Air compressor modeling method and system based on data fitting driving

Abstract

This invention discloses a data-driven modeling method and system for air compressors, comprising: acquiring operating data of an air compressor under various operating conditions; preprocessing the operating data to obtain cleaned operating data; dividing the cleaned operating data into time windows, performing multi-order polynomial regression fitting within each time window to generate an initial fitting parameter set corresponding to each time window; constructing a fitting parameter matrix based on all initial fitting parameter sets, performing matrix decomposition operations, and extracting principal component features of the fitting parameters; establishing an air compressor performance degradation trend model based on the principal component features to describe the performance decay law of the air compressor under different operating durations; and dynamically modeling based on the performance degradation trend model and combined with real-time acquired operating data to generate a real-time performance mapping model. This achieves automatic extraction of performance degradation features from historical data and dynamic compensation modeling.

Description

Technical Field

[0001] This invention relates to the field of air compressor performance modeling technology, specifically to an air compressor modeling method and system based on data fitting. Background Technology

[0002] During long-term operation, air compressors experience gradual performance degradation due to factors such as mechanical wear, carbon buildup, and seal aging, leading to drift in key parameters like flow rate and power under the same operating conditions. In industrial settings, fixed models based on initial calibration states are typically used to describe air compressor operating characteristics. These models fail to reflect the performance degradation over time; as operating time increases, model prediction bias gradually widens, making it difficult to meet the accuracy requirements for equipment energy efficiency assessment and optimized scheduling. Some existing practices assess degradation by analyzing trends in single parameters, such as monitoring only the time-varying curves of exhaust pressure or power. These methods ignore the coupling relationships between multiple parameters, making them prone to misjudgment when operating conditions fluctuate. Another approach involves fitting a global degradation function to overall operating data, mixing data from different time periods. This smooths out the phased characteristics of the performance degradation process, resulting in a smooth transition of identified degradation patterns and a loss of the ability to capture local performance abrupt changes. Furthermore, when using degradation information to correct models, the conventional approach is to scale the model parameters as a whole based on the average degradation rate. This uniform correction method does not consider the differences in the degree of degradation in different regions of the performance mapping surface, and the accuracy of the corrected model remains low in some operating regions. This addresses the problems in existing technologies that cannot separate low-dimensional features reflecting the essence of performance degradation from historical data under multiple operating conditions, and the difficulty in performing differentiated dynamic corrections to static performance models based on degradation features. Summary of the Invention

[0003] This paper proposes a data-fit-driven modeling method and system for air compressors. It extracts principal component features that characterize performance degradation from historical operating data and uses these features to dynamically correct the performance mapping model, enabling the model to adapt to the equipment's performance degradation state and output accurate real-time performance mapping relationships.

[0004] To achieve the above objectives, the present invention provides the following technical solution: The present invention provides a data-driven air compressor modeling method, comprising: acquiring operating data of an air compressor under various operating conditions, the operating data including intake temperature, exhaust pressure, speed, and flow rate; performing data preprocessing on the operating data to obtain cleaned operating data, effectively filtering out transient interference and improving data quality by removing outliers and extracting steady-state operating conditions; dividing the cleaned operating data into time windows, performing multi-order polynomial regression fitting on the cleaned operating data within each time window, generating an initial fitting parameter set corresponding to each time window, thereby capturing the mapping between air compressor operating parameters and power at different time periods. The relationship is as follows: Based on the initial fitting parameter set corresponding to all time windows, a fitting parameter matrix is ​​constructed. Matrix decomposition is performed on the fitting parameter matrix to extract the principal component features of the fitting parameters. Redundancy and noise are removed through dimensionality reduction to highlight the main trend of performance degradation. Based on the principal component features of the fitting parameters, an air compressor performance degradation trend model is established. This performance degradation trend model is used to describe the performance decay law of the air compressor under different operating durations and can accurately characterize the long-term degradation process. Based on the performance degradation trend model, combined with real-time collected operating data, the air compressor is dynamically modeled to generate a real-time performance mapping model, thereby reflecting the current performance status in real time and improving the timeliness and accuracy of modeling.

[0005] As a preferred embodiment of the present invention, the step of preprocessing the operating data to obtain cleaned operating data includes: performing local mean calculation based on a sliding window on the data sequence of each dimension of the operating data to obtain a local mean sequence; calculating the deviation value between each data point in the operating data and its corresponding local mean, marking data points with deviation values ​​exceeding a preset deviation threshold as outliers and removing them to obtain initial screening data; performing variance calculation on the operating data of continuous time periods in the initial screening data, marking the time periods with variance less than a preset variance threshold as steady-state operating condition time periods, and extracting the operating data within the steady-state operating condition time periods as the cleaned operating data. This method can effectively remove transient fluctuations and outliers, retain steady-state data reflecting the main operating characteristics of the air compressor, and improve the stability and representativeness of subsequent fitting.

[0006] As a preferred embodiment of the present invention, the step of dividing the post-cleaning operating data into time windows and performing multi-order polynomial regression fitting on the post-cleaning operating data within each time window to generate an initial fitting parameter set corresponding to each time window includes: setting a fixed time window length based on the time span of the post-cleaning operating data; dividing the post-cleaning operating data into multiple consecutive time windows at equal intervals based on the time window length; for each time window, using the intake air temperature, exhaust pressure, speed, and flow rate within that time window as input variables and the air compressor power as the output variable, performing third-order polynomial regression fitting to generate a polynomial coefficient set corresponding to that time window as the initial fitting parameter set. Using third-order polynomial fitting, the nonlinear relationship between multivariate inputs and power output within each time window can be accurately described with moderate complexity.

[0007] As a preferred embodiment of the present invention, the step of constructing a fitting parameter matrix based on the initial fitting parameter set corresponding to all time windows, and performing matrix decomposition operation on the fitting parameter matrix to extract the principal component features of the fitting parameters includes: treating the initial fitting parameter set corresponding to each time window as a row vector, arranging the row vectors corresponding to all time windows in chronological order to form a two-dimensional fitting parameter matrix; performing singular value decomposition operation on the fitting parameter matrix to obtain a left singular matrix, a singular value diagonal matrix, and a right singular matrix; extracting the three largest singular values ​​from the singular value diagonal matrix, and reconstructing the dimension-reduced fitting parameter feature matrix based on the left and right singular matrices corresponding to the three largest singular values, and using the dimension-reduced fitting parameter feature matrix as the principal component features of the fitting parameters. Extracting principal components through singular value decomposition can eliminate multicollinearity and random fluctuations of parameters between time windows, and condense the essential features that best characterize performance degradation.

[0008] As a preferred embodiment of the present invention, the step of establishing an air compressor performance degradation trend model based on the principal component features of the fitted parameters includes: arranging the principal component features of the fitted parameters in chronological order to construct a principal component feature time series; performing exponential smoothing on the principal component feature time series to remove high-frequency noise and obtain a smoothed feature series; performing piecewise linear regression fitting on the smoothed feature series, dividing the smoothed feature series into multiple linear segments, each segment described by a linear equation, the breakpoint of the piecewise linear regression fitting being determined by minimizing the sum of squared residuals of each segment, and using the combination of the linear equations obtained from the piecewise linear regression fitting as the performance degradation trend model. Using a piecewise linear model can capture the phased changes in the degradation trend and has the advantages of simple analytical form, easy online updating, and long-term prediction, thus enhancing the robustness and interpretability of the degradation description.

