Method and system for estimating time-varying thermal failure probability of deep groove ball bearing

Abstract

The invention discloses a time-varying thermal failure probability estimation method and system for a deep groove ball bearing, and belongs to the field of bearing design. The method comprises the following steps: constructing a basic parameter model containing a mixed random parameter vector and a limit state function; establishing a transient thermal network model to calculate time-varying temperature response; constructing an agent model to replace high-time-consumption heat generation rate calculation; a self-adaptive time node sampling strategy is adopted, a proxy model and a thermal network model are combined to process large-scale samples, and the time-varying thermal failure probability is estimated. The system comprises a basic parameter modeling module, a transient thermal network simulation module, an agent model construction module and a self-adaptive probability evaluation module which correspond to the system. According to the method, the time-varying and random dual uncertainty is fused, and the proxy model and the adaptive sampling strategy are utilized, so that the defects of conservative property of a traditional static evaluation method and low efficiency of a traditional probability simulation method are effectively overcome, and accurate evaluation of the thermal behavior of the bearing under the dynamic working condition and remarkable improvement of probability calculation efficiency are realized.

Description

Technical Field

[0001] This invention relates to the field of bearing design, specifically to a method and system for estimating the probability of time-varying thermal failure of deep groove ball bearings. Background Technology

[0002] Deep groove ball bearings are critical components widely used in rotating machinery, and their reliability directly affects the performance of the entire transmission system. During the bearing design phase, accurately assessing the probability of thermal failure under specified operating conditions and within the lifespan is crucial. The aim is to quantify the impact of various uncertainties, such as dynamic operating conditions and material properties, thereby guiding design optimization and reducing the risk of failure.

[0003] In actual operation, the thermal characteristics of deep groove ball bearings are affected by two uncertainties: first, the inherent random dispersion of material and structural parameters; and second, the dynamic fluctuations of operating conditions such as rotational speed, load, and ambient temperature. The coupling effect of these factors may lead to instantaneous overheating of critical parts of the bearing, causing irreversible thermal failure.

[0004] To control the risk of thermal failure, existing technologies mainly employ two types of solutions:

[0005] The first type of approach uses fixed extreme operating condition parameters (such as maximum speed and maximum ambient temperature) as input for verification. While this method is simple, it often leads to overly conservative designs because it does not consider the dynamic characteristics of bearings that primarily operate under normal conditions and only withstand short periods of extreme conditions. This conservative design may not only reduce the bearing's rated dynamic load and fatigue life by selecting excessively large safety clearances, but it may also result in over-design of materials and lubrication schemes, leading to unnecessary performance redundancy and cost waste.

[0006] The second approach employs Monte Carlo simulation, using a large number of random samples to statistically analyze the impact of uncertainty on bearing thermal behavior. However, when dealing with time-varying uncertainties, this method requires frequent calls to complex physical models (such as thermal network models) for each sample throughout the entire timeframe. This results in a dramatic increase in computational burden as the dimensionality of variables increases, making it difficult to meet the needs of rapid iterative evaluation in engineering practice and limiting its application in optimization design.

[0007] Therefore, there is a lack of existing technologies for estimating the thermal failure probability of deep groove ball bearings that can both accurately reflect the time-varying characteristics of bearing thermal behavior under dynamic operating conditions and effectively balance computational accuracy and efficiency. Summary of the Invention

[0008] To overcome the above-mentioned shortcomings, this invention aims to provide a method and system for estimating the time-varying thermal failure probability of deep groove ball bearings. This method and system can accurately reflect the time-varying thermal behavior of bearings under dynamic operating conditions coupled with multiple uncertainties, and can significantly reduce the computational burden of the evaluation process, achieving an effective balance between accuracy and efficiency. This provides an efficient and accurate quantitative tool for the reliability design and optimization of bearings.

[0009] The primary objective of this invention is to provide a method for estimating the probability of time-varying thermal failure in deep groove ball bearings, comprising the following steps:

[0010] A basic parameter model for thermal failure analysis is constructed, which includes the deterministic geometric parameters of the bearing, a mixed random parameter vector for simulating dynamic working conditions and inherent discreteness, and a time-varying limit state function for determining failure.

[0011] Based on the aforementioned basic parameter model, a transient thermal network model of the deep groove ball bearing is established, and the time-varying temperature response sequence of the bearing under dynamic operating conditions is calculated.

[0012] A surrogate model for predicting the frictional heat generation rate is constructed, wherein the training of the surrogate model is based on sample data generated by the transient thermal network model, so that the trained surrogate model can replace the calculation of the frictional heat generation rate in the transient thermal network model.

[0013] Based on the surrogate model and the transient thermal network model, an adaptive time node sampling strategy is used to process a large-scale sample set in order to estimate the time-varying thermal failure probability of the deep groove ball bearing.

[0014] Preferably, the hybrid random parameter vector includes time-varying random parameters and time-invariant random parameters; wherein, the time-varying random parameters are simulated for their dynamic fluctuations by a stochastic process model, and the time-invariant random parameters are described for their inherent discreteness by a probability distribution model.

[0015] Preferably, establishing the transient thermal network model includes: calculating the frictional heat generation rate inside the bearing based on the basic parameter model; constructing a nodal thermal impedance network of the bearing, and using the frictional heat generation rate as a heat source to solve the thermal network to obtain the time-varying temperature response sequence.

[0016] Preferably, constructing the surrogate model includes: using the transient thermal network model to generate a real frictional heat generation rate response for a set of training samples extracted in the distribution space of the mixed random parameter vector; and training a surrogate model for predicting the frictional heat generation rate based on the training samples and their real responses.

[0017] Preferably, the adaptive time node sampling strategy includes: performing preliminary temperature calculation and sample screening based on a first precision time node sequence; and performing precise temperature calculation on the screened samples based on a second precision time node sequence; wherein the density of the second precision time node sequence is higher than that of the first precision time node sequence.

[0018] The second objective of this invention is to provide a time-varying thermal failure probability estimation system for deep groove ball bearings, comprising:

[0019] The basic parameter modeling module is used to construct the basic parameter model for thermal failure analysis. The basic parameter model includes the deterministic geometric parameters of the bearing, a mixed random parameter vector for simulating dynamic working conditions and inherent discreteness, and a time-varying limit state function for determining failure.

[0020] The transient thermal network simulation module is used to establish a transient thermal network model of a deep groove ball bearing. Taking the basic parameter model as input, it calculates the frictional heat generation rate and solves the thermal network to output the time-varying temperature response sequence of key parts of the bearing.

[0021] The proxy model construction module is used to construct and train a proxy model. The proxy model is trained based on the training sample pairs generated by the transient thermal network simulation module and is used to replace the frictional heat generation rate calculation step in the transient thermal network simulation module.

[0022] The adaptive probability assessment module is used to employ an adaptive time node sampling strategy, combined with the surrogate model construction module and the transient thermal network simulation module, to perform failure screening and probability statistics on a large-scale sample set generated based on probability sampling, and output the time-varying thermal failure probability estimate of the deep groove ball bearing.

