A multi-stage health state evaluation method based on wind turbine SCADA signal data

Abstract

The application discloses a kind of multistage health state evaluation method based on wind turbine SCADA signal data.Collect and pre-process temperature, power, pressure, angle and speed and other SCADA operating data, construct parameter layer, component layer and whole machine layer three-level health state evaluation index system;Through correlation analysis, skewness analysis and operation mechanism checking, screen key indicators, and use corresponding single degradation function to map the index to the [0,1] interval;Using the analytic hierarchy process and entropy weight method combination weighting, obtain component comprehensive degradation degree, component health degree, whole machine comprehensive degradation degree and whole machine health degree step by step;According to health grade membership degree and engineering correction rule, determine health grade, and identify dominant weak components according to component weighted degradation contribution.The application can evaluate different dimension operating parameters, identify local degradation and trace abnormal source, and can be used for wind turbine condition monitoring, fault warning and operation and maintenance.

Description

Technical Field

[0001] This invention relates to the field of wind power equipment condition monitoring and fault early warning technology, specifically to a multi-level health status assessment method based on SCADA signal data of wind turbine generators. Background Technology

[0002] With the continuous expansion of new energy installed capacity, wind turbines are increasingly widely used in power systems. Wind turbines typically operate in complex environments such as strong winds, low temperatures, high humidity, freezing, and dust storms. They comprise multiple functional systems, including pitch control, converter grid connection, generator, yaw, hydraulic braking, and control and monitoring systems. Over long periods, thermal stress, mechanical wear, electromagnetic stress, and control execution deviations gradually accumulate, potentially leading to a degradation in the wind turbine's operating condition. This, in turn, affects the wind turbine's power generation capacity, operational safety, and grid connection capabilities.

[0003] The SCADA system of wind turbines can continuously collect operating parameters such as temperature, power, pressure, angle, and speed during wind turbine operation, providing a data foundation for wind turbine condition monitoring and fault early warning. Existing wind turbine health status assessment methods typically determine whether an anomaly has occurred based on whether a single or a few SCADA operating parameters exceed preset thresholds. These methods usually only trigger alarms after operating parameters have clearly exceeded limits, making it difficult to promptly identify the gradual deviation of parameters and the gradual degradation of components before a fault occurs.

[0004] Meanwhile, wind turbine SCADA operating parameters are numerous, and these parameters differ in dimensions, numerical ranges, directions of change, and physical meanings. Furthermore, some operating parameters exhibit strong correlations. Directly using all SCADA operating parameters for health status assessment can easily lead to indicator redundancy, increasing the complexity of the health status assessment process, and potentially causing some duplicate information to unnecessarily affect the assessment results.

[0005] Furthermore, existing health status assessment methods typically analyze individual parameters or components, lacking a hierarchical correspondence between parameters / components and the entire turbine. This makes it difficult to integrate the operating states of different components into a unified overall health status of the wind turbine. Even if some methods can output a health score or health level for the entire turbine, it is difficult to further determine which component or operating parameter is primarily responsible for the decline in overall health status. This results in insufficient traceability and interpretability of the evaluation results, making it difficult to provide a clear basis for on-site operation and maintenance.

[0006] In the process of health status assessment, the method of determining the weights of each evaluation indicator also affects the evaluation results. Using fixed weights or only subjective weighting methods may fail to fully reflect the differences between different sample data; using only objective weighting methods may ignore the operating mechanism of wind turbine units, failure risks, and engineering experience. Therefore, a single weighting method is difficult to take into account both engineering experience and sample data characteristics.

[0007] Therefore, there is a need to provide a multi-level health status assessment method based on SCADA signal data of wind turbine units. On the basis of screening and uniformly quantifying SCADA operation data, a hierarchical evaluation relationship is established between the parameter layer, component layer and whole machine layer to realize the step-by-step fusion of the health status of wind turbine units, the determination of health level and the identification of the main weak components, thereby improving the completeness and interpretability of the health status assessment results. Summary of the Invention

[0008] This invention addresses the problems existing in the prior art by providing a multi-level health status assessment method based on SCADA signal data of wind turbine units. This method solves the problems of existing wind turbine health status assessment methods, such as over-reliance on a single threshold, redundancy in evaluation indicators, difficulty in uniformly evaluating operating parameters with different dimensions and different directions of change, difficulty in integrating health information of different components into the overall health status, and difficulty in tracing the overall evaluation results to specific weak components.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows: S1. Collect SCADA operation data during the operation of the wind turbine, and preprocess the SCADA operation data to obtain a valid sample dataset.

[0010] Specifically, temperature, power, pressure, angle, and speed parameters are collected during the operation of the wind turbine. Data from wind turbine shutdown, power-limited operation, communication anomalies, and obvious defects are removed from the collected SCADA operation data. Missing and outlier values ​​in the removed SCADA operation data are cleaned to obtain a valid sample dataset for health status assessment.

[0011] S2. Based on the correspondence between SCADA operating parameters and wind turbine components in the effective sample dataset, a three-level health status evaluation index system including parameter layer, component layer and whole machine layer is constructed.

[0012] Specifically, SCADA operating parameters are categorized according to the pitch system, converter grid-connected system, generator system, yaw system, and hydraulic braking system. Indicators characterizing specific operating variables are defined as parameters at the parameter level; the pitch system, converter grid-connected system, generator system, yaw system, and hydraulic braking system are defined as evaluation objects at the component level; and the wind turbine as a whole is defined as the evaluation object at the turbine-wide level. This establishes a hierarchical correspondence between SCADA operating parameters, wind turbine components, and the wind turbine as a whole.

[0013] To reflect the thermal state differences within the converter grid-connected system, the highest temperature of the IGBT power module on the machine side of converter 1 is subtracted from the highest temperature of the corresponding IGBT power module on the grid side of converter 1 to obtain the IGBT temperature difference between the machine and grid sides of converter 1; similarly, the highest temperature of the IGBT power module on the machine side of converter 2 is subtracted from the highest temperature of the corresponding IGBT power module on the grid side of converter 2 to obtain the IGBT temperature difference between the machine and grid sides of converter 2.

[0014] To reflect the local thermal state of the generator windings and stator, the maximum value was selected from the 12 temperature measurement points of the generator segment windings to obtain the highest temperature of the generator windings; the maximum value was selected from the 12 temperature measurement points of the generator stator to obtain the highest temperature of the generator stator.

