A Wear Prediction Method for Landing Gear Retraction Mechanism Based on Digital Twin

Abstract

The present invention discloses a method for predicting the wear of a landing gear retraction mechanism based on digital twin. First, a three-dimensional model of the landing gear including geometric dimensions and material properties is established, and a multi-body dynamics simulation model is constructed to simulate the force and wear process of the pin under actual working conditions. The Archard wear calculation model considering key parameters is used to calculate the wear of the pin in the simulation model in real time. On this basis, an uncertainty analysis of the parameters in Archard is carried out, and the parameters are considered to follow a normal distribution. By setting reasonable mean and standard deviation, a prediction model under multivariate uncertainty is established. Finally, based on the digital twin model, the particle filter method is used to initialize the particle swarm, update the particle weights through the state and observation equations, resample to approximate the real state, iteratively update the curve, calibrate the model parameters and state, improve the prediction accuracy, enhance the prediction accuracy and reliability, discover potential wear problems in advance, and provide a basis for the maintenance plan.

Description

Technical Field

[0001] The present invention relates to the technical field of wear reliability prediction of landing gear pin shafts, and particularly to the application of digital twin technology in the aviation industry and a wear prediction and analysis method. Background Art

[0002] With the maturity of the reliability analysis methods and design theories of aircraft fixed structures, the accidents caused by failures of aircraft fixed structures have become increasingly rare. In contrast, the failure problems of moving mechanisms have become increasingly prominent. As a moving mechanism with a relatively long service life, the landing gear retraction mechanism has achieved fruitful results in reliability research based on mechanism kinematics and dynamics at the initial stage of design. However, from the perspective of continuous airworthiness, considering the decisive impact of the landing gear on the takeoff and landing safety of the aircraft, it may be more important to study its reliability based on damage accumulation under time-varying conditions. The pin shafts of the landing gear retraction mechanism are extremely prone to wear due to the frequent takeoffs and landings of the aircraft, which repeatedly bear complex loads and stresses, seriously threatening the normal operation of the landing gear and the flight safety of the aircraft.

[0003] However, there are many deficiencies in the current detection and prediction methods for landing gear pin shaft wear. Traditional manual inspection and measurement methods, such as using calipers and micrometers to measure dimensions and visually inspecting wear marks, although they can initially judge the wear situation, have limited detection accuracy, cannot monitor the wear process in real time, and are even more difficult to predict the wear trend. As the number of landing gear retractions increases, inevitable wear will occur at the key bearings between components, resulting in a reduction in the pin shaft radius, which may further affect the reliability of the retraction mechanism. Studying damage accumulation helps to predict and evaluate the impact of this wear on the performance of the landing gear. With the development of technology, sensor technology has been applied to obtain the operating parameters of the landing gear to infer the wear state of the pin shaft. However, it can only provide partial and indirect information and lacks a comprehensive and accurate understanding of the pin shaft wear process.

[0004] Digital twin technology has attracted much attention in the industrial field and has been applied to aspects such as the health monitoring of aerospace aircraft structures. However, in the field of landing gear pin shaft wear prediction, its application is still in its infancy, and no perfect methods and systems have been formed.

[0005] The limitations of the existing technology in landing gear pin shaft wear prediction pose great risks to the landing gear maintenance and safety guarantee in the aerospace industry. Without being able to accurately predict the pin shaft wear situation, it is difficult to formulate a reasonable maintenance plan, which may lead to increased costs due to over-maintenance or safety accidents due to insufficient maintenance. Therefore, there is an urgent need for a more accurate and effective landing gear pin shaft wear prediction method, which should be able to overcome the deficiencies of the existing technology, comprehensively and accurately predict the wear situation of the pin shaft, and provide strong support for the maintenance of the landing gear and the safe flight of the aircraft. Summary of the Invention

[0006] In order to overcome the limitations of the prior art in predicting the wear of landing gear pin shafts, the present invention aims to provide a wear prediction method for the landing gear retraction mechanism based on digital twin, which can accurately predict the wear condition of the landing gear pin shafts through the wear prediction method combining digital twin technology, and provide a reliable basis for the maintenance of the landing gear and the safe flight of the aircraft.