[0023] Preferably, the transient thermal network simulation module includes:

[0024] The heat generation rate calculation unit is used to calculate the frictional heat generation rate inside the bearing based on the basic parameter model.

[0025] The thermal network construction and solution unit is used to construct the nodal thermal impedance network of the bearing, and solve the thermal network using the frictional heat generation rate output by the heat generation rate calculation unit as the heat source to obtain the time-varying temperature response sequence.

[0026] Preferably, the proxy model construction module includes:

[0027] The training data preparation unit is used to extract a set of training samples in the distribution space of the mixed random parameter vector, and use the transient thermal network simulation module to generate a real frictional heat generation rate response for the training samples to form training data.

[0028] The model training unit is used to train a surrogate model for predicting the rate of frictional heat generation based on the training data.

[0029] The present invention has the following beneficial effects:

[0030] 1) By integrating time-varying and stochastic uncertainties to construct a dynamic reliability model, the conservatism of traditional static extreme condition assessment methods is overcome, making the failure probability assessment more accurate and providing a reliable basis for optimization design.

[0031] 2) By replacing complex physical simulations with surrogate models, heat generation rate prediction is transformed into efficient computation, which greatly reduces the cost of large-scale Monte Carlo simulations and makes rapid and massive reliability assessments possible.

[0032] 3) An innovative adaptive time-node sampling strategy, through a computational mode of "sparse screening and local encryption" and adaptive control of the sample size based on the coefficient of variation, achieves optimal allocation of computing resources while ensuring estimation accuracy. Attached Figure Description

[0033] Figure 1 This is a schematic flowchart of an embodiment of the time-varying thermal failure probability estimation method for deep groove ball bearings according to the present invention;

[0034] Figure 2 This is a cross-sectional view of the geometric structure of the deep groove ball bearing model 6208 according to the method of this embodiment;

[0035] Figure 3 This is an example diagram of the time-varying speed curve under dynamic operating conditions in this embodiment.

[0036] Figure 4 This is an example diagram of the time-varying ambient temperature curve under dynamic operating conditions of the method in this embodiment;

[0037] Figure 5 This is a schematic diagram of the bearing node thermal network model of the method in this embodiment;

[0038] Figure 6 This is a schematic diagram of the bearing thermal impedance network in the method of this embodiment;

[0039] Figure 7 This is a flowchart illustrating the specific process of constructing and training the proxy model using the method described in this embodiment.

[0040] Figure 8 This is a flowchart illustrating the process of estimating the probability of time-varying thermal failure based on a surrogate model and an adaptive time node sampling strategy in this embodiment.

[0041] Figure 9 This is a comparison chart of the preliminary temperature sequence and the precise temperature sequence of the method in this embodiment;

[0042] Figure 10 This is a system interface diagram of the random input space and limit state construction module of the method in this embodiment;

[0043] Figure 11 This is a system interface diagram of the dynamic thermo-mechanical coupling physics simulation module of the method in this embodiment;

[0044] Figure 12 This is a system interface diagram of the Kriging proxy model construction module in this embodiment.

[0045] Figure 13 This is a system interface diagram of the adaptive time-varying thermal failure probability assessment module of the method in this embodiment. Detailed Implementation

[0046] Preferred embodiments of the invention will now be described in more detail with reference to the accompanying drawings. It should be understood that the following description is intended to illustrate the general principles of the invention by way of example and is not intended to limit the scope of protection defined by the appended claims.

[0047] To enable those skilled in the art to accurately understand the present invention, the key terms used in the present invention will first be explained.

[0048] Terminology Explanation:

[0049] Markov chains: a type of discrete-time stochastic process with "memoryless" properties, meaning the system... The state distribution at time t depends only on The state of being at any given moment, and with It is irrelevant to the previous historical situation.

[0050] A composite Gaussian process is a continuous-time stochastic process uniquely determined by its mean and covariance functions. Its arbitrary finite-dimensional distribution follows a multivariate normal distribution, accurately characterizing the autocorrelation of random variables in the time domain.

[0051] Quasi-statics: an approximate solution method that neglects inertial forces (or only considers steady-state inertial forces such as centrifugal force) in dynamic analysis and assumes that the system satisfies the static equilibrium condition at any instant.

[0052] Thermal impedance network: This term refers both to a numerical method for calculating heat transfer based on the lumped parameter method and to the physical heat flow network constructed based on this method. As a method, it discretizes a continuous medium into several isothermal nodes; as a network model, it is characterized by nodes being connected to thermally capacitive elements through thermal resistance (conduction / convection), forming a heat flow path structure similar to a circuit topology.

[0053] Proxy model: A data-driven approximate mathematical model designed to construct a mapping between a high-dimensional input space and the output response, replacing computationally expensive physical simulation models.

[0054] Monte Carlo simulation: a random statistical experiment method based on the law of large numbers. It approximates population parameters (such as failure probability) by using sample statistics (such as frequency) through extensive repeated sampling from a probability distribution.

[0055] Coefficient of variation: A normalized statistic that measures the dispersion of a probability distribution, defined as the standard deviation. With mathematical expectation The ratio.

[0056] Example 1

[0057] The following detailed description, with reference to the accompanying drawings and using a deep groove ball bearing of model 6208 as an example, illustrates the specific implementation of the method of the present invention. The method of this embodiment mainly includes four steps. See also... Figure 1 and Figure 2 . Figure 1 This is a flowchart illustrating a time-varying thermal failure probability estimation method for deep groove ball bearings according to this embodiment. Figure 2 This is a cross-sectional view of the geometric structure of the deep groove ball bearing model 6208 according to the method of this embodiment.

[0058] S1: Construct the basic parametric model for thermal failure analysis.

[0059] This step aims to establish the digital foundation for thermal failure analysis of deep groove ball bearings, providing complete input definitions and failure criteria for subsequent simulation and evaluation. The basic parameter model specifically includes the bearing's deterministic geometric parameters, a mixed random parameter vector for simulating dynamic operating conditions and inherent discreteness, and a time-varying limit state function for determining failure. S11: Obtain and define the deterministic geometric parameters of the deep groove ball bearing.

[0060] This sub-step aims to determine the physical references of the evaluation object. Specifically, it is necessary to obtain key dimensional parameters such as the bearing's inner diameter, outer diameter, rolling element diameter, raceway curvature radius coefficient, and number of rolling elements. These parameters serve as deterministic constant inputs in the subsequent mechanical and thermal models. Taking the 6208 deep groove ball bearing selected in this embodiment as an example, its specific structural parameters are shown in Table 1.

[0061] Table 1 6208 Bearing Structural Parameters

[0062]

[0063] S12: Construct a hybrid random parameter vector based on dynamic working conditions and inherent discreteness.

[0064] This step aims to systematically characterize and distinguish two types of uncertainties affecting the thermal properties of bearings: operating parameters that fluctuate dynamically over time (time-varying uncertainties) and material and load parameters with inherent dispersion (random uncertainties), thereby establishing an input space for subsequent probabilistic simulations.

