A cylinder action system modeling method based on physical information neural network

Abstract

This invention provides a method for modeling a cylinder motion system based on a physical information neural network, comprising: acquiring time-series data of the cylinder motion system, including time-series control quantities and system state quantities; constructing a physical information neural network model with a dynamic feature input layer and a physical parameter input layer, receiving the time-series control quantities and physical parameter vectors respectively; performing a nonlinear transformation on the physical parameter vectors through a physical parameter encoding network to obtain encoded physical feature vectors; fusing the time-series control quantities and physical feature vectors to form a joint input vector; inputting the joint input vector into the backbone neural network, synchronously predicting the system state quantities through multi-layer nonlinear transformations; constructing a composite loss function including a data loss term and a physical loss term; training the model using time-series data, updating the model parameters by minimizing the composite loss function until the model converges, thereby achieving high-precision modeling using only single motion data.

Description

Technical Field

[0001] This invention relates to the field of cylinder motion system modeling and control technology, and more particularly to a cylinder motion system modeling method based on physical information neural network. Background Technology

[0002] Pneumatic actuators are widely used in industrial automation and robotics due to their advantages such as high power density, cleanliness, and low cost. Their working principle is based on the energy conversion of compressed gas, achieving mechanical motion through components such as cylinders or pneumatic motors. However, traditional modeling methods typically use simplified models based on physical equations, which struggle to accurately describe the nonlinear dynamic characteristics of the system, such as the effects of friction, gas compressibility, and leakage. This modeling bias can easily lead to problems such as response lag, steady-state error, and energy loss in the control system, limiting further improvements in pneumatic system performance. In recent years, data-driven neural network methods have been introduced to compensate for the shortcomings of traditional models, significantly improving trajectory tracking accuracy. However, their performance is highly dependent on training data within a specific operating range. If data is scarce or the operating conditions exceed the training range, the neural network is prone to overfitting, leading to a decrease in control reliability.

[0003] To address the aforementioned issues, Physical Information Neural Networks (PINNs), as a method integrating physical priors and data-driven approaches, have shown potential advantages. Existing research largely focuses on modeling pneumatic soft actuators, which have gained attention in specific fields (such as medical robots) due to their compliant characteristics. However, traditional pneumatic systems (such as cylinder-driven systems) are more widely used in industry, and their dynamic characteristics differ significantly from those of soft actuators. Currently, research on PINN modeling for traditional pneumatic systems is relatively lacking, especially in digital pneumatic systems, where effectively combining physical laws with data-driven methods remains a technological gap. While pure data-driven methods can improve accuracy locally, their generalization ability is insufficient; and traditional physical models struggle to cover complex nonlinear factors. Therefore, a modeling method that balances physical interpretability and data adaptability is urgently needed to improve the control performance of pneumatic systems under varying operating conditions. Summary of the Invention

[0004] To address the aforementioned technical problems of existing cylinder system models, such as their inability to balance accuracy and model adaptability under multiple operating conditions, and the weak generalization ability and strong data dependency of purely data-driven methods, this invention provides a cylinder motion system modeling method based on Physical Information Neural Networks (PINN). This invention applies Physical Information Neural Networks (PINN) to a digitally controlled cylinder motion system with strong nonlinearity and discrete control, achieving a balance between high-precision modeling and strong generalization ability.

