Isolation forest-based power transmission system health assessment method and system

Abstract

The present application relates to a kind of power transmission system health assessment method and system based on isolated forest, belong to equipment condition monitoring and health management technical field.The method can be carried out feature position-feature structure coding to power transmission system monitoring signal, then the data of system normal operation is as training set, the abnormal score of each sample is calculated using isolated forest algorithm, and the minimum-maximum normalization is used to map health index to abnormal score, the original health index curve changing with time is constructed, finally the original health index curve is smoothed by exponential weighted moving average method, it is converted into health assessment curve, and the related index of the effectiveness of health assessment curve is counted.Effective help is provided for the health management of power transmission system without relying on prior label, by learning the feature distribution of normal operation sample, sensitive response is generated to abnormal or degradation state, the accurate evaluation of the health state of power transmission system is realized.

Description

Technical Field

[0001] This invention belongs to the field of equipment condition monitoring and health management technology, specifically relating to a health assessment method and system for power transmission systems based on isolated forests. Background Technology

[0002] Currently, Prognostics and Health Management (PHM) technology has become a crucial means globally for ensuring the safe operation and efficient maintenance of various high-reliability equipment. In recent years, the research and application of PHM technology has expanded from traditional aerospace and military equipment to various special vehicles and industrial equipment, such as intelligent engineering machinery, emergency rescue vehicles, mining transportation equipment, and high-end logistics platforms, becoming an important technological support for advanced manufacturing and intelligent operation and maintenance. With the deepening of national strategies such as intelligent manufacturing and "Industrial Internet+", PHM technology has gradually gained attention. Some achievements have been experimentally applied in fields such as emergency equipment and intelligent engineering vehicles, accumulating certain technical reserves and engineering experience, laying the foundation for the intelligent operation and maintenance of key equipment. Therefore, conducting health assessments of power transmission systems to provide effective assistance for system health management has always been a research hotspot in the field of health management.

[0003] In power transmission systems, key components operate under complex loads and fluctuating operating conditions for extended periods, and their operating status is reflected in dynamic response characteristics through monitoring signals. These signals not only exhibit strong dynamic changes but are also subject to noise interference and operating condition switching, causing characteristic parameters that truly reflect the system degradation process to be masked or weakened, making it difficult for traditional signal analysis methods to accurately assess the system's true state.

[0004] Currently, data-driven methods, especially time-series modeling strategies based on deep learning, have shown great potential in nonlinear feature extraction and latent pattern recognition, providing new approaches for quantifying the health status of complex systems. However, the "black box" nature of deep models also limits their interpretability and reliability in practical engineering. Therefore, how to accurately model the system degradation process, thereby quantifying and assessing the system's health status and achieving precise perception of the system's operating state, has become a critical research challenge and key issue that urgently needs to be addressed in the field of powertrain system health assessment. Summary of the Invention

[0005] The purpose of this invention is to overcome the inability of existing assessment methods to accurately perceive the operating status of a system, and to provide a powertrain health assessment method and system based on isolated forests.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a method for health assessment of a powertrain system based on isolated forests, comprising the following steps: The detection signals of the power transmission system are collected, the collected monitoring signals are divided into samples, the multidimensional statistical features of each sample are extracted, and the position of the features is numerically encoded. The continuous features are discretized using fuzzy C-means clustering and elbow rule, structural information is extracted, and a feature position-feature structure encoding framework is established to obtain the feature encoding dataset. Based on the obtained feature encoding dataset, the data of normal operation of the power transmission system is selected as the training set, and the data of various faults of the power transmission system are selected as the test set. The anomaly score of each sample is calculated using the isolated forest algorithm. Based on the calculated anomaly score of each sample, a minimum-maximum normalization method is used for mapping to obtain a health index that reflects the state of the power transmission system represented by the sample, and an original health index curve that changes over time is constructed. Based on the obtained original health index curve, the exponentially weighted moving average method is used to process local fluctuations and sampling errors, resulting in a health assessment curve showing the true change of the system's health status over time. Relevant indicators for evaluating the effectiveness of the powertrain system health index curve are also statistically analyzed.

