Equipment predictive maintenance method and system based on residual life quantile

Abstract

The invention provides an equipment predictive maintenance method and system based on residual life quantiles, and belongs to the field of equipment maintenance and reliability engineering. According to the strategy, firstly, a Gamma process is adopted to construct an equipment degradation model, and Beta distribution is adopted to establish a residual degradation amount model; then designing a discrete check strategy based on the residual life quantile, determining a calculation mode of a discrete check interval, and formulating a maintenance decision rule; calculating maintenance related cost, including preventive maintenance cost and operation cost; and finally, constructing an optimization model with the goal of minimizing the average cost rate, and determining optimal maintenance parameters by adopting a discrete approximate iteration method. The method can accurately grasp the state change of the equipment, formulate a scientific and reasonable maintenance strategy, effectively reduce the maintenance cost, improve the reliability of the equipment, and is suitable for predictive maintenance of various industrial equipment.

Description

Technical Field

[0001] This invention relates to the field of equipment maintenance and reliability engineering, and specifically to a predictive maintenance method and system for equipment based on remaining life quantiles. Background Technology

[0002] In modern industrial production, the stable operation of equipment is crucial for ensuring production efficiency and reducing production costs. As equipment ages and its performance deteriorates, malfunctions may occur, impacting production schedules and increasing maintenance costs. Therefore, developing a reasonable equipment maintenance strategy has become a key focus for enterprises. Traditional equipment maintenance strategies mainly include reactive maintenance and scheduled maintenance. Reactive maintenance involves repairing equipment only after a failure, which can lead to prolonged production interruptions and high repair costs. Scheduled maintenance is performed at fixed intervals, regardless of the actual condition of the equipment, potentially resulting in over-maintenance or under-maintenance. Predictive maintenance is a condition-based maintenance strategy that predicts the remaining lifespan of equipment by monitoring and assessing its condition, thus enabling maintenance to be performed at the appropriate time. Remaining life quantiles reflect the probability distribution characteristics of the equipment's remaining lifespan; maintenance strategies based on these quantiles can more accurately determine maintenance timing, balancing maintenance costs and equipment reliability. Summary of the Invention

[0003] Based on the above background, the purpose of this invention is to propose a predictive maintenance method and system for equipment based on remaining lifetime quantiles. This aims to address the shortcomings of traditional maintenance strategies and improve the scientific and economic efficiency of equipment maintenance. This invention achieves optimal maintenance decisions with the goal of minimizing the average cost rate by constructing equipment degradation models, designing inspection strategies, and establishing maintenance decision rules. This optimizes equipment maintenance decisions, reduces maintenance costs, and improves equipment reliability. It is particularly suitable for scenarios requiring high reliability, such as semiconductor manufacturing and energy equipment, and achieves precise maintenance by integrating degradation modeling and dynamic decision-making.

[0004] To achieve the above-mentioned technical features, the objective of this invention is as follows: a predictive maintenance method for equipment based on remaining life quantiles, characterized in that the method includes the following steps: Step 1: Collect equipment operation data and construct an equipment degradation model based on the Gamma process. The degradation model describes the change of equipment degradation over time. Step 2: Dynamically calculate the next inspection time of the equipment based on the current degradation status of the equipment and the preset quantile threshold; Step 3: When the equipment reaches its inspection time, check the actual amount of degradation of the equipment; Step 4: Perform the corresponding maintenance operation according to the range of the actual degradation amount: if the degradation amount is less than the preventive maintenance threshold, no maintenance is performed; if the degradation amount is greater than or equal to the preventive maintenance threshold but less than the failure threshold, imperfect preventive maintenance is performed; if the degradation amount is greater than or equal to the failure threshold, the equipment is replaced. Step 5: Calculate maintenance-related costs, including preventative maintenance costs and operating costs; Step 6: Build an optimization model with the goal of minimizing the average cost rate and determine the optimal maintenance parameters; Step 7: After each maintenance, determine whether the optimization goal has been achieved. If so, output the optimal maintenance strategy; otherwise, update the degradation status of the device and return to Step 3.

