Fuel gear pump behavior prediction method based on mechanism-data fusion
By employing a mechanism-data fusion approach, combining fuel pump integrated test bench data and co-kriging modeling, the prediction challenge of fuel gear pumps under high temperature and high pressure conditions was solved, achieving high-precision and low-cost prediction results, and supporting the performance evaluation and health management of aero-engines.
Patent Information
- Application Number
- CN202511487987.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-17
- Publication Date
- 2026-01-09
AI Technical Summary
Existing methods for predicting the behavior of fuel gear pumps are difficult to accurately describe the strong coupling effect of fluid-structure-thermal multiphysics fields under high temperature, high pressure, and high speed conditions, leading to microscale contact fatigue and cavitation phase transformation erosion of gear pairs. Traditional mechanism models are prone to failure, and data-driven methods require a large amount of highly reliable data and are prone to overfitting, making them unable to cope with untrained conditions.
A mechanism-data fusion-based prediction method for fuel gear pump behavior is established. Multi-condition data are obtained through a comprehensive fuel pump test bench. By combining the co-kriging modeling method with a small amount of high-confidence experimental data, a hybrid prediction model is established to improve prediction accuracy and generalization ability.
It significantly improves the accuracy and generalization ability of fuel gear pump behavior prediction, reduces experimental costs, and provides a reliable basis for the performance evaluation and health management of aero-engines.
Smart Images
Figure CN121302899A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of fuel gear pump technology for aero-engines, and in particular to a fuel gear pump behavior prediction method based on mechanism-data fusion. Background Technology
[0002] In next-generation advanced aero-engines, the fuel gear pump, as a core power component, operates under extreme conditions of high temperature, high pressure, and high speed for extended periods. The strong coupling effect of fluid-structure-thermal multiphysics fields within the pump accelerates the accumulation of nonlinear damage such as microscale contact fatigue and cavitation phase transformation erosion in the gear pairs, leading to system performance degradation and even sudden catastrophic failures. Against this backdrop, predicting the behavior of the fuel gear pump is of urgent engineering necessity. Existing methods for predicting gear pump behavior fall into two categories: traditional mechanistic model methods and data-driven prediction methods.
[0003] Traditional mechanistic modeling methods are based on exact differential equations, but they struggle to fully describe the strong coupling between the flow field, structure, and thermal field. For example, when a gear pump rotates at high speed, the interaction between fuel cavitation phase change and gear contact fatigue leads to the accumulation of nonlinear damage. However, existing models often neglect cavitation effects or simplify them with only ideal fluid assumptions, resulting in pressure pulsations and flow prediction errors. Furthermore, these models assume constant inlet pressure and stable rotational speed, but dynamic disturbances such as fuel pulsations and filter blockages in actual operating conditions are not included, making the models prone to failure under transient conditions and lacking in reliability.
[0004] While purely data-driven methods can describe the nonlinear characteristics within a fuel pump by constructing a surrogate model, they require extensive training with highly reliable data. However, samples of fuel gear pump failures are relatively scarce. When training samples are insufficient, the model is prone to overfitting. For example, relying solely on a dataset of 30 geometric parameters to predict the impact of top clearance error on flow pulsation will result in prediction errors exceeding permissible limits. Furthermore, purely data-driven models struggle to handle untrained operating conditions. For instance, when inlet pressure suddenly increases or fuel viscosity abruptly changes, the model, lacking integration of physical constraints such as changes in the fuel's elastic modulus, cannot accurately predict volumetric efficiency degradation based on historical data. Summary of the Invention
[0005] To overcome the above technical problems, the present invention aims to provide a fuel gear pump behavior prediction method based on mechanism-data fusion. Based on the dynamic evolution law of the internal flow field of the gear pump and the multi-path leakage characteristics, an accurate mechanism model of the fuel gear pump is established. External characteristic data under multiple operating conditions are collected through a comprehensive fuel pump test bench. Using the co-kriging modeling method, a small amount of external characteristic experimental data of the fuel pump under multiple operating conditions is used as a high-confidence input, and the prediction results of the mechanism model are used as auxiliary input to establish a hybrid prediction model of the fuel gear pump that integrates the advantages of mechanism and data, which significantly improves the prediction accuracy and generalization ability.
