Two-level imperfect inspection strategy optimization method and system for covert function system based on monte carlo simulation

Abstract

The application discloses a two-level imperfect detection strategy optimization method and system for a hidden function system based on Monte Carlo simulation. The method comprises the following steps: acquiring system degradation parameters, random impact parameters, two-level imperfect detection parameters and maintenance parameters; taking a detection time interval as a decision variable; determining a state evolution path, a detection result and an update type under different detection time intervals; calculating expected maintenance costs and an expected update cycle and constructing a maintenance cost rate model; and determining an optimal detection time interval through Monte Carlo simulation. The application can comprehensively consider the influence between system degradation, random impact, detection error and update behavior, quantitatively compare the maintenance costs corresponding to different detection time intervals, and provide a basis for two-level imperfect detection strategy optimization.

Description

Technical Field

[0001] This invention relates to the field of maintenance and support technology, and in particular to an optimization method and system for a two-level imperfection detection strategy of a concealed functional system based on Monte Carlo simulation. Background Technology

[0002] Covertly functional systems are widely used in safety-critical scenarios such as aerospace protection devices, industrial units, and online monitoring equipment. These systems may experience continuous performance degradation during operation, gradually progressing from a normal state to a defective state, and further developing into a failure state. Because their defective and failure states are usually not self-manifesting, periodic testing is required to identify the system's current operating state. Simultaneously, the system may be affected by random shocks from the external environment during operation; when these shocks reach a certain level, they can cause sudden system failures. Therefore, the actual state of a covered functional system at the time of testing is not only affected by its own degradation process but also by random shocks, making the system's state evolution process highly uncertain.

[0003] Existing technologies typically acquire system status through periodic inspections and implement corresponding preventative or corrective maintenance based on the inspection results. However, due to factors such as the accuracy of inspection equipment, the inspection environment, and human operation, false positives and false negatives often occur during actual inspections, and the inspection results are not entirely consistent with the true state of the system. For example, a normal state may be misjudged as a defective state, a defective state may be misjudged as a normal state or a failure state, and a failure state may also be misjudged as a defective state. When using a single inspection level, a trade-off usually needs to be made between inspection cost and inspection accuracy; while using different inspection levels allows for different inspection accuracies to be configured according to the system status, the relationships between different true states, different inspection results, and corresponding false positives become more complex.

[0004] When system degradation and random shocks coexist, the system state at the same detection moment may be formed by different state evolution processes. System failure may be caused by gradual degradation, random shocks, or a combination of degradation failure and random shocks. Different state evolution paths may produce different detection results under imperfect detection conditions, which in turn correspond to different system update methods. Therefore, if maintenance decisions are made solely based on detection results, or if system degradation, random shocks, and detection errors are considered separately, it is difficult to fully describe the correspondence between state evolution paths, detection results, and update behaviors, thus affecting the accuracy of determining the probability of different update scenarios, maintenance costs, and update cycles.

[0005] Furthermore, the detection interval of periodic inspections affects the timing of system state detection, the number of inspections, inspection costs, and downtime costs resulting from undetected failure states. Shorter intervals lead to more inspections and higher costs; longer intervals may prolong the undetected duration of defective or failed states, increasing system failure-related costs. Therefore, in situations involving system degradation, random impacts, and imperfect inspections, determining the probability of corresponding update scenarios, maintenance costs, and update cycles based on different state evolution paths and inspection results, and accordingly, rationally determining the periodic inspection interval, remains a problem to be solved in optimizing the inspection and maintenance strategy for concealed function systems. Summary of the Invention

[0006] Therefore, the technical problem to be solved by the present invention is to overcome the difficulty in the prior art in accurately characterizing the state evolution path, the correlation between detection results and update behavior under the combined effects of hidden function system degradation, random impact and two-level imperfect detection, and thus the difficulty in reasonably determining the detection time interval based on the maintenance cost and update cycle corresponding to different update scenarios.

[0007] To address the aforementioned technical problems, this invention provides an optimization method for a two-level imperfection detection strategy of a concealed function system based on Monte Carlo simulation, comprising: Obtain the degradation parameters, random impact parameters, two-level imperfection detection parameters, and maintenance parameters of the concealed function system, determine the detection time interval of the periodic detection as a decision variable, and determine the candidate value set of the detection time interval; For each candidate value in the candidate value set, the corresponding detection time and detection interval are determined based on the candidate value; the degradation process of the concealment function system is established based on the degradation parameter, and the random impact process of the concealment function system is established based on the random impact parameter; the degradation state corresponding to each detection time is determined based on the degradation process, and the occurrence of random impacts leading to sudden failure within each detection interval is determined based on the random impact process; the state evolution path corresponding to each detection time and the probability of occurrence of each state evolution path are determined based on the degradation state and the occurrence of random impacts. Based on the two-level imperfection detection parameters, determine the detection results corresponding to each state evolution path and the probability of occurrence of each detection result, and determine the corresponding update type based on each detection result; The probability of occurrence of each update type is determined based on the probability of occurrence of each state evolution path and the probability of occurrence of each detection result. The expected maintenance cost and expected update cycle corresponding to each update type are determined based on the probability of occurrence of each update type and the maintenance parameters. A maintenance cost rate model is constructed based on the expected maintenance cost and the expected update cycle. Monte Carlo simulations are performed on each candidate value in the candidate value set based on the maintenance cost rate model to obtain the expected maintenance cost rate corresponding to each candidate value. The candidate value corresponding to the minimum expected maintenance cost rate is determined as the optimal detection time interval, thus obtaining the two-level imperfect detection strategy of the hidden function system.

[0008] In one embodiment of the present invention, the method for determining the state evolution path corresponding to each detection time and the probability of occurrence of each state evolution path based on the degradation state and the occurrence of the random shock is as follows: Let any candidate value in the candidate value set be denoted as , No. The detection time corresponding to this detection is ; exist When the degradation state at a given time is a normal state and no random shock that would cause sudden failure occurs, the corresponding state evolution path is determined to be a normal state evolution path. exist When the degradation state at a given time is a defective state and no random shock that would cause sudden failure occurs, the corresponding state evolution path is determined to be the defective state evolution path. exist When the degradation state at a given time is a failure state and no random shock that would cause sudden failure occurs, the corresponding state evolution path is determined to be a soft failure state evolution path. exist The degradation state at any given time is either normal or defective, and the detection range is... When at least one random shock leading to sudden failure occurs within the time limit, the corresponding state evolution path is determined as the hard failure state evolution path; exist The degradation state at time t is a soft failure state, and the detection interval When at least one random shock leading to sudden failure occurs within the time limit, the corresponding state evolution path is determined to be a composite failure state evolution path in which both soft and hard failures occur. The probability of occurrence of each state evolution path is determined based on the occurrence of the degenerate state corresponding to each state evolution path during the degenerate process and the occurrence of the corresponding random shock.

[0009] In one embodiment of the present invention, the method for determining the detection result corresponding to each of the state evolution paths and the probability of occurrence of each of the detection results based on the two-level imperfection detection parameters is as follows: The two-level imperfection detection parameters include low-level detection accuracy. High level of detection accuracy And the probability parameter of false detection of defect status ,in, ; Based on the low level of detection accuracy The detection result corresponding to the normal state is determined as either a normal state or a defective state, where the probability of a normal state being detected as a normal state is... The probability that a normal state is detected as a defective state is ; Based on the high level of detection accuracy and the false detection probability parameter of the defect state The detection result corresponding to the defect state is determined as a normal state, a defect state, or a failure state, where the probability of a defect state being detected as a normal state is... The probability that a defective state is detected as a defective state is The probability that a defective state is detected as a failure state is ; Based on the high level of detection accuracy The detection result corresponding to the failure state is determined as either a defect state or a failure state, where the probability of a failure state being detected as a defect state is... The probability that a failure state is detected as a failure state is ; Based on the state corresponding to each state evolution path, the two-level imperfection detection parameters, and the occurrence of detection results before the corresponding detection time, the probability of occurrence of each detection result corresponding to each state evolution path is determined.

