DC switch health state assessment method based on analytic hierarchy process and entropy weight method
A DC switch health status assessment system was constructed by using the hierarchical analysis method and entropy weight method, which solved the problems of inaccurate assessment and high cost in the existing technology and achieved a more scientific and concise health status assessment and life prediction.
Patent Information
- Application Number
- CN202410364808.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-03-28
- Publication Date
- 2025-09-30
AI Technical Summary
Existing DC switch health status assessment methods are costly, have a significant impact on equipment operation, and have high requirements for the quality of indicator data, resulting in inaccurate and inscientific assessments.
The analytic hierarchy process and entropy weight method are used to construct an evaluation index system. The remaining service life of the DC switch is predicted by calculating the equipment health score. The subjective weight and objective weight are combined to unify the evaluation index weights and construct a life model for the DC switch.
It achieves a more scientific and accurate health status assessment, simplifies the calculation process, improves the scientificity and accuracy of the assessment, and can predict the remaining service life of the equipment.
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Figure CN120724641A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of DC switch health status assessment, and in particular to a DC switch health status assessment method based on a hierarchy analysis method and an entropy weight method. Background Art
[0002] DC switches play a crucial role in urban rail transit systems, serving as the final barrier to ensuring train power supply security. Therefore, ensuring the operational reliability of DC high-speed switches is crucial for stable train operations and regular train departures. Only by ensuring the stable operation of this critical equipment can we provide safe and reliable transportation services for passengers.
[0003] Currently, common technical approaches for detecting equipment health status include collecting vibration signals from the equipment and using intelligent algorithms to identify their characteristics. Another approach uses tools such as cloud models and fuzzy algorithms to evaluate and score relevant indicator data to calculate the equipment's health status. However, these methods have some shortcomings in practical application. For example, some methods require the installation of additional detection devices on the equipment, which not only increases costs but may also affect the normal operation of the equipment. At the same time, other methods have high requirements for the quality of indicator data, requiring tedious data processing to obtain relatively accurate health status calculation results. Therefore, these methods have certain limitations and inconveniences in practical application. Summary of the Invention
[0004] The purpose of the present invention is to calculate the equipment health score by constructing an evaluation index system based on the hierarchical analysis method and the entropy weight method, thereby evaluating the equipment health and constructing a DC switch service life model to predict the remaining service life.
[0005] To achieve the above objectives, the present invention proposes a DC switch health status assessment method based on the analytic hierarchy process and the entropy weight method, comprising:
[0006] Step 1: Determine evaluation indicators related to the health status of the DC switch, refine specific evaluation sub-indicators under each evaluation indicator, and construct a DC switch health status evaluation system with a hierarchical evaluation structure. The DC switch health status evaluation system includes a target layer, a characteristic layer, and an indicator layer. The target layer is the health status score, the characteristic layer is the evaluation indicator, and the indicator layer is the evaluation sub-indicator.
[0007] Step 2: Establish a judgment matrix based on the hierarchical analysis method, calculate the subjective weight of each evaluation indicator according to the judgment matrix, calculate the information entropy of one or more evaluation indicators using the entropy weight method, calculate the objective weight of the corresponding evaluation indicator based on the information entropy, and obtain the weight of each evaluation indicator by combining the subjective weight and the objective weight;
[0008] Step 3: Calculate the indicator score of each evaluation indicator, establish a calculation formula for the health status score based on the DC switch health status evaluation system and in combination with the weights and indicator scores of each evaluation indicator, calculate the health status score using the calculation formula, construct a life model of the DC switch based on the health status scores of previous years, and use the life model of the DC switch to predict the remaining service life of the DC switch.
[0009] In one embodiment, the evaluation indicators include basic parameters, operating environment, operating test parameters, component reliability, and adverse operating conditions;
[0010] The evaluation sub-indicators under the basic parameters include: static resume and dynamic resume;
[0011] The evaluation sub-indicators under the operating environment include temperature, humidity, and pollution level;
[0012] The evaluation sub-indicators under the operation test parameters include main contact circuit resistance, copper busbar insulation to ground, closing / opening time, and fixed value verification;
[0013] The evaluation sub-indicators under the component reliability include secondary circuit elements, terminal block secondary cables, relay protection devices, and transmitters;
[0014] The evaluation sub-indicators under the adverse working conditions include open-circuit current, short-circuit current, and excessive operation.
