A Method for Modeling the Accelerated Degradation and Reliability Evaluation of Grease

Abstract

The present invention discloses a method for grease accelerated degradation modeling and reliability evaluation, which relates to the technical field of grease performance degradation research. The method includes: determining the grease performance degradation characterization index, constructing a non-linear accelerated degradation reliability model of the grease by using the gamma function; introducing an error term that follows a normal distribution; deriving the life distribution function of each performance degradation characterization index; using the Frank Copula function as the connection function to establish a coupled reliability function between the performance degradation characterization indexes; using the maximum likelihood estimation method and combining with the non-linear regression method to derive the estimated values of all unknown parameters in the model under actual working conditions; substituting the estimated values of each unknown parameter into the reliability function to calculate the equivalent life of the grease under actual working conditions. Through the present invention, the degradation reliability evaluation of grease considering multi-source randomness and multi-performance degradation indexes is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of research on the performance degradation of greases, and particularly to a method for accelerating the degradation modeling and reliability evaluation of greases. Background Art

[0002] As a lubricating material commonly used in key functional components of mechanical equipment, the lubricating performance of grease directly affects the working performance and service life of mechanical products. However, in the core transmission mechanism of mechanical equipment, due to the complex structure and narrow space, it is difficult to add and replace grease. Therefore, studying the degradation law of grease is of great significance for evaluating the reliability of mechanical products, formulating reasonable maintenance strategies, and improving the service life of equipment.

[0003] Traditional methods for evaluating the reliability of grease mainly rely on failure data. However, due to the relatively high reliability of grease itself, it is very difficult to obtain failure data, and these data cannot accurately describe its degradation law under actual working conditions. Even if some failure data can be collected, these data are often affected by environmental factors and human factors and have poor accuracy, resulting in the accuracy of reliability evaluation results being difficult to meet the requirements. Therefore, developing a reliability evaluation method for grease based on accelerated degradation not only has important theoretical significance but also plays a key role in engineering applications.

[0004] The composition of grease is complex, and different lubricity requirements for grease are needed in different usage scenarios. Therefore, multiple performance parameters are required for characterization. However, there are often certain internal connection attributes between the performance characterization parameters. Therefore, describing the correlation relationship between the performance characterization parameters is also an important link to ensure the accuracy of reliability modeling and evaluation. Existing methods often select the performance index with the most obvious degradation trend as the evaluation target, ignoring the mutual relationship between the performance indexes, which affects the accuracy of the degradation model. Summary of the Invention

[0005] The present invention aims to provide a method for accelerating the degradation modeling and reliability evaluation of grease, aiming to solve the technical problems mentioned in the above background art.

[0006] To achieve the above object, the present invention adopts the following technical solutions: According to one aspect of the present invention, a grease accelerated degradation modeling and reliability evaluation method is provided, including: determining the grease performance degradation characterization index, setting the degradation increment of the performance degradation characterization index to follow a gamma distribution, and constructing a non-linear accelerated degradation reliability model of the grease using the gamma function. The non-linear accelerated degradation reliability model is used to describe the degradation process of the grease performance under different stress conditions; based on the non-linear accelerated degradation reliability model, an error term following a normal distribution is introduced during the non-linear gamma accelerated degradation process of the grease to establish a grease accelerated degradation reliability model considering measurement errors; according to the grease accelerated degradation reliability model, the life distribution function of each performance degradation characterization index is derived. The life distribution function is used to describe the probability distribution of the grease performance degradation at different time points; the Frank Copula function is used as the connection function to establish a coupled reliability function between the performance degradation characterization indexes; the maximum likelihood estimation method is used, combined with the non-linear regression method, to derive the estimated values of all unknown parameters in the grease accelerated degradation reliability model under actual working conditions; according to the obtained estimated values of each unknown parameter, substituting them into the reliability function to calculate the equivalent life of the grease under actual working conditions, thereby realizing reliability evaluation.

[0007] Optionally, constructing the non-linear accelerated degradation reliability model of the grease using the gamma function includes:

[0008] The performance degradation path of the grease follows a gamma process. According to the characteristics of the gamma process, the non-linear accelerated degradation reliability model of the grease is expressed as:

[0009] ;

[0010] In the formula, represents the th performance degradation characterization index of the grease, , is the total number of grease performance degradation characterization indexes; represents the degradation increment of the th performance degradation characterization index of the grease sample at the th measurement under the accelerated stress level ; represents the rd accelerated stress level; represents the th shape parameter of the th performance degradation characterization index under the accelerated stress level ; represents the measurement interval between two adjacent measurements; represents the th diffusion coefficient of the performance degradation characterization index. It is indicated that the degradation path follows a gamma distribution;

[0011] For , the Arrhenius model is used for description to explain the influence on the degradation increment of the th performance degradation characterization index of the grease under different accelerated stress levels. Among them, the Arrhenius model is expressed as:

[0012] ;

[0013] In the formula, represents the first unknown parameter of the th performance degradation characterization index; represents the second unknown parameter of the th performance degradation characterization index; represents the standardized value of the stress level; represents the normal working stress of the grease; represents the maximum accelerated stress of the grease.

