A dynamic calibration method for fluid pressure sensor based on real-time temperature compensation

Abstract

This invention discloses a dynamic calibration method for fluid pressure sensors based on real-time temperature compensation. The invention constructs a thermo-mechanical coupled digital twin model of the measured fluid pipeline and the sensor. It employs laser-induced fluorescence transient full-field temperature measurement technology to acquire a two-dimensional transient temperature field, simultaneously acquiring high-frequency pressure signals and contact temperature signals from the sensitive core. Through adaptive unscented Kalman filtering using graph convolution and deep reinforcement learning, it achieves time axis alignment and noise filtering for multi-source data with different sampling rates. Real-time closed-loop compensation is performed via hardware-in-the-loop, and feedback is used to correct the parameters of the digital twin model. This invention solves the problems of inaccurate reference in traditional single-point temperature measurement compensation, time misalignment of multi-source data, and asynchronous dynamic compensation, improving the measurement accuracy and calibration reliability of fluid pressure sensors under transient phase change conditions.

Description

Technical Field

[0001] This invention belongs to the field of sensor dynamic calibration and fluid parameter detection technology, specifically relating to a dynamic calibration method for fluid pressure sensors based on real-time temperature compensation. Background Technology

[0002] Existing fluid pressure sensor temperature compensation schemes typically involve attaching a single-point contact temperature sensor to the surface of the sensor's sensitive core to obtain localized temperatures, and then using a preset temperature compensation curve to statically correct the original pressure signal using a lookup table. However, in conditions involving transient phase changes, such as gas-liquid two-phase flow, the phase change in the fluid medium can lead to a drastic temperature gradient within the pipeline. Since single-point contact measurement can only obtain temperature values ​​at a fixed local location and cannot capture the overall temperature distribution across the fluid region, the system can only use the local single-point temperature as the compensation benchmark. Furthermore, conventional compensation schemes simply concatenate the low-frequency signal from the temperature sensor with the high-frequency signal from the pressure sensor using a simple timestamp, and use the clock difference between the two as the basis for delay compensation.

[0003] Based on the existing technical solutions, when a fluid undergoes a transient phase change, an uneven temperature gradient distribution is generated inside the pipeline. Using a local single-point temperature as a compensation reference will cause the reference value to deviate from the actual temperature state of the fluid phase change region, resulting in inaccurate compensation reference. Simply splicing low-frequency temperature signals with high-frequency pressure signals using timestamps cannot eliminate the time axis misalignment and compensation asynchrony error caused by the difference in sampling period under dynamic fluctuation conditions of multi-source data with different sampling rates. This results in the inability to output the correct dynamic calibration correction amount under high-frequency dynamic pressure fluctuations. Summary of the Invention

[0004] The purpose of this invention is to provide a solution that can effectively address the problems described in the background section.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation, characterized by comprising: Construct a thermo-solid coupling digital twin model of the measured fluid pipeline and the pressure sensor; Laser-induced fluorescence transient full-field thermometry is used to acquire two-dimensional transient temperature field distribution data of the fluid under test, and high-frequency raw pressure signal of pressure sensor and contact temperature signal of sensitive core are acquired simultaneously. The time axis alignment and noise removal of two-dimensional transient temperature field distribution data, high-frequency raw pressure signal and contact temperature signal are completed by adaptive unscented Kalman filtering method. The aligned data is input into the thermo-solid coupling digital twin model to solve the temperature gradient distribution of the sensor sensitive surface and the pressure measurement deviation caused by the fluid phase change under the current working conditions, and output the temperature compensation reference value and dynamic calibration correction amount. The hardware-in-the-loop real-time closed-loop calibration receives dynamic calibration corrections to compensate the original pressure output in real time, and feeds back the compensated calibration data to the thermo-mechanical coupled digital twin model to complete real-time parameter correction.

[0006] Preferably, the dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation is characterized by performing time axis alignment and noise filtering using an adaptive unscented Kalman filter method, including: A deep reinforcement learning interactive environment is constructed, with the filtered residual sequence as the state space, the adjustment coefficients of the process noise covariance matrix and the measurement noise covariance matrix as the action space, and the negative value of the mean square error of the state estimation as the reward function. By using a proximal policy optimization method to update the policy network parameters online and outputting the optimal adjustment coefficient at the current moment, the noise covariance matrix in the adaptive unscented Kalman filter method is dynamically updated, thereby achieving adaptive tracking and filtering of abrupt noise in multi-source data with different sampling rates.

[0007] Preferably, the dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation is characterized in that the aligned data is input into a thermo-mechanical coupled digital twin model to solve for the temperature gradient distribution and pressure measurement deviation, including: A physical information neural network is used to replace the traditional numerical solver. The aligned full-field temperature field data and the original pressure signal are used as boundary conditions and initial conditions to input the physical information neural network. The physical constraint residuals of the fluid dynamics control equation and the heat conduction partial differential equation are embedded in the loss function of the physical information neural network. By minimizing the weighted sum of the data-driven loss and the physical constraint loss, the temperature gradient distribution of the sensor sensitive surface and the pressure measurement deviation caused by the fluid phase change are solved by backpropagation.