[0015] In one embodiment, in step 2, the information entropy of the operating test parameters is calculated using the entropy weight method, the objective weight of the operating test parameters is calculated based on the information entropy, and the combined weight of the operating test parameters is obtained by combining the subjective weight and the objective weight. The combined weight is the weight of the operating test parameters.
[0016] In one embodiment, in step 2, the subjective weight w a The calculation formula is Pw a =λ max w a ,λ max is the maximum eigenvalue of the judgment matrix P.
[0017] In one embodiment, the entropy weight method is used to calculate the information entropy of one or more evaluation indicators, and the objective weight of the corresponding evaluation indicator is calculated based on the information entropy. The weight of each evaluation indicator is obtained by combining the subjective weight and the objective weight. Specifically,
[0018] in accordance with Normalize the data, x ij is the value of the i-th sample under the j-th evaluation sub-indicator, m is the number of evaluation sub-indicators, a ijThis is the standardized indicator data;
[0019] according to Calculate the information entropy E of all evaluation sub-indicators under this evaluation indicator j , n is the number of samples;
[0020] Combine The objective weight w of each evaluation sub-indicator is obtained b =[w1w2…w j ];
[0021] Calculate the subjective weight w of each evaluation sub-indicator according to the judgment matrix P of the evaluation indicator a , according to the formula Obtain the combined weight of each evaluation sub-indicator, w ia is the subjective weight of the i-th sample, w ib is the objective weight of the i-th sample, and the combined weight is the weight of the evaluation index.
[0022] In one embodiment, the calculation formula for the health status score in step 3 is:
[0023] HI=k(w1HI1+w2HI2+w3HI3+w4HI4)
[0024] Among them, w1, w2, w3, and w4 represent the weights of basic parameters, operating environment, operating test parameters, and component reliability, respectively;
[0025] HI1, HI2, HI3, and HI4 represent the index scores of basic parameters, operating environment, operating test parameters, and component reliability, respectively;
[0026] k is a correction factor used to correct the negative impact of poor operating conditions on the DC switch.
[0027] In one embodiment, the calculation formula for the index score of the basic parameter is as follows:
[0028] HI1=k a HI jt
[0029] Among them, HI jt The index score of the static resume is calculated as follows: HI jt =1-(1-HI0)e BT , HI0 is 0.95, B=0.0924, T is the commissioning time of the DC switch, and the unit of commissioning time is year;
[0030] k a is the correction coefficient, which is calculated based on the dynamic history of the DC switch.
[0031] In one embodiment, the lifespan model of the DC switch is constructed by using the health status scores over the years:
[0032] The health status scores of the DC switch over the years are fitted to obtain the health status curve of the DC switch.
[0033] The DC switch health status assessment method based on the analytic hierarchy process and entropy weight method of the present invention has the following beneficial effects:
[0034] 1. The present invention establishes a DC switch health status evaluation system with a hierarchical evaluation structure. The evaluation indicators used are more sufficient, reliable, effective, and comprehensive, with a wider range of considerations. Compared with the original status evaluation method, it is more scientific and reasonable.
[0035] 2. The calculation process of health status assessment in the present invention is simpler and more reliable, and the process of calculating indicator weights achieves the unity of subjective and objective, improving the problem of strong subjectivity of the original assessment method. The indicator weights are more balanced, so that the indicator information that changes dramatically during equipment operation can better fit the actual situation, and the calculation efficiency is significantly improved.
[0036] 3. Based on the health status assessment, the present invention constructs a service life model of the DC switch, which can predict the remaining service life of the DC switch and further approach the intelligent assessment method. BRIEF DESCRIPTION OF THE DRAWINGS
[0037] Figure 1 The figure is a flow chart of a method for evaluating the health status of a DC switch based on the analytic hierarchy process and the entropy weight method according to an embodiment of the present invention. DETAILED DESCRIPTION
[0038] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the invention and are not intended to limit the invention.
