Compressor temperature rise efficiency uncertainty mathematical analysis model construction method

Abstract

The invention provides a method for constructing a mathematical analysis model for uncertainty of temperature rise efficiency of a gas compressor. The method comprises the following steps: S1, collecting basic parameters and data; s2, a compressor temperature rise efficiency calculation model is determined; s3, identifying an uncertainty source; s4, performing quantitative calculation on each uncertainty component; s5, calculating the uncertainty of the synthesis standard; s6, evaluating the expansion uncertainty; s7, model verification and feedback correction; and S8, model output and document processing. According to the method, a high-precision and full-data-driven mathematical analysis model for the uncertainty of the temperature rise efficiency of the gas compressor is constructed, the problems of subjective weight deviation, large noise interference and difficulty in compensation of nonlinear interference in traditional uncertainty quantification are solved, and a scientific and reliable uncertainty basis is provided for performance evaluation of the gas compressor.

Description

Technical Field

[0001] This invention relates to the fields of aerospace propulsion systems, ground gas turbines and energy power equipment, and in particular to a method for constructing a mathematical analysis model for the uncertainty of compressor temperature rise efficiency. Background Technology

[0002] As a core component of aero-engines and gas turbines, the compressor's temperature rise efficiency is a key indicator for evaluating energy conversion performance, and it needs to be calculated through experimental measurements of parameters such as inlet / outlet total temperature and pressure. However, existing uncertainty analysis methods have the following limitations: 1. High dependence on subjectivity: Traditional methods (such as the Analytic Hierarchy Process, AHP) rely on expert subjective scoring to determine the weights of each parameter, which is easily affected by differences in experience, leading to deviations in weight allocation from actual measurement patterns; 2. Data noise interference: Sensor measurement data contains random noise and electromagnetic interference. Directly using it for analysis will overestimate the uncertainty components, and there is a lack of targeted noise reduction mechanisms. 3. Difficulty in modeling environmental disturbances: The impact of environmental temperature and pressure fluctuations on the measurement benchmark is nonlinear, and traditional linear compensation methods are difficult to quantify accurately, resulting in distorted assessment of environmental disturbance components; 4. Lack of algorithm collaboration: Data preprocessing, weight allocation, error compensation and other steps are independent of each other and do not form a closed-loop optimization, which limits the overall quantization accuracy. Summary of the Invention

[0003] This invention provides a method for constructing a mathematical analysis model for compressor temperature rise efficiency uncertainty. It addresses the subjective bias and insufficient accuracy issues of traditional analysis methods through data-driven algorithm fusion and full-process collaborative optimization. First, compressor design parameters, experimental measurement data, instrument characteristics, and environmental monitoring data are collected. Based on thermodynamic theory, a temperature rise efficiency calculation model is established, systematically identifying three sources of uncertainty: the measurement process, model assumptions, and environmental interference. Then, adaptive Kalman filtering is used to reduce noise in the measurement data. Principal component analysis-entropy weighting is used to objectively allocate the weights of each parameter and quantify the measurement process components. Least squares support vector machine modeling is employed to compensate for environmental interference components and to provide feedback optimization of the adaptive Kalman filter. Next, the combined standard uncertainty is calculated based on the uncertainty propagation law, and the expanded uncertainty is obtained by combining the inclusion factor. Finally, the model stability is verified through multiple sets of experimental data, and feedback corrections are made, resulting in a complete document containing data, algorithm parameters, and results. The key innovation lies in replacing expert subjective judgment with a fully data-driven algorithm. Through closed-loop collaboration of multiple algorithms, high-precision quantification of uncertainty components is achieved, providing a standardized method for reliability assessment of compressor performance testing.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: A method for constructing a mathematical analysis model for the uncertainty of compressor temperature rise efficiency includes the following steps: S1: Collect basic parameters and data, including compressor design and operation parameters, multiple sets of repeated test measurement data, working fluid characteristic data and environmental monitoring data; S2: Based on fundamental parameters and data, and combined with thermodynamic theory, a calculation model for compressor temperature rise efficiency is established; S3: Based on the compressor temperature rise efficiency calculation model and basic parameters and data, identify the sources of uncertainty affecting temperature rise efficiency; S4: Quantify the components corresponding to the sources of uncertainty; use adaptive Kalman filtering to reduce noise in multiple sets of repeated experimental measurement data, and output the filtered measurement data and filtering residuals; using the filtered measurement data as input, first extract the contribution through principal component analysis, then analyze the dispersion through entropy weight method, and calculate the comprehensive weight; combine the comprehensive weight to calculate and output the standard uncertainty component of the measurement process; construct input features based on environmental monitoring data and filtering residuals, weight the input features with comprehensive weights, train the environmental interference error model through least squares support vector machine, output the environmental interference error compensation value, and then combine the initial environmental interference components calculated through environmental monitoring data to calculate the compensated environmental interference standard uncertainty component; based on the working fluid characteristic data, determine the variation range of the specific heat capacity ratio of the working fluid under actual working conditions, take the half-width to calculate the deviation, and comprehensively obtain the model assumption standard uncertainty component; S5: Based on the compressor temperature rise efficiency calculation model and the standard uncertainty components of the measurement process, environmental disturbance, and model assumptions, the combined standard uncertainty is calculated using the uncertainty propagation law. S6: Based on the combined standard uncertainty, determine the coverage factor and calculate the expanded uncertainty; S7: Select experimental data that were not used in training to verify the model, and verify the model stability by calculating the relative deviation of the expanded uncertainty; S8: After successful verification, integrate the results of the previous steps and output the mathematical analysis model of compressor temperature rise efficiency uncertainty.

[0005] In this specification, in step S4, the three algorithms form an interactive closed loop: the filtered measurement data output by the adaptive Kalman filter is used as the input of the principal component analysis-entropy weighting method coupling; the comprehensive weight output by the principal component analysis-entropy weighting method coupling is used to weight the input features of the least squares support vector machine; the environmental interference error compensation value output by the least squares support vector machine is fed back to the adaptive Kalman filter to adjust its observation noise covariance.

[0006] In this specification, step S4, the model construction of the adaptive Kalman filter includes: defining the state vector and the observation vector, determining the initial observation noise covariance, training and iteratively adjusting the process noise covariance, so that the output filter residual follows a normal distribution.

[0007] In this specification, step S4, the principal component analysis-entropy weight method coupled calculation of the comprehensive weight includes: standardizing the filtered measurement data, calculating the covariance matrix, extracting principal components and determining the principal component contribution rate, and calculating the principal component weights based on the principal component loadings and contribution rates; normalizing the standardized measurement data, calculating the information entropy, and calculating the entropy weights based on the information entropy; determining the coupling coefficient through grid search, and weighting the principal component weights and entropy weights according to the coupling coefficient to obtain the comprehensive weights.

[0008] In this specification, in step S4, the input features of the least squares support vector machine include environmental monitoring data and filter residuals. The input features are used for model training after being weighted by comprehensive weights. The environmental disturbance error compensation value output by the model is used to calculate the compensated environmental disturbance uncertainty component and to dynamically adjust the observation noise covariance of the adaptive Kalman filter.

