Waste part state mapping model construction method based on Dirichlet distribution

Abstract

The invention provides a Dirichlet distribution-based waste part state mapping model construction method, and aims to solve the problem of uncertainty of waste part quality evaluation, a Dirichlet distribution-based damage-quality state mapping model (DBMS) is constructed, the model determines main failure characteristics through waste part failure behavior analysis, and the Dirichlet distribution-based damage-quality state mapping model (DBMS) is constructed through the Dirichlet distribution-based damage-quality state mapping model (DBMS). Mathematical abstraction is carried out on part damage amount data by adopting multinomial distribution, Dirichlet distribution is selected as prior probability distribution, and posterior distribution parameters are obtained by combining Bayesian formula updating, so that posterior probability expected values of the damage amount data mapped to different quality grades are obtained. And further, a D-S evidence theory is introduced to fuse damage information, so that the comprehensive evaluation of the quality condition of the waste parts is realized. In order to verify the feasibility and effectiveness of the model, a waste turbine worm is taken as a case research object, and compared with the existing literature method, the experimental result shows that the model has advantages in prediction precision and generalization ability.

Description

Technical Field

[0001] The invention belongs to the technical field of Dirichlet distribution, and in particular relates to a method for constructing a waste parts state mapping model based on Dirichlet distribution. Background Art

[0002] The rapid progress of industrial technology and the continuous expansion of global economic activities have prompted the production and use of electromechanical products to reach an unprecedented scale. Faced with the realistic challenges of limited resources and the urgent need for environmental protection, the recycling and reuse of retired electromechanical products has become one of the important ways to promote the circular economy and achieve sustainable development. Retired electromechanical products contain a large number of waste parts. These parts have been used for a long time in different service environments, and their quality status often becomes a key factor restricting their remanufacturing or reuse. Accurately and efficiently evaluating the quality status of waste parts is of great significance to improving the quality of remanufactured products and realizing the classified utilization and efficient allocation of resources.

[0003] Compared with the quality of manufactured parts, the quality of scrap parts varies significantly due to differences in working conditions, operation time and degree of wear. This uncertainty increases the complexity of remanufacturing process planning and leads to unstable quality of remanufactured products. Many scholars have realized the necessity of quality assessment of scrap parts during their remanufacturing process. The quality level of parts is introduced into the remanufacturing batch scheduling problem, and an optimal scheduling model suitable for both deterministic and random quality levels is constructed. In view of the inherent uncertainty in the quality assessment process of parts, the changing trend of the benefits brought by quality assessment operations is discussed by numerical analysis methods. In view of this, it is crucial to explore and construct a scientific quality assessment method for scrap parts in the remanufacturing field. In early studies, quality assessment often relied on subjective judgment and experience, lacking systematic assessment methods and quantitative standards. With the development of intelligent technology, many scholars have begun to explore more scientific and objective quality assessment methods.

[0004] According to existing literature, current research on quality assessment focuses less on key components of electromechanical equipment. However, data shows that the annual losses caused by the failure and scrapping of electromechanical equipment due to wear and deformation are as high as 100 billion yuan, and the resulting waste of resources also has an inestimable impact on the ecological environment. In addition, existing research mainly focuses on classifying the quality of scrapped parts through fuzzy sets, rough sets, random sets and other methods, which usually lack flexible adjustment mechanisms and fail to make full use of damage data to accurately quantify the quality status of in-service electromechanical products and their components. Its applicability is limited in the large-scale remanufacturing process of scrapped parts. Summary of the invention

[0005] The purpose of the present invention is to propose a method for constructing a state mapping model of waste parts based on Dirichlet distribution, propose a damage-quality state mapping model (Damage-Based Multi-State Mapping Model, DBMS) to evaluate the quality of waste parts, and map the damage amount of the failure form to the posterior probability expected value of different quality levels. First, for the waste parts obtained by disassembling retired electromechanical products, the quantitative information of the damage amount of the failure form of the waste parts is obtained by intelligent detection means, and a waste parts failure sample data set is constructed. Then, the damage amount of the failure form is mathematically abstracted by multiple distributions, and Dirichlet distribution is used as the prior probability distribution. On this basis, the prior Dirichlet distribution parameters are determined by non-information priors, and the posterior Dirichlet distribution parameters are updated according to the Bayesian formula, and the posterior probability expected value is obtained. The posterior probability expected value is introduced into the basic probability mass allocation process, and the DS evidence theory is used to fuse the damage information to comprehensively evaluate the quality status of the waste parts. Finally, the effectiveness of the proposed evaluation method is verified by examples.