[0039] The present invention proposes a DC switch health status assessment method based on the analytic hierarchy process and the entropy weight method. The method combines subjective judgment (analytic hierarchy process) and objective data characteristics (entropy weight method) to determine the weight of the assessment index, thereby improving the accuracy and scientificity of the assessment. Figure 1 As shown, including:
[0040] Step 1: Identify evaluation indicators related to the health status of the DC switch, refine the specific sub-indicators under each evaluation indicator, and construct a DC switch health status evaluation system with a hierarchical evaluation structure. The DC switch health status evaluation system consists of a target layer, a characteristic layer, and an indicator layer. The target layer is the health status score, the characteristic layer is the evaluation indicator, and the indicator layer is the evaluation sub-indicator. Step 1 helps to systematically organize and refine the evaluation indicators related to the health status of the DC switch, ensuring the comprehensiveness and accuracy of the evaluation. Furthermore, the hierarchical evaluation structure of the DC switch health status evaluation system also makes subsequent calculations and analysis clearer and more organized.
[0041] Step 2: Establish a judgment matrix based on the Analytic Hierarchy Process (AHP) and calculate the subjective weights of each evaluation metric based on the judgment matrix. The information entropy of each evaluation metric is calculated using the entropy weight method, and the objective weights of each evaluation metric are calculated based on this information entropy. The subjective and objective weights are combined to obtain the combined weights of each evaluation metric. In step 2, the AHP combined with the entropy weight method improves the weights of the evaluation metrics, enabling a more scientific, effective, and quantitative assessment of the health status of the DC switch. Specifically, using the AHP to calculate the subjective weights fully considers the experience and judgment of experts, ensuring that the evaluation results are more consistent with actual conditions. Simultaneously, using the entropy weight method to calculate the objective weights determines the weights based on the data's discreteness and information content, reducing the influence of subjective factors on the results. Combining the subjective and objective weights yields more comprehensive and accurate evaluation metric weights, improving the accuracy and scientific nature of the assessment.
[0042] Step 3: Calculate the indicator scores for each evaluation indicator. Based on the DC switch health status assessment system and incorporating the combined weights of each evaluation indicator and the indicator scores, a formula for calculating the health status score is established. This formula is used to calculate the health status score, which quantitatively assesses the health status of the DC switch. A lifespan model for the DC switch is constructed using the historical health status scores. This lifespan model is used to predict the remaining useful life of the DC switch, facilitating the implementation of relevant maintenance strategies. In one embodiment, constructing the DC switch lifespan model using historical health status scores involves fitting the historical health status scores of the DC switch to obtain a health status curve for the DC switch.
[0043] Specifically, the evaluation indicators include basic parameters, operating environment, operating test parameters, component reliability, and adverse operating conditions. The evaluation sub-indicators under the basic parameters include: static history and dynamic history. The evaluation sub-indicators under the operating environment include temperature, humidity, and pollution level. The evaluation sub-indicators under the operating test parameters include main contact circuit resistance, copper busbar insulation to ground, closing / opening time, and constant value verification. The evaluation sub-indicators under component reliability include secondary circuit elements, terminal block secondary cables, relay protection devices, and transmitters. The evaluation sub-indicators under adverse operating conditions include open / short-circuit current and excessive operation.
[0044] Specifically, in step 2, the information entropy of the operating test parameters is calculated using the entropy weight method, and the objective weight of the operating test parameters is calculated based on the information entropy. The combined weight of the operating test parameters is obtained by combining the subjective weight and the objective weight. The combined weight is the weight of the operating test parameters.
[0045] Furthermore, in step 2, the subjective weight w a The calculation formula is Pw a =λ max w a ,λ max is the maximum eigenvalue of the judgment matrix P.
[0046] Furthermore, the entropy weight method is used to calculate the information entropy of one or more evaluation indicators, and the objective weight of the corresponding evaluation indicator is calculated based on the information entropy. The weight of each evaluation indicator is obtained by combining the subjective weight and the objective weight, which is specifically:
[0047] in accordance with Normalize the data, x ij is the value of the i-th sample under the j-th evaluation sub-indicator, m is the number of evaluation sub-indicators, a ij This is the standardized indicator data;
[0048] according to Calculate the information entropy E of all evaluation sub-indicators under this evaluation indicator j , n is the number of samples;
[0049] Combine The objective weight w of each evaluation sub-indicator is obtained b =[w1w2…w j ];
[0050] Calculate the subjective weight w of each evaluation sub-indicator according to the judgment matrix P of the evaluation indicator a , according to the formula Obtain the combined weight of each evaluation sub-indicator, w ia is the subjective weight of the i-th sample, w ib is the objective weight of the i-th sample, and the combined weight is the weight of the evaluation index.