[0015] The IGBT temperature difference on the grid side of converter No. 1, the IGBT temperature difference on the grid side of converter No. 2, the maximum temperature of the generator winding, the maximum temperature of the generator stator, and the SCADA operating parameters classified according to the components of the wind turbine are used as candidate indicators in the parameter layer.

[0016] S3 performs Pearson correlation analysis and skewness analysis on the candidate indicators in the parameter layer, and selects key indicators from the candidate indicators by combining the wind turbine operation mechanism, fault mapping relationship, data quality and model interpretability.

[0017] Specifically, the Pearson correlation coefficient between any two candidate indicators is calculated, and the redundancy relationship between the candidate indicators is identified based on the Pearson correlation coefficient; the skewness of each candidate indicator is calculated, and the direction and degree of the sample distribution of the corresponding candidate indicator shifting towards higher or lower values ​​are determined based on the skewness.

[0018] Based on the redundancy relationships among candidate indicators and the offset direction and degree of the candidate indicator sample distribution, and in conjunction with the wind turbine operating mechanism, fault mapping relationship, data quality, and model interpretability, key indicators for health status assessment are determined from the candidate indicators. For candidate indicators that meet the preset strong correlation conditions but represent different risk dimensions, the corresponding candidate indicators are retained to avoid missing different types of operational risks during the process of eliminating redundant information.

[0019] S4. Based on the physical meaning of each key indicator, the key indicators are divided into smaller and better indicators and intermediate best indicators. A single degradation function corresponding to the indicator type is used to map each key indicator to the [0,1] interval to obtain the single degradation degree of each key indicator.

[0020] For indicators where smaller is better, when the current value of the indicator is less than or equal to the upper limit of the healthy range, the corresponding single degree of degradation is set to 0; when the current value of the indicator is greater than or equal to the degradation threshold, the corresponding single degree of degradation is set to 1; when the current value of the indicator is between the upper limit of the healthy range and the degradation threshold, the corresponding single degree of degradation is linearly increased from 0 to 1 as the current value of the indicator increases.

[0021] For intermediate-optimal indicators, when the current value of the indicator is less than or equal to the left boundary threshold or greater than or equal to the right boundary threshold, the corresponding single degradation degree is set to 1; when the current value of the indicator is equal to the optimal value or the center value, the corresponding single degradation degree is set to 0; when the current value of the indicator is between the left boundary threshold and the optimal value or the center value, the corresponding single degradation degree is linearly reduced from 1 to 0 as the current value of the indicator increases; when the current value of the indicator is between the optimal value or the center value and the right boundary threshold, the corresponding single degradation degree is linearly increased from 0 to 1 as the current value of the indicator increases.

[0022] In this system, a single degradation degree of 0 indicates that the corresponding key indicator is in a healthy or optimal state, while a single degradation degree of 1 indicates that the corresponding key indicator deviates from the normal state to the greatest extent. Through single degradation degree mapping, key indicators with different dimensions, different numerical ranges, and different directions of change are transformed into evaluation data with a unified value range and a unified degradation direction.

[0023] S5. For multiple key indicators corresponding to the same component, the analytic hierarchy process is used to determine the subjective weight of each key indicator, the entropy weight method is used to determine the objective weight of each key indicator, and the subjective and objective weights are combined to obtain the combined weight of each key indicator.

[0024] Specifically, the individual degradation degrees of each key indicator corresponding to the same component are used to form a parameter-level degradation degree vector for that component. The analytic hierarchy process (AHP) is then used to determine the subjective weights corresponding to each individual degradation degree in the parameter-level degradation degree vector, thus obtaining a subjective weight vector.

[0025] The information entropy of each key indicator is calculated using the entropy weight method. The difference between 1 and the information entropy of each key indicator is determined as the indicator redundancy of the corresponding key indicator. The objective weight of each key indicator is determined based on the indicator redundancy of each key indicator.

[0026] The combined weight of a key indicator is obtained by adding the product of its subjective weight and subjective weight coefficient to the product of its objective weight and objective weight coefficient. The sum of the subjective and objective weight coefficients is 1, and both are located in the interval [0,1].

[0027] S6. The overall degradation degree of the corresponding component is obtained by weighting and fusing the individual degradation degree and combined weight of each key indicator corresponding to the same component, and the component health degree of the corresponding component is obtained based on the overall degradation degree of the component.

[0028] Specifically, the individual degradation degree and combined weights of each key indicator corresponding to the same component are weighted and summed to obtain the overall degradation degree of the corresponding component; the difference between 1 and the overall degradation degree of the component is determined as the component health degree of the corresponding component. Thus, the overall degradation degree and component health degree of the pitch system, converter grid-connected system, generator system, yaw system, and hydraulic braking system are obtained respectively.

[0029] S7. The overall deterioration degree of each component and the corresponding weight of the whole unit are weighted and integrated to obtain the overall deterioration degree of the wind turbine, and the overall health degree of the whole unit is obtained based on the overall deterioration degree of the whole unit.

[0030] Specifically, the preset component weights for the pitch system, converter grid connection system, generator system, yaw system, and hydraulic braking system are obtained respectively, forming a component weight vector, and the sum of the preset component weights for each component is set to 1. The overall degradation degree of each component and its corresponding preset component weight are weighted and summed to obtain the overall degradation degree of the whole machine; the difference between 1 and the overall degradation degree of the whole machine is determined as the overall health degree of the whole machine.

[0031] S8. Based on the component weight and overall degradation degree of each component at the whole machine level, determine the weighted degradation contribution of each component to the overall degradation, and identify the component with the largest weighted degradation contribution as the dominant weak component.

[0032] Specifically, the weight of each component at the whole machine level is calculated by multiplying it by the overall degradation degree of the corresponding component at the current moment to obtain the weighted degradation contribution of each component at the current moment; the weighted degradation contribution of each component at the current moment is compared, and the component with the largest weighted degradation contribution is identified as the dominant weak component at the current moment, so as to identify the component that contributes the most to the decline in the overall health status of the machine.

[0033] S9. The overall deterioration degree of the entire unit is used as the health level determination variable. The membership degree of the current state of the wind turbine to each health level is calculated according to the membership function corresponding to each health level. The health status membership vector is obtained, and the health level of the wind turbine is determined according to the health status membership vector.

