A hydraulic system lag analysis and leakage compensation method and system based on a multi-scale deep residual PINN

Abstract

The application discloses a hydraulic system lag and leakage analysis system based on a multi-scale deep residual PINN and a corresponding compensation method in real-time control of the hydraulic system. The method realizes deep fusion of physical constraints and data driving by constructing a deep neural network containing a residual block structure. The system combines multi-scale feature engineering and an adaptive smooth transition mechanism to eliminate the prediction mutation problem of traditional segmented models in different load intervals. Through multi-scale feature engineering, the original load data is converted into a 5-dimensional feature vector containing original values, logarithmic values, square root values, hyperbolic tangent values and region indicators, which can effectively capture the nonlinear characteristics of different load intervals. Through a dynamic weight scheduling strategy, the weights of physical constraints and smooth constraints are gradually increased during the training process, thereby significantly improving the prediction accuracy and stability of the model. The application realizes high-precision leakage prediction of the hydraulic loading system, and provides reliable technical support and new ideas for real-time control and predictive maintenance of the hydraulic system.

Description

Technical Field

[0001] This invention relates to the field of hydraulic system control and fault diagnosis technology, and in particular to a method and system for hydraulic system hysteresis analysis and leakage compensation based on multi-scale deep residual physical information neural network (MSDR-PINN, abbreviated as multi-scale deep residual PINN). It can be applied to real-time monitoring and intelligent control of hydraulic systems in fields such as engineering machinery, aerospace, and deep-sea exploration. Background Technology

[0002] Hydraulic systems, as a core power transmission technology in modern industry, play an irreplaceable role in aerospace, engineering machinery, precision manufacturing, and deep-sea exploration due to their advantages of high power density, fast response speed, and high control precision. With the deepening exploration of extreme environments such as the deep sea and deep space, and the rapid development of Industry 4.0 and intelligent manufacturing, hydraulic systems face three major technological upgrade demands: extreme operating conditions (deep-sea high pressure, space vacuum, ultra-high temperature / low temperature), intelligent control (adaptive adjustment, predictive maintenance, multi-system collaboration), and energy efficiency and greening (energy consumption reduction of over 30%, leakage reduction of 50%). These demands place unprecedentedly high requirements on the stability, control precision, and reliability of hydraulic systems. Traditional design methods based on empirical formulas and linear assumptions are no longer sufficient, necessitating breakthroughs in intelligent modeling and control technologies that integrate multidisciplinary theories.

[0003] The following are the main technical challenges in the practical application of hydraulic systems:

[0004] First, modeling nonlinear characteristics is difficult. Hydraulic systems exhibit complex nonlinear characteristics, including nonlinear flow-pressure relationships, friction nonlinearity, and oil compressibility. Traditional linear models struggle to accurately describe system behavior, especially dynamic responses under different load conditions. Existing nonlinear modeling methods, such as polynomial fitting and lookup table methods, suffer from low accuracy and poor adaptability.

[0005] Secondly, there is an urgent need for leakage compensation. Hydraulic systems inevitably suffer from internal and external leakage. Internal leakage mainly occurs at the mating clearances of components such as pumps, valves, and cylinders; external leakage occurs at locations where seals fail. The leakage amount changes dynamically with conditions such as load, temperature, and pressure, making traditional fixed compensation methods unsuitable for complex operating conditions.

[0006] Third, the multi-physics coupling is complex. Hydraulic systems involve the coupling effects of multiple physical fields, including fluid mechanics, solid mechanics, and thermodynamics. The multi-field interactions of fluid, solid, and heat increase the complexity of system modeling, making it difficult for traditional methods to comprehensively consider various physical constraints.

[0007] Current technical solutions mainly include the following categories:

[0008] Traditional filtering methods, such as Kalman filtering, extended Kalman filtering, and particle filtering, are based on state-space models and use recursive estimation to handle noise and uncertainty. However, they typically assume linear or weakly nonlinear characteristics, making them difficult to handle the strong nonlinearity and complex coupling relationships of hydraulic systems. Purely data-driven methods, based on black-box models using machine learning algorithms such as neural networks, support vector machines, and random forests, do not require prior knowledge of the system and can fit arbitrarily complex nonlinear relationships. However, they lack physical constraints, are prone to producing physically unreasonable predictions, have poor generalization ability, and require large amounts of training data.

[0009] Simple physical models: analytical models based on idealized assumptions, such as linearized models and lumped parameter models. These models are simple in form and computationally efficient, but they cannot adapt to the complex changes in actual working conditions and have limited prediction accuracy.

[0010] Hybrid modeling methods combine physical models and data-driven approaches, such as gray-box models and physics-guided machine learning. These methods attempt to balance physical constraints and data fitting, but existing methods still have shortcomings in areas such as the embedding of physical constraints, multi-scale feature extraction, and dynamic weight adjustment. Physics-Informed Neural Networks (PINNs) are a novel modeling method that has emerged in recent years. By embedding physical equations into the loss function of the neural network, it achieves a combination of physical constraints and data-driven approaches. However, standard PINN methods have the following limitations when dealing with complex systems such as hydraulic systems, which have strong nonlinearity and multi-scale characteristics: the network structure is simple, making it difficult to capture complex nonlinear mappings; the weights of physical constraints are fixed, failing to adapt to dynamic changes during training; there is a lack of targeted feature engineering, hindering the effective extraction of multi-scale information; and insufficient smoothness constraints easily lead to predictive abrupt changes.

[0011] Therefore, there is an urgent need for a new technology that can comprehensively consider the advantages of physical constraints and data-driven approaches, while overcoming the limitations of existing methods, in order to achieve high-precision modeling, hysteresis characteristic analysis, and real-time leakage compensation of hydraulic systems. Summary of the Invention

[0012] To address the shortcomings of existing technologies, the present invention aims to provide a method and system for analyzing the hysteresis characteristics and compensating for leakage in hydraulic systems based on multi-scale deep residual PINN. By constructing a deep neural network containing residual block structures and combining multi-scale feature engineering and dynamic weight scheduling strategies, the invention achieves a deep fusion of physical constraints and data-driven approaches, significantly improving the modeling accuracy and leakage compensation effect of hydraulic systems.

