A method and system for predicting the inclination angle of the cylinder of an axial plunger pump based on a physical information neural network

Abstract

The application provides an axial plunger pump cylinder overturn angle prediction method and system based on a physical information neural network, and belongs to the fields of fluid pressure and electric digital data processing. The application correlates pressure change and cylinder overturn angle by establishing an oil pressure-cylinder overturn angle mapping model of the axial plunger pump, and provides physical consistency constraints for the physical information neural network. Meanwhile, a bidirectional long short-term memory network is selected as a core prediction model, and "data loss + physical loss" is jointly introduced into a loss function, so that the predicted cylinder overturn angle meets the mechanical equation and experimental data. Finally, the technical path of non-invasive accurate prediction of unmeasurable attitude is realized through measurable pressure signals without damaging the structural integrity of the pump body. The application can provide early warning at the initial stage of overturning abnormality, helps to avoid flow distribution pair instability and wear aggravation, and thus improves the reliability and life cycle performance of aviation hydraulic equipment.

Description

Technical Field

[0001] This invention relates to the fields of fluid pressure and electronic digital data processing, and specifically to a method and system for predicting the overturning angle of an axial piston pump cylinder based on a physical information neural network. Background Technology

[0002] Axial piston pumps, due to their high power density, high response speed, and reliability, are widely used in aerospace electro-hydraulic systems, serving as a core power source for flight attitude control, actuation system drive, and critical mission execution. As equipment evolves towards higher pressure, higher speed, longer lifespan, and greater intelligence, the internal friction pairs of the pump exhibit stronger nonlinearity and higher sensitivity under fluid-solid-thermal coupling conditions. Their stability directly affects mission safety and the accuracy of the flight control system. Engineering practice shows that under high pressure and high speed conditions, cylinder rollover behavior is the earliest and most dynamic precursor reflecting internal force shifts. Changes in this behavior significantly affect the seal load, oil film pressure distribution, and the stability of the flow distribution pair, subsequently triggering a degradation chain including increased leakage, decreased volumetric efficiency, frictional instability, and accelerated wear. Therefore, achieving accurate and real-time prediction of the cylinder rollover angle is a crucial prerequisite for building a hydraulic system health monitoring system.

[0003] Early research on the health monitoring of plunger pumps mainly focused on key friction pairs, aiming to reveal the stress and wear patterns at the interface through lubrication models, dynamic models, and surface morphology evolution models. While these models provided a deeper understanding of the friction mechanism from the perspective of local interfaces, they generally assumed that the cylinder block attitude was known or in a steady state. However, cylinder block overturning, as an upstream variable determining the load distribution of the friction pair, did not have its dynamic changes adequately characterized in these models.

[0004] As research has gradually extended from local friction interfaces to system dynamics, scholars have further shifted their focus to the cylinder block tilting mechanism itself. Junhui Zhang established a dynamic model of the rotating components of a high-speed piston pump, revealing significant cylinder block tilting under high-speed, low-pressure conditions, and pointing out that the oil film carrying capacity limit is the root cause of limited high-speed performance (Modeling and Analysis of the tilt behavior of the cylinder block in a high-speed axial piston pump). Subsequently, Haogong Xu analyzed the tilting formation mechanism and its sensitive parameters from structural and operating condition perspectives, and proposed optimization strategies (Performance optimization for high speed axial piston pump considering cylinder block tilt). Zhang further established an analytical method based on tilting state criteria to evaluate the critical operating range of EHA pumps, and pointed out a strong correlation between the tilting angle and leakage (Critical operating range of electro-hydrostatic actuator pumps based on cylinder block tilting states). Meanwhile, Xu et al. proposed a low-modification, non-contact measurement method. By deploying eddy current sensors, they inverted the dynamic response of the overturning angle. Their research showed that the overturning angle varies periodically with pressure and is closely related to the forces acting on the friction pair (The direct measurement of the cylinder block dynamic characteristics based on a non-contact method in an axial piston pump). Although the above methods deepened the understanding of the overturning mechanism, directly measuring the overturning angle requires drilling holes to install sensors, which not only compromises the integrity of the pump structure but also alters the local dynamic boundaries, making it difficult to apply to aerospace equipment. More importantly, the cylinder block overturning angle is the upstream dynamic state quantity that best reflects the internal force shift, but there is still no technical path that can accurately predict it using measurable signals without modifying the pump structure. Summary of the Invention

[0005] To address the aforementioned problems, this invention establishes a mapping model between oil pressure and cylinder tilting angle in an axial piston pump cylinder, correlating oil pressure changes with cylinder tilting angle. This approach, without compromising the pump's structural integrity, enables accurate prediction of unmeasurable attitudes using measurable signals. The technical solution adopted by this invention is as follows:

[0006] This invention provides a method for predicting the overturning angle of an axial piston pump cylinder based on a physical information neural network, comprising the following steps:

[0007] S1: Establish the oil pressure-cylinder tilt angle model of the axial piston pump;

[0008] S2: Conduct experiments on the axial piston pump under different speed and pressure conditions, obtain oil pressure signal data and cylinder displacement signal data at different cylinder overturning angles, and convert the cylinder displacement signal data into cylinder overturning angle signal data.

[0009] S3: Preprocess the oil pressure signal data obtained in S2 to ensure the robustness of the subsequent training process of the physical information neural network PINN and the temporal correlation of the oil pressure signal data, and to eliminate the influence of the oil pressure signal data dimension on the model.

[0010] S4: The PINN is trained using the data preprocessed in S3; the PINN takes a periodically changing high-frequency oil pressure signal as input and outputs a cylinder displacement signal that changes periodically accordingly.

[0011] S5: Obtain the oil pressure signal data in the axial piston pump to be predicted, input the oil pressure signal data into PINN trained by step S4 and predict the cylinder displacement, and convert the cylinder displacement to obtain the cylinder overturning angle.

[0012] Preferably, step S1 specifically includes:

[0013] S11: Establish an OXYZ spatial rectangular coordinate system with the intersection of the plane where the distributor plate and the cylinder block contact each other and the main shaft of the axial piston pump as the origin O. The plane where the distributor plate and the cylinder block contact each other is the XOY plane. The Y-axis points in the same direction as the outer dead point of the axial piston pump, and the Z-axis points along the axis towards the swashplate.