[0008] Preferably, the dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation is characterized by acquiring two-dimensional transient temperature field distribution data of the measured fluid region, including: For continuous low-resolution temperature field image sequences acquired by laser-induced fluorescence technology, optical flow method is used to extract the fluid motion vector field between adjacent frames; A spatiotemporal attention-based super-resolution reconstruction network is constructed based on fluid motion vector field guidance. It integrates low-resolution images of the current frame with high-resolution features of historical frames to fill in the missing spatial details of the temperature field caused by fluorescence lifetime limitation, and outputs high spatiotemporal resolution two-dimensional transient temperature field distribution data.

[0009] Preferably, the dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation is characterized in that the hardware-in-the-loop real-time closed-loop calibration receives dynamic calibration corrections and performs real-time compensation on the original pressure output, including: The real-time compensation process is deconstructed into multiple microservice tasks, and the execution time and cache hit rate of each microservice task are monitored in real time. An edge computing resource scheduling model is constructed based on a deep deterministic policy gradient. According to the frequency characteristics of fluid pressure fluctuations and the urgency of microservice tasks, heterogeneous computing resources are dynamically allocated to ensure that the solution and compensation of dynamic calibration corrections are completed within a strict time window.

[0010] Preferably, the dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation is characterized by constructing a deep reinforcement learning interactive environment, including: Multi-source heterogeneous sampling rate data are constructed into graph structure data according to spatial topological relationships, where nodes represent sampling points at different spatial locations and edges represent fluid heat conduction relationships between sampling points; A graph convolutional neural network is used to extract spatial features from graph structure data. The extracted spatial features are then concatenated and fused with the residual sequence in the time dimension to form a high-dimensional state space that integrates spatiotemporal correlation features. This space is then input into a proximal policy optimization method.

[0011] Preferably, the dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation is characterized by solving the problem through weighted sum and backpropagation to minimize data-driven loss and physical constraint loss, including: A meta-learning mechanism is introduced to extract the prior distribution parameters of the network weights in the physical information neural network during the historical multi-condition training phase. In the current new working condition solution stage, the prior distribution parameters are used as constraints for the initialization of the physical information neural network. The network weights are fine-tuned by using a small amount of aligned data from the current working condition to accelerate the convergence speed of the physical constraint loss and data-driven loss in the phase transition boundary region.

[0012] Preferably, the dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation is characterized by outputting high spatiotemporal resolution two-dimensional transient temperature field distribution data, including: A phase transition boundary sensing head is embedded in the spatiotemporal attention super-resolution reconstruction network. An unsupervised clustering method is used to perform pixel-level clustering segmentation on the reconstructed temperature field feature map to identify the phase transition boundary region of gas-liquid two-phase fluid. The segmentation mask of the phase transition boundary region is superimposed as an additional attention weight into the decoder of the spatiotemporal attention super-resolution reconstruction network to enhance the reconstruction fidelity of temperature gradient details in the phase transition boundary region.

[0013] Preferably, the dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation is characterized in that prior distribution parameters are used as constraints for initializing the physical information neural network, including: The parameter correction of the thermo-structure coupled digital twin model is decoupled into two sub-tasks: fluid flow field parameter correction and sensor structure thermal response parameter correction. Independent meta-learning agents are deployed for the two sub-tasks respectively, and a multi-agent collaborative framework is constructed. While sharing the underlying prior distribution parameters, each agent exchanges its gradient update direction by maximizing mutual information, and collaboratively optimizes the parameter correction accuracy of the physical information neural network at the multi-physics coupling interface.

[0014] Preferably, the dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation is characterized by co-optimizing the parameter correction accuracy of the physical information neural network at the multi-physics coupling interface, including: A federated learning mechanism is introduced among multiple multi-agent collaborative frameworks deployed at different fluid pipeline nodes; After each node completes the parameter correction of the physical information neural network locally, the multi-agent collaborative framework only uploads the encrypted network weight update and the physical constraint loss descent gradient to the central aggregation server. The central aggregation server uses an adaptive federated averaging strategy to aggregate the received updates and gradients, and distributes global model parameters to achieve collaborative evolution of the compensation benchmark of multi-node digital twin models and data privacy protection.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention employs laser-induced fluorescence transient full-field temperature measurement technology to acquire two-dimensional transient temperature field distribution data of a fluid region. It combines optical flow method to extract the fluid motion vector field and utilizes a spatiotemporal attention super-resolution reconstruction network to complete the spatial details of the temperature field, solving the problem that single-point temperature measurement cannot obtain the overall temperature distribution. The aligned full-field temperature field data and the original pressure signal are input into a thermo-mechanical coupled digital twin model. A physical information neural network with embedded fluid dynamics control equations and heat conduction partial differential equations as physical constraints replaces the numerical solver. Prior distribution parameters are extracted through a meta-learning mechanism to constrain the network initialization. A phase change boundary sensing head is embedded in the super-resolution reconstruction network to identify the phase change boundary region, which is then superimposed onto the decoder to enhance reconstruction fidelity. This allows for the calculation of the temperature gradient distribution of the sensor's sensitive surface under current operating conditions and the pressure measurement deviation caused by fluid phase change. The output is a temperature compensation benchmark value and dynamic calibration correction amount that conform to the actual phase change state temperature gradient, eliminating the phenomenon of inaccurate compensation benchmarks.