[0010] In one embodiment of the present invention, the method for determining the corresponding update type based on each of the detection results is as follows: Let the number of tests be ; In the If the test result is normal during the second test, the corresponding update type will be determined as age-based preventive replacement; In the When the detection result is a defect status during the second inspection, the corresponding update type will be determined as defect-based preventive replacement; In the When the detection result is a failure status during the next test, the corresponding update type will be determined as a fault-based corrective replacement. .

[0011] In one embodiment of the present invention, the probability of occurrence of each update type is determined based on the probability of occurrence of each state evolution path and the probability of occurrence of each detection result, and the method for determining the expected maintenance cost and expected update cycle corresponding to each update type based on the probability of occurrence of each update type and the maintenance parameters is as follows: Based on the detection results corresponding to each state evolution path, the occurrence probability of each state evolution path and the occurrence probability of the corresponding detection result are combined according to the update type to obtain the occurrence probabilities of age-based preventive replacement, defect-based preventive replacement, and failure-based corrective replacement, respectively. Based on the occurrence probability, corresponding number of detections, and detection level of each update type, the detection cost and replacement cost corresponding to each update type are determined from the maintenance parameters; for the state evolution path of failure, the corresponding downtime cost is determined based on the time between the occurrence of failure and the detection of failure, and the expected maintenance cost corresponding to each update type is determined based on the detection cost, the replacement cost, and the downtime cost; Let the number of tests be It will be in the first The expected update cycle for the age-based preventative replacement during the next test is determined as follows: It will be in the first The expected update cycle for the defect-based preventive replacement and the failure-based corrective replacement during the next inspection is determined as follows: ,in, .

[0012] In one embodiment of the present invention, the method for constructing a maintenance cost rate model based on each of the expected maintenance costs and each of the expected replacement cycles is as follows: The expected maintenance costs for the age-based preventative replacement, the defect-based preventative replacement, and the failure-based corrective replacement are respectively denoted as... , and The corresponding expected update periods are respectively , and ; Based on the ratio of expected maintenance cost to expected maintenance cycle for each update type, the maintenance cost rate model is constructed as follows: , in, This represents the expected maintenance cost rate. Indicates the detection time interval. Indicates the preset number of tests. This indicates the number of inspections required when a defect-based preventative replacement or a failure-based corrective replacement occurs.

[0013] In one embodiment of the present invention, the method for establishing the degradation process of the concealment function system based on the degradation parameters and the method for establishing the random impact process of the concealment function system based on the random impact parameters are as follows: The duration distribution of the concealed functional system in the normal stage and the defective stage is determined based on the degradation parameters. Based on the duration distribution of the normal stage and the defective stage, a degradation process of the concealed functional system from the normal state to the defective state and from the defective state to the failure state is established. The arrival pattern, impact force distribution, and impact failure threshold of the random impact are determined based on the random impact parameters. The random impact process is established based on the arrival pattern and impact force distribution of the random impact. Random impacts with impact forces greater than the impact failure threshold are identified as random impacts that lead to sudden failure.

[0014] In one embodiment of the present invention, the method for determining the degradation state corresponding to each detection time according to the degradation process, and the method for determining the occurrence of random shocks leading to sudden failure within each detection interval according to the random shock process, is as follows: Based on the correspondence between the duration of the normal and defective stages in the degradation process and each detection time, the degradation state corresponding to each detection time is determined to be a normal state, a defective state, or a failure state. Based on the arrival status of random impacts in each detection interval during the random impact process and the comparison results of the impact force of each random impact with the impact failure threshold, it is determined whether a random impact leading to sudden failure occurs in each detection interval.

[0015] In one embodiment of the present invention, the method for obtaining the expected maintenance cost rate corresponding to each candidate value by performing Monte Carlo simulation on each candidate value in the candidate value set based on the maintenance cost rate model is as follows: Assign values ​​to the parameters in the maintenance cost rate model; Each candidate value in the candidate value set is selected as the detection time interval. Monte Carlo simulation is performed based on the detection time and detection interval corresponding to each candidate value to determine the state evolution path, detection result and update type corresponding to each candidate value. Based on the expected maintenance cost and expected update cycle corresponding to each update type, the expected maintenance cost rate corresponding to each candidate value is calculated using the maintenance cost rate model.

[0016] Based on the same inventive concept, this invention also provides an optimization system for a two-level imperfection detection strategy of a concealed function system based on Monte Carlo simulation, comprising: The parameter determination module is used to obtain the degradation parameters, random impact parameters, two-level imperfection detection parameters and maintenance parameters of the concealed function system, determine the detection time interval of the periodic detection as a decision variable, and determine the candidate value set of the detection time interval; The state evolution path determination module is used to determine the corresponding detection time and detection interval for each candidate value in the candidate value set; establish the degradation process of the concealment function system based on the degradation parameters; establish the random impact process of the concealment function system based on the random impact parameters; determine the degradation state corresponding to each detection time based on the degradation process; determine the occurrence of random impacts leading to sudden failure within each detection interval based on the random impact process; and determine the state evolution path corresponding to each detection time and the probability of occurrence of each state evolution path based on the degradation state and the occurrence of random impacts. The detection update determination module is used to determine the detection result corresponding to each of the state evolution paths and the probability of occurrence of each of the detection results based on the two levels of imperfect detection parameters, and to determine the corresponding update type based on each of the detection results; The maintenance cost rate construction module determines the occurrence probability of each update type based on the occurrence probability of each state evolution path and the occurrence probability of each detection result, determines the expected maintenance cost and expected update cycle corresponding to each update type based on the occurrence probability of each update type and the maintenance parameters, and constructs a maintenance cost rate model based on each expected maintenance cost and each expected update cycle. The detection strategy optimization module is used to perform Monte Carlo simulation on each candidate value in the candidate value set based on the maintenance cost rate model, obtain the expected maintenance cost rate corresponding to each candidate value, determine the candidate value corresponding to the minimum expected maintenance cost rate as the optimal detection time interval, and obtain the two-level imperfect detection strategy of the hidden function system.

[0017] The technical solution of the present invention has the following advantages compared with the prior art: This invention simultaneously considers the degradation process and random impact process of the concealed functional system. It determines the corresponding state evolution path based on the degradation state and the occurrence of random impacts at different detection times, and combines two levels of imperfect detection parameters to determine the detection results and their occurrence probabilities corresponding to different state evolution paths. This integrates the actual state of the system, the impact of random impacts, and detection errors into the analysis process of detection and maintenance strategies, making the determination of different update scenarios more complete.

[0018] Based on this, the present invention determines the expected maintenance cost and expected update cycle according to the occurrence probability of each update type and the corresponding maintenance parameters, and constructs a maintenance cost rate model. The expected maintenance cost rate corresponding to different detection time intervals is calculated through Monte Carlo simulation. The detection time interval corresponding to the minimum expected maintenance cost rate is determined as the optimal detection time interval. Thus, the two-level imperfect detection strategy is optimized by comprehensively considering the detection cost, replacement cost and failure-related cost, thereby improving the rationality of the detection and maintenance decision of the hidden function system. Attached Figure Description