[0014] S12: Establish a hydraulic pressure-cylinder tilting angle model for when an axial piston pump tilts, with the cylinder block subjected to an axial clamping force F in the Z-axis direction. i Oil film support force F between the distributor plate and the cylinder block h The residual support force F generated when the cylinder block overturns and comes into contact with the distributor plate. r Satisfying the force balance equation

[0015] ;

[0016] The cylinder block is subjected to an overturning moment M in the XOY plane by the slipper plunger assembly. o The anti-overturning moment M generated by the oil film between the distributor plate and the cylinder block a and the reaction torque M generated by the distribution plate rSatisfying the torque balance equation

[0017] ;

[0018] R1 represents the inner radius of the inner sealing ring of the distribution plate, R2 represents the outer radius of the inner sealing ring of the distribution plate, R3 represents the inner radius of the outer sealing ring of the distribution plate, and R4 represents the outer radius of the outer sealing ring of the distribution plate; M ox M oy M respectively o The components in the X and Y directions, M ay M represents a The component in the Y direction, M a The component in the X direction is 0, M r Indicates the reaction torque;

[0019] Among them, the axial clamping force F i The oil pressure F in the axial piston pump p With the central spring force F s Together constitute;

[0020] The contact pressure distribution when the cylinder block and distributor plate come into contact under three conditions—slight overturning, severe overturning, and complete overturning—is simplified into a linear pressure distribution model, which is associated with the cylinder block overturning angle. F is obtained by piecewise integration of the linear pressure distribution model under the three overturning conditions. r (R1,R2),F r (R3,R4) and M r (R1,R2), M r Substituting (R3,R4) into the force balance equation and torque balance equation, we can establish the oil pressure-cylinder overturning angle model.

[0021] Preferably, step S2 specifically includes:

[0022] S21: Select multiple sets of speed conditions and multiple sets of pressure conditions to form a full-coverage test condition that extends from low pressure and low speed to high pressure and high speed, and conduct experiments on each set of conditions in sequence.

[0023] S22: The oil pressure signal data in the axial piston pump during each set of working condition tests is obtained by pressure sensors installed at the inlet, outlet and leakage ports of the axial piston pump.

[0024] S23: Install a set of eddy current sensors X1, X3 and X2, X4 on two planes parallel to the XOY plane on the axial piston pump. The cylinder displacement signal data is characterized by the displacement signal of the eddy current sensor and the displacement signal of the eddy current sensor is filtered.

[0025] S24: Convert the eddy current displacement signal data processed in S23 to obtain the cylinder overturning angle signal data. The formula is as follows:

[0026]

[0027] in, Indicates the cylinder tilt angle. , , , These represent the displacement signals of the four eddy current sensors, with z1 and z2 representing the distances between eddy current sensors X1 and X2, and between X3 and X4, along the Z-axis.

[0028] Preferably, in step S4, the neural network in the PINN includes a bidirectional long short-term memory network BiLSTM and an attention module;

[0029] The periodically changing high-frequency oil pressure signal is input into the BiLSTM in PINN. In the feature transformation layer of BiLSTM, sine and cosine functions are selected as feature transformation basis functions. The initial phase of the feature function is set according to the phase characteristics of the input high-frequency oil pressure signal, and the frequency of the feature function is selected according to the physical rotation frequency of the axial piston pump and the reciprocating motion frequency of the piston. The four independent output nodes set in the BiLSTM of PINN correspond to the displacement signals of the four sensors, realizing parallel prediction and physical consistency modeling of multi-point displacement states.

[0030] Preferably, the training of PINN in step S4 includes a pre-training stage and a training stage. In the pre-training stage, only data loss is used for initial training, so that PINN can initially learn the time series features of sensor signals. Subsequently, in the training stage, a physical loss term is introduced. By weighted combination of data loss and physical loss, the fusion optimization of data-driven and physical constraints is achieved, thereby improving the physical interpretability and prediction stability of the model.

[0031] Preferably, the data loss in the pre-training phase is:

[0032]

[0033] in, This is represented as the length of the data sample. This represents the displacement signal of the eddy current sensor predicted by the physical information neural network, where x is the displacement signal obtained through actual measurement.

[0034] Preferably, the total loss function during the training phase is Loss total Loss for data loss data and physical loss phyWeighted combination:

[0035]

[0036] in, This is a weighting factor used to balance data precision and physical consistency; Loss data With Loss pre_data same.

[0037] This invention also provides an axial piston pump overturning angle prediction system based on a physical information neural network, applicable to the aforementioned prediction method, including an axial piston pump, a test bench, a control system, a sensor measurement system, and a data prediction system; the axial piston pump is fixed on the test bench; the control system is used to control the speed and pressure conditions of the axial piston pump.

[0038] The sensor measurement system includes a pressure sensor and an eddy current sensor. The pressure sensor is installed at the inlet, outlet, and leakage ports of the axial piston pump and is used to measure the oil pressure signal inside the cylinder at different cylinder tilt angles. There are two sets of eddy current sensors, two in each set. Each set of eddy current sensors is installed on two planes on the axial piston pump that are parallel to the plane where the distributor plate and the cylinder block contact. The eddy current sensors are used to measure the cylinder displacement signal at different cylinder tilt angles.

[0039] The data prediction system deploys a physical information neural network, which reads data from the sensor measurement system and outputs a predicted cylinder displacement signal. The data prediction system calculates the predicted cylinder overturning angle based on the predicted cylinder displacement signal data.

[0040] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0041] (1) Propose an oil pressure-cylinder tilt angle mapping model: Establish a cylinder tilt dynamic model, construct the physical relationship between oil pressure change and cylinder tilt angle, and realize the theoretical path from measurable pressure to unmeasurable attitude parameters.

[0042] (2) Introduce mechanical consistency constraints in PINN: Introduce “data loss + physical loss” in the loss function to ensure that the predicted overturning angle satisfies both the mechanical equation and experimental data, thereby improving the interpretability of the model and its ability to generalize across working conditions.

