Industrial equipment preventive maintenance decision-making method based on discrete time Markov chain

Abstract

The invention provides an industrial equipment preventive maintenance decision-making method based on a discrete time Markov chain, and relates to the technical field of industrial equipment reliability management and maintenance strategy optimization. The method comprises the following steps: based on historical maintenance record statistics, establishing a discrete time Markov chain maintenance effect state transition model and determining a state transition probability matrix thereof, carrying out eigenvalue decomposition on the state transition probability matrix to obtain state probability distribution after n times of maintenance, and determining each state probability; carrying out weighted fusion on the random intensity functions of the three maintenance processes through corresponding state probabilities, and constructing a mixed fault rate function; calculating an expected failure frequency based on the mixed failure rate function; and based on the expected failure times, establishing a long-term cost rate function, and solving to determine an optimal replacement period. According to the method, three basic maintenance effect types are integrated through the dynamic probability, and accurate prediction of the number of failure times of equipment and calculation of the optimal maintenance period are achieved.

Description

Technical Field

[0001] This application relates to the field of industrial equipment reliability management and maintenance strategy optimization technology, and in particular to a preventive maintenance decision-making method for industrial equipment based on discrete-time Markov chains. Background Technology

[0002] In the field of industrial equipment reliability management and maintenance strategies, maintenance effect modeling based on stochastic processes is a core technology for optimizing maintenance decisions. Existing technologies mainly employ three types of models with fixed maintenance effects. These models all suffer from the fundamental flaw of determinizing maintenance effects and cannot accurately describe the randomness and uncertainty present in real-world maintenance activities.

[0003] The Generalized Pólya Process (GPP) model, proposed by Cha, JH, et al., describes the "worse than minimum maintenance" effect. It assumes that each maintenance leads to accelerated equipment degradation, with the failure rate increasing linearly with the number of historical maintenance visits. The limitation of this model lies in its forced assumption that every maintenance inevitably leads to equipment deterioration, ignoring the possibility of high-quality maintenance in actual operations. This assumption of permanent, monotonic deterioration leads to overly pessimistic predictions of equipment failure, resulting in prematurely calculated optimal replacement cycles and a significant waste of maintenance resources. The Non-homogeneous Poisson Process (NHPP) model describes the "minimum maintenance" effect. This model assumes that maintenance only restores the equipment to its pre-failure state, with the failure rate remaining constant before and after maintenance. The drawback of this model is its idealistic assumption that all maintenance is standardized and has consistent effects, ignoring the quality fluctuations inherent in maintenance activities. It fails to reflect the reliability improvements brought about by highly skilled workers and cannot accommodate accidental damage caused by operational errors. It represents an overly stable and idealized assumption, severely detached from engineering realities. The Extended Generalized Pólya Process (EGPP) model is used to describe the "better than minimum maintenance" effect. This model assumes that certain inherent defects can be eliminated during maintenance, gradually reducing the equipment failure rate until a finite value is reached. Its limitation is that it forcibly assumes a monotonic improvement process, which cannot simulate the random maintenance failures or state fluctuations that may occur during the improvement process. It can produce overly optimistic predictions, and making decisions based on this will lead to a huge risk of downtime.

[0004] The common drawback of these existing technologies lies in their "deterministic" assumptions about maintenance outcomes, which fail to describe the stochastic nature of maintenance results in practical applications. This stochasticity stems from the combined effects of fluctuations in maintenance personnel skills, on-site environmental conditions, differences in spare parts quality, and the degradation state of the equipment itself. Because existing models cannot capture this crucial characteristic, their resulting equipment reliability predictions and optimal maintenance strategies deviate significantly from reality, failing to provide a reliable basis for industrial maintenance decisions. This is precisely the technical problem that this invention aims to solve. The model structure and mathematical expression employed in existing technical solutions dictate their forced assumptions of a single, fixed maintenance outcome; this structural deficiency is the foundation and starting point of this invention. Summary of the Invention