[0007] The technical solution of the present invention is as follows:

[0008] Step 1: Construct a three-dimensional model of the landing gear retraction mechanism and the corresponding multi-body dynamics model, simulate the retraction and extension frequency of the landing gear, the load distribution, and the motion states of each part of the retraction and extension mechanism, and obtain simulation data;

[0009] Step 2: Embed the Archard wear calculation model considering key factors including normal pressure, pin shaft rotation angle, friction coefficient, and Brinell hardness, calculate the pin shaft wear volume increment V in the multi-body dynamics simulation model in real time, accumulate to obtain the total wear volume, and update the three-dimensional model;

[0010] Step 3: Conduct uncertainty analysis on each key parameter in the Archard wear calculation model, set the key parameters as random variables subject to normal distribution, and determine the value range according to the physical meaning and actual monitoring data; integrate within this range to reach the preset confidence level, and then construct the probability distribution model of the parameters; construct a multivariate random variable matrix according to the probability distribution model of the parameters, generate different parameter combinations through a large number of random samplings, substitute them into the Archard wear calculation model described in Step 2 to calculate the wear values; finally, use probability statistics methods to analyze the wear values, obtain the uncertainty distribution data about the wear amount, construct an accurate wear prediction model, and obtain the wear prediction curve;

[0011] Step 4: Construct a digital twin model, initialize the particles based on the particle filter method, and update the particle weights based on the state and observation equations. On this basis, make the particle state gradually approach the real state through resampling operations. At the same time, continuously iterate and update the wear prediction curve, construct the prior distribution of particles for the model parameters and states, and improve the prediction accuracy.

[0012] Preferably, in Step 1, in order to drive the model to measure the contact force, an actuator driving force is added where F f is the frictional force, F air is the air resistance, and η is the actuator efficiency.

[0013] Preferably, in the 3D modeling software, rigid body models of each component are created based on the geometric dimensions and material property parameters of the landing gear pin shafts, and the connections and interactions between components are simulated through constraint pairs and force elements; the pin shafts are modeled as cylindrical rigid bodies and connected to the surrounding connectors by adding contact; in the dynamic simulation software, considering the connection relationships, motion constraints, and actual working condition load distributions of each component, a multi-body dynamics model is established; the boundary conditions of the multi-body dynamics model are set according to the actual installation configuration of the landing gear, connection stiffness characteristics, and buffer performance parameters; the load distribution is simulated according to characteristics such as different load conditions of the aircraft.

[0014] Preferably, in step 1, based on the retraction and extension frequency of the landing gear, retraction and extension time, aircraft weight distribution data, landing gear structure, and mechanical principles, the ranges of axial force, radial force, and torque on the pin shafts during takeoff and landing are estimated, as well as the position areas of the key pin shafts that are more affected during the retraction and extension of the landing gear.

[0015] Preferably, in step 2, the normal pressure P is determined by simulating and calculating the contact force between the pin shaft and adjacent components through the multi-body dynamics model, the relative slip distance L is calculated based on the kinematic analysis of the landing gear, the Brinell hardness H of the material is adopted from the collected parameter values, and the wear factor K is adopted as a reference value.

[0016] Preferably, in step 2, the Archard wear calculation model calculates the wear volume increment for mechanical and material properties: V = KPL / H (1), where the normal pressure P and relative slip distance L are obtained by simulating the multi-body dynamics model, H is the Brinell hardness of the material, and K is the wear factor; a single wear process analysis is carried out: according to the motion characteristics of the landing gear, the relative rotation angle and the number of wear times n of the pin shaft are determined, and the relative slip distance is calculated: Based on geometric relationships, the wear volume increment of a single pin shaft is calculated: V = [π(r + Δr) 2 - πr 2 b = 2πrbΔr (3), and by combining equations (1) - (3), the wear amount of the pin shaft radius is obtained: where r is the radius of the pin shaft and b is the height of the pin shaft.

[0017] Preferably, in step 2, the wear factor of the Archard wear model is dynamically calibrated according to the pin shaft material pairing characteristics, grease type, and working condition temperature change curve; during the wear calculation process, the wear parameters are updated at preset time intervals to improve the adaptability of the wear calculation to the dynamic changes of actual working conditions.

[0018] Preferably, in step 4, it includes:

[0019] Step 4.1: Construct a digital twin model with a multi-body dynamics model, a wear calculation model, and a wear prediction model as the core, combined with the monitoring data of metal particles in the pin lubricating oil.

[0020] Step 4.2: Through the particle filter algorithm, construct a prior distribution of particles based on historical experience and initial state estimation to characterize the probability distribution of the pin wear state; based on the dynamics and wear models, establish a state equation to predict the change of particle state; at the same time, use real-time monitoring data to construct an observation equation to update the particle weights; in addition, update the posterior distribution of particles through resampling technology, and iteratively update the wear curve, calibrate the model parameters and state estimation values, so as to continuously improve the accuracy of wear prediction and the overall reliability of the model.

[0021] Preferably, in Step 4.2, first, construct a prior distribution of particles according to the early wear monitoring data of the pin; in the prediction stage, rely on the state equation and various input information obtained in real time to promote the state transfer of particles, so as to obtain the prediction distribution of the system state; in the update link, use real-time monitoring data to construct an observation equation, update the particle weights, update the posterior distribution of particles through resampling technology, and iteratively update the wear curve, calibrate the model parameters and state estimation values.