[0043] (3) Achieving overturning angle prediction without modifying the pump body structure: After training, the model can invert the cylinder overturning angle by relying only on the pressure signals that are easily obtained during operation, so that overturning state monitoring can be shifted from direct measurement based on structural damage to non-invasive indirect sensing. This technology can provide early warning in the early stage of overturning anomalies, which helps to avoid instability of the flow distribution pair and accelerated wear, thereby improving the reliability and life cycle performance of aviation hydraulic equipment. Attached Figure Description

[0044] Figure 1 A schematic diagram of the physical model of the pressure-cylinder tilt angle of an axial piston pump;

[0045] Figure 2 This is a schematic diagram of the cylinder block tilting angle;

[0046] Figure 3 Installation diagram for eddy current sensor measurement;

[0047] Figure 4 A schematic diagram for calculating the cylinder block tilt angle;

[0048] Figure 5 The graph shows the displacement signal prediction results of the PINN model.

[0049] Figure 6 A comparison chart of displacement prediction indicators under different working conditions;

[0050] Figure 7 This is the predicted result for the cylinder block tilt angle. Detailed Implementation

[0051] The present invention will be further described and illustrated below with reference to specific embodiments. The technical features of each embodiment of the present invention can be combined accordingly, provided that there is no mutual conflict.

[0052] The axial piston pump tested in this invention is the HP5V45-AV10RB2S1MA-N type swashplate axial piston pump manufactured by Hengli Hydraulics. It contains nine piston slipper assemblies, has a theoretical displacement of 45cc / r, a rated pressure of 29MPa, and a rated speed of 2700rpm. The axial piston pump test bench uses a high-precision servo motor and a proportional relief valve to control the tested axial piston pump to operate under stable drive and load.

[0053] This invention first provides an axial piston pump overturning angle prediction system based on physical information neural network, including an axial piston pump, a test bench, a control system, a sensor measurement system, and a data prediction system; the axial piston pump is fixed on the test bench; the control system is used to control the speed and pressure conditions of the axial piston pump.

[0054] The sensor measurement system includes pressure sensors and eddy current sensors. The pressure sensors are installed at the inlet, outlet, and leakage ports of the axial piston pump to measure the oil pressure signal inside the cylinder at different cylinder tilt angles. To monitor the cylinder tilt angle without affecting the normal operation of the core rotating components of the axial piston pump, two sets of four eddy current sensors are installed on the axial piston pump housing, as shown in the specific installation method. Figure 3 As shown, eddy current sensors are mounted on two planes of the axial piston pump, parallel to the plane where the distributor plate and cylinder block contact. Two sensors, X1 and X3, and X2 and X4, are mounted on each plane. The eddy current sensors are perpendicular to the axis in the radial direction, while X1 and X2 are horizontal in the axial direction, and X3 and X4 are also horizontal in the axial direction. The included angle between two eddy current sensors on the same plane is 135°. Since the signal from the eddy current sensor is weak, with variations in the micrometer range, a short distance between the sensors would amplify the calculation error of the subsequent overturning angle. Considering the cylinder block length limitation, the distance between the two mounting planes of the eddy current sensors is set to 35mm. Given the detection range of the eddy current sensor is 0-1mm, the initial installation gap between the eddy current sensor probe and the axial piston pump cylinder block is set to 0.5mm. This gap ensures maximum measurement of cylinder block displacement. A sealing ring is installed between the nut of the eddy current sensor and the housing of the axial piston pump, and a double-nut structure is used to prevent the eddy current sensor from loosening.

[0055] The data prediction system deploys a Physics-Informed Neural Network (PINN). The PINN is used to read data from the sensor measurement system and output the predicted cylinder displacement signal. The data prediction system calculates the predicted cylinder overturning angle based on the predicted cylinder displacement signal data.

[0056] This invention also provides a method for predicting the overturning angle of an axial piston pump cylinder based on a physical information neural network. The method utilizes the aforementioned axial piston pump overturning angle prediction system based on a physical information neural network and includes the following steps:

[0057] S1: Establish an oil pressure-cylinder tilt angle model for the axial piston pump to provide physical consistency constraints for PINN;

[0058] S2: Conduct experiments on the axial piston pump under different speed and pressure conditions to obtain oil pressure signal data and cylinder displacement signal data at different cylinder tilt angles;

[0059] S3: Preprocess the oil pressure signal data obtained in S2 to ensure the robustness of the subsequent PINN training process and the temporal correlation of the oil pressure signal data, and to eliminate the influence of the oil pressure signal data dimension on the model.

[0060] S4: The PINN is trained using the data preprocessed in S3; the PINN takes a periodically changing high-frequency oil pressure signal as input and outputs a cylinder displacement signal that changes periodically accordingly.

[0061] S5: Obtain actual oil pressure signal data, input the oil pressure signal data into PINN trained by step S4 and predict cylinder displacement, and convert the cylinder displacement to obtain the cylinder overturning angle.

[0062] in,

[0063] S1 specifically includes:

[0064] S11: To better establish physical models, such as Figure 1 As shown, an OXYZ spatial rectangular coordinate system is established with the intersection of the plane where the distributor plate and the cylinder block contact each other and the main shaft of the axial piston pump as the origin O. The plane where the distributor plate and the cylinder block contact each other is the XOY plane. The Y-axis points in the same direction as the outer dead point of the axial piston pump, and the Z-axis points along the axis towards the swashplate.

[0065] S12: Establish a model of oil pressure and cylinder tilt angle when an axial piston pump tilts.

[0066] During normal operation of the axial piston pump, the cylinder block can maintain a tight fit with the distributor plate, thanks to the axial clamping force F. i The effect of axial clamping force F i The oil pressure F in the cylinder bore p With the central spring force F s Composed of superposition in the same direction, that is, satisfying

[0067] F i =F p +F s ;

[0068] Axial clamping force F i The cylinder block is pressed against the surface of the distributor plate along the Z-axis. At this time, the gap between the distributor plate and the cylinder block is filled with oil, forming a thin oil film that provides oil film support force F for the cylinder block. h However, when the cylinder block tilt angle is too large, solid contact will occur between the cylinder block and the distributor plate, resulting in residual support force F at the contact surface. r .

[0069] The above analysis shows that the cylinder block is subjected to an axial clamping force F in the Z-axis direction. i Oil film support force F hWith remaining support force F r The combined effect of these forces satisfies the force balance equations.

[0070]

[0071] On the XOY plane, it is subjected to an overturning moment M generated by the slipper plunger assembly. o The anti-overturning moment M generated by the oil film between the distributor plate and the cylinder block a and the reaction torque M generated by the distribution plate r The effect satisfies the torque balance equation.