[0005] This application provides a preventive maintenance decision-making method for industrial equipment based on discrete-time Markov chains. Addressing the technical shortcomings of existing technologies where GPP, NHPP, and EGPP models employ fixed maintenance effect assumptions and fail to accurately describe the randomness and uncertainty inherent in actual maintenance processes, this application aims to solve the following technical problems: First, overcoming the limitations of existing models that forcibly assume maintenance effects by introducing discrete-time Markov chains to dynamically describe the random transition characteristics between the three maintenance effect states; Second, establishing a hybrid failure rate function that reflects the randomness of maintenance effects by combining the random intensity of the three processes (EGPP, NHPP, and GPP) with the time-varying state probabilities generated by DTMC to construct a more practical equipment reliability assessment model; Third, developing an optimal periodic replacement strategy based on the hybrid maintenance effect model by deriving analytical expressions for the expected value of the number of failures and the long-term cost rate to determine the optimal equipment replacement cycle that minimizes maintenance costs, providing a scientific basis and quantitative guidance for preventive maintenance of industrial equipment.

[0006] This application ultimately provides a new technical solution for industrial equipment maintenance management by establishing a hybrid model that considers the randomness of maintenance outcomes, thereby improving the accuracy of equipment reliability prediction, optimizing maintenance resource allocation, and reducing the maintenance cost throughout the equipment's life cycle.

[0007] Firstly, this application provides a preventive maintenance decision-making method for industrial equipment based on discrete-time Markov chains, including: Based on historical maintenance records, a discrete-time Markov chain maintenance effect state transition model is established and its state transition probability matrix is ​​determined. The state transition probability matrix is ​​then subjected to eigenvalue decomposition to obtain the state probability distribution after n maintenance cycles. Based on this probability distribution, the probability of each state is determined. The discrete-time Markov chain maintenance effect state transition model is a discrete-time Markov chain model containing three maintenance effect states: state S1 (better than minimum maintenance), state S2 (minimum maintenance), and state S3 (worse than minimum maintenance). The probability of each state includes the state probabilities corresponding to states S1, S2, and S3. The stochastic intensity functions of the three maintenance processes are fused together by weighting the corresponding state probabilities to construct a hybrid failure rate function; wherein the three maintenance processes are the maintenance processes corresponding to state S1, state S2 and state S3 respectively. Based on the hybrid failure rate function, the expected number of failures is calculated; Based on the expected number of failures, a long-term cost rate function is established, and the long-term cost rate function is solved to determine the optimal replacement cycle.

[0008] In one possible design, the state transition probability matrix is ​​represented as: In the formula, Here is the state transition probability matrix. This indicates the state within a single discrete time step. Transition to state The probability, and j For any index of the state, ,satisfy .

[0009] In one possible design, the state transition probability matrix is ​​decomposed into eigenvalues ​​to obtain the state probability distribution after n repairs, and the probability of each state is determined based on the probability distribution, including: The state transition probability matrix is ​​decomposed into eigenvalues ​​using the following formula: In the formula, Here is the state transition probability matrix. For the reason The matrix formed by the eigenvectors of , For the reason The eigenvalues ​​are diagonal matrices composed of diagonal elements. For matrix The inverse matrix.

[0010] The resulting state probability distribution after n repairs is as follows: In the formula, Let n be the state transition probability matrix. For a matrix to undergo n transformations, This refers to the discrete time steps, i.e., the number of maintenance operations the equipment undergoes. Based on the probability distribution, the probability of each state is determined by the following formula: In the formula, Let be the instantaneous probability that the equipment is in the i-th repair outcome state after n repairs. Indices of eigenvalues ​​and eigenvectors ( =1, 2, 3), The initial state probability vector With eigenvector matrix The row vector obtained by multiplication The kth component, For the kth eigenvalue nth power, Inverse matrix The element in the k-th row and i-th column, The index of the state.