[0009] In this specification, the multiple sets of repeated test measurement data in step S1 include the total inlet and outlet temperature measurement value and the total inlet and outlet pressure measurement value. The environmental monitoring data includes the ambient temperature and ambient pressure.

[0010] In this specification, in step S5, the application of the uncertainty propagation law is based on the propagation coefficient of each measurement parameter in the temperature rise efficiency calculation model. The sum of the squares of the three standard uncertainty components in S4 multiplied by their corresponding propagation coefficients is taken to obtain the combined standard uncertainty.

[0011] In this specification, in step S6, the inclusion factor is selected based on a 95% confidence level and is set to 2; the expanded uncertainty is the product of the inclusion factor and the combined standard uncertainty.

[0012] In this specification, in step S7, the verification method is as follows: calculate the relative deviation of the expanded uncertainty of multiple sets of experimental data. If all relative deviations are less than 5%, the verification is deemed successful. If it fails, the coupling coefficient of the principal component analysis-entropy weight method coupled model and the kernel parameters of the least squares support vector machine are adjusted first.

[0013] In this specification, the termination condition for closed-loop interaction is: the change in the environmental disturbance error compensation value output by the least squares support vector machine is less than 0.01K for three consecutive times, or the number of iterations reaches the preset maximum number.

[0014] In summary, the present invention has at least the following beneficial effects: 1. Eliminate subjective bias: Replace expert subjective scoring with principal component analysis-entropy weight method coupling (PCA-EWM), and objectively allocate weights based on the inherent correlation and dispersion of data to ensure that the contribution measurement of each parameter is more in line with the actual measurement law; 2. Improve data quality: Adaptive Kalman filtering (AKF) specifically filters out random noise in measurement data, providing high signal-to-noise ratio data for subsequent analysis and avoiding overestimation of uncertainty caused by noise; 3. Accurate compensation for nonlinear interference: Least squares support vector machine (LSSVM) fits the nonlinear relationship between environmental factors and interference error, and combines objective weights to enhance feature attention, significantly improving the quantification accuracy of environmental interference components; 4. Forming a closed-loop optimization: The three algorithms AKF, PCA-EWM, and LSSVM work together (filtered data drives weight calculation, weight optimizes interference modeling, and modeling results are fed back to adjust filter parameters) to achieve dynamic optimization of uncertainty components, thereby improving the overall stability and adaptability of the model. 5. Enhanced result reliability: The entire process is data-driven with logical closed loops between steps, ensuring that the uncertainty analysis results are closer to the actual error level, providing a more scientific basis for compressor performance evaluation and design improvement. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating the method for constructing a mathematical analysis model for the uncertainty of compressor temperature rise efficiency involved in this invention.

[0016] Figure 2 This is a schematic diagram illustrating the process of establishing the temperature rise efficiency model involved in this invention.

[0017] Figure 3 This is a schematic diagram of the process for identifying uncertainty sources and quantizing components involved in this invention.

[0018] Figure 4 This is a schematic diagram of the synthesis evaluation and verification correction process involved in this invention. Detailed Implementation

[0019] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0020] like Figure 1 As shown, this embodiment provides a method for constructing a mathematical analysis model for the uncertainty of compressor temperature rise efficiency, including the following steps: S1: Collect basic parameters and data, including compressor design and operation parameters, multiple sets of repeated test measurement data, working fluid characteristic data and environmental monitoring data; S2: Based on fundamental parameters and data, and combined with thermodynamic theory, a calculation model for compressor temperature rise efficiency is established; S3: Based on the compressor temperature rise efficiency calculation model and basic parameters and data, identify the sources of uncertainty affecting temperature rise efficiency; S4: Quantify the components corresponding to the sources of uncertainty; use adaptive Kalman filtering to reduce noise in multiple sets of repeated experimental measurement data, and output the filtered measurement data and filtering residuals; using the filtered measurement data as input, first extract the contribution through principal component analysis, then analyze the dispersion through entropy weight method, and calculate the comprehensive weight; combine the comprehensive weight to calculate and output the standard uncertainty component of the measurement process; construct input features based on environmental monitoring data and filtering residuals, weight the input features with comprehensive weights, train the environmental interference error model through least squares support vector machine, output the environmental interference error compensation value, and then combine the initial environmental interference components calculated through environmental monitoring data to calculate the compensated environmental interference standard uncertainty component; based on the working fluid characteristic data, determine the variation range of the specific heat capacity ratio of the working fluid under actual working conditions, take the half-width to calculate the deviation, and comprehensively obtain the model assumption standard uncertainty component; S5: Based on the compressor temperature rise efficiency calculation model and the standard uncertainty components of the measurement process, environmental disturbance, and model assumptions, the combined standard uncertainty is calculated using the uncertainty propagation law. S6: Based on the combined standard uncertainty, determine the coverage factor and calculate the expanded uncertainty; S7: Select experimental data that were not used in training to verify the model, and verify the model stability by calculating the relative deviation of the expanded uncertainty; S8: After successful verification, integrate the results of the previous steps and output the mathematical analysis model of compressor temperature rise efficiency uncertainty.

[0021] In some embodiments, in step S4, the three algorithms form an interactive closed loop: the filtered measurement data output by the adaptive Kalman filter is used as the input of the principal component analysis-entropy weighting method coupling; the comprehensive weight output by the principal component analysis-entropy weighting method coupling is used to weight the input features of the least squares support vector machine; the environmental interference error compensation value output by the least squares support vector machine is fed back to the adaptive Kalman filter to adjust its observation noise covariance.

[0022] In some embodiments, step S4, the model construction of the adaptive Kalman filter includes: defining a state vector and an observation vector, determining the initial observation noise covariance, training and iteratively adjusting the process noise covariance, so that the output filter residual follows a normal distribution.

[0023] In some embodiments, step S4, the principal component analysis-entropy weight method coupled calculation of the comprehensive weight includes: standardizing the filtered measurement data, calculating the covariance matrix, extracting principal components and determining the principal component contribution rate, and calculating the principal component weight based on the principal component loading and contribution rate; normalizing the standardized measurement data, calculating the information entropy, and calculating the entropy weight based on the information entropy; determining the coupling coefficient through grid search, and weighting the principal component weight and the entropy weight according to the coupling coefficient to obtain the comprehensive weight.

[0024] In some embodiments, in step S4, the input features of the least squares support vector machine include environmental monitoring data and filter residuals. The input features are used for model training after being weighted by comprehensive weights. The environmental disturbance error compensation value output by the model is used to calculate the compensated environmental disturbance uncertainty component and to dynamically adjust the observation noise covariance of the adaptive Kalman filter.

[0025] In some embodiments, the multiple sets of repeated test measurement data in step S1 include the total inlet and outlet temperature measurement value and the total inlet and outlet pressure measurement value, and the environmental monitoring data includes the ambient temperature and ambient pressure.

[0026] In some embodiments, in step S5, the uncertainty propagation law is applied based on the propagation coefficient of each measurement parameter in the temperature rise efficiency calculation model. The three standard uncertainty components in S4 are multiplied by their corresponding propagation coefficients, and the sum of the squares and the square root of the result are taken to obtain the combined standard uncertainty.