[0016] 2. This invention constructs multi-source heterogeneous sampling rate data into graph-structured data according to spatial topological relationships. It uses a graph convolutional neural network to extract spatial features and fuse spatiotemporal correlation features to form a high-dimensional state space. It uses a near-end policy optimization method to dynamically update the noise covariance matrix in the adaptive unscented Kalman filter method, eliminating time axis misalignment and compensation asynchronous errors caused by sampling period differences in multi-source heterogeneous sampling rate data. It constructs an edge computing resource scheduling model through a deep deterministic policy gradient to allocate heterogeneous computing resources and ensure calibration execution time window. It combines a multi-agent collaborative framework to decouple fluid flow field and structural thermal response parameter correction and optimizes interface parameters by maximizing mutual information exchange gradient. It also uses a federated learning mechanism to aggregate multi-node model parameters, realizing the collaborative evolution of compensation benchmarks for multi-node digital twin models and data privacy protection. Attached Figure Description

[0017] Figure 1 This is a flowchart of the overall method (main flow) of the present invention; Figure 2 This is a flowchart of the laser-induced fluorescence thermometry + temperature field super-resolution process of the present invention; Figure 3 This is a flowchart of the adaptive unscented Kalman filter + deep reinforcement learning optimization process of the present invention; Figure 4 This is a flowchart of the solution process for the Physical Information Neural Network (PINNs) of this invention. Figure 5 This is a flowchart of the phase change boundary sensing and temperature field enhancement of the present invention; Figure 6 This is a flowchart of the hardware-in-the-loop real-time compensation + edge computing power scheduling process of the present invention. Detailed Implementation

[0018] Please refer to the attached document. Figure 1A thermo-solid coupling digital twin model of the measured fluid pipeline and the pressure sensor was constructed. This model comprises two computational domains: a fluid domain and a solid domain. The fluid domain represents the fluid flow space within the measured fluid pipeline, while the solid domain includes the pressure sensor's sensing core, mounting base, and pipeline wall structure. The specific construction process involves: constructing solid geometric models of the measured fluid pipeline and the pressure sensor using 3D modeling software; meshing the geometric models; using a hexahedral structured mesh for the fluid domain and a tetrahedral unstructured mesh for the solid domain; matching mesh nodes at the fluid-solid coupling interface; and setting the mesh boundary layer thickness to 0.1 mm and the number of layers to 5 to ensure the computational accuracy of the coupling interface. Define the physical property parameters of the model: Fluid domain medium properties include the density, dynamic viscosity, thermal conductivity, specific heat at constant pressure, latent heat of phase change, and gas-liquid two-phase equation of state of the measured fluid; solid domain material properties include the elastic modulus, Poisson's ratio, thermal conductivity, and coefficient of thermal expansion of the silicon material of the sensing core, as well as the density, thermal conductivity, and elastic modulus of the stainless steel materials of the mounting base and piping. Define the multiphysics coupling relationship: the coupling interface between the fluid and solid domains satisfies the heat flow continuity condition and the stress continuity condition; the mathematical expression for the heat flow continuity condition is:

[0019] in, The thermal conductivity of the fluid is denoted as . For the temperature of the fluid domain, Let be the normal vector of the coupling interface. Let be the thermal conductivity of the solid domain. Let be the temperature of the solid domain; the mathematical expression for the stress continuity condition is:

[0020] in, Let be the fluid stress tensor of the fluid domain. Let be the solid stress tensor in the solid domain. A thermo-structure coupled digital twin model is constructed, configured to accept boundary and initial conditions, and the temperature gradient distribution and pressure measurement deviation of the sensor's sensitive surface are solved.

[0021] Secondly, laser-induced fluorescence transient full-field thermometry is used to acquire two-dimensional transient temperature field distribution data of the measured fluid region, while simultaneously acquiring the high-frequency raw pressure signal from the pressure sensor and the contact temperature signal from the sensitive core. The signal acquisition unit uses... The synchronous square wave trigger signal enables synchronous acquisition of multi-source data, including the laser-induced fluorescence thermometry module. Camera trigger frequency is The corresponding temperature field data sampling rate is The pressure sensor sampling frequency is The corresponding high-frequency raw pressure signal sampling rate is The sampling frequency of the contact temperature sensor is... The corresponding contact temperature signal sampling rate is The specific process of the laser-induced fluorescence transient full-field thermometry is as follows: A fluorescent tracer injection device is used to inject a fluorescent tracer into the pipeline containing the fluid being measured, with a mass concentration of... Rhodamine Fluorescent tracer; pulsed laser output The pulsed laser beam is expanded by a cylindrical lens to form a sheet light source, which illuminates the two-dimensional fluid region corresponding to the optical observation window of the fluid pipeline under test, and excites the fluorescent tracer to produce fluorescence. The camera acquires fluorescence signals through an optical lens and outputs a continuous sequence of fluorescence images. Based on the calibration relationship between fluorescence intensity and temperature obtained from preliminary experiments, the fluorescence image sequence is converted into initial two-dimensional transient temperature field distribution data. The calibration relationship is as follows: Within range, step size The linear fitting curve obtained from the calibration is expressed as follows: ,in For temperature The corresponding fluorescence intensity, , For the calibration results of the fitting coefficients, please refer to the appendix. Figure 2 .

