A steady-state data extraction method for an aeroengine
By determining the initial steady-state threshold and time window processing, and combining the fitting compensation function with real-time adjustment, the accuracy problem of steady-state data extraction in aero-engine testing was solved, achieving adaptability and accuracy to different data characteristics.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-05-16
- Publication Date
- 2026-04-14
AI Technical Summary
Existing steady-state data extraction methods cannot effectively adapt to changes in different data characteristics in aero-engine testing, resulting in low accuracy of steady-state data extraction and difficulty in processing database data and real-time data simultaneously.
By determining initial steady-state thresholds, including data variance thresholds and trend thresholds, data preprocessing and time window processing are performed. Combined with fitting compensation functions and real-time threshold adjustment, the steady-state segment of engine test data can be extracted.
It improves the accuracy and adaptability of steady-state data extraction, can identify different influencing factors, adapt to changes in experimental site conditions, and ensure the precision and accuracy of data processing.
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Figure CN117033914B_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of aero-engine data processing technology, and specifically relates to a method for extracting steady-state data from aero-engines. Background Technology
[0002] Steady-state data processing plays a crucial role in aero-engine test data processing. Aero-engine test data is diverse in type and volume, with significant differences in data characteristics. Existing steady-state data extraction methods cannot adequately adapt to these variations. The complex conditions at test sites and numerous interfering factors influence steady-state determination; if the determination criteria are not adjusted according to the test data, the accuracy of steady-state data extraction will be severely impacted. Most existing methods cannot simultaneously achieve steady-state extraction and determination for both database data and real-time data while maintaining accuracy.
[0003] In summary, existing data processing methods are not very effective for batch processing of large amounts of data. As the demands for test data processing in aero-engine testing become increasingly sophisticated, a method with strong adaptability to test data, capable of batch processing test data and extracting steady-state segments, is needed.
[0004] Therefore, it is desirable to have a technical solution to overcome or at least mitigate one of the aforementioned defects of the prior art. Summary of the Invention
[0005] The purpose of this application is to provide a method for extracting steady-state data from aero-engines to solve at least one problem existing in the prior art.
[0006] The technical solution of this application is:
[0007] A method for extracting steady-state data from an aero-engine, comprising:
[0008] Step 1: Obtain engine steady-state data and determine the initial steady-state threshold based on the engine steady-state data;
[0009] Step 2: Obtain engine test data, and perform time window processing on the engine test data according to the steady-state threshold to determine the state of the engine test data.
[0010] In at least one embodiment of this application, step one, namely acquiring engine steady-state data and determining an initial steady-state threshold based on the engine steady-state data, includes:
[0011] S101. Obtain engine steady-state data and preprocess the engine steady-state data;
[0012] S102. Determine an initial steady-state threshold based on the engine steady-state data, wherein the initial steady-state threshold includes a data variance threshold and a data trend threshold;
[0013] S103. Determine the relevant parameters of the initial steady-state threshold, fit the relevant parameters and the initial steady-state threshold to obtain a compensation function, and perform calculations on the compensation function and the initial steady-state threshold to obtain the final initial steady-state threshold.
[0014] In at least one embodiment of this application, in step S102, determining a data variance threshold based on the engine steady-state data includes:
[0015] Obtain n steady-state data segments from the engine steady-state data;
[0016] Calculate the average value of each steady-state data segment, and the deviation of each data point from the average value;
[0017] Calculate the variance of the deviation values and determine the data variance threshold coefficient to obtain the data variance threshold:
[0018]
[0019] in, σ is the data variance threshold. 2 k is the variance of the deviation values. σ2 This is the data variance threshold coefficient.
[0020] In at least one embodiment of this application, in step S102, determining a data trend threshold based on the engine steady-state data includes:
[0021] Obtain n steady-state data segments from the engine steady-state data;
[0022] The least squares method was used to fit each steady-state data segment to obtain the slope coefficients of n fitted lines;
[0023] Calculate the variance and mean of the slope coefficient, and determine the data trend threshold coefficient to obtain the data trend threshold:
[0024]
[0025]
[0026] Among them, TH XL k is the data trend threshold. XL This is the data trend threshold coefficient. σ is the average value of the slope coefficients. XL 2 denoted as the variance of the slope coefficient.