[0027] In some embodiments, in step S6, the inclusion factor is selected based on a 95% confidence level and is set to 2; the expanded uncertainty is the product of the inclusion factor and the combined standard uncertainty.

[0028] In some embodiments, in step S7, the verification method is as follows: calculate the relative deviation of the expanded uncertainty of multiple sets of experimental data. If all relative deviations are less than 5%, the verification is deemed successful. If it fails, the coupling coefficient of the principal component analysis-entropy weight method coupled model and the kernel parameters of the least squares support vector machine are adjusted first.

[0029] In some embodiments, the termination condition for closed-loop interaction is: the change in the environmental disturbance error compensation value output by the least squares support vector machine is less than 0.01K for three consecutive times, or the number of iterations reaches the preset maximum number.

[0030] The technical approach of this invention is as follows: This solution constructs a fully data-driven, multi-algorithm collaborative mathematical analysis model for compressor temperature rise efficiency uncertainty through eight closely linked steps, the specific details of which are as follows: S1: Basic Parameters and Data Collection This step provides all the raw data for model building. All data will serve as the input for subsequent steps, and their completeness and accuracy must be ensured. Data collection must cover compressor core parameters, experimental measurement data, instrument characteristics, and environmental monitoring data, as detailed below: 1. Compressor design and operating parameters: Design pressure ratio (Ratio of total outlet to inlet pressure under design conditions); Design flow rate (Unit: kg / s, mass flow rate under design conditions); Design rotational speed (Unit: r / min, rotor speed under design conditions); Design value of total inlet temperature (Unit: K) Design value of total outlet temperature (Unit: K); Design value of total inlet pressure (Unit: kPa), Design value of total outlet pressure (Unit: kPa).

[0031] 2. Test measurement data: At least 5 sets of repeated experimental data should be collected (10 sets or more are recommended to improve algorithm accuracy). Each set of data should include: Import total temperature measurement value (i=1,2,...,n, where n is the number of test groups, unit: K); Total outlet temperature measurement (Unit: K); Inlet total pressure measurement value (Unit: kPa); Total outlet pressure measurement (Unit: kPa).

[0032] 3. Basic data of measuring instruments: Temperature sensor: Model number, maximum permissible error (Unit: K, e.g.) Calibration certificate number; Pressure sensor: model, maximum permissible error (Unit: kPa, e.g.) Calibration certificate number; Flow sensor: model, maximum permissible error (Unit: %FS, e.g.) ), calibration certificate number.

[0033] 4. Environmental monitoring data: Test ambient temperature (Ambient temperature during each test, unit: K); Test ambient pressure (Ambient atmospheric pressure during each test, unit: kPa); Ambient temperature fluctuation range (Unit: K); Range of environmental pressure fluctuations (Unit: kPa).

[0034] 5. Working Fluid Thermodynamic Data (Source: Working Fluid Thermodynamics Handbook): Working Fluid Type: Air is used in this scheme; dry air must be clearly specified in the handbook. Temperature Characteristics of Specific Heat Ratio k: Data on the variation of k values ​​for air in the range of 288K (room temperature) to 800K (typical compressor outlet temperature) from the handbook, specifically: k=1.400 at 288K, k=1.398 at 300K, k=1.390 at 400K, k=1.382 at 500K, k=1.374 at 600K, k=1.365 at 700K, and k=1.357 at 800K. Range of k Variation: Based on the above data, the half-width of k in the model assumptions is determined. (That is, k fluctuates between 1.39 and 1.41, covering the commonly used operating range of 288K to 350K in the manual.)

[0035] Data transmission instructions: This step collects... , , , Enter S4's AKF directly; , LSSVM feature construction for S4; instrument error , AKF initialization for S4 The k-values ​​and their ranges from the working fluid thermodynamics handbook are used for the derivation of the efficiency formula for S2 and the model assumptions for S4, respectively. calculate.

[0036] S2: Compressor temperature rise efficiency calculation model established Based on the parameters of S1, and combined with thermodynamic theory, the mathematical expression for the temperature rise efficiency is derived, clarifying the correspondence between the model input and the data processed by S1 and S4, thus providing a calculation basis for subsequent uncertainty analysis. The process for establishing the temperature rise efficiency model is as follows: Figure 2 As shown.

[0037] 1. Definition and formula derivation of temperature rise efficiency: Compressor temperature rise efficiency It is the ratio of the actual temperature rise to the ideal isentropic temperature rise, reflecting the energy conversion efficiency. According to the ideal gas law, the relationship between temperature and pressure in an isentropic process is: ( (where the total isentropic outlet temperature is), therefore: (2-1) The actual pressure ratio (calculated from the total inlet / outlet pressure); k is the specific heat ratio of the working fluid, k=1.4 (taken from the working fluid thermodynamics handbook in S1 at 288K ambient temperature; if the test temperature deviates significantly, the k value for the corresponding temperature in the handbook can be selected, such as k=1.395 at 350K). The actual measured value (subsequent values ​​will be the AKF filtered values ​​from S4) (to improve accuracy).

[0038] 2. Model rationality verification: Select any set of original data in S1 (e.g., when i=1) , , , Substitute into equation (2-1) to calculate the preliminary efficiency: ; Ideal temperature rise Actual temperature rise ; (76.1%).

[0039] This result will be used to compare the consistency between S7 and uncertainty analysis results.

[0040] Data transmission instructions: This step establishes... The formula will serve as the basis for the S5 uncertainty propagation, and the formula contains... The data will subsequently be replaced with the AKF-filtered data from S4. etc., to reduce the impact of noise.

[0041] S3: Uncertainty Source Identification Based on the efficiency model of S2, combined with the data type of S1 and the algorithm processing target of S4, the system identifies the impact. All sources of uncertainty are identified, ensuring that each source can be quantified or compensated for in subsequent steps. The uncertainty source identification and component quantification process is as follows: Figure 3 As shown.

[0042] 1. Measurement process uncertainty (caused by sensor error and data fluctuation): Total inlet temperature Measurement error (including sensor random noise and systematic error); total outlet temperature Measurement error; total inlet pressure Measurement error; total outlet pressure Measurement error (due to) The calculation shows that the error is contributed by both factors.

[0043] Note: This type of error will be denoised by the AKF filter of S4 and quantized by PCA-EWM with assigned weights.

[0044] 2. Model assumption uncertainty (caused by simplification of the theoretical model): Error in the specific heat ratio k of the working fluid: In reality, k varies with temperature (e.g., k=1.4 for air at 300K and k=1.37 at 600K), but the model uses a constant value of 1.4, which introduces an error.

[0045] Note: This type of error is quantified using a fixed formula in S4 (and is not involved in algorithm fusion).

[0046] 3. Environmental interference uncertainty (caused by environmental factors affecting the measurement standard): Ambient temperature fluctuations This causes temperature sensor reference drift, affecting... Measurement; Environmental pressure fluctuations This causes pressure sensor reference drift, affecting... Measurement.

[0047] Note: This type of error will be compensated by modeling LSSVM in S4 and fed back to optimize AKF.