[0005] The technical means employed in this invention are as follows: A method for modeling a cylinder motion system based on a physical information neural network includes: S1. Obtain the timing data of the cylinder action system, including timing control quantities and system state quantities. The timing control quantities include the time sequence and binary control signals of multiple high-speed switching valves. The system state quantities include cylinder displacement, cylinder rodless chamber pressure and cylinder rod chamber pressure. S2. Construct a physical information neural network model. The model has a dynamic feature input layer and a physical parameter input layer. The dynamic feature input layer receives the timing control quantity, and the physical parameter input layer receives a physical parameter vector, including sound velocity conductance, critical pressure ratio, air supply pressure, effective area of ​​the rod chamber of the cylinder, effective area of ​​the rodless chamber of the cylinder, load mass, and cylinder stroke. S3. The physical parameter vector is nonlinearly transformed through a physical parameter encoding network to obtain the encoded physical feature vector; S4. The timing control quantity received by the dynamic feature input layer and the encoded physical feature vector are fused to form a joint input vector; S5. Input the joint input vector into the backbone neural network and predict the system state variables synchronously through multi-layer nonlinear transformation. The backbone neural network is equipped with multiple independent regression output heads, which output the predicted values ​​of cylinder displacement, rodless chamber pressure and rod chamber pressure respectively. S6. Construct a composite loss function, which includes a data loss term and a physical loss term. The data loss term is calculated based on the difference between the predicted system state variables and the actual values. The physical loss term is calculated based on the residual obtained by calculating the predicted system state variables from the aerodynamic system dynamic equations. The dynamic equations include the piston dynamic equation, the rodless chamber pressure dynamic equation, and the rod chamber pressure dynamic equation. S7. The physical information neural network model is trained using the time series data. The parameters of the physical information neural network model are updated by minimizing the composite loss function until the model converges, thus achieving high-precision modeling using only a single motion data.

[0006] Further, step S1 includes: S11. Install displacement sensors and two-chamber pressure sensors at the corresponding measurement points on the cylinder body, and connect the signals of each sensor to the data acquisition system. S12. Introduce the drive signal of the high-speed switching valve into the same data acquisition system so that the valve opening / closing status is recorded synchronously with the sensor signal; S13. Set the sampling frequency and sampling duration. The sampling frequency is sufficient to capture the dynamic characteristics of the cylinder, and the sampling duration at least covers the cylinder's single complete extension motion and subsequent steady-state phase. S14. Perform low-pass filtering on the original time series to remove high-frequency noise; S15. Perform outlier detection and correction on the filtered displacement signal. The outliers are determined by the differential rate of change between adjacent time points and are filled in by interpolation. S16. Correct the zero-point drift of the pressure signal. The correction amount is determined based on the average value of the static interval before the start of the stroke. S17. Align the time series, binary control signal, corrected displacement and two-chamber pressure data according to the timestamp to form complete time series data corresponding to a single motion, which will be used as the unique sample for subsequent model training.

[0007] Further, step S2 includes: S21. Configure a dynamic feature input layer and a physical parameter input layer in parallel at the input end of the physical information neural network model. The two layers are independent of each other and their dimensions can be expanded as needed. S22. The timing control quantities obtained in step S1 are aligned according to time steps and then sent into the dynamic feature input layer to form a dynamic feature tensor. S23. The physical parameter vector is fed into the physical parameter input layer, and the physical parameter vector is copied and expanded in the temporal length direction to obtain a physical parameter tensor consistent with the time step of the dynamic feature tensor.

[0008] Further, step S3 includes: S31. The physical parameter vector output by the physical parameter input layer is fed into the physical parameter encoding network. The physical parameter encoding network consists of at least one layer of sequentially connected structure. Each layer first performs a linear transformation and then applies a point-by-point nonlinear function to the transformation result. S32. The linear transformation is accomplished through a weight matrix and a bias vector. The number of rows and columns of the weight matrix and the length of the bias vector are determined by the network configuration and are iteratively updated during training. S33. The pointwise nonlinear function acts on all elements after the linear transformation one by one. The function type is selected during the coding network construction stage and remains unchanged within a single training cycle. S34. Set a normalization operation and a random deactivation operation between two adjacent layers. The normalization operation standardizes the mean and variance of the features, and the random deactivation operation sets some features to zero according to a preset probability. S35. The dimension of the physical feature vector output by the last layer is determined by the number of rows in the weight matrix of this layer, and is independent of the dimension of the original physical parameter vector.