[0027] In at least one embodiment of this application, step two, which involves acquiring engine test data, performing time window processing on the engine test data based on the steady-state threshold, and determining the state of the engine test data, includes:
[0028] S201. Obtain engine test data and preprocess the engine test data;
[0029] S202. Perform time window processing on the engine test data according to the steady-state threshold to obtain the state of the engine test data;
[0030] S203. Adjust the steady-state threshold in real time and return to step S202.
[0031] In at least one embodiment of this application, data preprocessing includes:
[0032] This involves removing duplicate, out-of-limit, and abnormal data from the data, as well as performing data filtering.
[0033] Remove duplicate data from the data based on the duplication criterion, the time criterion, and the first removal principle:
[0034] The duplication criterion is that two consecutive data values are the same;
[0035] The time criterion is that the time for which the data is identical is less than the longest update cycle;
[0036] The first elimination principle is to eliminate duplicate data when the duplicate criteria and the time criteria are met;
[0037] Data exceeding the limit is removed based on the difference criterion, the range criterion, and the second rejection principle:
[0038] The difference criterion is that the difference between the current interpolated data and the average value of the data points over a previous period exceeds a limit.
[0039] The range criterion is that the data exceeds the range of the data measurement;
[0040] The second rejection principle is to reject out-of-limit data when the difference criterion and the range criterion are met;
[0041] Outliers were removed from the data based on the mutation criterion, the time invariance criterion, and the third elimination principle.
[0042] The mutation criterion is that the difference between the current data and the previous data exceeds a first threshold.
[0043] The invariance time criterion is that the data remains unchanged for a longer time than the second threshold.
[0044] The third elimination principle is to eliminate abnormal data when the mutation criterion and the invariant time criterion are met;
[0045] Data filtering includes:
[0046] The data is filtered using the following data filtering function:
[0047]
[0048] Where, x t For the original data, X i The filtered data is represented by n, which is the number of samples used in one filtering operation.
[0049] In at least one embodiment of this application, in S202, the step of performing time window processing on the engine test data according to the steady-state threshold to obtain the state of the engine test data includes:
[0050] Two time windows are defined. When there is no data in either time window, the length t1 of time window 1 is 0, and the length t2 of time window 2 is the detection time T. 检测 ;
[0051] If the number of data points and the duration of the first and last data points in time window 2 meet the detection requirements, then calculate the first data feature value of time window 2. Next, determine if the first data feature value meets the steady-state threshold requirement. If so, determine that the data in time window 2 has entered a stable state, and adjust the length of time window 1 to the steady-state determination reaction time T. 反应 ;
[0052] Determine whether the number of data in time window 1 and the time length of the first and last data meet the detection requirements. If so, calculate the second data feature value of time window 1; and determine whether the second data feature value meets the steady-state threshold requirement. If so, determine that the data in time window 1 has entered a steady state.
[0053] When the data in both time window 2 and time window 1 have entered a stable state, the data state is determined based on the first data feature value and the second data feature value.
[0054] In at least one embodiment of this application, determining the data state based on the first data feature value and the second data feature value includes:
[0055] Select key data from the engine test data and determine the stability coefficient K. 稳定 and volatility coefficient K 波动 ;
[0056] Calculate the ratio R between the first data feature value and the second data feature value. 1 / 2and the difference R |1-2| ,but:
[0057] When R 1 / 2 <K 稳定 / R |1-2| <K 稳定 At that time, the data in time window 1 and the data in time window 2 are in the same stable state;
[0058] When K 稳定 <R 1 / 2 <K 波动 / K 稳定 <R |1-2| <K 波动 At that time, the judgment result of the data in time window 1 is the same as that of the flag data;
[0059] When R 1 / 2 >K 波动 / R |1-2| >K 波动 At that time, the data in time window 1 and the data in time window 2 are not in the same stable state.