[0006] In order to achieve the above object, the present invention provides a method for constructing a state mapping model of scrapped parts based on Dirichlet distribution, the method comprising:

[0007] Integrate the key features of scrap parts into a failure data set, and construct a failure feature matrix based on the data set; wherein the key features of scrap parts include wear, fracture, deformation and quality grade labels;

[0008] Randomly select n instances from the quality grade labels as training data. Each failure mode contains n values, which are divided into intervals to identify the specific distribution of damage under different failure modes.

[0009] According to the specific distribution identified, the introduced parameters are a=(a1, a2, ..., a k ) is used as the multinomial distribution component damage data to construct a priori probability model, and the probability vector θ of the priori probability model is regarded as a random variable under the priori reference a condition, that is, p(θ)~Dir(a);

[0010] Construct a probability model for a given failure mode f and quality level h, denoted as DPMS fh , H probability models are integrated to obtain the combined probability model under failure form f, which is recorded as DPMS f, in order to form a comprehensive probability description of the failure form s, all combined probability models are integrated, and for each failure form f, its corresponding damage data is used as the input parameter, processed by the corresponding DBMS model, and the posterior probability expected value of the given failure form f assigned to different quality levels is matched, and finally the sum of the posterior probability expected values ​​of all quality levels under the failure form f is calculated. f , according to T f Different basic probability allocation strategies are adopted for different value situations.

[0011] Furthermore, the feature matrix is ​​expressed as follows:

[0012]

[0013] Among them, w ij represents the wear amount of the i-th scrapped component in the j-th failure mode, w 11 represents the wear amount of the first scrapped component in the first failure mode, w 12 represents the wear amount of the first scrapped component in the second failure mode, w 1j represents the wear amount of the first scrapped component in the jth failure mode, w 21 represents the wear amount of the second scrapped component in the first failure mode, w 22 represents the wear amount of the second scrapped component in the second failure mode, w 21 represents the wear amount of the second scrapped component in the first failure mode, w 2j represents the wear amount of the first scrapped component in the jth failure mode, w i1 represents the wear amount of the i-th scrapped component in the first failure mode, w i2 Represents the wear amount of the i-th scrapped component in the second failure mode.

[0014] Furthermore, the interval division is performed to identify the specific distribution of damage under different failure modes. Specifically, the Freedman-Diaconi rule is used for adaptive interval division to determine the appropriate number of intervals K for each failure mode f, thereby discretizing the continuous damage data into finite interval categories, which is expressed as follows:

[0015]

[0016] Where n represents the number of instances, IQR represents the interquartile range, and f represents each failure mode.

[0017] Furthermore, when the used parts fail, the damage amount of a specific failure mode must fall within a certain range. Through statistical analysis of the event frequency, the probability distribution of each interval category is estimated:

[0018] The frequency falling in the kth interval is represented by n k , with a probability associated with it of θ i , then the set of damage data is formally expressed as (n1,n2,...,n k )~Mult(θ1,θ2,...,θ k ), and satisfies

[0019] Furthermore, the method also includes, before performing the prior Dirichlet, performing a Jeffreys non-information prior, which is constructed based on the Fisher information matrix, as shown below:

[0020]

[0021] Among them, p(·) represents the probability distribution function, and k represents the number of divided intervals;

[0022] According to the Bayesian nonparametric statistical method, when the prior distribution of the probability parameters of the multiple distributions of scrap parts is specified as Dirichlet distribution, the probability density function has the following characteristics:

[0023]

[0024] Among them, a i represents the parameters of the Dirichlet distribution.

[0025] Furthermore, when Jeffreys non-informative prior is used, the parameter a of the Dirichlet distribution can be uniquely determined, and a1=a2=…=a k =1 / 2. After determining the parameters of the prior Dirichlet distribution, according to the property that the Bayesian posterior distribution is proportional to the product of the likelihood function and the prior distribution, we can obtain

[0026] P(θ1,θ2,...,θ k |n1,n2,...,n k )∝

[0027] Dir(1 / 2+n1,1 / 2+n2,...,1 / 2+n k )

[0028] Where Dir(·) represents Dirichlet distribution;

[0029] That is, when the multinomial distribution data of the damage amount of scrapped parts is observed to be n = (n1, n2, ..., n k ), it is deduced that its posterior distribution is parameter updated to a=(1 / 2+n1,1 / 2+n2,...,1 / 2+nk ) is a Dirichlet distribution, then the expected value of the posterior probability of the Dirichlet distribution is calculated by the following formula

[0030]

[0031] in, represents the expected value of the posterior probability of the i-th interval.