[0009] Further, step S4 includes: S41. Obtain the temporal control quantity feature tensor output by the dynamic feature input layer, and at the same time obtain the encoded physical feature vector output by step S3. S42. Copy and expand the encoded physical feature vector in the time dimension so that it is consistent with the time step of the dynamic feature tensor, forming a physical feature tensor that matches the shape of the dynamic feature tensor. S43. Concatenate the dynamic feature tensor and the physical feature tensor along the feature dimension to obtain the joint feature tensor; S44. The joint feature tensor is used as a joint input vector and fed into the subsequent backbone neural network to complete the fusion of dynamic information and physical information.

[0010] Further, step S5 includes: S51. The joint input vector obtained in step S4 is fed into the backbone neural network. The backbone neural network is composed of any number of hidden layers connected in series. Each layer performs a linear transformation on the input features and then applies a point-by-point nonlinear function. The width and depth of the hidden layers are freely set during the model building stage. S52. Each hidden layer sequentially performs a progressive nonlinear mapping on the joint input vector, outputting a new feature representation. The coefficients of the nonlinear mapping are automatically optimized through training. The mapping method remains consistent within a single layer and allows for differences between layers. S53. Insert normalization, random deactivation, or residual connection operations between any adjacent hidden layers to enhance the stability and generalization ability of feature propagation. The operation type and order are determined during the model building stage. S54. The ends of the backbone neural network are connected in parallel to multiple independent regression output heads. Each regression output head performs a linear transformation on the final hidden layer features to generate predicted values ​​for cylinder displacement, rodless chamber pressure and rod chamber pressure, respectively. S55. Each regression output head shares the joint features extracted by the backbone neural network, and their respective weight parameters are updated independently, realizing synchronous prediction of multiple state variables in the same forward propagation process.

[0011] Further, step S6 includes: S61. For the predicted values ​​of cylinder displacement, rodless chamber pressure and rod chamber pressure output by the backbone neural network, calculate the difference between them and the corresponding real observed values ​​to form a data loss term. S62. Substitute the predicted values ​​and their first and second derivatives with respect to time into the piston dynamics equation, the rodless chamber pressure dynamics equation, and the rod chamber pressure dynamics equation. Obtain the residuals of each equation through automatic differentiation to form the physical loss term. S63. Combine the data loss term and the physical loss term by weighted summation. The weight coefficients are set before training and remain fixed or updated according to the scheduling strategy during training to form a composite loss function. S64. The composite loss function serves as the optimization objective, driving the synchronous update of parameters in the backbone neural network, the physical parameter encoding network, and all regression output heads.

[0012] Further, step S7 includes: S71. Divide the single cylinder extension motion timing data obtained in step S1 into batches, input them into the physical information neural network batch by batch, perform forward propagation, and obtain the predicted values ​​of the system state variables. S72. Based on the composite loss function constructed in step S6, calculate the loss value of the current batch and obtain the gradient of all the network parameters to be trained by automatic differentiation. S73. Using an optimization algorithm, update the network parameters once based on the gradient. The learning rate and momentum coefficient are set before training begins and adjusted during training according to a preset scheduling strategy. S74. Repeat S71 to S73 until the composite loss function decreases below the preset threshold or reaches the maximum number of iterations in several consecutive iterations. Then, determine that the model has converged and complete the high-precision modeling using only a single motion data.

[0013] Compared with the prior art, the present invention has the following advantages: 1. This invention significantly improves the prediction accuracy and generalization performance of the model. Validated on multiple experimental platforms, PINN has R²>0.99 in displacement and pressure prediction, which is better than the pure data-driven model, and has high accuracy and strong generalization ability.

[0014] 2. This invention achieves efficient and low-cost modeling, requiring only the timing data of a single cylinder extension movement to complete the training, significantly reducing data acquisition costs and ensuring data efficiency.

[0015] 3. This invention eliminates the dependence on continuous signals in traditional modeling and directly uses binary switching signals as input, making it suitable for digital cylinder action circuits controlled by high-speed switching valves.