[0034] Specifically, the health levels of wind turbine generators are set as healthy, sub-healthy, early warning, and faulty. Based on the membership functions corresponding to healthy, sub-healthy, early warning, and faulty states, the membership degree of the current state of the wind turbine generator to each health level is calculated, resulting in a health state membership vector. Based on the principle of maximum membership degree, the health level corresponding to the maximum membership degree in the health state membership vector is determined as the initial health level.

[0035] When a key thermal risk indicator used to characterize the thermal state of a component reaches a corresponding preset extreme anomaly threshold, the health level of the wind turbine is corrected to a fault. When the maximum and second-largest membership degrees in the health status membership vector are close, the initial health level is corrected based on the comprehensive deterioration degree of the dominant weak component to obtain the health level of the wind turbine.

[0036] S10 outputs the health status assessment results of the wind turbine.

[0037] The health status assessment results include the overall deterioration degree of the entire unit, the overall health degree, the health level, the component health degree of each component, the individual deterioration degree of each key indicator, and the dominant weak component. By simultaneously outputting the evaluation results at the overall unit level, component level, and parameter level, the health status of the wind turbine unit can be traced step by step from the overall unit level to the component level and parameter level.

[0038] Compared with the prior art, the present invention has the following beneficial effects: First, this invention categorizes the SCADA operating parameters of wind turbines according to the pitch system, converter grid connection system, generator system, yaw system, and hydraulic braking system, and constructs a three-level health status evaluation index system at the parameter level, component level, and whole machine level. This system can reflect the operating status of wind turbines from multiple levels and reduce the one-sidedness caused by using a single parameter or single component for evaluation.

[0039] Second, this invention identifies redundant relationships between candidate indicators through Pearson correlation analysis, determines the direction and degree of deviation in the distribution of candidate indicator samples through skewness analysis, and selects key indicators by combining wind turbine operation mechanism, fault mapping relationship, data quality and model interpretability. This helps to reduce the impact of redundant indicators on health status evaluation results, while retaining operation information that represents different risk dimensions.

[0040] Third, this invention sets a single degradation function for the smaller the better type of index and the intermediate optimal type of index, and maps key indicators with different dimensions, different numerical ranges and different directions of change to the [0,1] interval, so that different types of SCADA operating parameters can be integrated under a unified evaluation scale.

[0041] Fourth, this invention combines the subjective weights determined by the analytic hierarchy process (AHP) with the objective weights determined by the entropy weight method, so that the weights of key indicators simultaneously reflect the operating mechanism of the wind turbine and the differences in sample data. Through the step-by-step weighted fusion of parameter layer, component layer and whole machine layer, the comprehensive degradation degree of components, the health degree of components, the comprehensive degradation degree of the whole machine and the health degree of the whole machine are obtained.

[0042] Fifth, this invention determines the weighted degradation contribution of each component to the overall degradation by calculating the product of the component weight at the whole machine level and the overall degradation degree. The component with the largest weighted degradation contribution is identified as the dominant weak component. This can further identify the component that contributes the most to the decline in the overall health status of the machine, in addition to the overall health status of the machine, and reduce the masking of local component degradation by the overall evaluation results of the machine.

[0043] Sixth, this invention determines the initial health level through the health level membership function and the maximum membership principle, and corrects the initial health level by combining key thermal risk indicators and the comprehensive deterioration degree of the dominant weak components, which helps to reduce the deviation caused by judging the health level based on a single threshold or a single comprehensive score.

[0044] Seventh, this invention simultaneously outputs the overall deterioration degree of the entire machine, the overall health degree, the health level, the component health degree of each component, the individual deterioration degree of each key indicator, and the dominant weak component, so that the overall health status can be further traced back to the component level and parameter level, which is conducive to improving the interpretability of the health status evaluation results and providing a basis for wind turbine condition monitoring, fault early warning and operation and maintenance. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 This is a flowchart of a multi-level health status assessment method based on SCADA signal data of wind turbine generators, provided by an embodiment of the present invention. Figure 2 This is a schematic diagram of the three-level health status assessment model of parameter layer, component layer and whole machine layer provided in the embodiments of the present invention; Figure 3 This is a membership function graph of the health level determination rules provided in the embodiments of the present invention; Figure 4 This is a schematic diagram illustrating the number of cases for each fault category and the model recognition effect provided in the embodiments of the present invention, wherein, Figure 4 (a) is a diagram showing the number of samples for each fault category. Figure 4 (b) is a schematic diagram illustrating the model recognition performance for each fault category; Figure 5 This is a trend graph showing the change in the health status of each component over time in a typical fault case provided in the embodiments of the present invention. Detailed Implementation

[0047] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention. It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application.

[0048] Example 1 This embodiment provides a multi-level health status assessment method based on wind turbine SCADA signal data, the overall process of which is as follows: Figure 1 As shown, the multi-level health status assessment relationship between the parameter layer, component layer, and system layer is as follows: Figure 2 As shown. The method specifically includes the following steps.

[0049] S1. Collect SCADA operation data during the operation of the wind turbine, and preprocess the SCADA operation data to obtain a valid sample dataset.

[0050] In this embodiment, the collected SCADA operating data includes temperature parameters, power parameters, pressure parameters, angle parameters, and rotational speed parameters.

[0051] Data from wind turbine shutdown periods, power-limited operation periods, communication anomalies, and obvious defects were removed from the collected SCADA operational data. Missing and outlier values ​​in the remaining SCADA operational data were then cleaned to obtain a valid sample dataset for health status assessment.

[0052] By removing data from shutdowns, power limitations, communication anomalies, and obvious defects, the impact of abnormal operating conditions and data acquisition anomalies on subsequent health status assessment results is reduced.

[0053] S2. Based on the correspondence between SCADA operating parameters and wind turbine components in the effective sample dataset, a three-level health status evaluation index system including parameter layer, component layer and whole machine layer is constructed.

[0054] Specifically, SCADA operating parameters are assigned to the pitch system, converter grid connection system, generator system, yaw system, and hydraulic braking system.

[0055] The operating parameters for the pitch control system include the pitch control cabinet temperature and the pitch angles of the three blades. The pitch control cabinet temperature characterizes the thermal state of the pitch control cabinet, and the pitch angles of the three blades characterize the pitch execution status of each blade.