[0032] Furthermore, the basic probability allocation strategy includes:

[0033] A. Surplus distribution: When T f <1, 1-T f Assigned to the identification framework Θ, it represents a measure of global uncertainty, reflecting the uncertainty that cannot be accurately assigned to a specific quality level due to insufficient information about the failure form f;

[0034] B. Complete allocation: When T f =1, it naturally satisfies the constraints of the basic probability function, θ f Directly as a result of the effective basic probability allocation, that is, all probabilities are fully allocated to each quality level;

[0035] C. Normalization adjustment: When T f When >1, it indicates that the expected values ​​of the probabilities assigned to multiple quality levels are high. In order to maintain the rationality of the probability distribution, the expected values ​​of the posterior probability need to be normalized.

[0036] The beneficial technical effects of the present invention are at least as follows:

[0037] This paper proposes a Damage-Based Multi-State Mapping Model (DBMS) to evaluate the quality of scrapped parts, mapping the damage amount of failure forms to the posterior probability expectation values ​​of different quality levels. First, for scrapped parts obtained by disassembling retired electromechanical products, the quantitative information of the damage amount of the failure forms of scrapped parts is obtained by intelligent detection means, and a data set of scrapped parts failure samples is constructed. Then, the damage amount of failure forms is mathematically abstracted by multinomial distribution, and Dirichlet distribution is used as the prior probability distribution. On this basis, the parameters of the prior Dirichlet distribution are determined by non-informative priors, and the parameters of the posterior Dirichlet distribution are updated according to the Bayesian formula, and the posterior probability expectation value is obtained. The posterior probability expectation value is introduced into the basic probability mass allocation process, and the DS evidence theory is used to integrate the damage information to comprehensively evaluate the quality status of scrapped parts. Finally, the effectiveness of the proposed evaluation method is verified by examples. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The present invention is further described using the accompanying drawings, but the embodiments in the accompanying drawings do not constitute any limitation to the present invention. A person skilled in the art can obtain other drawings based on the following drawings without creative work.

[0039] Figure 1 The figure is a flow chart of the method for evaluating the quality of waste parts of the present invention.

[0040] Figure 2 It is a schematic diagram of the number of intervals of different failure modes within each quality level according to an embodiment of the present invention. DETAILED DESCRIPTION

[0041] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0042] Embodiment 1

[0043] DS evidence theory is a mathematical framework for processing uncertain information. It integrates evidence from different information sources through combination rules. It is applicable to decision-making and reasoning in various uncertain environments and provides strong support for problem solving in multiple fields. The identification framework Θ is the basis of DS evidence theory. It represents the complete set of all possible results of the problem. The number of elements in Θ is limited and mutually exclusive. Power set of identification framework 2 Θ It contains all subsets of Θ, each of which corresponds to a proposition. Basic Probability Assignment (BPA) is a mapping function that assigns the probability of different propositions in the power set. The mathematical expression is m:2 Θ →[0,1], and the following conditions are met

[0044]

[0045] In the formula, the basic probability mass m(A) quantifies the degree of support for the truth of proposition A. When m(A)>0, proposition A is called a focal element. DS evidence theory integrates uncertainty information from different evidence sources through the Dempster synthesis rule, and its mathematical expression is as follows:

[0046]

[0047] Among them, A and B i is a proposition in the power set 2Θ, m i (B i ) is Proposition B iThe basic probability mass under the i-th evidence source, K is the normalization coefficient, and the calculation formula is as follows

[0048]

[0049] Furthermore, the Dirichlet distribution is a widely used multivariate probability distribution whose parameters are a set of positive real vectors α = (α1, α2, …, α k ) and α i >0. The probability density function of the Dirichlet distribution is defined as

[0050]

[0051] Where θ=(θ1,θ2,…,θ k ) is a multivariate random variable, θ i Represents the probability value of the random variable in the i-th category and satisfies B(α) is the multivariate Beta function, defined as

[0052]