[0016] 4. This invention enhances the predictive reliability of the model in sparse data regions by embedding physical equations. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of the PINN modeling framework for the cylinder action system of the present invention.

[0019] Figure 2 This is a scatter plot comparing the predicted and actual displacement X values ​​over time, as provided in an embodiment of the present invention.

[0020] Figure 3 A scatter plot comparing the predicted and actual values ​​of the rod chamber pressure Pb over time, as provided in an embodiment of the present invention.

[0021] Figure 4 This is a scatter plot comparing the predicted and actual values ​​of the rodless chamber pressure Pa over time, as provided in an embodiment of the present invention.

[0022] Figure 5 The loss function curve of displacement X provided in the embodiment of the present invention.

[0023] Figure 6 The loss function curve of rod cavity pressure Pb provided for an embodiment of the present invention.

[0024] Figure 7 The loss function curve of the rodless cavity pressure Pa provided in the embodiment of the present invention. Detailed Implementation

[0025] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0026] It should be noted that the terms "comprising" and "having" and any variations thereof in the specification, claims and accompanying drawings of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such processes, methods, products or devices.

[0027] like Figure 1 As shown, this invention provides a method for modeling a cylinder motion system based on a physical information neural network, comprising: S1. Obtain the timing data of the cylinder action system, including timing control quantities and system state quantities. The timing control quantities include the time sequence and binary control signals of multiple high-speed switching valves. The system state quantities include cylinder displacement, cylinder rodless chamber pressure and cylinder rod chamber pressure. S2. Construct a physical information neural network model. The model has a dynamic feature input layer and a physical parameter input layer. The dynamic feature input layer receives the timing control quantity, and the physical parameter input layer receives a physical parameter vector, including sound velocity conductance, critical pressure ratio, air supply pressure, effective area of ​​the rod chamber of the cylinder, effective area of ​​the rodless chamber of the cylinder, load mass, and cylinder stroke. S3. The physical parameter vector is nonlinearly transformed through a physical parameter encoding network to obtain the encoded physical feature vector; S4. The timing control quantity received by the dynamic feature input layer and the encoded physical feature vector are fused to form a joint input vector; S5. Input the joint input vector into the backbone neural network and predict the system state variables synchronously through multi-layer nonlinear transformation. The backbone neural network is equipped with multiple independent regression output heads, which output the predicted values ​​of cylinder displacement, rodless chamber pressure and rod chamber pressure respectively. S6. Construct a composite loss function, which includes a data loss term and a physical loss term. The data loss term is calculated based on the difference between the predicted system state variables and the actual values. The physical loss term is calculated based on the residual obtained by calculating the predicted system state variables from the aerodynamic system dynamic equations. The dynamic equations include the piston dynamic equation, the rodless chamber pressure dynamic equation, and the rod chamber pressure dynamic equation. S7. The physical information neural network model is trained using the time series data. The parameters of the physical information neural network model are updated by minimizing the composite loss function until the model converges, thus achieving high-precision modeling using only a single motion data.

[0028] In a specific implementation, as a preferred embodiment of the present invention, step S1 includes: S11. Install displacement sensors and two-chamber pressure sensors at the corresponding measurement points on the cylinder body, and connect the signals of each sensor to the data acquisition system. S12. Introduce the drive signal of the high-speed switching valve into the same data acquisition system so that the valve opening / closing status is recorded synchronously with the sensor signal; S13. Set the sampling frequency and sampling duration. The sampling frequency is sufficient to capture the dynamic characteristics of the cylinder, and the sampling duration at least covers the cylinder's single complete extension motion and subsequent steady-state phase. S14. Perform low-pass filtering on the original time series to remove high-frequency noise; S15. Perform outlier detection and correction on the filtered displacement signal. The outliers are determined by the differential rate of change between adjacent time points and are filled in by interpolation. S16. Correct the zero-point drift of the pressure signal. The correction amount is determined based on the average value of the static interval before the start of the stroke. S17, Time Seriest binary control signals The corrected displacement and pressure data of the two chambers are aligned with timestamps to form complete time-series data corresponding to a single motion, which is used as the sole sample for subsequent model training.