[0011] In one possible design, the hybrid failure rate function is expressed as: In the formula, For a mixed failure rate function, , and These are the state probabilities corresponding to states S1, S2, and S3, respectively. , and These are the stochastic intensity functions of the maintenance process corresponding to states S1, S2, and S3, respectively. , and Represented as: , for In the formula, These are the improvement parameters for the EGPP model, characterizing the degree of improvement in the failure rate achieved by each high-quality maintenance. This represents the cumulative number of failures (or repairs) that occurred before time t. This represents the upper limit of the initial number of repairable defects in the EGPP model. The degradation parameter of the GPP model represents the degree to which each low-quality maintenance accelerates the failure rate.

[0012] In one possible design, the expected number of failures is calculated based on the hybrid failure rate function using the following formula: The probability distribution functions for each process are as follows: , In the formula, in the formula, The expected number of failures, , , Inverse matrix The elements in the table correspond to the weight coefficients of the EGPP, NHPP, and GPP states, respectively. The number of failures is the independent variable of the probability distribution function. For the kth eigenvalue nth power, Let n be the probability of n failures occurring at time t under the pure EGPP model. Let n be the probability of n failures occurring at time t under the pure NHPP model. Let n be the probability of n failures occurring at time t under the pure GPP model. Reference failure rate function The points, For gamma function, It is a natural constant.

[0013] In one possible design, the long-run cost rate function is expressed as: In the formula, For cost rate, The expected number of failures, The cost of repair after a single failure. To cover the fixed cost of performing a preventative replacement, This refers to the replacement cycle.

[0014] In one possible design, the method of solving the long-term cost rate function to determine the optimal replacement cycle includes finding the value that minimizes the cost rate within a set replacement cycle as the optimal replacement cycle.

[0015] Secondly, this application provides an industrial equipment preventive maintenance decision-making device based on discrete-time Markov chains, the device comprising: The model building module is configured to establish a discrete-time Markov chain maintenance effect state transition model based on historical maintenance record statistics and determine its state transition probability matrix. It then performs eigenvalue decomposition on the state transition probability matrix to obtain the state probability distribution after n maintenance cycles, and determines the probability of each state based on this probability distribution. The discrete-time Markov chain maintenance effect state transition model is a discrete-time Markov chain model containing three maintenance effect states: state S1 (better than minimum maintenance), state S2 (minimum maintenance), and state S3 (worse than minimum maintenance). The state probabilities include the state probabilities corresponding to states S1, S2, and S3. The function establishment module is configured to fuse the stochastic intensity functions of the three maintenance processes through corresponding state probabilities to construct a hybrid failure rate function; wherein the three maintenance processes are the maintenance processes corresponding to state S1, state S2 and state S3 respectively. The failure count calculation module is configured to calculate the expected number of failures based on the hybrid failure rate function. The strategy determination module is configured to establish a long-term cost rate function based on the expected number of failures, and solve the long-term cost rate function to determine the optimal replacement cycle.

[0016] Thirdly, embodiments of this application provide an electronic device, including: at least one processor and a memory; the memory stores computer-executable instructions; the at least one processor executes the computer-executable instructions stored in the memory, causing the at least one processor to perform the industrial equipment preventive maintenance decision-making method based on discrete-time Markov chains as described in the first aspect and various possible designs of the first aspect.

[0017] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer-executable instructions. When a processor executes the computer-executable instructions, it implements the industrial equipment preventive maintenance decision-making method based on discrete-time Markov chains as described in the first aspect and various possible designs of the first aspect.

[0018] Fifthly, embodiments of this application provide a computer program product, including a computer program that, when executed by a processor, implements the industrial equipment preventive maintenance decision-making method based on discrete-time Markov chains as described in the first aspect and various possible designs of the first aspect.