[0056] The operating parameters of the converter grid-connected system include active power, reactive power, converter cabinet temperature, maximum temperature of the converter machine-side IGBT power module, and maximum temperature of the converter grid-side IGBT power module.

[0057] The operating parameters of the generator system include the inner ring temperature of the generator bearing, the outer ring temperature of the generator bearing, the magnet temperature, the cooling water temperature, the temperature of the generator segmented windings, the generator stator temperature, and the generator speed.

[0058] The operating parameters of the yaw system include the yaw cable twist angle, which is used to characterize the operating status of the yaw system.

[0059] The operating parameters of a hydraulic braking system include hydraulic pressure parameters, hydraulic station oil temperature, and brake disc temperature, which are used to characterize the pressure and thermal states of the hydraulic braking system.

[0060] Based on the above SCADA operating parameters, in order to more sensitively reflect the thermal state differences within the converter grid-connected system, the highest temperature of the IGBT power module on the machine side of converter 1 is subtracted from the corresponding highest temperature of the IGBT power module on the grid side of converter 1, and the temperature difference between the IGBT on the machine side and the grid side of converter 1 is obtained according to formula (1); the highest temperature of the IGBT power module on the machine side of converter 2 is subtracted from the corresponding highest temperature of the IGBT power module on the grid side of converter 2, and the temperature difference between the IGBT on the machine side and the grid side of converter 2 is obtained according to formula (2): (1) (2) in, , These represent the highest temperatures of the IGBT power modules on the machine side of converters No. 1 and No. 2, respectively. , These represent the highest temperatures of the grid-side IGBT power modules for converters 1 and 2, respectively. A higher value indicates a more pronounced inconsistency in the thermal state within the corresponding converter unit.

[0061] When the temperature difference between the IGBTs on the generator and grid sides of the converter increases, it indicates that the thermal state difference between the generator side and the grid side inside the converter unit is increasing.

[0062] To reflect the local overheating state of the generator windings, the maximum value was selected from the temperature measurement points of 12 generator section windings, and the highest temperature of the generator windings was obtained according to formula (3): (3) in, Indicates the first Temperature measurement values ​​of each generator section winding ( =1,2,…,12). Taking the maximum temperature of each segment of the winding allows for more sensitive detection of local overheating phenomena.

[0063] The most unfavorable thermal state of the generator winding is characterized by selecting the maximum value among the temperature measurement points of each segment of the winding.

[0064] The maximum value is selected from the 12 generator stator temperature measurement points, and the highest generator stator temperature is obtained according to formula (4): (4) in, Indicates the first Temperature values ​​at each generator stator measuring point ( =1,2,…,12). This index is used to characterize the most unfavorable thermal state of the generator stator section.

[0065] The most unfavorable thermal state of the generator stator is characterized by selecting the maximum value among the temperature measurement points of each generator stator: The IGBT temperature difference on the grid side of converter No. 1, the IGBT temperature difference on the grid side of converter No. 2, the maximum temperature of the generator winding, the maximum temperature of the generator stator, and the SCADA operating parameters classified according to the components of the wind turbine are used as candidate indicators in the parameter layer.

[0066] When constructing a three-level health status evaluation index system, candidate indicators that characterize specific operating variables are determined as indicators at the parameter level, the pitch system, converter grid connection system, generator system, yaw system, and hydraulic braking system are determined as evaluation objects at the component level, and the wind turbine as a whole is determined as the evaluation object at the whole unit level.

[0067] Therefore, the attribution relationship between parameter-level indicators and component-level evaluation objects is established, and the correspondence between component-level evaluation objects and whole-machine-level evaluation objects is further established. As shown in Table 1, the wind turbine health status evaluation system: Table 1

[0068] S3 performs Pearson correlation analysis and skewness analysis on the candidate indicators in the parameter layer, and selects key indicators from the candidate indicators by combining the wind turbine operation mechanism, fault mapping relationship, data quality and model interpretability.

[0069] Specifically, for any two candidate indicators, the Pearson correlation coefficient between the two candidate indicators is calculated according to formula (5), and the linear correlation and redundancy relationship between the candidate indicators is identified based on the Pearson correlation coefficient: (5) in, Representing variables With variables The Pearson correlation coefficient; and Indicates the first The values ​​of each sample point; and Representing variables respectively With variables The sample mean; For sample size.

[0070] A high Pearson correlation coefficient between two candidate indicators indicates a strong linear correlation between them. For candidate indicators with strong correlation, the decision to retain them should be based on the corresponding component, physical meaning, and risk dimension.

[0071] When two highly correlated candidate indicators characterize different risk dimensions, both candidate indicators are retained. For example, although two temperature indicators are highly correlated, if they are used to characterize the thermal state of different locations or components, the two temperature indicators can reflect different operational risks, and therefore can be retained simultaneously.

[0072] The skewness of each candidate indicator is calculated according to formula (6), and the direction and degree of the sample distribution of the corresponding candidate indicator shifting towards higher or lower values ​​are determined based on the skewness: (6) in, Indicates sample skewness. The sample mean. The standard deviation of the sample is 1. For sample size.

[0073] Positive skewness reflects the shift of the sample distribution of candidate indicators towards higher values, while negative skewness reflects the shift of the sample distribution of candidate indicators towards lower values.

[0074] Based on the redundancy relationships among candidate indicators, the offset direction and degree of the candidate indicator sample distribution, and in combination with the wind turbine operating mechanism, fault mapping relationship, data quality and model interpretability, key indicators for entering the health status assessment process are determined from the candidate indicators.

[0075] S4. Based on the physical meaning of each key indicator, the key indicators are divided into smaller and better indicators and intermediate best indicators. A single degradation function corresponding to the indicator type is used to map each key indicator to the [0,1] interval to obtain the single degradation degree of each key indicator.

[0076] The individual degradation degree of each key indicator satisfies formula (7): (7) A single degradation level of 0 indicates that the corresponding key indicator is in a healthy or optimal state, while a single degradation level of 1 indicates that the corresponding key indicator deviates from the normal state to the greatest extent.

[0077] For temperature-related and thermal risk-related indices where smaller values ​​are better, a single degradation function as shown in formula (8) is used: (8) in, The current value of the parameter. This represents the upper limit of the healthy range. This is the degradation threshold.