[0029] In a specific implementation, as a preferred embodiment of the present invention, step S2 includes: S21. Configure a dynamic feature input layer and a physical parameter input layer in parallel at the input end of the physical information neural network model. The two layers are independent of each other and their dimensions can be expanded as needed. S22. The timing control quantities obtained in step S1 are aligned according to time steps and then sent into the dynamic feature input layer to form a dynamic feature tensor. S23. The physical parameter vector is fed into the physical parameter input layer, and the physical parameter vector is copied and expanded in the temporal length direction to obtain a physical parameter tensor consistent with the time step of the dynamic feature tensor.

[0030] In a specific implementation, as a preferred embodiment of the present invention, step S3 includes: S31. The physical parameter vector output from the physical parameter input layer is fed into the physical parameter encoding network. The physical parameter encoding network consists of at least one sequentially connected layer. Each layer first performs a linear transformation, and then applies a point-by-point nonlinear function to the transformation result. In this embodiment, the physical parameter encoding network is a 2-layer fully connected network that outputs a 7-dimensional encoded vector (sound velocity conductance C, critical pressure ratio b, air supply pressure Ps, effective area Aa of the rod cavity, effective area Ab of the rodless cavity, load mass m, cylinder stroke l). S32. The linear transformation is accomplished through a weight matrix and a bias vector. The number of rows and columns of the weight matrix and the length of the bias vector are determined by the network configuration and are iteratively updated during training. S33. The pointwise nonlinear function acts on all elements after the linear transformation one by one. The function type is selected during the coding network construction stage and remains unchanged within a single training cycle. S34. Set a normalization operation and a random deactivation operation between two adjacent layers. The normalization operation standardizes the mean and variance of the features, and the random deactivation operation sets some features to zero according to a preset probability. S35. The dimension of the physical feature vector output by the last layer is determined by the number of rows in the weight matrix of this layer, and is independent of the dimension of the original physical parameter vector.

[0031] In a specific implementation, as a preferred embodiment of the present invention, step S4 includes: S41. Obtain the temporal control quantity feature tensor output by the dynamic feature input layer, and at the same time obtain the encoded physical feature vector output by step S3. S42. Copy and expand the encoded physical feature vector in the time dimension so that it is consistent with the time step of the dynamic feature tensor, forming a physical feature tensor that matches the shape of the dynamic feature tensor. S43. Concatenate the dynamic feature tensor and the physical feature tensor along the feature dimension to obtain the joint feature tensor; S44. The joint feature tensor is used as a joint input vector and fed into the subsequent backbone neural network to complete the fusion of dynamic information and physical information.

[0032] In a specific implementation, as a preferred embodiment of the present invention, step S5 includes: S51. The joint input vector obtained in step S4 is fed into the backbone neural network. The backbone neural network is composed of any number of hidden layers connected in series. Each layer performs a linear transformation on the input features and then applies a point-by-point nonlinear function. The width and depth of the hidden layers are freely set during the model construction stage. In this embodiment, it includes multiple fully connected layers (6 fully connected layers with 128, 128, 64, 64, 32, and 16 nodes), activation function layers (activation function is ReLU), and random deactivation layers (p=0.3).

[0033] S52. Each hidden layer sequentially performs a progressive nonlinear mapping on the joint input vector, outputting a new feature representation. The coefficients of the nonlinear mapping are automatically optimized through training. The mapping method remains consistent within a single layer and allows for differences between layers. S53. Insert normalization, random deactivation, or residual connection operations between any adjacent hidden layers to enhance the stability and generalization ability of feature propagation. The operation type and order are determined during the model building stage. S54. The ends of the backbone neural network are connected in parallel to multiple independent regression output heads. Each regression output head performs a linear transformation on the final hidden layer features to generate cylinder displacement. x rodless chamber pressure Pa and rod chamber pressure Pb The predicted value; S55. Each regression output head shares the joint features extracted by the backbone neural network, and their respective weight parameters are updated independently, realizing synchronous prediction of multiple state variables in the same forward propagation process.