[0019] The industrial equipment preventive maintenance decision-making method based on discrete-time Markov chains provided in this application has at least the following beneficial effects: This application establishes a hybrid maintenance effect model by introducing a discrete-time Markov chain, resulting in significant technical improvements. The equipment maintenance cost rate function based on the hybrid model exhibits a distinct "U-shaped" curve characteristic, accurately identifying the optimal replacement time and overcoming the problem of large prediction bias in traditional single-model approaches. Ultimately, this application achieves a substantial optimization of the maintenance cost rate, reducing it to 273.12%, a 26.8% decrease compared to the GPP model, while extending the optimal replacement cycle to 119.7 days, a 34.0% improvement, providing an economical and reliable solution for industrial equipment maintenance. Attached Figure Description

[0020] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0021] Figure 1 A flowchart illustrating a preventive maintenance decision-making method for industrial equipment based on discrete-time Markov chains, provided for embodiments of this application; Figure 2 The failure rate branch evolution diagram provided in the embodiments of this application; wherein, , , This indicates a single transfer. , , This indicates two transfers; Figure 3 This is a structural diagram of an industrial equipment preventive maintenance decision-making device based on discrete-time Markov chains, provided in an embodiment of this application.

[0022] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0023] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0024] The collection, storage, use, processing, transmission, provision, and disclosure of financial data or user data involved in the technical solution of this application all comply with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0025] It should be noted that in the embodiments of this application, certain software, components, models and other existing solutions in the industry may be mentioned. These should be regarded as exemplary and are only intended to illustrate the feasibility of implementing the technical solution of this application. However, it does not mean that the applicant has used or necessarily used the solution.

[0026] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0027] This application provides a preventive maintenance decision-making method for industrial equipment based on discrete-time Markov chains. The method constructs a maintenance effect state transition matrix based on discrete-time Markov chains, dynamically integrates hybrid modeling of three maintenance processes—EGPP, NHPP, and GPP—and fuses the stochastic intensity functions of the three processes into a hybrid failure rate function through state probability weights. Finally, the optimal equipment replacement cycle is calculated based on this hybrid failure rate function, thereby enabling preventive maintenance decisions for industrial equipment.

[0028] like Figure 1 The diagram shows a flowchart of a preventive maintenance decision-making method for industrial equipment based on discrete-time Markov chains, provided in an embodiment of this application. The preventive maintenance decision-making method for industrial equipment based on discrete-time Markov chains includes the following steps S10 to S40.

[0029] S10: Based on historical maintenance records, establish a discrete-time Markov chain maintenance effect state transition model and determine its state transition probability matrix. Perform eigenvalue decomposition on the state transition probability matrix to obtain the state probability distribution after n maintenance cycles, and determine the probability of each state based on the probability distribution.

[0030] In this embodiment, the discrete-time Markov chain repair effect state transition model is a discrete-time Markov chain model containing three repair effect states. The three repair states are state S1 (corresponding to the EGPP process), which is better than minimum repair, state S2 (corresponding to the NHPP process), and state S3 (corresponding to the GPP process), which is worse than minimum repair. The probability of each state includes the state probability corresponding to state S1, state S2, and state S3.

[0031] In some embodiments, the state transition probability matrix is ​​represented as: In the formula, Here is the state transition probability matrix. This indicates the state within a single discrete time step. Transition to state The probability, and j For any index of the state, ,satisfy Its typical meanings include: Indicates a high-quality repair status Transfer to regular maintenance status The probability of; Indicates a change from normal maintenance status Deteriorated to a low-quality repair condition The probability of; Indicates a low-quality repair status Restored to high-quality repair condition The low probability.

[0032] In some embodiments, the state transition probability matrix is ​​decomposed into eigenvalues ​​using the following formula: In the formula, Here is the state transition probability matrix. For the reason The matrix formed by the eigenvectors of , For the reason The eigenvalues ​​are diagonal matrices composed of diagonal elements. For matrix The inverse matrix.