[0019] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0020] Figure 1 This is a flowchart illustrating the optimization method for a two-level imperfect detection strategy of a concealed function system based on Monte Carlo simulation provided in this embodiment of the invention. Figure 2 This is a schematic diagram of the two-level detection method of the two-stage concealment function system in an embodiment of the present invention; Figure 3 This is a schematic diagram of the system detection results and corresponding update scenarios under two levels of imperfect detection in an embodiment of the present invention; Figure 4 This is the first embodiment of the present invention. A schematic diagram of the three real states of the concealment function system during the second detection; Figure 5 This is the first embodiment of the present invention. Schematic diagram of the normal state evolution path during the second test; Figure 6 This is the first embodiment of the present invention. Schematic diagram of the defect state evolution path during the second inspection; Figure 7 This is the first embodiment of the present invention. Schematic diagram of the soft failure state evolution path during the second detection; Figure 8 This is the first embodiment of the present invention. Schematic diagram of the hard failure state evolution path during the second detection; Figure 9 This is the first embodiment of the present invention. A schematic diagram of the evolution path of a composite failure state in which both soft and hard failures occur during the second test; Figure 10 This is a comparison chart of the optimal detection strategies under single-level and two-level detection in this embodiment of the invention. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0022] Example 1: like Figure 1 As shown, this invention provides an optimization method for a two-level imperfection detection strategy of a concealed function system based on Monte Carlo simulation, comprising: Obtain the degradation parameters, random impact parameters, two-level imperfection detection parameters, and maintenance parameters of the concealed function system, determine the detection time interval of the periodic detection as a decision variable, and determine the candidate value set of the detection time interval; For each candidate value in the candidate value set, the corresponding detection time and detection interval are determined based on the candidate value; the degradation process of the concealment function system is established based on the degradation parameter, and the random impact process of the concealment function system is established based on the random impact parameter; the degradation state corresponding to each detection time is determined based on the degradation process, and the occurrence of random impacts leading to sudden failure within each detection interval is determined based on the random impact process; the state evolution path corresponding to each detection time and the probability of occurrence of each state evolution path are determined based on the degradation state and the occurrence of random impacts. Based on the two-level imperfection detection parameters, determine the detection results corresponding to each state evolution path and the probability of occurrence of each detection result, and determine the corresponding update type based on each detection result; The probability of occurrence of each update type is determined based on the probability of occurrence of each state evolution path and the probability of occurrence of each detection result. The expected maintenance cost and expected update cycle corresponding to each update type are determined based on the probability of occurrence of each update type and the maintenance parameters. A maintenance cost rate model is constructed based on the expected maintenance cost and the expected update cycle. Monte Carlo simulations are performed on each candidate value in the candidate value set based on the maintenance cost rate model to obtain the expected maintenance cost rate corresponding to each candidate value. The candidate value corresponding to the minimum expected maintenance cost rate is determined as the optimal detection time interval, thus obtaining the two-level imperfect detection strategy of the hidden function system.

[0023] This invention acquires degradation parameters, random impact parameters, two-level imperfect detection parameters, and maintenance parameters of a concealed functional system. It uses the detection time interval of periodic detection as a decision variable and establishes corresponding degradation and random impact processes for different candidate detection time intervals. Based on the degradation state at each detection moment and the occurrence of random impacts within the detection interval, it determines the state evolution path and its probability of occurrence. Combining the two-level imperfect detection parameters, it determines the detection result and its probability of occurrence for each state evolution path, and accordingly determines the corresponding update type. Based on the probability of occurrence of different update types and maintenance parameters, it calculates the expected maintenance cost and expected update cycle, constructs a maintenance cost rate model, obtains the expected maintenance cost rate corresponding to each candidate detection time interval through Monte Carlo simulation, and selects the candidate value corresponding to the minimum expected maintenance cost rate as the optimal detection time interval. This invention can uniformly incorporate system degradation, random impacts, detection errors, and different update behaviors into the detection strategy optimization process. By comprehensively considering multiple state evolution scenarios and detection results, it quantitatively compares different detection time intervals, reducing the bias caused by simply relying on experience to set the detection cycle, making the determined two-level imperfect detection strategy more consistent with the actual operation and maintenance needs of concealed functional systems.

[0024] In this embodiment of the invention, the concealment function system is self-contained. The system starts running constantly and identifies its operating status through periodic monitoring. The hidden functions of the system do not inherently reveal their internal state; normal, defective, and failed states must be identified through monitoring. In the absence of external random shocks, the system gradually degrades in performance over time, progressing from a normal state to a defective state, and further to a failed state. Functional failures caused by the system's own degradation process are classified as soft failures. Even after entering a defective state, the system can continue to operate, but defects requiring repair exist. If these defects continue to develop, the system may further progress to a failed state.

[0025] In addition to its own degradation, the concealed functional system is also affected by external random impacts during operation. When the impact force exceeds the set impact failure threshold, the random impact can directly cause a sudden system failure, which is called a hard failure. Both soft and hard failures are insidious and cannot be directly identified without detection. Therefore, after a system failure actually occurs, it is necessary to continue monitoring until a subsequent detection is performed to discover the corresponding failure state. The failure-related costs incurred during this period are determined based on the duration from the time the failure occurs to the time the failure is detected. Normal and defective states also need to be identified through periodic monitoring.

[0026] To adapt to the detection requirements of different stages of system operation, this embodiment adopts a two-level imperfect detection method. For example... Figure 2 As shown, low-level detection is used when the system is in the normal phase, and high-level detection is used after the system enters the defect phase. The probability of low-level detection accurately identifying the normal state is denoted as... The probability of high-level detection accurately identifying defect states and failure states is denoted as . And satisfy However, considering the accuracy of the testing equipment, the testing environment, and errors introduced during the testing process, the test results may not necessarily match the true state of the system. False detections occur based on adjacent states; a normal state can be detected as either a normal state or a defective state, a defective state can be detected as either a normal state, a defective state, or a failed state, and a failed state can be detected as either a defective state or a failed state. For a defective state, the probability of a high-level detection system accurately identifying it as a defective state is... The probability of a defective state being falsely detected as a normal state is calculated using the defective state false detection probability parameter. This means that, correspondingly, the probability of a defective state being detected as a failure state is... The above detection parameters together constitute two levels of imperfect detection parameters.

[0027] like Figure 3 As shown, the detection results further correspond to the system update behavior. When the system updates at the preset time... Second test, i.e. If the system is still detected as being in a normal state at a certain time, an age-based preventative replacement will be performed; if .... If the system is detected as defective during the first inspection, a defect-based preventative replacement is performed; when the system is detected as defective during the second inspection... If the system is detected as failing during the next inspection, a corrective replacement based on the failure will be performed. Each update establishes a corresponding update cycle. Subsequently, the expected maintenance cost and expected update cycle can be determined based on the probability of different update scenarios, detection costs, replacement costs, and failure-related costs.

[0028] Specifically, in this embodiment, degradation parameters, random impact parameters, two-level imperfection detection parameters, and maintenance parameters of the concealed function system are acquired. The degradation parameters include at least probability distribution parameters corresponding to the durations of the normal and defective stages; the random impact parameters include random impact arrival parameters, impact force distribution parameters, and impact failure thresholds; the two-level imperfection detection parameters include low-level detection accuracy. High level of detection accuracy And the probability parameter of false detection of defect status The maintenance parameters include cost parameters, replacement duration parameters, and preset number of tests required to determine the maintenance cost and update cycle for different update scenarios.

[0029] The detection time interval of the periodic detection The decision variable is determined, and multiple candidate values ​​are identified within the selectable range of the detection time interval, forming a candidate value set for the detection time interval. For any candidate value... The system operates according to time intervals. Perform periodic testing, the first The detection time corresponding to this detection is The corresponding detection interval between two adjacent detections Therefore, for each candidate detection time interval, a set of corresponding detection times and detection intervals can be formed. Subsequently, the system state evolution can be analyzed based on the degradation state of each detection time and the occurrence of random impacts within each detection interval.

[0030] For the degradation process, a time-delay model is used to characterize the two-stage degradation process of a hidden-function system from a normal state through a defective state to a failure state. The duration of the system in the normal stage is denoted as a random variable. The duration of the system in the defective phase is denoted as a random variable. The cumulative probability distribution function and probability density function corresponding to the two are denoted as follows: and ,in .

[0031] random variable The corresponding system duration from startup to entering a defective state, random variable This corresponds to the duration from when the system enters a defective state to when it further enters a failure state. Therefore, at a given detection time... Afterwards, it can be based on , and The relationship between the parameters determines the degradation state corresponding to the detection moment. When the normal phase has not yet ended, the system is in a normal state; when the normal phase has ended but the defective phase has not yet ended, the system is in a defective state; when both the normal and defective phases have ended, the system enters a failure state caused by its own degradation process.

