Vacuum carburizing furnace fault propagation path identification method based on stress-strength interference model

Abstract

The invention discloses a vacuum carburizing furnace fault propagation path identification method based on a stress-strength interference model, and the method comprises the steps: carrying out the construction of a layered topology directed graph of a vacuum carburizing furnace through employing a DEMATEL / ISM method, and obtaining a fault propagation path between subsystems; and a PageRank algorithm is used to solve the fault influence degree between the equipment subsystems. Mathematical modeling is carried out on the propagation intensity corresponding to the fault propagation path obtained by the layered topology directed graph, and the importance degree of the path is quantified by utilizing the propagation intensity numerical value. For any fault path of the vacuum carburizing furnace, the fault propagation intensity is represented by three variables, namely the fault influence degree, the fault probability of the subsystems and the edge betweenness of the path, and the propagation intensity is defined from three aspects, namely the mutual influence degree of the subsystems, the fault probability characteristic and the statistical characteristic. According to the method, the physical process of equipment failure is fully considered, and a new mathematical model is constructed for the reliability and the failure propagation strength of the vacuum carburizing furnace.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of vacuum carburizing furnace reliability modeling and fault propagation path identification. A fault propagation strength calculation method for a vacuum carburizing furnace based on a stress-strength interference model is mainly proposed. BACKGROUND

[0002] A vacuum carburizing furnace is an advanced material heat treatment equipment that can accurately control the carbon content in workpieces and greatly improve the surface quality of workpieces. However, due to its complex structure and long-term operation in a vacuum high-temperature environment, it is necessary to accurately and clearly express the fault propagation paths of each subsystem of the equipment in order to effectively maintain it.

[0003] For fault propagation path identification and calculation, the existing modeling approach is to consider reliability, fault influence degree between subsystems, fault edge betweenness, and other statistical quantities to calculate the fault propagation strength values between subsystems, thereby identifying the key fault propagation paths in the equipment. Among them, the common reliability calculation method requires recording the fault information of the equipment, calculating the fault interval time of the equipment, estimating the distribution characteristics of the variable, obtaining the life distribution of the equipment, and thus realizing the calculation of reliability.

[0004] However, for a vacuum carburizing furnace, the above life data cannot reflect the state changes during the equipment processing process, such as heating processing and cooling processing, resulting in weak interpretability of the calculation results and unclear description of the fault propagation paths when calculating the fault propagation strength based on this method. Therefore, a fault propagation strength calculation method based on a stress-strength interference model is proposed, which uses detectable physical signal values, i.e., generalized stress and strength levels, to represent reliability values, and introduces these two variables into the calculation process of fault propagation strength, providing a new approach for identification of key fault propagation paths and modeling of equipment reliability. SUMMARY

[0005] The present application provides a vacuum carburizing furnace fault propagation strength calculation method that combines stress-strength interference model with traditional probability and statistics model, aiming to integrate physical signal representation values such as generalized stress level and generalized strength level into the fault propagation calculation process, and use multi-dimensional distribution to realize fine reliability modeling and fault propagation path identification, providing reference for equipment operation and maintenance strategy formulation.

[0006] The technical scheme adopted by the present application is: the DEMATEL / ISM method is used to construct a hierarchical topological directed graph of the vacuum carburizing furnace, and the fault propagation path between each subsystem is obtained; then the PageRank algorithm is used to solve the fault influence degree pr between the device subsystems. On this basis, the propagation strength corresponding to the fault propagation path obtained by the hierarchical topological directed graph is mathematically modeled, and the importance of the path is quantified by using the numerical value of the propagation strength. For any fault path of the vacuum carburizing furnace, the fault propagation strength is represented by three variables, namely the fault influence degree pr, the fault probability P of the subsystem, and the edge betweenness L of the path, which defines the propagation strength from three aspects of the mutual influence degree of the subsystem, the fault probability characteristics, and the statistical characteristics.

[0007] The stress-strength interference model is used to express the fault probability P of the subsystem, that is, the fault probability is expressed by using the distribution and size relationship of the generalized stress and strength. The generalized stress is usually a random variable, and its probability distribution characteristics can be obtained by experimental measurement and appropriate distribution estimation; the strength level of the subsystem is also a random variable following a certain distribution characteristic. Therefore, the fault probability value can be represented as the cumulative probability of the generalized stress value being greater than the strength value. The fault propagation strength represented by the distribution characteristics of the generalized stress and strength is obtained by using the calculated fault probability, and the relationship between the properties of the device and the fault propagation path is established.