[0006] The technical solution adopted in this invention is: A method for predicting the behavior of a fuel gear pump based on mechanism-data fusion includes the following steps; Step 1: Establish an internal flow mechanism model for the fuel gear pump; this model is used to obtain low-confidence data based on physical constraints, serving as an auxiliary training dataset for the fuel gear pump mechanism-data fusion prediction model. Step 2: Acquisition of multi-condition experimental data of fuel gear pump. The experimental data is used as high-confidence data for training the fuel gear pump mechanism-data fusion prediction model to enhance the nonlinear fitting ability of the hybrid model. Step 3: Establish a fuel gear pump hybrid behavior prediction model based on co-kriging. Utilize the auxiliary training dataset obtained from the above-mentioned mechanism model and the high-confidence dataset obtained from the multi-condition test bench. Combine the co-kriging method with the physical boundary constraints of the mechanism model and the strong nonlinear fitting capability driven by data to train the fuel gear pump mechanism-data fusion prediction model, thereby achieving high-precision behavior prediction of the fuel gear pump.
[0007] Step one specifically involves: The internal flow mechanism model of a fuel gear pump analyzes the working principle of the fuel gear pump and constructs physical constraints based on the control volume method. Considering mass conservation and fluid state, the pressure changes within each control volume are defined by differential equations. The flow direction within the fuel gear pump is strictly driven by pressure difference, and the flow exchange mechanism between control volumes is defined by laminar flow equations and throttling equations, resulting in clear physical boundaries. However, in establishing the internal flow field model of the gear pump, it is unavoidable to make simplifications to some physical phenomena, such as the fact that the oil properties within the control volume only change with time, leading to errors between the simulation and reality. However, simulation data is readily available. Therefore, the simulation data of the fuel pump internal flow mechanism model can serve as a low-confidence auxiliary dataset with a large data base but low accuracy, participating in the training of the mechanism-data fusion model and providing certain physical boundaries for the fusion model.
[0008] The internal flow field of the gear pump is divided into a high-pressure cavity, a low-pressure cavity, a driving gear cavity, and a driven gear cavity. The high-pressure cavity corresponds to the outlet pressure-dominant region and is the source of oil output and high-pressure leakage. The low-pressure cavity is related to the inlet pressure region and is responsible for oil intake and receiving leakage backflow. The distinction between the driving gear cavity and the driven gear cavity focuses on the dynamic oil encapsulation of the gear rotation drive: the driving gear cavity reflects the volume change, pressure evolution and oil trapping phenomenon of the oil in the tooth groove of the driving gear, while the driven gear cavity independently characterizes the equivalent process of the driven gear. For the oil suction cavity and the oil discharge cavity, the pressure characteristic equations for the oil discharge cavity and the oil suction cavity are as follows: (1) For both the driving and driven tooth cavities, the pressure characteristic equation inside the tooth cavity during gear rotation is as follows: (2) In the above formula, To control the volume of the cavity, For the instantaneous pressure of the cavity, For effective bulk modulus, The flow rate into the cavity. The flow rate into the cavity; The flow characteristics modeling of the internal flow field of the fuel gear pump will focus on the driving and driven gear cavities. These cavities exchange flow with other control cavities through various connections such as clearances, unloading grooves, and cavity boundaries. Inflow into the gear cavity is defined as positive, and outflow as negative. For the flow of oil between adjacent gears through the tooth tip clearance and end face clearance, the oil flow in these clearances is considered laminar flow. The laminar flow in the gear end face clearance and tooth tip clearance is expressed as follows: (3) In the formula, These represent the oil film widths of the end face clearance and tooth tip clearance, respectively. These represent the oil film thicknesses for the end face clearance and the tooth tip clearance, respectively. Indicates hydraulic pressure difference. These represent the oil film lengths for the end face clearance and the tooth tip clearance, respectively. For fluid dynamic viscosity, These represent the oil film shear rates of the end face clearance and the inter-tooth clearance, respectively. The flow of oil in the inter-tooth volume, high-pressure zone, low-pressure zone, and the inter-tooth volume between the driving and driven gears in the meshing region cannot be considered laminar flow. A throttling equation is used to describe its flow: (4) In the formula, Indicates the throttling coefficient. Indicates the throttling area. Indicates the pressure difference across the front and rear. This represents the oil density. In summary, a flow mechanism model for a fuel gear pump based on the control volume method can be derived as follows: (5).