[0022] Furthermore, an adaptive unscented Kalman filter method is used to align the time axes and remove noise from the two-dimensional transient temperature field distribution data, the high-frequency raw pressure signal, and the contact temperature signal. For multi-source, heterogeneous sampling rate data, the system's state equations and measurement equations are established, and the system's state vector is defined. ,in for The actual fluid pressure value at any given time. for The average temperature of the fluid region at time [time]. for The contact temperature of the sensitive core at any given time; the state equation of the system is:

[0023] in, It is a 3rd order unit state transition matrix. The process noise is represented by the covariance matrix of the process noise. ; For measurement data with different sampling rates, corresponding measurement equations are established: The measurement equation for the high-frequency raw pressure signal is as follows: ,in , For pressure measurement noise, the covariance matrix is: The measurement equation for two-dimensional transient temperature field distribution data is: ,in , For fluid temperature measurement noise, the covariance matrix is: ; The measurement equation for contact temperature signals is as follows: ,in , For contact temperature measurement noise, the covariance matrix is: The process executes unscented Kalman filtering with sigma point sampling, time update, and measurement update steps. For data with different sampling rates, only the time update step is performed when there is no corresponding measurement data, and the measurement update step is performed when there is corresponding measurement data, thus achieving time axis alignment of multi-source data. Simultaneously, a covariance matching method based on the innovation sequence adaptively adjusts the process noise covariance matrix. With measurement noise covariance matrix The new information sequence ,in The state is predicted one step at a time, and is dynamically updated by minimizing the mean square error of the innovation sequence. and To achieve adaptive noise filtering, please refer to the appendix. Figure 3 .

[0024] Subsequently, the aligned data is input into the thermo-structure coupled digital twin model to solve for the temperature gradient distribution of the sensor's sensitive surface and the pressure measurement deviation caused by fluid phase change under the current operating conditions. The temperature compensation reference value and dynamic calibration correction are output. The time-axis aligned two-dimensional transient temperature field distribution data, high-frequency raw pressure signal, and contact temperature signal are used as the boundary and initial conditions of the thermo-structure coupled digital twin model. Specifically, the two-dimensional transient temperature field distribution data serves as the temperature boundary condition for the fluid domain, the contact temperature signal as the temperature boundary condition for the solid domain, and the high-frequency raw pressure signal as the pressure inlet boundary condition for the fluid domain. The thermo-structure coupled digital twin model is solved using the finite element numerical method to determine the fluid domain's... Equations, energy equations, phase field equations, as well as heat conduction equations and elastic equilibrium equations in the solid domain, yield the temperature gradient distribution of the sensor's sensitive surface under the current operating conditions. ,in , The coordinates of the sensitive surface are given in two dimensions. Simultaneously, the pressure abrupt change at the gas-liquid interface during the fluid phase transition, and the pressure measurement deviation caused by the thermal stress deformation of the sensitive core due to the temperature gradient, are calculated. Calculate the temperature compensation reference value based on the temperature gradient distribution. The temperature compensation reference value The area-weighted average temperature of the sensor's sensitive surface is expressed as:

[0025] in, The total area of ​​the sensor's sensitive surface. Coordinates of the sensitive surface Temperature value at that location; Dynamic calibration correction amount Pressure measurement deviation value The negative value, that is Please refer to the appendix. Figure 4 .

[0026] Finally, the hardware-in-the-loop real-time closed-loop calibration receives dynamic calibration corrections to compensate the original pressure output in real time, and feeds back the compensated calibration data to the thermo-mechanical coupled digital twin model to complete real-time parameter correction. The hardware-in-the-loop execution unit includes an FPGA real-time controller, a DA conversion module, and an AD conversion module. The FPGA real-time controller is connected to the edge computing unit via Ethernet communication and receives the dynamic calibration corrections output by the edge computing unit. The AD conversion module is connected to the signal output terminal of the pressure sensor to acquire the raw pressure output signal of the pressure sensor. The signal is converted into a digital signal and then input to the FPGA real-time controller; the FPGA real-time controller performs real-time compensation calculations, and the compensated calibration pressure value is... The DA conversion module will calibrate the pressure value. The signal is converted into an analog signal and output to the downstream measurement and control system. Simultaneously, the FPGA real-time controller outputs the compensated calibration data. Feedback is sent from edge computing units to the thermo-mechanical coupled digital twin model. The model uses calibration data as a reference for true values ​​and employs the least squares method to correct the model's physical property parameters in real time. The corrected parameters are then used for model solving in the next time step, forming a real-time closed-loop calibration. Please refer to the appendix. Figure 6 .

[0027] As a preferred embodiment, the time axis alignment and noise filtering steps are completed by an adaptive unscented Kalman filter method. This is achieved using an adaptive unscented Kalman filter method optimized by deep reinforcement learning, and the specific process is as follows.

[0028] First, the multi-source heterogeneous sampling rate data are constructed into a graph structure based on spatial topological relationships. The two-dimensional temperature field of the measured fluid region is then divided into... Each grid cell corresponds to a spatial sampling point. Sampling points from the pressure sensor and the contact temperature sensor are treated as independent nodes, collectively forming the node set of the graph-structured data. ,in The total number of nodes is given, and the initial features of each node are the sampled value and sampling timestamp of the corresponding sampling point. Construct the edge set of the graph structure. For any two nodes and If the spatial locations of two nodes satisfy the fluid heat conduction correlation, that is, the two nodes are located in the same fluid domain and the spatial distance is less than a preset correlation threshold, or the two nodes are located at the coupling interface between the fluid domain and the solid domain respectively, then at the nodes and Construct an undirected edge between them, with the edge weight expressed as:

[0029] in, Let be the equivalent thermal conductivity of the medium corresponding to the two nodes. The Euclidean distance between the two nodes; This completes the graph structure data. The construction of the graph convolutional neural network is as follows: A two-layer graph convolutional neural network is used to extract spatial features from graph-structured data. The calculation expression for each graph convolutional layer is:

[0030] in, For the first The node feature matrix of the layer Let be the initial feature matrix of the node. Let be the adjacency matrix of the graph. Let be the degree matrix of the graph. For the first The trainable weight matrix of the layer, This is the ReLU activation function.