[0032] For a random impact process, a homogeneous Poisson process is used to describe the process of a random impact reaching a concealed functional system. The arrival rate of the random impact is... The magnitudes of each random shock are independent and follow the same normal random variable. The magnitude of the impact force of the random impact is denoted as . Its distribution satisfies: , in, The average value of the impact force of a random impact. Let be the variance of the random impact force. Let the impact failure threshold be... When a random shock satisfies When the random impact is identified as a random impact leading to sudden failure, i.e., a fatal impact; when At this time, the random shock does not directly cause a sudden system failure. The two-stage degradation process and the random shock process are independent of each other. Based on the arrival of random shocks in each detection interval according to the homogeneous Poisson process and the impact force of each random shock, The comparison results can determine whether a random shock that caused a sudden failure occurred within the corresponding detection interval.

[0033] After establishing the degradation process and the random shock process, the detection time is targeted. Analyze the possible state evolution paths of the system. For example... Figure 4 As shown, in the first The corresponding test At any given moment, the system's true state can be categorized into normal, defective, and failed states. The system's state at the detection moment depends not only on its own two-stage degradation process but also on whether a fatal impact occurs within the corresponding timeframe. Therefore, it is necessary to classify the state evolution path according to different combinations of degradation states and random impact occurrences. In this embodiment, five scenarios are formed: normal state evolution path, defective state evolution path, soft failure state evolution path, hard failure state evolution path, and composite failure state evolution path where both soft and hard failures occur.

[0034] (1) such as Figure 5 As shown, when the first The corresponding test At that time, the system degradation process was still in a normal phase, and from the start of system operation until... If no fatal shock occurs at any given moment, this state evolution process is determined to be a normal state evolution path. Let... express The probability that the system's true state is the normal state at any given time depends on the duration of the normal phase. After the moment and in The calculation formula is as follows: (The condition that no fatal impact has occurred before the specified time is met.) , in, Indicates as of The probability that a fatal impact will not occur at any given moment is calculated using the following formula: , in, Indicates as of The number of random shocks arriving in a homogeneous Poisson random shock process at time t is Given a certain number of random impacts, each random impact must be less than the impact failure threshold. At that time, there was no fatal impact within the corresponding time range; the probability of all possible random impacts arriving was accumulated to obtain... .

[0035] (2) For example Figure 6 As shown, when The timekeeping system has ended its normal operation phase and entered the defect phase, while the time from the start of operation to... If no fatal impact occurs, this state evolution process is determined as the defect state evolution path. The system transitions from a normal state to a defect state within a certain detection interval; therefore, by accumulating the cases where the end of the normal phase falls within each detection interval, the defect state evolution path is determined. The probability that the true state at any given time is a defective state. Let... This probability is expressed by the following formula: , in, Indicates the system at the 1st The normal phase ends and the defect phase begins within each detection interval. Indicates as of the date The defect phase was not yet complete during the second inspection, therefore the system... It is still in a defective state at all times; with By combining these, we obtain the probability of the defect state evolution path occurring under the condition of no fatal impact.

[0036] (3) such as Figure 7 As shown, when the system is The moment has already entered the failure stage from its own degradation process, and as of... When a random impact process never results in a fatal impact, this state evolution process is defined as a soft failure state evolution path. Soft failure develops sequentially through normal and defect stages, distinguishing it from sudden failure caused by random impacts. Let... express The probability that the system's true state at any given time is a soft failure state is calculated using the following formula: , in, This indicates that the normal phase ends at the [number]th [position]. Each detection interval This indicates that the soft failure caused by the system's own degradation occurred in the first... Within a detection range. Under conditions without a fatal impact, this scenario corresponds to a soft failure purely caused by the system's own degradation.

[0037] (4) such as Figure 8 As shown, when The degradation process itself is used to determine whether the system is still in a normal or defective stage, but random shock processes are within the detection range. When at least one fatal impact occurs, the evolution process of this state is defined as a hard failure state evolution path. This path corresponds to a system that has not yet entered a soft failure state due to its own degradation, but experiences sudden failure due to an external random impact exceeding the impact failure threshold. Let... express The probability that the system's true state at any given time is a hard failure state is calculated using the following formula: , in, correspond The degradation process is still in a normal phase. correspond The degradation process has entered the defect stage but has not yet failed due to its own degradation. This corresponds to the probability that no fatal impact occurred before the previous detection time, but at least one fatal impact occurs within the current detection interval. Following the random impact process, [the probability is...]. Represented as ;in, Indicates as of The probability that a fatal impact will not occur at any given moment is calculated using the following formula: , Indicates the detection interval The probability of at least one fatal impact within the body is calculated using the following formula: .

[0038] therefore, and The product corresponds to the joint case where there is no fatal impact in the previous detection interval but a fatal impact occurs in the current detection interval. It is used to determine the probability of random impacts in the hard failure state evolution path and the subsequent composite failure state evolution path.

[0039] (5) such as Figure 9 As shown, when the system itself degrades in The time has entered the soft failure phase, and the random impact process is within the detection range. When at least one fatal impact occurs, the state evolution process is determined to be a composite failure state evolution path involving both soft and hard failures. This path simultaneously includes soft failures resulting from system degradation and hard failures caused by external random impacts. Let... The probability of this composite failure state evolution path occurring is represented by the following formula: , in, Indicates the system at the 1st Within each detection interval, the process transitions from the normal stage to the defect stage. Indicates as of the date During the second test, the system had already entered a soft failure state due to its own degradation; combined with The probability of the evolution path of a composite failure state where both soft and hard failures occur is obtained by considering the occurrence of fatal impacts in the current detection interval.

[0040] The five state evolution paths described above can cover scenarios where the system is still in a normal state, in a defective state, experiencing only soft failures, experiencing only hard failures, and experiencing both soft and hard failures at the detection time. Each path is determined by the stage characteristics of the degradation process and the occurrence of fatal shocks during the random impact process, forming the basis for analyzing the possible detection results and their probabilities under two perfect detections in different real states.

[0041] Furthermore, based on the aforementioned two-level imperfection detection rules, the detection results and their probabilities corresponding to each state evolution path are determined according to the actual state corresponding to each state evolution path, the two-level imperfection detection parameters, and the occurrence of detection results before the current detection time.

[0042] When calculating the probability of each detection result, it is necessary to consider the actual state at the current detection moment, the accurate identification probability or false detection probability corresponding to the current detection, and the detection results of each detection before the current detection moment. The fact that the system has not performed an update before the current detection moment indicates that none of the previous detections produced a result that could trigger a system update. Therefore, when the system... When transitioning from the normal stage to the defect stage within a detection interval, the process preceding the entry into the defect stage... The next lowest level of detection should all yield results indicating a normal state, with a corresponding probability factor of [missing value]. After the system enters the defect stage, if in the first... If no update is triggered before this detection, the corresponding high-level detection needs to continuously correct defect status errors to normal status, with a corresponding probability factor of [missing value]. When the system continues until the preset number of... If the update is not triggered after the second detection, the corresponding cumulative false positive probability is determined based on the actual number of detections. To maintain consistency with the notation in subsequent probability expressions, the probability of a normal state being incorrectly detected as a defective state is expressed as... Recorded as ,Right now By combining the historical detection results with the occurrence conditions of the five state evolution paths, the probability of different detection results under each state evolution path can be determined.

[0043] (1) For the normal state evolution path, the system in The situation remains normal, and as of [date / time]... No fatal impact occurred at any time. This path may produce two detection results: normal state and defective state.

[0044] Let the probability of a normal state being detected as a normal state be denoted as . The calculation formula is as follows: , in, This indicates that the normal phase lasts longer than The probability of; Indicates as of The probability that a fatal impact will not occur at any given moment; Indicates the period from the start of system operation to the [number]th [number]. Second test, consecutive The second-lowest level of detection accurately identified the actual normal state as normal.

[0045] The probability of a normal state being detected as a defective state is denoted as . The calculation formula is as follows: , in, Indicates the preceding The second-lowest level of detection accurately identified the actual normal state as normal. Indicates the first This test incorrectly identifies a normal state as a defective state. This test result corresponds to preventative replacement based on the defect.