[0009] As a preferred embodiment of the present invention, the step of dynamically modeling the air compressor based on the performance degradation trend model and combining it with real-time collected operating data to generate a real-time performance mapping model includes: real-time collection of the air compressor's current operating data, including current intake temperature, current exhaust pressure, current speed, and current flow rate; inputting the current operating data into the performance degradation trend model to calculate the degradation compensation coefficient corresponding to the current moment; and using a radial basis function-based interpolation method to dynamically correct a preset standard performance mapping model with the degradation compensation coefficient. The standard performance mapping model is a mathematical model describing the relationship between the air compressor's operating parameters and output parameters in its initial state. The corrected standard performance mapping model is used as the real-time performance mapping model. By correcting the standard model in real time with the degradation compensation coefficient, the model output can adaptively adjust to follow performance degradation, significantly improving the accuracy of real-time mapping.

[0010] As a preferred embodiment of the present invention, the method of using radial basis function-based interpolation to dynamically correct a preset standard performance mapping model with the degradation compensation coefficient includes: using the degradation compensation coefficient as the center point of the radial basis function and selecting a Gaussian function as the radial basis function; calculating the Euclidean distance between each model parameter in the standard performance mapping model and the center point of the radial basis function, and calculating the weight coefficient of each model parameter based on the Euclidean distance; multiplying the weight coefficient of each model parameter by the corresponding model parameter to generate corrected model parameters, and combining all corrected model parameters to obtain the corrected standard performance mapping model. Using Gaussian radial basis function weighting enables a smooth transition of model parameters near the degradation compensation coefficient, avoiding parameter abrupt changes during the correction process and ensuring the continuity of performance mapping.

[0011] As a preferred embodiment of the present invention, after generating the real-time performance mapping model, the method further includes: acquiring transient response data of the air compressor at multiple load switching points, wherein the transient response data includes the rate of change of rotational speed and the rate of change of exhaust pressure; performing system identification processing on the transient response data to generate a dynamic response transfer function of the air compressor; and embedding the dynamic response transfer function into the real-time performance mapping model to generate a comprehensive performance mapping model that includes steady-state performance and dynamic performance. Therefore, the resulting model not only reflects the steady-state characteristic changes caused by long-term degradation but also accurately describes the dynamic response process during sudden load changes, achieving performance reproduction of the air compressor under all operating conditions.

[0012] As a preferred embodiment of the present invention, the step of performing system identification processing on the transient response data to generate the dynamic response transfer function of the air compressor includes: using the speed change rate as the input signal and the exhaust pressure change rate as the output signal to construct a system identification equation based on an autoregressive moving average model; using a least squares recursive algorithm to estimate the parameters of the system identification equation online to obtain the coefficients of the system identification equation; and based on the coefficients of the system identification equation, converting the autoregressive moving average model into a continuous domain transfer function form through a Laplace transform, which serves as the dynamic response transfer function. Through online recursive estimation and continuous domain transformation, the dynamic response characteristics of the air compressor can be updated in real time, enabling the model to maintain good tracking capability and dynamic accuracy under varying operating conditions.

[0013] This invention also provides a data-fit-driven air compressor modeling system, including a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the steps of the aforementioned data-fit-driven air compressor modeling method. This system can be integrated into an air compressor monitoring platform. By processing operational data in real time, it automatically completes data cleaning, degradation feature extraction, trend modeling, and dynamic correction, outputting a high-precision real-time performance mapping model and a comprehensive performance mapping model, providing a reliable basis for air compressor energy efficiency assessment and predictive maintenance.

[0014] The technical effects and advantages provided by the present invention in the above technical solution are as follows: By dividing the operating data into time windows and performing multi-order polynomial regression fitting, a set of fitting parameters is obtained for each window. The parameters of all windows constitute the fitting parameter matrix. After performing singular value decomposition on the matrix, the principal component features corresponding to the three largest singular values ​​are extracted. This processing method compresses the original high-dimensional time-varying fitting parameter space into a low-dimensional principal component sequence, eliminating redundant information and noise interference between parameters. The extracted principal component features reflect the essential trend of air compressor performance degradation, avoiding the problem of being affected by operating condition fluctuations when directly analyzing the trend of a single operating parameter. At the same time, compared with the method of globally fitting the degradation function, it can retain the local features of different stages in the performance degradation process and capture the turning point of the degradation rate change. After establishing a performance degradation trend model based on the principal component features, the degradation compensation coefficient is calculated using real-time operating data, and the standard performance mapping model is dynamically corrected using the radial basis function interpolation method. Using the degradation compensation coefficient as the center point of the radial basis function, the Euclidean distance between each parameter in the standard model and this center is calculated and weights are generated to differentiate the model parameters. This approach ensures that the correction amount for different regions on the standard performance mapping surface varies depending on their correlation with the current degradation state, avoiding the accuracy loss caused by ignoring regional differences during overall scaling correction. The corrected real-time performance mapping model can accurately describe the characteristics of the air compressor under the current degradation state across the entire operating range. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0016] Figure 1 This is a flowchart of a data-fit-driven air compressor modeling method; Figure 2 This is a flowchart of the time window division of the cleaned running data and the generation of third-order polynomial regression fitting parameters; Figure 3 This is a schematic diagram of the third-order polynomial regression fitting results of the cleaned running data within the time window. Figure 4 This is a time series curve of the principal component characteristics of the fitting parameters of the air compressor; Figure 5 This is the coordinate value of the first principal component of the air compressor, the performance degradation trend, and the piecewise linear regression fitting graph. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] See Figure 1 This invention provides a data-driven air compressor modeling method, which includes the following steps: acquiring operating data of the air compressor under various operating conditions, including at least intake temperature, exhaust pressure, speed, and flow rate; preprocessing the acquired operating data to remove outliers and invalid data, generating cleaned operating data; dividing the cleaned operating data into time windows, performing multi-order polynomial regression fitting within each time window, using intake temperature, exhaust pressure, speed, and flow rate as independent variables, and variables reflecting the real-time performance of the air compressor as dependent variables, to obtain polynomial coefficients characterizing the performance state of that window, serving as the initial fitting parameter set for each time window; after obtaining the initial fitting parameter sets for all time windows, constructing a fitting parameter matrix, performing matrix decomposition on the fitting parameter matrix, and extracting principal component features of the fitting parameters, which can retain the main change information of the fitting parameters under different time windows while reducing dimensionality; and establishing an air compressor performance degradation trend model based on the extracted principal component features, which describes the performance decay law of the air compressor under different operating durations. Based on the performance degradation trend model, the air compressor is dynamically modeled by combining real-time collected operating data, and a real-time performance mapping model reflecting the current actual performance status of the air compressor is generated.

[0019] Example 1: In practice, the process of preprocessing the operational data to obtain cleaned operational data is achieved through the following methods.