[0053] An important property of the Dirichlet distribution is its conjugate relationship with the multinomial distribution, and it is often used as the conjugate prior distribution of the multinomial distribution. In Bayesian statistics, if one distribution is the conjugate prior of another distribution, then given the data, the posterior distribution will be of the same type as the prior distribution. Specifically, when a random variable X follows the multinomial distribution Mult(n,θ), where n is the number of trials and θ is a set of probability parameters. For a given sample data D, the likelihood function of the parameter θ is expressed as

[0054]

[0055] Using Dirichlet distribution as the prior distribution of θ, according to Bayes' theorem, the posterior distribution of θ is proportional to the product of the likelihood function and the prior distribution, that is, the posterior distribution can be expressed as

[0056]

[0057] This shows that, due to the conjugation of the Dirichlet distribution with the multinomial distribution, the posterior distribution of θ is still a Dirichlet distribution with its parameters adjusted to α + n based on the sample data.

[0058] like Figure 1As shown in the figure, in the field of electromechanical product remanufacturing research, the failure of parts is generally regarded as a key factor driving product retirement, covering a wide range of situations from complete loss of function to partial functional degradation. During the service life of electromechanical products, affected by multiple uncertain factors such as material properties, maintenance quality, operating environment and workload, the failure behavior of its internal parts has significant randomness and dispersion. Specifically, even parts of the same model may present different quality states due to differences in failure characteristics. Therefore, the characterization and quantification of failure characteristics are the basis for evaluating the quality status of parts. By deeply analyzing and measuring the failure form and degree of failure of scrap parts, a specific portrait of the failure behavior of parts can be constructed.

[0059] The quality assessment process of scrap parts of retired electromechanical products is as follows: Figure 1 As shown in the figure, firstly, the failure characteristics of scrap parts are quantified by intelligent detection means, including wear, fracture and deformation, and a sample data set of scrap parts failure is constructed. Then, the damage data is mathematically abstracted by multinomial distribution, and Dirichlet distribution is selected as the prior probability distribution. The Bayesian formula is used to calculate the posterior probability that the failure characteristics belong to different quality states, and the basic probability distribution is constructed through differential adjustment strategies. Finally, the quality status of scrap parts is comprehensively evaluated through evidence fusion reasoning.

[0060] Wear, fracture and deformation are the three most common failure characteristics of scrap parts. They are not only common in various retired electromechanical products, but also have a profound impact on the service life and reliability of parts. In the remanufacturing practice, qualitative or vague language is often used to describe the various failure characteristics and damage levels of scrap parts, which leads to subjectivity and uncertainty in quality assessment and increases the risk of performance degradation of parts after remanufacturing. To this end, the scrap parts obtained after disassembling retired electromechanical products are first properly cleaned, and then quantitative information on relevant failure characteristics is obtained through non-destructive testing technology to evaluate the quality status of the parts.

[0061] Table 1 provides quantitative data on the three main failure characteristics of the transmission spindle of scrap machine tools. The corresponding quantitative intervals are expressed in specific numerical ranges. For example, if a transmission spindle part has wear failure, when its wear amount w is less than 1.0 mm3, it is considered to be slightly worn, indicating that the damage amount is within an acceptable low level range; when the wear amount w is between 1.0 mm3 and 2.0 mm3, the degree of wear is defined as medium; and when the wear amount w exceeds 2.0 mm3, it is considered to be severely worn. For slightly and moderately worn transmission spindle parts, their original performance can be restored through remanufacturing, and for severely worn transmission spindle parts, a material recovery strategy is adopted and no further research is conducted on them.

[0062] Table 1 Quantification of failure characteristics of machine tool transmission spindle

[0063]

[0064]

[0065] Furthermore, in evidence theory, BPA is the process of calculating the basic probability of each piece of evidence in the identification framework Θ, which is completed through the basic probability allocation function. In practical applications, the determination of basic probability allocation has become a key issue. Traditional BPA methods often rely on expert experience or heuristic rules, which makes it difficult to ensure the consistency and objectivity of the allocation. To this end, a basic probability allocation method based on Dirichlet distribution in evidence theory is proposed.

[0066] Based on intelligent detection methods and digital technology, a dataset U of failed parts failure samples was systematically constructed. The three key failure characteristics of scrap parts were integrated in a structured way: wear (Fw), fracture (Fc), and deformation (Fd), and quality grade labels (H) were attached to reflect the comprehensive performance status of each scrap part.