[0048] S4's AKF addresses random noise in the measurement process; PCA-EWM addresses the differences in the contribution of measurement parameters; and LSSVM addresses the nonlinear effects of environmental interference. These three methods respectively cover the three types of sources identified in this step.

[0049] S4: Quantification calculation of each uncertainty component This step is the core of uncertainty quantification. Through the synergistic fusion of Adaptive Kalman Filtering (AKF), Principal Component Analysis-Entropy Weighting (PCA-EWM), and Least Squares Support Vector Machine (LSSVM), it achieves noise reduction of measurement data, objective weight allocation, and environmental interference compensation, outputting three high-precision uncertainty components. The three algorithms form a closed loop of data preprocessing → weight allocation → error correction → feedback optimization: AKF denoises the original measurement data, providing clean input for subsequent analysis; PCA-EWM calculates objective weights based on the denoised data, quantifying the contribution of each parameter to the uncertainty; LSSVM uses the weight information to construct an environmental interference model, outputs compensation values, and feeds back to adjust AKF, improving overall quantification accuracy.

[0050] 4.1 Algorithm 1: Adaptive Kalman Filter (AKF) – Measurement Data Noise Reduction Optimization Measurement data (such as total inlet temperature and total outlet pressure) are inevitably affected by random noise and electromagnetic interference from sensors during the acquisition process. Directly using this data for subsequent analysis can lead to an overestimation of uncertainty components. AKF effectively filters out noise and preserves the true trend of the data by dynamically adjusting the filter gain, providing a reliable analytical basis for PCA-EWM.

[0051] 4.1.1 Model Construction (Based on the Dynamic Characteristics of Measurement Parameters) The core of AKF is to describe the dynamic changes of parameters through state equations, correlate measured values ​​with true values ​​through observation equations, and then iteratively correct the estimation results. For compressor test data (where parameters change steadily over a short period), the model is constructed as follows: Definition 1: s — discrete time step (corresponding to the group number of the experimental data in S1, s=1,2,...,n, where n is the total number of experimental groups, such as n=10 indicating 10 repeated experiments); Definition 2: —The state vector at time s (4×1 dimension) represents the true values ​​of the four core measurement parameters, namely: ; in, This represents the true value of the total inlet temperature in the s-th group of experiments (the subscript "1t" represents the inlet + total parameters, and s represents the time step). This represents the true value of the total outlet temperature. This represents the true value of the total import pressure. This represents the true value of total export pressure. Definition 3: —The observation vector at time s (4×1 dimension), which is the raw experimental data directly collected in S1: ; in, This represents the measured total inlet temperature in the s-th group of experiments; the subscripts of the other parameters correspond to the state vector. Definition 4: —The process noise vector (4×1 dimension) follows a mean of 0 and a covariance of . normal distribution ( This reflects fluctuations in the parameters themselves (such as minor changes in the compressor's operating status). Definition 5: —Observation noise vector (4×1 dimension), which follows a mean of 0 and a covariance of . normal distribution ( This reflects the sensor measurement error (determined by the instrument's maximum permissible error in S1, such as that of a temperature sensor). ,but Since the measurement error follows a uniform distribution, to convert it to a normal distribution, the covariance needs to be divided by 3). Definition 6: —State transition matrix (4×4 dimensions), describing the state change from time s-1 to time s. Because the parameters in the compressor experiment change steadily over a short period (e.g., 30-second intervals between each test group), it is set as an identity matrix: ; Definition 7: —The observation matrix (4×4 dimensions) describes the mapping relationship between the state vector and the observation vector. Since the observed values ​​directly correspond to the state values ​​(the measured values ​​are the true values ​​superimposed with noise), it is set as the identity matrix: .

[0052] Based on the above definition, the iterative process of AKF is divided into a prediction step and an update step: 1. Prediction Step: Using the optimal estimate at time s-1, predict the state and error range at time s: (4-1) (4-2) In equation (4-1), The prior state estimate at time s (based on the optimal estimate at time s-1) ); In equation (4-2), Let be the prior covariance matrix at time s (reflecting the uncertainty of the prior estimate). Let be the optimal covariance matrix at time s-1.

[0053] 2. Update step: Combine the observations at time s By correcting the prior estimate, the optimal estimate is obtained: (4-3) (4-4) (4-5) In equation (4-3), Kalman gain (balances prior estimation error and observation error; a larger value indicates greater dependence on observations). In equation (4-4), The optimal state estimate at time s (filtered data, which eliminates most of the random noise); In equation (4-5), Let be the optimal covariance matrix at time s (reflecting the uncertainty of the optimal estimate).

[0054] 4.1.2 Model Training (Calibration Based on Historical Experimental Data) To ensure the filtering effect of AKF, it is necessary to train the system using historical experimental data from S1 (at least 3 sets, more sets are more reliable) to determine the initial parameters and verify the stability of the filter. 1. Training data preparation: Select n=10 complete experimental data sets from S1 (including...) ), forming the training set ; 2. Initial value settings: Initial state estimation : Take the mean of all parameters in the training set, i.e. ,in (This is the measured mean of "total inlet temperature," without a time step sign, as it is a statistical value for all groups). Initial covariance matrix : Take the sample variance of each parameter in the training set, i.e. ,in ; Initial process noise covariance Set as a diagonal matrix (Small values ​​indicate small fluctuations in the initial assumed parameters); Initial observation noise covariance Based on instrument errors in S1, such as temperature sensor errors. ,but Pressure sensor ,but ; 3. Iterative training and validation: Substitute the training set data into equations (4-1) to (4-5) one by one to calculate the residual at each step. (The deviation between observed and filtered values). If the mean of the residuals is close to 0 and the standard deviation is less than 30% of the standard deviation of the original data, the filtering is effective; otherwise, adjust... (If the residual is too large, increase it) (Allowing for greater process fluctuations), repeat training until the conditions are met.

[0055] 4.1.3 Model Application (Outputting noise-reduced measurement data) Substitute all experimental data from S1 (including new data outside the training set) into the trained AKF model, and output the filtered measurements as the input to PCA-EWM: (4-6) In equation (4-6), For optimal state estimation The j-th element (j=1 corresponds to the total inlet temperature, j=2 corresponds to the total outlet temperature, j=3 corresponds to the total inlet pressure, j=4 corresponds to the total outlet pressure). For example: If the raw data of the third group of experiments (s=3) are After AKF filtering, the result is obtained This indicates that 0.2K of random noise was filtered out; Core function: The filtered data eliminates sensor noise interference, ensuring that the weights calculated in subsequent PCA-EWM calculations can truly reflect the importance of the parameters themselves, rather than false fluctuations caused by noise.

[0056] 4.2 Algorithm 2: Principal Component Analysis-Entropy Weight Coupling (PCA-EWM) – Objective Weight Allocation Optimization Different measurement parameters (such as inlet temperature and outlet pressure) have varying degrees of impact on compressor temperature rise efficiency, and directly calculating the uncertainty components equally will lead to biased results. PCA-EWM uses a two-step objective analysis: first, PCA is used to extract the contribution of parameters to the overall uncertainty (principal component weights); then, EWM is used to analyze the dispersion of parameter data (entropy weights); finally, the two are coupled to obtain a comprehensive weight, quantifying the true impact of each parameter and providing a basis for the synthesis of uncertainty components in the measurement process.