[0022] Preferably, considering the number of retractions and extensions n, the normal pressure P, the rotation angle of the pin the wear factor K, the height b of the pin, and the error vector v obtained by sampling, the state transition formula representing the pin wear state:

[0023]

[0024] In the formula, the subscripts k and k - 1 are the kth and (k - 1)th moments, the subscripts 1, 2, and 3 are the first, second, and third state variables, and ɡ(·) is the state transition function, which is obtained from the calculation formula of the pin wear volume increment.

[0025] Preferably, Step 4.2 specifically includes: Step 4.21: Construct a prior distribution of particles: At the initial moment, determine the value range of the state vector X0 according to prior knowledge or initial monitoring data, randomly sample N particles from this range, and assign an initial weight to each particle:

[0026]

[0027] where i represents the particle number;

[0028] Step 4.22: State prediction: For each particle, update the particle state according to the state transition formula:

[0029]

[0030] where f(·) is the state transition function, u is the control input, and v k (i) is the error vector obtained by sampling, and the initial value is given in a normal distribution;

[0031] Step 4.23, weight update: Compare the calculation result with the actually monitored data, and redistribute the weights of the initially randomly obtained multiple groups of particles:

[0032]

[0033] where p is the k wear radius X updated by the state equation under the number of wear times k in the likelihood value obtained by comparing with the observed value;

[0034] Step 4.24, normalize the weights so that their sum is 1:

[0035]

[0036] The final system state estimate is obtained by weighted average and is expressed as:

[0037]

[0038] where is the system state estimate value at time k, is the state vector of the i-th particle at time k, which contains information on the pin wear amount, Brinell hardness, and radius state variables.

[0039] Beneficial effects

[0040] 1. By establishing a wear prediction model for the landing gear retraction and extension mechanism, and combining actual monitoring data and a reasonable wear prediction algorithm, the present invention can reflect the operating state of the pin in real time considering the uncertainty of multiple variables, and realizes a more accurate simulation of the wear process of the pin under actual conditions and an accurate prediction and evaluation of the wear conditions of the landing gear retraction and extension mechanism of the aircraft and its main pins.

[0041] 2. The present invention also relies on the feedback and correction of actual operation data, and combines the particle filter idea to update and correct the state of the specific wear model in real time, improving the reliability of the prediction. Therefore, the errors caused by model simplification or the inconsistency between the current size after wear and the theoretical model in the traditional method are reduced, so as to more accurately reflect the consistency between the theoretical model and the actual data.

[0042] 3. This method can accurately predict the wear trend of the landing gear pin within a certain number of future operations. By combining the analysis of historical data and real-time data, it provides airlines with detailed wear trend curves and prediction reports, enabling them to formulate reasonable maintenance plans in advance based on these prediction information, reduce maintenance costs, and lower the incidence of flight delays or safety accidents caused by sudden wear failures. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Flow chart for establishing the digital twin prediction model of an embodiment of the present invention;

[0044] Figure 2 Multi-body dynamics model of the landing gear (including key pins) of an embodiment of the present invention;

[0045] Figure 3 Particle filter correction curve of an embodiment of the present invention;

[0046] Figure 4 Simulation result of the wear model of an embodiment of the present invention - change of element force over time;

[0047] Figure 5 Simulation result of the wear model of an embodiment of the present invention - change of angular velocity, acceleration and speed over time;

[0048] Figure 6 Wear prediction result of an embodiment of the present invention - schematic diagram of wear amount distribution corresponding to the number of wear times;

[0049] Figure 7 Wear prediction result of an embodiment of the present invention - predicted value of wear amount per unit time and its 95% confidence interval;

[0050] Figure 8 Wear prediction result of an embodiment of the present invention - predicted value of cumulative wear amount and its 95% confidence interval. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0051] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with some of the drawings in the actual operation of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0052] The present invention mainly focuses on predicting the wear of landing gear pin shafts by using digital twin technology, providing technical and methodological support for the maintenance and reliability guarantee of landing gears. The present invention discloses a wear prediction method for landing gear retraction and extension mechanisms based on digital twin. First, a three-dimensional model of the landing gear including geometric dimensions and material properties is established, and a multi-body dynamics simulation model is constructed by combining actual operation data such as landing gear retraction and extension frequencies and load distributions, and boundary conditions and initial parameters are set to simulate the force and wear processes of the pin shafts under actual working conditions. The Archard wear calculation model considering key factors such as normal pressure, pin shaft rotation angle, friction coefficient, Brinell hardness, etc. is used to calculate the pin shaft wear in the multi-body dynamics simulation model in real time. On this basis, an uncertainty analysis of each parameter in the Archard model is carried out. In view of the fact that each parameter in the actual working conditions has uncertainty due to many factors such as material microstructure differences, manufacturing process fluctuations, and operating environment changes, and thus shows a certain probability distribution characteristic. Each parameter is considered to follow a normal distribution, and by setting reasonable means and standard deviations for these parameters, a prediction model under multivariate uncertainty is established. Finally, actual monitoring data is obtained by reading information data such as the content, composition, and particle size distribution of metal particles detected in the lubricating oil of the relevant mechanism for comparison and verification, and based on the digital twin model, the particle filter method is used to construct a prior distribution of particles, update the particle weights through the state and observation equations, resample to approximate the true state, iteratively update the curve, calibrate the model parameters and state, improve the prediction accuracy, enhance the prediction accuracy and reliability, discover potential wear problems in advance, provide a basis for the maintenance plan, reduce the failure risk, and at the same time provide a reference for the design improvement of the landing gear and extend the service life.