[0072]

[0073] Where R1 represents the inner radius of the inner sealing ring of the distribution plate, R2 represents the outer radius of the inner sealing ring of the distribution plate, R3 represents the inner radius of the outer sealing ring of the distribution plate, and R4 represents the outer radius of the outer sealing ring of the distribution plate. M ox M oy These represent the overturning moment M respectively. o The components in the X and Y directions, M ay M represents a The component in the Y direction.

[0074] The solutions for each force and torque are as follows:

[0075] (1) When the axial piston pump is running normally, the axial clamping force F i The oil pressure F in the cylinder bore p With the central spring force F s Together they constitute:

[0076]

[0077] Where, d p p is the diameter of the plunger. n Let Z represent the pressure in the nth plunger chamber, Z represent the number of plungers in the axial plunger pump, and θ represent the pressure in the nth plunger chamber. n This represents the angular displacement of the nth plunger cavity.

[0078] like Figure 1 As shown, the piston chamber of the axial piston pump is divided into a low-pressure zone and a high-pressure zone. When 0 < θ n ≤π, the plunger cavity is under high pressure (p n =p H When π < θ n ≤2π, the plunger cavity is under low pressure (p n =p LBecause the outlet pressure of the axial piston pump is greater than the inlet pressure, the axial clamping force generated by the pressure in the high-pressure zone piston cavity is greater than the axial clamping force in the low-pressure zone piston cavity. This causes the cylinder block to tilt towards the high-pressure zone side, and the resulting oil tilting torque M in the piston cavity... oo and its lever arm L pn It can be represented as

[0079]

[0080]

[0081] Among them, R p This indicates the radius of the cylinder bore pitch circle.

[0082] (2) In an axial piston pump, the slipper piston assembly reciprocates within the cylinder bore to complete the oil suction and discharge process. During this reciprocating motion, a rotational inertial force F is generated in the XOY plane. cpsn Simultaneously, its rotational motion within the cylinder bore will also generate an inertial force F in the Z-axis direction. ipsn , can be represented as

[0083]

[0084]

[0085] Where, m p Indicates the mass of the plunger, m s Indicates the quality of the skates. β represents the rotational speed of the axial piston pump, and β represents the angle of inclination of the swashplate.

[0086] In a constant displacement axial piston pump, the swashplate has a fixed tilt angle and remains in contact with the slippers. Due to this structure, the centroids of the nine slipper piston assemblies within the pump are not parallel to the plane of the distribution plate in space. This causes the slipper piston assemblies to generate two inertial forces F. cpsn and F ipsn An inertial overturning moment M is generated about the X-axis. im Inertial overturning moment M im The force transmitted to the cylinder bore causes the cylinder block to overturn towards the outer dead center (ODC). This inertial overturning moment M... im It can be represented as

[0087]

[0088]

[0089] Among them, L mn L represents the torque arm of the centrifugal force acting on the nth plunger cavity. moThis represents the Z-axis component of the distance between the center of mass of the slipper plunger assembly at the origin O and the inner dead center IDC. This is due to the inertial force F of the reciprocating motion. ipsn Acting on the oil, it is converted into oil pressure, therefore, in calculating the inertial overturning moment M im There is no need to consider this during the process.

[0090] (3) On the contact surface between the swashplate and the slipper of the axial piston pump, the swashplate will generate a lateral reaction force F on the slipper. ssyn

[0091]

[0092] Its component force along the Y-axis is transmitted to the cylinder block through the slipper plunger assembly, thereby generating a lateral overturning moment M on the cylinder block in the Z-axis direction. ss and its lever arm L ssn It can be represented as

[0093]

[0094]

[0095] Among them, L sso This represents the component of the distance from the center of the plunger ball head at IDC to the origin O along the Z-axis, where M... ss The component on the Z-axis represents the driving torque on the shaft, and the final overturning moment M. o This will not be considered in the calculation.

[0096] (4) In addition to the lateral reaction force, the swashplate also generates a total lateral force on the skate, and this total lateral force F scn The reaction force generated by the plunger spline coupling achieves equilibrium. Total lateral force F scn and its lever arm L scn It can be represented as

[0097]

[0098]

[0099] Due to the uniform distribution of the plunger, the total lateral force F can be reduced. scn Consider it as a concentrated force acting on the spline coupling center, the resulting lateral overturning moment M sc It can be represented as

[0100]

[0101] Among them, L scn This represents the component of the distance from the origin O to the spline coupling center in the Z-axis direction.

[0102] (5) The oil overturning moment M analyzed above oo Inertial overturning moment M im Lateral overturning moment M ss and lateral overturning moment M sc Adding them together, the overturning moment M of the cylinder block is... o It can be represented as

[0103]

[0104] (6) The cylinder bore and slipper piston assembly of the axial piston pump are uniformly distributed in the cylinder block. Based on the symmetry of its uniform angular distribution, the summation symbol in the above formula can be replaced by the integral average value. The simplified formula obtained is summarized as follows.

[0105]

[0106] The axial clamping force F is calculated according to the simplified formula above. i and overturning moment M o After simplification, we can obtain

[0107]

[0108] (7) This study uses the one-dimensional static Reynolds equation as the governing equation for calculating the pressure distribution between the cylinder block and the distributor plate, where the pressure distribution p at the outlet of the axial piston pump can be expressed as:

[0109]

[0110] The pressure at the outlet of the axial piston pump is integrated in segments to obtain the oil film support force F of the oil film on the cylinder block at the outlet. hH and overturning moment M aH It can be represented as

[0111]

[0112]

[0113]

[0114] Among them, M aHx M aHy M respectively aH The components in the X and Y axis directions, φ H1 and φ H2 This indicates the start and end angles of the effective high-pressure zone when the plunger rotates to the oil outlet.

[0115] When the axial piston pump is operating, the oil inside the piston chamber is connected to the oil at the pump's inlet and outlet ports via the engagement of the distributor plate and the slotted groove on the cylinder block. The connection state of these slotted grooves alters the oil film distribution, thereby changing the oil film support force F. h With overturning moment M a This study employs a symmetrically distributed distribution plate with waist-shaped slots, such as... Figure 1 As shown, this is to ensure the stability of pressure during the rotation of the plunger pump.