[0033] The resulting state probability distribution after n repairs is as follows: In the formula, Let n be the state transition probability matrix at step n. For a matrix to undergo n transformations, This refers to the discrete time steps, i.e., the number of maintenance operations the equipment undergoes. Based on the above probability distribution, the probability of each state is determined by the following formula: In the formula, Let be the instantaneous probability that the equipment is in the i-th repair outcome state after n repairs. Indices of eigenvalues ​​and eigenvectors ( =1, 2, 3), The initial state probability vector With eigenvector matrix The row vector obtained by multiplication The kth component, For the kth eigenvalue nth power, Inverse matrix The element in the k-th row and i-th column, The index of the state.

[0034] S20: The stochastic intensity functions of the three maintenance processes are fused together by weighting the corresponding state probabilities to construct a hybrid failure rate function; In this embodiment, the three maintenance processes are the maintenance processes corresponding to state S1, state S2, and state S3, respectively.

[0035] In some embodiments, the constructed hybrid failure rate function is expressed as: In the formula, For a mixed failure rate function, , and These are the state probabilities corresponding to states S1, S2, and S3, respectively. , and These are the stochastic intensity functions of the maintenance process corresponding to states S1, S2, and S3, respectively. , and Represented as: , for In the formula, These are the improvement parameters for the EGPP model, characterizing the degree of improvement in the failure rate achieved by each high-quality maintenance. This represents the cumulative number of failures (or repairs) that occurred before time t. This represents the upper limit of the initial number of repairable defects in the EGPP model. The degradation parameter of the GPP model represents the degree to which each low-quality maintenance accelerates the failure rate.

[0036] S30: Calculate the expected number of failures based on the hybrid failure rate function.

[0037] In some embodiments, based on the hybrid failure rate function constructed in step S20, the expected number of failures is calculated using the following formula: The probability distribution functions for each process are as follows: , In the formula, The expected number of failures, , , Inverse matrix The elements in the table correspond to the weight coefficients of the EGPP, NHPP, and GPP states, respectively. The number of failures is the independent variable of the probability distribution function. For the kth eigenvalue nth power, Let n be the probability of n failures occurring at time t under the pure EGPP model. Let n be the probability of n failures occurring at time t under the pure NHPP model. Let n be the probability of n failures occurring at time t under the pure GPP model. Reference failure rate function The points, For gamma function, It is a natural constant, approximately equal to 2.71828.

[0038] S40: Based on the expected number of failures, establish a long-term cost rate function and solve the long-term cost rate function to determine the optimal replacement cycle.

[0039] In some embodiments, the established long-run cost rate function is expressed as: In the formula, For cost rate, The expected number of failures, The cost of repair after a single failure. To cover the fixed cost of performing a preventative replacement, This refers to the replacement cycle.

[0040] In some embodiments, solving the long-term cost rate function to determine the optimal replacement cycle includes: finding the value that minimizes the cost rate within a set replacement cycle as the optimal replacement cycle. As an example, first, a reasonable range of values ​​for T is determined, such as the common equipment failure cycle interval; then, T is discretized within this range, and each discrete T value is substituted into the long-term cost rate function to calculate the corresponding cost rate; finally, by comparing the cost rates at all discrete points, the optimal replacement cycle is found. The minimum T value is the optimal replacement cycle. .

[0041] In some embodiments, based on the calculated optimal replacement cycle In actual maintenance, preventative equipment replacement is scheduled. Simultaneously, the state transition probability matrix is ​​updated based on real-time maintenance performance data to dynamically adjust maintenance strategies, ultimately achieving the lowest cost ratio. .