[0009] Step two specifically involves: The speed of the fuel gear pump is precisely adjusted by the coordinated control of the variable frequency motor and the gearbox. At the same time, high-precision pressure and flow sensors are used to monitor the pump inlet and outlet pressure and flow parameters in real time. The entire system is equipped with auxiliary units such as fuel supply device and back pressure regulating valve to ensure the stability of the test environment and the reliability of data. The various components of the test bench are interconnected through power transmission, fuel flow, and monitoring systems: the motor output shaft drives the gearbox, which in turn connects to the fuel gear pump main shaft via a transmission mechanism to provide rotational power; fuel enters the fuel gear pump suction port from the external fuel tank after being filtered for impurities by the inlet oil filter, and the pressurized fuel flows out from the pump outlet, passing sequentially through an outlet pressure sensor that monitors the outlet pressure in real time, a solenoid valve used to simulate load changes or start / stop control, and a flow sensor that measures the actual output flow rate, before finally returning to the fuel tank or connecting to the downstream load system; at the same time, an inlet pressure sensor is directly connected to the pump suction pipe to monitor the inlet pressure and prevent cavitation, and a speed sensor is installed on the motor output shaft or gearbox drive shaft to monitor the rotational speed in real time, forming a complete closed-loop test system.
[0010] The experiment used rotational speed, inlet pressure, and outlet pressure as key control variables. The working conditions were constructed by adjusting the motor speed and hydraulic circuit back pressure, and the data acquisition system was used to record the variation of the pump's average outlet flow rate. For the acquired experimental data, data preprocessing was performed using... The criteria exclude outliers that may be caused by sensor malfunctions or sudden changes in operating conditions. The valid data range is... : (6) After removing outliers, the experimental data were standardized using Z-scores to ensure a mean of 0 and a standard deviation of 1. (7) In the above formula, The mean of the sample; The total number of samples; Standard deviation; For the sample; These are the samples after normalization.
[0011] Step three specifically involves: The collaborative model, based on Bayesian theory, fuses data of varying confidence levels through an autoregressive model to obtain accurate prediction results. The operating conditions constructed using the fuel pump integrated test platform are used as the high-confidence data sample set, denoted as... Different rotational speeds, inlet pressures, and outlet pressures were selected as input variables for the internal flow mechanism model of the fuel gear pump. These variables were used as a low-confidence data sample set, denoted as... Then we have: (8) , Let x be the sample point set; In the formula, The number of low-confidence sample points; The number of high-confidence sample points, of which are ; The average pump outlet flow rate obtained from the experiment is denoted as... The average pump outlet flow rate obtained based on the internal flow mechanism model of the fuel gear pump is denoted as... : (9) , Physically, both refer to the average outflow rate. High-confidence data can be represented by low-confidence data using the following formula: (10) in , These represent the local characteristics of high-confidence and low-confidence data, respectively. for and difference; For the co-kriging model, its covariance matrix can be expressed as: (11) In the formula, and Random variables and The mean squared error; Correlation moments; two correlation functions and Therefore, more model parameters need to be trained: , , , and scaling factor This is obtained by maximizing the following log-likelihood function. , , and Maximum likelihood estimation (MLE): (12) The above formula is correct. and Taking the derivative and setting the reciprocal to zero, we get: (13) The set log-likelihood function is then as follows: (14) and The value can be obtained by finding the maximum value of the above formula. Here, the same method as Kriging's approach is used for maximum likelihood estimation. To estimate the parameters... , , and ,definition: (15) ye, yc, and Xe have been defined, and ρ is the defined proportionality coefficient; in for In Similarly, for values at the same position, we can have: (16) Similarly, the maximum likelihood estimation method can be used to obtain... mean Co-Kriging model at unknown points The estimated value and the mean squared error at the location can be expressed as: (17) In the formula, Unknown point With known sample points The column vector of covariance between them; .