[0053] As Figures 1 to 8 shown, the present invention is applicable to the landing gear retraction and extension mechanism and its sub-structures of an aircraft. Taking the multi-body dynamics model of the landing gear established by the present invention as an example:

[0054] Step 1: Construct a three-dimensional model and a multi-body dynamics model of the landing gear retraction and extension mechanism, simulate the landing gear retraction and extension frequencies, load distributions, and the motion states of each part of the retraction and extension mechanism, and obtain simulation data.

[0055] Specifically,

[0056] By referring to the aircraft flight manual, landing gear design manual, material manual, and relevant technical documents, and combining with the observation database of the airline operator, key information and parameters are collected, covering the diameter, length, three-dimensional shape characteristics of the landing gear pin, as well as its installation position, connection method, cooperation relationship with other components in the landing gear, and operation data such as the retraction and extension frequency and time of the landing gear. A three-dimensional model of the landing gear retraction and extension mechanism of the aircraft is constructed using three-dimensional modeling software, and then a multi-body dynamics model is established using multi-body dynamics software according to the actual structure and pin connection method. When modeling, rigid body models of each component are created in the software, and the connection and interaction of components are simulated through constraint pairs and force elements. The pin is modeled as a cylindrical rigid body and contacts are added with surrounding connecting parts to accurately simulate its degrees of freedom of motion and force conditions. The model contains accurate parameters of key components (such as the elastic modulus, Poisson's ratio, Brinell hardness, and yield strength of the pin material), and can accurately reflect the mechanical action and connection conditions.

[0057] In this embodiment, a driving force is added for simulation. Only by making the model able to move can the contact force be measured. Based on the calculation model of the actuator driving force, the actuator driving force is calculated as follows:

[0058]

[0059] Among them, the theoretical driving force F of the actuator d = F f + F air ; The frictional force F f is determined by considering the total mass m of the landing gear and related components, the acceleration due to gravity g, and the friction coefficient μ, that is, F f = μmg, where μ is referenced to the theoretical value in the manual or literature and corrected in combination with test and flight data. The air density ρ is determined according to the flight conditions and atmospheric model. The air resistance coefficient C d is obtained by referring to the wind tunnel test data. The windward area A is determined through geometric measurement and analysis. The retraction and extension speed v is determined according to the design specifications and operation requirements, and the air resistance The efficiency of the actuator is η; when determining the driving force, the actual driving force applied to the actuator is:

[0060]

[0061] Based on the above data, combined with the retraction and extension frequency of the landing gear, aircraft weight distribution, etc., the force range of the pin and the positions of key pins are estimated to obtain simulation data, providing support for subsequent research.

[0062] Step 2: Embed the Archard wear calculation model considering key factors such as normal pressure, pin rotation angle, friction coefficient, and Brinell hardness into the multi-body dynamics model. Accurately obtain parameters such as normal pressure, contact force, relative rotation angle, and relative slip distance of the pin movement through dynamic simulation, calculate the wear volume increment in real time and accumulate it to obtain the total wear volume, accurately deduce the change in the wear size of the pin, realize the accurate quantitative simulation of the wear process, and establish a wear prediction model that can accurately describe the wear process. The multi-body dynamics model of the landing gear and the key pin model are as Figure 3 shown. Adopt a suitable wear prediction algorithm and a wear calculation model that considers the influence of key factors such as the size, Brinell hardness, friction coefficient, retraction and extension movement angular velocity, and load magnitude of the pin material on wear. Subsequently, conduct real-time wear simulation to obtain multiple sets of parameters such as contact force and relative rotation angle.

[0063] Specifically:

[0064] Based on the multi-body dynamics model, calculate the wear volume increment for mechanics and material properties based on the Archard model:

[0065] V = KPL / H (1)

[0066] Among them, the normal pressure P is determined by simulating and calculating the contact force between the pin and the adjacent components; the relative slip distance L of each movement of the pin is calculated according to the kinematic analysis of the landing gear; the Brinell hardness H of the material adopts the collected parameter values, and the wear factor K is determined by referring to existing literature.