[0007] The specific method for discretizing continuous features using fuzzy C-means clustering and the elbow rule is as follows: Fuzzy C-means clustering is used to calculate the membership degree between continuous features and each cluster center, and the elbow rule is used to calculate... Determine the optimal number of cluster centers to achieve feature discretization: ; in, These are continuous feature points; As cluster center; For the first i One cluster; This represents the square of the Euclidean distance from a feature point to its corresponding cluster center.

[0008] In the step of extracting structural information, establishing a feature location-feature structure encoding framework, and obtaining the feature encoding dataset, the established feature location-feature structure encoding framework is as follows: ; in, This is a feature encoding dataset for the power transmission system. For dataset samples, For the first Statistical characteristics For the characteristic location, It is a characteristic structure.

[0009] The specific method for the step of selecting normal operation data of the power transmission system as the training set and various fault data of the power transmission system as the test set based on the obtained feature encoding dataset, and calculating the anomaly score of each sample using the isolated forest algorithm is as follows: Based on the obtained feature encoding dataset For the dataset The data is divided into two parts, and the data from the normal operation of the powertrain system is used as the training set. The various fault data of the powertrain system are used as a test set. ; Based on training set Multiple random trees are constructed using the isolated forest algorithm to obtain a trained multiple random tree model and anomaly scores in the training set; Test set The anomaly score for each input sample is calculated using the pre-trained model. The outlier score of the test set is obtained by using the average path length of the test set in each tree. This reflects the degree to which a sample is easily isolated.

[0010] Calculate each input sample abnormal scores The method is as follows: ; ; ; in, The total number of training samples; This is a normalization factor for the average path length of normal samples. For harmonic numbers, is the Euler-Marcheroni constant, with an approximate value of 0.5772.

[0011] The specific method for the step of mapping the calculated anomaly score of each sample using a minimum-maximum normalization method to obtain a health index that reflects the state of the power transmission system represented by the sample, and constructing the original health index curve over time, is as follows: After obtaining the anomaly score for each sample, these scores are converted into a health index using a min-max normalization method. Map abnormal scores uniformly to the interval [0,1]: ; in, The outlier score for the sample; The minimum of all abnormality scores among all samples; The maximum value among all abnormal scores; Based on the time-varying trend of the power transmission system, the health index is extracted into an original health index curve.

[0012] The specific method for the step of using the exponentially weighted moving average method to process local fluctuations and sampling errors based on the obtained original health index curve to obtain the health assessment curve of the system's health status changing over time, and statistically analyzing relevant indicators used to evaluate the effectiveness of the powertrain system's health index curve, is as follows: Based on the obtained original health index curve, the following was adopted: The exponentially weighted moving average method is used to calculate a health assessment curve by weighting time series data.

[0013] in The original health index, The health index is a weighted average. It is a smoothing factor; Based on the obtained health assessment curves, the effectiveness of health status outcomes is quantitatively assessed using monotonicity, robustness, and trend indicators.

[0014] The method for quantitatively assessing the effectiveness of health status outcomes using monotonicity indicators is as follows: ; in, This represents the health value of the powertrain system. The length of the health assessment curve; The derivative of adjacent health values, The positive and negative signs represent the positive and negative values; The following are methods for using robust indicators to quantitatively assess the effectiveness of health status outcomes: ; in, For the power transmission system in Health value at any given time; In order to be in The average trend value at any given time.

[0015] The following are methods for using trend indicators to quantitatively assess the effectiveness of health status outcomes: .

[0016] Secondly, the present invention provides a powertrain health assessment based on isolated forests, including: The signal acquisition and dataset establishment module is used to acquire detection signals from the power transmission system, divide the acquired monitoring signals into samples, extract multidimensional statistical features of each sample, and numerically encode the location of the features. It uses fuzzy C-means clustering and elbow rule to discretize continuous features, extract structural information, establish a feature location-feature structure encoding framework, and obtain a feature encoding dataset. The anomaly score calculation module is used to select the normal operation data of the power transmission system as the training set and the various fault data of the power transmission system as the test set based on the obtained feature encoding dataset, and to calculate the anomaly score of each sample using the isolated forest algorithm. The system health index construction module is used to map the calculated abnormal score of each sample using a minimum-maximum normalization method to obtain a health index that reflects the state of the power transmission system represented by the sample, and to construct the original health index curve that changes over time. The evaluation module is used to process local fluctuations and sampling errors based on the obtained original health index curve using the exponentially weighted moving average method, to obtain a health assessment curve of the actual change of the system health status over time, and to statistically analyze relevant indicators used to evaluate the effectiveness of the powertrain system health index curve.