[0065] The specific method is as follows: Uncertain variables are divided into two categories: time-varying random parameters and time-invariant random parameters.

[0066] 1. Time-varying random parameters: during the operating period (The running cycle in this embodiment is) The dynamic characteristics of a real-world operating condition are simulated by the dynamic fluctuations within a given time frame and the inherent randomness of the rotational speed. This primarily includes rotational speed. and ambient temperature .

[0067] 1) Regarding rotational speed To accurately reflect the engineering reality that a bearing "usually operates within its normal speed range but is subjected to extreme speed impacts for short periods," this embodiment uses the 6208 bearing's extreme speed of 11,000 rpm as an example and employs a multi-state Markov chain model to simulate its dynamic fluctuation characteristics.

[0068] First, the speed range can be divided into five discrete state intervals (e.g., low, medium, rated, high, and limiting speed).

[0069] state : rpm (low speed);

[0070] state : rpm (medium speed);

[0071] state : rpm (rated speed);

[0072] state : rpm (high speed);

[0073] state : rpm (maximum speed);

[0074] The random transitions between states can be represented by a state transition probability matrix. Control. An example of matrix form is as follows:

[0075]

[0076] Different typical durations are set for different states. For example, the normal speed state has a longer duration, while the extreme speed state has a shorter duration. In this example, the normal speed state ( ~ The duration of the test is relatively long (1-3 hours) to simulate the long-term stable operation of the bearing; the limiting speed state ( ~ The duration of the event is relatively short (0.5-1 hour) to simulate transient impact events. At the same time, a constant acceleration model is introduced when the speed state changes to smoothly simulate the inertial effect of the equipment's acceleration and deceleration.

[0077] Using the methods described above, time-varying speed curves that conform to specific statistical characteristics can be generated, such as... Figure 3 As shown in the figure. As can be seen from the figure, the preset operating cycle in this embodiment... Within this range, the generated random operating condition curves closely match the pre-defined Markov chain state characteristics: the curves in the figure are located in the low to medium speed range ( The waveform of the high-speed range exhibits a relatively wide horizontal plateau, intuitively reflecting the longer duration of normal operation; conversely, the waveform in the high-speed range ( The waveform of the signal exhibits a narrow transient spike, corresponding to the short-term impact setting under extreme conditions. Furthermore, the transition paths between states show a linear transition with a slope rather than a vertical jump, clearly verifying the acceleration and deceleration inertial effects of the mechanical system simulated by the constant acceleration model.

[0078] Table 2 shows the statistical breakdown of the various speed states generated based on the above model. Among them, the total duration of the normal state accounts for as high as 93.2%, which is consistent with the characteristic that the bearing is mainly in stable operation; while the extreme state occurs less frequently, its high thermal load characteristics are the key risk point leading to thermal failure.

[0079] Table 2. Percentage of different speed states

[0080]

[0081] 2) For time-varying ambient temperature This embodiment uses a stochastic process model to simulate its continuous random fluctuations. As an exemplary existing technical implementation, a composite Gaussian process model can be used. This model typically consists of a mean function, a covariance kernel function, and a random noise term, and can characterize the trend of ambient temperature fluctuations around a certain mean and its temporal correlation.

[0082] Finally, all time-varying random parameters are used to construct a time-varying vector. :

[0083]

[0084] The model in this embodiment can generate time-varying curves of ambient temperature under dynamic operating conditions, such as... Figure 4 As shown. The preset operating cycle in this embodiment. Unlike the abrupt changes in rotational speed, the time-varying curve of ambient temperature in the figure exhibits a continuous and smooth quasi-periodic fluctuation trend, which conforms to the physical laws of ambient thermal inertia. The discrete envelope formed by the superposition of multiple curves clearly shows the random fluctuation range of ambient temperature near the mean baseline, demonstrating the accurate characterization of time-varying uncertainties by the Gaussian process model.

[0085] 2. Time-invariant random parameters: used to characterize the inherent differences between different bearings or different batches of materials. These mainly include radial load. Material elastic modulus and material Poisson's ratio .

[0086] This embodiment assumes that these time-invariant random parameters follow a specific probability distribution (e.g., a normal distribution). To ensure sampling coverage, sampling can be performed within a range of several times the standard deviation of their mean.

[0087] For example, in this embodiment, to ensure sampling coverage, at the mean... of Double standard deviation Cutoff uniform sampling was performed within the range, and the specific distribution characteristics of each parameter and the sampling range are shown in Table 3:

[0088] Table 3 Time-invariant random parameter distribution and sampling range

[0089]

[0090] Construct a vector of all time-invariant random parameters , can be represented as:

[0091]

[0092] Thus far, from the time-varying vector With time-invariant vectors Together, these constitute a hybrid random parameter vector that drives the thermal behavior of the bearing. Based on this, the random vector is integrated with the deterministic geometric parameters defined in step S11 to form the complete set of input parameters describing the bearing system.

[0093] S13: Construct a time-varying thermal failure limit state function based on a hybrid random parameter vector.

[0094] This step aims to establish mathematical criteria for determining whether a bearing has experienced thermal failure during operation. By constructing a time-varying thermal failure limit state function, the hybrid random parameter vector defined in step S12 is transformed into a quantifiable reliability index.

[0095] First, it is important to clarify the position of the bearing inner ring at any given time. instantaneous temperature It is not a constant value, but a function that depends on the input, and can be represented as: ,in The dynamic operating condition time-varying vector defined in step S12, The time-invariant vector for the material properties defined in step S12.

[0096] The allowable temperature is set based on the material's heat resistance properties or lubrication failure criteria. For example, for the 6208 bearing in this embodiment, the following settings are made: .

[0097] To determine whether the effect of the mixed random parameter vector exceeds the safety boundary, a time-varying thermal failure limit state function is constructed. , can be represented as:

[0098]

[0099] For the entire preset running cycle (The running cycle in this embodiment is) The judgment logic is as follows: if at any time... function value If the instantaneous response temperature exceeds the allowable temperature, then the bearing is determined to have experienced thermal failure under the influence of the current mixed random parameter vector during this operating cycle.

[0100] S2: Establish a transient thermal network model for deep groove ball bearings.

[0101] This step aims to construct a physical model that can dynamically reflect changes in the internal temperature field of the bearing. This model takes the basic parameter model defined in step S1 (such as geometric parameters and a hybrid random parameter vector) as input, and through coupled mechanics and heat transfer calculations, outputs a time-varying temperature response sequence for key parts of the bearing (such as the inner ring). This sequence is the direct basis for determining thermal failure. S21: Calculate the rolling element contact mechanical parameters based on the full input parameters.

[0102] This step is the starting point for physical simulation, aiming to determine the mechanical basis of frictional heat generation, namely, the contact load and contact angle at the contact point between the rolling element and the raceway.

[0103] In specific implementation, firstly, the deterministic geometric parameters (such as inner and outer diameters, channel curvature radius, number of spheres, etc.) and the mixed random parameter vector from the full set of input parameters defined in step S1 are retrieved. Based on this, a structure containing the first... The set of mechanical equilibrium equations for the rolling elements and the inner ring as a whole.