[0005] Preferably, the model in Step 1 is a Gamma process, used to describe the cumulative degradation characteristics of the equipment. Its probability density function considers the accelerated degradation factors of the equipment in different maintenance cycles, and uses shape parameters and scale parameters to reflect the degradation rate and degree of the equipment. for: (1) in, For equipment In the The probability density function of the degradation amount within a maintenance cycle. For equipment In the Degradation amount within a maintenance cycle To maintain the periodic index, For device indexing, For the maintenance cycle time, and respectively equipment Shape parameters and scale parameters, For equipment The factors that accelerate degradation For equipment In the Shape parameters within a maintenance cycle This is the Gamma function.

[0006] Preferably, the inspection interval calculation method based on the remaining life quantile in Step 2 is used to determine a reasonable inspection time based on the probability distribution of the equipment's remaining life and to dynamically calculate the inspection time. The formula is: (2) in, For equipment In the Within the maintenance cycle, the first The interval between inspections For equipment In the Residual degradation within a maintenance cycle For equipment Preventive maintenance threshold, For equipment Predefined quantiles, For equipment The minimum inspection interval; For the first The initial check interval function in each maintenance cycle For equipment In the Within each maintenance cycle The amount of degradation of the time interval, The probability that the residual degradation amount plus the new degradation amount exceeds the threshold is equal to the quantile.

[0007] Preferably, in Step 4, the actual amount of degradation is detected at the inspection time point. And perform maintenance based on the degradation range: (1) If Maintenance is not performed. (2) If , Assuming a failure threshold, perform imperfect preventative maintenance, and assess the residual degradation of the equipment. obey The distribution has the following probability density function: (3) in, For equipment In the The probability density function of residual degradation over a maintenance cycle. For equipment Two hyperparameters, and respectively equipment Preventive maintenance thresholds and failure thresholds; (3) If To perform equipment replacement.

[0008] Preferably, the detailed calculation of maintenance-related costs in Step 5 provides accurate cost data for the subsequent optimization model, making the optimization results more consistent with actual economic conditions. The calculation formulas for the maintenance cost and operating cost of imperfect preventive maintenance are as follows: (4) in, For equipment The cost of preventative maintenance when the oxidation level drops to 0. For equipment The equipment characteristic parameters; (5) in, For equipment In the Operating costs within a maintenance cycle For fixed cost rate, The cost rate associated with the number of preventative maintenance operations. Cost rate related to cumulative operating time, For equipment No. The expected maintenance interval for each preventative maintenance cycle.

[0009] Preferably, in Step 6, the average cost rate is used as the optimization objective, comprehensively considering the total cost and total time of the equipment within a replacement cycle. The maintenance decision optimization adopts a discrete approximate iterative method to solve for the optimal parameter set. With a reasonable maintenance strategy, the average cost rate is: (6) in, It is an average cost rate function. and Each machine The expected total cost and expected total time for the new cycle.

[0010] Preferably, updating the degradation status of the device in Step 7 includes: recording the residual degradation amount after maintenance and using it as the initial degradation status for the next maintenance cycle.

[0011] Another aspect of the present invention provides a predictive maintenance system for equipment based on remaining lifetime quantiles, for performing the aforementioned predictive maintenance method for equipment, the system comprising: Data acquisition module: Real-time monitoring of equipment degradation data; Degradation modeling module: Generates the probability density function of degradation based on the Gamma process; Dynamic scheduling module: based on quantiles Dynamically calculate the inspection interval; Maintenance decision module: Performs interval-based maintenance operations and calculates the cost of imperfect preventative maintenance and operating costs; Model Solving Module: Determines optimal maintenance parameters with the objective of minimizing the average cost rate; Status update module: Records the residual degradation amount and triggers the next maintenance cycle.

