Aero-engine performance degradation estimation model modeling method

Abstract

The application discloses an aero-engine performance degradation estimation model modeling method. First, N optimal health parameters are selected; then the selected optimal health parameters are used as the augmented state variables of an aero-engine state variable model, a Kalman filter is used as a state observer to construct an aero-engine performance degradation estimation model, wherein N is the number of measurable controlled variables of the aero-engine; the N optimal health parameters are selected by the following method: preliminary screening of the health parameters is performed based on correlation, and then final screening of the health parameters is performed based on a condition number. The application further discloses an aero-engine performance degradation estimation model. Compared with the prior art, the application takes correlation and a condition number as core bases to determine optimal aero-engine health parameters, and can effectively improve the precision of the performance degradation estimation model and an airborne model.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aero-engine modeling and control technology, and particularly relates to a modeling method of an aero-engine performance degradation estimation model. BACKGROUND

[0002] The performance of an aero-engine will inevitably degrade under long-term harsh working environment. Due to the corrosion of compressor blades and turbine blades, the ablation of a flame tube, the deformation of an engine shell and other factors, the performance of the engine will change slowly with the increase of flight cycles, and the flow capacity and operating efficiency will also change, thereby causing deviation from the rated working state and failure. Among them, the failure caused by gas path degradation accounts for more than 90% of the total engine failures, and the determination of engine health parameters helps to improve the adaptive accuracy of the on-board model and is the basis for researching engine fault diagnosis and implementing comprehensive control, and has become one of the key problems to be solved in the field of aero-engines.

[0003] At present, many scholars at home and abroad have carried out a series of researches on engine health diagnosis. For example, the Glenn Research Center of NASA [Kobayashi T, Simon D L. Integration of on-line and off-line diagnostic algorithms for aircraft engine health management [J]. 2007] proposed a structure mixed with off-line, on-line Kalman filter and on-board nonlinear model, estimated the health parameters of the aero-engine off-line, and used these health parameters on-line to estimate the model output under degradation. In China, Huang Jinquan et al. [Lu Feng, Huang Jinquan, Lv Yiqiu, et al. Engine gas path component health diagnosis method based on nonlinear adaptive filtering [J]. Acta Aeronautica et Astronautica, 2013, 34(11): 2529-2538.] proposed a linear adaptive Kalman filter algorithm to solve the problem of low estimation accuracy of health parameters under engine gas path mutation and long algorithm engineering verification period, and extended it to a nonlinear system.

[0004] The above technical solutions have achieved good results, but there is little research on how to select health parameters. The running time of the engine will cause various degradations, such as fan flow, efficiency, compressor flow, efficiency, high / low pressure turbine flow, efficiency, etc. However, the number of actual sensors of the engine is limited, and since the number of estimable health parameters is generally not more than the number of measurable parameters, i.e. the number of sensors, the number of health parameters that can be set is limited. Considering that setting different combinations of health parameters has a great influence on the accuracy of the on-board model after engine degradation, how to select the optimal health parameters to improve the accuracy of the performance degradation estimation model and the on-board model has become a problem to be solved. SUMMARY

[0005] The technical problem to be solved by the present application is to overcome the deficiencies of the prior art, provide an aero-engine performance degradation estimation model modeling method, and determine the optimal aero-engine health parameters based on correlation and condition number, thereby effectively improving the accuracy of the performance degradation estimation model and the on-board model.

[0006] The present application specifically adopts the following technical solutions to solve the above technical problems:

[0007] An aero-engine performance degradation estimation model modeling method, first, select N optimal health parameters; then use the selected optimal health parameters as the augmented state variables of the aero-engine state variable model, use the Kalman filter as the state observer to construct the aero-engine performance degradation estimation model, wherein N is the number of measurable controlled variables of the aero-engine; the N optimal health parameters are obtained by the following method: step 1, based on the aero-engine component-level model, obtain the change amount of the same group of measurement parameters of the aero-engine generated by each health parameter under a preset degradation amount, and use the vector formed by the change amount of the measurement parameters as the feature vector representing the health parameter, and use the correlation between the feature vectors of any two health parameters as the correlation between the two health parameters;

[0008] Step 2, eliminate the combinations in which any two health parameters have a correlation greater than a preset threshold from all combinations of N health parameters, and use the remaining combinations as candidate health parameter combinations;

[0009] Step 3, for each candidate health parameter combination, use the matrix formed by the feature vectors of the N health parameters in the candidate health parameter combination as the feature matrix of the candidate health parameter combination, and select the N health parameters in the candidate health parameter combination with the smallest condition number of the feature matrix as the N optimal health parameters.