[0042] In some embodiments, a discrete-time Markov chain (DTMC) model is established using historical maintenance records, encompassing three states: Better-than-Minimum Maintenance (EGPP), Less-than-Minimum Maintenance (NHPP), and Worse-than-Minimum Maintenance (GPP), to determine the state transition probability matrix. Based on the decomposition of the state transition probability matrix, the time-varying probability distributions of each maintenance state are obtained. Then, the stochastic intensity functions of the three maintenance processes are weighted and fused according to state probabilities to construct a hybrid failure rate function. By simulating the stochastic transition process of the equipment between the three maintenance states and sub-states at different time steps, the failure rate values ​​at corresponding time points are calculated, and finally, a multi-branch failure rate evolution curve is plotted. Figure 2 As shown, the horizontal axis represents time T, and the vertical axis represents the failure rate (in Fit), reflecting the intensity of equipment failures at different time points. Figure 2 The curve shown contains two levels of evolutionary branches. The first-level branch corresponds to three basic maintenance effects, and the second-level branch is a subdivided evolutionary path under each basic maintenance effect, such as inferior to the minimum sub-branch, minimum sub-branch, and superior to the minimum sub-branch. Figure 2 It intuitively presents the multi-path evolution characteristics of failure rate caused by the randomness of maintenance effect (caused by factors such as maintenance personnel skills, environment, and spare parts quality), breaks the fixed failure rate assumption of the traditional single model, and shows the dynamic process of the failure rate gradually evolving from the initial value under different maintenance state transitions, thus verifying the rationality of the hybrid maintenance effect model.

[0043] This application also provides an industrial equipment preventive maintenance decision-making device based on discrete-time Markov chains, such as... Figure 3 As shown, the industrial equipment preventive maintenance decision-making device based on discrete-time Markov chains includes: The model building module 301 is configured to establish a discrete-time Markov chain maintenance effect state transition model based on historical maintenance record statistics and determine its state transition probability matrix. It then performs eigenvalue decomposition on the state transition probability matrix to obtain the state probability distribution after n maintenance cycles, and determines the probability of each state based on the probability distribution. The discrete-time Markov chain maintenance effect state transition model is a discrete-time Markov chain model containing three maintenance effect states: state S1 (better than minimum maintenance), state S2 (minimum maintenance), and state S3 (worse than minimum maintenance). The probability of each state includes the state probabilities corresponding to states S1, S2, and S3. The function establishment module 302 is configured to fuse the random intensity functions of the three maintenance processes by weighting them with the corresponding state probabilities to construct a hybrid failure rate function; wherein the three maintenance processes are the maintenance processes corresponding to state S1, state S2 and state S3 respectively. The failure count calculation module 303 is configured to calculate the expected number of failures based on the hybrid failure rate function. The strategy determination module 304 is configured to establish a long-term cost rate function based on the expected number of failures, and solve the long-term cost rate function to determine the optimal replacement cycle.

[0044] This application provides an electronic device. The electronic device may include a processor and a memory, wherein the processor and the memory can communicate; exemplarily, the processor and the memory communicate via a communication bus.

[0045] The processor executes computer execution instructions stored in memory, causing the processor to perform the scheme in the above embodiments. The processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0046] The communication bus can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The system bus can be divided into address bus, data bus, control bus, etc. Transceivers are used to enable communication between database access devices and other computers (e.g., clients, read-write libraries, and read-only libraries). Memory may include random access memory (RAM) and may also include non-volatile memory.

[0047] The electronic device provided in this application embodiment can be the terminal device described in the above embodiments.

[0048] This application also provides a computer-readable storage medium storing computer instructions. When the computer instructions are executed on a computer, the computer performs the technical solution of the industrial equipment preventive maintenance decision-making method based on discrete-time Markov chains described in the above embodiments.

[0049] This application also provides a computer program product, which includes a computer program stored in a computer-readable storage medium. At least one processor can read the computer program from the computer-readable storage medium. When the at least one processor executes the computer program, it can implement the technical solution of the industrial equipment preventive maintenance decision-making method based on discrete-time Markov chains in the above embodiments.