[0104] Subsequently, numerical iterative methods (such as the Newton-Raphson method) are used to numerically solve the mechanical equilibrium equations. Finally, the contact load between the rolling element and the inner and outer raceways is output. and contact angle This is used for subsequent calculations of the frictional heat generation rate.

[0105] S22: Calculate the frictional heat generation rate based on contact mechanical parameters.

[0106] This step aims to establish a quantitative relationship between microscopic mechanical states and macroscopic energy loss, generate the training data required for the surrogate model, and determine the input heat source terms required for subsequent solutions to the transient temperature field.

[0107] First, based on the mechanical contact parameters output from S21, and combined with the kinematic parameters (such as rotational speed) from the full set of input parameters in step S1, the power loss at each contact point is calculated using tribological empirical formulas. The final output is... The frictional heat generation rate of each rolling element applied to the inner and outer raceways ( ).

[0108] This step establishes a precise mapping dataset from all input parameters to the frictional heat generation rate, which can then be used to train the surrogate model, enabling it to learn how to quickly predict the frictional heat generation rate under dynamic operating conditions.

[0109] S23: Solve the transient temperature field based on the frictional heat generation rate and thermal impedance network, and output the time-varying temperature response sequence.

[0110] This step aims to use the frictional heat generation rate calculated in S22 as a heat source, and by establishing and solving the transient thermal network model of the bearing system, finally calculate the time-varying temperature response sequence of the key parts of the bearing (inner ring in this embodiment). This sequence is the direct input to the limit state function, used to determine whether thermal failure has occurred.

[0111] The specific implementation steps are as follows:

[0112] S231: Construct a nodal thermal impedance network.

[0113] This substep aims to discretize the continuous bearing entity into a thermal network consisting of nodes and thermal resistances, in order to numerically characterize its heat conduction and convection paths.

[0114] In practice, the bearing system (including the inner ring, outer ring, rolling elements, shaft, and bearing housing) is spatially discretized into several temperature-uniform nodes. The number and location of these nodes can be determined based on the required computational accuracy and the specific structure of the bearing.

[0115] Figure 5This embodiment demonstrates an example of node configuration for a nodal thermal network model of the 6208 bearing. In practical applications, the configuration of thermal network nodes offers a degree of flexibility. Those skilled in the art can adapt or re-divide the number and position of nodes according to the specific structural characteristics of the bearing, the complexity of the heat transfer path, and the specific requirements for computational accuracy. Such conventional adjustments based on specific operating conditions should all be included within the technical concept of this invention.

[0116] The black dots in the diagram represent the central nodes of each discrete control volume, and the symbol is... The temperature parameter representing this node, whose subscript specifically defines the physical path of heat transfer: inner ring nodes are defined. Outer ring nodes and rolling node These three types of nodes are located in the core area of ​​frictional contact and are the source of heat, directly receiving the heat generation rate input; multiple nodes are set along the axial direction on the rotating shaft ( This is used to simulate the gradient distribution of heat conduction from the inner ring to the shaft end. Nodes ( ) are set on the fixed bearing housing. This characterizes the radial diffusion of heat from the outer ring to the supporting structure and air. An ambient temperature node is set at the outermost perimeter of the system. This serves as the boundary condition for energy exchange between the entire thermal impedance network and the external environment.

[0117] Based on the principles of heat conduction and convection, the conductive thermal resistance between adjacent nodes and the convective thermal resistance at surface nodes are calculated to construct a nodal thermal impedance network reflecting the heat flow path; simultaneously, the heat generation rate calculated in step S22 is used... As a known heat flow term, it is directly applied to the nodes corresponding to the contact areas of the inner and outer raceways to simulate the injection of frictional heat.

[0118] In this embodiment, the constructed 6208 deep groove ball bearing node thermal impedance network is as follows: Figure 6 As shown in the figure, this diagram visually illustrates the complete physical path of heat dissipation from the heat source to the environment using a thermal impedance network. (Symbols) and These characters represent the contact thermal resistance between the rolling element and the inner raceway, and between the rolling element and the outer raceway, respectively. This is the critical bottleneck path for frictional heat conduction from the rolling element to the raceway. (Symbols) These symbols characterize the convective heat transfer resistance between the surfaces of the rolling elements, inner ring, and outer ring and the lubricating oil / gas medium within the bearing cavity, reflecting the ability of the fluid within the cavity to carry away heat. and These represent the radial and axial thermal resistances within the bearing housing, respectively; and and These represent the convective thermal resistances of the bearing housing surface for radial and axial heat dissipation from the ambient air, respectively. (Subscript band) Parameters (such as) (etc.) are collectively referred to as shaft thermal resistance, characterizing the impedance characteristics of heat transfer and dissipation along the radial and axial directions of the shaft. The contact friction heat generation rate of the inner and outer raceways calculated in step S22 is... and It is considered to be generated at the contact interface and, based on the principle of heat flow distribution at the contact surface, is set to be conducted evenly to both sides of the contact. The heat generation rate is... Half of it is applied to the outer nodes. The other half is applied to the rolling node. Total heat generation Half of it is applied to the inner circle nodes. The other half is also applied to the rolling node. .

[0119] S232: Solve the time-varying temperature sequence based on the nodal thermal impedance network model.

[0120] This sub-step aims to calculate the temperature of all nodes over time by solving the transient thermal equilibrium equations and extract the time-varying temperature response sequence of key components.

[0121] Based on the law of conservation of energy, a transient thermal equilibrium differential equation is established for each node in the thermal impedance network constructed by S231. This equation describes the balance relationship between the temperature change caused by the node's own heat capacity, the heat conduction between the node and its neighboring nodes, the convective heat transfer with the environment, and the internal heat source terms.

[0122] For example, for any node i, the transient thermal equilibrium equation can be established in the following form:

[0123]

[0124] in: and For material density and specific heat capacity, For nodes Volume; , For nodes With neighboring nodes Temperature; Thermal conductivity; , Inter-node heat transfer area and heat transfer distance; Surface convective heat transfer coefficient; For convective heat transfer area; The ambient temperature; To apply to the node The heat generation rate of the internal heat source on the surface.

[0125] By solving the system of equations consisting of all nodal equations using numerical integration methods (such as the Runge-Kutta method), the equations for the entire running cycle can be obtained. Within the bearing, the complete temperature field of each node varies with time. Extracting the temperature data of key nodes in the bearing's inner ring from this temperature field constitutes the desired time-varying temperature response sequence. .

[0126] This time-varying temperature sequence This will be used directly as the basis for failure determination: Substitute this sequence into the time-varying thermal failure limit state function defined in step S13. In the middle. If the temperature response at any given time leads to... (Right now If the condition is met, then the bearing is determined to have experienced thermal failure under the current set of input parameters.