[0057] 4.2.1 Model Construction The core of PCA-EWM is to determine weights based on the inherent correlation and dispersion of the data, eliminating the need for subjective expert judgment. The model parameters are defined as follows: Definition 8: j — Measurement parameter index (j=1,2,3,4, corresponding to the total inlet temperature respectively) Total outlet temperature Total import pressure Overall export pressure ); Definition 9: —PCA principal component weights (reflecting the contribution of the j-th parameter to the overall uncertainty; the larger the value, the more significant the impact of the parameter on the principal components). Definition 10: —EWM entropy weight (reflects the dispersion of the filtered data for the j-th parameter; the larger the value, the greater the data fluctuation and the more significant its contribution to uncertainty). Definition 11: —PCA-EWM composite weights (coupled with principal component weights and entropy weights, serving as the final measure of parameter importance). Definition 12: —Coupling coefficient ( To balance the influence of principal component contributions and data dispersion, the optimal value is determined through data fitting.

[0058] 4.2.2 Model Training Step 1: PCA Training PCA extracts the main directions of change in the data (principal components) through dimensionality reduction. The larger the parameter loading on the principal components, the greater its contribution to the overall uncertainty. Specific steps: 1. Data Standardization: Filtering the AKF output data. (s=1~n, j=1~4) Standardize to eliminate the influence of dimensions: (4-7) in, The filtered mean of the j-th parameter (e.g.) (i.e., the average of the total inlet temperature after filtering). Let be the standard deviation of the filter for the j-th parameter; Example: If the inlet total temperature is filtered , Then the first set of data (s=1) After standardization ; 2. Calculate the covariance matrix: The covariance matrix reflects the linear correlation between parameters and is calculated based on standardized data. (4-8) in, It is an n×4 standardized data matrix (each row corresponds to a set of data, and each column corresponds to a parameter). It is a 4×4 matrix with elements (Because the mean is 0 after standardization); Example: If n=10, the calculation is as follows Explain the total inlet temperature With total outlet temperature Strong correlation (0.8), total import pressure Overall export pressure Strong correlation (0.9); 3. Extraction of principal components and contribution rates: Solving the covariance matrix eigenvalues and corresponding feature vectors (The eigenvector is a unit vector, reflecting the direction of the principal components); Example: The above eigenvalues , , , eigenvectors , ; Calculate the principal component contribution rate (The sum of the total eigenvalues ​​is) ),have to (50%) (36%), with a cumulative contribution rate of 86% (≥85%), therefore the first two principal components are selected; 4. Calculate the principal component weights: The weighted sum of the parameter loadings (correlation strength) on the principal components and the principal component contribution rates yields the results. : (The loading of the j-th parameter on the m-th principal component); (4-9) (M is the number of principal components selected); (4-10) Example: The first parameter (j=1, corresponding to the total inlet temperature) Loadings on the two principal components: , ; Weighted sum: ; Similarly, after calculating other parameters, the sum is 0.596 + 0.61 + 0.42 + 0.42 ≈ 2.046. Therefore... , , , .

[0059] Step 2: EWM Training EWM determines weights based on the data's dispersion (entropy): the more dispersed the data (the smaller the entropy), the greater the parameter fluctuations, and the more significant the contribution to uncertainty. Specific steps: 1. Data normalization: standardizing data Mapping to the [0,1] interval avoids the negative sign affecting entropy calculation: (4-11) in, For all standardized data of the j-th parameter, , These are its minimum and maximum values, respectively. Example: If the total inlet temperature of If the range is [-1.5, 2.0], then the first group (s=1) After normalization ; 2. Calculate information entropy: (4-12) (4-13) in, (avoid lead to (meaningless) The normalized proportion of the j-th parameter in the s-th group. The entropy value of the j-th parameter ( (The smaller the value, the greater the dispersion). Example: n=10, the second parameter (j=2, corresponding to the total outlet temperature) )of The fluctuations are large, and the calculations are as follows (Large dispersion), the third parameter (j=3, corresponding to the total inlet pressure) )of Small fluctuations (Small dispersion); 3. Calculate the entropy weight: (4-14) Example: If ,but The sum is 0.78, therefore , , , .

[0060] Step 3: Coupled Training To balance principal component analysis (PCA) contributions with data dispersion (EWM), coupling coefficients are used. Combining the two: (4-15) Optimize through grid search (Values ​​range from 0.1, 0.2, ..., 0.9), select the value that minimizes the deviation between the weighted measurement component and the high-precision standard value. Example: when hour: (Corresponding to total inlet temperature) ); (Corresponding to total outlet temperature) ); (corresponding to total import pressure) ); (corresponding to total export pressure) ).

[0061] 4.2.3 Model Application (Calculating Weighted Measurement Uncertainty Components) Using the PCA-EWM combined weights, the contribution of each parameter to the measurement uncertainty is calculated, and the total components are synthesized: 1. Calculate the standard deviation of the filtered samples: based on the AKF output. Calculate the standard deviation of the j-th parameter (reflecting data fluctuation): (4-16) Example: Inlet total temperature After filtering Calculated ; 2. Calculate the weighted standard uncertainty components: The uncertainty component of each parameter is the standard error of its standard deviation ( Multiplied by the overall weight : (4-17) Example: n=10, then the total inlet temperature of ; 3. Total components of the composite measurement process: (4-18) Example: If , , , ,but ; Core function: To differentiate the impact of each parameter through objective weighting, avoiding excessive inclusion of fluctuations in minor parameters into the uncertainty, while simultaneously integrating the weights. This will be used as the feature weights of LSSVM to improve the accuracy of environmental interference modeling.

[0062] 4.3 Algorithm 3: Least Squares Support Vector Machine (LSSVM) – Environmental Interference Error Compensation Optimization Environmental factors (such as fluctuations in ambient temperature and pressure) can affect data accuracy through sensor measurement baseline drift, and their interference has nonlinear characteristics (e.g., the effect of temperature fluctuations on pressure measurement is nonlinear). LSSVM excels at fitting nonlinear relationships. By introducing the comprehensive weights of PCA-EWM as feature weights, the model can enhance its attention to key environmental factors, output environmental interference error compensation values, and provide feedback to adjust the noise covariance of AKF, forming a closed-loop optimization.

[0063] 4.3.1 Model Construction LSSVM maps input features to a high-dimensional space using kernel functions, fitting the nonlinear relationship between environmental factors and interference errors. The model parameters are defined as follows: Definition 13: —The input feature vector (3×1 dimension) for the s-th experiment (time s) contains: Ambient temperature fluctuations ( The ambient temperature during the s-th group of experiments, (For reference ambient temperature) Environmental pressure fluctuations ( The environmental pressure during the s-th group of experiments, (For reference environmental pressure) AKF residual (This reflects errors that still exist after filtering, which may be caused by environmental interference.) Definition 14: —The weighted input feature vector (3×1 dimension) is combined with PCA-EWM weights. Enhance key features: ; Due to the total temperature of the import Sensitive to temperature, using its weight Weighted Total import pressure Sensitive to pressure, use its weight Weighted ; Definition 15: —The output label at time s (true value of environmental interference error) was obtained from a high-precision environmental chamber experiment: control in the environmental chamber , Given a known value, compare the deviation between the measured value from the standard instrument and the measured value from the test sensor. ; Definition 16: —The weight vector of LSSVM; Definition 17: b — the bias term of LSSVM; Definition 18: — Kernel function (using the RBF kernel to fit nonlinear relationships): ;in, Here, r is the kernel parameter (controlling the space complexity after mapping), and r is the time step index of the support vector; Definition 19: C – Penalty factor (C>0, balancing the model’s fit to the training data and its generalization ability).