[0067] U=[F w ,F c ,F d ,H](8)

[0068] Since a single failure characteristic, such as wear, may cover multiple specific failure forms, its failure data can be represented by the following matrix form:

[0069]

[0070] Among them, w ij Represents the wear amount of the i-th scrap component in the j-th failure mode. Similarly, fracture and deformation can also be described in detail by a similar matrix structure. Based on the scrap parts failure sample data set, n instances are randomly selected from the quality grade h as training data. Each failure mode contains n values, and they are divided into intervals to identify the specific distribution of damage under different failure modes. The Freedman-Diaconi rule provides an adaptive interval partitioning strategy that can comprehensively consider the proportional relationship between the interquartile range (IQR) of the data and the sample size (n), and is suitable for data with different distribution forms. This rule can be used to determine the appropriate number of intervals K for each failure mode f, thereby discretizing the continuous damage data into a finite number of interval categories. The calculation expression is as follows

[0071]

[0072] When a scrapped component fails, the damage amount of a specific failure mode must fall within a certain range. Therefore, the damage amount data points under different failure modes can be regarded as the results of a test, and the observations falling within a specific interval correspond to the event frequency of the interval category. Through statistical analysis of event frequencies, the probability distribution of each interval category can be estimated, and the frequency falling within the kth interval is expressed as n i , with a probability associated with it of θ i , then the set of damage data can be formally expressed as, and satisfies Thus, a multinomial distribution model is constructed to describe the damage distribution of scrapped parts under specific failure modes.

[0073] Furthermore, in the Bayesian nonparametric method, the Dirichlet distribution is considered to be the natural conjugate prior of the multinomial distribution. The parameters introduced are a = (a1, a2, ..., a k ) is used as the prior probability model for the multinomial distribution of component damage data, and the probability vector θ is regarded as a random variable under the prior reference a, that is, p(θ)~Dir(a).

[0074] In most practical application scenarios, direct estimation of the prior Dirichlet distribution parameter a is often limited by the scarcity of failure data of scrapped parts or insufficient information. In order to reduce excessive reliance on prior knowledge or assumptions, non-informative prior inference methods are used to obtain a robust and effective prior distribution. Jeffreys prior is a commonly used non-informative prior [15-16], which is constructed based on the Fisher information matrix and does not depend on any specific parameter value. According to the mathematical derivation in the literature

[17] , in the context of a multinomial distribution of failure damage of scrapped parts, Jeffreys prior follows the following relationship

[0075]

[0076] In addition, according to the Bayesian nonparametric statistical method, when the prior distribution of the probability parameters of the multiple distributions of scrap parts is specified as Dirichlet distribution, the probability density function also has the following characteristics:

[0077]

[0078] It can be deduced from formula (11) and formula (12) that when Jeffreys non-information prior is used, the parameter a of the Dirichlet distribution can be uniquely determined, and a1=a2=…=a k =1 / 2. After determining the parameters of the prior Dirichlet distribution, according to the property that the Bayesian posterior distribution is proportional to the product of the likelihood function and the prior distribution, we can get

[0079] P(θ1,θ2,...,θ k |n1,n2,...,n k )∝

[0080] Dir(1 / 2+n1,1 / 2+n2,...,1 / 2+n k )(13)

[0081] That is, when the multinomial distribution data of the damage amount of scrapped parts is observed to be n = (n1, n2, ..., nk), it can be deduced that its posterior distribution is updated with parameters a = (1 / 2 + n1, 1 / 2 + n2, ..., 1 / 2 + n k ) is a Dirichlet distribution. According to the literature

[18] , the expected value of the posterior probability of the Dirichlet distribution can be calculated by the following formula:

[0082]

[0083] Furthermore, after the above steps, a probability model under the condition of a given failure mode f and quality level h can be constructed, denoted as DPMBfh, which provides the expected value of the posterior probability of each interval category, and its expression is as follows

[0084]

[0085] In order to determine the basic probability mass distribution of failure forms at different quality levels, H probability models are integrated to obtain the combined probability model under failure form f, denoted as DPMSf, to form a comprehensive probability description of failure form f.