[0078] When the current value of the smaller the better indicator is less than or equal to the upper limit of the healthy range, the corresponding single degradation degree is set to 0; when the current value of the indicator is greater than or equal to the degradation threshold, the corresponding single degradation degree is set to 1; when the current value of the indicator is between the upper limit of the healthy range and the degradation threshold, the corresponding single degradation degree is linearly increased from 0 to 1 as the current value of the indicator increases.

[0079] In this embodiment, the temperature of the pitch control cabinet, the temperature inside the converter cabinet, the maximum temperature of the IGBT power module on the converter machine side, the maximum temperature of the IGBT power module on the converter grid side, the temperature of the inner ring of the generator bearing, the temperature of the outer ring of the generator bearing, the temperature of the magnet, the temperature of the cooling water, the maximum temperature of the generator winding, the maximum temperature of the generator stator, the temperature of the hydraulic station oil, and the temperature of the brake disc are mapped using a single degradation degree function corresponding to the smaller the better type of index.

[0080] For the intermediate optimal indices of pressure, angle, and power, the single degradation function shown in formula (9) is adopted: (9) in, The current value of the parameter. and These are the left and right boundary thresholds, respectively. It is the optimal or central value.

[0081] When the current value of the intermediate optimal type indicator is less than or equal to the left boundary threshold, or greater than or equal to the right boundary threshold, the corresponding single degradation degree is determined to be 1; when the current value of the indicator is equal to the optimal value or the center value, the corresponding single degradation degree is determined to be 0.

[0082] When the current value of the indicator is between the left boundary threshold and the optimal or central value, the corresponding single degradation degree is linearly reduced from 1 to 0 as the current value of the indicator increases; when the current value of the indicator is between the optimal or central value and the right boundary threshold, the corresponding single degradation degree is linearly increased from 0 to 1 as the current value of the indicator increases.

[0083] In this embodiment, the pitch angle of the three blades, the yaw cable twist angle, the hydraulic pressure parameters, the active power and the reactive power are mapped using a single degradation function corresponding to the intermediate optimal index.

[0084] Through the above single degradation degree mapping, key indicators with different dimensions, numerical ranges, and directions of change are converted into a single degradation degree with a unified value range and consistent degradation direction. The single degradation degree function types and applicable parameters are shown in the table below: Table 2

[0085] S5, combine the individual degradation degrees of each key indicator corresponding to the same component into a parameter layer degradation degree vector for the corresponding component.

[0086] For the k-th component, the individual degradation degree of each key indicator corresponding to the component is used to form a parameter layer degradation degree vector according to formula (10): (10) in, Indicates the first The first component The single degradation degree after parameter mapping.

[0087] The parameter layer degradation vector of the pitch system is constructed according to formula (11). The parameter layer degradation vector includes the single degradation degree corresponding to the pitch control cabinet temperature and the single degradation degree corresponding to the pitch angle of the three blades respectively. (11) The parameter layer degradation vector of the converter grid-connected system is constructed according to formula (12): (12) The parameter layer degradation vector includes individual degradation degrees corresponding to active power, reactive power, converter cabinet temperature, converter machine-side IGBT power module maximum temperature, converter grid-side IGBT power module maximum temperature, and converter machine-grid-side IGBT temperature difference.

[0088] The parameter layer degradation vector of the generator system is constructed according to formula (13): (13) The parameter layer degradation vector includes individual degradation degrees corresponding to the generator bearing inner ring temperature, generator bearing outer ring temperature, magnet temperature, cooling water temperature, generator winding maximum temperature, generator stator maximum temperature, and generator speed, respectively.

[0089] The parameter layer degradation vector of the yaw system is constructed according to formula (14): (14) The parameter layer degradation vector includes a single degradation degree corresponding to the yaw cable twist angle.

[0090] The parameter layer degradation vector of the hydraulic braking system is constructed according to formula (15): (15) The parameter layer degradation vector includes individual degradation degrees corresponding to hydraulic pressure parameters, hydraulic station oil temperature, and brake disc temperature, respectively.

[0091] S6. For multiple key indicators corresponding to the same component, the combined weights of each key indicator are determined by the analytic hierarchy process and the entropy weight method.

[0092] First, the subjective weights of each key indicator corresponding to the same component are determined using the analytic hierarchy process, resulting in the subjective weight vector shown in formula (16): (16) Subjective weights are used to reflect the relative importance of different key indicators in terms of wind turbine operating mechanisms and engineering experience.

[0093] Secondly, the objective weights of each key indicator are determined using the entropy weight method. The information entropy of each key indicator is calculated according to formulas (17) and (18): (17) (18) According to formula (19), the difference between 1 and the information entropy of each key indicator is determined as the indicator redundancy of the corresponding key indicator, and according to formula (20), the objective weight of each key indicator is determined based on the indicator redundancy of each key indicator: (19) (20) Objective weights are used to reflect the data differences of each key indicator in the effective sample dataset.

[0094] According to formula (21), the combined weight of the key indicator is obtained by adding the product of the subjective weight and the subjective weight coefficient of the same key indicator to the product of the objective weight and the objective weight coefficient of the same key indicator: (twenty one) The subjective weighting coefficient and the objective weighting coefficient satisfy formula (22): (twenty two) That is, the sum of the subjective weight coefficient and the objective weight coefficient is 1, and both the subjective weight coefficient and the objective weight coefficient are located in the interval [0,1]. In this embodiment, both the subjective weight coefficient and the objective weight coefficient can be 0.5, so that the subjective weight determined by the analytic hierarchy process and the objective weight determined by the entropy weight method jointly participate in the determination of the combined weight.

[0095] S7: The overall degradation degree of the corresponding component is obtained by weighted fusion of the individual degradation degree and combined weight of each key indicator corresponding to the same component, and the component health degree of the corresponding component is obtained based on the overall degradation degree of the component.

[0096] For the k-th component, the individual degradation degree and combined weight of each key indicator corresponding to the component are weighted and summed according to formula (23) to obtain the overall degradation degree of the corresponding component: (twenty three) According to formula (24), the difference between 1 and the overall degradation degree of the component is determined as the component health of the corresponding component: (twenty four) Thus, the overall degradation and component health of the pitch system, converter grid connection system, generator system, yaw system, and hydraulic braking system are obtained respectively.