[0012] The beneficial effects of this invention are: This invention relates to the field of fuel gear pump technology for aero-engines, and provides a mechanism-data fusion-based method for predicting the behavior of fuel gear pumps. This method combines physical mechanism modeling with experimental data-driven approaches. First, it establishes an internal flow mechanism model of the fuel gear pump based on the dynamic evolution of the internal flow field and multi-path leakage characteristics. Simultaneously, it acquires measured external characteristic data under multiple operating conditions using a comprehensive fuel pump test bench. Based on this, a co-kriging modeling method is employed, using the prediction results of the mechanism model as auxiliary variables and establishing a correlation with a small amount of high-confidence experimental data to construct a hybrid prediction model integrating mechanism and data. This fusion method retains the ability of the mechanism model to characterize the physical essence while correcting model errors through experimental data, significantly improving prediction accuracy. The mechanism model provides physical constraints for data-driven approaches, while the experimental data validates and calibrates the mechanism model. The complementary advantages of both provide a reliable basis for predicting and optimizing the behavior of fuel gear pumps. Furthermore, this method effectively improves the response accuracy of the hybrid prediction model under multiple operating conditions through internal flow mechanism modeling and data feedback correction mechanism, while significantly reducing experimental costs, providing an effective solution for performance evaluation and health management of aero-engine fuel gear pumps. Attached Figure Description
[0013] Figure 1 This is a flowchart of the invention process.
[0014] Figure 2 This is a schematic diagram showing the division of the control cavity.
[0015] Figure 3 This is a schematic diagram of end face leakage and top gap leakage.
[0016] Figure 4 This is a test bench for the external characteristics of fuel gear pumps.
[0017] Figure 5 This is a schematic diagram comparing the predictions of the mechanistic model and the co-kriging model. Detailed Implementation
[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0019] like Figure 1 As shown, Part 1: Establishing an internal flow mechanism model for a fuel gear pump. To study the dynamic evolution of the internal flow field of a fuel gear pump and accurately capture the pressure state, fluid transport dynamics, and key physical processes in different regions, based on the structural characteristics and working principle of the gear pump, its internal flow field is divided into a high-pressure cavity, a low-pressure cavity, an active gear cavity, and a driven gear cavity, such as... Figure 2 As shown, the high-pressure cavity corresponds to the outlet pressure-dominant region and is the source of oil output and high-pressure leakage; the low-pressure cavity is associated with the inlet pressure region, responsible for oil intake and receiving leakage backflow. The division between the driving and driven gear cavities focuses on the dynamic oil encapsulation driven by gear rotation: the driving gear cavity reflects the volume change, pressure evolution, and oil trapping phenomenon of the oil in the driving gear tooth groove, while the driven gear cavity independently represents the equivalent process of the driven gear. This division emphasizes the differences in fluid transport characteristics, oil trapping dynamics, and leakage paths caused by the difference in rotation direction and position between the two gears, avoiding simplification errors due to symmetry. The four-cavity model, by isolating the high- and low-pressure zones from the rotating transport body, provides a physical basis for analyzing the dynamic evolution laws of leakage flow, oil trapping impact, pressure pulsation, and volumetric efficiency, revealing the intrinsic mechanism of the transient flow field.
[0020] The properties of the fluid within the control volume, such as pressure, density, and temperature, change with the rotation of the gears. The fluid characteristics within each control volume are considered uniform and change only over time. Pressure transmission and flow exchange occur between the control cavities through various connections based on the law of mass conservation and the flow continuity equation. The pressure and flow characteristics of the internal flow field of the fuel gear pump are modeled below.
[0021] For the oil suction cavity and oil discharge cavity, their volumes remain essentially constant during the rotation of the gear pump; only the flow rate exchanges with other control cavities occur. Therefore, the pressure characteristic equations for the oil discharge cavity and oil suction cavity are as follows: (1) For both the driving and driven gear cavities, during gear rotation, there is an inflow and outflow of oil between the internal oil and other adjacent control volumes. Furthermore, due to gear meshing, the inter-tooth volume changes. Therefore, the pressure characteristic equation inside the gear cavity is as follows: (2) In the above formula, To control the volume of the cavity, For the instantaneous pressure of the cavity, For effective bulk modulus, The flow rate into the cavity. The flow rate into the cavity; The flow characteristics modeling of the internal flow field of the fuel gear pump will take the driving and driven gear cavities as the target. The gear cavities exchange flow with other control cavities through various connections such as gaps, unloading grooves, and cavity boundaries. The flow into the gear cavity is defined as positive, and the flow out of the gear cavity is defined as negative.