[0031] After two layers of graph convolution, the spatial feature matrix of all nodes is output. ,right Perform global average pooling to obtain a one-dimensional spatial feature vector. .

[0032] Secondly, a deep reinforcement learning interactive environment is constructed. The residual sequence of the past 10 time steps of the adaptive unscented Kalman filter output is obtained. The residual sequence is flattened to obtain a one-dimensional time feature vector. ; spatial feature vector With time feature vector By splicing and merging, a high-dimensional state vector is obtained. This serves as the state space for deep reinforcement learning. A continuous action space is constructed, containing action vectors. ,in The process noise covariance matrix The adjustment coefficient, To measure the noise covariance matrix The adjustment coefficient, and The range of values ​​is Construct a reward function, which is the negative of the mean squared error of the state estimation, and its expression is:

[0033] in, for The state estimate of the filtered output at time step. for The true state value at time t, where MSE is the mean square error calculation function.

[0034] Subsequently, the policy network parameters are updated online using a proximal policy optimization method. The proximal policy optimization algorithm comprises a policy network and a value network, both employing a 3-layer fully connected neural network with 256, 128, and 64 hidden layer neurons respectively, and ReLU activation function. The algorithm's objective function is a pruned alternative objective function, expressed as:

[0035] in, These are the weight parameters of the policy network. This represents the probability ratio between the old and new strategies. For the dominant function, The pruning factor is 0.2. At each time step, the near-end policy optimization algorithm adjusts the pruning factor based on the current state. Output Action That is, the optimal adjustment coefficient and The noise covariance matrix is ​​dynamically updated according to the following formula:

[0036]

[0037] The updated and The input is an adaptive unscented Kalman filter. The filter performs filtering, time-axis alignment, and noise removal operations, while simultaneously obtaining the reward at the current time step. It is used to update the parameters of the policy network and value network online, and to achieve adaptive tracking and filtering of sudden noise in multi-source heterogeneous sampling rate data.

[0038] As a preferred embodiment, a physical information neural network is used instead of a traditional numerical solver. The physical information neural network is a fully connected feedforward neural network, and the input parameters of the input layer are spatial coordinates. Time coordinates The input layer has 3 neurons; the hidden layers are 8 fully connected layers with 128 neurons per layer, and the activation function is the Swish function; the output parameter of the output layer is the pressure of the fluid domain. ,temperature Phase field parameters and the temperature of the solid domain Displacement The number of neurons in the output layer is 5; the phase field parameters are... Corresponding liquid phase, Corresponding to the gas phase, Corresponding to the phase transition interface region. The aligned two-dimensional transient temperature field distribution data is used as the Dirichlet boundary condition for the fluid domain temperature, the aligned contact temperature signal is used as the Dirichlet boundary condition for the solid domain temperature, and the aligned high-frequency original pressure signal is used as the inlet boundary condition for the fluid domain pressure. Initial time... The initial values ​​of the output parameters are determined by the pre-calculation results under steady-state conditions.

[0039] The physical constraint residuals of the fluid dynamics control equations and heat conduction partial differential equations are embedded in the loss function of the physical information neural network. This loss function is a data-driven loss function. With physical constraint loss The weighted sum is expressed as:

[0040] in, The weighting coefficients for data-driven loss. These are the weighting coefficients for the physical constraint loss. The data-driven loss... The mean square error between the network output value and the measured data is expressed as:

[0041] in, This represents the sample size of the measured data. This is the measured fluid temperature value. This refers to the fluid temperature value output by the network. This is the measured pressure value. The stress value output by the network. This is the measured contact temperature value. This refers to the solid temperature value output by the network. The physical constraint loss... This is the sum of the residuals of the governing equations of fluid mechanics, the partial differential equations of heat conduction, the phase-field equations, and the equilibrium equations of elasticity, specifically including: Fluid mass conservation equation residuals ,in For fluid velocity vector; residuals of fluid momentum conservation equation ,in For fluid density, For fluid dynamic viscosity, It is the acceleration due to gravity; residuals of the fluid energy conservation equation ,in The specific heat capacity at constant pressure of the fluid. This is the latent heat source term for phase change; Residual of solid heat conduction equation ,in For solid density, This refers to the specific heat capacity of a solid at constant pressure. Phase field equation residuals ,in For phase field mobility, The variational derivative of the free energy; Residuals of the equilibrium equations of solid elasticity ,in For the solid stress tensor, For solid volume forces; The expression for the physical constraint loss is:

[0042] in, The number of configuration points is determined by the Latin hypercube sampling method, which randomly generates configuration points within the computational domain.

[0043] Minimize the total loss using the backpropagation algorithm. The weight parameters of the physical information neural network are updated. After training, the network outputs the temperature field distribution of the sensor's sensitive surface under the current operating conditions. The temperature gradient distribution was calculated. Simultaneously output the pressure measurement deviation value caused by fluid phase change. The final output temperature compensation reference value With dynamic calibration correction amount .