[0097] The higher the overall degradation of a component, the greater the deviation of the corresponding component from its healthy state; the higher the component health, the better the health of the corresponding component.

[0098] S8 calculates and integrates the overall degradation degree of each component and the corresponding component weights at the whole-machine level to obtain the overall degradation degree and overall health of the wind turbine.

[0099] Obtain the preset component weights for the pitch system, converter grid connection system, generator system, yaw system, and hydraulic braking system, respectively, and assemble the component weight vector according to formula (25): (25) The weights of each component in the overall system layer satisfy formula (26), that is, the sum of the weights of each component in the overall system layer is 1: (26) According to formula (27), the overall degradation degree of the pitch system, converter grid connection system, generator system, yaw system and hydraulic braking system and their corresponding component weights are weighted and summed to obtain the overall degradation degree of the wind turbine: (27) According to formula (28), the difference between 1 and the overall deterioration degree of the whole machine is determined as the overall health degree of the whole machine: (28) The greater the overall degradation of the wind turbine, the greater the degree to which the wind turbine deviates from its healthy state. The higher the overall health rating, the better the overall health status of the wind turbine.

[0100] S9 identifies the dominant weak component based on the overall component weight and comprehensive degradation degree of each component at the system level.

[0101] Calculate the product of the overall component weight of each component and the overall degradation degree of the corresponding component at the current moment to obtain the weighted degradation contribution of each component to the overall degradation at the current moment.

[0102] Compare the weighted degradation contribution of each component at the current moment, and determine the component with the largest weighted degradation contribution as the dominant weak component at the current moment according to formula (29): (29) in, express The dominant weak component at any given moment. For the first The weight of each component in the overall system layer For the first The overall degradation degree of a component at time t. If a component's... If the value is the largest, it means that the component contributes the most to the decline in the overall health of the machine, and it can be identified as the currently dominant weak component.

[0103] By simultaneously considering the overall degradation degree of components and the component weights at the whole machine level, the components that contribute the most to the decline in the overall health status of the machine are identified, thereby reducing the masking of local component degradation by the overall machine evaluation results.

[0104] S10 determines the health level of the wind turbine based on the overall deterioration of the unit and makes engineering corrections to the health level.

[0105] The overall deterioration degree of the whole machine is used as a variable for determining the health level, and the correspondence between the overall deterioration degree of the whole machine and the variable for determining the health level is established according to formula (30): (30) According to formula (31), the health levels of wind turbine units are set as healthy, sub-healthy, early warning, and faulty: (31)

[0106] Based on the membership functions corresponding to healthy, sub-healthy, early warning, and faulty states, calculate the membership degree of the current state of the wind turbine to each health level, and form a health state membership vector according to formula (32): (32) The specific formula is as follows: (33) (34) (35) (36) Visualize the formula as follows Figure 3 .

[0107] According to formula (37), based on the principle of maximum membership, the health level corresponding to the maximum membership in the health status membership vector is determined as the initial health level: (37) When the key thermal risk indicator used to characterize the thermal state of a component reaches the corresponding preset extreme anomaly threshold, the health level of the wind turbine is corrected to a fault. Equation (29) shows that the identification of the dominant weak component cannot be based solely on the degree of degradation; the impact of the component on the overall state of the turbine must also be considered. Both factors jointly determine the identification result. If a component has the highest weighted degradation degree, it indicates that its degradation is more severe. At the same time, it has a greater impact on the decline in the overall state of the turbine, and in this case, it can be judged as the dominant weak component.

[0108] When the maximum and second-largest membership degrees in the health status membership vector are close, the initial health level is corrected based on the comprehensive degradation degree of the dominant weak component to obtain the health level of the wind turbine. The health level determination criteria are shown in the table below: Table 3

[0109] After completing the health status assessment, the system outputs the overall degradation degree of the entire machine, the overall health degree of the machine, the health level, the health degree of each component, the individual degradation degree of each key indicator, and the main weak component.

[0110] The above output results allow us to trace the overall health status of the wind turbine unit back to the component and parameter levels, thereby determining the overall health status of the wind turbine, the health status of each component, and the key indicators that cause component degradation.

[0111] Example 2 This embodiment uses the method described in Embodiment 1 to assess the health status of wind turbine operating data for different fault categories.

[0112] The fault categories used include abnormal temperature, communication failure, abnormal pressure, converter failure, pitch assist failure, abnormal speed, yaw protection activation, pitch speed abnormality, and converter protection activation. The sample size for each fault category is as follows: Figure 4 As shown in (a), the model recognition performance for each fault category is as follows: Figure 4 As shown in (b). The overall statistics of the fault verification results are shown in the table below: Table 4

[0113] For each fault case, first obtain the SCADA operation data before and at the time of the fault, remove data with shutdown, power limitation, communication abnormality and obvious bad points, and clean up missing and outlier values.

[0114] Then, based on the attribution relationship between each SCADA operating parameter and the pitch system, converter grid connection system, generator system, yaw system and hydraulic braking system, candidate indicators for each component are determined.

[0115] Pearson correlation analysis and skewness analysis were performed on the candidate indicators, and key indicators were determined by combining the wind turbine operation mechanism, fault mapping relationship, data quality and model interpretability.

[0116] Based on the physical meaning of each key indicator, the single degradation degree of each key indicator at different times is calculated using the single degradation degree function corresponding to the smaller the better type of indicator or the intermediate best type of indicator.

[0117] Based on the combined weights of each key indicator, the individual degradation degree of each key indicator is gradually integrated into the overall degradation degree of the component and the overall degradation degree of the whole machine, and the component health degree and the overall health degree of the whole machine are obtained accordingly.

[0118] Based on the product of the component weight at the overall system level and the overall degradation degree, the weighted degradation contribution of each component to the overall system degradation at different times is determined, and the component with the largest weighted degradation contribution is identified as the dominant weak component.

[0119] Therefore, the degradation process of wind turbines can be evaluated based on the individual degradation degree of each key indicator, the component health of each part, and the trend of changes in the overall health of the turbine before the failure occurs, and the main sources of the decline in the overall health status can be determined based on the dominant weak component.

[0120] Example 3 This embodiment uses the example of a fan disconnection fault in the hub control cabinet of a WT01 wind turbine to illustrate the process of identifying the dominant weak component in the method described in Embodiment 1.