[0020] For the acquired air compressor operating data under various operating conditions, including inlet temperature, exhaust pressure, speed, and flow rate, a local mean calculation based on a sliding window is performed on the data sequence for each dimension of the operating data. The length of the sliding window is set according to the sampling frequency of the operating data and the minimum settling time of the air compressor under typical operating conditions. In some embodiments, the length of the sliding window is set to the time span corresponding to 5 to 15 sampling points at the air compressor sampling frequency. The sliding window moves point by point along the time axis, moving one sampling point at a time. After each movement, the arithmetic mean of the inlet temperature data points, the arithmetic mean of the exhaust pressure data points, the arithmetic mean of the speed data points, and the arithmetic mean of the flow rate data points contained within the sliding window are calculated. For each dimension of the data sequence, a local mean is generated each time the sliding window moves. All local means are arranged in chronological order to form a local mean sequence corresponding to that dimension of the data sequence. The inlet temperature data sequence corresponds to an inlet temperature local mean sequence, the exhaust pressure data sequence corresponds to an exhaust pressure local mean sequence, the speed data sequence corresponds to a speed local mean sequence, and the flow rate data sequence corresponds to a flow rate local mean sequence. The local mean is calculated as follows: in, Indicates the length of the sliding window. , This represents the number of sampling points included in the sliding window before the current sampling point. This represents the number of sampling points included in the sliding window after the current sampling point. and The index offset value is set based on a symmetric or asymmetric window. Indicates time index The original data value at that location, Indicates time index The local mean is calculated at this point. When the sliding window uses a symmetrical window... ,at this time It is an odd number. The intake air temperature, exhaust pressure, speed, and flow rate dimensions are all calculated independently in the manner described above.

[0021] For each data point in the operating data, the deviation between the intake air temperature data point and the corresponding value in the local mean sequence of intake air temperature is calculated; the deviation between the exhaust pressure data point and the corresponding value in the local mean sequence of exhaust pressure is calculated; the deviation between the speed data point and the corresponding value in the local mean sequence of speed is calculated; and the deviation between the flow rate data point and the corresponding value in the local mean sequence of flow rate is calculated. Data points whose absolute values ​​of intake air temperature deviation, exhaust pressure deviation, speed deviation, and flow rate deviation exceed preset threshold values ​​are marked as outliers. In some embodiments, the preset intake air temperature deviation threshold is determined based on the accuracy of the intake air temperature sensor and the normal fluctuation range of the air compressor intake air temperature; the preset exhaust pressure deviation threshold is determined based on the range of the exhaust pressure sensor and the allowable fluctuation range of the process; the preset speed deviation threshold is determined based on the speed control accuracy; and the preset flow rate deviation threshold is determined based on the flow rate measurement uncertainty. Data points marked as outliers, including intake air temperature, exhaust pressure, engine speed, and flow rate, are removed from the original data sequence. If a data point in any dimension is marked as an outlier at a given moment, all data points in all corresponding dimensions at that moment are removed to ensure the integrity of the data sample rows. The operational data obtained after removing outliers is used as the initial screening data.

[0022] Variance calculation is performed on the operational data segments with continuous time attributes in the initial screening data. The initial screening data is sorted by timestamp, and data segments with continuous and uninterrupted timestamps are identified, each segment corresponding to a continuous time period. For the operational data contained in each continuous time period, the variances of intake air temperature data, exhaust pressure data, engine speed data, and flow rate data are calculated. In some embodiments, the intake air temperature variance within a continuous time period is calculated by subtracting the square of the mean of all intake air temperature data points from the mean of all intake air temperature data points within the continuous time period. The calculated intake air temperature variance is compared with a preset intake air temperature variance threshold, the exhaust pressure variance is compared with a preset exhaust pressure variance threshold, the engine speed variance is compared with a preset engine speed variance threshold, and the flow rate variance is compared with a preset flow rate variance threshold. When the intake air temperature variance, exhaust pressure variance, engine speed variance, and flow rate variance within a continuous time period are all less than the preset intake air temperature variance threshold, the exhaust pressure variance is less than the preset exhaust pressure variance threshold, the engine speed variance is less than the preset engine speed variance threshold, and the flow rate variance is less than the preset flow rate variance threshold, then the continuous time period is marked as a steady-state operating condition time period. The preset intake air temperature variance threshold is set based on the standard deviation of intake air temperature fluctuation during steady-state operation of the air compressor, by multiplying the square of the standard deviation by a set coefficient. The preset exhaust pressure variance threshold, preset speed variance threshold, and preset flow rate variance threshold are set according to the same principle. In practice, the set coefficient is selected from 2 to 4. All operating data within the time period marked as steady-state operating conditions are extracted from the initial screening data to form the cleaned operating data. Through this method, data segments with significant interference from variable operating conditions and non-steady-state operation are eliminated.

[0023] Example 2: In specific implementation, please refer to Figure 2 The process of dividing the cleaned running data into time windows and performing multi-order polynomial regression fitting on the cleaned running data within each time window to generate the initial fitting parameter set corresponding to each time window is achieved in the following way.

[0024] The time span corresponding to the post-cleaning operation data is obtained, which is the difference between the last sampling moment and the first sampling moment in the post-cleaning operation data. A fixed time window length is set, the value of which is determined based on the sampling frequency of the post-cleaning operation data and the shortest duration of a single continuous operation of the air compressor under steady-state conditions. In some embodiments, the shortest duration of a single continuous steady-state operation of the air compressor is obtained through process specifications, and the time window length is set as the product of this shortest duration and the sampling frequency, so that a single time window exactly covers a complete steady-state operation process. For example, when the sampling frequency is 1 Hz and the shortest duration is 1800 seconds, the time window length is set to 1800 sampling points. In other embodiments, the time window length is set by identifying all continuous steady-state data segments with durations greater than a preset threshold from the post-cleaning operation data, calculating the minimum length of these steady-state data segments, and setting the time window length to this minimum value, to ensure that each divided time window corresponds to a complete steady-state process.

[0025] The cleaned running data is divided into equally spaced intervals within a fixed time window. Starting from the first sampling point of the cleaned running data, a new time window is formed by taking a continuous number of sampling points that fill the entire time window length. Adjacent time windows are non-overlapping and closely connected. The division stops when the number of remaining sampling points at the end of the cleaned running data is less than the length of a complete time window, and the remaining sampling points are discarded. This generates multiple time windows that are consecutive in time and of equal duration. Each time window contains a fixed number of cleaned running data points, equal to the time window length. The time windows are numbered sequentially according to their chronological order, forming a time window sequence.