[0127] It should be noted that the transient thermal network model of the deep groove ball bearing established in step S2 above essentially integrates the solution of contact mechanical parameters in step S21 and the solution of transient temperature field in step S23, reflecting the real-time coupling characteristics of mechanical state and thermal response. Therefore, to emphasize its physical meaning, in the subsequent description of this embodiment (e.g., step S32), this "transient thermal network model" is also referred to as the "dynamic thermo-mechanical coupling model," both referring to the same physical simulation object.

[0128] S3: Construct a proxy model to replace the time-consuming calculation of frictional heat generation rate.

[0129] This step aims to address the inefficiency of directly calling the transient thermal network model described in S2 for large-scale calculations. By constructing a surrogate model and training it using a small number of "input-output" samples generated by the S2 model, it learns the complex mapping relationship from the mixed random parameter vector to the frictional heat generation rate. This allows it to replace the frictional heat generation rate calculation step in S22 in subsequent analyses, achieving rapid prediction.

[0130] like Figure 7 As shown, this step specifically includes the following process:

[0131] S31: Generate the training sample set and the test sample pool.

[0132] This step aims to prepare the data foundation for both the training (learning phase) and subsequent reliability assessment (application phase) of the surrogate model.

[0133] The specific implementation steps are as follows:

[0134] S311: Define the joint sampling space. Based on the mixed random parameter vector constructed in step S12, determine the sampling boundary. Wherein, the time-varying random parameter vector... Discretize the process as a random process; time-invariant random parameter vector The range of values ​​is then determined based on its probability density function (such as the normal distribution).

[0135] S312: Generate a large-scale Monte Carlo sample pool based on the joint sampling space. To capture extremely low-probability failure events in subsequent steps, a sufficiently large sample size needs to be constructed. This embodiment uses the Monte Carlo method to randomly sample from the joint sampling space defined in S311. One sample (set in this embodiment) ), forming the sample pool to be tested :

[0136]

[0137] Each sample contains a single line throughout the entire time interval. Discretized time-varying parameter sequence and a fixed set of time-invariant parameter values .

[0138] Each sample in this sample pool represents a possible bearing life cycle condition, which will be input into the trained surrogate model for rapid prediction in subsequent steps.

[0139] S313: Generating a Small-Scale Experimental Training Sample Set Based on the Joint Sampling Space. To allow the surrogate model to traverse the features of the input space with minimal computational cost, an efficient experimental design method is used to generate initial training samples. This embodiment employs the Latin hypercube sampling method. Within the joint sampling space defined in S311, only samples are taken... One sample (set in this embodiment) ), forming the initial training sample set .

[0140] This method ensures that the distribution range of each random variable is uniformly covered by layers, thereby obtaining more representative model feature information with fewer sample points.

[0141] S32: Train and validate the surrogate model based on the training sample set.

[0142] This step aims to use the dynamic thermo-mechanical coupling model described in step S2 to generate true "input-output" data as training samples, and to establish a mathematical mapping relationship between the total input parameters and the frictional heat generation rate.

[0143] The specific implementation steps are as follows:

[0144] S321: Use the dynamic thermal-mechanical coupling model to obtain the true values ​​of the training data. Use the initial training sample set generated in step S313. For each sample (150 groups in this embodiment), the dynamic thermo-mechanical coupling model constructed in step S2 is called for high-precision calculation. The frictional heat generation rate in the calculation result is extracted as the target response value. Thus, a complete training dataset containing 150 pairs of "full input parameter set - frictional heat generation rate" is obtained.

[0145] S322: Construct and train a surrogate model based on the training dataset. Based on the dataset obtained in S321, train a surrogate model. As a preferred implementation, the Kriging Gaussian process regression algorithm can be used to construct the surrogate model. This model can establish a nonlinear mapping relationship between input parameters and output response, mathematically expressed as follows:

[0146]

[0147] in, The heat generation rate predicted by the model; The deterministic trend function (a second-order polynomial is used in this embodiment); This is a stationary Gaussian random process used to correct for local biases. Hyperparameters (such as the correlation length of the kernel function) are optimized by maximizing the likelihood function to achieve the best fitting accuracy of the model on the training data.

[0148] S323: Surrogate Model Accuracy Validation. To ensure the surrogate model is sufficiently reliable, it is validated using a set of independent test samples not used in training. This embodiment uses root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (COP). () was used as the evaluation index. The verification results are shown in Table 4:

[0149] Table 4. Validation results of regression evaluation index for frictional heat generation rate of the proxy model.

[0150]

[0151] Coefficient of determination The mean absolute error (MAE) reached 0.9982, which is extremely close to 1, indicating that the model explains 99.8% of the data variation patterns. The mean absolute error (MAE) was only 0.4622 W, which is negligible compared to the total heat generated during bearing operation.

[0152] The verification results show that the constructed proxy model has the ability to replace the calculation of contact mechanical parameters in S21 and frictional heat generation rate in S22, and can efficiently output high-precision frictional heat generation rate to meet the engineering requirements of subsequent large-scale reliability analysis.

[0153] S4: Estimate the time-varying thermal failure probability based on the surrogate model and an adaptive time node sampling strategy.

[0154] This step aims to efficiently and accurately calculate the time-varying thermal failure probability of deep groove ball bearings. Its core lies in using the surrogate model trained in step S3 and the transient thermal network model established in step S2 as computational tools to execute an adaptive time-node sampling strategy on a large-scale sample set generated based on probability sampling. This strategy achieves optimal allocation of computational resources while ensuring estimation accuracy through a two-stage calculation of "sparse screening and local refinement" and convergence control based on the coefficient of variation. In this embodiment, the evaluation process is as follows: Figure 8 As shown.

[0155] This step specifically includes the following sub-steps:

[0156] S41: Rapidly screen potentially failed samples based on sparse time nodes.

[0157] This step aims to optimize the large-scale Monte Carlo sample pool generated by S31 with minimal computational cost. (In this embodiment, 200,000 samples are used) for rapid initial screening to identify potentially failed samples that require further analysis, thereby reducing the scale of subsequent high-precision calculations.

[0158] The specific implementation steps are as follows:

[0159] S411: Set a sparse time node sequence To quickly capture the overall trend of temperature changes during the bearing's operating cycle. A small number of time points are selected within the time frame. For example, in this embodiment, a time step is set. Discretize 24 hours into A sparse time node.

[0160] S412: Preliminary calculation of the initial time-varying temperature sequence under sparse time node sequence based on surrogate model and thermal impedance network. The large-scale Monte Carlo sample pool generated in S31... Each sample is input into the surrogate model trained in step S32 to quickly predict its value. The predicted frictional heat generation rate sequence is obtained at sparse time points. Then, using the predicted frictional heat generation rate sequence as a heat source, the transient temperature field is solved through S23 to obtain the preliminary temperature sequence of the sample. .

[0161] S413: Screening potential failure samples based on preliminary temperature sequences and safety margin thresholds. To prevent missing transient high temperatures due to sparse sampling, a threshold temperature is set. Stricter screening thresholds (In this embodiment) Iterate through all samples. If the initial temperature sequence of a sample exceeds a certain value at any sparse time node... If so, it is marked as a potential failure sample and constitutes a potential failure sample set. .