[0086] DBMS f =(DPMS f1 ,DBMS f2 ,...,DBMS fH ) (16)

[0087] By analogy, we can obtain the combined probability model of all failure modes (DBMS1, DBMS2, …, DBMS F ). When evaluating the quality status of scrapped parts, for each failure mode f, the corresponding damage data is used as the input parameter, processed by the corresponding DBMS model, and the posterior probability expectation value of the given failure mode f assigned to different quality levels is obtained, denoted as θ f =(θ f1 ,θ f2 ,…,θ fH). These expected values ​​directly reflect the probability that the scrapped parts belong to each quality grade under the failure mode f. To ensure the consistency and completeness of the basic probability distribution, the sum of the expected values ​​of the posterior probabilities of all quality grades under the failure mode f is calculated. f ,Right now According to T f Different basic probability allocation strategies are adopted for different value situations.

[0088] 1. Surplus allocation: When T f When <1, 1-Tf is assigned to the identification framework Θ, which represents a measure of global uncertainty and reflects the uncertainty that cannot be accurately assigned to a specific quality level due to insufficient information about the failure form f.

[0089] 2. Complete allocation: When T f =1, it naturally satisfies the constraints of the basic probability function, θ f Directly as a result of the effective basic probability distribution, all probabilities are fully allocated to each quality level.

[0090] 3. Normalization adjustment: When T f When >1, it indicates that the expected values ​​of the probabilities assigned to multiple quality levels are high. In order to maintain the rationality of the probability distribution, the expected values ​​of the posterior probability need to be normalized.

[0091] Through the above method, a set of basic probability distributions that meet the requirements can be generated for each failure mode f, providing a quantitative and structured probability framework for the quality status assessment of scrap parts.

[0092] Embodiment 2

[0093] In order to specifically illustrate the calculation process of the proposed BPA generation method and verify the effectiveness of this method in the quality status assessment of scrap parts, scrap worm gears are selected as the main research object to verify its application value and accuracy in practical engineering problems. At the same time, in order to further verify the universality and robustness of the proposed method, the classic Iris dataset is introduced as an auxiliary verification tool.

[0094] Worm gears are common transmission components in electromechanical equipment. Due to the complexity of the working environment and operating conditions, their failure behaviors are diverse. After in-depth analysis and testing, the main failure characteristics of used worm gears are wear, fracture, and deformation. The specific failure forms are shown in Table 2.

[0095] Table 2 Failure characteristics of used turbine worm gears

[0096]

[0097] After systematic collection and sorting, 60 sets of failure sample data U of waste turbine worm gears were obtained. According to the actual remanufacturing cost, the quality status of waste turbine worm gears was divided into three levels: good quality (G), medium quality (M), and severe degradation (B), as shown in Table 3.

[0098] Table 3 Failure sample data set of used turbine worm gear

[0099]

[0100] The Iris dataset is a classic multivariate dataset that contains 150 samples. Each sample corresponds to an iris flower, which is divided into three different species (Setosa, Versicolor, Virginica). Each sample contains four features, namely sepal length (SL), sepal width (SW), petal length (PL) and petal width (PW). These features are all continuous variables.

[0101] For the waste turbine worm and Iris datasets, a stratified random sampling method was used to randomly select 80% of the data from each category as the training sample set to build the DPMB model; the remaining 20% ​​of the data was used as the test sample set to calculate the basic probability allocation (BPA) to evaluate the model performance.

[0102] In the quality assessment process of scrapped worm gears, an identification framework Θ = {G, M, B} is constructed, which includes three different quality levels. Using formula (10) and combining with the pre-established training sample set, the number of intervals of different failure modes in each quality level is calculated and determined. The results are shown in Figure 2 shown.

[0103] According to the number of intervals of different failure forms, the boundary value of each interval is obtained, and then the frequency statistics of the damage amount of the failure form in the training sample set are performed to identify its distribution in each interval. Furthermore, the expected value of the posterior probability of the failure form at different quality levels is calculated based on formula 14. Thus, a corresponding DPMB model is constructed for each failure form to achieve the probability mapping from damage amount to quality status. Taking the failure form w1 as an example, it is divided into three intervals at different quality levels, and the corresponding interval boundary values ​​and expected values ​​of the posterior probability are calculated. The results are summarized in Tables 4 and 5.

[0104] Table 4 Interval division of failure form w1

[0105]

[0106] Table 5 Expected value of posterior probability of failure form w1

[0107]

[0108] The test sample data set of the scrapped worm gear is shown in Table 6. According to the damage amount of each sample under different failure forms, the posterior probability expectation values ​​belonging to different quality levels are matched from the corresponding DPMB model. Furthermore, according to the sum of the calculated posterior probabilities, a differentiated basic probability allocation strategy is adopted to calculate the final basic probability allocation result.