[0010] Preferably, the Pearson correlation coefficient is used as the measure of the correlation.

[0011] Preferably, the preset degradation amount is 1% to 20%.

[0012] Based on the same inventive concept, the following technical solutions can also be obtained:

[0013] An aero-engine performance degradation estimation model is modeled using the modeling method according to any one of the above technical solutions.

[0014] Compared with the prior art, the technical solutions of the present application have the following beneficial effects:

[0015] The application is based on the characteristics of the influence of the health parameters of the aero-engine on the measured values, and first proposes a health parameter selection method based on correlation and condition number, the greater the correlation, the more obvious the coupling of the health parameters, and the greater the influence on the engine parameters, then the combination is screened through the condition number, and the best health parameter combination can be obtained through the above method, and the modeling performance degradation estimation model and the on-board model accuracy are effectively improved. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 is a sectional structure diagram of an aero-engine;

[0017] Figure 2 is a correlation coefficient diagram of the change of the measured parameters after degradation;

[0018] Figure 3 is a diagram of the influence of correlation on health parameter estimation;

[0019] Figure 4 is a condition number diagram of different combinations;

[0020] Figure 5 is a distribution diagram of the mean square deviation, mean value deviation and change amplitude of the measured parameters;

[0021] Figure 6 is a steady-state data screening effect diagram of the remaining measured parameters. DETAILED DESCRIPTION

[0022] In view of the deficiencies of the prior art, the solution idea of the application is based on the characteristics of the influence of the health parameters of the aero-engine on the measured values, and the optimal aero-engine health parameters are determined based on correlation and condition number as the core basis, the greater the correlation, the more obvious the coupling of the health parameters, and the greater the influence on the engine parameters, then the optimal health parameter combination is obtained by screening the combination through the condition number, and finally the optimal health parameter combination is used as the augmented control variable to construct an aero-engine performance degradation estimation model based on a Kalman filter.

[0023] The aero-engine performance degradation estimation model modeling method proposed in the application is as follows:

[0024] First, select N optimal health parameters, then use the selected optimal health parameters as the augmented state variables of the aero-engine state variable model, use a Kalman filter as a state observer to construct an aero-engine performance degradation estimation model, wherein N is the number of measurable controlled variables of the aero-engine, and the N optimal health parameters are selected by the following method:

[0025] Step 1, based on the engine component level model, obtain the variation of the same group of measurement parameters of the aero-engine generated by each health parameter under a preset degradation amount, and take the vector formed by the variation of the group of measurement parameters as the feature vector representing the health parameter, and take the correlation between the feature vectors of any two health parameters as the correlation of the two health parameters;

[0026] Step 2, eliminate the combinations in which any two health parameters have a correlation greater than a preset threshold from all combinations of N health parameters, and take the remaining combinations as candidate health parameter combinations;

[0027] Step 3, for each candidate health parameter combination, take the matrix formed by the feature vectors of the N health parameters in the candidate health parameter combination as the feature matrix of the candidate health parameter combination, and select the N health parameters in the candidate health parameter combination with the smallest condition number of the feature matrix as the N optimal health parameters.

[0028] In order to facilitate the public to understand, the technical solutions of the present application are described in detail below through an embodiment and in combination with the drawings:

[0029] The component level model used in this embodiment is for a certain type of turbofan engine, and the cross section of each component is as shown in Figure 1 The main air path components include: inlet, compressor, high pressure compressor, combustion chamber, high pressure turbine, low pressure turbine, mixing chamber and nozzle.

[0030] Suppose the component level model of the engine can be represented as:

[0031]

[0032] In the formula, the state variable x = [N1 N2] is the low pressure rotor speed and the high pressure rotor speed, the control variable u = [W fb A8] is the fuel flow and the minimum cross-sectional area of the throat, and the output variable y = [N1 N2 P3 P5] is the low and high pressure rotor speed, the compressor outlet total pressure, and the low pressure turbine outlet total pressure. The Taylor series is used to expand formula (1), and the high order components are ignored, to obtain the engine state variable model near the steady state point:

[0033]

[0034] However, the above linear state variable model only considers the rated working state, and the performance degradation of the aero-engine after long-term service is also considered. In order to more truly represent the state of the engine, a health parameter capable of representing performance degradation is added, and is represented as:

[0035]

[0036] where Δη is the 8 health parameters including fan efficiency and flow, compressor efficiency and flow, low pressure turbine efficiency and flow, high pressure turbine efficiency and flow degradation.