[0022] like Figure 3 As shown, for the flow of oil in the inter-tooth volume through the tooth tip clearance and end-face clearance, since the thickness, curvature, and width-to-length ratio of the oil film are negligible, the oil flow in the tooth tip clearance and end-face clearance can be considered as laminar flow. The laminar flow in the gear end-face clearance and tooth tip clearance can be expressed as: (3) In the formula, These represent the oil film widths of the end face clearance and tooth tip clearance, respectively. These represent the oil film thicknesses for the end face clearance and the tooth tip clearance, respectively. Indicates hydraulic pressure difference. These represent the oil film lengths for the end face clearance and the tooth tip clearance, respectively. For fluid dynamic viscosity, These represent the oil film shear rates of the end face clearance and the inter-tooth clearance, respectively. The flow of oil in the inter-tooth volume, high-pressure zone, low-pressure zone, and the inter-tooth volume between the driving and driven gears in the meshing region cannot be considered laminar flow. A throttling equation is used to describe its flow: (4) In the formula, Indicates the throttling coefficient. Indicates the throttling area. Indicates the pressure difference across the front and rear. This represents the oil density. In summary, a flow mechanism model for a fuel gear pump based on the control volume method can be derived as follows: (5).
[0023] The first part aims to deeply reveal the working principle and complex internal flow field characteristics of a fuel gear pump, laying the foundation for subsequent mechanism-data fusion models. It can dynamically simulate core working processes such as gear meshing, volume changes, oil trapping, and leakage flow, and quantitatively analyze flow pulsation, pressure shocks, and volumetric efficiency. More importantly, it can visualize and quantify microscopic flow field characteristics that are difficult to measure directly in experiments, such as gap leakage paths, local pressure distribution, and cavitation regions, revealing their formation mechanisms. The key effect of this model is its ability to efficiently and cost-effectively generate "low-confidence" simulation data covering a wide range of operating conditions. This data contains the physical laws of the system, providing crucial physical constraints, prior knowledge, and revealing the physical correlations between variables for subsequent fusion of high-confidence experimental data using co-kriging. Ultimately, this supports the construction of a hybrid model that combines physical interpretability with high predictive accuracy.
[0024] Part Two: Acquisition of Multi-condition Experimental Data for Fuel Gear Pump To comprehensively study the performance characteristics of fuel gear pumps under different operating conditions, this study constructed a high-precision test platform, such as... Figure 4 As shown, this platform achieves precise adjustment of the fuel gear pump speed through the coordinated control of a variable frequency motor and gearbox. Simultaneously, it employs high-precision pressure and flow sensors to monitor the pump inlet and outlet pressures and flow parameters in real time. The entire system is equipped with auxiliary units such as a fuel supply device and a back pressure regulating valve to ensure the stability of the test environment and the reliability of the data.
[0025] The various components of the test bench are interconnected through power transmission, fuel flow, and monitoring systems: the motor output shaft drives the gearbox, which in turn connects to the fuel gear pump main shaft via a transmission mechanism to provide rotational power; fuel enters the fuel gear pump suction port from the external fuel tank after being filtered for impurities by the inlet oil filter, and the pressurized fuel flows out from the pump outlet, passing sequentially through an outlet pressure sensor that monitors the outlet pressure in real time, a solenoid valve used to simulate load changes or start / stop control, and a flow sensor that measures the actual output flow rate, before finally returning to the fuel tank or connecting to the downstream load system; at the same time, an inlet pressure sensor is directly connected to the pump suction pipe to monitor the inlet pressure and prevent cavitation, and a speed sensor is installed on the motor output shaft or gearbox drive shaft to monitor the rotational speed in real time, forming a complete closed-loop test system.