[0013] The core innovation of this invention lies in proposing a novel "multi-scale deep physical fusion" modeling paradigm. Traditional Physical Information Neural Networks (PINNs) typically employ simple fully connected structures, making it difficult to capture the complex nonlinear characteristics of hydraulic systems. This invention overcomes the limitations of existing methods by introducing three innovative technologies: deep residual learning, multi-scale feature engineering, and dynamic physical constraints. This approach not only preserves the interpretability and generalization ability of the physical model but also fully leverages the advantages of deep learning in complex pattern recognition.

[0014] The technical concept of this invention is as follows: First, it is recognized that the hysteresis characteristics of hydraulic systems originate from the coupling effect of multiple physical mechanisms, including the compressibility of hydraulic fluid, elastic deformation of pipelines, and friction of seals. These mechanisms exhibit drastically different characteristics in different load ranges. Therefore, this invention innovatively proposes a multi-scale feature extraction strategy, enabling neural networks to adaptively learn system behavior under different operating conditions. Simultaneously, residual connections address the difficulty of training deep networks, and dynamic weight scheduling enables the gradual introduction of physical constraints.

[0015] To achieve the above objectives, the present invention adopts the following technical solution:

[0016] A method for hysteresis analysis and leakage compensation of hydraulic systems based on multi-scale deep residual PINN includes the following steps:

[0017] S1. Collect time-series data of load L and hydraulic cylinder oil volume V of the hydraulic system during loading and unloading processes;

[0018] S2. Prepare a multi-scale deep residual PINN network model. This model is a deep neural network containing an input layer, an initial feature extraction layer, 6 residual blocks, a final feature layer, and an output layer. Each residual block contains a main path and skip connections. The main path contains, in sequence, a first fully connected layer, a first normalization layer, a dropout layer, a second fully connected layer, and a second normalization layer. Skip connections perform dimension matching through projection fully connected layers when the input and output dimensions are different.

[0019] S3. Perform multi-scale feature engineering on the load L of S1, transform it according to different engineering requirements, and form a 5-dimensional feature vector. Use it together with the hydraulic cylinder oil volume V as the input of the model in S2.

[0020] S4. Physical Constraint Training: Define a composite loss function, including data fitting loss, physical constraint loss and smoothness loss. The weights of physical constraint loss and smoothness loss are dynamic weight functions. A dynamic weight scheduling strategy is adopted so that the dynamic weight functions of physical constraint and smoothness constraint increase with the training rounds.

[0021] S5. Hysteresis Characteristic Analysis: Based on the trained multi-scale deep residual PINN network model, the stiffness of the loading process and the stiffness of the unloading process are predicted respectively. The difference between loading and unloading stiffness is calculated, a hysteresis loop is constructed, the area enclosed by the hysteresis loop is calculated, and it is converted into hysteresis compensation volumetric flow rate for feedforward control of hydraulic pump servo valve, so that the servo valve can adjust the flow rate in real time.

[0022] S6. Leakage Prediction and Compensation: Based on a hybrid leakage prediction model that includes a physical model and a residual network, the leakage result is predicted.

[0023] In the above technical solution, further, the 5-dimensional feature vectors in S3 are: original load L, logarithmic load log(L+1), and square root load. Hyperbolic tangent transform tanh(L / 5000) and region indicator

[0024] Furthermore, the physical constraint loss in S4 is the sum of monotonicity constraint and prior constraint. The monotonicity constraint is used to ensure that the stiffness is always positive, which conforms to the basic physical laws of the hydraulic system. The prior constraint is a prior model obtained based on theoretical analysis and experimental data fitting. The smoothing constraint loss adopts a double smoothing constraint, which is the sum of the traditional smoothing loss represented by the second derivative and the enhanced smoothing loss represented by the rate of change of the derivative.

[0025] Furthermore, the dynamic weight scheduling strategy in S4 is as follows: dynamically adjust the weight physical constraint dynamic weight function and the smoothing constraint dynamic weight function according to the training round t. In the early stage, data fitting is the main focus, in the middle stage, physical constraints are gradually strengthened, and in the later stage, physical constraints reach their strongest.

[0026] Furthermore, in S5, the area enclosed by the hysteresis loop is calculated using the Shoelace formula, which represents the energy loss in a load-unload cycle. Based on this, after considering the piston area and pump speed, the hysteresis area is converted into the actual volumetric flow rate, and the flow rate is adjusted in real time by the servo valve to compensate for the volume loss caused by the hysteresis characteristics.

[0027] Furthermore, in the mixed leakage prediction model of S6, the physical model is:

[0028]

[0029] in Let a, b, and c be the damping function, and a, b, and c be the curve fitting parameters of the physical model.

[0030] Residual networks are used to capture complex nonlinear behaviors that physical models fail to describe;

[0031] The final predicted leakage amount is:

[0032] Q total (L)=Q physics (L;θ)+Q residual (L;φ);

[0033] Q physics (L; θ) represents the leakage predicted by the physical model, where θ is the set of physical model parameters; Q residual (L;φ) represents the leakage correction amount predicted by the residual network, and φ represents the set of residual network parameters.

[0034] Furthermore, the parameters in the physical model are obtained by training and fitting based on training data, wherein the training data is generated as follows:

[0035] Based on the loading and unloading stiffness differences obtained from the PINN network model with multi-scale depth residuals, and the hydraulic cylinder oil volume, the volume compensation requirement is obtained, and the average volume loss density is determined accordingly. Obtain the basic leakage amount:

[0036]

[0037] Among them, Q max k is the maximum leakage revolutions under the current load L. v p is the loss sensitivity coefficient. f The pressure influence factor is represented by tanh(), which denotes the hyperbolic tangent function.

