Generalized ARMA model-based gas turbine compressor blade tip clearance data modeling and prediction method

Abstract

The invention discloses a generalized ARMA model-based gas turbine compressor blade tip clearance data modeling and prediction method, and relates to data modeling and prediction. The method comprises the following steps: collecting multi-working-condition operation data of a gas turbine, and screening characteristic parameters related to blade tip gap height by using a grey relational analysis method; constructing a multi-input generalized ARMA model, replacing the random interference variable of the traditional ARMA model with a screening variable, and introducing a ridge regression algorithm to solve parameters; determining an optimal model order and parameters by using a particle swarm optimization algorithm; and evaluating a model prediction effect by using an average absolute percentage error, and performing adjustment and optimization. The complex coupling relation between the blade tip clearance and the multi-working-condition parameters is effectively captured, and high-precision, efficient and economical technical support is provided for active control over the blade tip clearance of the gas turbine.

Description

Technical Field

[0001] The present invention relates to the field of data modeling and prediction, and in particular to a gas turbine compressor tip clearance data modeling and prediction method based on a generalized ARMA model suitable for gas turbine operating status monitoring. Background Art

[0002] Compressor tip clearance refers to the radial distance between the tip of the compressor blade and the casing. In the field of gas turbines, numerous studies have shown that the size of the compressor tip clearance significantly affects the efficiency of the gas turbine in converting the chemical energy of the gas into mechanical energy. A reasonable tip clearance can improve the operating efficiency and reliability of the gas turbine. If the tip clearance is too large, it will lead to increased heat transfer in the tip area, exacerbating oxidation and erosion of the tip material, and reducing mechanical performance. Too small a tip clearance can easily cause collision or friction between the blade tip and the turbine casing. Because the tip clearance changes very complexly during gas turbine operation and often varies with changes in turbine operating conditions, accurately predicting the tip clearance and then actively controlling the tip clearance is a major problem that plagues companies and research institutes. Therefore, studying the prediction method of tip clearance is of great significance.

[0003] Currently, tip clearance prediction and feedback are primarily achieved through the construction of a tip clearance prediction model, supporting closed-loop control, turbine air system, structural design, and performance analysis. An efficient and highly accurate tip clearance prediction model is crucial for achieving tip clearance control.

[0004] Traditional methods for predicting tip clearance primarily focus on building physical models and deriving empirical formulas, but these methods suffer from low accuracy and limited applicability. Data-driven methods, as an emerging technology, have been widely used in industry in recent years due to their adaptability, strong nonlinear mapping capabilities, and low modeling costs. Gas turbines are complex systems with numerous variables and strong nonlinearities. Therefore, building a data model for gas turbines based on the concept of data-driven modeling, using the ARMA model from the time-domain series prediction and analysis model, offers unique advantages. Summary of the Invention

[0005] The present invention aims to address the existing problems of insufficient multivariable coupling relationship modeling and low parameter optimization efficiency by providing a method for modeling and predicting gas turbine compressor tip clearance data based on a generalized ARMA model. Based on the causal relationship between mechanics and thermodynamics, and utilizing simple, reliable, and non-invasive sensor measurements, a multivariable generalized ARMA model is established to construct a tip clearance model. This method achieves rapid and accurate prediction of tip clearance, providing feedback for active control.

[0006] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions.

[0007] A method for modeling and predicting gas turbine compressor tip clearance data based on a generalized ARMA model includes the following steps:

[0008] Step S1: Data collection and preprocessing: Collect gas turbine operating parameters and blade tip clearance data, and unify the sampling interval.

[0009] Step S2: Feature screening: Based on grey correlation analysis, the variables with high correlation with blade tip clearance are screened to construct an input variable set;

[0010] Step S3: Generalized ARMA modeling: construct a multi-input generalized ARMA model, expand the traditional ARMA model into a multi-input form, and introduce the ridge regression algorithm to solve the model parameters;

[0011] Step S4: Model order and parameter optimization: Use particle swarm optimization algorithm to determine the model order and optimal parameters and optimize the model structure;

[0012] Step S5: Model validation and blade tip clearance prediction: The model is validated using measured data, and the prediction effect is evaluated using the mean absolute percentage error. After adjusting the parameters, the blade tip clearance prediction is performed.