[0060] In at least one embodiment of this application, in S203, the real-time adjustment of the steady-state threshold includes:
[0061] Obtain the inertia coefficient K 惯性 ;
[0062] The adjusted steady-state threshold is:
[0063] TH 稳态 = (1-K) 惯性 )(TH 初始 +TH 适应 )+K 惯性 TH 当前
[0064] Among them, TH 稳态 TH is the adjusted steady-state threshold. 初始 TH is the initial steady-state threshold. 适应 To adapt to the compensation threshold, TH 当前 This is the current threshold.
[0065] In at least one embodiment of this application,
[0066] When a relevant parameter is included, the adaptation compensation threshold is:
[0067]
[0068] in, This represents the average value of the relevant parameters under the current steady state.
[0069] When multiple related parameters are included, the adaptation compensation threshold is:
[0070]
[0071] in, It is a vector of relevant parameters consisting of the average values of all relevant parameters under the current steady state.
[0072] The invention has at least the following beneficial technical effects:
[0073] The steady-state data extraction method for aero-engines disclosed in this application can extract steady-state data segments from different types of test data; effectively identify different influencing factors and improve the accuracy of steady-state data extraction. Attached Figure Description
[0074] Figure 1 This is an initial steady-state threshold determination method according to one embodiment of this application;
[0075] Figure 2 This is a method for determining the state of engine test data according to one embodiment of this application;
[0076] Figure 3 This is a schematic diagram of a normalized fitting compensation function curve according to one embodiment of this application;
[0077] Figure 4 This is a time window processing model implemented in this application. Detailed Implementation
[0078] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are some, but not all, embodiments of this application. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application. The embodiments of this application will be described in detail below with reference to the accompanying drawings.
[0079] In the description of this application, it should be understood that the terms "center", "longitudinal", "lateral", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting the scope of protection of this application.
[0080] The following is in conjunction with the appendix Figures 1 to 4 This application will be described in further detail.
[0081] This application provides a method for extracting steady-state data from an aero-engine, comprising the following steps:
[0082] Step 1: Obtain engine steady-state data and determine the initial steady-state threshold based on the engine steady-state data. This includes:
[0083] S101. Obtain engine steady-state data and preprocess the engine steady-state data;
[0084] S102. Determine the initial steady-state threshold based on the engine steady-state data. The initial steady-state threshold includes the data variance threshold and the data trend threshold.
[0085] S103. Determine the relevant parameters of the initial steady-state threshold, fit the relevant parameters and the initial steady-state threshold to obtain the compensation function, and perform calculations between the compensation function and the initial steady-state threshold to obtain the final initial steady-state threshold.
[0086] Step 2: Acquire engine test data, and perform time window processing on the engine test data according to the steady-state threshold to determine the state of the engine test data. Specifically, this includes:
[0087] S201. Obtain engine test data and preprocess the engine test data;
[0088] S202. Perform time window processing on the engine test data according to the steady-state threshold to obtain the state of the engine test data;
[0089] S203. Adjust the steady-state threshold in real time and return to step S202.
[0090] The steady-state data extraction method for aero-engines disclosed in this application first obtains an initial steady-state threshold by reading existing engine steady-state data. Then, when relevant parameters with a significant correlation exist between the threshold and the data, a compensation function for the threshold is derived to determine the final initial steady-state threshold. Next, the data state is determined through data stream processing. This application involves multiple data processing steps, including data preprocessing, extraction of data feature values, obtaining the initial steady-state threshold, time window processing, steady-state determination, and threshold adjustment.
[0091] In a preferred embodiment of this application, step S102, determining the data variance threshold based on the engine steady-state data, includes:
[0092] Obtain n steady-state data segments from the engine steady-state data;
[0093] Calculate the average value of each steady-state data segment, and the deviation of each data point from the average value;
[0094] Calculate the variance of the deviation values and determine the data variance threshold coefficient to obtain the data variance threshold:
[0095]
[0096] in, σ is the data variance threshold. 2 k is the variance of the deviation values. σ2 This is the data variance threshold coefficient.