[0044] Furthermore, a meta-learning mechanism is introduced to optimize network convergence performance. During the historical multi-condition training phase, a training task set containing 100 different fluid conditions is constructed. Each task corresponds to different fluid flow rates, temperatures, pressures, and phase transition states. The dataset for each task is divided into a support set and a query set. A model-independent meta-learning method is employed to learn a set of initial parameters for the network weights. This ensures that the initial parameters, after a small number of gradient updates on any new task, achieve the minimum loss value on the query set. The objective function expression for model-independent meta-learning is:

[0045] in, For the training task set, For a single training task, For the task The network weight parameters after one gradient update. For the inner loop learning rate, For the task The loss function; By minimizing the objective function, the prior distribution parameters of the network weights, including the prior mean, are obtained through training. with prior variance .

[0046] In the current solution phase for the new working condition, the prior distribution parameters are used as constraints for initializing the physical information neural network, and the initial values ​​of the network weights are... From the prior distribution The data was obtained through sampling; 50 aligned data sets under the current operating conditions were used as the support set to fine-tune the network weights. The loss function for fine-tuning included a weight regularization term, and the expression was:

[0047] in, These are the regularization weight coefficients. Let L2 norm be the ratio of network weights to prior mean. The aforementioned meta-learning mechanism accelerates the convergence speed of physical constraint loss and data-driven loss in the phase transition boundary region.

[0048] Furthermore, a multi-agent collaborative framework is constructed to optimize parameter correction accuracy. The parameter correction of the thermo-structure coupled digital twin model is decoupled into two sub-tasks: fluid flow field parameter correction and sensor structure thermal response parameter correction. The fluid flow field parameter correction sub-task is responsible for optimizing the fluid-domain-related weight parameters in the network. The subtask corrects the physical parameters of the fluid domain and outputs the multiphysics distribution of the fluid domain; the subtask corrects the thermal response parameters of the sensor structure and optimizes the weight parameters related to the solid domain in the network. The physical parameters of the solid domain are corrected, and the multiphysics field distribution of the solid domain is output. Independent meta-learning agents are deployed for the two sub-tasks, namely, a fluid agent. With structural intelligent agents The two agents share the underlying prior distribution parameters. and .

[0049] Two agents exchange gradient update directions by maximizing mutual information, thus defining the gradient update direction of the fluid agent. ,in The loss function for the fluid flow field subtask; the gradient update direction of the structural agent. ,in Let be the loss function for the structural thermal response subtask; the mutual information expression for the two gradients is:

[0050] in, for Information entropy for Information entropy for and The joint information entropy; Constructing the joint loss function for multiple agents:

[0051] in, The weights are the mutual information weights; the two agents minimize the joint loss function. They collaboratively update their respective network weight parameters to optimize the parameter correction accuracy of the physical information neural network at the multi-physics coupling interface.

[0052] Furthermore, a federated learning mechanism is introduced to achieve collaborative evolution of multi-node models. The system includes... Each local client is deployed at different fluid pipeline nodes, and each client corresponds to an independent multi-agent collaborative framework and a local physical information neural network model. The central aggregation server is connected to all local clients via an encrypted communication link. The execution process of federated learning is as follows: Initialization phase: The central aggregation server initializes the global model weight parameters. This includes the underlying prior distribution parameters, which are then distributed to all local clients. Local training phase: Each local client receives the global model parameters as the initial parameters for its local model, uses local operating data to correct the parameters, and obtains the local weight update. and the gradient of physical constraint loss descent ; Encrypted upload phase: Each local client uses a homomorphic encryption algorithm to encrypt the local update amount and gradient, and uploads the ciphertext to the central aggregation server, without uploading the original local data; Global aggregation phase: The central aggregation server decrypts the received data and aggregates it using an adaptive federated averaging strategy. The aggregation formula is as follows:

[0053] in, For the first The number of local training samples per client. The total number of samples across all clients is determined by introducing adaptive weights. Optimize aggregation effect, among which The initial physical constraint loss for the local model. The physical constraint loss after training; Global distribution phase: The central aggregation server distributes the aggregated global model parameters to all local clients, and each client updates its local model to enter the next iteration.

[0054] Through the aforementioned federated learning mechanism, the co-evolution of compensation benchmarks for multi-node digital twin models and data privacy protection are achieved.

[0055] As a preferred embodiment, this relates to a sequence of continuous low-resolution temperature field images acquired using laser-induced fluorescence technology. ,in for Time resolution is For low-resolution temperature field images, the Lucas-Kanade optical flow method is used to extract the fluid motion vector field between adjacent frames. Time and The basic constraint equations of the optical flow method for adjacent frames at time t are:

[0056] in, For the image in Gray-scale gradient in direction, For the image in Gray-scale gradient in direction, The gray-level gradient of the image over time. for Optical flow components in the direction, for The optical flow component in the direction; by solving the least-squares solution of the above constraint equations within a neighborhood window of each pixel, the fluid motion vector field between adjacent frames is obtained. ,in for The motion vector matrix of the direction, for The motion vector matrix in the direction.