[0014] Optionally, the method further includes randomizing the shape parameter in the non-linear accelerated degradation reliability model of the grease to introduce the difference between sample individuals, so as to describe the influence of the difference between sample individuals on the degradation increment of the th performance degradation characterization index of the grease. The shape parameter is expressed as: ;

[0015] In the formula, is the mean coefficient of the randomization of the shape parameter of the th performance degradation characterization index; is the variance coefficient of the randomization of the th performance degradation characterization index; represents that the shape parameter of the th performance degradation characterization index follows a normal distribution.

[0016] Optionally, a normally distributed error term is introduced in the non-linear gamma accelerated degradation process of the grease to establish a reliability model for the accelerated degradation of the grease considering measurement errors; according to the reliability model for the accelerated degradation of the grease, the life distribution function of each performance degradation characterization index is derived, including:

[0017] When measurement errors are not considered, the Birnbaum-Saunders distribution is used to approximate the distribution of the degradation process, and the probability density function of the non-linear accelerated degradation reliability model is expressed as: ;

[0018] ;

[0019] ;

[0020] wherein, represents the probability density function of the degradation increment of the th performance degradation characterization index; represents the measurement time; represents the shape parameter of the th performance degradation characterization index; represents the scale parameter of the th performance degradation characterization index; represents the failure threshold of the th performance degradation amount;

[0021] The introduced error term follows a normal distribution and is expressed as:

[0022] ;

[0023] wherein, represents the measured degradation amount; represents the true degradation amount; represents the random measurement error, which is related to the accuracy of the measuring instrument, ; represents the standard deviation of the measurement error;

[0024] When the error term is introduced into the grease accelerated degradation general non - linear Gamma process, then considering the measurement error, the probability density function is expressed as:

[0025] ; ;

[0026] wherein, represents the life; represents the probability density function of the th performance degradation characterization index considering the measurement error; represents the probability density function of the measurement error; represents the diffusion coefficient of the th performance degradation characterization index.

[0027] Optionally, after deriving the life distribution function of each performance degradation characterization index according to the grease accelerated degradation reliability model, the method further includes:

[0028] Constructing the cumulative distribution function of each performance degradation characterization index according to the grease accelerated degradation reliability model:

[0029] ;

[0030] Among them, represents the cumulative distribution function of the degradation increment of the th performance degradation characterization index; , which represents that under the accelerated stress level , for the grease sample at the th measurement, the degradation increment of the th performance degradation characterization index, represents the time point of the th measurement; , which represents the failure threshold of the th performance degradation characterization index after considering the error; represents the shape parameter of the th performance degradation characterization index under the accelerated stress level ; represents the diffusion coefficient of the th performance degradation characterization index; represents the measurement error; represents the simplified form of the probability density function of the th performance degradation characterization index without measurement error.

[0031] Optionally, using the Frank Copula function as the copula function, the reliability function coupling the performance degradation characterization indices includes:

[0032] The reliability function coupling the performance degradation characterization indices is:

[0033] ;

[0034] Among them, represents the reliability function coupling the th performance degradation characterization index; represents the Copula linear correlation coefficient under normal temperature stress; represents the reliability function of the first performance degradation characterization index; represents the reliability function of the second performance degradation characterization index; represents the corresponding Copula distribution function;

[0035] If the Frank Copula is selected as the copula function, then .

[0036] Optionally, using the maximum likelihood estimation method and combined with the nonlinear regression method, the estimated values of all unknown parameters in the grease accelerated degradation reliability model under actual working conditions include:

[0037] Obtain the unknown parameters in the grease accelerated degradation reliability model to form a set of unknown parameters;

[0038] Construct the log-likelihood function of the set of unknown parameters, solve it using a multivariate optimization search algorithm, and find the parameter values that maximize the log-likelihood function;

[0039] Based on the solved parameter values, calculate the unknown parameter values at each stress level using the maximum likelihood method;

[0040] According to the solved unknown parameter values at each stress level, use the nonlinear regression analysis method to extrapolate and obtain the estimated values of each parameter under natural storage stress.