[0026] The experiment used rotational speed, inlet pressure, and outlet pressure as key control variables. Ten typical operating conditions were constructed by adjusting the motor speed and hydraulic circuit back pressure, and the variation of the pump's average outlet flow rate was recorded using a data acquisition system. The experimental results are shown in Table 1. For the acquired experimental data, data preprocessing was performed using... The criteria exclude outliers that may be caused by sensor malfunctions or sudden changes in operating conditions. The valid data range is... : (6) After removing outliers, the experimental data were standardized using Z-scores to ensure a mean of 0 and a standard deviation of 1. (7) In the above formula, The mean of the sample; The total number of samples; Standard deviation; For the sample; These are the samples after normalization.
[0027] This provides high-confidence data for training the subsequent co-Kriging agent model.
[0028] Part Three: Establishing a Predictive Model for Fuel Gear Pump Mixing Behavior Based on Co-kriging The collaborative model, based on Bayesian theory, fuses data of varying confidence levels through an autoregressive model to obtain accurate prediction results. Ten typical operating conditions constructed from the fuel pump integrated test platform are used as a high-confidence data sample set, denoted as... Different rotational speeds, inlet pressures, and outlet pressures were selected as input variables for the internal flow mechanism model of the fuel gear pump. These variables were used as a low-confidence data sample set, denoted as... Then we have: (8) , Let x be the sample point set; In the formula, The number of low-confidence sample points; The number of high-confidence sample points, of which are ; The average pump outlet flow rate obtained from the experiment is denoted as... The average pump outlet flow rate obtained based on the internal flow mechanism model of the fuel gear pump is denoted as... : (9) , Physically, both refer to the average outflow rate. High-confidence data can be represented by low-confidence data using the following formula: (10) in , These represent the local characteristics of high-confidence and low-confidence data, respectively. for and difference; For the co-kriging model, its covariance matrix can be expressed as: (11) In the formula, and Random variables and The mean squared error; For correlation moments.
[0029] There are two related functions here. and Therefore, more model parameters need to be trained: , , , and scaling factor Since we assume that low-confidence data and high-confidence data are independent, we can obtain the following log-likelihood function by maximizing it. , , and Maximum likelihood estimation (MLE): (12) The above formula is correct. and Taking the derivative and setting the reciprocal to zero, we get: (13) The set log-likelihood function is then as follows: (14) and The value can be obtained by finding the maximum value of the above formula. Here, the same method as Kriging's approach is used for maximum likelihood estimation. To estimate the parameters... , , and ,definition: (15) ye, yc, and Xe have been defined, and ρ is the defined proportionality coefficient; in for In Similarly, for values at the same position, we can have: (16) Similarly, the maximum likelihood estimation method can be used to obtain... mean Co-Kriging model at unknown points The estimated value and the mean squared error at the location can be expressed as: (17) In the formula, Unknown point With known sample points The column vector of covariance between them; .
[0030] Part Four: Examples The advantages of this invention can be further illustrated by the following design examples. (1) Acquisition of high and low feasibility data and construction of co-kriging model Based on the high-reliability data obtained from the fuel pump integrated test platform, the high-reliability data was normalized to facilitate the subsequent construction of the co-kriging model, as shown in Table 1.
[0031] Table 1 Experimental Data project engine speed / rpm Inlet pressure / MPa Export pressure / MPa Average outlet flow rate (L / min) 1 0 0 0 0 2 0.430 0.395 0.333 0.497 3 0.860 1 0.667 1 4 0.803 1 0.667 0.898 5 0.803 1 0.333 0.957 6 0.028 0 0 0.008 7 1 1 1 0.398 8 0.889 1 0.667 0.988 9 0.574 0.395 0.333 0.651 10 0.344 0.395 0.333 0.377 Low-confidence data were obtained based on the internal flow mechanism model of the fuel gear pump. Due to the large number of low-confidence data, they are not listed here. The sample size of the low-confidence data must be greater than that of the high-confidence data, and the high-confidence sample set must be a subset of the low-confidence sample set. After obtaining the high and low-feasibility datasets, the datasets were Z-score standardized based on Equation (7) using MATLAB, and a co-kriging hybrid prediction model was established.