[0050] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or modules, and may be electrical, mechanical, or other forms.

[0051] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to implement the solution of this embodiment according to actual needs.

[0052] Furthermore, the functional modules in the various embodiments of this application can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The unit composed of the above modules can be implemented in hardware or in the form of hardware plus software functional units.

[0053] The integrated modules described above, implemented as software functional modules, can be stored in a computer-readable storage medium. These software functional modules, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods of the various embodiments of this application.

[0054] It should be understood that the aforementioned processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. A general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly manifested as execution by a hardware processor, or execution by a combination of hardware and software modules within the processor.

[0055] The memory may include high-speed RAM, and may also include non-volatile storage (NVM), such as at least one disk storage device, and may also be a USB flash drive, external hard drive, read-only memory, disk or optical disc, etc.

[0056] Buses can be Industry Standard Architecture (ISA) buses, Peripheral Component Interconnect (PCI) buses, or Extended Industry Standard Architecture (EISA) buses, etc. Buses can be categorized into address buses, data buses, control buses, etc.

[0057] The aforementioned storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The storage medium can be any available medium that can be accessed by a general-purpose or special-purpose computer.

[0058] An exemplary storage medium is coupled to a processor, enabling the processor to read information from and write information to the storage medium. Alternatively, the storage medium can be an integral part of the processor. The processor and storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and storage medium can exist as discrete components in an electronic control unit or main control device.

[0059] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0060] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A preventive maintenance decision-making method for industrial equipment based on discrete-time Markov chains, characterized in that, The method includes: Based on historical maintenance records, a discrete-time Markov chain maintenance effect state transition model is established and its state transition probability matrix is ​​determined. The state transition probability matrix is ​​then subjected to eigenvalue decomposition to obtain the state probability distribution after n maintenance cycles. Based on this probability distribution, the probability of each state is determined. The discrete-time Markov chain maintenance effect state transition model is a discrete-time Markov chain model containing three maintenance effect states: state S1 (better than minimum maintenance), state S2 (minimum maintenance), and state S3 (worse than minimum maintenance). The probability of each state includes the state probabilities corresponding to states S1, S2, and S3. The stochastic intensity functions of the three maintenance processes are fused together by weighting the corresponding state probabilities to construct a hybrid failure rate function; wherein the three maintenance processes are the maintenance processes corresponding to state S1, state S2 and state S3 respectively. Based on the hybrid failure rate function, the expected number of failures is calculated; Based on the expected number of failures, a long-term cost rate function is established, and the long-term cost rate function is solved to determine the optimal replacement cycle.

2. The industrial equipment preventive maintenance decision-making method based on discrete-time Markov chains according to claim 1, characterized in that, The state transition probability matrix is ​​expressed as follows: In the formula, Here is the state transition probability matrix. This indicates the state within a single discrete time step. Transition to state The probability, and j For any index of the state, ,satisfy .

3. The industrial equipment preventive maintenance decision-making method based on discrete-time Markov chains according to claim 1, characterized in that, The state transition probability matrix is ​​decomposed using eigenvalues ​​to obtain the state probability distribution after n repairs, and the probability of each state is determined based on the probability distribution, including: The state transition probability matrix is ​​decomposed into eigenvalues ​​using the following formula: In the formula, Here is the state transition probability matrix. For the reason The matrix formed by the eigenvectors of , For the reason The eigenvalues ​​are diagonal matrices composed of diagonal elements. For matrix The inverse matrix. The resulting state probability distribution after n repairs is as follows: In the formula, Let n be the state transition probability matrix. For a matrix to undergo n transformations, This refers to the discrete time steps, i.e., the number of maintenance operations the equipment undergoes. Based on the probability distribution, the probability of each state is determined by the following formula: In the formula, Let be the instantaneous probability that the equipment is in the i-th repair outcome state after n repairs. Indices of eigenvalues ​​and eigenvectors ( =1, 2, 3), The initial state probability vector With eigenvector matrix The row vector obtained by multiplication The kth component, For the kth eigenvalue nth power, Inverse matrix The element in the k-th row and i-th column, The index of the state.