[0038] Considering that the sealing characteristics of the hydraulic system vary across different load ranges, a zoned leakage factor is introduced, and the leakage is calculated as follows:

[0039] Q(L)=Q base (L)×F(L)

[0040] It generates training data and provides physically reasonable initial estimates for the physical model.

[0041] Furthermore, for different load ranges, the transition behavior is modeled using the sigmoid function, and the range correction of the leakage includes:

[0042] Preload transition:

[0043] Yield transition:

[0044] The specific partition leakage factor is:

[0045] F(L)=α static (1-f preload )+α dynamic (L)f preload (1-fyield )+α gxp (L)f yield

[0046] Among them, L preload For the load corresponding to the sealing preload, L yield For the load corresponding to the seal yield, α static As the static leakage factor, α dynamic (L) is the dynamic leakage factor function, α gxp This is the gap flow factor function.

[0047] Furthermore, the residual network includes a smooth transition mechanism to avoid abrupt changes.

[0048] Q residual (L; φ) represents the leakage correction amount predicted by the residual network:

[0049] Q residual (L;φ)=α adjust (L)·NN(f(L);φ)

[0050] NN(f(L); φ) is a neural network function whose input is the load f(L) after multi-scale feature engineering, α adjust (L) is the adjustment factor, where the smooth transition uses the sigmoid function g. transition (L) indicates:

[0051]

[0052] α adjust (L)=1.0×(1-g transition )+(0.35+0.05log(1+L / 1000))

[0053] ×g transition .

[0054] A hydraulic system hysteresis analysis and leakage compensation system based on multi-scale deep residual PINN, used to implement the method described above, comprising:

[0055] The neural network computing module includes a training unit and an inference unit. The training unit is used for offline training of the multi-scale deep residual PINN model, and the inference unit is used for online prediction.

[0056] Hysteresis analysis module: used to calculate the stiffness difference during loading and unloading processes and analyze hysteresis loop characteristics;

[0057] Leakage compensation module: used to predict leakage based on physical models and residual networks, and generate compensation control signals.

[0058] The beneficial effects of this invention are:

[0059] This invention proposes a method for analyzing the hysteresis characteristics and compensating for leakage in hydraulic systems based on multi-scale deep residual PINN. By deeply integrating physical constraints and data-driven techniques, it fully leverages the powerful nonlinear fitting capabilities of deep learning while strictly adhering to the physical laws of hydraulic systems, significantly improving modeling accuracy and generalization ability. Through multi-scale feature engineering to capture system characteristics under different operating conditions, and combined with dynamic physical constraint strategies, it achieves an optimized balance between data fitting and physical consistency. Compared with existing technologies, it has the following significant advancements:

[0060] 1) This paper proposes a deep residual network architecture customized for the physical characteristics of hydraulic systems, overcoming the limitations of traditional PINN in modeling complex nonlinear systems. High-precision modeling of hydraulic systems has always been a technical challenge in engineering. Traditional linearized models have limited accuracy, purely data-driven methods lack a physical basis, and the standard PINN network structure is too simplistic. This invention innovatively introduces six carefully designed residual blocks to form a deep network of 40+ layers, effectively solving the gradient vanishing problem through a residual connection mechanism. Furthermore, this invention designs hydraulic press loading and unloading experiments, and the results show that the equivalent stiffness prediction R... 2 Achieving 0.9968 (loading) and 0.9967 (unloading), compared to traditional methods (R... 2 The improvement of <0.95) is significant. This method of customizing network structures based on physical characteristics has important theoretical innovation and engineering value.

[0061] 2) For the first time, multi-scale feature engineering was systematically applied to hydraulic system modeling, enabling a single model to accurately describe the entire operating range. By converting the original load into a 5-dimensional feature vector containing linear, logarithmic, square root, hyperbolic tangent, and region indications, the network can adaptively learn different physical mechanisms such as static sealing leakage in the low-load zone, dynamic sealing effect in the medium-load zone, and gap flow in the high-load zone, completely solving the problem of limited applicability of traditional piecewise models.

[0062] 3) A hybrid leakage prediction architecture combining a physical model and a residual network was constructed, achieving a complementary advantage between physical mechanisms and data-driven approaches. The physical model captures fundamental leakage patterns, while the residual network learns the influence of complex factors such as temperature and wear. Experimental results show that the hybrid model's leakage prediction accuracy is [insert value here, but it's unclear what "R" means in this context]. 2 The R² value reached 0.9757, compared to the pure physics model (R²). 2 =0.7804) is a 25% improvement, and has stronger physical interpretability and generalization ability compared to the pure data-driven model.

[0063] 4) A smooth transition mechanism based on the sigmoid function is proposed, completely eliminating the prediction abruptness problem of traditional piecewise models. By designing preload transition functions and yield transition functions, continuous and smooth transitions between different working ranges are achieved. In the load transition region, the prediction jump of traditional methods reaches 15%, while the prediction change rate of this method remains continuous, significantly improving the generalization ability and robustness of the model, which is of great significance for hydraulic servo systems requiring precise control.

[0064] 5) The system achieves a complete technology chain from algorithm innovation to engineering application, demonstrating outstanding engineering practicality. It integrates high-precision sensors (pressure accuracy ±0.1% FS, displacement resolution 0.1 μm), real-time signal processing (SG filtering delay <1 ms), GPU-accelerated computing (single prediction <5 ms), and industrial communication interfaces (supporting Modbus, CAN, and EtherCAT), forming a plug-and-play solution. Predictive maintenance based on leak prediction can reduce unplanned downtime of hydraulic equipment by more than 60% and annual maintenance costs by 35%.

[0065] 6) This invention is significant in terms of theoretical innovation and technological breakthroughs. It is the first to deeply integrate deep residual learning, multi-scale feature engineering, dynamic physical constraints, and smooth transition mechanisms, providing a new paradigm for neural network modeling of physical information in complex nonlinear systems. This method is not only applicable to hydraulic systems but can also be extended to other electromechanical systems with hysteresis characteristics, such as pneumatic systems and servo systems, showing broad application prospects.