[0097] In a preferred embodiment of this application, S102, determining the data trend threshold based on engine steady-state data includes:
[0098] Obtain n steady-state data segments from the engine steady-state data;
[0099] The least squares method was used to fit each steady-state data segment to obtain the slope coefficients of n fitted lines;
[0100] Calculate the variance and mean of the slope coefficient, and determine the data trend threshold coefficient to obtain the data trend threshold:
[0101]
[0102]
[0103] Among them, TH XL k is the data trend threshold. XL This is the data trend threshold coefficient. σ is the average value of the slope coefficients. XL 2 denoted as the variance of the slope coefficient.
[0104] The steady-state data extraction method for aero-engines in this application requires removing the influence of a certain parameter when the steady-state threshold is significantly correlated with it. Specifically, this is achieved by fitting a compensation function (such as...) to the correlated parameter and the steady-state threshold. Figure 3 As shown in the figure, the compensation function is operated on with the initial steady-state threshold (usually by multiplication) to obtain the final initial steady-state threshold.
[0105] In one embodiment of this application, the contrast threshold of parameter A is clearly correlated with the current value of parameter B, and the correlation conforms to a functional relationship:
[0106] y = K 补偿 (1-3×(x-0.5) 2 )
[0107] Variance threshold of parameter A after compensation The relationship with the calculated variance threshold is as follows:
[0108]
[0109] Where B is the average value of parameter B under the current state.
[0110] The steady-state data extraction method for aero-engines in this application addresses the issue that the raw data may contain certain deviations due to interference, different data acquisition frequencies, or acquisition system channel failures. Data preprocessing reduces these deviations. Therefore, both steps one and two involve data preprocessing, which is described below:
[0111] This involves removing duplicate, out-of-limit, and abnormal data from the data, as well as performing data filtering.
[0112] Remove duplicate data from the data based on the duplication criterion, the time criterion, and the first removal principle:
[0113] The criterion for duplication is that two consecutive data values are the same.
[0114] The time criterion is that the time between the same data updates is less than the longest update cycle;
[0115] The first elimination principle is to eliminate duplicate data when the duplicate criteria and time criteria are met;
[0116] Data exceeding the limit is removed based on the difference criterion, the range criterion, and the second rejection principle:
[0117] The difference criterion is that the difference between the current interpolated data and the average value of the data points over a previous period exceeds a limit.
[0118] The range criterion is that the data exceeds the range of the data measurement;
[0119] The second elimination principle is to eliminate out-of-limit data when the difference criterion and the range criterion are met.
[0120] Outliers were removed from the data based on the mutation criterion, the time invariance criterion, and the third elimination principle.
[0121] The mutation criterion is that the difference between the current data and the previous data exceeds a first threshold;
[0122] The invariance time criterion is that the data remains unchanged for a period of time longer than the second threshold.
[0123] The third elimination principle is to eliminate outlier data when the mutation criterion and the time invariance criterion are met.
[0124] Data fluctuations that are too drastic require data filtering to simplify further data processing and improve the accuracy of steady-state data extraction.
[0125] Data filtering includes:
[0126] The data is filtered using the following data filtering function:
[0127]
[0128] Where, x t For the original data, X i The filtered data is represented by n, which is the number of samples used in one filtering operation.
[0129] In a preferred embodiment of this application, in S202, the engine test data is processed by a time window according to a steady-state threshold to obtain the state of the engine test data, such as... Figure 4 As shown, it includes:
[0130] Two time windows are defined. When there is no data in either time window, the length t1 of time window 1 is 0, and the length t2 of time window 2 is the detection time T. 检测 ;
[0131] Determine whether the number of data points and the duration of the first and last data points in time window 2 meet the detection requirements. If so, calculate the first data feature value of time window 2; and determine whether the first data feature value meets the steady-state threshold requirement. If so, determine that the data in time window 2 has entered a steady state, and adjust the length of time window 1 to the steady-state determination reaction time T. 反应 ;
[0132] Determine whether the number of data and the time length of the first and last data in time window 1 meet the detection requirements. If so, calculate the second data feature value of time window 1; and determine whether the second data feature value meets the steady-state threshold requirement. If so, determine that the data in time window 1 has entered a steady state.