[0051] In one embodiment, the calculation formula for the health status score in step 3 is:
[0052] HI=k(w1HI1+w2HI2+w3HI3+w4HI4)
[0053] Where w1, w2, w3, and w4 represent the weights of basic parameters, operating environment, operating test parameters, and component reliability, respectively. HI1, HI2, HI3, and HI4 represent the index scores for basic parameters, operating environment, operating test parameters, and component reliability, respectively. k is a correction factor. Considering the impact of adverse operating conditions on the overall health of the equipment, the correction factor k is used to correct the negative impact of adverse operating conditions on the DC switch and adjust the overall health score of the DC switch.
[0054] In one embodiment, the calculation formula for the index score of the basic parameter is as follows:
[0055] HI1=k a HI jt
[0056] Among them, HI jt The index score of the static resume is calculated as follows: HI jt =1-(1-HI0)e BT , HI0 is 0.95, B = 0.0924, T is the commissioning time of the DC switch (unit / year);
[0057] k a is the correction coefficient, which is calculated based on the dynamic history of the DC switch.
[0058] The following will further describe, in a specific embodiment, the entire process of conducting a health status assessment for a DC switch that has been in operation for 10 years. Based on the relevant national standards for DC switches and relevant expert recommendations, combined with the actual DC switch monitoring index data, the evaluation indicators related to the DC switch are selected. In this embodiment, the evaluation indicators are the same as described above, including: basic parameters, operating environment, operating test parameters, component reliability, and adverse working conditions. The evaluation sub-indicators under the basic parameters include: static history and dynamic history. The evaluation sub-indicators under the operating environment include temperature, humidity, and pollution level. The evaluation sub-indicators under the operating test parameters include main contact circuit resistance, copper busbar insulation to ground, closing / opening time, and constant value verification. The evaluation sub-indicators under component reliability include secondary circuit elements, terminal block secondary cables, relay protection devices, and transmitters. The evaluation sub-indicators under adverse working conditions include open / short circuit current and excessive operation. In this embodiment, the hierarchical evaluation structure is shown in Table 1 below.
[0059] Table 1 DC switch health status assessment system
[0060]
[0061] Based on expert experience, the judgment matrix P of basic parameters, operating environment, operating test parameters, and component reliability is established, see Table 2. a =λ max w a Calculate the weight of each element to the previous layer, where w1 = 0.48, w2 = 0.14, w3 = 0.26, w4 = 0.12, w1, w2, w3, w4 represent the weights of basic parameters, operating environment, operating test parameters, and component reliability, respectively, λ max is the maximum eigenvalue of the judgment matrix P.
[0062] Table 2 Feature layer judgment matrix
[0063]
[0064]
[0065] The basic parameters are divided into two aspects: static history and dynamic history, as follows:
[0066] Static resume is expressed as index score HI jt , calculated according to the following formula: HI jt =1-(1-HI0)e BT Where HI0 is 0.95, B = 0.0924, and T is the commissioning time of the DC switch. As can be seen from the above, the commissioning time of the DC switch in this embodiment is 10 years.
[0067] Dynamic history is used to evaluate the static health status value HI of the equipment based on the equipment operation record, fault record and maintenance record. jt Correction coefficient k a The calculation formula is: a =k 11 k 12 k 13 According to the dynamic history of the DC switch (operation record, long-term good operation; fault record, there are 5 faults; maintenance record, only repairs are performed when a fault occurs), select k 11 =1.05, k 12 =0.98, k 13 =0.98, then k a Calculated to be 1.01.
[0068] The index score of the basic parameter HI1=k a HI jt =0.80.
[0069] Similarly, a judgment matrix for the operating environment and component reliability was established. Based on the actual collected data, the device operating environment score and component reliability score were calculated, as shown in Table 3. The weight for the operating environment, w, is [0.30, 0.16, 0.54], and the weight for the component reliability parameter, w, is [0.14, 0.14, 0.26, 0.46]. The calculated index score, HI2, for the operating environment is 0.94, and the index score, HI4, for component reliability is 0.92.