[0012] The present invention has the following beneficial effects: Using Gamma processes and Beta distributions to describe the degradation process and remaining degradation of equipment, respectively, can more accurately reflect the actual changes in the equipment's condition. Designing inspection strategies based on remaining life quantiles makes the determination of inspection intervals more scientific, enabling timely detection of potential equipment problems while avoiding unnecessary inspection costs. The established maintenance decision rules provide targeted maintenance based on the equipment's degradation state, effectively reducing over-maintenance and under-maintenance, and improving equipment reliability. By comprehensively considering various maintenance costs and using the average cost rate as the optimization objective, an economically reasonable maintenance strategy can be obtained, reducing the enterprise's maintenance costs. In conclusion, this invention provides enterprises with an efficient and economical predictive maintenance solution for equipment, possessing significant practical application value. Attached Figure Description

[0013] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0014] Figure 1 A schematic diagram of a strategy based on state-based remaining lifetime quantiles.

[0015] Figure 2 Maintenance strategy process diagram. Detailed Implementation

[0016] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, examples of which are shown in the drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0017] Example 1: Step 1: Collect equipment operation data and construct an equipment degradation model based on the Gamma process. The degradation model describes the change of equipment degradation over time. The model is a Gamma process, which can well describe the cumulative degradation characteristics of equipment. Its probability density function considers the accelerated degradation factors of equipment in different maintenance cycles, and uses shape and scale parameters to reflect the degradation rate and degree of the equipment. Its probability density function... for: (1) in, For equipment In the The probability density function of the degradation amount within a maintenance cycle. For equipment In the Degradation amount within a maintenance cycle To maintain the periodic index, For device indexing, For the maintenance cycle time, and respectively equipment Shape parameters and scale parameters, For equipment The factors that accelerate degradation For equipment In the Shape parameters within a maintenance cycle This is the Gamma function.

[0018] Step 2: Dynamically calculate the next inspection time of the equipment based on the current degradation status of the equipment and the preset quantile threshold; The inspection interval calculation method based on remaining life quantiles can determine a reasonable inspection time according to the probability distribution of the equipment's remaining life, ensuring timely monitoring of equipment status while avoiding the increased costs caused by overly frequent inspections. Dynamic calculation of inspection time. The formula is: (2) in, For equipment In the Within the maintenance cycle, the first The interval between inspections For equipment In the Residual degradation within a maintenance cycle For equipment Preventive maintenance threshold, For equipment Predefined quantiles, For equipment The minimum inspection interval; For the first The initial check interval function in each maintenance cycle For equipment In the Within each maintenance cycle The amount of degradation of the time interval, The probability that the residual degradation amount plus the new degradation amount exceeds the threshold is equal to the quantile.

[0019] Step 3: When the equipment reaches its inspection time, check the actual amount of degradation of the equipment; Step 4: Perform the corresponding maintenance operation according to the range of the actual degradation amount: if the degradation amount is less than the preventive maintenance threshold, no maintenance is performed; if the degradation amount is greater than or equal to the preventive maintenance threshold but less than the failure threshold, imperfect preventive maintenance is performed; if the degradation amount is greater than or equal to the failure threshold, the equipment is replaced. The actual amount of degradation was measured at the inspection time point. And perform maintenance based on the degradation range: (1) If Maintenance is not performed. (2) If , Assuming a failure threshold, perform imperfect preventive maintenance (IPM) to determine the residual degradation of the equipment. obey The distribution has the following probability density function: (3) in, For equipment In the The probability density function of residual degradation over a maintenance cycle. For equipment Two hyperparameters, and respectively equipment IPM threshold and fault threshold; (3) If To perform equipment replacement.

[0020] Step 5: Calculate maintenance-related costs, including preventative maintenance costs and operating costs; Detailed calculations of maintenance-related costs provide accurate cost data for subsequent optimization models, making the optimization results more consistent with actual economic conditions. The formulas for calculating the maintenance and operating costs of imperfect preventative maintenance are as follows: (4) in, For equipment The cost of preventative maintenance when the oxidation level drops to 0. For equipment The equipment characteristic parameters; (5) in, For equipment In the Operating costs within a maintenance cycle For fixed cost rate, The cost rate associated with the number of preventative maintenance operations. Cost rate related to cumulative operating time, For equipment No. The expected maintenance interval for each preventative maintenance cycle.