[0046] (2) For the defect state evolution path, the system has ended the normal stage and entered the defect stage. At the corresponding detection time, it has not yet entered the failure state due to its own degradation, and no fatal impact has occurred up to the corresponding detection time. Under this path, three detection results may be generated: normal state, defect state, and failure state.

[0047] When the system has entered a defective state, but high-level detection continuously and incorrectly detects the defective state as a normal state, and this continues until a preset number of errors occurs... During the second inspection, the probability of a defective state being detected as a normal state is denoted as . The calculation formula is as follows: , in, ) indicates that the system is in the first... The normal phase ends and the defect phase begins within each detection interval, and this continues until the [number]th [time period]. It had not yet failed due to its own degradation at the time of the test; Indicates the period before entering the defect stage. The results of the second-lowest level tests were all normal. Indicates from the first The second test up to the first Although the system was already in a defective state during the first test, it continued to be detected. The second-highest level of inspection incorrectly detected defective states as normal states.

[0048] The probability of a defect state being accurately detected as a defect state is denoted as . The calculation formula is as follows: , in, This indicates that the system has entered the defect stage up to the [number]th [stage]. Prior to this inspection, the defect status was repeatedly and incorrectly detected as a normal status; Indicates the first The actual defect condition is accurately detected as a defect condition during the next inspection. This inspection result corresponds to preventative replacement based on the defect.

[0049] The probability of a defective state being incorrectly detected as a failure state is denoted as . The calculation formula is as follows: , in, Indicates the first The second-highest level of detection incorrectly detects a defective state as a failed state. Although the actual system state is still defective in this case, the actual detection result is a failed state, so it is processed according to the update method corresponding to a failed state.

[0050] (3) For the soft failure state evolution path, the system has already entered the defect stage from the normal stage, and further entered the soft failure state due to its own degradation within the current detection interval, while no fatal impact has occurred up to the current detection time. Under this path, the actual failure state may be detected as a defect state or a failure state.

[0051] The probability of a soft failure state being incorrectly detected as a defect state is denoted as . The calculation formula is as follows: , The probability of a soft failure state being accurately detected as a failure state is denoted as . The calculation formula is as follows: , The two probabilities mentioned above have the same soft failure state evolution conditions and historical detection result occurrence conditions, the difference being in the first... The second-highest level of detection results in the identification of actual failure states. When the first... When the detection incorrectly identifies an actual failure state as a defect state, the corresponding probability factor is: When the first When the failure state is accurately identified in the second detection, the corresponding probability factor is: .

[0052] (4) For the hard failure state evolution path, the system in The system continuously assesses its own degradation process to determine whether it is still in a normal or defective stage, but at least one fatal impact occurs within the current detection range, causing a hard failure. This path includes two scenarios: the system degradation process is still in the normal stage when the fatal impact occurs, and the system has entered the defective stage but has not yet experienced a soft failure.

[0053] The probability of a hard failure state being incorrectly detected as a defect state is denoted as . The calculation formula is as follows: , The first item corresponds to the situation where the system's degradation process is still in a normal stage when a fatal impact occurs, and the second item corresponds to the situation where the system has entered the defect stage but has not yet experienced a soft failure. This represents the probability that no fatal impact occurred before the previous detection time, but at least one fatal impact occurs within the current detection interval.

[0054] The probability of a hard failure state being accurately detected as a failure state is denoted as . The calculation formula is as follows: , Both probabilities mentioned above preserve the two degradation scenarios before a hard failure: the system is in a normal stage and a defective stage. They also incorporate prior detection history into the calculation. The difference between the two formulas lies in the... The results of the second-highest level detection on the identification of actual failure states correspond to the following: and .

[0055] (5) For the combined failure state evolution path where soft failure and hard failure occur together, the system's own degradation process has entered the soft failure stage, and at least one fatal impact has occurred within the current detection interval. Under this path, the actual failure state may also be detected as a defect state or a failure state.

[0056] The probability of a composite failure state being incorrectly detected as a defect state is denoted as . The calculation formula is as follows: , The probability of a composite failure state being accurately detected as a failure state is denoted as . The calculation formula is as follows: , By using the above probability of occurrence of detection results, the five real-state evolution paths obtained earlier can be further mapped to actual detection results. Each probability expression considers not only the... The recognition results corresponding to the second detection are also obtained through , The equal probability factor retains the detection history before the current detection, so that the process of the system evolving from the real state to the actual detection result remains continuous.

[0057] Based on the previously established correspondence between detection results and update types, the probability of occurrence of detection results corresponding to each state evolution path is merged according to the final triggered update type. This process reaches the preset threshold. If the second test result is still normal, a preventative replacement based on age is recommended; When the first inspection result indicates a defect, preventative replacement based on the defect should be performed; When the test result indicates a failure, a corrective replacement based on the failure is required. .when Furthermore, if the test result is normal, the system continues to run until the next test time without performing an update.

[0058] The same update type can be formed by different state evolution paths and different detection results. For example, defect-based preventive replacement may be formed by a true normal state being mistakenly detected as a defective state, or by a true defective state being accurately detected as a defective state, or by three true failure states being mistakenly detected as defective states. Failure-based corrective replacement may be formed by a true defective state being incorrectly detected as a failure state, or by a soft failure, hard failure, or combined failure being accurately detected as a failure state. Therefore, based on the final triggered update type, the occurrence probabilities of the aforementioned detection results are combined to obtain the occurrence probabilities of the three update types.

[0059] Age-based preventative replacement is recorded as APR. When the system reaches the preset [number]th [period]... If the system is detected and the result is still normal, an age-based preventative replacement is performed. This update may correspond to a system that is actually in a normal state and has been accurately detected as normal, or it may correspond to a system that has entered a defective state but has been repeatedly and incorrectly detected as normal. The probability of age-based preventative replacement occurring is: , Age-based preventative replacement occurs in the first year. For this detection, the corresponding expected update cycle is .

[0060] Defect-based preventative replacement is denoted as DPR. When the first... When the detection result indicates a defect state, defect-based preventative replacement is performed. Combining the scenarios of being falsely detected as a defect state under the normal state evolution path, being accurately detected as a defect state under the defect state evolution path, and being falsely detected as a defect state under the three failure state evolution paths, the probability of defect-based preventative replacement occurring is: , Defect-based preventative replacement occurs in the first... For this detection, the corresponding expected update cycle is .

[0061] Failure-based corrective replacement is denoted as FCR. When the... When the detection result indicates a failure state, a failure-based corrective replacement is performed. Combining the scenarios of being falsely detected as a failure state under the defect state evolution path and being accurately detected as a failure state under the three failure state evolution paths, the probability of failure-based corrective replacement occurring is: , Repair replacement based on failure occurred in the first For this detection, the corresponding expected update cycle is .

[0062] Furthermore, the expected maintenance cost for each update type is determined based on the state evolution path, detection results, number of detections, and detection level corresponding to different update types. The cost of a single low-level detection is denoted as... The cost of a single high-level test is denoted as The cost of preventative replacement is denoted as The cost of corrective replacement is denoted as The failure cost parameter corresponding to the period from the occurrence of failure to its detection is denoted as . The downtime cost parameter during the update operation is denoted as The duration of preventative replacement is recorded as The duration of the corrective replacement is recorded as .

[0063] For the system to always be in a normal state, and in the... In cases where the system is still detected as normal during the next test, the system has experienced a total of [number missing] tests. The second lowest level of detection corresponds to a detection cost of For the system in the first... The first detection interval enters the defect stage, but until the first... If the second inspection still detects a normal state, the process before entering the defect stage... The second lowest level of detection, after entering the defect stage, until the... This testing experience The second-highest level of testing corresponds to a testing cost of: Combining the cost of preventative replacement with the downtime costs incurred during the preventative replacement period, the expected maintenance cost for age-based preventative replacement is: .