[0066] In summary, by deeply integrating physical knowledge and data-driven technology, this invention not only significantly improves the modeling accuracy and leakage compensation effect of hydraulic systems, but also provides a general methodology for solving complex nonlinear modeling problems in the engineering field, which has important theoretical value and practical application significance. Attached Figure Description

[0067] Figure 1 This is a model diagram of the experimental apparatus used in this invention;

[0068] Figure 2 This is a comparison chart of the Savitzky-Golay filtering effects;

[0069] Figure 3 Comparison of the equivalent stiffness derivative after Savitzky-Golay filtering;

[0070] Figure 4 This is a schematic diagram of the multi-scale deep residual PINN network architecture of the present invention;

[0071] Figure 5 A graph showing the dynamic weighted scheduling strategy;

[0072] Figure 6 A comparison chart of prediction results during the loading process;

[0073] Figure 7 A comparison chart of predicted results for the unloading process;

[0074] Figure 8 This is a schematic diagram of the derivative hysteresis loop;

[0075] Figure 9 This is a graph showing the predicted leakage amount.

[0076] Figure 10 This is a flowchart illustrating the overall process of the method used in this embodiment of the invention. Detailed Implementation

[0077] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0078] In a first aspect, the present invention provides a method for analyzing the hysteresis characteristics and compensating for leakage in a hydraulic system based on multi-scale deep residual PINN, comprising the following steps:

[0079] S1. Data Acquisition and Preprocessing:

[0080] S1.1 Data Acquisition: Time-series data of the hydraulic system during loading and unloading processes are acquired through pressure and displacement sensors, including load L(t) and oil volume V(t) in the hydraulic cylinder. The sampling frequency is not less than 1kHz to ensure the capture of the dynamic characteristics of the system.

[0081] S1.2 Data Cleaning: Remove outliers and noise, identify outliers using the 3σ criterion, and fill in missing data using linear interpolation;

[0082] S1.3 Innovative Application of Savitzky-Golay Filtering: This invention innovatively applies the Savitzky-Golay filter to hydraulic system data processing for comparison with subsequent neural network model results. This filter, through local polynomial fitting, can directly obtain high-quality derivative information while smoothing the data. A window size of 11 and a polynomial order of 3 are selected; these are parameters optimized through extensive experiments, ensuring both smoothing effects and preservation of the signal's dynamic characteristics.

[0083] S1.4 Derivative Calculation and Verification: Calculate the equivalent stiffness of the system The rationality of the derivative is verified through physical constraints to ensure that K > 0.

[0084] S2. Construct a multi-scale deep residual PINN network model:

[0085] This step embodies the first key innovation of this invention—the deep residual network architecture. Traditional PINNs typically have only 3-5 layers, making it difficult to capture complex nonlinear mappings. This invention constructs a deep network that can contain 40+ layers, solving the training challenges of deep networks through a residual connection mechanism.

[0086] S2.1 Network Architecture Design: Constructing a deep neural network containing the following layers:

[0087] Input layer: Receives 2D input [L,V]

[0088] Initial feature extraction layer: Dense(64, activation = elu) + LayerNormalization()

[0089] Residual network module: 6 residual blocks with the following numbers of neurons: [128, 192, 256, 192, 128, 64]

[0090] Final feature layer: Dense(32, activation = elu) + LayerNormalization()

[0091] Output layer: Dense(1, activation=linear), output

[0092] The design concept of this hourglass-shaped structure is: first, to increase the expressive power of the network by expanding (128→192→256) to capture complex nonlinear patterns; then, to extract key features by shrinking (256→192→128→64) to avoid overfitting.

[0093] S2.2 Residual Block Design: Each residual block contains:

[0094] Main path: Input→Dense→LayerNorm→Dropout(0.1)→Dense→LayerNorm; Skip connection: When the input and output dimensions are different, projection is performed through the Dense layer to match the dimensions (for details, please refer to DenselyConnected Convolutional Networks[J].IEEE Computer Society,2016.DOI:10.1109 / CVPR.2017.243.).

[0095] Residual connection: The output of the main path is added to the jump connection;

[0096] The physical meaning of residual connection: In hydraulic system modeling, residual connection can be understood as preserving the basic linear characteristics of the system while learning complex nonlinearity, which is consistent with the physical characteristics of hydraulic system being approximately linear under small disturbances.

[0097] S2.3 Weight Initialization: The weights of the Dense layer are initialized using the He initialization method, and L2 regularization (λ = 1e-4) is used to prevent overfitting. He initialization is a method for setting initial values ​​for the weights of a neural network layer, specifically optimized for the ReLU activation function. Its core idea is to ensure that the variance of the weights during initialization meets specific conditions, thus preventing the signal from disappearing or exploding during the forward and backward propagation of the neural network. L2 regularization is a technique to prevent model overfitting by adding a regularization term to the loss function to penalize excessively large weight parameters.

[0098] S3, Multi-scale Feature Engineering Processing:

[0099] This step embodies the second key innovation of this invention—multi-scale feature engineering. The physical mechanisms of a hydraulic system differ across different load ranges: at low loads, static seal leakage is primary; at medium loads, dynamic sealing effects occur; and at high loads, gap flow occurs. This invention, through multi-scale feature transformation, enables the network to adaptively learn these different physical mechanisms.

[0100] S3.1 Feature Transformation: Transform the original load L into a 5-dimensional feature vector:

[0101] f1 = L (original features)

[0102] f2 = log(L+1) (Logarithmic feature, capturing behavior in low-load regions)

[0103] (Square root characteristic, medium load region)

[0104] f4 = tanh(L / 5000) (S-shaped characteristic, high load region transition)

[0105] (Binary region indicator)

[0106] S3.2 Feature Standardization: Use MinMaxScaler to normalize all features to the [0,1] interval.