[0034] In a specific implementation, as a preferred embodiment of the present invention, step S6 includes: S61. For the predicted values ​​of cylinder displacement, rodless chamber pressure and rod chamber pressure output by the backbone neural network, calculate the difference between them and the corresponding real observed values ​​to form a data loss term. S62. Substitute the predicted values ​​and their first and second derivatives with respect to time into the piston dynamics equation, the rodless chamber pressure dynamics equation, and the rod chamber pressure dynamics equation. Obtain the residuals of each equation through automatic differentiation to form the physical loss term. In this embodiment, the physical loss is constructed based on the following aerodynamic system dynamics equations:

[0035]

[0036]

[0037] The residual calculation formula for the piston dynamics equation is as follows:

[0038] The pressure dynamics equation for the rodless cavity (chamber A) and the formula for calculating its residuals are as follows:

[0039] The residual calculation formula for the pressure dynamics equation of the rod chamber (chamber B) is as follows:

[0040] S63. The data loss term and the physical loss term are combined using a weighted summation method. The weight coefficients are set before training and remain fixed or updated according to the scheduling strategy during training to form a composite loss function. In this embodiment, the formula for the composite loss function is as follows:

[0041] in, This is a hyperparameter used to adjust the weights of physical constraints.

[0042] S64. The composite loss function serves as the optimization objective, driving the synchronous update of parameters in the backbone neural network, the physical parameter encoding network, and all regression output heads.

[0043] In a specific implementation, as a preferred embodiment of the present invention, step S7 includes: S71. Divide the single cylinder extension motion timing data obtained in step S1 into batches, input them into the physical information neural network batch by batch, perform forward propagation, and obtain the predicted values ​​of the system state variables. S72. Based on the composite loss function constructed in step S6, calculate the loss value of the current batch, and obtain the gradient of all the network parameters to be trained by automatic differentiation; in this embodiment, Smooth L1 Loss is used as the data loss. S73. Using an optimization algorithm, the network parameters are updated once based on the gradient. The learning rate and momentum coefficient are set before training begins and adjusted during training according to a preset scheduling strategy. In this embodiment, the Reduce LRonPlateau scheduling strategy is used to dynamically adjust the learning rate.

[0044] S74. Repeat S71 to S73 until the composite loss function decreases below the preset threshold or reaches the maximum number of iterations in several consecutive iterations. Then, determine that the model has converged and complete the high-precision modeling using only a single motion data.

[0045] Figures 2-7 The prediction results and loss curves of this method after training with only single cylinder extension motion data in the same embodiment are given. Figure 2 The curves showing the predicted value of piston displacement X over time are compared with the actual value using scatter plots. The two values ​​are closely distributed along the diagonal, indicating that the displacement prediction error is extremely small. Figure 3 and Figure 4 The predicted-actual scatter plots corresponding to the rod chamber pressure Pb and the rodless chamber pressure Pa, respectively, also show a high degree of linear correlation, verifying the model's ability to simultaneously capture the dynamics of the two chamber pressures. Figures 5-7 The composite loss reduction curves of displacement X, rod cavity pressure Pb, and rodless cavity pressure Pa during the training process are given in sequence. The loss decreases rapidly in the initial stage and then tends to stabilize. No obvious overfitting is observed, which proves that the physical constraints effectively improve sample efficiency and generalization performance.