[0064] For defect-based preventative replacement, if the system's actual state is always normal, and the defect occurs on the [missing information]... If a defect is incorrectly detected during the second inspection, the system will experience... The second lowest level of detection corresponds to a detection cost of If the system is in the first... The first detection interval enters the defect stage, and in the second... If the defect status is detected during the second inspection, then the process before entering the defect stage involves... The second lowest level of detection, after entering the defect stage, undergoes... The second-highest level of testing corresponds to a testing cost of: .

[0065] When a system has actually failed, but is incorrectly identified as defective during detection, the cost incurred between the failure occurrence and detection must also be considered. The duration between the actual failure occurrence and the corresponding detection time is denoted as... Its expectation is denoted as Neither soft nor hard failures can be directly identified without detection. There is a period of time between a system failure and its subsequent detection that remains undetected; the cost of this undetected period is... .

[0066] Performing preventative replacements also incurs replacement costs. Duration of preventive replacement The corresponding downtime cost is Based on the evolution paths of each state and their detection results, the expected maintenance cost corresponding to preventive replacement based on defects is: , The maintenance costs corresponding to soft failure state evolution paths, hard failure state evolution paths, and combined failure state evolution paths all include... This reflects the cost incurred during the duration of failure from actual system failure to detection. The two costs corresponding to the hard failure state evolution path consider two scenarios: when the system's degradation process is still in a normal stage during the fatal impact, and when it has entered the defect stage but has not yet experienced a soft failure. Therefore, the corresponding low-level detection cost and high-level detection cost have different compositions.

[0067] For fault-based corrective replacements, if the system is truly in a defective state, but on the [missing information]... If a system is incorrectly detected as failing during a subsequent test, it has not actually failed. The corresponding repair costs include the costs of prior low-level testing, high-level testing, and corrective replacement. And the downtime costs incurred during corrective replacement. For cases where soft, hard, and combined failures are accurately detected as failure states, the system has already actually failed before detection. Therefore, in addition to the corresponding detection costs, corrective replacement costs, and downtime costs during corrective replacement, the costs incurred between the occurrence of the failure and its detection are also included. .

[0068] The expected repair cost for corrective replacement based on failure is: , in, , and Let represent the expected maintenance costs for age-based preventative replacement, defect-based preventative replacement, and failure-based corrective replacement, respectively. The expected replacement cycles for these three replacement types are as follows: , and Each expected maintenance cost is combined according to the state evolution path and detection results that can form the corresponding update type, and the detection cost is included based on the number of low-level and high-level detections the system underwent before the update; for paths where the actual state has failed, the expected duration between the failure occurrence and detection is also considered. Include the corresponding failure cost.

[0069] Furthermore, based on the expected maintenance costs and expected replacement cycles corresponding to the three replacement types, a maintenance cost rate model for the concealed function system is constructed. For age-based preventative replacement, the expected replacement cycle is... For both defect-based preventative replacement and failure-based corrective replacement, the expected replacement cycle is [missing information]. Based on the relationship between the expected maintenance cost and the expected maintenance period for each update type within the corresponding update cycle, the maintenance cost rate model is expressed as: , in, This represents the expected maintenance cost rate for concealed functional systems. Indicates the detection time interval for periodic detection; Indicates the preset number of tests; This indicates the number of inspections required for either a defect-based preventative replacement or a failure-based corrective replacement. .

[0070] This maintenance cost rate model incorporates different update scenarios that may occur within an update cycle, along with their corresponding maintenance costs and update cycles, into the cost rate calculation. The detection time interval is also considered. The detection time interval simultaneously affects the location of each detection moment and interval, the corresponding degradation state of the system at each detection moment, the time range within which random shocks are included in the state evolution path, the timing of the detection of system defects or failures, and the number of detections corresponding to the update occurrence. Therefore, the probability of state evolution path occurrence, detection result occurrence, update type occurrence, and expected maintenance cost rate may all differ for different detection time intervals. By using the detection time interval as a decision variable, the maintenance cost rate model can be used to compare the maintenance cost levels under different candidate detection time intervals.

[0071] Furthermore, Monte Carlo simulations were performed on the candidate set of detection time intervals based on the maintenance cost rate model to solve for the optimal detection time interval under two levels of imperfect detection conditions.

[0072] The degradation parameter, random impact parameter, two-level imperfect detection parameter, and maintenance parameter in the maintenance cost rate model are assigned values, and each candidate value is selected from the previously determined candidate value set for the detection time interval as the detection time interval. For any candidate value, the corresponding periodic detection time and the detection interval between adjacent detection times are determined based on the candidate value, and Monte Carlo simulation is performed according to the aforementioned degradation process and random impact process.

[0073] For the current candidate detection time interval, based on the duration of the normal phase. Duration of the defect phase The value of determines the degradation state corresponding to each detection time, based on the arrival of random impacts within each detection interval and the impact force and impact failure threshold of each random impact. The comparison results determine whether a fatal impact occurs within each detection interval. Combining the degradation state and the occurrence of fatal impacts, the evolution path at the corresponding detection time is determined to be either a normal state evolution path, a defect state evolution path, a soft failure state evolution path, a hard failure state evolution path, or a composite failure state evolution path where both soft and hard failures occur simultaneously.

[0074] After determining the state evolution path, the actual detection result corresponding to each state evolution path is determined according to the aforementioned two-level imperfection detection rules and the occurrence of detection results before the current detection time. When the system is in the normal stage, the detection result is determined according to the detection accuracy corresponding to the low-level detection; after the system enters the defect stage or an actual failure occurs, the detection result is determined according to the detection accuracy corresponding to the high-level detection and the false detection probability parameter of the defect state. At the same time, the historical detection results generated by the previous low-level and high-level detections are retained to ensure that the current detection result is consistent with the previous operation process when the system has not triggered an update.

[0075] The corresponding update type is determined based on the detection results obtained from the simulation. When the system reaches the preset threshold... When the second test result is still normal, an age-based preventative replacement is initiated; when the third... When the first inspection result is a defective state, a defect-based preventative replacement is initiated; when the second inspection result is a defective state, a defect-based preventative replacement is initiated. When the detection result indicates a failure state, a fault-based corrective replacement is initiated. By combining the evolution paths of each state and the occurrence of detection results, the occurrence probabilities of the three update types are obtained, and the corresponding expected maintenance costs and expected update cycles are determined according to the cost calculation method established earlier.

[0076] The results obtained at the current candidate detection time interval , and and the corresponding and Substitute the values ​​into the maintenance cost rate model to calculate the expected maintenance cost rate corresponding to the current candidate value. .

[0077] Monte Carlo simulations were performed on other candidate values ​​in the candidate set of detection time intervals in the same manner to obtain the expected maintenance cost rate corresponding to each candidate value. Since different candidate detection time intervals correspond to different detection times and detection intervals, the timing of the discovery of system defect states, soft failure states, and hard failure states, as well as the number of detections, also change accordingly. The corresponding detection costs, replacement costs, costs incurred between the occurrence of failure and its discovery, and update cycles are all reflected in the expected maintenance cost rate corresponding to each candidate value.

[0078] Compare the expected maintenance cost rates corresponding to all candidate values ​​in the candidate set of detection time intervals, and determine the candidate value corresponding to the minimum expected maintenance cost rate as the optimal detection time interval. ,Right now .

[0079] Will As the detection time interval for the periodic detection of the concealed function system, and combined with the imperfect detection rules corresponding to the aforementioned low-level and high-level detection, a two-level imperfect detection strategy for the concealed function system is obtained.

[0080] Using the above method, the determination of the detection time interval simultaneously considers the system's own two-stage degradation, sudden failures caused by random shocks, detection errors generated by two-level detection, and update behaviors corresponding to different detection results, enabling candidate detection time intervals to be compared under a unified maintenance cost rate model. The resulting optimal detection time interval... Based on the expected maintenance cost rate, without changing the aforementioned degradation model, random impact model, and detection rules, the selection of the detection time interval is implemented as a quantifiable optimization result, thus completing the determination of the two-level imperfect detection strategy for the concealed function system.