[0107] S3.3 Feature Fusion: Combine the 5-dimensional feature vector with the hydraulic cylinder oil volume V to form a 6-dimensional input vector. S4. Physical Constraint Training:

[0108] This step embodies the third key innovation of this invention—a dynamic physical constraint strategy. Traditional methods use fixed physical constraint weights, which can easily lead to training instability. This invention proposes a progressive dynamic weight scheduling, achieving an optimal balance between data fitting and physical constraints.

[0109] S4.1 Loss Function Design: L total =L data +λ physics (t)×L physycs +λ smooth (t)×

[0110] L smooth

[0111] S4.2 Data Fitting Loss: S4.3 Physical constraint loss: L physucs =L monotonic +L prior

[0112] in:

[0113] Monotonicity constraint: Ensure that the stiffness is always positive, in accordance with the basic physical laws of hydraulic systems;

[0114] Prior constraints:

[0115] Where N is the total number of data points, Let be the predicted stiffness value at the i-th point, softplus() be the soft positive function, and ∈ be a small constant to prevent division by zero. It is a priori model obtained based on theoretical analysis and fitting of experimental data.

[0116] S4.4 Smoothness Loss:

[0117] in:

[0118] This represents the traditional smoothing loss (second derivative). The second partial derivative of load with respect to oil quantity is calculated at the i-th data point to measure the change in curvature of the prediction curve. This represents the enhanced smoothing loss (rate of change of derivative), and this dual smoothing constraint ensures the continuity and differentiability of the prediction.

[0119] S4.5 Dynamic Weight Scheduling: Dynamically adjusts the physical constraint dynamic weight function λ according to the training round t. physics (t) and smoothing constraint dynamic weight function λ smooth(t). In the early stage (usually t<10), the focus is on data fitting; in the middle stage (usually 10≤t<50), physical constraints are gradually strengthened; and in the later stage (usually t≥50), physical constraints reach their strongest.

[0120] S5. Hysteresis Characteristic Analysis:

[0121] This step innovatively links the geometric characteristics of the hysteresis loop with the system's volume compensation requirements, providing a physical basis for subsequent leakage compensation.

[0122] S5.1 Train loading and unloading models separately: Using the same network structure but with independent parameters, train the loading process model and the unloading process model separately. This separate training strategy can better capture the asymmetry of the loading and unloading processes.

[0123] S5.2 Stiffness Prediction: For a given point (L,V), predict the stiffness value K using both the loading and unloading models. loading and K unloading .

[0124] S5.3 Stiffness difference calculation: ΔK(L,V)=K loading (L,V)-K unloading (L,V), the stiffness difference directly reflects the hysteresis of the system.

[0125] S5.4 Hysteresis Loop Construction: On the LV plane, a complete load-unload closed loop is constructed using interpolation methods.

[0126] S5.5 Area Calculation: The area enclosed by the hysteresis loop is calculated using the Shoelace formula, which is based on Green's theorem and calculates the area of ​​the region through boundary integrals.

[0127] This area represents the energy loss during a load-unload cycle and is a key indicator for evaluating system efficiency.

[0128] S5.6 After considering the piston area and pump speed, the hysteresis area is converted into the actual volumetric flow rate: This transformation converts the geometric hysteresis loop area into a directly applicable volumetric flow rate compensation value. This compensation flow rate is adjusted in real-time by a servo valve to actively compensate for volumetric losses caused by system hysteresis, thus implementing a feedforward control strategy. It's important to note that this is a direct result of the hysteresis loop, representing the ideal volumetric compensation requirement for feedforward control, but it is not the leakage rate. Real-world systems cannot perfectly compensate for this; the difference manifests as leakage, Q. compensation This provides a physical basis for leakage estimation, which is independent of the subsequent leakage compensation mechanism and together improves the control accuracy and response characteristics of the hydraulic system.

[0129] S6. Leakage Prediction and Compensation:

[0130] This step embodies the fourth key innovation of this invention—a hybrid prediction combining physical models and data-driven approaches. Pure physical models are overly simplistic, while purely data-driven approaches lack a physical foundation. This invention organically combines the two, achieving high-precision leak prediction for fault diagnosis and maintenance decision-making.

[0131] S6.1 Calculation of volume compensation requirements:

[0132] Based on the loading and unloading stiffness differences obtained from the PINN network model with multi-scale depth residuals, and the hydraulic cylinder oil volume, the volume compensation requirement is obtained:

[0133]

[0134] Among them, K load,i K represents the stiffness of the i-th data point during the loading process. unload,i This represents the stiffness of the i-th data point during the unloading process.

[0135] Average volumetric loss density: S6.2 Physical Model Construction:

[0136]

[0137] a: Leakage coefficient, related to sealing gap and oil properties; b: Load sensitivity index, reflecting the leakage-pressure relationship; c: Sealing threshold parameter, characterizing the preload effect. The damping function D(L) introduces a suppression effect under high load, stemming from mechanisms such as increased viscosity and enhanced sealing contact pressure.

[0138] This combined model can fully describe the staged leakage characteristics of the hydraulic system from low load to high load (sealing pre-tightening → linear growth → nonlinear growth → high pressure suppression), which not only ensures the physical rationality of the boundary conditions (zero leakage at zero load), but also provides a solid physical foundation for the subsequent residual network to learn complex nonlinear factors, reflecting the modeling concept of "physical mechanism guidance + data-driven enhancement".

[0139] The basic leakage rate is:

[0140]

[0141] Among them, Q max k is the maximum leakage revolutions under the current load L. v p is the loss sensitivity coefficient. f The pressure influence factor is represented by tanh(), which denotes the hyperbolic tangent function. The use of the hyperbolic tangent function ensures the boundedness and smoothness of the leakage.