[0026] For each defined time window, the intake air temperature sequence, exhaust air pressure sequence, speed sequence, flow rate sequence, and corresponding air compressor power sequence falling within that time window are extracted from the cleaned operational data. Intake air temperature, exhaust air pressure, speed, and flow rate are used as input variables for a third-order polynomial regression model, and air compressor power is used as the output variable. Third-order polynomial regression fitting is then performed. The form of the third-order polynomial regression model is as follows: in, This indicates the power of the air compressor, which is the actual power consumed or output by the air compressor under the corresponding operating conditions. The polynomial coefficient vector is a column vector consisting of the fitting coefficients to be determined, where each element corresponds to a specific polynomial term coefficient. A monomial eigenvector is a column vector composed of monomials constructed from the input variables: intake air temperature, exhaust air pressure, engine speed, and flow rate. The specific construction method is as follows: Enumerate all monomials consisting of intake air temperature, exhaust pressure, speed, and flow rate, requiring that the sum of the powers of intake air temperature, exhaust pressure, speed, and flow rate in each monomial does not exceed 3. The set of monomials includes a constant term (1), first-order terms of intake air temperature, second-order terms of intake air temperature, third-order terms of intake air temperature, first-order terms of exhaust pressure, second-order terms of exhaust pressure, third-order terms of exhaust pressure, first-order terms of speed, second-order terms of speed, third-order terms of speed, first-order terms of flow rate, second-order terms of flow rate, third-order terms of flow rate, and cross terms of all products of two variables with a total power not exceeding 3 and all products of three variables with a total power not exceeding 3. All these monomials are arranged in a pre-defined fixed order to form a monomial feature vector. Polynomial coefficient vector The order of arrangement and the eigenvectors of monomials The order of the monomials corresponds one-to-one.

[0027] In practical implementation, for a given time window, the input and output sample set of a third-order polynomial regression model is constructed: for each sampling point within the time window, the intake air temperature, exhaust pressure, engine speed, and flow rate are used to calculate the monomial feature vector corresponding to that sampling point according to the aforementioned monomial construction rules. The numerical values ​​are used to construct a design matrix by sequentially arranging the univariate eigenvectors of all sampling points. The number of rows in the design matrix corresponds to the number of sampling points within the time window, and the number of columns corresponds to the polynomial coefficient vectors. The dimension is determined by the compressor power values ​​corresponding to all sampling points within the time window, which form the output vector. The output vector is minimized by multiplying the design matrix by the polynomial coefficient vector. The objective is to solve for the polynomial coefficient vector by taking the sum of squared errors between the obtained predicted value vectors. The solution process employs the least squares method, obtaining the polynomial coefficient vector by calculating the generalized inverse of the design matrix or solving the normal equations. The estimated value. The obtained polynomial coefficient vector. This refers to the initial set of fitting parameters corresponding to that time window, where each coefficient corresponds to a monomial feature vector. A specific monomial in .

[0028] The above-described third-order polynomial regression fitting operation is performed on each of the time windows obtained after the cleaning of the running data, generating a corresponding polynomial coefficient vector for each time window. This allows us to obtain the sequence of initial fitting parameters corresponding to the time window sequence. The initial fitting parameter sets corresponding to each time window are stored separately, and their temporal order relationship with the corresponding time window is preserved.

[0029] See Figure 3 In the graph, the horizontal axis represents the sampling point number, indicating the time series points within the time window, and the vertical axis represents the air compressor power in kilowatts (kW). In the legend, the blue scatter dots represent the actual measured air compressor power data, and the red solid line represents the power value predicted based on the third-order polynomial regression model.

[0030] As shown in the figure, the third-order polynomial regression model fitted the air compressor power data within the corresponding time window after cleaning. The fitted curve closely matches the actual power data, reflecting the model's good ability to fit the trend of air compressor power changes. The power curve generally shows a trend of first rising and then falling, with the maximum power value around sampling point number 300, exceeding 500kW. Within the sampling point number range of 0 to 300, both the actual power and the predicted power show a slow upward trend with small fitting errors, indicating that the model can accurately capture the power change over time under steady-state conditions. Within the sampling point number range of 300 to 600, the power gradually decreases, and the rate of decrease gradually accelerates. The fitted curve begins to show some deviation in the negative power value range, but the overall trend is still well fitted.

[0031] Example 3: In practice, the process of constructing a fitting parameter matrix based on the initial fitting parameter set corresponding to all time windows, performing matrix decomposition on the fitting parameter matrix, and extracting the principal component features of the fitting parameters is achieved in the following way.

[0032] Obtain the initial fitting parameter sets corresponding to all time windows. Each time window corresponds to one initial fitting parameter set, which is in the form of a polynomial coefficient vector obtained after fitting a third-order polynomial regression. Each element in the polynomial coefficient vector corresponds to a specific monomial feature term. Treat the initial fitting parameter set vector corresponding to each time window as a row vector, with the dimension of the row vector equal to the dimension of the polynomial coefficient vector. The order of the elements in the row vector is consistent with the order of the coefficients in the polynomial coefficient vector.

[0033] Arrange the row vectors corresponding to all time windows in chronological order from top to bottom. The chronological order is determined by the start time of each time window, with the row vector corresponding to the earliest start time at the top, followed by the row vector corresponding to the second earliest start time, and so on, with the row vector corresponding to the latest start time at the bottom. After arrangement, a two-dimensional fitting parameter matrix is ​​formed. The number of rows in the fitting parameter matrix equals the total number of time windows, and the number of columns in the fitting parameter matrix equals the dimension of the initial fitting parameter set.

[0034] In practical implementation, assume the total number of time windows is... The initial fitting parameter set has a dimension of . Then the dimension of the fitting parameter matrix is Each matrix element represents the fitting coefficient value corresponding to a specific polynomial term within a certain time window.

[0035] Perform singular value decomposition on the fitted parameter matrix. Let the fitted parameter matrix be denoted as... , for A real matrix. For the matrix Perform singular value decomposition, and the result of the decomposition is expressed as: in, This represents the fitting parameter matrix, which consists of the initial set of fitting parameters corresponding to all time windows. The number of rows in the matrix represents the total number of time windows. The number of columns is equal to the dimension of the initial fitting parameter set; Let represent a left singular matrix, the dimension of which is . The column vectors of the left singular matrix are matrices. The eigenvectors of the left singular matrix are mutually orthogonal and have a magnitude of 1; Let represent a singular value diagonal matrix, the dimension of which is . A singular value diagonal matrix has non-zero elements only on the main diagonal. The non-zero elements on the main diagonal are matrix elements. The singular values ​​are arranged from top to bottom in descending order, and each singular value represents the degree of data variation in the corresponding direction. Let represent a right singular matrix, the dimension of which is . The column vectors of the right singular matrix are matrices. The eigenvectors of the right singular matrix are mutually orthogonal and have a magnitude of 1; This represents the transpose of a right singular matrix.

[0036] After completing the singular value decomposition, from the singular value diagonal matrix Extract the three largest singular values. The extraction method is: read the singular value diagonal matrix. The first three elements on the main diagonal are the singular values ​​at the positions of the first row and first column, the second row and second column, and the third row and third column. This is the singular value diagonal matrix. Set all singular values ​​on the main diagonal to zero to construct a truncated singular value diagonal matrix. truncating singular value diagonal matrices The dimension and singular value diagonal matrix Similarly, truncating singular value diagonal matrices Only the three largest singular values ​​on the main diagonal are retained, with all other positions set to zero. The rule for extracting the three largest singular values ​​is to calculate the proportion of the sum of the squares of the three largest singular values ​​to the sum of the squares of all singular values. When this proportion exceeds a preset threshold for retaining principal component information, the three largest singular values ​​are considered sufficient to characterize the fitted parameter matrix. The main variation characteristics. In some embodiments, the preset threshold for retaining principal component information is set to 0.85. This setting is based on the minimum requirement for the cumulative contribution rate of principal components in statistics. When the cumulative contribution rate exceeds 0.85, the dimensionality-reduced principal components can retain most of the structural information in the original data.