[0109] Table 6. Sample data set of waste turbine worm test

[0110]

[0111]

[0112] Table 7 shows the basic probability distribution and fusion results of the waste turbine worm sample T1. Each failure form is regarded as an evidence source, and each value represents the basic probability distribution of the corresponding evidence source for a specific quality level. According to the Dempster synthesis rule in formula (2), the basic probability distribution from different evidence sources is synthesized. The fusion results show that for the waste turbine worm sample T1, the basic probability mass of its quality status belonging to grade B is the highest, which is 0.9169, while the basic probability mass belonging to grades G and M is relatively low, which are 0.0235 and 0.0592 respectively. The probability distribution of the uncertain quality state in the whole set Θ is extremely low, which is 0.0004. This shows that under the current evaluation framework, according to all evidence information, combined with the maximum membership principle, the quality status of the test sample T1 is judged to be grade B, which is consistent with the quality grade results in Table 6.

[0113] Table 7 Basic probability distribution and fusion results of waste turbine worm sample T1

[0114]

[0115] In order to verify the effectiveness and feasibility of the proposed basic probability allocation method, it is compared and analyzed with the methods in the existing literature. Specifically, the experiment is carried out on the waste turbine worm dataset U and the iris dataset Iris. Ten independent experiments are conducted on each dataset to ensure the reliability of the results. In each set of experiments, the dataset is randomly divided into a training set and a test set, and the average recognition accuracy is finally calculated. The results of the ten sets of experiments are summarized in Table 8.

[0116] Table 8 Comparison of evaluation results of different methods

[0117]

[0118]

[0119] By comparing the performance of different evaluation methods on the waste turbine worm dataset U and the iris dataset Iris, it can be seen that the evaluation method proposed in this paper shows high accuracy and stability on both datasets, especially on dataset U, where its average accuracy is slightly higher than that of the other two methods, verifying its effectiveness in uncertainty modeling and reasoning.

[0120] In summary, this paper proposes a damage-quality state mapping model that integrates Dirichlet distribution and evidence theory. The main failure characteristics are determined by analyzing the failure behavior of parts. Based on the obtained damage data samples, the quality probability of scrap parts is modeled by combining multinomial distribution and Dirichlet distribution in the Bayesian framework. It is introduced into the evidence theory to construct the basic probability mass of each failure form. The combination rule is used to fuse different evidence bodies to obtain the final probability output, thereby establishing a probability mapping mechanism from failure form damage to quality state, providing decision support for the quality status assessment of scrap parts of retired electromechanical products. The scrap turbine worm is selected as the case study object, supplemented by the classic iris data set, and the method in this paper is compared with two existing literature methods to verify the feasibility and effectiveness of the model established in this paper. The experimental results show that the model has certain advantages in prediction accuracy and generalization ability.

[0121] Given that high-quality damage data of scrapped parts is often difficult to obtain in practical applications, further research can focus on reducing the high dependence on a single data source by integrating existing data resources such as historical maintenance records and actual operating conditions. At the same time, we are committed to exploring the integration of this model into the existing remanufacturing quality control process to achieve a wider range of practical applications.

[0122] Although embodiments of the present invention have been shown and described, those skilled in the art will appreciate that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the claims and their equivalents.

Claims

1. A method for constructing a state mapping model of scrapped parts based on Dirichlet distribution, characterized in that: The method comprises: Integrate the key features of scrap parts into a failure data set, and construct a failure feature matrix based on the data set; wherein the key features of scrap parts include wear, fracture, deformation and quality grade labels; Randomly select n instances from the quality grade labels as training data. Each failure mode contains n values, which are divided into intervals to identify the specific distribution of damage under different failure modes. According to the specific distribution identified, the introduced parameters are a=(a1, a2, ..., a k ) is used as the multinomial distribution component damage data to construct a priori probability model, and the probability vector θ of the priori probability model is regarded as a random variable under the priori reference a condition, that is, p(θ)~Dir(a); Construct a probability model for a given failure mode f and quality level h, denoted as DPMS fh , H probability models are integrated to obtain the combined probability model under failure form f, which is recorded as DPMS f , in order to form a comprehensive probability description of the failure form f, all combined probability models are integrated, and for each failure form f, its corresponding damage data is used as the input parameter, processed by the corresponding DBMS model, and the posterior probability expected value of the given failure form f assigned to different quality levels is matched, and finally the sum of the posterior probability expected values ​​of all quality levels under the failure form f is calculated. f , according to T f Different basic probability allocation strategies are adopted for different value situations.