[0021] Step 6: Build an optimization model with the goal of minimizing the average cost rate and determine the optimal maintenance parameters; With average cost rate as the optimization objective, and comprehensively considering the total cost and total time of equipment within a replacement cycle, the maintenance decision optimization employs a discrete approximate iterative method to solve for the optimal parameter set. This allows for a more reasonable maintenance strategy. The average cost rate is: (6) in, It is an average cost rate function. and Each machine The expected total cost and expected total time for the new cycle.

[0022] Step 7: After each maintenance, determine whether the optimization goal has been achieved. If so, output the optimal maintenance strategy; otherwise, update the degradation status of the device and return to Step 3.

[0023] Updating the degradation status of equipment includes recording the residual degradation amount after maintenance and using it as the initial degradation status for the next maintenance cycle.

[0024] Example 2: Another aspect of the present invention provides a predictive maintenance system for equipment based on remaining lifetime quantiles, for performing the aforementioned predictive maintenance method for equipment, the system comprising: Data acquisition module: Real-time monitoring of equipment degradation data; Degradation modeling module: Generates the probability density function of degradation based on the Gamma process; Dynamic scheduling module: based on quantiles Dynamically calculate the inspection interval; Maintenance decision module: Performs interval-based maintenance operations and calculates the cost of imperfect preventative maintenance and operating costs; Model Solving Module: Determines optimal maintenance parameters with the objective of minimizing the average cost rate; Status update module: Records the residual degradation amount and triggers the next maintenance cycle.

[0025] Example 3: See Figure 1-2 , Figure 1 This diagram illustrates a strategy for state-based remaining lifetime quantiles and is the core content of this invention. The vertical axis in the diagram... Indicates the amount of equipment degradation. This is the fault threshold (the device will malfunction if it exceeds this value). This represents the preventative maintenance threshold (the critical value for early intervention to avoid failure). The horizontal axis represents time / production cycle, reflecting the degradation process of equipment over time. In the graph, the black curve represents the degradation trajectory of the same type of equipment (or the same equipment at different times); the blue curve represents the probability distribution of degradation amount, describing "the probability of degradation to a certain degree at a certain moment"; the shaded area... This indicates that the degradation has exceeded the preventative maintenance threshold. The probability. During equipment degradation, the probability distribution covers the preventative maintenance threshold. (Shaded area) Preventative maintenance is triggered when the risk of degradation exceeds a certain threshold (PM indicator). After maintenance (green dashed line), the equipment degrades to a lower level and enters the next cycle, repeating the degradation-maintenance cycle. Curves and probability distributions illustrate "Equipment degrades over time → When degradation risk exceeds a certain threshold..." probability The process of "reaching the threshold → triggering preventive maintenance → degradation reset" is a typical visual representation of predictive maintenance strategies.

[0026] Figure 2 This is a flowchart illustrating the maintenance strategy process. The flowchart describes the equipment maintenance management process: First, monitor equipment degradation data in real time; then, generate a probability density function for degradation based on the Gamma process; and finally, based on the quantiles... Calculate the inspection interval; after performing interval maintenance operations, determine the triggering conditions and decide whether to not perform maintenance, perform imperfect preventive maintenance, or replace the equipment; at the same time, calculate the maintenance cost, operating cost, and expected total cost, and finally record the residual degradation amount to trigger the next maintenance cycle, thereby realizing maintenance decision-making and cost control throughout the entire equipment life cycle.

[0027] Model assumptions: Considering the characteristics and manageability of the practical problem, the following reasonable assumptions are made regarding the predictive maintenance problem of equipment studied in this invention: 1) The degradation process of the equipment can be described by the Gamma process, and the degradation process of each maintenance cycle is independent of each other; 2) Preventive maintenance is incomplete maintenance, and the remaining degradation of the equipment after maintenance follows a Beta distribution; 3) The inspection process does not affect the degradation state of the equipment, and the inspection cost is negligible; 4) The equipment's fault threshold and preventative maintenance threshold are known constants; 5) The time and cost required for the maintenance activity are known, and the equipment cannot be operated during the maintenance period; 6) The equipment is in brand new condition at the beginning of the replacement cycle. After a series of maintenance activities, it is eventually replaced, forming a new replacement cycle. Key symbol definitions:

[0028] Algorithm Design: The algorithm performs discrete approximate iterative optimization of equipment maintenance parameters. To minimize the average cost rate The general steps are as follows: 1) Input known parameters: Input the relevant parameters for each device; 2) Initialize parameters: Set initial values ​​for decision variables: number of maintenance cycles Step length Maintenance threshold and failure probability threshold The step sizes are respectively , .