[0037] Based on the truncated singular value diagonal matrix and left singular matrix And right singular matrix The feature matrix of the fitted parameters after dimensionality reduction is reconstructed. The reconstruction is calculated by converting the left singular matrix... 1. Truncate singular value diagonal matrices And right singular matrix Multiplying them yields the feature matrix of the fitted parameters after dimensionality reduction. The number of rows in the feature matrix of the fitted parameters after dimensionality reduction is equal to the number of rows in the fitted parameter matrix. The number of rows is the same, and the number of columns in the feature matrix of the dimensionality-reduced fitting parameters is the same as that in the fitting parameter matrix. The number of columns is the same. Each row in the dimensionality-reduced fitting parameter feature matrix corresponds to a time window, and each column corresponds to a feature dimension. The rank of the dimensionality-reduced fitting parameter feature matrix is ​​3. The dimensionality-reduced fitting parameter feature matrix is ​​the principal component feature of the fitting parameters. The principal component feature of the fitting parameters is stored in matrix form, and each row vector in the matrix represents the coordinate value of the corresponding time window in the three principal component directions.

[0038] See Figure 4 In the figure, the vertical axis represents the principal component coordinate values ​​of the fitted parameters, and the horizontal axis represents the time window number obtained according to the time window division in Example 2. The figure contains three curves, corresponding to the coordinate values ​​of the first principal component (blue solid line), the second principal component (orange dashed line), and the third principal component (green dotted line), respectively, reflecting the changing trends of the fitted parameters in the three principal component directions under different time windows.

[0039] Analysis of the curve trends reveals that the coordinate values ​​of the first principal component exhibit a monotonically decreasing trend, gradually decreasing from approximately 5 at the initial time window number 0 to approximately 1 near time window number 500, indicating a significant decay of the performance parameter characteristics corresponding to this principal component over time. The coordinate values ​​of the second principal component show a slow upward trend, starting at approximately -2 and rising to approximately 0.6 near time window number 500, indicating a gradual strengthening or change in the performance characteristics of this dimension. The coordinate values ​​of the third principal component exhibit approximately periodic oscillations, with the amplitude remaining within the ±0.5 range, reflecting periodic fluctuations or seasonal changes in the performance characteristics corresponding to this principal component.

[0040] Combining the technical solution of extracting principal component features of the fitted parameters through singular value decomposition in Example 3, this figure intuitively shows the feature evolution of the first, second, and third principal components of the fitted parameter matrix as a function of the operating time window after dimensionality reduction. In particular, the continuous downward trend of the first principal component may indicate the overall degradation trend of the air compressor performance; the upward trend of the second principal component reflects minor performance changes; and the fluctuation of the third principal component reveals the influence of potential dynamic or periodic factors.

[0041] Example 4: In practice, the process of establishing a model of air compressor performance degradation trend based on the principal component characteristics of the fitted parameters is achieved in the following way.

[0042] The rows of the principal component feature matrix of the fitted parameters are arranged chronologically according to their corresponding time windows. The principal component feature matrix is ​​a dimensionality-reduced matrix; each row corresponds to a time window and contains three elements: the coordinates of that time window along the three principal component directions. The row vectors from the principal component feature matrix are extracted sequentially according to the starting times of the time windows, from earliest to latest, forming a strictly time-varying principal component feature time series. Each sampling moment in the principal component feature time series corresponds to the starting time of a time window. The observation value at each sampling moment is a three-dimensional vector, where the first dimension represents the coordinates of the first principal component, the second dimension the coordinates of the second principal component, and the third dimension the coordinates of the third principal component. The length of the principal component feature time series is equal to the total number of time windows.

[0043] Exponential smoothing is applied to the principal component feature time series. The exponential smoothing process uses a cubic exponential smoothing model, smoothing each dimension of the principal component feature time series independently. Taking the time series of the first principal component coordinate values ​​as an example, let the original sequence before exponential smoothing be denoted as... ,in, Indicates a time index. , The length of the principal component feature time series. Indicates time index The coordinates of the first principal component at the given location. The calculation method for first-order exponential smoothing is: time index... At that time, the first exponential smoothed value Set as For time index The first exponential smoothing value is obtained recursively from the first exponential smoothing value of the previous time index and the original value of the current time index. The second exponential smoothing value is calculated recursively based on the first exponential smoothing value in the same way, and the third exponential smoothing value is calculated recursively based on the second exponential smoothing value in the same way. The smoothing coefficient in the exponential smoothing recursive formula is denoted as . , The value ranges from 0.1 to 0.3. In some embodiments, The smoothing coefficient is set to 0.2. This setting is based on the understanding that the degradation process in air compressor performance degradation trend analysis is slow, and assigning appropriate weight to recent data balances trend tracking and noise suppression capabilities. The same smoothing coefficient is used for the time series of the second and third principal component coordinate values. The same first, second, and third exponential smoothing recursion processes are performed independently.

[0044] After performing three exponential smoothing processes on the original sequences of the three-dimensional components in the principal component feature time series, the smoothed sequences corresponding to each dimension component are obtained. The three-dimensional smoothed sequences are then aligned and combined according to their time indices to obtain the smoothed feature sequence. Each sampling time point of the smoothed feature sequence still corresponds to a three-dimensional vector, which consists of the smoothed coordinate values ​​of the first principal component, the second principal component, and the third principal component.

[0045] Piecewise linear regression fitting is performed on the smoothed feature sequence. The goal of piecewise linear regression fitting is to divide the smoothed feature sequence into multiple linear segments along the time axis, and use a linear equation within each segment to describe the change of the three-dimensional vector in the smoothed feature sequence over time. For the th segment of the smoothed feature sequence... dimensional components, The values ​​of are the first principal component, the second principal component, and the third principal component, and a linear equation is used. To fit the corresponding component sequence within this segment, where, Indicates a time index. Indicates the intercept. Indicates the slope.

[0046] The locations of breakpoints in a piecewise linear regression fit are determined by searching among all possible locations, with the goal of minimizing the sum of squared residuals for each segment. The number of breakpoint locations is denoted as . , The value of is set according to the time span of the smoothed feature sequence and the expected number of performance degradation stages. In some embodiments, The setting is 2, based on the fact that air compressor performance degradation typically goes through an initial stable phase and a later accelerated degradation phase; the two breakpoints correspond to these three phases. The breakpoint location vector is denoted as... Each breakpoint Indicates the division of the first Section and the The time index position of the segment. The candidate values ​​are 2 to Integers between [a certain range].