[0041] Optionally, the set of unknown parameters composed of the unknown parameters is:

[0042] ;

[0043] Among them, represents the set of unknown parameters of the th performance degradation characterization index;

[0044] The log-likelihood function of the set of unknown parameters is: ;

[0045] Among them, represents the Copula connection log-likelihood function, represents the marginal log-likelihood function; ; ;

[0046] Among them, represents the number of stress levels; represents the sample size; represents the number of sample detections; represents the probability density function of Copula; represents the standardized form of the degradation increment of the first performance degradation characterization index after deformation; represents the standardized form of the degradation increment of the second performance degradation characterization index after deformation; represents the Copula correlation coefficient to be estimated under each stress; is the standardized form of the degradation increment of the th performance degradation characterization index after deformation; represents the th accelerated stress level; represents the th drift coefficient of the performance degradation characterization index; represents the The mean coefficient of the shape parameter randomization of the performance degradation characterization index; ;

[0047] Wherein, represents the total number of measurements; represents the approximate matrix of the variance matrix of the degradation amount of the th sample; represents the th sample's degradation amount vector; represents the th sample's measurement time; the superscript represents taking the derivative.

[0048] Optionally, substituting the estimated values of the obtained unknown parameters into the reliability function, calculating the equivalent life of the grease under actual working conditions includes: obtaining the relevant parameters of the grease accelerated degradation reliability model in the normal temperature storage state according to the temperature of the grease in the natural storage state; defining the failure threshold, substituting the obtained relevant parameters of the model in the normal temperature storage state and the failure threshold into the reliability function to obtain the reliability under each normal temperature storage stress state; predicting the reliability median life of the grease during natural storage based on the solved reliability.

[0049] The beneficial effects of the present invention are: The present invention establishes a grease accelerated degradation model considering measurement uncertainty and multiple performance degradation characterization indexes. Compared with traditional methods, this method has a more conservative reliability curve and a lower information criterion value, higher prediction accuracy, and is more in line with the actual detection process. The present invention uses the Frank Copula function to express the correlation relationship between multiple performance degradation characterization indexes of grease, improving the accuracy and reliability of the evaluation results. Description of the Drawings

[0050] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings:

[0051] Figure 1 is the flow schematic diagram of the grease accelerated degradation modeling and reliability evaluation method in the embodiment of the present invention;

[0052] Figure 2 is the common Copula function and its corresponding joint distribution function expression;

[0053] Figure 3 is the rank correlation coefficient and information quantity equation expression;

[0054] Figure 4 is the comparison of the rank correlation coefficient and information quantity in the embodiment of the present invention;

[0055] Figure 5 They are the parameter estimation values of the grease accelerated degradation reliability model in the embodiments of the present invention;

[0056] Figure 6 They are the estimated values of the parameters of the grease accelerated degradation reliability model under actual working conditions in the embodiments of the present invention;

[0057] Figure 7 They are the median life and AIC of the grease reliability in the embodiments of the present invention. Specific embodiments

[0058] In order to enable those skilled in the art to better understand the solutions of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application. It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments can be combined with each other.

[0059] The terms "first", "second", etc. in the description and claims of the present application and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, product or device that includes a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0060] Refer to Figure 1 , Figure 1 is a schematic flow chart of a grease accelerated degradation modeling and reliability evaluation method in the embodiments of the present invention. As Figure 1 shown, the method includes the following steps:

[0061] S1. Determine the grease performance degradation characterization index, set the degradation increment of the performance degradation characterization index to follow a gamma distribution, and use the gamma function to construct a non-linear accelerated degradation reliability model of the grease. The non-linear accelerated degradation reliability model is used to describe the degradation process of the grease performance under different stress conditions;

[0062] Grease is a semi-solid grease mainly used for mechanical moving parts such as gears and bearings, which plays a role in lubrication, protection and sealing. It is prepared by mixing a base oil and a thickening agent, and some contain additives. Among them, the base oil can be mineral oil or synthetic oil, the thickening agents include soap base, hydrocarbon base, organic and inorganic thickening agents, etc., and the additives include scale improvement agents, antioxidant additives, rust prevention additives, anti-wear and extreme pressure additives, etc.