[0037] From equation (3), it can be seen that Δu and Δη have the same effect on state variables, and Δη is augmented to Δu as a control variable, which can be expressed as:

[0038]

[0039] The performance degradation of engine components is a relatively slow process, so it can be assumed that Since Δη cannot be directly obtained, it is augmented as a state variable based on equation (2), and further calculated by an estimation algorithm, which is augmented as follows:

[0040]

[0041] According to the augmented state variable model equation (5), the Kalman filter is used as a state observer, and the following full-dimensional observer equation can be obtained:

[0042]

[0043] However, the number of actual engine sensors is limited. Since the number of estimable health parameters cannot exceed the number of measurable parameters, i.e. the number of sensors, the number of health parameters that can be set is limited, and all 8 health parameters cannot be estimated for performance degradation. Only four of them can be selected according to the actual number of sensors.

[0044] The optional health parameters in this embodiment are eight: fan flow Fan efficiency (η fan ), compressor flow Compressor efficiency (η com ), high pressure turbine flow High pressure turbine efficiency (η ht ), low pressure turbine flow Low pressure turbine efficiency (η lt ). The optimal 4 health parameters need to be selected from the 8 optional health parameters to construct the performance degradation estimation model. The optimal health parameter selection method in this embodiment is as follows:

[0045] First, the preliminary screening of health parameters is based on correlation:

[0046] Based on the engine component level model, the change amount of the same group of measurement parameters of the aero-engine generated by each health parameter under a preset degradation amount is obtained, and a vector formed by the change amount of the group of measurement parameters is taken as a feature vector representing the health parameter, and the correlation between the feature vectors of any two health parameters is taken as the correlation of the two health parameters.

[0047] In the embodiment, in order to illustrate the relationship between the health parameter selection and the degradation estimation accuracy, the design point is selected as the research object, and the operating state is ground height H=0km, Ma=0, and low-pressure rotor speed N1=100%; and in order to facilitate illustration and comparison, four parameters [N1, N2, P5, P3] are selected as measurement parameters, that is, the measurement parameters are compressor outlet total pressure P3, low-pressure turbine outlet total pressure P5, and fan and compressor speeds N1 and N2. For each health parameter, based on the engine component level model, the change amount of the measurement parameters generated when the health parameter degrades by a certain amount can be obtained, and a vector formed by the change amount of the group of measurement parameters is taken as a feature vector representing the health parameter. In the embodiment, the feature vector of the health parameter is [ΔN1, ΔN2, ΔP5, ΔP3].

[0048] The correlation is measured by the similarity between the two feature vectors, wherein the similarity is also referred to as a similarity coefficient. The similarity can be measured by existing similarity measurement methods such as Euclidean distance, Manhattan distance, Hamming distance, and information entropy; wherein the time complexity of the Pearson correlation coefficient is proportional to the length of the signal, and has the advantage of fast operation speed, and can meet the requirement of solving speed, so the Pearson correlation coefficient is preferably used in the present application.

[0049] The Pearson correlation coefficient, that is, the calculation of the data of the constant distance variable, is represented as: the similarity (similarity coefficient) r between two vectors u and v uv is the cosine of the included angle of the two vectors, that is, the ratio of the inner product to the product of the lengths of the two vectors:

[0050]

[0051] In the formula, θ is the included angle between the vectors, and are the lengths (Euclid norm) of the vectors u and v, respectively, and u and v correspond to the performance parameter change matrix [ΔN1, ΔN2, ΔP5, ΔP3] under the degradation of different components.

[0052] The Pearson correlation coefficient is r uv ≤1, r uvgreater than zero indicates that the two are positively correlated, and less than zero indicates that they are negatively correlated. It reflects the degree of linear correlation between the two health parameters, and the closer the absolute value of the similarity is to 1, the more relevant the vectors u and v are. For two health parameters, the closer the absolute value of the correlation is to 1, the more relevant the two health parameters are. According to formula (7), the correlation calculated in turn is greater than 0.8, which belongs to extremely strong correlation, and the combination with an absolute value of the correlation greater than 0.9 needs special attention. In this embodiment, the degradation amount of the eight health parameters is set to 2% respectively, Figure 2 is the correlation coefficient between the characteristic vectors of each health parameter at the design point under the degradation amount.

