three-dimensional temperature field in different regions, and calculates and predicts the overall temperature information of the system in real time. This method offers low measurement requirements, a large measurement area, fast response, and high accuracy in ensuring the temperature of active vibration suppression systems in low-temperature wind tunnel tests. It guarantees real-time, non-destructive monitoring of the entire field temperature, providing data support for precise control of the entire field temperature in the vibration suppression section. This method is applicable to various types of active vibration suppression systems. Attached Figure Description

[0044] Figure 1 This is a schematic diagram showing how the output performance of a piezoelectric actuator changes with temperature.

[0045] Figure 2 This is a flowchart of the temperature sensing method for the low-temperature wind tunnel piezoelectric active vibration suppression system of the present invention.

[0046] Figure 3 It serves as a low-temperature wind tunnel environment temperature measurement test platform.

[0047] Figure 4 This is a schematic diagram illustrating the construction and training process of the simulation agent model in this invention.

[0048] Figure 5 This is a schematic diagram illustrating the principle of spatial interpolation reconstruction of the temperature field using the method of the present invention. Detailed Implementation

[0049] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0050] (1) This method is based on a piezoelectric active vibration suppression system built by the research group for a wind tunnel, including a tail support system and circumferentially distributed piezoelectric actuators. To improve experimental efficiency, a key segment of the active vibration suppression system is established. The key segment model can accurately reflect the thermal behavior of all regions of interest in the system. Based on the laboratory environment, a low-temperature wind tunnel environmental temperature measurement test platform is built, including a small wind tunnel (such as...). Figure 3 As shown, the system includes a test section, a compression section, and a flow stabilization section; a liquid nitrogen tank; a key section of the active vibration damping system; a LabVIEW-based measurement platform; thermocouple temperature sensors; and a host computer. Before starting the low-temperature environment temperature measurement test, the layout of the measurement points needs to be designed to minimize the number of measurement points while ensuring temperature acquisition at key locations. To obtain the key temperature measurement area, finite element simulations under various operating conditions are conducted to determine the cooling law and temperature-sensitive areas. Based on the feasibility of implementation, the potential measurement point layout is determined. Then, principal component analysis is used to select the component among the potential measurement points that has the greatest impact on the system temperature change, thus determining the final measurement point layout. Finally, a precisely calibrated temperature measurement device is used to perform static and dynamic calibration of the thermocouple sensors used in this method to improve temperature measurement accuracy. The liquid nitrogen flow rate is controlled by valve pressure, and the angle of attack is adjusted by the curved blade device. Time-series signals of the measured point temperatures under different test conditions (corresponding to the simulation) are collected.

[0051] (2) After obtaining the measured data from some sampling points, in order to realize the three-dimensional reconstruction of the temperature field, a large amount of data needs to be prepared to ensure the accuracy of the reconstruction results. A large amount of discrete temperature information is obtained by simulating the process using a surrogate model, thereby reducing computation time. Figure 4 As shown, firstly, extensive finite element simulations were conducted based on the key segment model of the vibration suppression system to cover most of the test conditions. A large number of discrete points were selected to ensure sufficient data support for subsequent interpolation and reconstruction. The number and position of simulation nodes were adjusted according to the interpolation speed and reconstruction accuracy, forming a simulation node layout optimization method. Then, a surrogate model was constructed to represent the nonlinear mapping relationship between the measured point temperature and the simulated node temperature. The surrogate model was solved using a recurrent neural network, extracting the first and second derivatives (time-domain features) and amplitude and phase (frequency-domain features) of the measured temperature time-series data to form the input feature matrix. The simulated node temperature information at the next moment was obtained as the output. The input feature matrix and output vector for each test condition constituted a large dataset. Finally, the large dataset was divided according to a 6:2:2 ratio (training set: validation set: test set). The training set data was used to train the model, the validation set was used to adjust the model parameters, and the test set was used to evaluate the model accuracy, thus achieving the acquisition of discrete temperature information of the active vibration suppression system. This ensures that the system can quickly acquire and predict a large number of discrete point temperature information of the system, replacing finite element calculations.