[0013] In step S1, the gas turbine operating parameters include: guide vane angle, compressor exhaust temperature, compressor inlet temperature, compressor casing deep thermocouple, compressor shallow thermocouple and other characteristic parameter variables. The data set vectors of these key characteristic parameters of gas turbine operation are respectively recorded as X1(t), X2(t), ..., X k (t).

[0014] In step S2, the specific method of feature screening can be: screening the model input feature variables, screening the main correlation feature parameter variables of the blade tip clearance modeling based on the thermodynamic principle and the gray correlation analysis method, and rearranging the data set vectors of the screened feature parameters into X1(t), X2(t), ..., X i (t)(i≤k) form;

[0015] Grey relational analysis is calculated as follows:

[0016]

[0017] Here, ρ controls the discrimination of the ξ coefficient. ρ ranges from 0 to 1, with smaller ρ indicating greater discrimination. A value of 0.5 is generally appropriate. The ξ correlation coefficient ranges from 0 to 1. Here, i and k represent the i-th factor in the k-th dimension. The distance between the subsequence and the parent sequence is inversely proportional. The greater the distance between the two values, the smaller the correlation value, and vice versa. To avoid the influence of other interference and morphological features, vectors need to be normalized to the same scale and position. The distance to each point is then calculated.

[0018] In step S3, the generalized ARMA modeling replaces the random interference term of the traditional ARMA model with the screened input variables, and introduces the ridge regression algorithm to solve the model parameters. The specific steps are:

[0019] The random disturbance ε entering the system in the traditional ARMA model t Replace with the selected related variable X t .

[0020] The mathematical expression of the traditional ARMA model can be expressed as:

[0021]

[0022] Multi-input generalized ARMA model:

[0023]

[0024] Among them, X t is the input time series; Y t is the output time series; α k is the autoregressive coefficient of the model; β m is the sliding coefficient of the model; L represents the number of input variables; therefore, in the process of establishing a multi-input generalized ARMA model, the parameters that need to be determined are the autoregressive coefficient α of the model k , the sliding mean coefficient β of the model m , the autoregressive order of the model p, the sliding average order of the model q i , the number of input variables L.

[0025] In order to improve the robustness of the model, the ridge regression algorithm is introduced to calculate the parameters in the process of solving the parameters of the generalized ARMA model. The loss function of the ridge regression is as follows:

[0026]

[0027] The parameter estimates for ridge regression are as follows:

[0028] β=(X T X+λI) -1 XT y (5)

[0029] Among them, y is the response variable, x1, x2, ..., x p are predictor variables, β1,β2,…,β p are model parameters, X is the design matrix, I is the identity matrix, and λ is a positive adjustment parameter used to control the strength of the penalty term; the larger the value of λ, the stronger the penalty for the coefficient and the smaller the value of the coefficient.

[0030] The current value of the system Y t is the value Y of the system at the past moment t-1 ,Y t-2 ,……,Y t-p The linear combination of (autoregressive part) and multiple inputs of the system in the past The result of the linear combination (moving average part) of .

[0031] In step S4, the particle swarm optimization algorithm is used to determine the model order and optimal parameters and optimize the model structure. The specific steps may be:

[0032] The characteristic parameters are screened by the gray correlation algorithm, and the input variable L is obtained according to the number of parameter types after screening; the model parameter a is obtained by the ridge regression algorithm and the historical data set. k , β im ; Use particle swarm optimization algorithm to obtain the corresponding model order p and q i And optimize; Particle swarm algorithm optimizes model order p and q i The specific process and steps are as follows:

[0033] The first step is to initialize the particle position and velocity to generate the initial generalized ARMA model parameters;

[0034] The second step is to calculate the different model parameters represented by each particle, train the generalized ARMA model and calculate the fitness value of the model, take 1 / RMSE (root mean square error) as the fitness calculation formula, and update the fitness value P of the best particle at the same time. best and index g best ;

[0035] The third step is to update the velocity and position of the particle;

[0036] The fourth step is to retrain the generalized ARMA model using the updated parameters and calculate the fitness value P best , update the fitness value P of the best particle best and index g best ;

[0037] The fifth step is to determine whether the termination condition is met. If so, the model parameter optimization is completed; if not, it returns to the second step to loop;

[0038] The sixth step is to use the generalized ARMA model parameters corresponding to the optimal particles to construct the tip clearance model.