[0057] A spatiotemporal attention-based super-resolution reconstruction network is constructed based on fluid motion vector field guidance. The network consists of three parts: an encoder, a spatiotemporal attention fusion module, and a decoder. The specific structure and processing procedure are as follows: The encoder consists of two branches: a current frame feature extraction branch and a historical frame feature extraction branch. Both branches use three 3×3 convolutional layers with a stride of 1, padding of 1, and the LeakyReLU activation function. The current frame feature extraction branch takes the low-resolution image of the current frame as input. Output the low-resolution feature map of the current frame. Input to the historical frame feature extraction branch High-resolution feature maps obtained from time-reconstruction Output high-resolution feature maps of historical frames ; Spatiotemporal attention fusion module: based on fluid motion vector field High-resolution feature maps of historical frames Perform a reverse warping operation to map the features of historical frames to the coordinate space of the current frame, resulting in an aligned historical feature map. The expression for the reverse warp operation is:

[0058] in, These are the pixel coordinates of the feature map; The attention weights for the current frame features and the aligned historical features are calculated using the following expression:

[0059] in, It is a 1×1 convolutional layer. This is a channel-level splicing operation. Use the Sigmoid activation function; Historical features are weighted by attention weights and then fused with current frame features to obtain a fused spatiotemporal feature map. ; Decoder: Employs subpixel convolutional layers to achieve 4x upsampling, upsampling the fused spatiotemporal feature map to a high-resolution size, and outputting a high-resolution temperature field image. This completes the missing spatial details of the temperature field.

[0060] Furthermore, a phase transition boundary sensing head is embedded in the spatiotemporal attention super-resolution reconstruction network to enhance the reconstruction fidelity of the phase transition boundary region. The input of the phase transition boundary sensing head is the fused spatiotemporal feature map output by the encoder. The output is a segmentation mask for the phase transition boundary region. The specific processing steps are as follows: Unsupervised K-means clustering is used to perform pixel-level clustering segmentation on the fused spatiotemporal feature map, with two clusters corresponding to the gas phase and liquid phase regions, respectively. The feature vector of each pixel is used as a clustering sample, and the K-means clustering algorithm is used to complete pixel classification, obtaining the initial gas-liquid two-phase segmentation result. The Canny edge detection operator is used to extract edges from the segmentation result, obtaining a binary segmentation mask for the phase transition boundary region. In the mask, regions with a pixel value of 1 correspond to phase transition boundary regions, and regions with a pixel value of 0 correspond to non-boundary regions. Please refer to the appendix. Figure 5 .

[0061] The segmentation mask of the phase transition boundary region As additional attention weights, they are superimposed on the decoder. Before the sub-pixel convolutional layer, the segmentation mask and the fused spatiotemporal feature map are multiplied pixel by pixel to weight and enhance the features of the phase transition boundary region. The weighted feature map is as follows:

[0062] in, For the enhancement coefficients; the weighted enhanced feature map The input decoder performs upsampling reconstruction, and finally outputs high spatiotemporal resolution two-dimensional transient temperature field distribution data.

[0063] As a preferred embodiment, the real-time compensation process is deconstructed into multiple independent microservice tasks, specifically including: a data acquisition and preprocessing microservice, responsible for acquiring multi-source data, format conversion, and outlier removal; a filtering and time axis alignment microservice, responsible for adaptive unscented Kalman filtering and multi-source data time axis alignment; a digital twin model solving microservice, responsible for solving the thermo-structure coupling digital twin model and calculating the temperature compensation baseline value and dynamic calibration correction; a real-time compensation execution microservice, responsible for the compensation calculation of the original pressure signal and the output of calibration data; and a model parameter correction microservice, responsible for the feedback of calibration data and the real-time correction of the digital twin model parameters. Each microservice task is deployed in a containerized environment of the edge computing unit and communicates with each other through message queues to monitor the execution time of each microservice task in real time. Cache hit rate CPU usage and memory usage.

[0064] An edge computing resource scheduling model is constructed based on a deep deterministic policy gradient. The model includes an actor network and a critic network, both employing a 3-layer fully connected neural network with 128, 64, and 32 hidden layer neurons respectively, and using ReLU as the activation function. The model's state space is defined as: a state vector. This is a 10-dimensional continuous vector, including the execution time of 5 microservice tasks, the cache hit rate of 5 microservice tasks, and the frequency characteristics of current fluid pressure fluctuations. The utilization rate of heterogeneous computing resources in the current system; including the frequency characteristics of fluid pressure fluctuations. The main frequency is obtained by performing a fast Fourier transform on the high-frequency raw pressure signal.

[0065] Define the action space of the model: action vectors The continuous action space includes the number of CPU cores, memory capacity, and GPU computing power ratio allocated to each microservice task. The range of values ​​for the action space is determined by the total resources of the edge computing unit, including its 8-core CPU, 16GB memory, and integrated GPU.

Claims

1. A dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation, characterized in that, include: Construct a thermo-solid coupling digital twin model of the measured fluid pipeline and the pressure sensor; Laser-induced fluorescence transient full-field thermometry is used to acquire two-dimensional transient temperature field distribution data of the fluid under test, and high-frequency raw pressure signal of pressure sensor and contact temperature signal of sensitive core are acquired simultaneously. The time axis alignment and noise removal of two-dimensional transient temperature field distribution data, high-frequency raw pressure signal and contact temperature signal are completed by adaptive unscented Kalman filtering method. The aligned data is input into the thermo-solid coupling digital twin model to solve the temperature gradient distribution of the sensor sensitive surface and the pressure measurement deviation caused by the fluid phase change under the current working conditions, and output the temperature compensation reference value and dynamic calibration correction amount. The hardware-in-the-loop real-time closed-loop calibration receives dynamic calibration corrections to compensate the original pressure output in real time, and feeds back the compensated calibration data to the thermo-mechanical coupled digital twin model to complete real-time parameter correction.