[0046] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for modeling a cylinder motion system based on a physical information neural network, characterized in that, include: S1. Obtain the timing data of the cylinder action system, including timing control quantities and system state quantities. The timing control quantities include the time sequence and binary control signals of multiple high-speed switching valves. The system state quantities include cylinder displacement, cylinder rodless chamber pressure and cylinder rod chamber pressure. S2. Construct a physical information neural network model. The model has a dynamic feature input layer and a physical parameter input layer. The dynamic feature input layer receives the timing control quantity, and the physical parameter input layer receives a physical parameter vector, including sound velocity conductance, critical pressure ratio, air supply pressure, effective area of ​​the rod chamber of the cylinder, effective area of ​​the rodless chamber of the cylinder, load mass, and cylinder stroke. S3. The physical parameter vector is nonlinearly transformed through a physical parameter encoding network to obtain the encoded physical feature vector; S4. The timing control quantity received by the dynamic feature input layer and the encoded physical feature vector are fused to form a joint input vector; S5. Input the joint input vector into the backbone neural network and predict the system state variables synchronously through multi-layer nonlinear transformation. The backbone neural network is equipped with multiple independent regression output heads, which output the predicted values ​​of cylinder displacement, rodless chamber pressure and rod chamber pressure respectively. S6. Construct a composite loss function, which includes a data loss term and a physical loss term. The data loss term is calculated based on the difference between the predicted system state variables and the actual values. The physical loss term is calculated based on the residual obtained by calculating the predicted system state variables from the aerodynamic system dynamic equations. The dynamic equations include the piston dynamic equation, the rodless chamber pressure dynamic equation, and the rod chamber pressure dynamic equation. S7. The physical information neural network model is trained using the time series data. The parameters of the physical information neural network model are updated by minimizing the composite loss function until the model converges, thus achieving high-precision modeling using only a single motion data.

2. The method for modeling a cylinder motion system based on a physical information neural network according to claim 1, characterized in that, Step S1 includes: S11. Install displacement sensors and two-chamber pressure sensors at the corresponding measurement points on the cylinder body, and connect the signals of each sensor to the data acquisition system. S12. Introduce the drive signal of the high-speed switching valve into the same data acquisition system so that the valve opening / closing status is recorded synchronously with the sensor signal; S13. Set the sampling frequency and sampling duration. The sampling frequency is sufficient to capture the dynamic characteristics of the cylinder, and the sampling duration at least covers the cylinder's single complete extension motion and subsequent steady-state phase. S14. Perform low-pass filtering on the original time series to remove high-frequency noise; S15. Perform outlier detection and correction on the filtered displacement signal. The outliers are determined by the differential rate of change between adjacent time points and are filled in by interpolation. S16. Correct the zero-point drift of the pressure signal. The correction amount is determined based on the average value of the static interval before the start of the stroke. S17. Align the time series, binary control signal, corrected displacement and two-chamber pressure data according to the timestamp to form complete time series data corresponding to a single motion, which will be used as the unique sample for subsequent model training.

3. The method for modeling a cylinder motion system based on a physical information neural network according to claim 1, characterized in that, Step S2 includes: S21. Configure a dynamic feature input layer and a physical parameter input layer in parallel at the input end of the physical information neural network model. The two layers are independent of each other and their dimensions can be expanded as needed. S22. The timing control quantities obtained in step S1 are aligned according to time steps and then sent into the dynamic feature input layer to form a dynamic feature tensor. S23. The physical parameter vector is fed into the physical parameter input layer, and the physical parameter vector is copied and expanded in the temporal length direction to obtain a physical parameter tensor consistent with the time step of the dynamic feature tensor.

4. The method for modeling a cylinder motion system based on a physical information neural network according to claim 1, characterized in that, Step S3 includes: S31. The physical parameter vector output by the physical parameter input layer is fed into the physical parameter encoding network. The physical parameter encoding network consists of at least one layer of sequentially connected structure. Each layer first performs a linear transformation and then applies a point-by-point nonlinear function to the transformation result. S32. The linear transformation is accomplished through a weight matrix and a bias vector. The number of rows and columns of the weight matrix and the length of the bias vector are determined by the network configuration and are iteratively updated during training. S33. The pointwise nonlinear function acts on all elements after the linear transformation one by one. The function type is selected during the coding network construction stage and remains unchanged within a single training cycle. S34. Set a normalization operation and a random deactivation operation between two adjacent layers. The normalization operation standardizes the mean and variance of the features, and the random deactivation operation sets some features to zero according to a preset probability. S35. The dimension of the physical feature vector output by the last layer is determined by the number of rows in the weight matrix of this layer, and is independent of the dimension of the original physical parameter vector.