[0121] SCADA operating data was collected near the time of the WT01 wind turbine failure, and the SCADA operating data was preprocessed. Based on the relationship between SCADA operating parameters and various components, the overall degradation degree and component health of the pitch system, converter grid-connected system, generator system, yaw system, and hydraulic braking system were calculated respectively.

[0122] The trend of the health status of each component over time is as follows: Figure 5 As shown.

[0123] Near the time of the fault, the calculated overall health score of the wind turbine was 0.85652. Based on this overall health score, the overall turbine status is still considered healthy.

[0124] However, the component health score of the pitch system is 0.37997, corresponding to an overall degradation score of 0.62003. The health score of the pitch system is significantly lower than that of other components.

[0125] The weighted degradation contributions of the pitch system, converter grid connection system, generator system, yaw system, and hydraulic braking system were further calculated. The pitch system had the largest weighted degradation contribution, and therefore it was identified as the dominant weak component at the current moment. The identified dominant weak component is consistent with the component where the actual fault occurred.

[0126] Further analysis was conducted on the individual degradation degree of the parameter layer corresponding to the pitch system. The individual degradation degree corresponding to the pitch angle of all three blades in the pitch system reached 1, while the individual degradation degree corresponding to the pitch control cabinet temperature was 0.025.

[0127] Therefore, it can be concluded that the decline in the health of the pitch system mainly stems from the pitch execution status of the three blades, rather than from abnormal temperature in the pitch control cabinet.

[0128] This embodiment demonstrates that when local components have shown significant degradation while the overall turbine health remains at a high level, calculating the weighted degradation contribution of each component and identifying the dominant weak component can reduce the masking of local anomalies by the overall turbine evaluation results. Furthermore, by analyzing the individual degradation degree of each key indicator in the dominant weak component, component-level anomalies can be traced back to the parameter level, providing a basis for wind turbine condition monitoring and maintenance.

[0129] Finally, it should be noted that the above content is only used to illustrate the technical solution of the present invention, and is not intended to limit the scope of protection of the present invention. Simple modifications or equivalent substitutions made by those skilled in the art to the technical solution of the present invention do not depart from the essence and scope of the technical solution of the present invention.

Claims

1. A multi-level health status assessment method based on SCADA signal data of wind turbine generators, characterized in that, include: S1. Collect SCADA operation data during the operation of the wind turbine, preprocess the SCADA operation data to obtain a valid sample dataset; S2. Based on the correspondence between SCADA operating parameters and wind turbine components in the effective sample dataset, construct a three-level health status evaluation index system including parameter layer, component layer and whole machine layer. S3, perform Pearson correlation analysis and skewness analysis on the candidate indicators in the parameter layer, identify the redundant relationship between the candidate indicators based on the correlation analysis results, determine the direction and degree of the sample distribution of the candidate indicators shifting towards high or low values ​​based on the skewness analysis results, and select key indicators from the candidate indicators by combining the wind turbine operation mechanism, fault mapping relationship, data quality and model interpretability. S4. Based on the physical meaning of each key indicator, the key indicators are divided into smaller and better indicators and intermediate best indicators. A single degradation function corresponding to the indicator type is used to map each key indicator to the [0,1] interval to obtain the single degradation degree of each key indicator. S5. For multiple key indicators corresponding to the same component, the analytic hierarchy process is used to determine the subjective weight of each key indicator, the entropy weight method is used to determine the objective weight of each key indicator, and the subjective weight and the objective weight are combined to obtain the combined weight of each key indicator. S6. The overall degradation degree of the corresponding component is obtained by weighted fusion of the single degradation degree and combined weight of each key indicator corresponding to the same component, and the difference between 1 and the overall degradation degree of the component is determined as the component health degree of the corresponding component. S7, obtain the preset whole-machine layer component weights corresponding to each component, the sum of the weights of each whole-machine layer component is 1, and perform weighted fusion based on the overall degradation degree of each component and the corresponding whole-machine layer component weight to obtain the overall degradation degree of the wind turbine, and determine the difference between 1 and the overall degradation degree of the wind turbine as the overall health degree. S8, multiply the overall component weight of each component by the overall degradation degree of the corresponding component to obtain the weighted degradation contribution of each component to the overall degradation, and determine the component with the largest weighted degradation contribution as the dominant weak component; S9, the overall deterioration degree of the whole machine is used as the health level determination variable. The membership degree of the current state of the wind turbine to each of the health levels is calculated according to the membership function corresponding to each health level to obtain the health state membership vector. The initial health level is determined based on the principle of maximum membership degree. When the key thermal risk indicator used to characterize the thermal state of the component reaches the corresponding preset extreme abnormal threshold, the health level of the wind turbine will be corrected to fault. When the maximum membership degree in the health status membership degree vector is close to the second largest membership degree, the initial health level is corrected according to the comprehensive deterioration degree of the dominant weak component to obtain the health level of the wind turbine. S10, output the overall degradation degree of the whole machine, the overall health degree of the whole machine, the health level, the component health degree of each component, the individual degradation degree of each key indicator, and the dominant weak component.

2. The multi-level health status assessment method based on wind turbine SCADA signal data according to claim 1, characterized in that, S1 includes: S11 collects temperature, power, pressure, angle, and speed parameters during the operation of the wind turbine. S12, Remove data from the collected SCADA operation data during wind turbine shutdown, during power-limited operation, communication anomaly data, and data with obvious defects; S13, clean the missing and outlier values ​​in the SCADA running data after the removal process to obtain the effective sample dataset.

3. The multi-level health status assessment method based on wind turbine SCADA signal data according to claim 1, characterized in that, S2 includes: S21, the SCADA operating parameters are assigned to the pitch system, converter grid connection system, generator system, yaw system and hydraulic braking system; S22, the indicators characterizing specific operating variables are determined as the indicators of the parameter layer, the pitch system, the converter grid-connected system, the generator system, the yaw system and the hydraulic braking system are determined as the evaluation objects of the component layer, and the wind turbine as a whole is determined as the evaluation object of the whole machine layer; S23, subtract the corresponding maximum temperature of the IGBT power module on the grid side of converter 1 from the maximum temperature of the IGBT power module on the machine side of converter 1 to obtain the IGBT temperature difference between the machine and grid sides of converter 1, and subtract the corresponding maximum temperature of the IGBT power module on the grid side of converter 2 from the maximum temperature of the IGBT power module on the machine side of converter 2 to obtain the IGBT temperature difference between the machine and grid sides of converter 2. S24: Select the maximum value from the 12 generator segment winding temperature measurement points to obtain the highest generator winding temperature; S25, select the maximum value from the 12 generator stator temperature measurement points to obtain the highest generator stator temperature; S26, the temperature difference of the IGBT on the grid side of converter No. 1, the temperature difference of the IGBT on the grid side of converter No. 2, the maximum temperature of the generator winding, the maximum temperature of the generator stator, and the SCADA operating parameters assigned according to the components of the wind turbine are used as candidate indicators in the parameter layer.