[0116]

[0117]

[0118] Where φ H φ represents the included angle of the effective pressure zone in the high-pressure area. L φ represents the included angle of the effective pressure zone in the low-pressure area. C φ1 represents the included angle of the cylinder block waist groove, φ2 represents the starting angle of the oil outlet, and φ3 represents the ending angle of the oil outlet. Based on the above formula, the oil film support force F at the oil outlet of the axial piston pump... hH and overturning moment M aHx M aHy It can be simplified to:

[0119]

[0120]

[0121]

[0122] Oil film support force F at the inlet of the axial piston pump hL and overturning moment M aL Similarly, by integrating the oil film support force and the anti-overturning moment at the oil inlet and outlet respectively and then summing them, we can obtain the total oil film support force F at the distribution plate. h Total overturning moment M a Because of M ax Since M is 0, a That is, M ay .

[0123]

[0124]

[0125] (8) As the wear process of the axial piston pump gradually evolves, the overturning angle of the cylinder block relative to the distributor plate will continuously change, and its tilting degree will gradually develop from slight overturning to severe overturning, eventually reaching a complete overturning state. Correspondingly, the lubrication state of the sealing surface will also transition from completely mixed lubrication to partially mixed lubrication, eventually leading to lubrication failure. In the model of this study, the variation law of the clearance height h between the cylinder block and the distributor plate (i.e., the circumferential clearance height of the sealing strip) is simplified to a linear pressure variation distribution, thereby simplifying the oil film pressure distribution under mixed lubrication state into a linear model. This linear pressure variation distribution p r It can be represented as

[0126]

[0127] in, It is the reactive stiffness of the oil film. It is the threshold height of the gap between the cylinder block and the distributor plate when the sealing surface reaches the critical state of mixed lubrication, and its size range is generally 10-15μm.

[0128] To better illustrate, such as Figure 2 As shown, establishing a coordinate system, the circumferential gap height h of the sealing strip can be expressed as...

[0129]

[0130] Where h0 represents the center clearance height between the distributor plate and the cylinder block, and r represents the distance from the seal belt to the origin O of the coordinate system. θ represents the overturning angle of the cylinder block. r This represents the angular displacement between the cylinder block and the Y-axis in the coordinate system.

[0131] When the cylinder of the axial piston pump experiences slight tilting, the maximum value of the circumferential clearance height h of the sealing strip is... max All at the threshold height The following (i.e.) The remaining support force F on the sealing surface r and reaction torque M r Can represent

[0132]

[0133]

[0134] Where R i and R o These represent the inner and outer radii of the sealing surface, respectively.

[0135] When the cylinder of an axial piston pump tilts severely, the circumferential clearance height h of the sealing band exhibits a wedge-shaped distribution, and the maximum value of the circumferential clearance height h will exceed the threshold height. ,Right now( In this situation, the oil film between the cylinder block and the distributor plate will experience some rupture. Areas with smaller clearances will experience frictional wear, accelerating the degradation of the axial piston pump. Areas with larger clearances will experience increased leakage flow due to seal failure. At this point, the remaining support force F on the sealing surface will be affected. r and reaction torque M r It can be represented as

[0136]

[0137]

[0138] Where θ r1 and θ r2 This indicates that the circumferential gap height h of the sealing strip is equal to the threshold height. The azimuth angle at time can be determined using the following formula.

[0139]

[0140] When the cylinder block completely tilts (i.e., the clearance height is satisfied) The remaining support force and moment of the sealing surface are 0. The remaining support force F under three different overturning modes... r and reaction torque M r Integration yields

[0141]

[0142]

[0143] in ; ;

[0144] ; h min This represents the minimum value of the circumferential clearance height h of the sealing strip.

[0145] At this point, the axial clamping force F experienced by the axial piston pump is... i Oil film support force F h Remaining support force F r and the overturning moment M o Overturning moment M a and reaction torque M r All have been expressed, and the force balance equation and torque balance equation must be satisfied. From S12(8), it can be seen that the circumferential clearance height h of the sealing strip is related to the overturning angle of the cylinder. This leads to the remaining support force F r and reaction torque M r All are related to the cylinder block tilt angle Therefore, a hydraulic pressure-cylinder tilting angle model of the axial piston pump was established through the force balance equation and the force balance equation, and the physical relationship between hydraulic pressure change and cylinder tilting angle was constructed, converting the unmeasurable attitude parameter into measurable pressure.

[0146] S2 specifically includes:

[0147] S21: To fully verify the accuracy and generalization ability of the PINN (Physical Information Neural Network) model, a multi-condition experimental scheme was designed: five typical speed conditions (1500 rpm, 2000 rpm, 2500 rpm, 2700 rpm, 3250 rpm) and five characteristic pressure conditions (23 MPa, 26 MPa, 29 MPa, 32 MPa, 35 MPa) were selected, forming 25 sets of fully covered experimental conditions. The selected conditions range from low pressure and low speed to high pressure and high speed, completely covering the design operating range of the piston pump tested in this invention, and highly matching the distribution of operating conditions in actual engineering applications, effectively verifying the predictive performance of the model across the entire operating range.

[0148] Experiments were conducted on each set of working conditions on the test bench to obtain oil pressure signal data and cylinder displacement signal data under different cylinder tilting angles.

[0149] S22: The oil pressure signal data in the axial piston pump during each set of working condition tests is obtained by pressure sensors installed at the inlet, outlet and leakage port of the axial piston pump.

[0150] S23: In order to monitor the cylinder overturning angle without affecting the normal operation of the core rotating components of the axial piston pump, four eddy current sensors are installed on the housing of the axial piston pump. The displacement of the eddy current sensors can characterize the cylinder displacement.

[0151] Because there is an initial mounting gap between the measuring probe of the eddy current sensor and the cylinder surface, it is necessary to eliminate the DC bias in the displacement signal output by the eddy current sensor. This paper uses an averaging filter for this purpose, denoted as:

[0152]

[0153] Where, x i and x k All represent the raw displacement signal data of the eddy current sensor at the i-th sampling point, where n is the total number of samples. This represents the displacement signal data of the eddy current sensor at the i-th sampling point after averaging and filtering.

[0154] S24: The displacement signal data from the eddy current sensor, after being filtered by S23, is converted into cylinder overturning angle signal data. The formula is as follows:

[0155]

[0156] in, This indicates the cylinder tilt angle of an axial piston pump. , , , These represent the displacement signals measured by the four eddy current sensors, where z1 and z2 represent the distances between eddy current sensors X1 and X2, and between X3 and X4, along the Z-axis. Figure 4 .