2. The method for constructing a waste parts state mapping model based on Dirichlet distribution according to claim 1, characterized in that: The feature matrix is ​​expressed as follows: Among them, w ij represents the wear amount of the i-th scrapped component in the j-th failure mode, w 11 represents the wear amount of the first scrapped component in the first failure mode, w 12 represents the wear amount of the first scrapped component in the second failure mode, w 1j represents the wear amount of the first scrapped component in the jth failure mode, w 21 represents the wear amount of the second scrapped component in the first failure mode, w 22 represents the wear amount of the second scrapped component in the second failure mode, w 21 represents the wear amount of the second scrapped component in the first failure mode, w 2j represents the wear amount of the first scrapped component in the jth failure mode, w i1 represents the wear amount of the i-th scrapped component in the first failure mode, w i2 Represents the wear amount of the i-th scrapped component in the second failure mode.

3. The method for constructing a waste parts state mapping model based on Dirichlet distribution according to claim 1, characterized in that: The interval division is performed to identify the specific distribution of damage under different failure forms. Specifically, the Freedman-Diaconi rule is used for adaptive interval division to determine the appropriate number of intervals K for each failure form f, thereby discretizing the continuous damage data into finite interval categories, which is expressed as follows: Where n represents the number of instances, IQR represents the interquartile range, and f represents each failure mode.

4. The method for constructing a waste parts state mapping model based on Dirichlet distribution according to claim 3 is characterized in that: When a scrapped component fails, the damage amount of a specific failure mode must fall within a certain range. Through statistical analysis of the event frequency, the probability distribution of each interval category is estimated: The frequency falling in the kth interval is represented by n k , with a probability associated with it of θ i , then the set of damage data is formally expressed as (n1,n2,...,n k )~Mult(θ1,θ2,...,θ k ), and satisfies 5. The method for constructing a waste parts state mapping model based on Dirichlet distribution according to claim 1, characterized in that: The method further includes, before performing the prior Dirichlet, performing a Jeffreys non-information prior, and constructing it based on the Fisher information matrix, which is expressed as follows: Among them, p(·) represents the probability distribution function, and k represents the number of divided intervals; According to the Bayesian nonparametric statistical method, when the prior distribution of the probability parameters of the multiple distributions of scrap parts is specified as Dirichlet distribution, the probability density function has the following characteristics: Among them, a i represents the parameters of the Dirichlet distribution, which represent the prior belief about the probability of each interval.

6. The method for constructing a waste parts state mapping model based on Dirichlet distribution according to claim 5, characterized in that: When Jeffreys non-informative prior is used, the parameter a of the Dirichlet distribution can be uniquely determined, and a1=a2=…=a k =1 / 2. After determining the parameters of the prior Dirichlet distribution, according to the property that the Bayesian posterior distribution is proportional to the product of the likelihood function and the prior distribution, we can obtain Where Dir(·) represents Dirichlet distribution; That is, when the multinomial distribution data of the damage amount of scrapped parts is observed to be n = (n1, n2, ..., n k ), it is deduced that its posterior distribution is parameter updated to a=(1 / 2+n1,1 / 2+n2,...,1 / 2+n k ) is a Dirichlet distribution, then the expected value of the posterior probability of the Dirichlet distribution is calculated by the following formula in, represents the expected value of the posterior probability of the i-th interval.

7. The method for constructing a waste parts state mapping model based on Dirichlet distribution according to claim 1, characterized in that: The basic probability allocation strategy includes: A. Surplus distribution: When T f <1, 1-T f Assigned to the identification framework Θ, it represents a measure of global uncertainty, reflecting the uncertainty that cannot be accurately assigned to a specific quality level due to insufficient information about the failure form f; B. Complete allocation: When T f =1, it naturally satisfies the constraints of the basic probability function, θ f Directly as a result of the effective basic probability allocation, that is, all probabilities are fully allocated to each quality level; C. Normalization adjustment: When T f When >1, it indicates that the expected values ​​of the probabilities assigned to multiple quality levels are high. In order to maintain the rationality of the probability distribution, the expected values ​​of the posterior probability need to be normalized.

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