[0067] Analysis of a single wear process: According to the movement characteristics of the landing gear, determine the relative rotation angle of the pin and the number of wear times n, and calculate the relative slip distance L in combination with Equation (2):

[0068]

[0069] Calculate the wear volume increment of a single pin based on geometric relationship through Equation (3), where b is the height of the pin:

[0070] V = [π(r + Δr) 2 - πr 2 b = 2πrbΔr (3)

[0071] Combine Equations (1) to (3) to obtain the wear amount of the pin radius (Equation 4):

[0072]

[0073] Formula (1) and formula (3) calculate the wear volume increment from two perspectives, and the formula for the wear amount of the pin radius is obtained by combining formulas (1)-(3), which facilitates the model update. In the model, according to the pin size, material parameters, and the force and motion parameters calculated by the multi-body dynamics model, the wear amount of each movement is calculated in real time and the total wear amount is accumulated. The simulation model is updated according to the pin radius wear amount and the total wear amount. For example, the pin radius wear amount Δr is obtained, that is, Δr is reduced on the original three-dimensional model to achieve the update.

[0074] The wear factor of the Archard wear model is dynamically calibrated based on the pin material pairing characteristics, grease type, and operating temperature change curve. During the wear calculation process, the wear parameters are updated at preset time intervals to improve the adaptability of the wear calculation to the dynamic changes of actual operating conditions.

[0075] Step 3: Explore the sources of uncertainty in the Archard model parameters, which may come from material properties (such as composition fluctuations, processing technology differences and microstructural changes), load conditions (fluctuating due to the diversity of flight missions and environmental factors), and friction coefficients (due to dynamic changes in lubrication conditions, surface roughness evolution and temperature effects).

[0076] In order to build an accurate wear prediction model, the wear prediction model is connected to Matlab, and each parameter is deeply analyzed. For example, the Brinell hardness of the pin is affected by material composition and heat treatment; the friction coefficient is affected by lubrication, surface roughness and other factors. The above key parameters are regarded as random variables that obey the normal distribution. The value range of each parameter is determined according to the physical meaning and monitoring data, and the probability distribution model of the wear calculation parameters is constructed by integrating the interval to reach the preset confidence level. Specifically, the angular velocity and load of the retraction and release are diverse and uncertain, which are clarified by statistical analysis of simulation data. An initial parameter distribution model is established based on multiple groups of observation data, and multiple groups of variables are substituted into the wear model calculation using a random number generation algorithm. The interval estimation is optimized using small sample test data, and the wear results are obtained according to the variable group for each retraction and release simulation. After multiple simulations, the predicted distribution of the wear radius is obtained, and the multi-body dynamics model is updated accordingly, the value range of the relevant parameters is adjusted, and the value and calculation steps are repeated. After multiple cycles, the total predicted distribution and confidence interval of the wear radius changing with the number of retraction and release simulations are obtained. In this embodiment, the simulation results of the wear model are as follows: Figures 4 to 5 As shown in Figure 2, the wear prediction results and confidence intervals of the wear simulation model are shown in Figure 2. Figures 6 to 8 As shown in the figure, these results are obtained based on the constructed multi-body dynamics model, Archard wear calculation model, uncertainty analysis and particle filtering algorithm. Figure 4The elemental forces of two contact points (CONTACT_1 and CONTACT_2) in the X and Y directions over time (the abscissa represents time, and the ordinate represents the magnitude of the force). In the multi-body dynamics model, the interaction between components is simulated through kinematic pairs, drives, and force elements. The driving force of the actuator affects the motion state of the components, thereby generating contact forces. Figure 5 For the angular velocity, acceleration, and velocity of a component (PART_34_CM) over time (the abscissa represents time, and the ordinate represents the magnitudes of the angular velocity, acceleration, and velocity). Specifically, CONTACT_1 has tensile or compressive forces in the X direction. In the Y direction, the overall trend is relatively stable, but there are peaks at certain moments. CONTACT_2 is similar to CONTACT_1 in the X direction, but the numerical range is larger and the fluctuations are more intense. In the Y direction, it also shows certain fluctuations. The magnitudes of the angular velocity, acceleration, and velocity of the component (PART_34_CM) all show periodic fluctuations over time. The maximum angular velocity is close to 70 degrees per second, the maximum acceleration is close to 5 m / s², and the velocity value is relatively small. Figure 6 The scatter plot shows the wear amount distribution corresponding to each wear count (the abscissa represents the wear count, and the ordinate represents the wear amount per count). The shade of the color represents the density of the data points. The darker the color, the more data points in that area. It can be seen that the wear amount per count fluctuates around approximately 0.12, and as the wear count increases, the variation range of the wear amount gradually decreases. Figure 7 Shows the predicted value of the wear amount per count and its 95% confidence interval (the abscissa represents the wear count, and the ordinate represents the wear amount per count). It can be seen that the predicted value is higher when the wear count is low and tends to be stable when the wear count is high. The confidence interval is wider when the wear count is low and gradually narrows when the wear count is high. Figure 8 Shows the predicted value of the cumulative wear amount and its 95% confidence interval (the abscissa represents the wear count, and the ordinate represents the cumulative wear amount). It can be seen that the cumulative wear amount increases linearly with the increase of the wear count. The confidence interval is narrower when the wear count is low and gradually widens when the wear count is high.