[0017] Compared with the prior art, the present invention has the following beneficial effects: The feature location-feature structure encoding method proposed in this invention can effectively preserve the key variation patterns in the original features, avoid interference from feature scale on model training, and improve modeling efficiency and generalization ability.

[0018] The isolated forest algorithm used in this invention can better extract the dynamic characteristics of the power transmission system and is more sensitive and accurate in responding to abnormal or degraded states of the system.

[0019] The health index proposed in this invention enables the comparability of the degree of abnormality among different samples, and provides an intuitive understanding of health status.

[0020] The exponentially weighted moving average method used in this invention can effectively filter out short-term local fluctuations and noise, and more clearly show the long-term trend of equipment health status over time.

[0021] The power transmission system health assessment method of the present invention is simple, reliable, and highly adaptable, and can effectively realize dynamic quantitative monitoring and assessment of the system's operating status. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating the working principle of the health assessment method involved in this invention; Figure 2This invention relates to a flowchart for calculating the anomaly score of isolated forests. Figure 3 This is a graph showing the clustering results of the elbow rule in an embodiment of the present invention. Figure 4 This is a health assessment curve for cylinder compression ratio reduction failure in an embodiment of the present invention; Figure 5 This is a health assessment curve of cylinder compression ratio reduction at 15dB noise level according to an embodiment of the present invention. Figure 6 This is a comparison curve of the health assessment curves for cylinder compression ratio reduction failures in embodiments of the present invention. Detailed Implementation

[0023] To further understand the content of this invention, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments are merely illustrative and not limiting of the invention.

[0024] Example 1 like Figure 1 As shown, a powertrain health assessment method based on isolated forests includes the following steps: S1: Collect the detection signals of the power transmission system, divide the collected monitoring signals into samples, create a dataset, extract the multidimensional statistical features of each sample, and numerically encode the position of each feature; use fuzzy C-means clustering and elbow rule to discretize the continuous features, extract structural information, and obtain feature position-feature structure encoded data. S2: Based on the obtained feature encoding dataset, select the data of normal operation of the power transmission system as the training set, select the data of various faults of the power transmission system as the test set, and use the isolated forest algorithm to calculate the anomaly score of each sample. S3: Based on the calculated abnormal score of each sample, the abnormal score is mapped to the [0,1] interval using the minimum-maximum normalization method to obtain a health index that reflects the state of the power transmission system represented by the sample, and the original health index curve changing over time is constructed. S4: Based on the obtained original health index curve, the exponentially weighted moving average method is used to process local fluctuations and sampling errors to obtain a health assessment curve of the actual change of the system health status over time, and relevant indicators for evaluating the effectiveness of the power transmission system health index curve are statistically analyzed.

[0025] Specifically, in S1, the monitoring signals of the powertrain system are divided into samples, a dataset is created, multidimensional statistical features of each sample are extracted, and the location of each feature is numerically encoded. The specific method is as follows: First, the monitoring signals of the power transmission system are collected. The monitoring signals are divided into samples according to different system states, and a dataset is made. The multidimensional statistical features of each sample in the time domain, frequency domain, and time-frequency domain are extracted, and the feature positions are encoded starting from 0 and 1 according to the position of the features.

[0026] Secondly, fuzzy C-means clustering is used to calculate the membership degree between continuous features and each cluster center, and the elbow rule is used to calculate... Determine the optimal number of cluster centers to achieve feature discretization: ; in, These are continuous feature points; As cluster center; For the first i One cluster; This represents the square of the Euclidean distance from a feature point to its corresponding cluster center.

[0027] Finally, a feature location-feature structure encoding framework is established to obtain the feature encoding dataset. : ; in, This is a feature encoding dataset for the power transmission system. For dataset samples, For the first Statistical characteristics For the characteristic location, It is a characteristic structure.