[0029] 3) Parameter space sampling and clustering: Randomly generate 1 million groups The parameters were combined, and 500 representative combinations were selected as the starting point for initialization using k-means clustering.

[0030] 4) Iterative search: The outer loop follows the step size. Incremental maintenance times The inner loop calculates each of the 500 parameter combinations: (a) based on the current... Calculate the objective function (b) Record the current target value and its corresponding parameters, and the expected maintenance interval. Maintenance time and fault waiting time .

[0031] 5) Neural Network Prediction: Use a BP neural network to predict the performance of 1 million sets of parameters on the average cost rate (ACR), select 500 sets of combinations with good prediction performance and meet the minimum maintenance interval constraint, and accurately calculate their ACR (repeated inner layer calculation).

[0032] 6) Update the optimal solution: Combine the results of 1000 calculations and select the optimal solution that satisfies the constraints. If the new solution is better than the historical best solution and If the change does not exceed the preset tolerance, update the optimal solution. 7) Conversely, the loop terminates if the condition is not met.

[0033] Output: Returns the optimal parameter combination. and its target value .

[0034] Numerical Experiment: This invention uses 15 devices for numerical experiments. The relevant parameters of each device (as shown in Table 1) are input into the algorithm program for selection and combination, and the results are shown in Table 2. As can be seen from the table, each decision variable for each device can output a detailed maintenance plan.

[0035] Comparison of maintenance strategies: To verify the effectiveness of the maintenance strategy proposed in this invention, this invention compared 17 maintenance strategies in relevant literature (i.e., all OM cycles have the same and constant reliability threshold and PM frequency). Table 3 shows the optimal maintenance plan of this maintenance strategy under the same parameter settings. It can be seen that the average cost rate (ACR) of the maintenance strategy proposed in this invention is lower, indicating that the maintenance strategy proposed in this invention is significantly better than traditional maintenance strategies.

[0036] Table 1 Maintenance parameters for all equipment

[0037] Table 2 Maintenance Plan for All Equipment

[0038] Table 3. Optimal ACR for 17 maintenance strategies

[0039] Note: "-" means there is no feasible solution; the optimal result is marked in bold.

[0040] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A predictive maintenance method for equipment based on remaining life quantiles, characterized in that, The method includes the following steps: Step 1: Collect equipment operation data and construct an equipment degradation model based on the Gamma process. The degradation model describes the change of equipment degradation over time. Step 2: Dynamically calculate the next inspection time of the equipment based on the current degradation status of the equipment and the preset quantile threshold; Step 3: When the equipment reaches its inspection time, check the actual amount of degradation of the equipment; Step 4: Perform the corresponding maintenance operation according to the range of the actual degradation amount: if the degradation amount is less than the preventive maintenance threshold, no maintenance is performed; if the degradation amount is greater than or equal to the preventive maintenance threshold but less than the failure threshold, imperfect preventive maintenance is performed; if the degradation amount is greater than or equal to the failure threshold, the equipment is replaced. Step 5: Calculate maintenance-related costs, including preventative maintenance costs and operating costs; Step 6: Build an optimization model with the goal of minimizing the average cost rate and determine the optimal maintenance parameters; Step 7: After each maintenance, determine whether the optimization goal has been achieved. If so, output the optimal maintenance strategy; otherwise, update the degradation status of the device and return to Step 3.