[0008] The calculation steps of the method are as follows:

[0009] Step one: select the subsystem combination i-j in the device that has a fault propagation relationship, and determine the calculation formula of the propagation strength I by using the fault influence degree pr, the fault probability P of the subsystem, and the edge betweenness L, as shown in equation (1). Fault probability P i , and edge betweenness

[0010]

[0011] In equation (1), is the dynamic fault propagation characteristic, which is determined by the fault probability and the fault influence degree of the subsystem i, and the calculation formula is:

[0012]

[0013] Step two: calculate the reliability and fault probability of the subsystem. According to the stress-strength interference model, the physical signals detected during the operation of the device are used instead of the traditional fault time interval to calculate the reliability value. In the single stress condition, the generalized stress corresponding to the load received by the subsystem i is σ, and the strength corresponding to the generalized stress in the device is S. The calculation formula of this step is shown in equation (3): ​

[0014]

[0015] Under ideal conditions, both σ and S are numerically determined parameters, determined by the working condition of the system, working condition and the system itself. But in practical engineering applications, σ and S are two random variables subject to certain distribution characteristics.

[0016] The physical meaning represented by formula (3) is: given any one generalized stress value σ, the cumulative probability of the generalized stress level of the device is less than the strength S of the device, that is, the reliability of the device. In the formula, f σ (σ) and f s (S) are the probability density functions of generalized stress and strength. When both are known, the reliability value of the subsystem can be obtained. The formula for calculating the failure probability of the device is shown in formula (4):

[0017]

[0018] Step three: substitute formula (4) into formula (1) and formula (2) to obtain the dynamic failure propagation properties and failure propagation strength represented by the distribution characteristics of generalized stress σ and strength S.

[0019] First, determine the probability density function in formula (4): Weibull distribution conforms to the failure distribution characteristics of most mechanical, electronic and other equipment, so when calculating the failure probability, consider that the generalized stress σ and the strength S both satisfy the Weibull distribution, and substitute the probability density function into formula (4) for calculation.

[0020] The probability density function of the two-parameter Weibull distribution is:

[0021]

[0022] Where σ is the random variable described by the probability density function. λ is the scale parameter, and k is the shape parameter.

[0023] The reliability solving formula based on the stress-strength interference model is:

[0024]

[0025] Substitute the probability distribution of stress level and strength level as Weibull distribution into formula (6) to obtain:

[0026]

[0027] Formula (7) is a double integral form. First, calculate the inner integral to obtain the simplified stress-strength interference model formula:

[0028]

[0029] When the shape parameters k of random variables σ and S are... σ k S When the values ​​are unequal, equation (8) and subsequent calculations of the fault propagation intensity become more complex and require numerical solutions. However, when the shape parameter k... σ k S When they are equal, that is, when they satisfy equation (9), a closed-form solution can be calculated.

[0030] k S =k σ =k (9)

[0031] When equation (9) is satisfied, the logarithmic terms in equation (8) can be combined and simplified to obtain:

[0032]

[0033] To simplify the calculation process, substitute each term in the integral term with a different variable. Let:

[0034]

[0035] Substituting the result of the variable substitution into equation (10), the integral term of the original equation can be transformed into a gamma function form, specifically:

[0036]

[0037] In formula (12), the exponents in the integral term, after being combined and calculated, conform to the expression form of the gamma function, that is:

[0038]

[0039] After simplification, the gamma function has a value of 1. Therefore, under the calculation conditions described above, the integral term in the original function can be eliminated. The final simplified formula for reliability is:

[0040]

[0041] As can be seen from formula (14), based on the stress-strength interference model, the mathematical model of reliability can be simplified to a function jointly expressed by the scale parameter λ and the shape parameter k of the two random variables, generalized stress and strength, of the subsystem.

[0042] Then, calculate the dynamic fault propagation properties and fault propagation strength, let:

[0043]

[0044] The failure probability of the subsystem is expressed by formula (16):

[0045]

[0046] Therefore, the formula of the dynamic fault propagation attribute is:

[0047]

[0048] Therefore, the formula (1) of the fault propagation strength formula can be expressed as:

[0049]

[0050] The formulas (14) and (18) provide a method for representing reliability and fault propagation strength by statistical characteristic values of physical signals of the equipment itself. In actual application, the above physical signals are continuously monitored by experiments to obtain real-time data, and dynamic updating of the values of reliability and fault propagation strength is realized.