[0028] Specifically, in S2, based on the obtained feature encoding dataset, data from normal operation of the powertrain system is selected as the training set, and data from various faults of the powertrain system are selected as the test set. The isolated forest algorithm is then used to calculate the anomaly score for each sample. The specific method is as follows: First, based on the obtained feature encoding dataset For the dataset The data is divided into two parts, and the data from the normal operation of the powertrain system is used as the training set. The various fault data of the powertrain system are used as a test set. : ; in, For the first Feature encoding dataset for class-specific faults.

[0029] Secondly, based on the training set The Isolation Forest algorithm is used to construct multiple random trees, resulting in a trained multi-random tree model and anomaly scores on the training set. An Isolation Forest consists of multiple random trees, each independently constructed using a random subset of the training set.

[0030] Finally, the test set The anomaly score for each input sample is calculated using the pre-trained model. The outlier score of the test set is obtained by using the average path length of the test set in each tree. This reflects the degree to which a sample is easily isolated.

[0031] Calculate each input sample abnormal scores : ; ; ; in, The total number of training samples; This is a normalization factor for the average path length of normal samples. For harmonic numbers, is the Euler-Marcheroni constant, with an approximate value of 0.5772.

[0032] Specifically, in S3, based on the calculated anomaly score for each sample, a min-max normalization method is used to map the anomaly score to the [0,1] interval, obtaining a health index that reflects the state of the powertrain system represented by the sample, and constructing the original health index curve that changes over time. The specific method is as follows: First, after obtaining the anomaly score for each sample, these scores are transformed into a more intuitive health index using a min-max normalization method. Map abnormal scores uniformly to the interval [0,1]: ; in, The outlier score for the sample; The minimum of all abnormality scores among all samples; This represents the maximum abnormal score among all samples.

[0033] Secondly, based on the time-varying trend of the power transmission system, the health index is extracted into an original health index curve.

[0034] Specifically, in S4, based on the obtained original health index curve, the exponentially weighted moving average method is used to handle local fluctuations and sampling errors, resulting in a health assessment curve showing the true change of the system's health status over time. Relevant indicators used to evaluate the effectiveness of the powertrain system's health index curve are then statistically analyzed. The specific method is as follows: First, based on the obtained original health index curve, the following methods are used: The exponentially weighted moving average method is used to calculate a health assessment curve by weighting time series data.

[0035] in The original health index, The health index is a weighted average. As a smoothing factor, , When the value is large, recent data has a larger weight, and the model reacts more quickly to changes in new data; when When the value is small, the weight of long-term data is relatively large, the model focuses more on the long-term trend of the data, and is less sensitive to short-term fluctuations.

[0036] As a preferred embodiment of this invention, such as Figure 4 As shown, the health index of cylinder compression ratio reduction failure gradually decreased from about 0.9 to about 0.2. Overall, the degradation process was approximately linear, showing a uniform downward trend.

[0037] Then, a 15dB noise was added to the cylinder compression ratio reduction fault signal, such as... Figure 5 As shown, a comparison with the health index curve under noise-free conditions reveals that as the noise level increases, the fluctuation of the fitted HI curve increases; however, the overall degradation trend remains quite obvious, and no abnormal trend has been observed.

[0038] Secondly, after obtaining the health assessment curve, the effectiveness of the health status results is quantitatively assessed using monotonicity, robustness, and trend indicators.

[0039] Furthermore, the performance degradation of a powertrain system caused by equipment damage is usually irreversible. Therefore, an ideal health indicator should exhibit monotonicity: ; in, The health value of the powertrain system is represented by an instantaneous sampling point on the health assessment curve. The length of the health assessment curve; The derivative of adjacent health values, The positive and negative signs represent the positive and negative values.

[0040] In the actual operation of a powertrain system, sensor signals are susceptible to external factors such as noise disturbances and fluctuations in operating conditions, leading to potential variability in measurement results. Therefore, health assessment methods must possess strong robustness. ; in, For the power transmission system in Health value at any given time; The length of the health assessment curve; In order to be in The average trend value at any given time.