[0039] Root mean square error RMSE:

[0040]

[0041] in is the predicted value, y i is the true value.

[0042] In step S5, the prediction effect is evaluated by the mean absolute percentage error, and the mean absolute percentage error MAPE is calculated as follows:

[0043]

[0044] in, is the predicted value, y i is the true value.

[0045] MAPE is expressed as a percentage, representing the average percentage error between the predicted value and the actual value. The MAPE value range is [0, +∞), with smaller values ​​indicating more accurate prediction models.

[0046] Compared with the prior art, the advantages and outstanding technical effects of the present invention are:

[0047] (1) The present invention is suitable for short-term prediction of tip clearance of gas turbines. By rationally screening variables related to tip clearance and constructing a generalized ARMA model, it can accurately capture the complex relationship between tip clearance and related variables. In practical applications, compared with the traditional ARMA model prediction method, the present model can consider the modeling of multiple characteristic variables, more accurately predict the changes in tip clearance, effectively reduce prediction errors, and provide reliable tip clearance prediction data for the efficient operation of gas turbines.

[0048] (2) This invention leverages the advantages of data-driven development and, given a sufficient training dataset, can adapt to the operation of gas turbines under different operating conditions. Whether under varying load conditions, speed changes, or complex operating conditions such as varying ambient temperature and pressure, the model can adaptively adjust based on actual operating data, maintaining high prediction accuracy and demonstrating excellent adaptability and generalization capabilities.

[0049] (3) The present invention takes advantage of the simplicity of ARMA model modeling and models based on simple and reliable sensor measurement data and the causal relationship between mechanics and thermodynamics, avoiding the complex physical model construction process and the derivation of a large number of empirical formulas.

[0050] (4) The present invention uses an intelligent optimization algorithm to further improve the generalized ARMA model. By using intelligent algorithms to quickly optimize the model structure and parameters, the modeling time is greatly shortened, the modeling efficiency is improved, and an effective blade tip clearance prediction model can be established in a relatively short time. The powerful search capability and global optimization characteristics of the particle swarm algorithm are used to deeply explore the hidden information in the data and fine-tune the model to obtain a more accurate blade tip clearance prediction model. In a complex and changing operating environment, the particle swarm algorithm enables the model to more accurately fit the actual operating conditions, providing more powerful support for the stable operation of the gas turbine.

[0051] (5) The modeling computational cost of the present invention is low, and a highly accurate prediction model can be obtained at a relatively low computational cost. The generalized ARMA modeling method of the present invention utilizes historical gas turbine data for modeling. Furthermore, the low modeling cost also makes the method more economically feasible and valuable for industrial applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 is a flow chart of a specific embodiment of the present invention;

[0053] Figure 2 It is a schematic diagram of the generalized ARMA model;

[0054] Figure 3 Flowchart for optimizing model parameters of generalized ARMA model using particle swarm parameters;

[0055] Figure 4 Historical compressor tip clearance values;

[0056] Figure 5 Key parameters of steam turbine operation;

[0057] Figure 6 Grey relational analysis results;

[0058] Figure 7 Comparison chart of predicted values ​​and true values. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the following embodiments will be further described in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0060] A method for modeling and predicting gas turbine compressor tip clearance data based on a generalized ARMA model includes the following steps:

[0061] Step S1, modeling data collection, obtains different operating condition data of the gas turbine during long-term operation from the gas turbine data acquisition system; the operating condition data include characteristic parameter variables such as guide vane angle, compressor exhaust temperature, compressor inlet temperature, compressor casing deep thermocouple, compressor shallow thermocouple, etc., and the data set vectors of these key characteristic parameters of gas turbine operation are respectively recorded as X1(t), X2(t), ..., X k (t).