[0063] The performance degradation characterization indexes of grease are used to reflect the performance degradation of grease during use, including penetration, dropping point, evaporation loss, colloidal stability, oxidation stability, water resistance, oil separation degree, etc. Among them, penetration (cone penetration) is the depth that a standard cone sinks into the grease within 5 seconds under specified temperature and load, and it is an index used to measure the consistency of grease. The larger the value, the softer the grease, and vice versa; the dropping point is the temperature at which the grease softens with the increase of temperature and reaches a certain fluidity under specified conditions. The dropping point can generally determine the use temperature of the grease; evaporation loss refers to the percentage of the evaporation amount of the grease in the total amount under specified conditions, which is an important factor affecting the service life of the grease, expressed as a mass fraction, and the smaller the evaporation loss, the better; colloidal stability (oil bleeding) refers to the ability of the grease to retain oil in the framework of its thickening agent under external force; oxidation stability refers to the ability of the grease to resist oxidation during storage and use; water resistance refers to the ability of the grease not to dissolve in water, not to absorb water from the surrounding medium and not to be washed away by water; oil separation means that a small amount of oil will precipitate during the storage and use of the grease, and the better-quality grease has less oil separation.

[0064] In an embodiment of the present invention, by analyzing the degradation degree of each performance index parameter that can characterize the failure of the grease, it is determined that the temperature is the sensitive stress, and the penetration and oil separation degree are the performance degradation characterization indexes for the accelerated degradation test, and a corresponding accelerated degradation model is constructed by using the gamma function. Specifically, it includes:

[0065] S11, assuming that the performance degradation path of the grease follows a Gamma process. According to the characteristics of the Gamma process, the performance degradation increment of the grease follows a gamma distribution, then the non-linear accelerated degradation reliability model of the grease is expressed as:

[0066] ;

[0067] In the formula, represents the th performance degradation characterization index of the grease, , is the total number of performance degradation characterization indexes of the grease; represents that under the accelerated stress level , the grease sample at the At the second measurement, the degradation increment of the th performance degradation characterization index; Indicates the th accelerated stress level; Indicates the th performance degradation characterization index at the accelerated stress level under the shape parameter; Indicates the measurement interval between two adjacent measurements; Indicates the th diffusion coefficient of the performance degradation characterization index; Indicates that the degradation path follows a gamma distribution.

[0068] S12, for which , is described by the Arrhenius model to explain the influence on the degradation increment of the th performance degradation characterization index of the grease under different accelerated stress levels;

[0069] The Arrhenius model is a model used in accelerated life tests, mainly used to shorten the test time by increasing the test stress, so as to evaluate the life characteristics of products under normal stress. This model was proposed by Arrhenius in Sweden in 1889 and was initially used to describe the relationship between the reaction rate constant of chemical reactions and temperature, but later it was widely used in accelerated life tests. The Arrhenius model is expressed as:

[0070] ;

[0071] In the formula, Indicates the first unknown parameter of the th performance degradation characterization index; Indicates the second unknown parameter of the th performance degradation characterization index; Indicates the standardized value of the stress level; Indicates the normal working stress of the grease; Indicates the maximum accelerated stress of the grease; The first unknown parameter and the second unknown parameter are parameters in the accelerated degradation model, one is the activation energy and the other is a factor related to temperature. The parameters corresponding to different degradation characterization indexes are different.

[0072] S13, randomize the shape parameter in the model to introduce the differences between sample individuals, so as to describe the influence of the differences between sample individuals on the degradation increment of the th performance degradation characterization index of the grease. The shape parameter is expressed as: ;

[0073] In the formula, is the mean coefficient of the shape parameter randomization of the th performance degradation characterization index; is the variance coefficient of the randomization of the th performance degradation characterization index; represents that the shape parameter of the th performance degradation characterization index follows a normal distribution.

[0074] S2. Based on the non-linear accelerated degradation reliability model, an error term that follows a normal distribution is introduced during the non-linear gamma accelerated degradation process of the grease, and an accelerated degradation reliability model of the grease considering measurement error is established; according to the accelerated degradation reliability model of the grease, the life distribution function of each performance degradation characterization index is derived, and the life distribution function is used to describe the probability distribution of the grease performance degradation at different time points;

[0075] S21. Without considering measurement error, the probability density function is expressed as: ;

[0076] where represents the probability density function of the degradation increment of the th performance degradation characterization index; represents the shape parameter of the th performance degradation characterization index; represents the scale parameter of the th performance degradation characterization index; represents the diffusion coefficient of the th performance degradation characterization index; represents the measurement time; when , when ; , is the Gamma function; the mean of the Gamma process is and the variance is ; is the shape parameter of the Gamma process;

[0077] S22. The Birnbaum-Saunders distribution (also known as the fatigue life distribution) is used to approximate the distribution of the degradation process, and the probability density function (PDF) of the Birnbaum-Saunders distribution is as follows:

[0078] Let the random variable t follow the Birnbaum-Saunders distribution, and its probability density function is: ;

[0079] where is the scale parameter, is the shape parameter.