[0133] When the data in both time window 2 and time window 1 have entered a stable state, the data state is determined based on the first data feature value and the second data feature value.
[0134] In a preferred embodiment of this application, determining the data status based on a first data feature value and a second data feature value includes:
[0135] Select key data from engine test data and determine the stability coefficient K. 稳定 and volatility coefficient K 波动 Indicator data are data that are sensitive to changes in data and have a high accuracy rate in judging steady-state data.
[0136] Calculate the ratio R between the first data feature value and the second data feature value. 1 / 2 and the difference R |1-2| :
[0137] When R 1 / 2 <K 稳定 / R |1-2| <K 稳定 At that time, the latest data in time window 1 and the current data in time window 2 are in the same stable state;
[0138] When K 稳定 <R 1 / 2 <K 波动 / K 稳定 <R |1-2| <K 波动 At that time, the latest data in time window 1 has the same judgment result as the flag data;
[0139] When R 1 / 2 >K 波动 / R |1-2| >K 波动 At that time, the latest data in time window 1 and the current data in time window 2 are not in the same stable state.
[0140] The steady-state data extraction method for aero-engines in this application requires continuous adjustment of the steady-state threshold during the steady-state process. In a preferred embodiment of this application, step S203 involves real-time adjustment of the steady-state threshold, including:
[0141] Obtain the inertia coefficient K 惯性 The interval range is [0, 1].
[0142] The adjusted steady-state threshold is:
[0143] TH 稳态 = (1-K) 惯性 )(TH 初始 +TH 适应 )+K 惯性 TH 当前
[0144] Among them, TH 稳态 TH is the adjusted steady-state threshold. 初始 TH is the initial steady-state threshold. 适应 To adapt to the compensation threshold, TH 当前 This is the current threshold. The current threshold TH 当前 The current threshold is calculated for the current steady-state segment of the current parameters.
[0145] Adaptive compensation threshold TH 适应 Associated with relevant parameters;
[0146] When a relevant parameter is included, the adaptation compensation threshold is:
[0147]
[0148] Among them, X 相关 This represents the average value of the relevant parameters under the current steady state.
[0149] When multiple relevant parameters are included, the adaptive compensation threshold is:
[0150]
[0151] in, It is a vector of relevant parameters consisting of the average values of all relevant parameters under the current steady state.
[0152] The steady-state data extraction method for aero-engines proposed in this application has low dependence on engine models and advantages in batch data processing. In terms of real-time detection, it can meet the requirements of the test site in terms of calculation speed and judgment accuracy. It can also be adjusted to a certain extent according to changes in the test conditions to ensure the accuracy of the extraction results.
[0153] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.
Claims
1. A method for extracting steady-state data from an aero-engine, characterized in that, include: Step 1: Obtain engine steady-state data and determine the initial steady-state threshold based on the engine steady-state data; Step 2: Acquire engine test data, and perform time window processing on the engine test data according to the steady-state threshold to determine the state of the engine test data, including: S201. Obtain engine test data and preprocess the engine test data; S202. Perform time window processing on the engine test data according to the steady-state threshold to obtain the state of the engine test data; S203. Adjust the steady-state threshold in real time and return to step S202; In S202, the step of performing time window processing on the engine test data according to the steady-state threshold to obtain the state of the engine test data includes: Two time windows are defined. When there is no data in either time window, the length t1 of time window 1 is 0, and the length t2 of time window 2 is the detection time. ; If the number of data points and the duration of the first and last data points in time window 2 meet the detection requirements, then calculate the first data feature value of time window 2; and determine if the first data feature value meets the steady-state threshold requirement. If so, determine that the data in time window 2 has entered a stable state, and adjust the length of time window 1 to the reaction time for steady-state determination. ; Determine whether the number of data in time window 1 and the time length of the first and last data meet the detection requirements. If so, calculate the second data feature value of time window 1; and determine whether the second data feature value meets the steady-state threshold requirement. If so, determine that the data in time window 1 has entered a steady state. When the data in both time window 2 and time window 1 have entered a stable state, the data state is determined based on the first data feature value and the second data feature value. The step of determining the data status based on the first data feature value and the second data feature value includes: Select key data from the engine test data and determine the stability coefficient. and volatility coefficient ; Calculate the ratio of the first data feature value to the second data feature value. and difference ,but: when At that time, the data in time window 1 and the data in time window 2 are in the same stable state; when At that time, the judgment result of the data in time window 1 is the same as that of the flag data; when At that time, the data in time window 1 and the data in time window 2 are not in the same stable state.