[0157] S3 specifically includes:

[0158] S31: For high and low pressure oil pressure signal data, long-tailed outliers are truncated using the 0.5% and 99.5% quantiles. Missing values ​​in the pressure signal data are replaced with the column mean, and infinite values ​​in the pressure signal data are replaced with the 99.5% quantile of the column. This enhances the stability and availability of the pressure signal, thereby ensuring the robustness of the subsequent network training process.

[0159] S32: To address the issue of high-frequency noise in the original measured high-frequency pressure signal data, a fourth-order low-pass filter is used for noise suppression. Considering that the sampling frequency of the pressure signal is 10000 Hz, the cutoff frequency of the filter in this model is set to 1000 Hz. The phase characteristics of the fourth-order low-pass filter can avoid the signal phase shift caused by traditional filtering, ensuring that the time correlation of the time-series data is not disrupted.

[0160] To eliminate the influence of data dimensions on model training, the Min-Max normalization method is used to preprocess the oil pressure signal data, mapping the inlet and outlet oil pressure signal data collected by the pressure sensor to the [0, 1] interval.

[0161]

[0162] Where, p n F represents the normalized pressure signal. p This represents the raw pressure signal data, p min and p max These represent the minimum and maximum values ​​in the original pressure sequence, respectively, with a small constant 10 added to the denominator. -8 To avoid the denominator being zero.

[0163] All preprocessing operations remain linear and do not change the relative amplitude and phase relationship of the signal, thus not affecting the effectiveness of subsequent mechanical consistency constraints.

[0164] S4 specifically refers to:

[0165] After data preprocessing, the Physical Information Neural Network (PINN) needs to be trained. PINN takes a periodically varying high-frequency oil pressure signal as input and a corresponding periodically varying eddy current sensor displacement signal (as the cylinder displacement signal) as output. The cylinder tilt angle can be obtained from the eddy current sensor displacement signal. Because this type of signal has significant temporal correlation and bidirectional dependency characteristics, the neural network in PINN in this paper includes a Bidirectional Long Short-Term Memory Network (BiLSTM) and an attention module to achieve accurate modeling and prediction of complex temporal relationships.

[0166] Considering the typical combined rotational and reciprocating motion characteristics of the axial piston pump during operation, both its internal oil pressure signal and eddy current sensor displacement signal exhibit obvious periodicity and harmonic characteristics. Therefore, sine and cosine functions are selected as the feature transformation basis functions in the feature transformation layer to capture the periodic variation of the system. The initial phase of the feature functions is set based on the phase characteristics of the input oil pressure signal to ensure the temporal consistency between the model input and the physical process; the frequency of the feature functions is selected based on the physical rotational frequency of the piston pump and the reciprocating motion frequency of the piston, constructing a frequency sequence. , , , , Where Z represents the number of plungers in the axial plunger pump. The output layer of the physical information neural network corresponds to the displacement signal from the eddy current sensor. The model design sets four independent output nodes, each corresponding to one of the four sensor displacement signals, to achieve parallel prediction and physically consistent modeling of multi-point displacement states.

[0167] In the training process of a physical information neural network, the design of the loss function is a core element in achieving the organic integration of data-driven learning and physical constraint modeling. By constructing a loss function, the model can achieve high-precision fitting of experimental data while ensuring that its prediction results conform to the physical laws of the system, thereby improving the model's generalization ability and interpretability.

[0168] To ensure a good balance between data-driven learning and physical constraint modeling, this study proposes that the training process of the cylinder rollover prediction model be divided into two processes: pre-training and training, and sets corresponding hyperparameters.

[0169] During the pre-training phase, only data loss is used for initial training, allowing PINN to initially learn the time-series features of the sensor signals. PINN's BiLSTM-Attention is the core structure, and the Adam optimizer is used for pre-training to obtain stable initial weights for model training. Its main parameters are shown in the table below.

[0170] Table 1 Model training parameters

[0171]

[0172] During the pre-training phase, the loss function is the data loss function Loss. pre_data The data loss term measures the deviation between the model's predicted signal and the actual measured signal. Its objective is to minimize the error between the predicted result and the measured data, enabling the network to fully learn the time-series features of the signal. Its expression is:

[0173]

[0174] in, This is represented as the length of the data sample. This represents the displacement signal of the eddy current sensor predicted by the physical information neural network, where x is the displacement signal obtained through actual measurement.

[0175] Building upon the pre-training phase, the training phase further introduces a physical loss term. By weightedly combining data loss and physical loss, a fusion optimization of data-driven and physical constraints is achieved, thereby improving the model's physical interpretability and predictive stability. Based on the force and torque balance equations in S12, the physical loss function in this study can be further constructed. Since the cylinder overturning angle lacks an explicit analytical expression, this paper uses the cylinder overturning angle obtained from the eddy current sensor displacement predicted by PINN as the state estimate. This is substituted into the torque balance equation to calculate the physical residual. This residual characterizes the degree to which the predicted state deviates from the true physical equilibrium conditions and is a key indicator for evaluating the model's interpretability and physical consistency. By minimizing the physical loss during training, the error amplification effect in state inversion can be suppressed, allowing PINN to maintain mechanical consistency under multiple operating conditions. This improves the stability and reliability of the cylinder overturning angle estimation, providing more reliable state information for subsequent degradation analysis and risk assessment. Physical Loss phy The expression is:

[0176]

[0177] in, Represented as a norm operator, This represents the cylinder rollover angle predicted by a physical information neural network.

[0178] Data loss during training phase data Loss on data loss during pre-training phase pre_dataSimilarly, the physical model for physical loss is the oil pressure-cylinder overturning angle model established in S1. The cylinder overturning angle obtained from the displacement of the eddy current sensor predicted by the physical neural network is input into the torque balance equation established in S12 to calculate the physical loss. phy The value of the total loss function. total Loss for data loss data and physical loss phy weighted combination

[0179]

[0180] in, The weighting factor is used to balance data accuracy and physical consistency. By introducing the oil pressure-cylinder rollover angle model, a dynamic mechanism reflecting cylinder rollover is added, thereby significantly improving the physical interpretability and prediction accuracy of the model.