[0051] Beneficial effects:

[0052] The present application fully considers the physical process of equipment failure, and constructs a new mathematical model for the reliability and fault propagation strength of the vacuum carburizing furnace, and proposes a more accurate and intuitive definition method. Firstly, the generalized stress and strength with more definite physical meaning are used to replace the traditional life statistical data, and the physical meaning of the reliability value of the vacuum carburizing furnace is revealed through the new mathematical model; and then the values of the two physical signals of the generalized stress and strength are introduced into the calculation of the fault propagation strength, and the fault propagation path identification method of the equipment is more clearly defined from the physical level. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 is a layered directed topological graph of the vacuum carburizing furnace.

[0054] Figure 2 is a temperature change curve of the working process of the vacuum carburizing furnace.

[0055] Figure 3 is a fault propagation strength calculation process based on a stress-strength interference model. DETAILED DESCRIPTION

[0056] Now, the steps of the present application will be described in detail in combination with specific scenarios:

[0057] In the vacuum carburizing furnace, the subsystem i and the subsystem j having a fault propagation relationship are selected for analysis, and the propagation path passes through the directed edge e i-j .

[0058] Step one: using the DEMATEL / ISM method and the PageRank algorithm to construct the fault propagation directed graph of the system, and calculating the fault influence degree value of the directed edge e i-j and the edge betweenness ​

[0059] Step 2: Subsystem i exhibits a fault phenomenon. Determine the generalized stress σ and the corresponding intensity level S present in subsystem i during operation. σ and S follow a two-parameter Weibull distribution, and the characteristic parameters of the Weibull distribution are: scale parameter λ. σ , λ S Same shape parameter k.

[0060] Step 3: Calculate the reliability value corresponding to subsystem i:

[0061]

[0062] Step 4: Calculate the failure probability P of subsystem i. i :

[0063]

[0064] Step 5: Substitute the fault probability calculated above into the formula for calculating fault propagation strength to obtain the directed edge e. i-j Fault propagation strength:

[0065]

[0066] The following is an example calculation process to more clearly explain the application of this calculation approach.

[0067] First, the vacuum carburizing furnace of a certain model is divided into subsystems, and the main components of the equipment include: furnace chamber, furnace body, heating system, vacuum system, carburizing system, gas quenching system, water circulation system, control system, oil quenching system, and feeding system, totaling 10 subsystems.

[0068] Step 1: Obtain the hierarchical directed topology graph of the device using the DEMATEL / ISM method, as shown in the attached figure. Figure 1 As shown. The calculation is performed using a directed edge consisting of two subsystems: the furnace chamber (i) and the vacuum system (j). The generalized stress level σ of the furnace chamber during operation is determined as the rated temperature, and its corresponding strength level S is the maximum operating temperature the furnace body can withstand. An investigation of the actual use of the vacuum carburizing furnace reveals that its maximum operating temperature is 1320℃, and the rated operating temperature for processing a certain type of workpiece is 960℃.

[0069] The failure impact between the two subsystems is obtained using the PageRank algorithm. The value is 0.101; the betweenness number of this directed edge is 4.25 according to the directed topology graph. Similarly, the fault influence degree and betweenness number between other subsystems can also be obtained.

[0070] Step Two: Determine the random variable distribution characteristics of the physical signals corresponding to the furnace chamber. There will be a slight error between the actual operating temperature and the rated temperature of the equipment. Each batch of workpieces processed in the vacuum carburizing furnace undergoes a complete temperature rise and fall process. At each stable temperature stage, actual temperature data is acquired at a certain sampling frequency. This process is repeated multiple times to obtain a set of sample values, and the distribution parameters of these samples are estimated. The actual extreme temperature value will also fluctuate due to factors such as manufacturing processes; therefore, its distribution characteristics can be estimated based on empirical data.

[0071] For the generalized stress σ, considering the actual processing of the vacuum furnace, a period of stable equipment operation was selected, and temperature data was sampled at a sampling frequency of 2 seconds per sampling. The data source is attached. Figure 2 As shown in Table 1, some of the sampled data are presented. Using the Weibull distribution parameter estimation method, the distribution characteristics of the temperature data were calculated as: k = 3.44, λ = 961.5; for intensity level S, considering its rated maximum operating temperature of 1320℃, k = 3.44, λ = 1500.