[0142] S6.3 Interval Correction – The Fifth Key Innovation:

[0143] This invention innovatively proposes a partitioned leakage model based on physical mechanisms, and connects each interval through a smooth transition function:

[0144] Preload transition:

[0145] Yield transition:

[0146] Zone leakage factor: F(L)=α static (1-f preload )+α dynamic (L)f preload (1-

[0147] f yield )+α gxp (L)f yield

[0148] Among them, L preload For the load corresponding to the sealing preload, L yield For the load corresponding to the seal yield, α static As the static leakage factor, α dynamic (L) is the dynamic leakage factor function, α gxp This is a function of the gap flow factor. According to a specific embodiment of the present invention, it can take the following values: Static leakage: α static =0.03, dynamic leakage: Interstitial flow: S6.4 Considering that the sealing characteristics of the hydraulic system vary in different load ranges, a zoned leakage factor is introduced. The leakage amount is calculated as: Q(L) = Q base (L)×F(L)

[0149] It generates training data, which does not directly participate in the final prediction, but is used to provide physically reasonable initial estimates for the physical model.

[0150] S6.5 Residual Network Enhancement: A 4-layer fully connected network [1,32,16,1] is constructed, with the input being the load L and the output being the residual ΔQ. The residual network is used to learn complex factors that the physical model fails to capture, such as temperature effects and wear effects. The leakage correction amount predicted by the residual network is:

[0151] Q residual (L;φ)=α adjust (L)·NN(f(L);φ)

[0152] NN(f(L); φ) is a neural network function whose input is the load f(L) after multi-scale feature engineering.

[0153] NN(f;φ)=W3·σ(LN(W2·σ(LN(W1·f+b1))+b2))+b3

[0154] f(L) represents the multi-scale feature changes (mentioned earlier), expressed as:

[0155]

[0156] Capturing complexities that physical models fail to describe, α adjust (L) is the adjustment factor.

[0157] S6.6 Smooth Transition Mechanism: Transition Function: Adjustment factor: α adjust (L)=1.0×(1-g transition )+(0.35+0.05log(1+

[0158] L / 1000))×g transition

[0159] S6.7 Final Prediction: Q total (L)=Q physics (L;θ)+Q residual (L;φ)

[0160] Load-related correction:

[0161] This multi-level prediction and correction ensures high accuracy of the model across the entire operating range.

[0162] Secondly, this invention provides a hydraulic system hysteresis analysis and leakage compensation system based on multi-scale deep residual PINN, which implements the above method in an engineering manner:

[0163] Data acquisition module: includes a high-precision pressure sensor (accuracy ±0.1%FS), a laser displacement sensor (resolution 0.1μm), a temperature sensor, and a 24-bit AD converter, with a sampling frequency of up to 10kHz; Signal processing module: based on a DSP chip, it realizes real-time Savitzky-Golay filtering and derivative calculation, with a processing delay of less than 1ms;

[0164] Feature Engineering Module: Implements multi-scale feature extraction and normalization processing, and supports online feature updates; Neural Network Computation Module: Includes a training unit for offline training of multi-scale deep residual PINN models, based on NVIDIA GPU and TensorFlow framework, supporting batch training and parameter optimization; Inference Unit: Used for online prediction, employing an inference engine optimized with TensorRT, with a single prediction time of less than 5ms.

[0165] Hysteresis analysis module: calculates stiffness differences and hysteresis characteristics in real time and generates compensation suggestions;

[0166] Leakage compensation module: integrates physical model and residual network, outputs 0-10V or 4-20mA compensation control signal;

[0167] Human-computer interaction module: Provides a touch screen interface, supporting parameter setting, real-time monitoring, historical data query and alarm management;

[0168] Communication interface module: Supports industrial communication protocols such as Modbus RTU / TCP, CANopen, and EtherCAT.

[0169] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above-described method.

[0170] Fourthly, the present invention provides an electronic device including one or more processors and a memory, the memory being used to store one or more programs, which, when executed by the processor, cause the processor to implement the above-described method.

[0171] Hysteresis Characteristics Analysis Experiment of Hydraulic Press Loading and Unloading

[0172] This embodiment takes a certain type of 5-ton hydraulic press as the research object. For example... Figure 1 As shown, the hydraulic cylinder has a cylinder diameter of 170mm, a rod diameter of 100mm, a stroke of 400mm, and a maximum working pressure of 20MPa.

[0173] S1. Data Acquisition and Preprocessing:

[0174] During normal operation of the hydraulic press, data is collected through the following sensors:

[0175] • Pressure sensor: Kistler 4067A, range 0-60MPa, accuracy ±0.1%FS

[0176] • Displacement sensor: MTS LH series, measuring range 650mm, resolution 5μm

[0177] • Temperature sensor: PT100, measuring range -50~200℃, accuracy ±0.1℃

[0178] • Data acquisition system: NI cDAQ-9178, sampling rate set to 2kHz

[0179] The experiment set the load range to 20000N and collected 6 sets of loading process data and 6 sets of unloading process data, each containing approximately 500 data points.

[0180] Data preprocessing steps:

[0181] 1. Outlier detection: Using the 3σ criterion, 37 outliers were detected and removed (0.12%).

[0182] 2. Missing value imputation: 12 missing values ​​were imputed using linear interpolation.

[0183] 3. Savitzky-Golay filter:

[0184] Comparison before and after filtering during the loading process Figure 2 , Figure 3 As shown, the raw acquired data is affected by factors such as sensor accuracy, electromagnetic interference, and mechanical vibration, resulting in significant random noise. After Savitzky-Golay filtering, high-frequency noise is effectively suppressed, and signal quality is significantly improved, providing high-quality input data for subsequent modeling. Unlike methods such as simple moving averages, this filter effectively preserves the peak, edge, and dynamic change characteristics of the signal while denoising, which is crucial for accurately capturing the transient response of the hydraulic system.