[0162] In the specific screening of this embodiment, 16,832 potentially invalid samples were identified from the 200,000 original samples (i.e., the large-scale Monte Carlo sample pool) generated in S31. This means that 91.5% of the safe samples were successfully eliminated, and only the remaining 8.45% need to be calculated.

[0163] S42: Perform global time node encryption calculations on potentially failed samples.

[0164] This step aims to address the potential failure sample set identified in S41. Through high-density, full-time-domain fine-grained calculations, transient high-temperature peaks that might be missed by sparse nodes are accurately captured, ensuring the accuracy of the final judgment. The specific implementation steps are as follows:

[0165] S421: Construct a dense time node sequence. To avoid missing transient high-temperature peaks due to sparse sampling, during the bearing operating cycle... Select a larger set of time points. For example, encrypt the time step to... Thus, within 24 hours, a system containing A dense sequence of time points.

[0166] S422: Calculation of accurate time-varying temperature sequences under dense time node sequences based on surrogate models and thermal impedance networks. This involves the potential failure sample set selected in S41. Each sample in the dataset undergoes a fine-grained computation: using the surrogate model trained in S32, it predicts the value defined in S421. Frictional heat generation rate at several dense time points; accurate temperature sequence is obtained by solving the transient temperature field using S23. .

[0167] In this embodiment, the surrogate model is used to predict the frictional heat generation rate of the 16,832 potential failure samples identified in S413 at 300 dense time nodes defined in S421, and finally the accurate temperature sequence of each potential failure sample is obtained.

[0168] A comparison chart of the differences between the preliminary temperature series and the precise temperature series is shown below. Figure 9As shown in the figure, this figure selects a typical sample from the potential failure sample set as an example of data content. As the figure shows, the preliminary temperature sequence based on sparse nodes and the precise temperature sequence based on dense nodes maintain a high degree of consistency in overall trend. However, in the peak region of drastic operating condition fluctuations (approximately 13-14 hours), the preliminary temperature sequence, due to insufficient sampling points, fails to capture the transient highest temperature peak, thus failing to reflect actual failures exceeding the threshold. This visually demonstrates that while sparse sampling can reflect the overall trend, it carries the risk of missing transient extreme high temperatures.

[0169] S43: Count the number of failure samples based on the accurate temperature sequence and calculate the initial failure probability.

[0170] This step aims to determine the failure state of potential failure samples based on accurate temperature sequences and to statistically analyze the proportion of failure samples, thereby obtaining an initial estimate of the time-varying thermal failure probability.

[0171] The specific implementation steps are as follows:

[0172] S431: Determine the failure state of each potential failure sample based on the precise temperature sequence. Based on the failure criteria defined in step S13, examine the precise temperature sequence traversed by each potential failure sample. If there exists any time in the precise temperature sequence Temperature exceeds allowable temperature Then determine the failure indication function Otherwise, it is 0.

[0173] S432: Calculate and statistically analyze the initial probability estimate based on the failure determination results. This sub-step aims to statistically analyze the failure indication functions of all samples in the potential failure sample. The number of failure samples is determined. The initial time-varying thermal failure probability is calculated using the ratio of the number of failure samples to the total number of samples. .

[0174] In this embodiment, statistical analysis revealed that among the 16,832 potential failure samples identified in S413, 267 samples had failure indication functions. That is, its actual maximum temperature exceeds the allowable temperature set in this embodiment. Therefore, the initial failure probability estimate based on the 200,000 samples generated by S31 is:

[0175]

[0176] S44: Sample adaptive expansion and convergence control based on initial time-varying thermal failure probability and coefficient of variation.

[0177] Since thermal failure is a low-probability event, the estimated failure probability often exhibits significant statistical fluctuations with a limited sample size. To assess the reliability of the current estimation results, this invention introduces the coefficient of variation. The coefficient of variation characterizes the relative dispersion of the estimated value; the smaller the coefficient of variation, the more stable the estimated value and the closer it is to the true probability.

[0178] The specific implementation steps are as follows:

[0179] S441: Calculate the initial coefficient of variation based on the initial time-varying thermal failure probability.

[0180] In this embodiment, a preset target engineering accuracy threshold is set. The initial time-varying thermal failure probability calculated based on S432 The coefficient of variation of the current estimate is calculated using statistical formulas, based on the original sample size set in S312. For example, the coefficient of variation of the current failure probability estimate can be estimated using the following formula. :

[0181]

[0182] If the coefficient of variation of the current estimated value is greater than the preset target engineering accuracy threshold This indicates that the estimation results under the current sample size have high dispersion and insufficient reliability, and the sample size must be increased.

[0183] In this embodiment, the initial time-varying thermal failure probability calculated by S432 The number of original samples set in S312 After substituting and calculating, we get Because this value is greater than the target engineering accuracy threshold preset in this embodiment. Therefore, the sample size must be increased.

[0184] S442: Calculate and expand the new sample size based on the initial coefficient of variation and the target engineering accuracy threshold.

[0185] In this embodiment, the initial coefficient of variation calculated based on S441 is... With respect to the set target engineering accuracy threshold The difference, calculated using statistical formulas, determines the required new sample size. For example, it can be based on the current coefficient of variation. With target value The ratio is used to estimate the required additional sample size using the following formula. :

[0186]

[0187] After calculation and rounding, the new sample set is generated according to the method in step S31. .

[0188] In this embodiment, the initial coefficient of variation calculated in S441 is substituted. With respect to the set target engineering accuracy threshold and the number of original samples set in S312. After substituting into the formula and rounding, the new sample size is determined. .

[0189] S443: Based on the newly added sample set, perform iterative calculations and finally converge to obtain the time-varying thermal failure probability and coefficient of variation after iteration.

[0190] This step involves processing the newly generated sample set from S442. Repeat the screening and actuarial process of S41-S43 to obtain the time-varying thermal failure probability and coefficient of variation after iteration. Merge the old and new data and calculate the total sample size. And count the total number of failure samples. Based on the total number of failure samples and the total sample size, update the failure probability estimate. Based on the updated failure probability estimate With total sample size Update the coefficient of variation Until the coefficient of variation Less than the target engineering accuracy threshold set by S441 If the iteration fails, it is considered convergent, and the iteration stops.

[0191] In this embodiment, statistical analysis revealed that among the 100,000 newly added samples in S442, 3,120 potentially failed samples were identified through screening and calculation in S41-S43, and 138 failed samples were confirmed. The total sample size after merging the old and new samples is... The total number of failures is 267 + 138 = 405. The probability of a thermal failure during an update can be represented as follows:

[0192]

[0193] The updated coefficient of variation can be represented as follows:

[0194]

[0195] at this time Less than the target engineering accuracy threshold set by S441 Once the accuracy requirements are met, the calculation converges, and the iteration stops.

[0196] S45: Output the final time-varying thermal failure probability assessment result.

[0197] Based on the converged statistical data, output the time-varying thermal failure probability of deep groove ball bearings under specified dynamic conditions. Final coefficient of variation Total number of samples calculated The evaluation results are pending.