4. The industrial equipment preventive maintenance decision-making method based on discrete-time Markov chains according to claim 1, characterized in that, The hybrid failure rate function is expressed as follows: In the formula, For a mixed failure rate function, , and These are the state probabilities corresponding to states S1, S2, and S3, respectively. , and These are the stochastic intensity functions of the maintenance process corresponding to states S1, S2, and S3, respectively. , and Represented as: , for In the formula, These are the improvement parameters for the EGPP model, characterizing the degree of improvement in the failure rate achieved by each high-quality maintenance. This represents the cumulative number of faults or repairs that occurred before time t. This represents the upper limit of the initial number of repairable defects in the EGPP model. The degradation parameter of the GPP model represents the degree to which each low-quality maintenance accelerates the failure rate.

5. The industrial equipment preventive maintenance decision-making method based on discrete-time Markov chains according to claim 4, characterized in that, Based on the hybrid failure rate function, the expected number of failures is calculated using the following formula: The probability distribution functions for each process are as follows: , In the formula, The expected number of failures, , , Inverse matrix The elements in the table correspond to the weight coefficients of the EGPP, NHPP, and GPP states, respectively. The number of failures is the independent variable of the probability distribution function. For the kth eigenvalue nth power, Let n be the probability of n failures occurring at time t under the pure EGPP model. Let n be the probability of n failures occurring at time t under the pure NHPP model. Let n be the probability of n failures occurring at time t under the pure GPP model. Reference failure rate function The points, For gamma function, It is a natural constant.

6. The industrial equipment preventive maintenance decision-making method based on discrete-time Markov chains according to claim 1, characterized in that, The long-run cost rate function is expressed as: In the formula, For cost rate, The expected number of failures, The cost of repair after a single failure. To cover the fixed cost of performing a preventative replacement, This refers to the replacement cycle.

7. The industrial equipment preventive maintenance decision-making method based on discrete-time Markov chains according to claim 6, characterized in that, Solving the long-term cost rate function to determine the optimal replacement cycle includes finding the value that minimizes the cost rate within the set replacement cycle as the optimal replacement cycle.

8. A decision-making device for preventive maintenance of industrial equipment based on discrete-time Markov chains, characterized in that, The device includes: The model building module is configured to establish a discrete-time Markov chain maintenance effect state transition model based on historical maintenance record statistics and determine its state transition probability matrix. It then performs eigenvalue decomposition on the state transition probability matrix to obtain the state probability distribution after n maintenance cycles, and determines the probability of each state based on this probability distribution. The discrete-time Markov chain maintenance effect state transition model is a discrete-time Markov chain model containing three maintenance effect states: state S1 (better than minimum maintenance), state S2 (minimum maintenance), and state S3 (worse than minimum maintenance). The state probabilities include the state probabilities corresponding to states S1, S2, and S3. The function establishment module is configured to fuse the stochastic intensity functions of the three maintenance processes through corresponding state probabilities to construct a hybrid failure rate function; wherein the three maintenance processes are the maintenance processes corresponding to state S1, state S2 and state S3 respectively. The failure count calculation module is configured to calculate the expected number of failures based on the hybrid failure rate function. The strategy determination module is configured to establish a long-term cost rate function based on the expected number of failures, and solve the long-term cost rate function to determine the optimal replacement cycle.

9. An electronic device, characterized in that, include: A processor, and a memory communicatively connected to the processor; The memory stores computer-executed instructions; The processor executes the computer execution instructions stored in the memory to implement the industrial equipment preventive maintenance decision-making method based on discrete-time Markov chains as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the industrial equipment preventive maintenance decision-making method based on discrete-time Markov chains as described in any one of claims 1-7.

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