[0062] Step S2, the model input characteristic variable screening, according to the thermodynamic principle and the grey correlation analysis method to screen the main correlation prominent characteristic parameter variables of the blade tip clearance modeling, the screened characteristic parameter data set vector is rearranged into X1(t), X2(t), ..., X i (t)(i≤k) form;

[0063] Grey correlation analysis is a multi-factor statistical analysis method. It determines the correlation between factors based on the similarity of their trends. Simply put, it involves understanding the relative strength of the influence of other factors on a particular factor within a grey system.

[0064] The specific mathematical expression of grey relational analysis can be expressed as:

[0065]

[0066] Here, ρ controls the discrimination of the ξ coefficient. ρ ranges from 0 to 1, with smaller ρ indicating greater discrimination. A value of 0.5 is generally appropriate. The ξ correlation coefficient ranges from 0 to 1. Here, i and k represent the i-th factor in the k-th dimension. The distance between the subsequence and the parent sequence is inversely proportional. The greater the distance between the two values, the smaller the correlation value, and vice versa. To avoid the influence of other interference and morphological features, vectors need to be normalized to the same scale and position. The distance to each point is then calculated.

[0067] Step S3: Propose a generalized ARMA model, improve it on the basis of the ARMA model, and change the random interference ε t Replace with the selected related variable X t .

[0068] The mathematical expression of the traditional ARMA model can be expressed as:

[0069]

[0070] Multi-input generalized ARMA model:

[0071]

[0072] Among them, X t is the input time series; Y t is the output time series; α k is the autoregressive coefficient of the model; β m is the sliding coefficient of the model; L represents the number of input variables. Therefore, in the process of establishing a multi-input generalized ARMA model, the parameters that need to be determined are p, q i , α k , β im , L. Its determination method will be mentioned later.

[0073] In order to improve the robustness of the model, the ridge regression algorithm is introduced to calculate the parameters in the parameter solution process of the generalized ARMA model.

[0074] Ridge regression, also known as Tikhonov regularization, is a variant of linear regression that addresses the multicollinearity problem by adding an L2 regularization term to the ordinary least squares (OLS) regression, thereby improving the generalization and robustness of the model.

[0075] The loss function of ridge regression is:

[0076]

[0077] Parameter estimates for ridge regression:

[0078] β=(X T X+λI) -1 X T y (5)

[0079] Among them, y is the response variable, x1, x2, ..., x p are predictor variables, β1,β2,…,β p are model parameters, X is the design matrix, I is the identity matrix, and λ is a positive adjustment parameter used to control the strength of the penalty term. The larger the value of λ, the stronger the penalty on the coefficient and the smaller the value of the coefficient.

[0080] Therefore, the practical meaning of the multi-input generalized ARMA model is: the value Y of the system at the current moment t is the value Y of the system at the past moment t-1 ,Y t-2 ,……,Y t-p The linear combination of (autoregressive part) and multiple inputs of the system in the past The result of the linear combination (moving average part) of .

[0081] Step S4: Model structure is established and optimized. The characteristic parameters are screened by gray correlation algorithm, and the input variable L is obtained according to the number of parameters after screening; the model parameter a is obtained by ridge regression algorithm and historical data set. k , β im ; Use particle swarm optimization algorithm to obtain the corresponding model order p and q i And optimize. Particle swarm optimization model order p and q i The specific process and steps are as follows:

[0082] The first step is to initialize the particle position and velocity to generate the initial generalized ARMA model parameters;

[0083] The second step is to calculate the different model parameters represented by each particle, train the generalized ARMA model and calculate the fitness value of the model, take 1 / RMSE (root mean square error) as the fitness calculation formula, and update the fitness value P of the best particle at the same time. best and index g best ;

[0084] The third step is to update the velocity and position of the particle;

[0085] The fourth step is to retrain the generalized ARMA model using the updated parameters and calculate the fitness value P best , update the fitness value P of the best particle best and index g best ;

[0086] The fifth step is to determine whether the termination condition is met. If so, the model parameter optimization is completed; if not, it returns to the second step to loop;

[0087] The sixth step is to use the generalized ARMA model parameters corresponding to the optimal particles to construct the tip clearance model.

[0088] Root Mean Squared Error (RMSE):

[0089]

[0090] in is the predicted value, yi 为 True value.