2. The method for extracting steady-state data of an aero-engine according to claim 1, characterized in that, In step one, acquiring engine steady-state data and determining an initial steady-state threshold based on the engine steady-state data includes: S101. Obtain engine steady-state data and preprocess the engine steady-state data; S102. Determine an initial steady-state threshold based on the engine steady-state data, wherein the initial steady-state threshold includes a data variance threshold and a data trend threshold; S103. Determine the relevant parameters of the initial steady-state threshold, fit the relevant parameters and the initial steady-state threshold to obtain a compensation function, and perform calculations on the compensation function and the initial steady-state threshold to obtain the final initial steady-state threshold.
3. The method for extracting steady-state data of an aero-engine according to claim 2, characterized in that, In S102, determining the data variance threshold based on the engine steady-state data includes: Obtain n steady-state data segments from the engine steady-state data; Calculate the average value of each steady-state data segment, and the deviation of each data point from the average value; Calculate the variance of the deviation values and determine the data variance threshold coefficient to obtain the data variance threshold: ; in, The data variance threshold. The variance of the deviation values. This is the data variance threshold coefficient.
4. The method for extracting steady-state data of an aero-engine according to claim 3, characterized in that, In S102, determining the data trend threshold based on the engine steady-state data includes: Obtain n steady-state data segments from the engine steady-state data; The least squares method was used to fit each steady-state data segment to obtain the slope coefficients of n fitted lines; Calculate the variance and mean of the slope coefficient, and determine the data trend threshold coefficient to obtain the data trend threshold: ; ; in, For data trend threshold, This is the data trend threshold coefficient. The average value of the slope coefficients. This is the slope coefficient.
5. The method for extracting steady-state data of an aero-engine according to claim 1 or 2, characterized in that, Data preprocessing includes: This involves removing duplicate, out-of-limit, and abnormal data from the data, as well as performing data filtering. Remove duplicate data from the data based on the duplication criterion, the time criterion, and the first removal principle: The duplication criterion is that two consecutive data values are the same; The time criterion is that the time for which the data is identical is less than the longest update cycle; The first elimination principle is to eliminate duplicate data when the duplicate criteria and the time criteria are met; Data exceeding the limit is removed based on the difference criterion, the range criterion, and the second rejection principle: The difference criterion is that the difference between the current interpolated data and the average value of the data points over a previous period exceeds a limit. The range criterion is that the data exceeds the range of the data measurement; The second rejection principle is to reject out-of-limit data when the difference criterion and the range criterion are met; Outliers were removed from the data based on the mutation criterion, the time invariance criterion, and the third elimination principle. The mutation criterion is that the difference between the current data and the previous data exceeds a first threshold. The invariance time criterion is that the data remains unchanged for a time longer than the second threshold. The third elimination principle is to eliminate abnormal data when the mutation criterion and the invariant time criterion are met; Data filtering includes: The data is filtered using the following data filtering function: ; in, The original data, The filtered data is represented by n, which is the number of samples used in one filtering operation.
6. The method for extracting steady-state data of an aero-engine according to claim 5, characterized in that, In S203, the real-time adjustment of the steady-state threshold includes: Obtaining the inertia coefficient ; The adjusted steady-state threshold is: ; in, The adjusted steady-state threshold, The initial steady-state threshold, To adapt to the compensation threshold, This is the current threshold.
7. The method for extracting steady-state data of an aero-engine according to claim 6, characterized in that, When a relevant parameter is included, the adaptation compensation threshold is: ; in, This represents the average value of the relevant parameters under the current steady state. When multiple related parameters are included, the adaptation compensation threshold is: ; in, It is a vector of relevant parameters consisting of the average values of all relevant parameters under the current steady state.
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