[0064] The optimization objective of LSSVM is to minimize the weight vector norm and the fitting error. (4-19) st (4-20) in, For kernel space mapping function (to Mapping to higher-dimensional space). This represents the fitting error. It is transformed into a system of linear equations using the Lagrange multiplier method: (4-21) in, It is a Lagrange multiplier. For an n×n kernel matrix ( ), This is for outputting label vectors.

[0065] 4.3.2 Model Training (Calibration Based on Environmental Chamber Test Data) 1. Training data preparation: Input features: Set up 10 different sets of features in the environmental chamber. (e.g., 1K, 2K, ..., 10K) and (e.g., 0.5 kPa, 1.0 kPa, ..., 5.0 kPa), collect the corresponding test data. ,according to Weighted ; Output label: The true value of environmental interference error for each group measured synchronously. (as when) hour, ), forming the training set ; 2. Parameter optimization: Optimal parameters are searched using 5-fold cross-validation (the training set is divided into 5 parts, and 4 parts are used for training and 1 part for validation alternately). And C: like When C=100, the root mean square error (RMSE) of the validation set is minimized (e.g., RMSE=0.05K), so this parameter combination should be selected. 3. Solve for model parameters: Optimize Substitute C into equation (4-21) and solve. And b, filter The samples are used as support vectors (e.g., 6 support vectors are selected) to complete model training.

[0066] 4.3.3 Model Application (Compensating for Environmental Interference and Feedback Optimization of AKF) 1. Predicting environmental interference errors: This involves using real-time environmental data ( , , Weighted Substitute the input into the trained LSSVM to output the compensation value: (4-22) Where S is the support vector index set; Example: Real-time , Calculated ; 2. Calculate the compensated environmental disturbance components: Initial environmental disturbance components This is used to quantify the raw interference of ambient temperature and pressure fluctuations on the measurement system (without LSSVM compensation). Its calculation is based on the range of environmental parameter fluctuations and the sensor's sensitivity coefficient to the environment, as detailed below: —The ambient temperature sensitivity coefficient of the temperature sensor refers to the measurement error caused by a 1K fluctuation in ambient temperature. It is provided by the sensor calibration report and the unit is K / K. —The environmental pressure sensitivity coefficient of the pressure sensor refers to the measurement error caused by a 1 kPa fluctuation in environmental pressure. It is provided by the sensor calibration report and the unit is kPa / kPa. —Standard uncertainty component caused by ambient temperature fluctuations, unit: K; —Standard uncertainty component caused by environmental pressure fluctuations, unit: kPa.

[0067] Errors caused by environmental disturbances follow a uniform distribution (with fluctuations within a symmetrical range), and the standard uncertainty is half the width divided by 1 / 2. ,specific: Ambient temperature fluctuation components: Environmental pressure fluctuation components: Total components of the original environmental disturbance (combination of square root): ; It reflects the total interference of environmental fluctuations on the measurement system without LSSVM compensation. Its value will serve as the benchmark for LSSVM compensation in S4 and directly affect the final quantization accuracy of the environmental interference components.

[0068] Initial environmental disturbance components Subtract the impact of the compensation value: (4-23) Example: (Accuracy improved by 25% after compensation); 3. Feedback adjustment of AKF observation noise covariance: As an effect of environmental interference on observation, dynamically reducing AKF (To make the filter more trusting of the observations): (4-24) in, (Adjustment coefficient) This represents the historical maximum compensation value (e.g., 0.5K); Example: ,but ; Core function: It compensates for environmental interference errors through nonlinear modeling, and at the same time optimizes the filtering effect of AKF, forming a closed loop of AKF noise reduction → PCA-EWM weighting → LSSVM compensation → AKF optimization, which significantly improves the quantization accuracy of uncertainty components.

[0069] 4.4 Output of final uncertainty components After the combined processing of the above three algorithms, three uncertainty components are finally output as inputs for the S5 composite calculation: 1. Measurement process components: (Equation 4-18, after AKF noise reduction and PCA-EWM weighting); 2. Model assumption components: 3. Environmental disturbance components: (Equation 4-23, compensated by LSSVM).

[0070] The fusion logic of the three algorithms is clear and closed-loop: AKF provides high-quality data for subsequent analysis, PCA-EWM objectively allocates weights based on the data, and LSSVM uses weights to optimize modeling and feedback to improve the performance of AKF, ultimately achieving high-precision quantification of uncertainty components, laying the foundation for the reliability analysis of compressor temperature rise efficiency.

[0071] S5: Calculation of Combined Standard Uncertainty Based on the temperature rise efficiency model of S2 and the three components of the output of S4, the uncertainty propagation law is used to calculate... Combined standard uncertainty This quantifies the combined impact of each component on the total uncertainty. The composite evaluation and verification correction process is as follows: Figure 4 As shown.

[0072] 1. Derive the uncertainty transmission coefficient: For S2 The formula calculates the partial derivatives (transfer coefficients) of each influencing parameter, reflecting the sensitivity of efficiency to parameter changes: right Partial derivatives: ; right Partial derivatives: ; right Partial derivatives: (After simplification and) (Related) right Partial derivatives: similar The directions are opposite; Partial derivative with respect to k: .

[0073] 2. Substitute the components to calculate the combined uncertainty: According to the law of transmission, the combined standard uncertainty is the square root of the sum of the squares of the products of the uncertainties of each parameter and the transmission coefficient: (5-1) The standard uncertainty of each parameter after AKF filtering in S4 is ( ); The output of S4 is directly quoted.

[0074] Example calculation: Using the verification data from S2, if , , , , , After substituting the transmission coefficient, the result is calculated. (2.1%).

[0075] Data transmission instructions: The output of this step It will be used as input for the calculation of the expanded uncertainty in S6.

[0076] S6: Evaluation of Expanded Uncertainty Based on the combined standard uncertainty of S5, the inclusion factor is determined in conjunction with industry standards, and the expanded uncertainty U is calculated for the final uncertainty report, which intuitively reflects the credibility range of the efficiency measurement results.

[0077] 1. Selection of inclusion factor: According to Part 3 of the Reciprocating Internal Combustion Engine Performance Specification: Test Measurements, the confidence level for compressor testing is typically taken as 95%, and the corresponding coverage factor is uniformly used throughout the entire process. =2 (covers 95% of the probability distribution range). For a higher confidence level (e.g., 99%), then... =2.58, which needs to be clearly stated in the report.