[0185] like Figure 3 The comparison of equivalent stiffness derivative calculations shown demonstrates the core technical advantages of this invention:

[0186] (1) Improved accuracy of derivative calculation: Traditional numerical difference methods amplify noise significantly when calculating derivatives, causing drastic fluctuations in dL / dV results, making them unsuitable for accurate modeling. Savitzky-Golay filtering directly obtains derivatives through local polynomial fitting, resulting in smooth and stable calculations that provide high-quality training labels for deep learning models.

[0187] (2) The physical meaning remains intact: the processed equivalent stiffness curve can still clearly reflect the difference in loading and unloading characteristics of the hydraulic system, laying a reliable foundation for subsequent hysteresis analysis.

[0188] S2. Construct a multi-scale deep residual PINN network model:

[0189] S2.1 Network Architecture Design

[0190] like Figure 4 As shown, the network employs a deep residual structure and includes the following layers:

[0191] (1) Input layer: Receives a 2D input vector [L,V]

[0192] (2) Initial feature extraction layer:

[0193] h1=LayerNorm(ELU(W1·[L,V]+b1))

[0194] in

[0195] (3) Residual Network Module: Contains 6 residual blocks with a neuron count configuration of [128, 192, 256, 192, 128, 64], forming an hourglass-shaped structure. The mathematical expression for each residual block is:

[0196] ResBlock i (x)=ELU(F i (x)+H i (x))

[0197] Where F i (x) represents the main path transformation of the i-th residual block, H i (x) represents the identity mapping or projection transformation of the i-th residual block.

[0198] (4) Output layer: Output equivalent stiffness prediction value S2.2 Residual Block Structure

[0199] Main path:

[0200] z1 = W i,1 ·x+b i,1

[0201] z2 = LayerNorm(z1)

[0202] z3 = ELU(z2)

[0203] z4 = Dropout(z3, p = 0.1)

[0204] z5=W i,2 ·z4+b i,2

[0205] z6 = LayerNorm(z5)

[0206] Skip connections: When the input dimension and output dimension are the same, H i (x) = x; otherwise, through the projection matrix W proj

[0207] Perform dimensional matching, i.e., H i (x)=W proj ·x

[0208] Residual output: output = ELU(z6 + H) i (x))

[0209] S3, Multi-scale Feature Engineering Processing:

[0210] The original load L is transformed into a 5-dimensional feature vector. The physical meaning of each feature is as follows:

[0211] F(L) = [f1, f2, f3, f4, f5] T

[0212] in:

[0213] f1 = L / L max Normalized linear features

[0214] f2 = log(L+1) / log(L) max +1): Logarithmic characteristics, capturing low load sensitivity.

[0215] Square root characteristics describe nonlinearity under moderate loads.

[0216] f4 = tanh(L / 5000): Hyperbolic tangent characteristic, simulating high load saturation.

[0217] Zone indicators distinguish work areas

[0218] Feature correlation analysis showed that the condition number of the Pearson correlation coefficient matrix for the five features was 12.7, indicating that the features have moderate independence, which helps the model learn patterns at different scales.

[0219] S4, Physical Constraint Training:

[0220] The total loss function consists of three parts:

[0221]

[0222] Training configuration:

[0223] Batch size: 32

[0224] Initial learning rate: 0.001

[0225] • Optimizer: Adam (β1 = 0.9, β2 = 0.999)

[0226] Training rounds: 150

[0227] Dynamic weight scheduling, such as Figure 5 :

[0228] Training process monitoring:

[0229] • Epochs 1-10: Data loss decreased from 0.823 to 0.156

[0230] • Epoch 11-30: Physical loss decreased from 0.234 to 0.089

[0231] • Epochs 31-50: Smoothing loss decreased from 0.167 to 0.045

[0232] • Epoch 51-150: Total loss converges to 0.021

[0233] S5. Results of hysteresis characteristic analysis:

[0234] like Figure 6 As shown, the loading process model is evaluated as follows:

[0235] MSE: 9.6265

[0236] MAE: 1.9566

[0237] ·R 2 0.9968

[0238] from Figure 6 It can be seen that, within the entire load range of 0-20000N, the prediction curve (red) of the multi-scale deep residual PINN model of this invention is in high agreement with the actual derivative curve (blue) calculated by the Savitzky-Golay filter, and the coefficient of determination R0 is very high. 2 The accuracy reached 0.9968, indicating that the model successfully learned the complex nonlinear characteristics of the hydraulic system loading process. The predicted curve maintained good smoothness (eliminating the influence of data noise) and accurately captured the true trend of system stiffness changes, demonstrating the advantages of deep integration of physical constraints and data-driven approaches.

[0239] like Figure 7 As shown, the unloading process model is evaluated as follows:

[0240] MSE: 19.1015

[0241] MAE: 2.4978

[0242] ·R 2 0.9967

[0243] The unloading process is usually noisier due to factors such as frictional hysteresis and oil viscosity (due to system relaxation, backlash, etc.), and exhibits different stiffness characteristics than the loading process. Figure 7 This demonstrates that the model of the present invention accurately captures this difference, R 2 The result of 0.9967 demonstrates the effectiveness of the separation modeling strategy and reflects the strong robustness of deep residual networks.

[0244] Lag hysteresis Figure 8 As shown, it exhibits a typical "fusiform" shape. Key parameters include:

[0245] (1) Maximum stiffness difference:

[0246] ΔK max =K loading-K unloading

[0247] (2) Area of ​​the hysteresis loop (using the Shoelace formula):

[0248]

[0249] (3) Actual volumetric flow rate:

[0250]

[0251] (4) Base leakage:

[0252]

[0253] S6. Leakage prediction results:

[0254] Leakage prediction results are as follows Figure 9 As shown, the prediction accuracy analysis is as follows:

[0255] • Physical model R 2 0.7804

[0256] ·Total model R 2 0.9757

[0257] The above embodiments demonstrate that the hydraulic system hysteresis characteristic analysis and leakage compensation method based on multi-scale deep residual PINN provided by this invention can effectively improve the modeling accuracy, control performance, and fault diagnosis capability of hydraulic systems, and has significant engineering application value. The overall process is as follows: Figure 10 As shown.