[0077] Based on this probability distribution model, a multi-variable matrix containing multiple random variables is generated. Different parameter combinations are generated through a large number of random samplings and substituted into the Archard wear model to calculate the wear values. Probability and statistical techniques are used to analyze these results to obtain information about the uncertainty distribution of the wear amount.

[0078] In this embodiment, considering that there is a certain cognitive uncertainty in the key parameters, they need to be determined before the initial calculation (b, P, The actual observed uncertainty when components such as

[0079] are not worn. Assuming that these parameters follow a specific distribution (e.g., normal distribution), several observed values can be randomly selected from this distribution to establish a new multivariate variable matrix. Using this new matrix, multiple sets of wear amounts and their cumulative values are recalculated.

[0080]

[0081] After the first iteration, according to the current distribution of each parameter and the information obtained from the previous loop optimization, a new matrix is formed by resampling using a random number generation algorithm. The sampling process uses a random number table sampling method based on the normal distribution to ensure the randomness of sampling and the coverage of parameter combinations. Then, this new matrix is input into the Archard wear model to update the wear amount estimation, and this process is repeated until the stopping condition is met, as shown in Equation (5) specifically.

[0082] Step 4: Based on the Bayesian estimation and Monte Carlo sampling strategy, use particle filtering to realize the update and prediction of the wear curve by the digital twin model. Specifically, with the multi-body dynamics model and the wear prediction model as the core, combined with the monitoring data of metal particles in the pin shaft lubricating oil, a digital twin model is constructed. A large number of particles are used in this model to characterize the probability distribution of the system state, and these states include not only the wear amount of the pin shaft but also the associated parameter set. A state equation is constructed through the wear calculation model to describe the dynamic evolution process of the particles with the number of wear times.

[0083] First, through the particle filtering algorithm, a particle prior distribution is constructed based on historical experience and initial state estimation to characterize the state vector of the pin shaft wear state.

[0084] For the wear amount X k , according to the Archard wear formula, considering factors such as the number of retractions and extensions n, the normal pressure P, the rotation angle of the pin shaft the wear factor K, the height b of the pin shaft, the number of wear times n, the error vector v obtained by sampling, etc., its state transition relationship can be expressed as:

[0085]

[0086] The subscripts k and k - 1 represent the kth and (k - 1)th moments, and the subscripts 1, 2, and 3 represent the first, second, and third state variables, that is, X k 、X k-1 represent the wear amounts at adjacent moments k and k - 1, and Xk-1,2 , X k-1,3 represent the second and third state variables of the pin wear state at the (k - 1)-th moment. The function g(·) is the state transition function, which updates the wear amount estimate in the Archard wear model, i.e., Equation (3) above.

[0087] Based on the dynamics and wear model, a state equation is established to predict the change of particle state; meanwhile, an observation equation is constructed using real-time monitoring data to update the particle weights. In addition, the distribution of particles is optimized through resampling technology, and the wear curve, calibration model parameters, and state estimation values are iteratively updated to continuously improve the accuracy of wear prediction and the overall reliability of the model.

[0088] In this embodiment, an initialization operation is first performed. Based on the empirical data accumulated in the past (pin early wear monitoring data), particles are established in the parameter space, and each particle is assigned an initial weight to construct a probabilistic description of the initial state of the system.

[0089] At the initial moment, according to prior knowledge or a small amount of initial monitoring data, the value range of the state vector Xo is determined, N particles are randomly sampled from this range, and each particle is assigned an initial weight:

[0090]

[0091] For each particle, according to the state equation:

[0092]

[0093] where f(·) is the state transition function, u is the control input, and v k (i) is the error vector obtained by sampling, which is assigned with a normal distribution.

[0094] Calculate the new state of each particle according to the above update formulas for wear amount, Brinell hardness, and radius respectively. For example, for the i-th particle, according to its previous state and the current input vector, combined with the state transition function and the sampled process noise, calculate

[0095] Compare the calculation results with the actually monitored data to complete the reallocation of the weights of the initially randomly obtained multiple groups of particles:

[0096]

[0097] where p is the likelihood value obtained by comparing the wear radius Xk updated by the state equation under Nk wear times with the observed value.