[0052] (3) After obtaining a large amount of discrete temperature information under different experimental conditions, the interpolation region is divided based on the temperature gradient change. The principle is as follows: Figure 5 As shown, firstly, for local areas with large temperature gradients, an RBF interpolation model is constructed, and the model parameters are optimized by minimizing the interpolation error to achieve high-precision interpolation in areas with large temperature changes. Secondly, for global areas with small temperature gradients, a multidimensional cubic spline interpolation model is constructed, and the model coefficients are determined through boundary conditions to obtain smooth and accurate temperature interpolation results for the global area. Finally, for the entire system, a weighted fusion model of full-field temperature interpolation is constructed to form a regional three-dimensional temperature field interpolation method, achieving a smooth transition between local and global interpolation results and ensuring real-time perception and prediction of full-field temperature information of the active vibration suppression system.

Claims

1. A temperature sensing method for a piezoelectric active vibration suppression system in a low-temperature wind tunnel test, characterized in that, Includes the following steps: 1) Based on the wind tunnel tail support type active vibration suppression system, finite element simulation analysis was carried out. By drawing temperature cloud maps, the temperature distribution of piezoelectric actuators in all directions was visualized, revealing the temperature distribution law and sensitive areas. Taking into account the limitations of simulation analysis results and actual operation, the most representative temperature measurement points were selected to determine the number and distribution of potential temperature measurement points. Statistical analysis methods were used to optimize the potential temperature measurement points, ensuring that a small number of measured points could reflect the changes in the entire temperature field to the greatest extent possible. Finally, the number and distribution of measured points were determined, forming a method for optimal measurement point selection. Finally, a low-temperature wind tunnel environment temperature measurement test platform was built, and the temperature sensors used in the temperature measurement test were comprehensively calibrated. Temperature measurement tests were conducted under low-temperature conditions to reproduce the low-temperature wind tunnel test environment and collect measured temperature data. 1.1) Establish the geometric model of the wind tunnel tail support active vibration suppression system, including four structural parts: tail support rod, piezoelectric actuator, piezoelectric balance and curved blade; use tetrahedral and hexahedral elements for mesh generation, and perform local densification in key areas, namely the piezoelectric actuator installation location; To meet the practical needs of low-temperature wind tunnel testing, finite element simulations were conducted under various operating conditions in a low-temperature wind tunnel environment, varying the angle of attack and the incoming flow velocity. The temperature field distribution was calculated using the heat transfer equation, as shown in the following formula: ； Where k is thermal conductivity and Q is the heat source term. For density, Specific heat capacity, T is temperature; 1.2) Based on the simulation results of the temperature field distribution above, regions with drastic temperature changes are identified, and the temperature gradient at each node in the temperature field is calculated using the gradient operator: ； Temperature cloud maps are plotted to identify areas with large gradient changes. Combined with practical operational feasibility and structural geometric characteristics, including three influencing factors such as sensor size, sensor installation difficulty, and whether it is a stress concentration area, a large number of potential temperature measurement points are selected. 1.3) Based on the partial simulation results of step 1.1), obtain the temperature time-series data of potential temperature measurement points under different experimental conditions. Organize the extracted temperature time-series data into a matrix form, with each column representing the temperature time-series data of one temperature measurement point. Check the data and standardize it. ； in, It is the coordinate matrix of potential temperature measurement points. It is the average value. It is the standard deviation; Calculate the covariance matrix of the standardized matrix. As shown in the following formula: ； in, yes The transpose of the matrix, It is the number of potential temperature measurement points; then feature decomposition is performed: ； in, It is 1 eigenvalue, Is with The corresponding feature vector; Potential temperature measurement points are prioritized based on their eigenvalues. Those eigenvalues ​​that contribute more than 85% to the cumulative temperature change of the wind tunnel's tail-support active vibration damping system are selected as actual measurement points, thus