[0078] 2. Calculation of expanded uncertainty: (6-1) Example: If , =2, then U=0.042 (4.2%), which means that at a 95% confidence level, the measured result of the compressor temperature rise efficiency is . .

[0079] Data transmission instructions: U and its corresponding confidence level and inclusion factor will be the core results of S8 documentation.

[0080] S7: Model Validation and Feedback Correction The stability and accuracy of the model are verified through multiple sets of experimental data. If the verification fails, the previous steps need to be traced back to make corrections to ensure the reliability of the model.

[0081] 1. Verification method: Select the remaining experimental data from S1 (e.g., i=2,3,...,10), and repeat the calculations from S4 to S6 to obtain 10 sets. and U; Calculate the relative deviation of the results for each group: ,in The mean of 10 groups of U; If all If the result is positive, the model is stable and effective; otherwise, it needs to be corrected.

[0082] 2. Feedback and Correction Process: If the deviation originates from the measurement component: check the coupling coefficient of PCA-EWM in S4. Re-optimize via grid search (as in the original) This caused a deviation, so it was adjusted to Recalculate ); If the deviation originates from environmental components: check the kernel parameters of LSSVM in S4. Add a penalty factor C, increase the number of training samples (e.g., from 10 groups to 15 groups), retrain the model, and correct the error. ; If the deviation originates from the filtering effect: adjust the initial value of AKF in S4. (as from) Increase to This enhances the adaptability to process fluctuations and re-outputs filtered data.

[0083] Example correction: If the 5th group of trials , , Upon inspection, it was found that LSSVM... The fitting error is large, so three more sets of high temperature fluctuation data were added. Retraining, after correction .

[0084] S8: Model Output and Documentation Integrate all data, algorithm parameters, calculation results, and verification records from previous steps to form a complete model document, ensuring traceability and reusability. The document should include the following: 1. Summary of basic information: S1 parameter list (including design parameters, 10 sets of test data, instrument error, and environmental fluctuation range); Data collection time, location, and operators (to ensure the experiment is reproducible).

[0085] 2. Algorithm and Model Details: Initial Parameters of AKF in S4 ( ), after training Adjust the records; eigenvalues, contribution rates, and overall weights of PCA-EWM. and the optimized Values; LSSVM kernel parameters The data includes: the penalty factor C, the number of support vectors, and the verification data of the compensation effect; the temperature rise efficiency formula for S2 and the combined uncertainty propagation formula for S5 (including the calculation process of the propagation coefficient).

[0086] 3. Calculation Result Report: Quantification Table of Each Component of S4 ( (Values ​​and units); Combined standard uncertainty of S5 S6: Expanded uncertainty U (including confidence level and k value); S7: Deviation analysis table of 10 sets of verification data and correction records (if any).

[0087] 4. Model Application Instructions: Clearly define the applicable range of the model (e.g., pressure ratio 1.5~3.0, ambient temperature 283~303K). Precautions for subsequent use (e.g., if the number of experimental groups is less than 10, the AKF training strategy needs to be adjusted).

[0088] Through the synergy of the above eight steps, a complete mathematical analysis model for compressor temperature rise efficiency uncertainty was constructed. Among them, the three fusion algorithms in S4 significantly improved the quantification accuracy through data noise reduction, objective weighting, and nonlinear compensation. The data transmission between each step was clear, and the feedback mechanism ensured the reliability of the model, which can provide a scientific basis for uncertainty analysis for compressor performance evaluation.

[0089] In some embodiments, the ReliefF feature weighting algorithm is introduced to optimize the local sensitivity feature weights. The ReliefF algorithm calculates feature weights by evaluating the ability of features to distinguish local differences in samples, effectively capturing the local correlations in the data (compensating for the deficiency of PCA, which only focuses on global principal components). This algorithm, coupled with PCA-EWM, forms a global-local dual-dimensional weight, while providing more accurate feature weights for LSSVM and providing filtering accuracy feedback with AKF, achieving multi-algorithm collaborative optimization.

[0090] Model Construction (Feature Importance Assessment Based on Local Differences in Samples) ReliefF quantifies the contribution of features to classification (or regression) by comparing the feature differences between a sample and its nearest neighbors of the same or different classes. The model parameters are defined as follows: Definition 20: f — Feature index (f=1,2,3,4, corresponding to the measurement parameters: f=1 is the total inlet temperature) f=2 is the total outlet temperature f=3 is the total inlet pressure. f=4 represents the total outlet pressure. ); Definition 21: —ReliefF feature weights (reflecting the ability of the f-th feature to distinguish local differences in the samples; the larger the value, the more important the feature). Definition 22: —Sample set after AKF filtering ( n is the number of samples. (where s is the filtered data vector of the s-th sample). Definition 23: —Feature difference function: For feature f, the sample and The normalized difference is calculated using the following formula: (4-25) in, For the sample The f-th eigenvalue, , Features f in the sample set The maximum and minimum values ​​in; Definition 24: --sample H nearest neighbors of the same kind (and) Samples from the same working condition, where H is the nearest neighbor number, taken as H=3). Definition 25: --sample M1 heterogeneous nearest neighbors in category C (and) Samples from different working conditions, M1=2, C is the number of working condition categories). Definition 26: —Prior probability of category C (the proportion of samples of category C in the sample set).

[0091] Model training (calculating the weights of local sensitivity features) ReliefF captures the impact of features on local differences by iteratively updating weights. The steps are as follows: 1. Initialize weights: Set the initial weights of all features to 0, i.e. (f=1,2,3,4); 2. Iteratively calculate weights for the sample set. Each sample in (s=1,2,...,n): Step 2.1: Find H = 3 nearest neighbors of the same type ; Step 2.2: For each outlier category C (e.g., different speed operating conditions), find M1=2 outlier nearest neighbors. ; Step 2.3: Update feature weights : ; in, For the sample The categories are divided into two categories: the first penalizes feature differences among samples of the same category (the smaller the difference, the more important the feature), and the second rewards feature differences among samples of different categories (the larger the difference, the more important the feature).

[0092] 3. Weight normalization: Map the weights to the [0,1] interval to ensure the sum is 1. ; Example calculation: Sample set n=10, H=3, M1=2, number of categories 2 (C=1,2, P(1)=0.6, P(2)=0.4); For feature f=1 ( ), obtained through iterative calculation Similarly , , ; After normalization: , , , .

[0093] Model application ReliefF weights are integrated with other algorithms through three dimensions: global-local coupling, feature enhancement, and filter feedback, forming a collaborative optimization: (1) Coupling with PCA-EWM: forming global-local synthesis weights PCA-EWM reflects the global principal component contribution, while ReliefF reflects the sensitivity to local differences. Coupled, the two yield a more comprehensive set of feature weights. : ; in, Coupling coefficient ( This is determined by minimizing the deviation of the weights from the standard error, for example. ).

[0094] Example: Combining PCA-EWM With ReliefF ,have to: , , , .

[0095] (2) Interacting with LSSVM: Enhancing input feature weights LSSVM input feature vector Originally based on , now replaced with Increase attention to locally sensitive features: ; in, The updated input feature vector allows LSSVM to focus more on features with significant local differences (such as f=2). ).