[0032] (2) Simulation results Ten additional operating conditions different from the training set were selected, and experimental conditions and model boundary conditions were set. Experimental verification and simulation were conducted to verify the accuracy of the data-mechanism fusion-based fuel gear pump behavior prediction model. Figure 5 The figure shows the overall prediction trends of the mechanistic model and the fuel gear pump behavior prediction model based on data-mechanistic fusion. The prediction curve of the hybrid prediction model closely matches the true value, with a consistent fluctuation trend and small error. In contrast, the prediction results of the mechanistic model fluctuate more, especially deviating significantly from the true value at some sample points, indicating a large systematic error. The average relative error of the prediction results of the hybrid prediction model is 6.3%, while the average relative error of the prediction results of the mechanistic model is 19.7%, indicating that the hybrid prediction model has significant advantages in global prediction accuracy and dynamic response by fusing mechanistic priors and data-driven methods.
Claims
1. A method for predicting the behavior of a fuel gear pump based on mechanism-data fusion, characterized in that, Includes the following steps; Step 1: Establish an internal flow mechanism model for the fuel gear pump; this model is used to obtain low-confidence data based on physical constraints, serving as an auxiliary training dataset for the fuel gear pump mechanism-data fusion prediction model. Step 2: Acquisition of multi-condition experimental data of fuel gear pump. The experimental data will be used as high-confidence data for training the fuel gear pump mechanism-data fusion prediction model. Step 3: Establish a fuel gear pump hybrid behavior prediction model based on co-kriging. Utilize the auxiliary training dataset obtained from the above-mentioned mechanism model and the high-confidence dataset obtained from the multi-condition test bench. Combine the co-kriging method with the physical boundary constraints of the mechanism model and the strong nonlinear fitting capability driven by data to train the fuel gear pump mechanism-data fusion prediction model, thereby achieving high-precision behavior prediction of the fuel gear pump.
2. The fuel gear pump behavior prediction method based on mechanism-data fusion according to claim 1, characterized in that, Step one specifically involves: The internal flow field of the gear pump is divided into a high-pressure cavity, a low-pressure cavity, a driving gear cavity, and a driven gear cavity. The high-pressure cavity corresponds to the outlet pressure-dominant region and is the source of oil output and high-pressure leakage. The low-pressure cavity is related to the inlet pressure region and is responsible for oil intake and receiving leakage backflow. The distinction between the driving gear cavity and the driven gear cavity focuses on the dynamic oil encapsulation of the gear rotation drive: the driving gear cavity reflects the volume change, pressure evolution and oil trapping phenomenon of the oil in the tooth groove of the driving gear, while the driven gear cavity independently characterizes the equivalent process of the driven gear. For the oil suction cavity and the oil discharge cavity, the pressure characteristic equations for the oil discharge cavity and the oil suction cavity are as follows: (1) For both the driving and driven tooth cavities, the pressure characteristic equation inside the tooth cavity during gear rotation is as follows: (2) In the above formula, To control the volume of the cavity, For the instantaneous pressure of the cavity, For effective bulk modulus, The flow rate into the cavity. The flow rate into the cavity; The flow characteristics modeling of the internal flow field of the fuel gear pump will focus on the driving and driven gear cavities. These cavities exchange flow with other control cavities through various connections such as clearances, unloading grooves, and cavity boundaries. Inflow into the gear cavity is defined as positive, and outflow as negative. For the flow of oil between adjacent gears through the tooth tip clearance and end face clearance, the oil flow in these clearances is considered laminar flow. The laminar flow in the gear end face clearance and tooth tip clearance is expressed as follows: (3) In the formula, These represent the oil film widths of the end face clearance and tooth tip clearance, respectively. These represent the oil film thicknesses for the end face clearance and the tooth tip clearance, respectively. Indicates hydraulic pressure difference. These represent the oil film lengths for the end face clearance and the tooth tip clearance, respectively. For fluid dynamic viscosity, These represent the oil film shear rates of the end face clearance and the inter-tooth clearance, respectively. The flow of oil in the inter-tooth volume, high-pressure zone, low-pressure zone, and the inter-tooth volume between the driving and driven gears in the meshing region cannot be considered laminar flow. A throttling equation is used to describe its flow: (4) In the formula, Indicates the throttling coefficient. Indicates the throttling area. Indicates the pressure difference across the front and rear. This represents the oil density. In summary, a flow mechanism model for a fuel gear pump based on the control volume method can be derived as follows: (5).