[0098] Subsequently, the particle weights are normalized so that their sum is 1:

[0099]

[0100] The final system state estimate can be obtained through weighted averaging and is expressed as

[0101] where is the system state estimate value at time k, is the state vector of the i-th particle at time k, including the estimated values of state variables such as pin shaft wear amount, Brinell hardness, and radius. For example, during the entire wear process, if it is assumed that the height of the pin shaft does not change with wear (there may be extremely small changes due to wear in reality, which is simplified here), then its estimated value remains unchanged at the initial value at each moment, that is:

[0102]

[0103] where is the estimated value of the pin shaft height at time k, and v0 is the initial value of the pin shaft height. If more complex situations are considered, assuming that the change in the pin shaft height is related to the wear amount or other factors, and the change relationship is set as b k+1 = b k -βΔr k+1 (β is a coefficient related to the pin shaft material and wear characteristics), then the estimated value is calculated as:

[0104]

[0105] where is the pin shaft height state value of the i-th particle at time k, is the normalized particle weight, and the same applies to the other components.

[0106] After completing the above particle filter prediction, repeat step 3 to correct the total prediction distribution curve of the wear prediction radius with the number of retraction and extension simulation times. This iterative update mechanism enables the digital twin model to be optimized over time and with more data accumulation, improving the accuracy and reliability of the model. Finally, we obtain the total prediction distribution and its confidence interval of the wear prediction radius with the number of retraction and extension simulation times after iterative update. The particle filter correction curve is as Figure 3 shown.

[0107] In the prediction stage, relying on the state equation and various input information obtained in real time, such as complex and variable working conditions and operating parameters, etc., promote the state transfer of particles to accurately describe the evolution of particle states, so as to obtain the prediction distribution of the system state.

[0108] In the update process, based on the constructed observation equation and the latest obtained monitoring data, the likelihood value of each particle is calculated. The new weight setting is directly proportional to the likelihood value and the prior weight, thereby achieving the dynamic update of the particle weights. Subsequently, the resampling process is carried out, and targeted replication or discard operations are performed on the particles according to the updated weight situation to ensure that the number of particles remains constant all the time, effectively preventing the occurrence of particle degradation and ensuring that the particles can reflect the true distribution of the system state.

[0109] Through multiple iterative loops, the particle set gradually converges to the high-likelihood region, presenting the true probability distribution of the wear state. Finally, based on the parameter expectations contained in the particles, the predicted value of the wear curve is updated to improve the accuracy of wear prediction and the overall reliability of the digital twin model.

[0110] Step 5: In the actual application process, continuously collect the operation data of the aircraft landing gear pin and the information related to the actual wear situation. Compare and analyze the wear results predicted by the model with the actual wear data, and continuously optimize the parameters of the model according to the comparison differences. By continuously repeating this process, continuously improve the prediction accuracy and reliability of the model to better adapt to different flight conditions and landing gear usage conditions, and provide more accurate support for the wear prediction and maintenance decision-making of the aircraft landing gear pin.

[0111] This application embeds the Archard wear model into the multi-body dynamics simulation, and combines parameter uncertainty analysis (such as normal distribution random variables and Monte Carlo sampling) to solve the prediction deviation problem caused by the simplified model in the traditional method. The particle filter algorithm is introduced, and through the interaction between the state equation and the real-time monitoring data, the model parameters and the wear curve are dynamically corrected, overcoming the limitation that the static model is difficult to adapt to the dynamic changes of the working conditions. Through the digital twin framework, multi-source data (simulation data, monitoring data, material parameters) are integrated to realize the full-process closed-loop optimization of wear prediction. Compared with the traditional method, this solution significantly improves the accuracy and reliability of wear prediction (such as confidence interval analysis) by quantifying parameter uncertainty and dynamically calibrating the model, can identify potential wear risks in advance, optimize the maintenance plan, and reduce the costs and safety risks brought by over-maintenance or under-maintenance.

[0112] Finally, it should be noted that the above are only the preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, for those skilled in the art, they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A wear prediction method for the landing gear retraction mechanism based on digital twin, characterized in that, including the following steps: Step 1: Construct a three-dimensional model of the landing gear retraction mechanism and the corresponding multi-body dynamics model, simulate the retraction frequency, load distribution of the landing gear, and the motion states of various parts of the retraction mechanism, and obtain simulation data; Step 2: Embed the Archard wear calculation model that takes into account key factors including normal pressure, pin rotation angle, friction coefficient, and Brinell hardness, calculate the pin wear volume increment V in the multi-body dynamics simulation model in real time, accumulate it to obtain the total wear volume, and calculate the pin radius wear amount Δr: In the formula, n is the number of wear times, K is the wear factor, P is the normal pressure, is the relative rotation angle of the pin, b is the pin height, H is the Brinell hardness of the material, and update the 3D model; Step 3: Conduct uncertainty analysis on each key parameter in the Archard wear calculation model. Set the key parameters as random variables subject to normal distribution, and determine the value range based on physical meaning and actual monitoring data; Integrate within this range to achieve a preset confidence level, and then construct a probability distribution model of the parameters; Construct a multivariate random variable matrix according to the probability distribution model of the parameters, and generate different parameter combinations through a large number of random samplings. Substitute them into the Archard wear calculation model described in Step 2 to calculate the wear values; Finally, use probability statistical methods to analyze the wear values, obtain uncertainty distribution data on the wear amount, construct an accurate wear prediction model, and obtain a wear prediction curve; Step 4: Construct a digital twin model, and construct a prior distribution of particles based on the method of particle filter combined with the early wear monitoring data of the pin shaft; In the prediction stage, rely on the state equation and the input information obtained in real time to drive the state transfer of the particles, so as to obtain the prediction distribution of the system state; In the update link, use the real-time monitoring data to construct an observation equation, update the particle weights, update the posterior distribution of the particles through resampling technology, and iteratively update the wear curve, calibrate the model parameters and the state estimation values.