[0181] S5 specifically involves: acquiring actual oil pressure signal data, inputting the oil pressure signal data into the PINN trained in step S4 and predicting the displacement of the eddy current sensor, and converting the eddy current sensor displacement signal according to the formula in step S24 to obtain the cylinder overturning angle.

[0182] To objectively evaluate the generalization ability and engineering reliability of the prediction method of this invention across operating conditions and health states, after the model training was completed, oil pressure signal data and eddy current sensor displacement data collected from distribution plates with different wear levels were used for testing and verification. By inputting oil pressure signals and predicting eddy current sensor displacement, the evaluation results are as follows.

[0183] Figure 5 The figure presents the displacement prediction results of the eddy current sensor under a typical operating condition of 2500 rpm and 29 MPa. This condition lies in the central region of all 25 speed-pressure combinations, representing the most common operating load level of the axial piston pump in a typical mission profile. Therefore, it is suitable as a benchmark condition to demonstrate the predictive capability of the PINN model under normal service conditions. As can be seen from the figure, the PINN model can accurately reconstruct the displacement change of the eddy current sensor over time. The predicted curves are highly consistent with the measured results in terms of amplitude, phase, and trend, without phase shift or abnormal fluctuations. This high consistency indicates that the PINN model can effectively capture minute displacement changes related to overturning behavior, helping to improve the sensitivity of early anomaly detection. The physical constraints introduced into the PINN model significantly enhance the stability and physical rationality of the time-domain prediction, enabling the PINN model to maintain reliable outputs even under pressure pulsations and noise interference, providing a solid foundation for subsequent reliability assessments.

[0184] As can be seen from the typical operating condition evaluation results in Table 2, the PINN model can maintain [performance] at 2500 rpm and 29 MPa. A tiny error of magnitude, where the MSE stabilizes at... The magnitude of the accuracy indicates that the PINN model has a good ability to distinguish minute changes in displacement signals. This level of accuracy can effectively capture slight shifts that appear in the early stages of overturning behavior, which has practical engineering significance for subsequent risk identification and health status monitoring. In addition, the error distribution among the various indicators is consistent and there is no significant deviation, reflecting the stability and reliability of the model output, and it can be used as a reliable input in reliability assessment.

[0185] The evaluation results under this typical working condition show that physical constraints play an effective role in enhancing the temporal consistency of the model, enabling it to maintain robust performance under dynamic loads and noise interference.

[0186] Table 2 Evaluation Results of Typical Working Conditions

[0187]

[0188] In the comprehensive evaluation of all 25 speed and pressure combinations, the PINN model demonstrated consistent and robust characteristics in terms of error level, goodness of fit, and output stability, reflecting its excellent cross-condition adaptability to the complex dynamic behavior of hydraulic pumps. Figure 6 .

[0189] Regarding error levels, the MAE of the prediction indicators for each operating condition remained stable within the range of 0.002 to 0.008, with some operating conditions reaching a minimum of 0.0018; the MSE of the prediction indicators for each operating condition were mostly distributed within... to The order of magnitude of the error distribution is evident; the RMSE of the predicted indicators for each operating condition consistently remains within the range of 0.003 to 0.01. This indicates a highly concentrated error distribution, demonstrating that the model maintains consistent statistical performance under different load and speed conditions. This consistency is particularly important for reliability assessment, as it reduces the risk of prediction deviations due to changes in operating conditions and helps improve the reliability of the PINN model as a health monitoring input. Regarding goodness of fit, the R² for most combined operating conditions is higher than 0.80, and the R² for some typical operating conditions reaches 0.93 to 0.96, indicating that the PINN model can stably capture the key nonlinear relationship between oil pressure signals and rollover behavior.

[0190] Figure 7 The results of the PINN model's prediction of the cylinder rollover angle are presented. From Figure 7 As can be seen from (a), the prediction error distribution of the cylinder overturning angle is relatively concentrated, and the prediction points are stably distributed around y=x, indicating that the PINN model can accurately predict the actual change law of the cylinder overturning angle. Figure 7 (b) The mean error of the overturning angle under all operating conditions was stably controlled within the range of 0.24% to 5.7%, with approximately two-thirds of the operating conditions below 3%. This error level is sufficient to reflect small changes in the cylinder block overturning angle, enabling the model to not only accurately track transient dynamic processes but also robustly characterize long-term statistical features. In the main operating range of the axial piston pump (1500 to 2700 rpm), the error further converged, indicating that the model possesses higher reliability and generalization ability under typical task conditions.

[0191] Overall, the PINN model demonstrated high accuracy, strong consistency, and good physical plausibility across all 25 operating conditions. It not only accurately reconstructed the dynamic displacement of the eddy current sensor but also stably predicted the cylinder rollover angle, a key precursor parameter in dynamics. Its error variation trend remained consistent with the physical behavior of the actual system, making the model a reliable input for rollover risk identification, health monitoring, and remaining life prediction. This demonstrates practical engineering value for the reliability analysis of safety-critical hydraulic systems.