[0198] In this embodiment, the time-varying thermal failure probability assessment results of the 6208 deep groove ball bearing under specified dynamic operating conditions are output, as shown in Table 5.

[0199] Table 5. Evaluation Results of Time-Varying Thermal Failure Probability for Bearing 6208

[0200]

[0201] Example 2

[0202] This embodiment provides a system for estimating the probability of time-varying thermal failure of deep groove ball bearings, as described in Embodiment 1. Figures 10 to 13 As shown, this system adopts a modular design and is deployed in a high-performance computing environment, enabling it to efficiently handle parallel computing tasks with massive amounts of samples. The system mainly consists of the following four core modules:

[0203] 1. Basic Parameter Modeling Module

[0204] This module is responsible for establishing the digital input and failure criteria for bearing thermal failure analysis, corresponding to step S1 in method embodiment 1. Specifically, it includes:

[0205] 1) Deterministic geometry definition unit: Provides an interactive interface or data interface for inputting or loading bearing deterministic geometry parameters (such as inner and outer diameters, ball diameters, groove curvature radius, etc.) as shown in Table 1 of Example 1.

[0206] 2) Hybrid Random Parameter Vector Construction Unit: This unit integrates a probabilistic model generation algorithm. For time-varying random parameters, this unit incorporates a multi-state Markov chain model and a composite Gaussian process model, which can respectively generate... Figure 3 , Figure 4 The dynamic rotational speed sequence and ambient temperature sequence are shown. For time-invariant random parameters, this unit generates parameter values ​​such as radial load and material elastic modulus based on a preset normal distribution equal probability model, and the distribution characteristics are shown in Table 3 of Example 1. The unit finally outputs a hybrid random parameter vector composed of a time-varying vector A(t) and a time-invariant vector B.

[0207] 3) Failure Criterion Definition Unit: Used to set the allowable temperature threshold T allow (e.g., 114℃), and construct the time-varying thermal failure limit state function according to the logic defined in S13 of Example 1. This serves as a unified criterion for subsequent failure assessment of the system.

[0208] 2. Transient thermal network simulation module

[0209] This module is the core of achieving high-fidelity physical simulation, corresponding to step S2 in method embodiment 1. It is used to generate surrogate model training data and provide accurate temperature field solution capabilities. Specifically, it includes:

[0210] 1) Heat Generation Rate Calculation Unit: Used to calculate the frictional heat generation rate inside the bearing based on the aforementioned basic parameter model. Specifically, it receives all input parameters from the basic parameter modeling module, first calls the built-in quasi-static model (whose equilibrium equation is as described in S212 of Example 1) to calculate the rolling element contact load and contact angle, and then calculates the frictional heat generation rate of the inner and outer raceways of the bearing based on the tribological formulas of Palmgren et al. (as described in S221 of Example 1). The frictional heat generation rate output by this unit is the training target for subsequent surrogate models.

[0211] 2) Thermal Network Construction and Solving Unit: This unit constructs the nodal thermal impedance network of the bearing and solves the thermal network using the frictional heat generation rate output by the heat generation rate calculation unit as the heat source to obtain the time-varying temperature response sequence. Specifically, based on the bearing geometry and material properties, it can automatically construct the network as shown in Example 1. Figure 5 , Figure 6 The shown is a nodal thermal impedance network. This unit receives heat source input from the heat generation rate calculation unit and outputs the time-varying temperature response sequence T(t) of key bearing parts (such as the inner ring) by solving the transient thermal balance equations as in Example 1 (using numerical integration methods such as the Runge-Kutta method).

[0212] 3. Proxy Model Construction Module

[0213] This module is responsible for constructing an efficient approximate model to replace the time-consuming calculation of the heat generation rate, corresponding to step S3 in method embodiment 1. Specifically, it includes:

[0214] 1) Training Data Preparation Unit: This unit is used to extract a set of training samples within the distribution space of the mixed random parameter vector and generate realistic frictional heat generation rate responses for these training samples using the transient thermal network simulation module, thus forming training data. Specifically, experimental design methods such as Latin hypercube sampling (LHS) can be used to intelligently extract a small number (e.g., 150) of samples from the joint distribution space of the mixed random parameter vector to form an initial training sample set. Subsequently, the transient thermal network simulation module is automatically invoked to calculate accurate true values ​​of the frictional heat generation rate for these training samples, thereby forming a paired training dataset of "input parameters - heat generation rate response".

[0215] 2) Model Training Unit: Used to train a surrogate model for predicting the frictional heat generation rate based on the training data. Specifically, based on the above training dataset, the surrogate model can be trained using the Kriging Gaussian process regression algorithm (whose mathematical model is described in S322 of Example 1). By maximizing the likelihood function to optimize the model hyperparameters, a lightweight surrogate model capable of quickly predicting the heat generation rate corresponding to any input parameters is finally established. Before being put into use, this model needs to be validated on an independent test set to ensure that it meets the high accuracy requirements (e.g., R² > 0.99) shown in Table 4 of Example 1.

[0216] 4. Adaptive Probability Evaluation Module

[0217] This module is the core of the system's scheduling and execution, corresponding to step S4 in method embodiment 1, achieving an intelligent balance between accuracy and efficiency. Specifically, it includes:

[0218] 1) Sparse Screening Unit: Sets a sparse time node sequence (e.g., 30 nodes). For a massive Monte Carlo sample pool (e.g., 200,000 samples), this unit first calls the surrogate model to quickly predict its heat generation rate at the sparse nodes, and then calls the thermal network construction and solution unit to calculate the preliminary temperature sequence. A safety margin threshold (e.g., T0) is introduced. allow -5°C) quickly eliminates the vast majority of safe samples, filtering out a small subset (e.g., about 8%) of potentially failed samples.

[0219] 2) Global Encryption Calculation Unit: For the selected potentially failed sample set, a dense time node sequence (e.g., 300 nodes) is automatically constructed. The surrogate model and thermal network solution unit are invoked again to perform full-time high-resolution temperature calculations on these samples, accurately capturing transient high-temperature peaks that may have been missed by sparse sampling, as described in Example 1. Figure 9 As shown.

[0220] 3) Convergence Control and Sample Expansion Unit: Based on the accurate calculation results, this unit statistically analyzes failed samples and calculates the initial failure probability estimate and its coefficient of variation (COV). This unit has a preset target accuracy threshold (e.g., COV ≤ 0.05). If the current COV does not meet the requirements, it automatically calculates the number of new samples to be added according to the formula (as described in S442 of Example 1), and triggers the basic parameter modeling module to generate new samples, starting a new round of screening and calculation process until the evaluation results meet the convergence conditions.

[0221] 4) Evaluation result output unit: integrate and output the final evaluation report, including the converged time-varying thermal failure probability, coefficient of variation, total number of calculated samples, etc., in the form shown in Table 5 of Example 1.