[0080] After the embodiments of the present invention are sorted out by using the Birnbaum-Saunders distribution, the probability density function is expressed as: ;

[0081] Wherein, , represents the shape parameter of the th performance degradation characterization index; , represents the scale parameter of the th performance degradation characterization index; represents the failure threshold of each performance degradation amount; represents the th probability density function of the degradation increment of the performance degradation characterization index;

[0082] S23. Introduce the error term into the grease accelerated degradation general non-linear Gamma process. The error term follows a normal distribution and is expressed as:

[0083] ;

[0084] Wherein, represents the measured degradation amount; represents the true degradation amount; represents the random measurement error, , which is usually related to the accuracy of the measuring instrument; represents the standard deviation of the measurement error;

[0085] S24. Then, considering the measurement error, the probability density function is expressed as:

[0086] ;

[0087] Wherein, represents the life; represents the probability density function of the th performance degradation characterization index considering the measurement error; , represents the probability density function of the measurement error.

[0088] According to the established accelerated degradation model of the unknown parameter set, fit the degradation amount data of the two performance degradation characterization indexes of the grease penetration and bleeding degree, determine the marginal distribution they follow, and select the optimal Copula function by comparing the distribution density image, rank correlation coefficient and information quantity test of the fitting degree, so as to establish the reliability function of the coupling of the two performance parameters. Specifically, it includes:

[0089] According to the established accelerated degradation model of the set of unknown parameters, construct the cumulative distribution function of the degradation increment of each performance degradation characterization index, and the cumulative distribution function is expressed as:

[0090] ;

[0091] where , represents at the accelerated stress level , the degradation increment of the th performance degradation characterization index of the grease sample at the th measurement, represents the time point of the th measurement; , represents the failure threshold of the rd performance degradation characterization index after considering errors; represents the shape parameter of the th performance degradation characterization index at the accelerated stress level ; represents the diffusion coefficient of the th performance degradation characterization index; represents the cumulative distribution function of the degradation increment of the th performance degradation characterization index; represents the simplified form of the probability density function of the th performance degradation characterization index without measurement error.

[0092] The main purpose of constructing the cumulative distribution function is for subsequent quantitative calculation. The probability density function, that is, the life distribution function, describes the probability density of a continuous random variable near a specific value. First, the probability density function is derived, and then the cumulative distribution function is obtained by integration. The cumulative distribution function calculates the probability of falling within a certain interval, that is, the probability that the random variable is less than or equal to a certain value. The probability density function describes the distribution of the variable, and the cumulative distribution function is the probability that the variable falls within a certain interval, that is, the probability of failure.

[0093] S3. Adopt the Frank Copula function as the connection function to establish the reliability function of the coupling between multiple performance degradation characterization indexes;

[0094] The Copula function is a tool for describing the dependence relationship between multi-dimensional random variables. In the implementation of the present invention, the Copula function is used to deal with the correlation between multiple performance degradation characterization indexes.

[0095] When different Copula functions are selected, the joint distribution of multiple performance degradation characterization indexes has different expressions. The commonly used Copula functions and their corresponding joint distribution function expressions are as Figure 2 shown.

[0096] Figure 2 In represents the cumulative distribution function of the first performance degradation characterization index; represents the cumulative distribution function of the second performance degradation characterization index; represents and the correlation coefficient between two random variables; represents the Copula function; represents the standardized form;

[0097] According to the rank correlation coefficient and the information quantity test result, select the Copula function with the best fitting degree. Among them, the expressions of the rank correlation coefficient and the information quantity equation are as Figure 3 shown.

[0098] Figure 3 In represents the value of the Debye function measured for the first time; represents the value of the Debye function measured for the second time; represents the squared Euclidean distance of each type of Copula function; represents the Coupla empirical function value of the represents the overall log-likelihood function; represents the number of unknown parameters; ) is the Debye function, ;

[0099] Analyzing the performance degradation data of the penetration and bleeding of the grease shows that the two characteristic parameters present a peak and thick tail, and the tails are basically symmetric. Therefore, the bivariate Gaussian Copula function and the bivariate Frank Copula function are selected to describe the correlation characteristics of the performance index parameters.

[0100] Respectively solve the Pearson linear correlation coefficient, Kendall rank correlation coefficient, and Spearman rank correlation coefficient of the bivariate Gaussian Copula function and the bivariate Frank Copula function. The results are as Figure 4 shown.

[0101] Based on Figure 4 the comprehensive analysis results, the embodiment of the present invention selects the Frank Copula function as the connection function to express the bivariate correlation of multiple performance parameters, and establishes a reliability function for coupling the performance degradation characterization indexes. This reliability function can comprehensively consider the influence of multiple indexes on the reliability of the grease. Among them, the reliability function for coupling the two performance parameters is:

[0102] ;

[0103] represents the Copula linear correlation coefficient under normal temperature stress; represents the reliability function of the first performance degradation characterization index; represents the reliability function of the second performance degradation characterization index; represents the corresponding Copula distribution function;

[0104] If Frank Copula is the copula function, then .