[0192] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A method for predicting the overturning angle of an axial piston pump cylinder based on a physical information neural network, characterized in that, Includes the following steps: S1: Establish a hydraulic pressure-cylinder tilting angle model for the axial piston pump; specifically: S11: Establish an OXYZ spatial rectangular coordinate system with the intersection of the plane where the distributor plate and the cylinder block contact each other and the main shaft of the axial piston pump as the origin O. The plane where the distributor plate and the cylinder block contact each other is the XOY plane. The Y-axis points in the same direction as the outer dead point of the axial piston pump, and the Z-axis points along the axis towards the swashplate. S12: Establish a hydraulic pressure-cylinder tilting angle model for when an axial piston pump tilts, with the cylinder block subjected to an axial clamping force F in the Z-axis direction. i Oil film support force F between the distributor plate and the cylinder block h The residual support force F generated when the cylinder block overturns and comes into contact with the distributor plate. r Satisfying the force balance equation ； The cylinder block is subjected to an overturning moment M in the XOY plane by the slipper plunger assembly. o The anti-overturning moment M generated by the oil film between the distributor plate and the cylinder block a and the reaction torque M generated by the distribution plate r Satisfying the torque balance equation ； R1 represents the inner radius of the inner sealing ring of the distribution plate, R2 represents the outer radius of the inner sealing ring of the distribution plate, R3 represents the inner radius of the outer sealing ring of the distribution plate, and R4 represents the outer radius of the outer sealing ring of the distribution plate; M ox M oy M respectively o The components in the X and Y directions, M ay M represents a The component in the Y direction, M a The component in the X direction is 0, M r Indicates the reaction torque; Among them, the axial clamping force F i The oil pressure F in the axial piston pump p With the central spring force F s Together constitute; The contact pressure distribution when the cylinder block and distributor plate come into contact under three conditions—slight overturning, severe overturning, and complete overturning—is simplified into a linear pressure distribution model. In the cases of slight and severe overturning, this linear pressure distribution model is negatively correlated with the cylinder block overturning angle. Piecewise integration of the linear pressure distribution model under the three overturning conditions yields F. r (R1,R2),F r (R3,R4) and M r (R1,R2), M r (R3,R4) are then substituted into the force balance equation and the torque balance equation to establish the oil pressure-cylinder overturning angle model. S2: Conduct experiments on the axial piston pump under different speed and pressure conditions, obtain oil pressure signal data and cylinder displacement signal data at different cylinder overturning angles, and convert the cylinder displacement signal data into cylinder overturning angle signal data. S3: Preprocess the oil pressure signal data obtained in S2 to ensure the robustness of the subsequent training process of the physical information neural network PINN and the temporal correlation of the oil pressure signal data, and to eliminate the influence of the oil pressure signal data dimension on the model. S4: The PINN is trained using the data preprocessed in S3; the PINN takes a periodically changing high-frequency oil pressure signal as input and outputs a cylinder displacement signal that changes periodically accordingly. S5: Obtain the oil pressure signal data in the axial piston pump to be predicted, input the oil pressure signal data into PINN trained by step S4 and predict the cylinder displacement, and convert the cylinder displacement to obtain the cylinder overturning angle.

2. The prediction method according to claim 1, characterized in that, Step S2 specifically includes: S21: Select multiple sets of speed conditions and multiple sets of pressure conditions to form a full-coverage test condition that extends from low pressure and low speed to high pressure and high speed, and conduct experiments on each set of conditions in sequence. S22: The oil pressure signal data in the axial piston pump during each set of working condition tests is obtained by pressure sensors installed at the inlet, outlet and leakage ports of the axial piston pump. S23: Install a set of eddy current sensors X1, X3 and X2, X4 on two planes parallel to the XOY plane on the axial piston pump. The cylinder displacement signal data is characterized by the displacement signal of the eddy current sensor and the displacement signal of the eddy current sensor is filtered. S24: Convert the eddy current displacement signal data processed in S23 to obtain the cylinder overturning angle signal data. The formula is as follows: ； in, Indicates the cylinder tilt angle. , , , These represent the displacement signals of the four eddy current sensors, with z1 and z2 representing the distances between eddy current sensors X1 and X2, and between X3 and X4, along the Z-axis.

3. The prediction method according to claim 1, characterized in that, Step S3 specifically includes: S31: The 0.5% and 99.5% quantiles are used to smooth the high and low pressure oil pressure signal data; S32: A fourth-order low-pass filter is used to suppress high-frequency noise in the original measured high-frequency pressure signal data, and the Min-Max normalization method is used to normalize the oil pressure signal data.

4. The prediction method according to claim 2, characterized in that, In step S4, the neural network in PINN includes a bidirectional long short-term memory network BiLSTM and an attention module; The periodically changing high-frequency oil pressure signal is input into the BiLSTM in PINN. In the feature transformation layer of BiLSTM, sine and cosine functions are selected as feature transformation basis functions. The initial phase of the feature function is set according to the phase characteristics of the input high-frequency oil pressure signal, and the frequency of the feature function is selected according to the physical rotation frequency of the axial piston pump and the reciprocating motion frequency of the piston. The four independent output nodes set in the BiLSTM of PINN correspond to the displacement signals of the four sensors, realizing parallel prediction and physical consistency modeling of multi-point displacement states.

5. The prediction method according to claim 1, characterized in that, The training of PINN in step S4 includes a pre-training phase and a training phase. In the pre-training phase, only data loss is used for initial training, so that PINN can initially learn the time series features of sensor signals. Then, in the training phase, a physical loss term is introduced. By weighted combination of data loss and physical loss, the fusion optimization of data-driven and physical constraints is achieved, thereby improving the physical interpretability and prediction stability of the model.

6. The prediction method according to claim 5, characterized in that, The data loss during the pre-training phase is: ； in, Represented as the length of the data sample. This represents the displacement signal of the eddy current sensor predicted by the physical information neural network, where x is the displacement signal obtained through actual measurement.

7. The prediction method according to claim 6, characterized in that, The total loss function during the training phase. total Loss for data loss data and physical loss phy Weighted combination: ； in, This is a weighting factor used to balance data precision and physical consistency; Loss data With Loss pre_data same.

8. A tilting angle prediction system for an axial piston pump based on a physical information neural network, applicable to the prediction method described in any one of claims 1-7, characterized in that, It includes an axial piston pump, a test bench, a control system, a sensor measurement system, and a data prediction system; the axial piston pump is fixed on the test bench; the control system is used to control the speed and pressure conditions of the axial piston pump. The sensor measurement system includes a pressure sensor and an eddy current sensor. The pressure sensor is installed at the inlet, outlet, and leakage ports of the axial piston pump and is used to measure the oil pressure signal inside the cylinder at different cylinder tilt angles. There are two sets of eddy current sensors, two in each set. Each set of eddy current sensors is installed on two planes on the axial piston pump that are parallel to the plane where the distributor plate and the cylinder block contact. The eddy current sensors are used to measure the cylinder displacement signal at different cylinder tilt angles. The data prediction system deploys a physical information neural network, which reads data from the sensor measurement system and outputs a predicted cylinder displacement signal. The data prediction system calculates the predicted cylinder overturning angle based on the predicted cylinder displacement signal data.

9. The prediction system according to claim 8, characterized in that, The eddy current sensor is perpendicular to the axis in the radial direction, and each group of eddy current sensors is kept horizontal in the axial direction; the included angle between two eddy current sensors on the same plane is 135°, the distance between the two mounting planes of the eddy current sensor is 35mm, the initial distance between the eddy current sensor probe and the axial piston pump cylinder is 0.5mm, and a sealing ring is installed between the nut of the eddy current sensor and the housing of the axial piston pump, and a double nut structure is adopted to prevent the eddy current sensor from loosening.

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