5. The method for modeling a cylinder motion system based on a physical information neural network according to claim 1, characterized in that, Step S4 includes: S41. Obtain the temporal control quantity feature tensor output by the dynamic feature input layer, and at the same time obtain the encoded physical feature vector output by step S3. S42. Copy and expand the encoded physical feature vector in the time dimension so that it is consistent with the time step of the dynamic feature tensor, forming a physical feature tensor that matches the shape of the dynamic feature tensor. S43. Concatenate the dynamic feature tensor and the physical feature tensor along the feature dimension to obtain the joint feature tensor; S44. The joint feature tensor is used as a joint input vector and fed into the subsequent backbone neural network to complete the fusion of dynamic information and physical information.

6. The method for modeling a cylinder motion system based on a physical information neural network according to claim 1, characterized in that, Step S5 includes: S51. The joint input vector obtained in step S4 is fed into the backbone neural network. The backbone neural network is composed of any number of hidden layers connected in series. Each layer performs a linear transformation on the input features and then applies a point-by-point nonlinear function. The width and depth of the hidden layers are freely set during the model building stage. S52. Each hidden layer sequentially performs a progressive nonlinear mapping on the joint input vector, outputting a new feature representation. The coefficients of the nonlinear mapping are automatically optimized through training. The mapping method remains consistent within a single layer and allows for differences between layers. S53. Insert normalization, random deactivation, or residual connection operations between any adjacent hidden layers to enhance the stability and generalization ability of feature propagation. The operation type and order are determined during the model building stage. S54. The ends of the backbone neural network are connected in parallel to multiple independent regression output heads. Each regression output head performs a linear transformation on the final hidden layer features to generate predicted values ​​for cylinder displacement, rodless chamber pressure and rod chamber pressure, respectively. S55. Each regression output head shares the joint features extracted by the backbone neural network, and their respective weight parameters are updated independently, realizing synchronous prediction of multiple state variables in the same forward propagation process.

7. The method for modeling a cylinder motion system based on a physical information neural network according to claim 1, characterized in that, Step S6 includes: S61. For the predicted values ​​of cylinder displacement, rodless chamber pressure and rod chamber pressure output by the backbone neural network, calculate the difference between them and the corresponding real observed values ​​to form a data loss term. S62. Substitute the predicted values ​​and their first and second derivatives with respect to time into the piston dynamics equation, the rodless chamber pressure dynamics equation, and the rod chamber pressure dynamics equation. Obtain the residuals of each equation through automatic differentiation to form the physical loss term. S63. Combine the data loss term and the physical loss term by weighted summation. The weight coefficients are set before training and remain fixed or updated according to the scheduling strategy during training to form a composite loss function. S64. The composite loss function serves as the optimization objective, driving the synchronous update of parameters in the backbone neural network, the physical parameter encoding network, and all regression output heads.

8. The method for modeling a cylinder motion system based on a physical information neural network according to claim 7, characterized in that, Step S7 includes: S71. Divide the single cylinder extension motion timing data obtained in step S1 into batches, input them into the physical information neural network batch by batch, perform forward propagation, and obtain the predicted values ​​of the system state variables. S72. Based on the composite loss function constructed in step S6, calculate the loss value of the current batch and obtain the gradient of all the network parameters to be trained by automatic differentiation. S73. Using an optimization algorithm, update the network parameters once based on the gradient. The learning rate and momentum coefficient are set before training begins and adjusted during training according to a preset scheduling strategy. S74. Repeat S71 to S73 until the composite loss function decreases below the preset threshold or reaches the maximum number of iterations in several consecutive iterations. Then, determine that the model has converged and complete the high-precision modeling using only a single motion data.

Images