4. The multi-level health status assessment method based on wind turbine SCADA signal data according to claim 1, characterized in that, S3 includes: S31, calculate the Pearson correlation coefficient between any two candidate indicators, and identify redundant relationships between the candidate indicators based on the Pearson correlation coefficient; S32, calculate the skewness of each candidate index, and determine the direction and degree of the sample distribution of the corresponding candidate index shifting towards the high value direction or the low value direction based on the skewness; S33. Based on the redundancy relationship, the direction and degree of the offset, and in combination with the wind turbine operation mechanism, fault mapping relationship, data quality and model interpretability, determine the key indicators from the candidate indicators; Among them, for candidate indicators that meet the preset strong correlation conditions and represent different risk dimensions, the candidate indicators that meet the preset strong correlation conditions and represent different risk dimensions are retained.

5. The multi-level health status assessment method based on wind turbine SCADA signal data according to claim 1, characterized in that, S4 includes: S41, based on the physical meaning of the key indicators, the key indicators are divided into smaller-than-average indicators and intermediate-optimal indicators. S42, for the smaller the better type of indicator, when the current value of the indicator is less than or equal to the upper limit of the healthy range, the corresponding single degradation degree is determined to be 0; when the current value of the indicator is greater than or equal to the degradation threshold, the corresponding single degradation degree is determined to be 1; when the current value of the indicator is between the upper limit of the healthy range and the degradation threshold, the corresponding single degradation degree is linearly increased from 0 to 1 as the current value of the indicator increases. S43, for the intermediate optimal type index, when the current value of the index is less than or equal to the left boundary threshold or greater than or equal to the right boundary threshold, the corresponding single degradation degree is determined to be 1; when the current value of the index is equal to the optimal value or the center value, the corresponding single degradation degree is determined to be 0; when the current value of the index is between the left boundary threshold and the optimal value or the center value, the corresponding single degradation degree is linearly decreased from 1 to 0 as the current value of the index increases; when the current value of the index is between the optimal value or the center value and the right boundary threshold, the corresponding single degradation degree is linearly increased from 0 to 1 as the current value of the index increases. Wherein, a single degradation degree of 0 indicates that the corresponding key indicator is in a healthy or optimal state, and a single degradation degree of 1 indicates that the corresponding key indicator deviates from the normal state to the greatest extent.

6. The multi-level health status assessment method based on wind turbine SCADA signal data according to claim 1, characterized in that, S5 includes: S51, the single degradation degree of each key indicator corresponding to the same component is combined into a parameter layer degradation degree vector of the corresponding component. S52, the subjective weights corresponding to each single degree of degradation in the parameter layer degradation vector are determined by the analytic hierarchy process, and the subjective weight vector is obtained. S53, the information entropy of each key indicator is calculated using the entropy weight method, the difference between 1 and the information entropy of each key indicator is determined as the indicator redundancy of the corresponding key indicator, and the objective weight of each key indicator is determined based on the indicator redundancy of each key indicator. S54, add the product of the subjective weight and the subjective weight coefficient of the same key indicator and the product of the objective weight and the objective weight coefficient of the key indicator to obtain the combined weight of the key indicator. Wherein, the sum of the subjective weight coefficient and the objective weight coefficient is 1, and both the subjective weight coefficient and the objective weight coefficient are located in the interval [0,1].

7. The multi-level health status assessment method based on wind turbine SCADA signal data according to claim 1, characterized in that, S6 includes: S61, the single degradation degree and combined weight of each key indicator corresponding to the same component are weighted and summed to obtain the comprehensive degradation degree of the corresponding component. S62, the difference between 1 and the overall deterioration degree of the component is determined as the component health degree of the corresponding component; S63, respectively obtain the overall degradation degree and component health of the pitch system, the converter grid system, the generator system, the yaw system and the hydraulic braking system.

8. The multi-level health status assessment method based on wind turbine SCADA signal data according to claim 1, characterized in that, S7 includes: S71, obtain the preset whole-machine layer component weights corresponding to the pitch system, the converter grid system, the generator system, the yaw system and the hydraulic braking system respectively, form a component weight vector, and make the sum of the preset whole-machine layer component weights equal to 1; S72, the overall degradation degree of each component and the corresponding preset component weights of the whole machine layer are weighted and summed to obtain the overall degradation degree of the whole machine; S73, the difference between 1 and the overall deterioration degree of the whole machine is determined as the overall health degree of the whole machine.

9. The multi-level health status assessment method based on wind turbine SCADA signal data according to claim 1, characterized in that, S8 includes: S81, calculate the product of the overall component weight of each component and the overall degradation degree of the corresponding component at the current time to obtain the weighted degradation contribution of each component at the current time. S82, compare the weighted degradation contribution of each component at the current moment, and determine the component with the largest weighted degradation contribution as the dominant weak component at the current moment.

10. The multi-level health status assessment method based on wind turbine SCADA signal data according to claim 1, characterized in that, S9 includes: S91, the overall deterioration degree of the entire unit is used as a health level determination variable, and the health level of the wind turbine is set as healthy, sub-healthy, early warning and fault; S92, based on the membership functions corresponding to the health, sub-health, early warning and fault respectively, calculate the membership degree of the current state of the wind turbine to each of the health levels, and obtain the health state membership vector; S93, based on the principle of maximum membership, the health level corresponding to the maximum membership in the health status membership vector is determined as the initial health level; S94, when the key thermal risk indicator reaches the corresponding preset extreme abnormal threshold, the health level of the wind turbine is corrected to fault. S95, when the maximum membership degree in the health status membership degree vector is close to the second largest membership degree, the initial health level is corrected according to the comprehensive deterioration degree of the dominant weak component to obtain the health level of the wind turbine.

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