[0072] Table 1 Temperature Data Sampling Table (Partial)

[0073]

[0074] Step 3: Calculate the reliability value of the furnace shell:

[0075]

[0076] Step 4: Calculate the failure probability of the furnace chamber:

[0077] P i =1 - 0.822 = 0.178

[0078] Step 5: Calculate the dynamic fault propagation attribute P of the directed edge. ei-j :

[0079]

[0080] Step Six: Repeat steps one through five for each directed edge to obtain the dynamic fault propagation attributes of the directed edges corresponding to each subsystem of the equipment. Substituting these attributes into the calculation formula (18) for fault propagation intensity, the propagation intensity of fault propagation between the furnace and the vacuum system can be obtained:

[0081]

[0082] Step 7: Monitor the temperature of the vacuum furnace in real time, repeat the data acquisition and calculation process from Step 2 to Step 6, and dynamically update the calculation results.

[0083] The specific calculation procedure of the above steps 1 to 7 is shown in the attached Figure 3 diagram.

Claims

1. A method for identifying a failure propagation path of a vacuum carburizing furnace based on a stress-strength interference model, characterized by, The implementation steps of the method are as follows: Step one: select the subsystem combination i-j with fault propagation relationship in the device, and determine the calculation formula of the propagation strength I through the fault influence degree Fault probability P i , and edge betweenness , as shown in equation (1). In formula (1), The dynamic failure propagation characteristics are determined by the failure probability and the failure influence degree of subsystem i, and the calculation formula is as follows: Step two: calculate the reliability and failure probability of the subsystem; according to the stress-strength interference model, use the physical signals detected in the device operation to replace the traditional failure time interval to calculate the reliability value; under the condition of single stress, the generalized stress corresponding to the load borne by the subsystem i is σ, and the strength corresponding to the generalized stress in the device is S, and the calculation formula of this step is shown as formula (3): Wherein, σ and S are numerical determined parameters, which are determined by the working condition, working condition and system attribute of the system; but in actual engineering application, σ and S are two random variables subject to certain distribution characteristics; The physical meaning of formula (3) is: given any one generalized stress value σ, the cumulative probability of the generalized stress level of the device being less than the device strength S, i.e. the reliability of the device; in the formula, f σ (σ) and f S (S) are the probability density functions of the generalized stress and strength, respectively, and the reliability value of the subsystem is obtained; then the formula for calculating the device failure probability is shown in formula (4): Step three: substitute formula (4) into formula (1) and formula (2) to obtain the dynamic failure propagation attribute and failure propagation strength represented by the distribution characteristics of generalized stress σ and strength S.

2. The vacuum carburizing furnace failure propagation path identification method based on stress-strength interference model according to claim 1, characterized in that, In step three, first, determine the probability density function in formula (4): when calculating the failure probability, consider that the generalized stress σ and the strength S both satisfy the Weibull distribution, and substitute the probability density function into formula (4) for calculation; The probability density function of two-parameter Weibull distribution is: Wherein, σ is a random variable described by the probability density function; λ is the scale parameter, and k is the shape parameter; The reliability solving formula based on the stress-strength interference model is: Substitute the probability distribution of stress level and strength level into formula (6) as Weibull distribution, and the following formula can be obtained: Formula (7) is a double integral form; first calculate the inner integral to obtain the simplified stress-strength interference model formula: When the shape parameters k of random variables σ and S are... σ k S When the values ​​are unequal, equation (8) and subsequent calculations of the fault propagation intensity become more complex and require numerical solutions; while when the shape parameter k σ k S When they are equal, that is, when they satisfy equation (9), a closed-loop solution is obtained; k S = k σ = k (9) When formula (9) is satisfied, the logarithmic term in formula (8) is combined and simplified to obtain: Replace each term in the integral term with a variable to simplify the calculation steps; let: Substitute the result of the variable replacement into equation (10) to convert the integral term of the original equation into a gamma function form. Specifically In formula (12), the exponent in the integral term is combined and calculated to meet the expression form of the gamma function, that is: After simplification, the value of the gamma function is 1; finally, the formula of reliability is obtained as: Through formula (14), it can be known that based on the stress-strength interference model, the mathematical model of reliability can finally be simplified as a function expressed by the scale parameter λ and the shape parameter k of the two random variables of generalized stress and strength of the subsystem; Then, calculate the dynamic failure propagation attribute and failure propagation strength, and let: Then the failure probability of the subsystem is expressed by formula (16): Therefore, the formula of the failure propagation strength of formula (1) is expressed as: Formulas (14) and (18) provide a method for expressing reliability and failure propagation strength by statistical characteristic values of physical signals of the device itself. ​

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