[0053] It is calculated that the combinations with an absolute value greater than 0.9 are: R uv (η fan ,η lt ), R uv (η fan ,η ht ). It is shown that the fan flow degradation and the low-pressure turbine flow degradation have a very strong correlation, the fan efficiency degradation and the high-pressure turbine flow degradation, the low-pressure turbine efficiency degradation have a very strong correlation, the compressor efficiency degradation and the high-pressure turbine efficiency degradation have a very strong correlation, and the compressor flow degradation has a smaller correlation with the other several degradations.

[0054] In order to verify that two health parameters with high correlation do not need to be set at the same time, taking the combination of fan flow, compressor flow, high-pressure turbine efficiency and low-pressure turbine efficiency degradation as an example, the propelling system compressor efficiency is set to degrade η fan = 0.02 at t = 0s. It can be seen from Figure 3 that the estimated value of the high-pressure turbine efficiency is 0.015, and the rest of the fan flow, compressor flow and low-pressure turbine efficiency degradation are close to 0. This is mainly because, as shown in Figure 2 , the correlation between the high-pressure turbine efficiency degradation and the compressor efficiency degradation reaches 0.99, and the two health parameters have very similar effects on the changes of engine parameters. In the case of limited number of sensors, it is impossible to set all the health parameters at the same time. According to the correlation theory analysis, the stronger the correlation between the health parameters is, the more relevant the influence on the engine parameters is. For the on-board model used to analyze the margin, only the model accuracy is required, not the health parameter estimation accuracy, so only one of the health parameters with strong correlation needs to be set.

[0055] All combinations of 4 health parameters selected from all 8 health parameters are eliminated, and the combinations with an absolute value of the Pearson correlation coefficient greater than 0.9 are eliminated. The remaining combinations are used as the candidate health parameter combinations.

[0056] To further narrow down the selection range of health parameter combination, the final screening of condition number analysis is further conducted on the basis of the above correlation-based health parameter analysis. Specifically, for each candidate health parameter combination, the matrix composed of the eigenvectors of the 4 health parameters therein is taken as the characteristic matrix of the candidate health parameter combination, and the 4 health parameters in the candidate health parameter combination with the minimum condition number of the characteristic matrix are selected as the optimal health parameters.

[0057] Since the matrix condition number cond(A) = |A||A -1 | depicts the sensitivity of the solution of the equation set to the change of the original data, i.e., the degree of "ill-condition" of the equation set. The larger the condition number is, the more ill-conditioned the solution of the equation set is, resulting in the solution of Ax = b being more sensitive to the perturbation of the coefficient matrix. Meanwhile, the larger the condition number of the characteristic matrix is, the more relevant the vectors of each row of the matrix are, and the more similar the effects of the combination on the engine parameters are, which leads to the less accurate engine health parameter estimation.

[0058] By using the singular value matrix decomposition theorem, it is made that A ∈ R m×n , there exist positive unitary matrices U ∈ R m×m and V ∈ R n×n , and the expression of A is:

[0059] A = UΣV T (8)

[0060] In the formula,

[0061]

[0062] B = [ΔN1, ΔN2, ΔP5, ΔP3] (10)

[0063] wherein A is a 4 × 4 matrix formed by the parameters [B1, B2, B3, B4] under the degradation of different components, wherein Σ1 = diag(σ1, σ2,..., σ r ), the singular value is the diagonal element of the matrix, which is arranged in the order of formula (10):

[0064] σ1≥σ2≥...≥σ r > 0, r = rank(A) (11)

[0065] Then the condition number is finally defined according to the singular value as

[0066] cond(A) = σ1 / σ r (12)