[0081] Example 2: To verify the correctness and effectiveness of the model established in Example 1, a numerical simulation analysis was conducted using a typical two-stage hidden-function system capacitor bank as an example. Capacitor banks are critical components in power systems, frequently subjected to random external shocks during operation, including voltage fluctuations, electromagnetic interference, and environmental corrosion. Their degradation process exhibits a distinct two-stage characteristic: transitioning from a normal operating state to a defective state, ultimately leading to complete failure. All states require detection to be identified.

[0082] In this embodiment, two exponential distributions are used to characterize the normal and defective phases of the system, respectively. and ,in , The impact process is characterized using a homogeneous Poisson process, where the impact arrival rate is... The impact magnitude follows a normal distribution, with a mean and variance of 1 / 2. , Impact failure threshold The parameters for two-level imperfection detection are set as follows: , , Maintenance-related cost parameters are set to... , , , , , Preventive replacement interval is The repair replacement time is Preset maximum number of detections .

[0083] Substituting the above parameters into the maintenance cost rate model established in Example 1, and using the periodic detection time interval... Using [variable name] as the decision variable, Monte Carlo simulations were performed with different values ​​selected from the candidate value set. Simulation results show that when [variable name] is selected, [variable name] is selected. At this time, the system's expected maintenance cost rate reaches its minimum value, which is Under this optimal detection strategy, the system achieves a balance between detection cost, replacement cost, and failure-related cost under two levels of imperfect detection conditions.

[0084] like Figure 10 As shown, to illustrate the effectiveness of the two-level detection strategy, the two-level detection strategy proposed in this embodiment is compared with a single-level detection strategy. Only low-level detection is used (detection accuracy is constant). When the optimal expected cost rate is ), Only high-level detection is used (detection accuracy is always 100%). When the optimal expected cost rate is ), The optimal expected cost rate under a two-level detection strategy. The results are lower than those of the two single-level detection strategies mentioned above, indicating that the two-level detection strategy effectively balances the contradiction between detection cost and recognition accuracy by using low-level detection for low-cost preliminary screening and high-level detection for high-precision confirmation. This verifies the effectiveness of the model established in Example 1 in reducing the long-term operating cost of the system.

[0085] Further sensitivity analysis was conducted to examine the impact of detection accuracy parameters on the optimization results. A high-level detection accuracy was fixed at [value missing]. This leads to low-level detection accuracy. from Increase to Optimal detection interval from shortened to The optimal expected cost rate is from Rise to The results indicate that while simply improving the accuracy of low-level detection can enhance the recognition accuracy of normal states, it also increases the detection cost. This, in turn, forces an increase in the detection frequency to compensate for the lack of accuracy, verifying that the core value of low-level detection lies in low-cost preliminary screening rather than high-precision recognition.

[0086] Fixed the low-level detection accuracy to To achieve high-level detection accuracy from Increase to Optimal detection interval Stable The optimal expected cost rate is from Continue to decline to The results demonstrate that improving the accuracy of high-level detection can effectively reduce the total system cost without changing the detection frequency, proving that high-level detection is a key element in optimizing the cost of concealed systems, and that improving its accuracy has clear economic value.

[0087] The numerical simulation results above verify the effectiveness of the maintenance cost rate model and optimization method constructed in Example 1 from different perspectives, and also provide quantitative basis for the application of the two-level imperfection detection strategy in actual engineering.

[0088] Example 3: Based on the same inventive concept as Embodiment 1, this invention also provides a two-level imperfection detection strategy optimization system for concealed function systems based on Monte Carlo simulation, comprising: The parameter determination module is used to obtain the degradation parameters, random impact parameters, two-level imperfection detection parameters and maintenance parameters of the concealed function system, determine the detection time interval of the periodic detection as a decision variable, and determine the candidate value set of the detection time interval; The state evolution path determination module is used to determine the corresponding detection time and detection interval for each candidate value in the candidate value set; establish the degradation process of the concealment function system based on the degradation parameters; establish the random impact process of the concealment function system based on the random impact parameters; determine the degradation state corresponding to each detection time based on the degradation process; determine the occurrence of random impacts leading to sudden failure within each detection interval based on the random impact process; and determine the state evolution path corresponding to each detection time and the probability of occurrence of each state evolution path based on the degradation state and the occurrence of random impacts. The detection update determination module is used to determine the detection result corresponding to each of the state evolution paths and the probability of occurrence of each of the detection results based on the two levels of imperfect detection parameters, and to determine the corresponding update type based on each of the detection results; The maintenance cost rate construction module determines the occurrence probability of each update type based on the occurrence probability of each state evolution path and the occurrence probability of each detection result, determines the expected maintenance cost and expected update cycle corresponding to each update type based on the occurrence probability of each update type and the maintenance parameters, and constructs a maintenance cost rate model based on each expected maintenance cost and each expected update cycle. The detection strategy optimization module is used to perform Monte Carlo simulation on each candidate value in the candidate value set based on the maintenance cost rate model, obtain the expected maintenance cost rate corresponding to each candidate value, determine the candidate value corresponding to the minimum expected maintenance cost rate as the optimal detection time interval, and obtain the two-level imperfect detection strategy of the hidden function system.

[0089] Each module of the Monte Carlo simulation-based concealed function system two-level imperfection detection strategy optimization system proposed in this embodiment is used to implement each step in the Monte Carlo simulation-based concealed function system two-level imperfection detection strategy optimization method in Embodiment 1. To avoid redundancy, it will not be described again here.

[0090] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0091] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0092] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0093] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0094] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for optimizing a two-level imperfect detection strategy for a concealed function system based on Monte Carlo simulation, characterized in that, include: Obtain the degradation parameters, random impact parameters, two-level imperfection detection parameters, and maintenance parameters of the concealed function system, determine the detection time interval of the periodic detection as a decision variable, and determine the candidate value set of the detection time interval; For each candidate value in the candidate value set, the corresponding detection time and detection interval are determined based on the candidate value; the degradation process of the concealment function system is established based on the degradation parameter, and the random impact process of the concealment function system is established based on the random impact parameter; the degradation state corresponding to each detection time is determined based on the degradation process, and the occurrence of random impacts leading to sudden failure within each detection interval is determined based on the random impact process; the state evolution path corresponding to each detection time and the probability of occurrence of each state evolution path are determined based on the degradation state and the occurrence of random impacts. Based on the two-level imperfection detection parameters, determine the detection results corresponding to each state evolution path and the probability of occurrence of each detection result, and determine the corresponding update type based on each detection result; The probability of occurrence of each update type is determined based on the probability of occurrence of each state evolution path and the probability of occurrence of each detection result. The expected maintenance cost and expected update cycle corresponding to each update type are determined based on the probability of occurrence of each update type and the maintenance parameters. A maintenance cost rate model is constructed based on the expected maintenance cost and the expected update cycle. Monte Carlo simulations are performed on each candidate value in the candidate value set based on the maintenance cost rate model to obtain the expected maintenance cost rate corresponding to each candidate value. The candidate value corresponding to the minimum expected maintenance cost rate is determined as the optimal detection time interval, thus obtaining the two-level imperfect detection strategy of the hidden function system.

2. The optimization method for two-level imperfection detection strategy of concealed function system based on Monte Carlo simulation according to claim 1, characterized in that: The method for determining the state evolution path corresponding to each detection time and the probability of occurrence of each state evolution path based on the degradation state and the occurrence of the random shock is as follows: Let any candidate value in the candidate value set be denoted as , No. The detection time corresponding to this detection is ; exist When the degradation state at a given time is a normal state and no random shock that would cause sudden failure occurs, the corresponding state evolution path is determined to be a normal state evolution path. exist When the degradation state at a given time is a defective state and no random shock that would cause sudden failure occurs, the corresponding state evolution path is determined to be the defective state evolution path. exist When the degradation state at a given time is a failure state and no random shock that would cause sudden failure occurs, the corresponding state evolution path is determined to be a soft failure state evolution path. exist The degradation state at any given time is either normal or defective, and the detection range is... When at least one random shock leading to sudden failure occurs within the time limit, the corresponding state evolution path is determined as the hard failure state evolution path; exist The degradation state at time t is a soft failure state, and the detection interval When at least one random shock leading to sudden failure occurs within the time limit, the corresponding state evolution path is determined to be a composite failure state evolution path in which both soft and hard failures occur. The probability of occurrence of each state evolution path is determined based on the occurrence of the degenerate state corresponding to each state evolution path during the degenerate process and the occurrence of the corresponding random shock.