[0105] S4. Adopt the maximum likelihood estimation method and combine it with the nonlinear regression method to derive the estimated values of all unknown parameters in the grease accelerated degradation reliability model under actual working conditions;

[0106] The unknown parameters in the model include shape parameters, diffusion coefficients, drift coefficients, etc.

[0107] S41. Obtain the unknown parameters in the grease accelerated degradation reliability model and form a set of unknown parameters :

[0108] ;

[0109] S42. Construct the log-likelihood function of the set of unknown parameters : ;

[0110] where represents the Copula connection log-likelihood function, represents the marginal log-likelihood function; ; ;

[0111] where represents the number of stress levels; represents the sample size; represents the number of sample detections; represents the probability density function of Copula; represents the standardized form of the degradation increment of the first performance degradation characterization index after deformation; represents the standardized form of the degradation increment of the second performance degradation characterization index after deformation; represents the Copula correlation coefficient at each stress to be estimated; is the standardized form of the degradation increment of the th performance degradation characterization index after deformation; represents the th accelerated stress level; represents the drift coefficient of the th performance degradation characterization index; represents the mean coefficient of the randomization of the shape parameter of the th performance degradation characterization index; ;

[0112] wherein, represents the total number of measurements; represents the approximate matrix of the variance matrix of the degradation amount of the th sample; represents the degradation amount vector of the th sample; represents the measurement time of the th sample; the superscript represents taking the derivative;

[0113] Taking the first-order partial derivatives of and according to the above formula and setting them equal to 0, the estimated values are obtained as: ;

[0114] represents the estimated value of; represents the estimated value of; represents the th performance degradation characterization index of the th sample's degradation amount vector matrix; represents the inverse matrix of the approximate matrix of the variance matrix of the degradation amount of the th sample at the th stress level; represents the th performance degradation characterization index of the th sample's approximate matrix of the variance matrix of the degradation amount's inverse matrix; represents the estimated value of;

[0115] S43, substituting the obtained parameter estimated values back into the established log-likelihood function, and using the multi-variable optimization search algorithm to solve, to find the parameter values that maximize the log-likelihood function;

[0116] S44, based on the solved parameter values, using the maximum likelihood method to calculate the unknown parameter values at each stress level;

[0117] S45, according to the solved unknown parameter values at each stress level, using the non-linear regression analysis method to extrapolate and obtain the estimated values of each parameter under the natural storage stress.

[0118] Nonlinear regression analysis first determines a model for fitting the nonlinear relationship based on the data, and then uses the values of the unknown parameters at each solved stress level as inputs to extrapolate the parameter values under normal stress through nonlinear regression analysis. As Figure 5 shown, Figure 5 the parameter estimation values of the model are presented.

[0119] S5. Substitute the estimated values of the unknown parameters obtained into the reliability function to calculate the equivalent life of the grease under actual working conditions, thereby realizing reliability assessment.

[0120] The equivalent life refers to the time required for the performance of the grease to degrade to a certain predetermined level under a specific stress level.

[0121] S51. Obtain the relevant parameters of the reliability model for the accelerated degradation of the grease in the normal temperature storage state based on the temperature of the grease in the natural storage state;

[0122] Through experiments, it is determined that the temperature of the grease under actual working conditions is 25°C, and substitute it into the degradation model established based on the degradation data of the grease penetration and bleeding degree. The relevant parameters obtained by solving are as Figure 6 shown;

[0123] S52. Define the failure threshold, and substitute the relevant parameters of the model and the failure threshold obtained in the normal temperature storage state into the reliability function to obtain the reliability under each normal temperature storage stress state;

[0124] The failure threshold is used to determine whether the grease fails and can be set according to experience or experimental data.

[0125] S53. Based on the solved reliability, predict the median reliability life of the grease during natural storage.

[0126] The median reliability life refers to the time corresponding to the reliability dropping to 0.5.

[0127] As Figure 7 shown, Figure 7 is the median reliability life of the grease and AIC for the accelerated degradation reliability model.

[0128] By analysis Figure 7 it can be seen that the median reliability life related to the double performance parameters of penetration and bleeding degree of Frank considering measurement errors is approximately 10.49 years. Compared with the median reliability life of approximately 11.57 years related to the double performance parameters of Frank considering sample differences, and the median reliability life of approximately 13.06 years without considering sample and measurement uncertainties, the potential degradation state of the grease under accelerated stress is not ignored, and the life characteristics are estimated more conservatively. Therefore, the method proposed in the present invention is closer to engineering practice compared with the method that does not consider multi-source randomness.