[0047] Given a set of breakpoint location vectors, the entire time interval is divided into: The formula for calculating the sum of squared residuals of the piecewise fitting of a linear segment is: in, Represents a vector indicating the location of a given breakpoint. The sum of squared residuals from the piecewise fit; Indicates the principal component index. The values ​​of 1, 2, and 3 correspond to the first principal component coordinate value component, the second principal component coordinate value component, and the third principal component coordinate value component in the smoothed feature sequence, respectively. Indicates the number of breakpoints; Indicates the sequence number of the linear segment. From 1 to ; This indicates the index position preceding the first time index, and its value is always 0. This represents the last time index, with a fixed value. ; Indicates a time index; Indicating the first smooth feature sequence Dimensional components in time index The smoothing value at that point; Indicates the first Within the nth linear segment The intercept of the linear equation of the dimensional component is estimated by ordinary least squares over the data points contained in that segment; Indicates the first Within the nth linear segment The slope of the three-dimensional component linear equation is also estimated using ordinary least squares on the data points contained in that segment. For each breakpoint location vector, the segments are first divided according to the breakpoint location. Then, linear regression fitting is performed on the three-dimensional components within each segment to obtain the intercept and slope parameters corresponding to each segment. These parameters are then substituted into the formula for the sum of squared residuals of the piecewise fitting to calculate... The value of .

[0048] By searching over all possible combinations of breakpoint location vectors, find the one that makes The breakpoint location vector with the smallest value is taken as the optimal breakpoint location. The search method uses exhaustive search; when the number of breakpoints... Time series length When the computational complexity is no more than several thousand, exhaustive search is within an acceptable range. In some embodiments, when When the value is large, a dynamic programming algorithm is used to find the optimal breakpoint location while satisfying computational resource constraints.

[0049] Divided according to the optimal breakpoint location The linear segments, along with the intercept and slope parameters of the corresponding three-dimensional component linear regression equations within each segment, constitute a complete performance degradation trend model. The performance degradation trend model consists of... The model consists of a set of linear equations, each containing three equations that describe the changes in the coordinate values ​​of the first, second, and third principal components over time. The performance degradation trend model is stored as a piecewise function, containing the start and end indices of each segment, as well as the intercepts and slopes of the three corresponding linear equations. This model is used to describe the performance degradation of an air compressor at different operating durations.

[0050] See Figure 5 In the graph, the horizontal axis represents the cumulative operating time of the air compressor in hours (h), and the vertical axis represents the coordinate values ​​of the first principal component after three exponential smoothing processes. The graph uses blue dots to mark the discrete observation data of the smoothed first principal component coordinate values, and the red solid line represents the performance degradation trend model curve obtained based on piecewise linear regression fitting. The vertical dashed line divides the operating time into three stages, corresponding to different linear segments of the piecewise linear fit.

[0051] As shown in the figure, the coordinate values ​​of the first principal component gradually decrease with increasing operating time, reflecting the gradual degradation of air compressor performance over time. In the first stage (approximately 0–300 hours), the coordinate values ​​of the first principal component decrease slowly, indicating relatively stable and slow performance degradation. In the second stage (approximately 300–700 hours), the downward trend accelerates, and the rate of performance degradation increases significantly. In the third stage (approximately 700–1000 hours), the coordinate values ​​of the first principal component decrease rapidly, and the performance degradation tends to accelerate.

[0052] Example 5: In practice, the process of dynamically modeling the air compressor based on the performance degradation trend model and combining it with real-time collected operating data to generate a real-time performance mapping model is achieved in the following way.

[0053] The air compressor uses a temperature sensor installed on its intake pipe to collect real-time data on the intake air temperature, a pressure sensor installed on its exhaust pipe to collect real-time data on the exhaust air pressure, a speed sensor installed on its drive shaft to collect real-time data on the speed, and a flow sensor installed on either the intake or exhaust pipe to collect real-time data on the flow rate. The current intake air temperature, current exhaust pressure, current speed, and current flow rate are used as the current operating data, and each physical quantity in the current operating data includes a synchronized data collection timestamp.

[0054] A performance degradation trend model is obtained, comprising multiple sets of linear equations. Each set of linear equations corresponds to a runtime interval, and each set contains three linear equations. These three equations describe the changes in the coordinate values ​​of the first, second, and third principal components of the fitted parameters over time. Based on the total cumulative operating time of the air compressor since its commissioning, the runtime interval within which the cumulative operating time falls is determined, and the intercept and slope parameters of the three linear equations corresponding to this runtime interval are extracted. The total cumulative operating time is substituted into the time variables of the three linear equations to calculate the predicted coordinate values ​​of the first, second, and third principal components at the current moment. These predicted coordinate values ​​are combined into a three-dimensional vector, which is used as the degradation compensation coefficient for the current moment. The degradation compensation coefficient quantifies the direction and magnitude of the performance deviation of the air compressor relative to its initial state due to long-term operation in three-dimensional space.

[0055] Obtain the preset standard performance mapping model. The standard performance mapping model is a mathematical model describing the relationship between the operating parameters and output parameters of the air compressor in its initial factory state. The standard performance mapping model is expressed in functional form. The input variables of the standard performance mapping model include intake air temperature, exhaust pressure, speed, and flow rate. The output variable of the standard performance mapping model is the air compressor power. The standard performance mapping model contains a set of model parameters; the number of model parameters is denoted as... Each model parameter corresponds to an adjustable coefficient in the standard performance mapping model. In some embodiments, the standard performance mapping model adopts the same functional form as the regression model obtained by fitting a third-order polynomial regression under the initial state, and the model parameters of the standard performance mapping model are the polynomial coefficients calibrated based on the operating data of the air compressor under brand-new conditions at the initial stage of air compressor commissioning.

[0056] An interpolation method based on radial basis functions is employed to dynamically correct the standard performance mapping model using degradation compensation coefficients. Specifically, the degradation compensation coefficient is used as the center point of the radial basis functions. The degradation compensation coefficient is a point in three-dimensional space, where the first-dimensional coordinates are the predicted coordinates of the first principal component, the second-dimensional coordinates are the predicted coordinates of the second principal component, and the third-dimensional coordinates are the predicted coordinates of the third principal component. A Gaussian function is selected as the radial basis function; its expression is given in subsequent formulas.

[0057] For each model parameter in the standard performance mapping model, calculate the distance between the parameter's position in the parameter space and the center point of the radial basis function. In practice, the spatial mapping of the model parameters is constructed as follows: [The text then abruptly shifts to a different topic:] ...in the standard performance mapping model... Each model parameter is mapped to a fixed sequence. A point in 3D space, that point is in the 3D space. The coordinates of the dimension are the first The original values ​​of the model parameters, where, The value ranges from 1 to Calculate integers. The Euclidean distance between the model parameter points and the center points of the degradation compensation coefficients in 3D space. Since the degradation compensation coefficients reside in 3D space, while the model parameter points reside in 4D space... In 3D space, when When the value is not equal to 3, the degradation compensation coefficient is mapped from three-dimensional space to... In dimensional space, the mapping method preserves the coordinate values ​​of the three principal components of the degradation compensation coefficient unchanged, and in additional... Fill in zeros in each dimension to form a dimensional vector, which A dimensional vector serves as the center point of the radial basis function. Coordinates in 3D space. The calculation range of Euclidean distance is... Two in dimensional space The straight-line distance between vectors of dimension.