[0091] Root mean square error (RMSE) is a metric used to measure the accuracy of a prediction model on continuous data. It measures the root mean square difference between the predicted value and the true value, indicating the average deviation between the predicted value and the true value. It is a commonly used performance evaluation metric in regression tasks.

[0092] Step S5: Use the measured data to make predictions, and use MAPE (mean absolute error) as an indicator to measure the prediction effect of the model, that is, the prediction error. Adjust the model parameters according to the effect of the model to further optimize the model.

[0093] Mean Absolute Percentage Error (MAPE)

[0094]

[0095] in is the predicted value, y i is the true value.

[0096] The mean absolute error (MAPE) is a commonly used metric to evaluate the difference between predicted and actual values ​​and is an important indicator of forecast accuracy. MAPE is expressed as a percentage, representing the average percentage difference between the predicted and actual values. The MAPE range is [0, +∞), with smaller values ​​indicating more accurate forecast models.

[0097] Specific examples are given below.

[0098] like Figure 1 As shown, an embodiment of the present invention provides a method for constructing a gas turbine compressor tip clearance prediction model. Figure 2 As shown in the figure, the method mainly generalizes the ARMA model to a generalized multi-input form with multiple inputs and can predict non-stationary signals. A simple prediction model can be established based on the historical key operating parameters of the gas turbine and the historical compressor tip clearance to achieve accurate and rapid prediction of the gas turbine tip clearance. Figure 3 As shown in the figure, the intelligent optimization algorithm and particle swarm optimization algorithm are used to select the parameters of the generalized ARMA model, select the local optimal parameters, and realize the final construction of the generalized ARMA model.

[0099] The embodiment of the present invention specifically includes the following steps:

[0100] Step S1: Obtain the time series data of the gas turbine operating status and blade tip clearance from the gas turbine monitoring system, pre-process the data, and unify the sampling interval. In the prediction test case of a certain type of gas turbine, 86,360 seconds of data were constructed based on the various operating parameters of the gas turbine and the compressor blade tip clearance. Each data point is in seconds, and the data sampling interval is about 30 seconds. The operating parameters include ten features, including certain ones, which are replaced by features 1 to 10 below. The collected data set is sorted into clearance value data and feature value data

[0101] Step S2: Calculate the correlation value between each operating parameter in the data set and the gas turbine compressor tip clearance using a grey correlation algorithm, select operating parameters with correlations higher than the average value and retain them in the data set, and remove operating parameters with correlations lower than the average value from the data set.

[0102] Step S3: Divide the first three quarters of the total sample of the processed and screened data set into a training set and a validation set, use the training set to calculate (train) the parameters of the prediction model, and take the last quarter of the data as the prediction object; set it in the algorithm program.

[0103] Step S4: Use the training set and validation set as input for model training.

[0104] Step S5: Use the ridge regression method to obtain the model parameter a on the training set k , β im The matrix composed of cR. Training p and q i Parameters used Figure 3 The particle swarm optimization algorithm shown in the figure uses the inverse of the root mean square error RMSE as the fitness calculation formula and takes the fitness value P of the best particle. best , that is, the model parameter corresponding to the minimum value of the root mean square error is the modeling parameter.

[0105] The specific training process and steps are as follows:

[0106] 1) Initialize the particle position and velocity to generate the initial generalized ARMA model parameters;

[0107] 2) Calculate the different model parameters represented by each particle, train the generalized ARMA model and calculate the fitness value of the model, and update the fitness value P of the best particle at the same time best and index g best ;

[0108] 3) Update the particle's velocity and position;

[0109] 4) Use the updated parameters to retrain the generalized ARMA model and calculate the fitness value, and update the fitness value P of the best particle best and index g best ;

[0110] 5) Determine whether the termination condition is met. If so, the model parameter optimization is completed; if not, return to the loop;

[0111] 6) The tip clearance model is constructed using the generalized ARMA model parameters corresponding to the optimal particles.

[0112] Step S6: The model parameters obtained by step S3 training are constructed as follows Figure 2The generalized ARMA model is able to capture the impact of changes in gas turbine operating parameters on the tip clearance value in the short term, and accurately and quickly predict the tip clearance value at the current moment based on the tip clearance values ​​at past moments.