[0129] The grease accelerated degradation modeling and reliability evaluation method in the embodiments of the present invention can improve the accuracy of evaluation results, reduce the cost of grease reliability tests, and provide an important theoretical basis for improving the reliability of grease in the field of accelerated degradation modeling and reliability evaluation.

[0130] The embodiments of the present invention also provide a storage medium storing a computer program, wherein the computer program is configured to execute the steps in any one of the above method embodiments when running.

[0131] Specific examples in this embodiment may refer to the examples described in the above embodiments and optional implementation manners, and will not be elaborated herein.

[0132] Optionally, in this embodiment, the above storage medium may include, but is not limited to, various media capable of storing computer programs such as USB flash drives, read-only memories (ROM for short), random access memories (RAM for short), mobile hard disks, magnetic disks, or optical discs.

[0133] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0134] In the above embodiments of the present invention, the descriptions of the respective embodiments have their own focuses. For the parts not detailed in a certain embodiment, reference may be made to the relevant descriptions of other embodiments.

[0135] The steps in the method of the above embodiments of the present invention can be adjusted, combined, and deleted according to actual needs. The technical features can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in the present invention.

[0136] The above is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. A method for modeling and reliability assessment of accelerated grease degradation, characterized in that: include: Determine a grease performance degradation characterization index, set the degradation increment of the performance degradation characterization index to obey the gamma distribution, and use the gamma function to construct a nonlinear accelerated degradation reliability model of the grease, wherein the nonlinear accelerated degradation reliability model is used to describe the degradation process of the grease performance under different stress conditions; Based on the nonlinear accelerated degradation reliability model, an error term obeying normal distribution is introduced in the nonlinear gamma accelerated degradation process of grease, and a grease accelerated degradation reliability model considering measurement error is established; According to the grease accelerated degradation reliability model, a life distribution function of each performance degradation characterization index is derived, wherein the life distribution function is used to describe the probability distribution of grease performance degradation at different time points; The Frank Copula function is used as the connection function to establish the reliability function of the coupling between the performance degradation characterization indicators; The maximum likelihood estimation method is used in combination with the nonlinear regression method to derive the estimated values ​​of all unknown parameters in the grease accelerated degradation reliability model under actual working conditions. Substituting the estimated values ​​of the unknown parameters into the reliability function, the equivalent life of the grease under actual working conditions is calculated to achieve reliability evaluation; The nonlinear accelerated degradation reliability model of grease constructed using the gamma function includes: The performance degradation path of the grease obeys the gamma process. According to the characteristics of the gamma process, the nonlinear accelerated degradation reliability model of the grease is expressed as: ； In the formula, Grease performance degradation characterization indicators, , The total number of indicators that characterize the degradation of grease performance; Indicates the accelerated stress level Next, the grease sample was When measuring for the first time, The degradation increment of a performance degradation characterization indicator; Indicates accelerated stress levels; Indicates Performance degradation indicators at accelerated stress levels The shape parameters below: Indicates the measurement interval between two adjacent measurements; Indicates The diffusion coefficient of each performance degradation indicator; Indicates that the degradation path follows a gamma distribution; To which The Arrhenius model is used to describe the grease under different accelerated stress levels. The impact of the degradation increment of the performance degradation characterization index, wherein the Arrhenius model is expressed as: ； In the formula, Indicates A first unknown parameter of a performance degradation characterization indicator; Indicates A second unknown parameter of a performance degradation characterization indicator; represents the normalized value of stress level; Indicates the normal working stress of grease; Indicates the maximum accelerated stress of grease; The nonlinear accelerated degradation reliability model is also included. Randomization introduces differences between sample individuals to describe the different effects of sample individuals on grease The influence of the degradation increment on the performance degradation characterization index, the shape parameter It is expressed as: ; In the formula, For the The mean coefficient of randomization of shape parameters of performance degradation characterization indicators; For the The variance coefficient of the randomization of the performance degradation characterization indicators; Indicates The shape parameters of the performance degradation characterization indicators follow the normal distribution; In the nonlinear gamma accelerated degradation process of grease, an error term that obeys normal distribution is introduced, and a reliability model of grease accelerated degradation considering measurement error is established; based on the grease accelerated degradation reliability model, the life distribution function of each performance degradation characterization index is derived, including: Without considering the measurement error, the Birnbaum-Saunders distribution is used to approximate the distribution of the degradation process. The probability density function of the nonlinear accelerated degradation reliability model is expressed as: ; ； ； in, Indicates The probability density function of the degradation increment of each performance degradation characterization indicator; Indicates the measurement time; Indicates Shape parameters of performance degradation indicators; Indicates A scale parameter of a performance degradation characterization indicator; Indicates The failure threshold of a performance degradation amount; The introduced error term follows a normal distribution and is expressed as: ； in, represents the amount of measured degradation; represents the actual degradation amount; Represents random measurement error, which is related to the accuracy of the measuring instrument. ; represents the standard deviation of measurement error; Introducing the error term into the general nonlinear Gamma process of accelerated grease degradation, the probability density function is expressed as follows when the measurement error is taken into account: ； ； in, Indicates life span; Indicates the case where measurement error is taken into account. The probability density function of the performance degradation characterization index; Represents the probability density function of measurement error.