[0058] For the first There are several model parameters, and the original values ​​of these model parameters are assumed to be... , In the standard performance mapping model, the first... The initial calibration values ​​of each model parameter. The center point of the degradation compensation coefficient is at... The coordinate vector in 3D space is denoted as , The first three coordinate components represent the predicted coordinates of the first, second, and third principal components of the degradation compensation coefficient, respectively; the remaining coordinate components are zero. The model parameter points are located at... The coordinate vector in 3D space is denoted as , The Middle The coordinate component is the first The original values ​​of the model parameters, where, The value ranges from 1 to The weighting coefficients are integers. The weighting coefficients are calculated using the following formula: in, Indicates the first The weight coefficients corresponding to each model parameter The value range is greater than 0 and does not exceed 1. When the model parameter point is in When the position in 3D space completely coincides with the center point of the degradation compensation coefficient Take the maximum value of 1, when the distance approaches infinity. Approaching 0; Indicates the index number of the model parameter. From 1 to Integers; Indicates the model parameter points at Coordinate vectors in 3D space The dimension is ; Indicates the center point of the degradation compensation coefficient at Coordinate vectors in 3D space The dimension is , The first three coordinate components are equal to the predicted coordinate values ​​of the first, second, and third principal components of the degradation compensation coefficient, respectively. The remaining coordinate components are zero; Representing vectors with vector The Euclidean distance between them; This represents the shape parameter of the Gaussian function. The value of controls the rate at which the weighting coefficient decays with increasing distance. The method for obtaining the data is to statistically analyze the distribution of the difference amplitudes between the parameters of the actual performance mapping model and the parameters of the standard performance mapping model at different degradation stages during the historical operation of the air compressor, and use the standard deviation of the difference amplitude as... The set value. In some embodiments, when historical data is insufficient to calculate the standard deviation of the difference magnitude, The value of is set to half the standard deviation of the original values ​​of all model parameters in the standard performance mapping model. This setting allows the weight coefficients to produce discriminative changes within the typical fluctuation range of the model parameters.

[0059] Calculation yields the first Weight coefficients of each model parameter Then, the weighting coefficients With the The original values ​​of each model parameter Multiply, the product is the corrected i-th There are 1 model parameter. The corrected model parameter is denoted as . , For all of the standard performance mapping models Each model parameter undergoes the above weight coefficient calculation and multiplication operations one by one to generate... The corrected model parameters. All The corrected model parameters are combined according to their respective positions to replace the original model parameters in the standard performance mapping model, resulting in a corrected standard performance mapping model. The input variables of the corrected standard performance mapping model are the same as those of the standard performance mapping model: intake temperature, exhaust pressure, speed, and flow rate. The output variable of the corrected standard performance mapping model is also the same as that of the standard performance mapping model: air compressor power. The internal model parameters of the corrected standard performance mapping model are all the corrected model parameters. This corrected standard performance mapping model is the real-time performance mapping model. The real-time performance mapping model can output an air compressor power value reflecting the current actual performance state of the air compressor, given any current intake temperature, current exhaust pressure, current speed, and current flow rate.

[0060] After generating the real-time performance mapping model, transient response data of the air compressor at multiple load switching points are acquired. The load switching point is the moment when the air compressor load undergoes a step change. The load switching point is identified by monitoring the air compressor exhaust valve opening command signal or the user's air demand signal. When the change in the exhaust valve opening command signal or the user's air demand signal exceeds a preset amplitude threshold within a preset short time, the corresponding moment of the load switching point is recorded. Transient response data includes the rate of change of rotational speed and the rate of change of exhaust pressure. The rate of change of rotational speed is obtained by collecting multiple consecutive samples of the air compressor drive shaft speed signal near the load switching point moment, and then numerically differentiating the speed signal to obtain the rate of change of rotational speed sequence. The rate of change of exhaust pressure is obtained by collecting multiple consecutive samples of the air compressor exhaust pressure signal near the same load switching point moment, and then numerically differentiating the exhaust pressure signal to obtain the exhaust pressure rate of change sequence. The number of sampling points collected covers the duration of the transient transition process caused by the load switching, and the duration of the transient transition process is determined based on the response time constant of the air compressor system.

[0061] Using the rate of change of engine speed as the input signal and the rate of change of exhaust pressure as the output signal, a system identification equation based on an autoregressive moving average model is constructed. The autoregressive moving average model consists of an autoregressive part and a moving average part; the order of the autoregressive part is denoted as... The order of the moving average is denoted as . In some embodiments, Set to 2. The value is set to 1, based on the fact that in modeling the dynamic characteristics of air compressors, a second-order autoregressive structure can describe the inertial and damping characteristics of rotating machinery, while a first-order moving average structure can describe the temporal correlation of sensor measurement noise. The discrete-time form of the system identification equation is: in, Indicates the first The rate of change of exhaust pressure at each sampling time; Indicates the first The rate of change of exhaust pressure at each sampling time; Indicates the first The rate of change of exhaust pressure at each sampling time; Indicates the first The rate of change of rotational speed at each sampling time; Indicates the first The rate of change of rotational speed at each sampling time; and These are autoregressive coefficients, which are system parameters that need to be estimated online; and These are external input coefficients, which are system parameters that need to be estimated online; Indicates the first White noise residuals at each sampling time; Indicates the first White noise residuals at each sampling time; The moving average coefficients are system parameters that need to be estimated online.

[0062] The parameters of the system identification equation are estimated online using a least-squares recursive algorithm. The least-squares recursive algorithm updates the parameter estimates progressively on a sampling basis. At each sampling time, a parameter vector is constructed. and information vector The recursive process includes the following steps: In the first recursive step, the parameter vector is set. The initial value is a zero vector. The initial value of the covariance matrix is ​​set to be a matrix with large positive numbers on the diagonal and zero elements on the off-diagonal. The large positive numbers are between 10 to the power of 4 and 10 to the power of 6. At each sampling time... The residual is calculated based on the parameter estimates from the previous sampling time. The estimated value is used to update the information vector. Update the parameter vector at the current sampling time using a recursive formula. The covariance matrix is ​​obtained by recursively iterating through the transient response data at all load switching points, eventually converging to obtain the autoregressive coefficients. Autoregression coefficient External input coefficients External input coefficients and moving average coefficient The online estimates are used as coefficients of the system identification equation.

[0063] Based on the coefficients of the system identification equation, the autoregressive moving average model is transformed into a transfer function form in the continuous domain. This is achieved by introducing a hysteresis operator into the discrete difference equation. The system identification equation is rewritten in rational fractional form, and then the discrete-domain transfer function is mapped to the continuous domain using the bilinear transform method or the zero-order hold method. The bilinear transform method uses a substitution relation. ,in, Indicates the sampling period of transient response data. Let represent the Laplace complex variable. The transformation yields the transfer function in the continuous domain, which uses the Laplace variable as an expression. The rational fractional expression, where the numerator is about The polynomial, with denominator in terms of The transfer function of a polynomial over a continuous domain is called the dynamic response transfer function. The dynamic response transfer function describes the input-output relationship of the exhaust pressure dynamic response when the air compressor speed undergoes a transient change.