optimizing the layout of these measurement points. ； ； in, It was before A matrix composed of eigenvectors It is the projected data matrix. It is The projection vector of each measurement point in the principal component space yes Euclidean norm; 1.4) Construct a low-temperature wind tunnel environmental temperature measurement test platform, including a wind tunnel, a liquid nitrogen tank, a key section of an active vibration damping system, a LabVIEW-based measurement platform, thermocouple temperature sensors, and a host computer. The wind tunnel includes a test section, a compression section, and a steady-flow section. The key section of the active vibration damping system is placed in the test section of the wind tunnel. The liquid nitrogen tank is connected to the steady-flow section of the tunnel via pipelines. Thermocouple temperature sensors are arranged at selected measurement points. The thermocouple temperature sensors are connected to the temperature acquisition board of the LabVIEW-based measurement platform. The LabVIEW-based measurement platform is connected to the host computer for data transmission. Temperature measurement tests under different operating conditions are completed to obtain the temperature time-series data of the measurement points. 2) Construct a surrogate model to approximate the simulation process by mapping the measured temperature to the simulated discrete temperature points; considering both interpolation accuracy and computation speed, design an optimization method for the simulation node layout of the surrogate model to achieve uniform node distribution and coverage of key areas; combine the derivatives and frequency domain characteristics of the measured time series data to form an input feature matrix, and use the simulated node temperature information at the next time step as the output to construct a large dataset; use deep learning methods to construct a nonlinear mapping model from the measured temperature points to the simulated node temperatures to obtain the discrete temperature information of the active vibration damping system; 2.1) To achieve accurate interpolation of the three-dimensional temperature field, a large number of temperature measurement points are needed to cover the entire three-dimensional space. Temperature information from a large number of discrete points is obtained through finite element simulation, and then the simulation results are approximated using a simulation proxy model to quickly capture the nonlinear mapping relationship between a limited number of temperature measurement points and other discrete nodes. The layout of a large number of discrete nodes in the simulation affects the final accuracy of the temperature field reconstruction. First, a large number of discrete nodes are extracted from the finite element simulation results, and their positions are initialized to ensure that the discrete nodes cover the entire three-dimensional space and are distributed as evenly as possible. A mean squared error loss function is defined to measure the impact of the selected simulation discrete nodes on the interpolation accuracy. ； in, It represents the number of discrete nodes in the simulation. It is The actual temperature of a simulated discrete node. It is The interpolated temperature of each simulated discrete node is used to calculate the gradient of the loss function with respect to the location of the simulated discrete node. With interpolation accuracy and computation speed as optimization objectives, the ADAM algorithm is used to update the positions of discrete nodes in the simulation: ； ； In the formula, For first-order moments, The second moment is used, and the deviation is corrected through multiple iterations. It is the gradient of the loss function with respect to the discrete node positions in the simulation; , The attenuation rate; Controlling the smoothness of the first-order moment estimation, Control the smoothness of the second-order moment estimation; update the positions of the simulated discrete nodes and optimize the layout of the simulated discrete nodes until the loss function reaches its minimum value; during the optimization process, periodically verify the accuracy and speed of the interpolation results, and adjust the optimization parameters according to the verification results to form a simulation discrete node layout optimization method. 2.2) Data collection during simulation The temperature data at the next time step of each simulated discrete node will be compared with the time series data of the measured points. The frequency domain representation is obtained by converting the data to the frequency domain using Fourier transform. The amplitude and phase of the main frequency components are extracted and used as the frequency domain features of the measured temperature. The derivatives of the measured temperature data are calculated to form the time domain features. The frequency domain features and time domain features together form the measured feature matrix. The measured feature matrix is ​​used as input and the simulated node temperature at the next time step is used as the output vector to construct a large dataset, which is divided into training set, validation set and test set in a ratio of 6:2:

2. 2.3) Using the measured feature matrix as input and the instantaneous temperature of the simulated node as output, a simulation surrogate model is constructed based on a recurrent neural network to capture the temporal dependency between the measured data and the simulated node information, and to characterize the complex nonlinear relationship between the two. The simulation surrogate model is shown in the following equation: ； ； in, For time steps, For the input vector, The hidden state vector. For the output vector, For the input weight matrix, The hidden state weight matrix is... To output the weight matrix, , These are the bias vectors corresponding to the hidden layer and the output layer, respectively. The activation function here is... The simulation agent model is trained using the training set from step 2.2; the simulation agent model parameters are adjusted using the validation set; and the simulation agent model accuracy is evaluated using the test set. 3) Considering the non-uniformity of system temperature distribution, the interpolation region is divided based on the temperature gradient. The local large gradient temperature interpolation method and the global smooth temperature interpolation method are studied. The combination method of multi-region interpolation is studied, and a weighted fusion model of full-field temperature interpolation is constructed to form a regional three-dimensional temperature field interpolation method, so as to realize the real-time and accurate reconstruction of the full-field temperature of the system through discrete point temperature information. 3.1) Based on the temperature field simulation results, regions with significant temperature changes are identified. These regions have high temperature gradients and require high accuracy in temperature interpolation, and are designated as local regions. Regions with relatively gentle temperature changes are divided into global regions. For discrete simulation nodes within local regions, Gaussian functions are selected as the basis functions of the RBF interpolation model. The RBF interpolation model is as follows: ； Wherein, basis functions ,and , These are shape parameters. This represents the number of discrete points in the region. It's weight. These are polynomial terms; the weights are determined by minimizing the interpolation error. and polynomial : ； basis functions and polynomial Combine to construct an augmented matrix and augmented vector : ； ； in, This is the temperature value of the first discrete node. It is the temperature value of the second discrete node. Given the temperature value of the nth discrete node, use numerical methods to solve the system of linear equations and determine the weights. and polynomial As shown in the following formula: ； in, It is a weight coefficient vector. It is a polynomial coefficient vector. Substituting the coefficients into the RBF interpolation model forms a temperature interpolation method for a local region. 3.2) For three-dimensional interpolation of the global region, firstly, based on the cubic spline interpolation method, single-dimensional cubic spline interpolation is performed. One-dimensional cubic spline interpolation is performed in the direction. , With the direction fixed, we obtain Cubic spline interpolation function in direction :for ； in, , , , The constant, linear, quadratic, and cubic coefficients of the one-dimensional cubic spline interpolation function in the x-direction are determined by the boundary condition that the first and second derivatives at the connection points are equal. One-dimensional cubic spline interpolation is performed in the direction. With the direction fixed, we obtain : ； in, , , , Let be the constant term coefficients, linear term coefficients, quadratic term coefficients, and cubic term coefficients in the one-dimensional cubic spline interpolation function in the y-direction; finally, in One-dimensional cubic spline interpolation is performed in the direction to obtain the final three-dimensional cubic spline interpolation function. : (20) ； in, , , , Here are the constant term coefficients, linear term coefficients, quadratic term coefficients, and cubic term coefficients in the one-dimensional cubic spline interpolation function in the z-direction; through the above interpolation process, a smooth and accurate temperature interpolation result for the global region is obtained; 3.3) A smooth transition between local and global interpolation results is achieved through distance-weighted averaging, for the query point. The temperature interpolation result is expressed as follows: (21) ； in, Output temperature results for the local RBF interpolation model. Output temperature results for the global cubic spline interpolation model. To determine the proportion of local results, a regional three-dimensional temperature field interpolation method is developed to achieve real-time and accurate perception of the dynamic temperature of the entire field in the active vibration suppression system.

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