2. The predictive maintenance method for equipment based on remaining life quantiles according to claim 1, characterized in that, The model in Step 1 is a Gamma process, used to describe the cumulative degradation characteristics of the equipment. Its probability density function considers the accelerated degradation factors of the equipment in different maintenance cycles, and reflects the degradation rate and degree of the equipment through shape parameters and scale parameters. for: （1） in, For equipment In the The probability density function of the degradation amount within a maintenance cycle. For equipment In the Degradation amount within a maintenance cycle To maintain the periodic index, For device indexing, For the maintenance cycle time, and respectively equipment Shape parameters and scale parameters, For equipment The factors that accelerate degradation For equipment In the Shape parameters within a maintenance cycle This is the Gamma function.

3. The predictive maintenance method for equipment based on remaining life quantiles according to claim 1, characterized in that, The inspection interval calculation method based on the remaining life quantile in Step 2 is used to determine a reasonable inspection time based on the probability distribution of the equipment's remaining life and to dynamically calculate the inspection time. The formula is: （2） in, For equipment In the Within the maintenance cycle, the first The interval between inspections For equipment In the Residual degradation within a maintenance cycle For equipment Preventive maintenance threshold, For equipment Predefined quantiles, For equipment The minimum inspection interval; For the first The initial check interval function in each maintenance cycle For equipment In the Within each maintenance cycle The amount of degradation of the time interval, The probability that the residual degradation amount plus the new degradation amount exceeds the threshold is equal to the quantile.

4. The predictive maintenance method for equipment based on remaining life quantiles according to claim 1, characterized in that, In Step 4, the actual amount of degradation is detected at the inspection time point. And perform maintenance based on the degradation range: (1) If Maintenance is not performed. (2) If , Assuming a failure threshold, perform imperfect preventative maintenance, and assess the residual degradation of the equipment. obey The distribution has the following probability density function: （3） in, For equipment In the The probability density function of residual degradation over a maintenance cycle. For equipment Two hyperparameters, and respectively equipment Preventive maintenance thresholds and failure thresholds; (3) If To perform equipment replacement.

5. The predictive maintenance method for equipment based on remaining life quantiles according to claim 1, characterized in that, The detailed calculation of maintenance-related costs in Step 5 provides accurate cost data for the subsequent optimization model, making the optimization results more consistent with actual economic conditions. The formulas for calculating the maintenance cost and operating cost of imperfect preventive maintenance are as follows: （4） in, For equipment The cost of preventative maintenance when the oxidation level drops to 0. For equipment The equipment characteristic parameters; （5） in, For equipment In the Operating costs within a maintenance cycle For fixed cost rate, The cost rate associated with the number of preventative maintenance operations. Cost rate related to cumulative operating time, For equipment No. The expected maintenance interval for each preventative maintenance cycle.

6. The predictive maintenance method for equipment based on remaining life quantiles according to claim 1, characterized in that, In Step 6, the average cost rate is used as the optimization objective. The total cost and total time of the equipment within a replacement cycle are comprehensively considered. The maintenance decision optimization adopts the discrete approximate iterative method to solve for the optimal parameter set. With a reasonable maintenance strategy, the average cost rate is: （6） in, It is an average cost rate function. and Each machine The expected total cost and expected total time for the new cycle.

7. The predictive maintenance method for equipment based on remaining life quantiles according to claim 1, characterized in that, Step 7 updates the device's degradation status by recording the residual degradation amount after maintenance and using it as the initial degradation status for the next maintenance cycle.

8. A predictive maintenance system for equipment based on remaining life quantiles, characterized in that, The system is used to perform the predictive maintenance method for equipment according to any one of claims 1 to 7, the system comprising: Data acquisition module: Real-time monitoring of equipment degradation data; Degradation modeling module: Generates the probability density function of degradation based on the Gamma process; Dynamic scheduling module: based on quantiles Dynamically calculate the inspection interval; Maintenance decision module: Performs interval-based maintenance operations and calculates the cost of imperfect preventative maintenance and operating costs; Model Solving Module: Determines optimal maintenance parameters with the objective of minimizing the average cost rate; Status update module: Records the residual degradation amount and triggers the next maintenance cycle.

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