2. The grease accelerated degradation modeling and reliability assessment method according to claim 1, characterized in that: After deriving the life distribution function of each performance degradation characterization index according to the grease accelerated degradation reliability model, the method further includes: According to the grease accelerated degradation reliability model, the cumulative distribution function of each performance degradation characterization index is constructed: ； in, Indicates The cumulative distribution function of the degradation increment of each performance degradation characterization indicator; , indicating that at the accelerated stress level Next, the grease sample was When measuring for the first time, The degradation increment of a performance degradation characterization indicator, Indicates The time point of the measurement; , which means that after considering the error The failure threshold of a performance degradation indicator; Indicates no measurement error The simplified form of the probability density function of the performance degradation characterization index is shown in Figure 2.

3. The grease accelerated degradation modeling and reliability assessment method according to claim 2, characterized in that: The Frank Copula function is used as the connection function to establish the reliability function of coupling between the performance degradation characterization indicators, including: The reliability function of the performance degradation characterization index coupling is: ； in, Indicates A reliability function coupled with performance degradation characterization indicators; represents the Copula linear correlation coefficient under normal temperature stress; represents the reliability function of the first performance degradation characterization index; represents the reliability function of the second performance degradation characterization index; Represents the corresponding Copula distribution function; Select Frank Copula as the link function. .

4. The grease accelerated degradation modeling and reliability assessment method according to claim 3, characterized in that: The maximum likelihood estimation method is used in combination with the nonlinear regression method to derive the estimated values ​​of all unknown parameters in the grease accelerated degradation reliability model under actual working conditions, including: Obtain unknown parameters in the grease accelerated degradation reliability model to form an unknown parameter set; Constructing a log-likelihood function of the unknown parameter set, solving it using a multivariate optimization search algorithm, and finding the parameter value that maximizes the log-likelihood function; Based on the solved parameter values, the maximum likelihood method is used to calculate the unknown parameter values ​​at each stress level; According to the unknown parameter values ​​solved at each stress level, the estimated values ​​of each parameter under natural storage stress are extrapolated using nonlinear regression analysis method.

5. The grease accelerated degradation modeling and reliability assessment method according to claim 4, characterized in that: The unknown parameter set composed of the unknown parameters is: ； in, Indicates A set of unknown parameters that characterize performance degradation indicators; The log-likelihood function of the unknown parameter set for: ; in, represents the Copula connection log-likelihood function, represents the marginal log-likelihood function; ; ; in, represents the stress level number; represents the sample size; Indicates the number of sample tests; represents the normalized form of the first performance degradation characterization indicator after the degradation increment is deformed; represents the normalized form of the degradation increment of the second performance degradation characterization indicator after deformation; Represents the Copula correlation coefficient under each stress to be estimated; For the The normalized form of the degradation increment of each performance degradation characterization indicator after deformation; Indicates accelerated stress levels; Indicates The drift coefficient of a performance degradation indicator; Indicates The mean coefficient of randomization of shape parameters of performance degradation characterization indicators; ; in, Indicates the total number of measurements; Indicates The approximate matrix of the variance matrix of the degradation amount of samples; Indicates The degradation vector of samples; Indicates The measurement time of each sample; upper right It means to find the derivative.

6. The grease accelerated degradation modeling and reliability assessment method according to claim 1, characterized in that: Substituting the estimated values ​​of the unknown parameters into the reliability function, the equivalent life of the grease under actual working conditions is calculated, including: According to the temperature of the grease in the natural storage state, the relevant parameters of the reliability model of the accelerated degradation of the grease under the normal temperature storage state are obtained; Define the failure threshold, substitute the relevant parameters of the model under the normal temperature storage state and the failure threshold into the reliability function, and obtain the reliability under each normal temperature storage stress state; Based on the solved reliability, predict the reliability median life of the grease during natural storage.

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