[0070] Table 3 DC switch operating environment and reliability parameter index scores
[0071]
[0072]
[0073] The analytic hierarchy process was used to establish a judgment matrix for the test parameters, see Table 4 below.
[0074] Table 4 Judgment matrix of DC switch operation test parameters
[0075]
[0076] According to the formula Pw a =λ max w a , calculate the subjective weight w of the running test parameters a =[0.38 0.12 0.08 0.160.26]. The data of the operating test parameters of the DC switch are shown in Table 5. The entropy weight method is used. The data were standardized. Calculate the information entropy E of the five evaluation sub-indicators of the running experimental parameters j , and combined with The objective weight w of each evaluation sub-indicator is obtained b =[0.10 0.42 0.34 0.06 0.08].
[0077] Table 5 Data of DC switch operation test parameters
[0078]
[0079] Combined with the subjective weight w obtained previously a and objective weight w b , according to the formula The combined weight w = [0.26 0.34 0.19 0.07 0.14] can be obtained, and the indicators of the five evaluation sub-indicators are 97, 90, 95, 89 and 87 points respectively, so the indicator score HI3 is calculated to be 0.922.
[0080] Table 6 shows the statistics for two types of DC switch adverse operating conditions. Based on the degree of harm and frequency of occurrence, two correction coefficients, k1 = 0.95 and k2 = 0.98, were selected. Referring to k = k1k2, the overall correction coefficient k for adverse operating conditions was calculated to be 0.94.
[0081] Table 6 Record of DC switch bad working condition
[0082]
[0083] According to the above-mentioned calculation formula of the health status score HI=k(w1HI1+w2HI2+w3HI3+w4HI4), the final health status score HI of the DC switch can be obtained as 0.823.
[0084] By fitting the health status scores of DC switches over the years, the equipment health status curve is obtained as HI = 1.017-0.06184e 0.1388T From this, we can calculate that when the health status value of the equipment is close to retirement, that is, when the HI is 0.2, the operating time T is 22.7 years. Based on the current usage intensity, the remaining life of the DC switch is about 10.7 years.
[0085] The DC switch health status assessment method based on the analytic hierarchy process and entropy weight method of the present invention has the following beneficial effects:
[0086] 1. The present invention establishes a DC switch health status evaluation system with a hierarchical evaluation structure. The evaluation indicators used are more sufficient, reliable, effective, and comprehensive, with a wider range of considerations. Compared with the original status evaluation method, it is more scientific and reasonable.
[0087] 2. The calculation process of health status assessment in the present invention is simpler and more reliable, and the process of calculating indicator weights achieves the unity of subjective and objective, improving the problem of strong subjectivity of the original assessment method. The indicator weights are more balanced, so that the indicator information that changes dramatically during equipment operation can better fit the actual situation, and the calculation efficiency is significantly improved.
[0088] 3. Based on the health status assessment, the present invention constructs a service life model of the DC switch, which can predict the remaining service life of the DC switch and further approach the intelligent assessment method.
[0089] The above embodiments are merely further explanations of the present invention and are not intended to limit the present invention in any other manner. The present invention may also have various other embodiments. Those skilled in the art may make various corresponding modifications and variations based on the present invention without departing from the spirit and substance of the present invention, and such corresponding modifications and variations shall fall within the scope of protection of the present invention.
Claims
1. A DC switch health status assessment method based on analytic hierarchy process and entropy weight method, characterized in that: include: Step 1: Determine evaluation indicators related to the health status of the DC switch, refine specific evaluation sub-indicators under each evaluation indicator, and construct a DC switch health status evaluation system with a hierarchical evaluation structure. The DC switch health status evaluation system includes a target layer, a characteristic layer, and an indicator layer. The target layer is the health status score, the characteristic layer is the evaluation indicator, and the indicator layer is the evaluation sub-indicator. Step 2: Establish a judgment matrix based on the hierarchical analysis method, calculate the subjective weight of each evaluation indicator according to the judgment matrix, calculate the information entropy of one or more evaluation indicators using the entropy weight method, calculate the objective weight of the corresponding evaluation indicator based on the information entropy, and obtain the weight of each evaluation indicator by combining the subjective weight and the objective weight; Step 3: Calculate the indicator score of each evaluation indicator, establish a calculation formula for the health status score based on the DC switch health status evaluation system and in combination with the weights and indicator scores of each evaluation indicator, calculate the health status score using the calculation formula, construct a life model of the DC switch based on the health status scores of previous years, and use the life model of the DC switch to predict the remaining service life of the DC switch.