[0041] As the operating time of a powertrain system increases, its health typically deteriorates gradually. The correlation between operating time and health status can be used to measure trends in health indicators. ; Example 2 This embodiment verifies the effectiveness of the invention by combining a diesel engine fault element dataset. To verify the effectiveness and advantages of the health status assessment method proposed in this invention, three representative classical assessment methods—principal component analysis (PCA), self-organizing map network (SOM), and Gaussian mixture model (GMM)—are selected for comparative analysis.

[0042] like Figure 6 As shown, the health status of cylinder compression ratio reduction faults under 0dB conditions was assessed and the EWMA curves were fitted. Monotonicity, robustness, and trend were calculated and compared. Table 1 shows the evaluation index results of the four health status assessments: Table 1 Comparison of Fault Assessment Indicators for Reduced Cylinder Compression Ratio

[0043] In summary, the powertrain health assessment method based on isolated forests demonstrates superior performance in identifying early degradation and minor anomalies. Furthermore, it exhibits greater stability in assessing severe failure stages, providing a clearer and more intuitive reflection of the equipment's health degradation trend. This significantly outperforms traditional methods under nonlinear conditions.

[0044] Example 3 A powertrain health assessment based on isolated forests includes: The signal acquisition and dataset establishment module is used to acquire detection signals from the power transmission system, divide the acquired monitoring signals into samples, extract multidimensional statistical features of each sample, and numerically encode the location of the features. It uses fuzzy C-means clustering and elbow rule to discretize continuous features, extract structural information, establish a feature location-feature structure encoding framework, and obtain a feature encoding dataset. The anomaly score calculation module is used to select the normal operation data of the power transmission system as the training set and the various fault data of the power transmission system as the test set based on the obtained feature encoding dataset, and to calculate the anomaly score of each sample using the isolated forest algorithm. The system health index construction module is used to map the calculated abnormal score of each sample using a minimum-maximum normalization method to obtain a health index that reflects the state of the power transmission system represented by the sample, and to construct the original health index curve that changes over time. The evaluation module is used to process local fluctuations and sampling errors based on the obtained original health index curve using the exponentially weighted moving average method, to obtain a health assessment curve of the actual change of the system health status over time, and to statistically analyze relevant indicators used to evaluate the effectiveness of the powertrain system health index curve.

[0045] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for health assessment of a powertrain system based on isolated forests, characterized in that, Includes the following steps: Sensor monitoring signals from the power transmission system are collected, the collected sensor monitoring signals are divided into samples, multidimensional statistical features of each sample are extracted, and the location of the features is numerically encoded. Continuous features are discretized using fuzzy C-means clustering and the elbow rule, structural information is extracted, and a feature location-feature structure encoding framework is established to obtain the feature encoding dataset. Based on the obtained feature encoding dataset, the data of normal operation of the power transmission system is selected as the training set, and the data of various faults of the power transmission system are selected as the test set. The anomaly score of each sample is calculated using the isolated forest algorithm. Based on the calculated anomaly score of each sample, a minimum-maximum normalization method is used for mapping to obtain a health index that reflects the state of the power transmission system represented by the sample, and an original health index curve that changes over time is constructed. Based on the obtained original health index curve, the exponential weighted moving average method is used to process local fluctuations and sampling errors, and a health assessment curve of the actual change of the system health status over time is obtained. Relevant indicators for evaluating the effectiveness of the power transmission system health index curve are also statistically analyzed. In the step of extracting structural information, establishing a feature location-feature structure encoding framework, and obtaining the feature encoding dataset, the established feature location-feature structure encoding framework is as follows: ； in, This is a feature encoding dataset for the power transmission system. For each sample in the feature encoding dataset, each sample contains n statistical features. This is the nth statistical feature; For the characteristic location, For characteristic structure; Based on the obtained original health index curve, the exponentially weighted moving average method is used to process local fluctuations and sampling errors, resulting in a health assessment curve showing the true change of the system's health status over time. The specific methods for statistically evaluating the effectiveness of the powertrain system's health index curve are as follows: Based on the obtained original health index curve, the following was adopted: The exponentially weighted moving average method is used to calculate a health assessment curve by weighting time series data. in The original health index, The health index is a weighted average. It is a smoothing factor; Based on the obtained health assessment curves, the effectiveness of health status outcomes is quantitatively assessed using monotonicity, robustness, and trend indicators.