[0113] Step S7: After completing the construction of model parameters, you can start prediction. It can predict the data points in the last quarter of the data set. The specific verification example is as follows.

[0114] The data source is collected from the normal operation of a gas turbine. Various operating parameters and compressor tip clearance are recorded. There are 1 data set in total. Figure 4 and Figure 5 As shown in the figure, the data set contains 86,360 seconds of data, each data point is in seconds, and the data collection interval is 30 seconds. The collected gas turbine operating parameters include several features, including certain ones, which are represented by features 1 to 10 below. After the gray correlation analysis method, the operating parameters with high correlation with the blade tip clearance are screened out, such as Figure 6 As shown in Figure 1, the dataset is updated and the first three quarters of the total sample of the dataset are divided into a training set and a validation set (64,800 seconds of data, 2,159 data points). The training set is used to calculate the parameters of the prediction model (training), and the last quarter of the data (21,570 seconds of data, 719 data points) is taken as the prediction object. The error between the true value and the predicted value of a single point is defined as 10% as the tolerance. The initial parameter settings of the particle swarm algorithm are shown in Table 1.

[0115] Table 1 Initial parameter settings of particle swarm algorithm

[0116]

[0117] The optimized generalized ARMA parameters are shown in Table 2;

[0118] Table 2 Optimized generalized ARMA parameters

[0119]

[0120] The comparison results between the predicted value and the true value are as follows Figure 7 As shown in the figure; after verification by the measured data of this example, the time used to establish the model in this case is 65.101985 seconds, and the prediction error of the model is less than 1%, indicating that this gas turbine compressor tip clearance prediction method based on the generalized ARMA model is accurate in short-term prediction.

[0121] The multi-input generalized ARMA model can well characterize the dynamic characteristics of mechanical systems and can well predict the system's response. This invention expands the traditional ARMA model through multivariable inputs and combines it with an intelligent optimization algorithm to address the low precision and poor adaptability of traditional methods. It provides an effective gas turbine compressor tip clearance data modeling and prediction method with high prediction accuracy, good adaptability and generalization capabilities, and low modeling costs. It achieves high-precision prediction of tip clearance (error <1%), has the advantages of high modeling efficiency and strong generalization capabilities, and provides reliable technical support for the efficient operation of gas turbines and the active control of tip clearance.

[0122] The above embodiments are only preferred embodiments of the present invention and should not be considered to limit the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the patent of the present invention.

Claims

1. A gas turbine compressor tip clearance data modeling and prediction method based on a generalized ARMA model, characterized by The following steps are involved: Step S1: Data collection and preprocessing: Collect gas turbine operating parameters and blade tip clearance data, and unify the sampling interval; Step S2: Feature screening: Based on grey correlation analysis, the variables with high correlation with blade tip clearance are screened to construct an input variable set; Step S3: Generalized ARMA modeling: construct a multi-input generalized ARMA model, expand the traditional ARMA model into a multi-input form, and introduce the ridge regression algorithm to solve the model parameters; Step S4: Model order and parameter optimization: Use particle swarm optimization algorithm to determine the model order and optimal parameters and optimize the model structure; Step S5: Model validation and blade tip clearance prediction: The model is validated using measured data, and the prediction effect is evaluated using the mean absolute percentage error. After adjusting the parameters, the blade tip clearance prediction is performed.

2. A gas turbine compressor tip clearance data modeling and prediction method based on a generalized ARMA model as claimed in claim 1, characterized in that In step S1, the gas turbine operating parameters include: guide vane angle, compressor exhaust temperature, compressor inlet temperature, compressor casing deep thermocouple, compressor shallow thermocouple and other characteristic parameter variables. The data set vectors of these key characteristic parameters of gas turbine operation are respectively recorded as X1(t), X2(t), ..., X k (t).