2. The DC switch health status assessment method based on the analytic hierarchy process and entropy weight method according to claim 1 is characterized in that: The evaluation indicators include basic parameters, operating environment, operating test parameters, component reliability, and adverse operating conditions; The evaluation sub-indicators under the basic parameters include: static resume and dynamic resume; The evaluation sub-indicators under the operating environment include temperature, humidity, and pollution level; The evaluation sub-indicators under the operation test parameters include main contact circuit resistance, copper busbar insulation to ground, closing / opening time, and fixed value verification; The evaluation sub-indicators under the component reliability include secondary circuit elements, terminal block secondary cables, relay protection devices, and transmitters; The evaluation sub-indicators under the adverse working conditions include open-circuit current, short-circuit current, and excessive operation.
3. The DC switch health status assessment method based on the analytic hierarchy process and entropy weight method according to claim 2 is characterized in that: In step 2, the information entropy of the operating test parameters is calculated using the entropy weight method, and the objective weight of the operating test parameters is calculated based on the information entropy. The combined weight of the operating test parameters is obtained by combining the subjective weight and the objective weight. The combined weight is the weight of the operating test parameters.
4. The DC switch health status assessment method based on the analytic hierarchy process and entropy weight method according to claim 2 is characterized in that: In step 2, the subjective weight w a The calculation formula is Pw a =λ max w a ,λ max is the maximum eigenvalue of the judgment matrix P.
5. The DC switch health status assessment method based on the analytic hierarchy process and entropy weight method according to claim 4 is characterized in that: The entropy weight method is used to calculate the information entropy of one or more evaluation indicators, and the objective weight of the corresponding evaluation indicator is calculated based on the information entropy. The weight of each evaluation indicator is obtained by combining the subjective weight and the objective weight. Specifically, in accordance with Normalize the data, x ij is the value of the i-th sample under the j-th evaluation sub-indicator, m is the number of evaluation sub-indicators, a ij The index data is standardized; according to Calculate the information entropy E of all evaluation sub-indicators under this evaluation indicator j , n is the number of samples; Combine The objective weight w of each evaluation sub-indicator is obtained b =[w1w2…w j ]; Calculate the subjective weight w of each evaluation sub-indicator according to the judgment matrix P of the evaluation indicator a , according to the formula Obtain the combined weight of each evaluation sub-indicator, w ia is the subjective weight of the i-th sample, w ib is the objective weight of the i-th sample, and the combined weight is the weight of the evaluation index.
6. The DC switch health status assessment method based on the analytic hierarchy process and entropy weight method according to claim 2 is characterized in that: The calculation formula for the health status score in step 3 is: HI=k(w1HI1+w2HI2+w3HI3+w4HI4) Among them, w1, w2, w3, and w4 represent the weights of basic parameters, operating environment, operating test parameters, and component reliability, respectively; HI1, HI2, HI3, and HI4 represent the index scores of basic parameters, operating environment, operating test parameters, and component reliability, respectively; k is a correction factor used to correct the negative impact of poor operating conditions on the DC switch.
7. The DC switch health status assessment method based on the analytic hierarchy process and entropy weight method according to claim 6 is characterized in that: The calculation formula for the indicator score of the basic parameters is as follows: HI1=k a HI jt Among them, HI jt The index score of the static resume is calculated as follows: HI jt =1-(1-HI0)e BT , HI0 is 0.95, B=0.0924, T is the commissioning time of the DC switch, and the unit of commissioning time is year; k a is the correction coefficient, which is calculated based on the dynamic history of the DC switch.
8. The DC switch health status assessment method based on the analytic hierarchy process and entropy weight method according to claim 1 is characterized in that: The lifespan model of the DC switch constructed by using the health status scores over the years is: The health status scores of the DC switch over the years are fitted to obtain the health status curve of the DC switch.