[0258] Those skilled in the art should understand that the above embodiments are merely for illustrating the present invention and are not intended to limit the invention. It will be apparent to those skilled in the art that other variations or modifications can be made based on the above description, and these variations or modifications still fall within the protection scope of the present invention.

Claims

1. A hydraulic system hysteresis analysis and leakage compensation method based on a multi-scale deep residual PINN, characterized in that, Includes the following steps: S1. Collect time-series data of load L and hydraulic cylinder oil volume V of the hydraulic system during loading and unloading processes; S2. Prepare a multi-scale deep residual PINN network model. This model is a deep neural network containing an input layer, an initial feature extraction layer, 6 residual blocks, a final feature layer, and an output layer. Each residual block contains a main path and skip connections. The main path contains, in sequence, a first fully connected layer, a first normalization layer, a dropout layer, a second fully connected layer, and a second normalization layer. Skip connections perform dimension matching through projection fully connected layers when the input and output dimensions are different. S3, transfer the load of S1 Multi-scale feature engineering is performed, transforming the data according to different engineering requirements to form a 5-dimensional feature vector. This vector, along with the hydraulic cylinder oil volume V, serves as the input to the model in S2. The 5-dimensional feature vector represents: the original load... Logarithmic load Square root load Hyperbolic Tangent Transform and area indicator ; S4. Physical Constraint Training: Define a composite loss function, including data fitting loss, physical constraint loss and smoothness loss. The weights of physical constraint loss and smoothness loss are dynamic weight functions. A dynamic weight scheduling strategy is adopted so that the dynamic weight functions of physical constraint and smoothness constraint increase with the training rounds. S5. Hysteresis Characteristic Analysis: Based on the trained multi-scale deep residual PINN network model, the stiffness of the loading process and the unloading process are predicted respectively. The difference between loading and unloading stiffness is calculated, a hysteresis loop is constructed, the area enclosed by the hysteresis loop is calculated, and it is converted into hysteresis compensation volumetric flow rate for feedforward control of hydraulic pump servo valve, so that the servo valve can adjust the flow rate in real time. S6. Leakage Prediction and Compensation: Based on a hybrid leakage prediction model that includes a physical model and a residual network, the leakage result is predicted; in the hybrid leakage prediction model: the physical model is: ， in Let a be the damping function, and b and c be the curve fitting parameters of the physical model. Residual networks are used to capture complex nonlinear behaviors that physical models fail to describe; The final predicted leakage amount is: ； The leakage amount predicted by the physical model. For the set of physical model parameters; This is the leakage correction amount predicted by the residual network. This is the set of parameters for the residual network.

2. The method of claim 1, wherein, The physical constraint loss in S4 is the sum of monotonicity constraint and prior constraint. The monotonicity constraint is used to ensure that the stiffness is always positive, which conforms to the basic physical laws of the hydraulic system. The prior constraint is an a priori model obtained based on theoretical analysis and experimental data fitting. The smoothness loss adopts a double smoothness constraint, which is the sum of the traditional smoothness loss represented by the second derivative and the enhanced smoothness loss represented by the rate of change of the derivative.

3. The method of claim 1, wherein, The dynamic weight scheduling strategy in S4 is as follows: based on the training rounds... The dynamic weight function and the smoothing constraint dynamic weight function are dynamically adjusted. In the early stage, the focus is on data fitting. In the middle stage, the physical constraints are gradually strengthened. In the later stage, the physical constraints reach their strongest.

4. The method of claim 1, wherein, In S5, the area enclosed by the hysteresis loop is calculated using the Shoelace formula, which represents the energy loss in a load-unload cycle. Based on this, after considering the piston area and pump speed, the hysteresis area is converted into the actual volumetric flow rate, and the flow rate is adjusted in real time by the servo valve to compensate for the volume loss caused by the hysteresis characteristics.

5. The method of claim 1, wherein, The parameters in the physical model are obtained by training and fitting based on training data, wherein the training data is generated as follows: The difference in loading and unloading stiffness obtained based on the multi-scale deep residual PINN network model, and the hydraulic cylinder oil volume, obtain the volume compensation demand, and determine the average volume loss density ; Obtain the basic leakage amount: ， in, For the current load Maximum leakage speed, For loss sensitivity coefficient, As a stress factor, Represents the hyperbolic tangent function; At the same time, considering the sealing characteristics of the hydraulic system in different load intervals, a partition leakage factor is introduced The leakage amount is calculated as ， It generates training data and provides physically reasonable initial estimates for the physical model.

6. The method of claim 5, wherein, For different load ranges, the transition behavior is modeled using the sigmoid function, and the range correction of the leakage includes: Pre-tension transition: , Yield transition: , The specific partition leakage factor is: ， wherein, is a sealing pre-tightening force corresponding load, is a sealing yield force corresponding load, is a static leakage factor, is a dynamic leakage factor function, is a gap flow factor function.

7. The method of claim 1, wherein, The residual network includes a smooth transition mechanism to avoid abrupt changes. The leakage correction amount predicted by the residual network is: ， This is a neural network function whose input is a load processed by multi-scale feature engineering. , The adjustment factor is used, where the sigmoid function is employed for smooth transitions. express: ， 。 8. A hydraulic system hysteresis analysis and leakage compensation system based on multi-scale deep residual PINN, used to implement the method described in any one of claims 1-7, characterized in that, include: The neural network computing module includes a training unit and an inference unit. The training unit is used for offline training of the multi-scale deep residual PINN model, and the inference unit is used for online prediction. Hysteresis analysis module: used to calculate the stiffness difference during loading and unloading processes and analyze hysteresis loop characteristics; Leakage compensation module: used for predicting the leakage amount based on a physical model and a residual network, and generating a compensation control signal.

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