[0096] Example: original After the update: Enhanced Weights of relevant features.

[0097] (3) Interacting with AKF: Feedback to adjust the state transition matrix The ReliefF weights reflect the local importance of features; important features should be given higher filtering stability (lower process noise). Therefore, the state transition matrix of AKF is adjusted accordingly. : ; Where c=0.01 is the adjustment coefficient. It is a diagonal matrix, with important features ( The diagonal elements of the larger features are close to 1 (more stable state), while the diagonal elements of the minor features are slightly larger (allowing for greater fluctuations).

[0098] Example: original After the update: , The state transition is more stable when (f=2).

[0099] Core contributions The ReliefF algorithm overcomes the limitation of PCA-EWM, which only focuses on global principal components, by capturing the sensitivity of local differences in features. Its integration with other algorithms is reflected in: 1. Coupled with PCA-EWM to form a global-local two-dimensional weight. This makes the measurement process components The quantification takes into account both the overall trend of the data and local fluctuations; 2. Provide optimized input feature weights for LSSVM This improves the accuracy of environmental interference error compensation; 3. Feedback and adjustments to AKF This makes the filtering of important features more stable and reduces information loss caused by over-smoothing.

[0100] Through the above interactions, ReliefF forms a complete closed loop with the original algorithm, consisting of local sensitivity, global correlation, noise suppression, and error compensation, further improving the quantization reliability of uncertainty components.

Claims

1. A method for constructing a mathematical analysis model for the uncertainty of compressor temperature rise efficiency, characterized in that, Includes the following steps: S1: Collect basic parameters and data, including compressor design and operation parameters, multiple sets of repeated test measurement data, working fluid characteristic data and environmental monitoring data; S2: Based on fundamental parameters and data, and combined with thermodynamic theory, a calculation model for compressor temperature rise efficiency is established; S3: Based on the compressor temperature rise efficiency calculation model and basic parameters and data, identify the sources of uncertainty affecting temperature rise efficiency; S4: Quantify the components corresponding to the sources of uncertainty; use adaptive Kalman filtering to reduce noise in multiple sets of repeated experimental measurement data, and output the filtered measurement data and the filtering residual; Using the filtered measurement data as input, the contribution is first extracted through principal component analysis, then the dispersion is analyzed through entropy weight method, and the comprehensive weight is obtained by weighted calculation. Calculate and output the standard uncertainty components of the measurement process by combining comprehensive weights; Input features are constructed based on environmental monitoring data and filter residuals. After the input features are weighted with comprehensive weights, the environmental interference error model is trained by least squares support vector machine, and the environmental interference error compensation value is output. Then, combined with the initial environmental interference components calculated by environmental monitoring data, the compensated environmental interference standard uncertainty components are calculated. Based on the working fluid characteristic data, the range of variation of the specific heat capacity ratio of the working fluid under actual working conditions is determined, the half-width is taken to calculate the deviation, and the standard uncertainty components of the model assumptions are obtained by combining them. S5: Based on the compressor temperature rise efficiency calculation model and the standard uncertainty components of the measurement process, environmental disturbance, and model assumptions, the combined standard uncertainty is calculated using the uncertainty propagation law. S6: Based on the combined standard uncertainty, determine the coverage factor and calculate the expanded uncertainty; S7: Select experimental data that were not used in training to verify the model, and verify the model stability by calculating the relative deviation of the expanded uncertainty; S8: After successful verification, integrate the results of the previous steps and output the mathematical analysis model of compressor temperature rise efficiency uncertainty.

2. The method for constructing a mathematical analysis model for the uncertainty of compressor temperature rise efficiency according to claim 1, characterized in that, In step S4, the three algorithms form an interactive closed loop: the filtered measurement data output by the adaptive Kalman filter is used as the input of the principal component analysis-entropy weighting method coupling; the comprehensive weight output by the principal component analysis-entropy weighting method coupling is used to weight the input features of the least squares support vector machine. The environmental disturbance error compensation value output by the least squares support vector machine is fed back to the adaptive Kalman filter to adjust its observation noise covariance.

3. The method for constructing a mathematical analysis model for the uncertainty of compressor temperature rise efficiency according to claim 1, characterized in that, In step S4, the model construction of the adaptive Kalman filter includes: defining the state vector and observation vector, determining the initial observation noise covariance, training and iteratively adjusting the process noise covariance so that the output filter residual follows a normal distribution.

4. The method for constructing a mathematical analysis model for the uncertainty of compressor temperature rise efficiency according to claim 1, characterized in that, In step S4, calculating the comprehensive weight includes: standardizing the filtered measurement data, calculating the covariance matrix, extracting principal components and determining their contribution rates, and calculating the principal component weights based on the principal component loadings and contribution rates; normalizing the standardized measurement data, calculating the information entropy, and calculating the entropy weights based on the information entropy; determining the coupling coefficients through grid search, and weighting the principal component weights and entropy weights according to the coupling coefficients to obtain the comprehensive weights.

5. The method for constructing a mathematical analysis model for the uncertainty of compressor temperature rise efficiency according to claim 1, characterized in that, In step S4, the input features of the least squares support vector machine include environmental monitoring data and filter residuals. The input features are used for model training after being weighted by comprehensive weights. The environmental disturbance error compensation value output by the model is used to calculate the compensated environmental disturbance uncertainty component and to dynamically adjust the observation noise covariance of the adaptive Kalman filter.

6. The method for constructing a mathematical analysis model for the uncertainty of compressor temperature rise efficiency according to claim 1, characterized in that, The multiple sets of repeated test measurement data in step S1 include the total inlet and outlet temperature measurement value and the total inlet and outlet pressure measurement value. The environmental monitoring data includes the ambient temperature and ambient pressure.

7. The method for constructing a mathematical analysis model for the uncertainty of compressor temperature rise efficiency according to claim 1, characterized in that, In step S5, the uncertainty propagation law is applied based on the propagation coefficients of each measurement parameter in the temperature rise efficiency calculation model. The sum of the squares of the three standard uncertainty components in S4 multiplied by their corresponding propagation coefficients is taken to obtain the combined standard uncertainty.

8. The method for constructing a mathematical analysis model for the uncertainty of compressor temperature rise efficiency according to claim 1, characterized in that, In step S6, the inclusion factor is selected based on a 95% confidence level and is set to 2; the expanded uncertainty is the product of the inclusion factor and the combined standard uncertainty.

9. The method for constructing a mathematical analysis model for the uncertainty of compressor temperature rise efficiency according to claim 1, characterized in that, In step S7, the verification method is as follows: calculate the relative deviation of the expanded uncertainty of multiple sets of experimental data. If all relative deviations are less than 5%, the verification is deemed successful. If it fails, prioritize adjusting the coupling coefficient of the principal component analysis-entropy weight method coupled model and the kernel parameters of the least squares support vector machine.

10. The method for constructing a mathematical analysis model for the uncertainty of compressor temperature rise efficiency according to claim 2, characterized in that, The closing condition for the closed-loop interaction is: the change in the environmental disturbance error compensation value output by the least squares support vector machine is less than 0.01K for three consecutive times, or the number of iterations reaches the preset maximum number.

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