[0222] This system can be deployed on Kubernetes-based cloud platforms or high-performance computing clusters. The adaptive probability assessment module acts as the main controller, responsible for task scheduling and process coordination; the transient hot network simulation module and the agent model construction module can be encapsulated as distributed microservices, receiving parallel computing tasks through message queues (such as Kafka). This architecture achieves elastic scaling and load balancing of computing resources, greatly improving the overall efficiency of processing massive amounts of time-varying uncertain samples.

[0223] Example 3

[0224] This embodiment provides an electronic device for implementing the aforementioned method for estimating the probability of time-varying thermal failure in deep groove ball bearings. This electronic device can be a workstation, server, high-performance computing cluster node, or cloud virtual machine, etc.

[0225] The electronic device in this embodiment includes a processor, a memory, a communication interface, and a system bus. The memory may include volatile memory (such as RAM) and non-volatile memory (such as ROM, flash memory, or hard disk drive). The system bus couples the various system components, including the processor and memory, together.

[0226] The memory stores a computer program (i.e., a software system) that can be executed by the processor. When the computer program is executed by the processor, the electronic device, as a whole, performs the steps of the method described in Embodiment 1, or performs all or part of the functions of the system described in Embodiment 2.

[0227] Specifically, when the processor executes the computer program, it is able to:

[0228] 1. Call the basic parameter modeling logic to construct a basic parameter model containing a mixed random parameter vector and a limit state function.

[0229] 2. Call the transient thermal network simulation logic to perform physical calculations of the frictional heat generation rate and temperature field.

[0230] 3. Call the surrogate model construction logic to train and validate the surrogate model for quickly predicting the heat generation rate.

[0231] 4. Invoke the adaptive probability evaluation logic, execute the "sparse screening-local encryption" sampling strategy and the iterative convergence control based on the coefficient of variation, and finally output the estimated value of time-varying thermal failure probability.

[0232] This electronic device can receive bearing parameters and operating condition settings input by the user through a communication interface, and can also transmit the final probability assessment results to a display device or other data analysis system.

[0233] Example 4

[0234] This embodiment provides a computer-readable storage medium for storing a computer program that implements the above-described method for estimating the probability of time-varying thermal failure of deep groove ball bearings.

[0235] The computer-readable storage medium can be any tangible medium that contains or stores a program, such as, but not limited to: USB flash drive, portable hard drive, read-only memory (ROM), random access memory (RAM), disk (including hard disk and floppy disk), optical disk (including CD-ROM and DVD-ROM), or cloud storage space, etc.

[0236] The storage medium stores a computer program (instructions). When the computer program is read and executed by one or more processors (e.g., the processor of the electronic device in Embodiment 3), the processor is able to perform the steps of the method described in Embodiment 1, or control the corresponding device to perform the functions of the system described in Embodiment 2.

[0237] The computer program includes a series of instructions that, when executed, specifically instruct the processor to complete the complete process of S1 to S4 as detailed in Example 1.

[0238] Through this storage medium, the efficient and accurate time-varying thermal failure probability estimation technology for deep groove ball bearings described in this embodiment of the invention can be saved, distributed, and deployed in the form of a software product, facilitating its widespread application in industrial design environments.

[0239] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for estimating the probability of time-varying thermal failure of deep groove ball bearings, characterized in that, Includes the following steps: A basic parameter model for thermal failure analysis is constructed, which includes the deterministic geometric parameters of the bearing, a mixed random parameter vector for simulating dynamic working conditions and inherent discreteness, and a time-varying limit state function for determining failure. Based on the aforementioned basic parameter model, a transient thermal network model of the deep groove ball bearing is established, and the time-varying temperature response sequence of the bearing under dynamic operating conditions is calculated. A surrogate model for predicting the frictional heat generation rate is constructed, wherein the training of the surrogate model is based on sample data generated by the transient thermal network model, so that the trained surrogate model can replace the calculation of the frictional heat generation rate in the transient thermal network model. Based on the surrogate model and the transient thermal network model, an adaptive time node sampling strategy is used to process a large-scale sample set in order to estimate the time-varying thermal failure probability of the deep groove ball bearing.

2. The method according to claim 1, characterized in that, The hybrid random parameter vector includes time-varying random parameters and time-invariant random parameters; wherein, the time-varying random parameters are simulated for their dynamic fluctuations by a stochastic process model, and the time-invariant random parameters are described for their inherent discreteness by a probability distribution model.

3. The method according to claim 1, characterized in that, Establishing the transient thermal network model includes: calculating the frictional heat generation rate inside the bearing based on the basic parameter model; constructing the nodal thermal impedance network of the bearing, and solving the thermal network with the frictional heat generation rate as the heat source to obtain the time-varying temperature response sequence.

4. The method according to claim 1, characterized in that, The construction of the surrogate model includes: using the transient thermal network model to generate a real frictional heat generation rate response for a set of training samples extracted in the distribution space of the mixed random parameter vector; and training a surrogate model for predicting the frictional heat generation rate based on the training samples and their real responses.

5. The method according to claim 1, characterized in that, The adaptive time-node sampling strategy includes: performing preliminary temperature calculation and sample screening based on a first-precision time-node sequence; and performing precise temperature calculation on the screened samples based on a second-precision time-node sequence, wherein the density of the second-precision time-node sequence is higher than that of the first-precision time-node sequence.

6. A time-varying thermal failure probability estimation system for deep groove ball bearings, characterized in that, include: The basic parameter modeling module is used to construct the basic parameter model for thermal failure analysis. The basic parameter model includes the deterministic geometric parameters of the bearing, a mixed random parameter vector for simulating dynamic working conditions and inherent discreteness, and a time-varying limit state function for determining failure. The transient thermal network simulation module is used to establish a transient thermal network model of a deep groove ball bearing. Taking the basic parameter model as input, it calculates the frictional heat generation rate and solves the thermal network to output the time-varying temperature response sequence of key parts of the bearing. The proxy model construction module is used to construct and train a proxy model. The proxy model is trained based on the training sample pairs generated by the transient thermal network simulation module and is used to replace the frictional heat generation rate calculation step in the transient thermal network simulation module. The adaptive probability assessment module is used to employ an adaptive time node sampling strategy, combined with the surrogate model construction module and the transient thermal network simulation module, to perform failure screening and probability statistics on a large-scale sample set generated based on probability sampling, and output the time-varying thermal failure probability estimate of the deep groove ball bearing.

7. The system according to claim 6, characterized in that, The transient thermal network simulation module includes: The heat generation rate calculation unit is used to calculate the frictional heat generation rate inside the bearing based on the basic parameter model. The thermal network construction and solution unit is used to construct the nodal thermal impedance network of the bearing, and solve the thermal network using the frictional heat generation rate output by the heat generation rate calculation unit as the heat source to obtain the time-varying temperature response sequence.

8. The system according to claim 6, characterized in that, The proxy model construction module includes: The training data preparation unit is used to extract a set of training samples in the distribution space of the mixed random parameter vector, and use the transient thermal network simulation module to generate a real frictional heat generation rate response for the training samples to form training data. The model training unit is used to train a surrogate model for predicting the rate of frictional heat generation based on the training data.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 5.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 5.

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