3. The fuel gear pump behavior prediction method based on mechanism-data fusion according to claim 1, characterized in that, Step two specifically involves: The speed of the fuel gear pump is precisely adjusted by the coordinated control of the variable frequency motor and the gearbox. At the same time, high-precision pressure and flow sensors are used to monitor the pump inlet and outlet pressure and flow parameters in real time. The entire system is equipped with auxiliary units such as fuel supply device and back pressure regulating valve to ensure the stability of the test environment and the reliability of data. The various components of the test bench are interconnected through power transmission, fuel flow, and monitoring systems: the motor output shaft drives the gearbox, which in turn connects to the fuel gear pump main shaft via a transmission mechanism to provide rotational power; fuel enters the fuel gear pump suction port from the external fuel tank after being filtered for impurities by the inlet oil filter, and the pressurized fuel flows out from the pump outlet, passing sequentially through an outlet pressure sensor that monitors the outlet pressure in real time, a solenoid valve used to simulate load changes or start / stop control, and a flow sensor that measures the actual output flow rate, before finally returning to the fuel tank or connecting to the downstream load system; at the same time, an inlet pressure sensor is directly connected to the pump suction pipe to monitor the inlet pressure and prevent cavitation, and a speed sensor is installed on the motor output shaft or gearbox drive shaft to monitor the rotational speed in real time, forming a complete closed-loop test system.
4. The method for predicting the behavior of a fuel gear pump based on mechanism-data fusion according to claim 3, characterized in that, The experiment used rotational speed, inlet pressure, and outlet pressure as key control variables. The working conditions were constructed by adjusting the motor speed and hydraulic circuit back pressure, and the data acquisition system was used to record the variation of the pump's average outlet flow rate. For the acquired experimental data, data preprocessing was performed using... The criteria exclude outliers that may be caused by sensor malfunctions or sudden changes in operating conditions. The valid data range is... : (6) After removing outliers, the experimental data were standardized using Z-scores to ensure a mean of 0 and a standard deviation of 1. (7) In the above formula, The mean of the sample; The total number of samples; Standard deviation; For the sample; These are the samples after normalization.
5. The fuel gear pump behavior prediction method based on mechanism-data fusion according to claim 1, characterized in that, Step three specifically involves: The collaborative model, based on Bayesian theory, fuses data of varying confidence levels through an autoregressive model to obtain accurate prediction results. The operating conditions constructed using the fuel pump integrated test platform are used as the high-confidence data sample set, denoted as... Different rotational speeds, inlet pressures, and outlet pressures were selected as input variables for the internal flow mechanism model of the fuel gear pump. These variables were used as a low-confidence data sample set, denoted as... Then we have: (8) , Let x be the sample point set; In the formula, The number of low-confidence sample points; The number of high-confidence sample points, of which are ; The average pump outlet flow rate obtained from the experiment is denoted as... The average pump outlet flow rate obtained based on the internal flow mechanism model of the fuel gear pump is denoted as... : (9) , Physically, both refer to the average outflow rate. High-confidence data can be represented by low-confidence data using the following formula: (10) in , These represent the local characteristics of high-confidence and low-confidence data, respectively. for and difference; For the co-kriging model, its covariance matrix can be expressed as: (11) In the formula, and Random variables and The mean squared error; Correlation moments; two correlation functions and Therefore, more model parameters need to be trained: , , , and scaling factor This is obtained by maximizing the following log-likelihood function. , , and Maximum likelihood estimation (MLE): (12) The above formula is correct. and Taking the derivative and setting the reciprocal to zero, we get: (13) The set log-likelihood function is then as follows: (14) and The value can be obtained by finding the maximum value of the above formula. Here, the same method as Kriging's approach is used for maximum likelihood estimation. To estimate the parameters... , , and ,definition: (15) ye, yc, and Xe have been defined, and ρ is the defined proportionality coefficient; in for In Similarly, for values at the same position, we can have: (16) Similarly, the maximum likelihood estimation method can be used to obtain... mean Co-Kriging model at unknown points The estimated value and the mean squared error at the location can be expressed as: (17) In the formula, Unknown point With known sample points The column vector of covariance between them; .