2. The method for health assessment of a powertrain system based on isolated forests according to claim 1, characterized in that, The specific method for discretizing continuous features using fuzzy C-means clustering and the elbow rule is as follows: Fuzzy C-means clustering is used to calculate the membership degree between continuous features and each cluster center, and the elbow rule is used to calculate... Determine the optimal number of cluster centers to achieve feature discretization: ； in, These are continuous feature points; As cluster center; For the first i One cluster; This represents the square of the Euclidean distance from a feature point to its corresponding cluster center.

3. The method for health assessment of a powertrain system based on isolated forests according to claim 1, characterized in that, The specific method for the step of selecting normal operation data of the power transmission system as the training set and various fault data of the power transmission system as the test set based on the obtained feature encoding dataset, and calculating the anomaly score of each sample using the isolated forest algorithm is as follows: Based on the obtained feature encoding dataset For the dataset The data is divided into two parts, and the data from the normal operation of the powertrain system is used as the training set. The various fault data of the powertrain system are used as a test set. ; Based on training set Multiple random trees are constructed using the isolated forest algorithm to obtain a trained multiple random tree model and anomaly scores in the training set; Test set The anomaly score for each input sample is calculated using the pre-trained model. The outlier score of the test set is obtained by using the average path length of the test set in each tree. This reflects the degree to which a sample is easily isolated.

4. The method for health assessment of a powertrain system based on isolated forests according to claim 3, characterized in that, Calculate each input sample abnormal scores The method is as follows: ； ； ； in, The total number of training samples; This is a normalization factor for the average path length of normal samples. For harmonic numbers, is the Euler-Marcheroni constant, with an approximate value of 0.5772.

5. The method for health assessment of a powertrain system based on isolated forests according to claim 4, characterized in that, The specific method for the step of mapping the calculated anomaly score of each sample using a minimum-maximum normalization method to obtain a health index that reflects the state of the power transmission system represented by the sample, and constructing the original health index curve over time, is as follows: After obtaining the anomaly score for each sample, these scores are converted into a health index using a min-max normalization method. Map abnormal scores uniformly to the interval [0,1]: ; in, The outlier score for the sample; The minimum of all abnormality scores among all samples; The maximum value among all abnormal scores; Based on the time-varying trend of the power transmission system, the health index is extracted into an original health index curve.

6. The method for health assessment of a powertrain system based on isolated forests according to claim 5, characterized in that, The following are methods for using monotonicity indicators to quantitatively assess the effectiveness of health status outcomes: ； in, This represents the health value of the powertrain system. The length of the health assessment curve; The derivative of adjacent health values, The positive and negative signs represent the positive and negative values; The following are methods for using robust indicators to quantitatively assess the effectiveness of health status outcomes: ； in, For the power transmission system in Health value at any given time; In order to be in The average trend value at any given time.

7. The method for health assessment of a powertrain system based on isolated forests according to claim 6, characterized in that, The following are methods for using trend indicators to quantitatively assess the effectiveness of health status outcomes: 。 8. A powertrain health assessment system based on isolated forests, based on the powertrain health assessment method based on isolated forests as described in any one of claims 1 to 7, characterized in that, include: The signal acquisition and dataset establishment module is used to acquire sensor monitoring signals of the power transmission system, divide the acquired sensor monitoring signals into samples, extract multidimensional statistical features of each sample, and numerically encode the location of the features. It uses fuzzy C-means clustering and elbow rule to discretize continuous features, extract structural information, establish a feature location-feature structure encoding framework, and obtain a feature encoding dataset. The anomaly score calculation module is used to select the normal operation data of the power transmission system as the training set and the various fault data of the power transmission system as the test set based on the obtained feature encoding dataset, and to calculate the anomaly score of each sample using the isolated forest algorithm. The system health index construction module is used to map the calculated abnormal score of each sample using a minimum-maximum normalization method to obtain a health index that reflects the state of the power transmission system represented by the sample, and to construct the original health index curve that changes over time. The evaluation module is used to process local fluctuations and sampling errors based on the obtained original health index curve using the exponentially weighted moving average method, to obtain a health assessment curve of the actual change of the system health status over time, and to statistically analyze relevant indicators used to evaluate the effectiveness of the powertrain system health index curve.

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