3. The optimization method for two-level imperfection detection strategy of concealed function system based on Monte Carlo simulation according to claim 1, characterized in that: The method for determining the detection result corresponding to each state evolution path and the probability of occurrence of each detection result based on the two-level imperfection detection parameters is as follows: The two-level imperfection detection parameters include low-level detection accuracy. High level of detection accuracy And the probability parameter of false detection of defect status ,in, ; Based on the low level of detection accuracy The detection result corresponding to the normal state is determined as either a normal state or a defective state, where the probability of a normal state being detected as a normal state is... The probability that a normal state is detected as a defective state is ; Based on the high level of detection accuracy and the false detection probability parameter of the defect state The detection result corresponding to the defect state is determined as a normal state, a defect state, or a failure state, where the probability of a defect state being detected as a normal state is... The probability that a defective state is detected as a defective state is The probability that a defective state is detected as a failure state is ; Based on the high level of detection accuracy The detection result corresponding to the failure state is determined as either a defect state or a failure state, where the probability of a failure state being detected as a defect state is... The probability that a failure state is detected as a failure state is ; Based on the state corresponding to each state evolution path, the two-level imperfection detection parameters, and the occurrence of detection results before the corresponding detection time, the probability of occurrence of each detection result corresponding to each state evolution path is determined.

4. The optimization method for two-level imperfection detection strategy of concealed function system based on Monte Carlo simulation according to claim 1, characterized in that: The method for determining the corresponding update type based on the detection results is as follows: Let the number of tests be ; In the If the test result is normal during the second test, the corresponding update type will be determined as age-based preventive replacement; In the When the detection result is a defect status during the second inspection, the corresponding update type will be determined as defect-based preventive replacement; In the When the detection result is a failure status during the next test, the corresponding update type will be determined as a fault-based corrective replacement. .

5. The optimization method for two-level imperfection detection strategy of concealed function system based on Monte Carlo simulation according to claim 1, characterized in that: The probability of occurrence of each update type is determined based on the probability of occurrence of each state evolution path and the probability of occurrence of each detection result. The method for determining the expected maintenance cost and expected update cycle corresponding to each update type based on the probability of occurrence of each update type and the maintenance parameters is as follows: Based on the detection results corresponding to each state evolution path, the occurrence probability of each state evolution path and the occurrence probability of the corresponding detection result are combined according to the update type to obtain the occurrence probabilities of age-based preventive replacement, defect-based preventive replacement, and failure-based corrective replacement, respectively. Based on the occurrence probability, corresponding number of detections, and detection level of each update type, the detection cost and replacement cost corresponding to each update type are determined from the maintenance parameters; For the state evolution path of failure, the corresponding downtime cost is determined based on the time between the occurrence of failure and the detection of failure, and the expected maintenance cost corresponding to each update type is determined based on the detection cost, the replacement cost and the downtime cost; Let the number of tests be It will be in the first The expected update cycle for the age-based preventative replacement during the next test is determined as follows: It will be in the first The expected update cycle for the defect-based preventive replacement and the failure-based corrective replacement during the next inspection is determined as follows: ,in, .

6. The optimization method for two-level imperfection detection strategy of concealed function system based on Monte Carlo simulation according to claim 5, characterized in that: The method for constructing a maintenance cost rate model based on the expected maintenance costs and expected replacement cycles is as follows: The expected maintenance costs for the age-based preventative replacement, the defect-based preventative replacement, and the failure-based corrective replacement are respectively denoted as... , and The corresponding expected update periods are respectively , and ; Based on the ratio of expected maintenance cost to expected maintenance cycle for each update type, the maintenance cost rate model is constructed as follows: ， in, This represents the expected maintenance cost rate. Indicates the detection time interval. Indicates the preset number of tests. This indicates the number of inspections required when a defect-based preventative replacement or a failure-based corrective replacement occurs.

7. The optimization method for two-level imperfection detection strategy of concealed function system based on Monte Carlo simulation according to claim 1, characterized in that: The method for establishing the degradation process of the concealment function system based on the degradation parameters and the method for establishing the stochastic impact process of the concealment function system based on the stochastic impact parameters are as follows: The duration distribution of the concealed functional system in the normal stage and the defective stage is determined based on the degradation parameters. Based on the duration distribution of the normal stage and the defective stage, a degradation process of the concealed functional system from the normal state to the defective state and from the defective state to the failure state is established. The arrival pattern, impact force distribution, and impact failure threshold of the random impact are determined based on the random impact parameters. The random impact process is established based on the arrival pattern and impact force distribution of the random impact. Random impacts with impact forces greater than the impact failure threshold are identified as random impacts that lead to sudden failure.

8. The optimization method for two-level imperfection detection strategy of concealed function system based on Monte Carlo simulation according to claim 1, characterized in that: The method for determining the degradation state corresponding to each detection time based on the degradation process, and the method for determining the occurrence of random shocks leading to sudden failure within each detection interval based on the random shock process, is as follows: Based on the correspondence between the duration of the normal and defective stages in the degradation process and each detection time, the degradation state corresponding to each detection time is determined to be a normal state, a defective state, or a failure state. Based on the arrival status of random impacts in each detection interval during the random impact process and the comparison results of the impact force of each random impact with the impact failure threshold, it is determined whether a random impact leading to sudden failure occurs in each detection interval.

9. The optimization method for a two-level imperfect detection strategy of a concealed function system based on Monte Carlo simulation according to claim 1, characterized in that: The method for obtaining the expected maintenance cost rate for each candidate value in the candidate value set by performing Monte Carlo simulation based on the aforementioned maintenance cost rate model is as follows: Assign values ​​to the parameters in the maintenance cost rate model; Each candidate value in the candidate value set is selected as the detection time interval. Monte Carlo simulation is performed based on the detection time and detection interval corresponding to each candidate value to determine the state evolution path, detection result and update type corresponding to each candidate value. Based on the expected maintenance cost and expected update cycle corresponding to each update type, the expected maintenance cost rate corresponding to each candidate value is calculated using the maintenance cost rate model.

10. A two-level imperfection detection strategy optimization system for concealed function systems based on Monte Carlo simulation, characterized in that, include: The parameter determination module is used to obtain the degradation parameters, random impact parameters, two-level imperfection detection parameters and maintenance parameters of the concealed function system, determine the detection time interval of the periodic detection as a decision variable, and determine the candidate value set of the detection time interval; The state evolution path determination module is used to determine the corresponding detection time and detection interval for each candidate value in the candidate value set; establish the degradation process of the concealment function system based on the degradation parameters; establish the random impact process of the concealment function system based on the random impact parameters; determine the degradation state corresponding to each detection time based on the degradation process; determine the occurrence of random impacts leading to sudden failure within each detection interval based on the random impact process; and determine the state evolution path corresponding to each detection time and the probability of occurrence of each state evolution path based on the degradation state and the occurrence of random impacts. The detection update determination module is used to determine the detection result corresponding to each of the state evolution paths and the probability of occurrence of each of the detection results based on the two levels of imperfect detection parameters, and to determine the corresponding update type based on each of the detection results; The maintenance cost rate construction module determines the occurrence probability of each update type based on the occurrence probability of each state evolution path and the occurrence probability of each detection result, determines the expected maintenance cost and expected update cycle corresponding to each update type based on the occurrence probability of each update type and the maintenance parameters, and constructs a maintenance cost rate model based on each expected maintenance cost and each expected update cycle. The detection strategy optimization module is used to perform Monte Carlo simulation on each candidate value in the candidate value set based on the maintenance cost rate model, obtain the expected maintenance cost rate corresponding to each candidate value, determine the candidate value corresponding to the minimum expected maintenance cost rate as the optimal detection time interval, and obtain the two-level imperfect detection strategy of the hidden function system.

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