2. The dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation according to claim 1, characterized in that, Time axis alignment and noise removal are achieved using an adaptive unscented Kalman filter method, including: A deep reinforcement learning interactive environment is constructed, with the filtered residual sequence as the state space, the adjustment coefficients of the process noise covariance matrix and the measurement noise covariance matrix as the action space, and the negative value of the mean square error of the state estimation as the reward function. The policy network parameters are updated online using a near-end policy optimization method, and the optimal adjustment coefficient at the current time is output to dynamically update the noise covariance matrix in the adaptive unscented Kalman filter method.

3. The dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation according to claim 1, characterized in that, The aligned data is input into the thermo-mechanical coupled digital twin model to solve for the temperature gradient distribution and pressure measurement deviation, including: A physical information neural network is used to replace the traditional numerical solver. The aligned full-field temperature field data and the original pressure signal are used as boundary conditions and initial conditions to input the physical information neural network. The physical constraint residuals of the fluid dynamics control equation and the heat conduction partial differential equation are embedded in the loss function of the physical information neural network. By minimizing the weighted sum of the data-driven loss and the physical constraint loss, the temperature gradient distribution of the sensor sensitive surface and the pressure measurement deviation caused by the fluid phase change are solved by backpropagation.

4. The dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation according to claim 1, characterized in that, Acquire two-dimensional transient temperature field distribution data of the measured fluid region, including: For continuous low-resolution temperature field image sequences acquired by laser-induced fluorescence technology, optical flow method is used to extract the fluid motion vector field between adjacent frames; A spatiotemporal attention-based super-resolution reconstruction network is constructed based on fluid motion vector field guidance. It integrates low-resolution images of the current frame with high-resolution features of historical frames to fill in the missing spatial details of the temperature field caused by fluorescence lifetime limitation, and outputs high spatiotemporal resolution two-dimensional transient temperature field distribution data.

5. The dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation according to claim 1, characterized in that, Hardware-in-the-loop real-time closed-loop calibration receives dynamic calibration corrections and performs real-time compensation on the original pressure output, including: The real-time compensation process is deconstructed into multiple microservice tasks, and the execution time and cache hit rate of each microservice task are monitored in real time. An edge computing resource scheduling model is constructed based on a deep deterministic strategy gradient, which dynamically allocates heterogeneous computing resources according to the frequency characteristics of fluid pressure fluctuations and the urgency of microservice tasks.

6. The dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation according to claim 2, characterized in that, Constructing a deep reinforcement learning interactive environment includes: Multi-source heterogeneous sampling rate data are constructed into graph structure data according to spatial topological relationships, where nodes represent sampling points at different spatial locations and edges represent fluid heat conduction relationships between sampling points; A graph convolutional neural network is used to extract spatial features from graph structure data. The extracted spatial features are then concatenated and fused with the residual sequence in the time dimension to form a high-dimensional state space that integrates spatiotemporal correlation features. This space is then input into a proximal policy optimization method.

7. The dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation according to claim 3, characterized in that, The solution is obtained by backpropagation through minimizing the weighted sum of data-driven loss and physical constraint loss, including: A meta-learning mechanism is introduced to extract the prior distribution parameters of the network weights in the physical information neural network during the historical multi-condition training phase. In the current new working condition solution stage, the prior distribution parameters are used as constraints for the initialization of the physical information neural network, and the network weights are fine-tuned using a small amount of aligned data from the current working condition.

8. The dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation according to claim 4, characterized in that, Outputs high spatiotemporal resolution two-dimensional transient temperature field distribution data, including: A phase transition boundary sensing head is embedded in the spatiotemporal attention super-resolution reconstruction network. An unsupervised clustering method is used to perform pixel-level clustering segmentation on the reconstructed temperature field feature map to identify the phase transition boundary region of gas-liquid two-phase fluid. The segmentation mask of the phase transition boundary region is superimposed as an additional attention weight into the decoder of the spatiotemporal attention super-resolution reconstruction network.

9. A dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation according to claim 7, characterized in that, Using prior distribution parameters as constraints for initializing the physical information neural network includes: The parameter correction of the thermo-structure coupled digital twin model is decoupled into two sub-tasks: fluid flow field parameter correction and sensor structure thermal response parameter correction. Independent meta-learning agents are deployed for the two sub-tasks respectively, and a multi-agent collaborative framework is constructed. While sharing the underlying prior distribution parameters, each agent exchanges its gradient update direction by maximizing mutual information, and collaboratively optimizes the parameter correction accuracy of the physical information neural network at the multi-physics coupling interface.

10. A dynamic calibration method for a fluid pressure sensor based on real-time temperature compensation according to claim 9, characterized in that, The parameter correction accuracy of the collaboratively optimized physical information neural network at the multi-physics coupling interface includes: A federated learning mechanism is introduced among multiple multi-agent collaborative frameworks deployed at different fluid pipeline nodes; After each node completes the parameter correction of the physical information neural network locally, the multi-agent collaborative framework only uploads the encrypted network weight update and the physical constraint loss descent gradient to the central aggregation server. The central aggregation server uses an adaptive federated averaging strategy to aggregate the received updates and gradients, and then distributes the global model parameters.

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