2. The method according to claim 1, characterized in that, In Step 1, to drive the model to measure the contact force, an actuator driving force is added where F f is the frictional force, F air is the air resistance, and η is the actuator efficiency.

3. The method according to claim 1, characterized in that, In the three-dimensional modeling software, create rigid body models of each component according to the geometric dimensions and material property parameters of the landing gear pin shaft, and simulate the connection and interaction between components through constraint pairs and force elements; The pin shaft is modeled as a cylindrical rigid body and connected to the surrounding connectors by adding contact methods; In the dynamic simulation software, consider the connection relationship, motion constraints and actual working condition load distribution of each component, and establish a multi-body dynamics model; The boundary conditions of the multi-body dynamics model are set according to the actual installation configuration of the landing gear, connection stiffness characteristics and buffer performance parameters; The load distribution is simulated according to the characteristics of different load conditions of the aircraft.

4. The method according to claim 3, wherein In Step 1, based on the retraction frequency, retraction time, aircraft weight distribution data, landing gear structure and mechanical principle of the landing gear, estimate the range of axial force, radial force and torque on the pin shaft during takeoff and landing, as well as the position area of the key pin shaft that is more affected during the retraction of the landing gear.

5. The method according to claim 4, characterized in that, In Step 2, the wear factor of the Archard wear model is dynamically calibrated according to the material pairing characteristics of the pin shaft, the type of grease and the working condition temperature change curve; During the wear calculation process, update the wear parameters at preset time intervals to improve the adaptability of the wear calculation to the dynamic changes of actual working conditions.

6. The method according to any one of claims 1-5, characterized in that, In Step 4, it includes: Step 4.1: Construct a digital twin model with the multi-body dynamics model, wear calculation model and wear prediction model as the core, combined with the metal particle monitoring data in the pin shaft lubricating oil; Step 4.2: Initialize the particle swarm based on historical experience and initial state estimation through the particle filter algorithm to represent the state vector of the pin wear state; establish a state equation based on the dynamics and wear model to predict the change of particle state; meanwhile, construct an observation equation using real-time monitoring data to update the particle weights; in addition, update the particle distribution through resampling technology, and iteratively update the wear curve, calibrate the model parameters and state estimation values, so as to continuously improve the accuracy of wear prediction and the overall reliability of the model.

7. The method according to claim 1, wherein Considering the number of retraction and extension operations \(n\), the normal pressure \(P\), the pin rotation angle within each iteration time interval, the wear factor \(K\), the pin height \(b\), and the error vector \(v\) obtained by sampling, the state transition formula representing the pin wear state: Where the subscripts k and k - 1 represent the kth and (k - 1)th moments, and the subscripts 1, 2, and 3 represent the first, second, and third state variables, and ɡ(·) is the state transition function, which is obtained from the calculation formula of the pin wear volume increment.

8. The method according to claim 7, wherein Step 4.2 specifically includes: Step 4.21: Initialize the particle distribution. At the initial moment, determine the value range of the state vector X0 according to prior knowledge or initial monitoring data, randomly sample N particles from this range, and assign an initial weight to each particle: where i represents the particle number; Step 4.22: State prediction. For each particle, update the particle state according to the state transition formula: where f(·) is the state transition function, u is the control input, and v k (i) is the error vector obtained by sampling, and is given an initial value with a normal distribution; Step 4.23: Weight update. Compare the calculation results with the actually monitored data, and redistribute the weights of multiple groups of particles initially randomly obtained: where p is from n k the wear radius X after updating the state equation under the number of wear times k the likelihood value obtained by comparing with the observed value; Step 4.24: Normalize the weights so that their sum is 1: The final system state estimation is obtained through weighted average and is expressed as: Among them is the system state estimation value at time k, is the state vector of the i-th particle at time k, including information on pin shaft wear, Brinell hardness, and radius state variables.

Images