[0064] The acquired dynamic response transfer function (RTF) is embedded into the real-time performance mapping model. The embedding method involves using the real-time performance mapping model as a mapping relationship between the air compressor's intake temperature, exhaust pressure, speed, flow rate, and power under steady-state operating conditions, and using the RTF as a dynamic compensation channel between the speed change rate and exhaust pressure change rate under transient operating conditions. During the calculation process of the real-time performance mapping model, when the air compressor is detected to be in a load switching transient process, the current speed change rate is collected and input into the RTF. The RTF outputs a dynamic prediction value of the exhaust pressure change rate, which is used to correct the exhaust pressure value input into the real-time performance mapping model. The corrected exhaust pressure value participates in the steady-state mapping calculation of the real-time performance mapping model, thus superimposing transient dynamic compensation on the steady-state performance mapping. The real-time performance mapping model with the embedded RTF serves as a comprehensive performance mapping model encompassing both steady-state and dynamic performance. This comprehensive performance mapping model can output a full-condition air compressor power value reflecting the current actual operating state under conditions of both long-term performance degradation and frequent load switching.

[0065] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A data-fit-driven air compressor modeling method, characterized in that, include: The system acquires operating data of the air compressor under various working conditions, including intake air temperature, exhaust pressure, speed, and flow rate. The operational data is preprocessed to obtain cleaned operational data; The cleaned running data is divided into time windows, and multi-order polynomial regression fitting is performed on the cleaned running data within each time window to generate the initial fitting parameter set corresponding to each time window. Based on the initial fitting parameter set corresponding to all time windows, a fitting parameter matrix is ​​constructed, and matrix decomposition operation is performed on the fitting parameter matrix to extract the principal component features of the fitting parameters. Based on the principal component characteristics of the fitted parameters, an air compressor performance degradation trend model is established. This performance degradation trend model is used to describe the performance decay law of the air compressor under different operating times. Based on the performance degradation trend model, the air compressor is dynamically modeled using real-time collected operating data to generate a real-time performance mapping model.

2. The air compressor modeling method based on data fitting as described in claim 1, characterized in that, The process of preprocessing the operational data to obtain cleaned operational data includes: Perform local mean calculation based on a sliding window on the data sequence of each dimension in the running data to obtain a local mean sequence; Calculate the deviation value of each data point in the running data from its corresponding local mean, mark the data points whose deviation value exceeds the preset deviation threshold as outliers and remove them to obtain the initial screening data; Variance calculation is performed on the continuous time period operation data in the initial screening data. The time period with variance less than a preset variance threshold is marked as the steady-state operating condition time period. The operation data within the steady-state operating condition time period is extracted as the cleaned operation data.

3. The air compressor modeling method based on data fitting as described in claim 1, characterized in that, The process involves dividing the cleaned operational data into time windows, performing multi-order polynomial regression fitting on the cleaned operational data within each time window, and generating an initial set of fitting parameters corresponding to each time window, including: Based on the time span of the cleaned operational data, a fixed time window length is set, and the cleaned operational data is divided into equal intervals according to the time window length to generate multiple consecutive time windows. For each time window, the intake temperature, exhaust pressure, speed and flow rate in the post-cleaning operation data within that time window are used as input variables, and the air compressor power is used as the output variable. A third-order polynomial regression fitting is performed to generate the polynomial coefficient set corresponding to that time window as the initial fitting parameter set.

4. The air compressor modeling method based on data fitting as described in claim 1, characterized in that, The process involves constructing a fitting parameter matrix based on the initial fitting parameter set corresponding to all time windows, performing matrix decomposition on the fitting parameter matrix, and extracting the principal component features of the fitting parameters, including: The initial set of fitting parameters corresponding to each time window is taken as a row vector, and the row vectors corresponding to all time windows are arranged in chronological order to form a two-dimensional fitting parameter matrix. Perform singular value decomposition on the fitted parameter matrix to obtain a left singular matrix, a singular value diagonal matrix, and a right singular matrix; Extract the three largest singular values ​​from the singular value diagonal matrix, and reconstruct the dimension-reduced fitting parameter feature matrix based on the left and right singular matrices corresponding to the three largest singular values. Use the dimension-reduced fitting parameter feature matrix as the principal component features of the fitting parameters.

5. The air compressor modeling method based on data fitting as described in claim 1, characterized in that, The step of establishing an air compressor performance degradation trend model based on the principal component characteristics of the fitted parameters includes: Arrange the principal component features of the fitted parameters in chronological order to construct a principal component feature time series. The principal component feature time series is subjected to exponential smoothing to remove high-frequency noise and obtain a smoothed feature series. Piecewise linear regression fitting is performed on the smooth feature sequence, dividing the smooth feature sequence into multiple linear segments, each segment is described by a linear equation, and the breakpoint of the piecewise linear regression fitting is determined by minimizing the sum of squared residuals of each segment. The combination of the linear equations of each segment obtained by the piecewise linear regression fitting is used as the performance degradation trend model.

6. The air compressor modeling method based on data fitting as described in claim 1, characterized in that, The process of dynamically modeling the air compressor based on the performance degradation trend model and combining it with real-time collected operating data to generate a real-time performance mapping model includes: The air compressor's current operating data is collected in real time, including the current intake air temperature, current exhaust pressure, current speed, and current flow rate. Input the current running data into the performance degradation trend model to calculate the degradation compensation coefficient corresponding to the current moment; An interpolation method based on radial basis functions is used to dynamically correct the preset standard performance mapping model with the degradation compensation coefficient. The standard performance mapping model is a mathematical model that describes the relationship between the operating parameters and output parameters of the air compressor in the initial state. The corrected standard performance mapping model is used as the real-time performance mapping model.

7. The air compressor modeling method based on data fitting as described in claim 6, characterized in that, The method of using radial basis function-based interpolation to dynamically correct the preset standard performance mapping model with the degradation compensation coefficient includes: The degradation compensation coefficient is used as the center point of the radial basis function, and the Gaussian function is selected as the radial basis function. Calculate the Euclidean distance between each model parameter in the standard performance mapping model and the center point of the radial basis function, and calculate the weight coefficient of each model parameter based on the Euclidean distance; The weight coefficient of each model parameter is multiplied by the corresponding model parameter to generate the corrected model parameters. All the corrected model parameters are combined to obtain the corrected standard performance mapping model.

8. The air compressor modeling method based on data fitting as described in claim 1, characterized in that, After generating a real-time performance mapping model by dynamically modeling the air compressor based on the performance degradation trend model and combining it with real-time collected operating data, the process further includes: Acquire transient response data of the air compressor at multiple load switching points, the transient response data including the rate of change of speed and the rate of change of exhaust pressure; The transient response data is processed by system identification to generate the dynamic response transfer function of the air compressor; The dynamic response transfer function is embedded into the real-time performance mapping model to generate a comprehensive performance mapping model that includes both steady-state and dynamic performance.

9. The air compressor modeling method based on data fitting as described in claim 8, characterized in that, The process of performing system identification processing on the transient response data to generate the dynamic response transfer function of the air compressor includes: Using the speed change rate as the input signal and the exhaust pressure change rate as the output signal, a system identification equation based on an autoregressive moving average model is constructed. The parameters of the system identification equation are estimated online using the least squares recursive algorithm to obtain the coefficients of the system identification equation; Based on the coefficients of the system identification equation, the autoregressive moving average model is transformed into a continuous domain transfer function form through Laplace transform, which serves as the dynamic response transfer function.

10. A data-fitting-driven air compressor modeling system, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the air compressor modeling method based on data fitting driven by any one of claims 1 to 9.

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