3. The method for modeling and predicting gas turbine compressor tip clearance data based on the generalized ARMA model according to claim 1, characterized in that In step S2, the specific method of feature screening is as follows: screening the model input feature variables, screening the main correlation feature parameter variables of the blade tip clearance modeling according to the thermodynamic principle and the grey correlation analysis method, and rearranging the data set vectors of the screened feature parameters into x1(t), X2(t), ..., X i (t)(i≤k) form; Grey relational analysis is calculated as follows: Among them, ρ is a coefficient that controls the discrimination of the ξ coefficient. ρ ranges from 0 to 1. The smaller ρ is, the greater the discrimination is. Generally, 0.5 is a more appropriate value. The ξ correlation coefficient ranges from 0 to 1. In the formula, i and k mean that the distance between the i-th factor and the parent sequence is inversely proportional to the distance between the subsequence and the parent sequence in the k-th dimension. The greater the distance between the two values, the smaller the correlation value, and vice versa. In order to avoid the influence of other interference and morphological characteristics, it is necessary to normalize the vectors, correct all vectors to the same scale and position, and then calculate the distance of each point.

4. The method for modeling and predicting gas turbine compressor tip clearance data based on a generalized ARMA model as claimed in claim 1, characterized in that In step S3, the generalized ARMA modeling is to replace the random interference term of the traditional ARMA model with the screened input variables, and introduce the ridge regression algorithm to solve the model parameters. The specific steps can be: The random disturbance ε entering the system in the traditional ARMA model t Replace with the selected related variable X t ; The mathematical expression of the traditional ARMA model can be expressed as: Multi-input generalized ARMA model: Among them, X t is the input time series; Y t is the output time series; α k is the autoregressive coefficient of the model; β m is the sliding mean coefficient of the model; L represents the number of input variables; therefore, in the process of establishing a multi-input generalized ARMA model, the parameters that need to be determined are the autoregressive coefficient α of the model k , the sliding mean coefficient β of the model m , the autoregressive order of the model p, the sliding average order of the model q i , the number of input variables L; In order to improve the robustness of the model, the ridge regression algorithm is introduced to calculate the parameters in the process of solving the parameters of the generalized ARMA model. The loss function of the ridge regression is as follows: The parameter estimates for ridge regression are as follows: β=(X T X+λI) -1 X T y (5) Among them, y is the response variable, x1, x2, ..., x p are predictor variables, β1,β2,…,β p is the model parameter, X is the design matrix, I is the identity matrix, and λ is a positive adjustment parameter used to control the intensity of the penalty term; the larger the value of λ, the stronger the penalty for the coefficient and the smaller the value of the coefficient; The current value of the system Y t is the value Y of the system at the past moment t-1 ,Y t-2 ,……,Y t-p The linear combination of (autoregressive part) and multiple inputs of the system in the past The result of the linear combination (moving average part) of .

5. The method for modeling and predicting gas turbine compressor tip clearance data based on the generalized ARMA model according to claim 1, characterized in that In step S4, the particle swarm optimization algorithm is used to determine the model order and optimal parameters and optimize the model structure. The specific steps may be: The characteristic parameters are screened by the gray correlation algorithm, and the input variable L is obtained according to the number of parameter types after screening; the model parameter a is obtained by the ridge regression algorithm and the historical data set. k , β im ; Use particle swarm optimization algorithm to obtain the corresponding model order p and q i And optimize; Particle swarm algorithm optimizes model order p and q i The specific process and steps are as follows: The first step is to initialize the particle position and velocity to generate the initial generalized ARMA model parameters; The second step is to calculate the different model parameters represented by each particle, train the generalized ARMA model and calculate the fitness value of the model, take 1 / RMSE (root mean square error) as the fitness calculation formula, and update the fitness value P of the best particle at the same time. best and index g best ; The third step is to update the velocity and position of the particle; The fourth step is to retrain the generalized ARMA model using the updated parameters and calculate the fitness value P best , update the fitness value P of the best particle best and index g best ; The fifth step is to determine whether the termination condition is met. If so, the model parameter optimization is completed; if not, it returns to the second step to loop; Step 6: Use the generalized ARMA model parameters corresponding to the optimal particles to construct the tip clearance model; Root mean square error RMSE: in is the predicted value, y i is the true value.

6. A gas turbine compressor tip clearance data modeling and prediction method based on a generalized ARMA model as claimed in claim 1, characterized in that In step S5, the prediction effect is evaluated by the mean absolute percentage error, and the mean absolute percentage error MAPE is calculated as follows: in, is the predicted value, y i is the true value.

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