[0067] The health parameter combinations meeting the correlation requirements are selected and combined to form a feature matrix. Each column of the matrix represents the change in the measured value under the degradation of a certain health parameter. Each column of data represents the change in the same measurement parameter under the degradation of different health parameters. Among the 70 combinations, the combinations with a correlation greater than 0.9 are removed, and 13 combinations are obtained after screening. The condition numbers corresponding to the 13 combinations are shown in Table 1. Figure 4 The number of the 13 combinations and the corresponding relationship with the health parameters are as follows: 1. fan flow, fan efficiency, compressor efficiency, compressor flow; 2. fan flow, fan efficiency, compressor flow, high-pressure turbine efficiency; 3. fan flow, compressor flow, compressor efficiency, high-pressure turbine flow; 4. fan flow, compressor flow, compressor efficiency, low-pressure turbine efficiency; 5. fan flow, compressor flow, high-pressure turbine efficiency, high-pressure turbine flow; 6. fan flow, compressor flow, high-pressure turbine efficiency, low-pressure turbine efficiency; 7. fan efficiency, compressor flow, compressor efficiency, low-pressure turbine flow; 8. fan efficiency, compressor flow, high-pressure turbine efficiency, low-pressure turbine flow; 9. fan efficiency, compressor efficiency, high-pressure turbine flow, low-pressure turbine flow; 10. compressor flow, compressor efficiency, high-pressure turbine flow, low-pressure turbine flow; 11. compressor flow, compressor efficiency, low-pressure turbine efficiency, low-pressure turbine flow; 12. compressor flow, high-pressure turbine efficiency, high-pressure turbine flow, low-pressure turbine flow; and 13. compressor flow, high-pressure turbine efficiency, low-pressure turbine efficiency, low-pressure turbine flow. The combinations are arranged in ascending order of matrix condition number, and the combination with the smallest condition number, i.e., combination 7 (fan flow, compressor flow, high-pressure turbine efficiency, low-pressure turbine efficiency), is selected to design an aero-engine performance degradation estimation model based on a Kalman filter.

[0068] The number of the 13 combinations and the corresponding relationship with the health parameters are as follows: 1. fan flow, fan efficiency, compressor efficiency, compressor flow; 2. fan flow, fan efficiency, compressor flow, high-pressure turbine efficiency; 3. fan flow, compressor flow, compressor efficiency, high-pressure turbine flow; 4. fan flow, compressor flow, compressor efficiency, low-pressure turbine efficiency; 5. fan flow, compressor flow, high-pressure turbine efficiency, high-pressure turbine flow; 6. fan flow, compressor flow, high-pressure turbine efficiency, low-pressure turbine efficiency; 7. fan efficiency, compressor flow, compressor efficiency, low-pressure turbine flow; 8. fan efficiency, compressor flow, high-pressure turbine efficiency, low-pressure turbine flow; 9. fan efficiency, compressor efficiency, high-pressure turbine flow, low-pressure turbine flow; 10. compressor flow, compressor efficiency, high-pressure turbine flow, low-pressure turbine flow; 11. compressor flow, compressor efficiency, low-pressure turbine efficiency, low-pressure turbine flow; 12. compressor flow, high-pressure turbine efficiency, high-pressure turbine flow, low-pressure turbine flow; and 13. compressor flow, high-pressure turbine efficiency, low-pressure turbine efficiency, low-pressure turbine flow. The combinations are arranged in ascending order of matrix condition number, and the combination with the smallest condition number, i.e., combination 7 (fan flow, compressor flow, high-pressure turbine efficiency, low-pressure turbine efficiency), is selected to design an aero-engine performance degradation estimation model based on a Kalman filter. Figure 5To design the Kalman filter of different parameter combinations for the performance degradation estimation of the aero-propulsion system components at a certain steady state point H = 0 km, Ma = 0, the baseline model based on the similarity conversion is selected, and the common degradation of 2% of the compression and turbine components of the propulsion system is set at t = 0 s. The accuracy of the steady state response is 1.07%, 1.13%, 2.91%, and 1.47% respectively. It can be seen that combination I has the highest dynamic and steady state response accuracy, and combination I also has the smallest condition number, which corresponds to the reliability of the condition number analysis. Figure 6 ​

Claims

1. An aero-engine performance degradation estimation model modeling method, preferably selecting N optimal health parameters; then taking the selected optimal health parameters as the augmented state variables of the aero-engine state variable model, using a Kalman filter as a state observer to construct an aero-engine performance degradation estimation model, wherein, N is the number of measurable controlled quantities of the aero-engine; characterized in that the N optimal health parameters are obtained by the following method: Step 1, based on the aero-engine component level model, obtaining the change amount of the same group of measurement parameters of the aero-engine generated by each health parameter under a preset degradation amount, and taking the vector composed of the change amount of the group of measurement parameters as the feature vector representing the health parameter, and taking the correlation between the feature vectors of any two health parameters as the correlation of the two health parameters; Step 2, eliminating the combinations in which there are any two health parameters with a correlation greater than a preset threshold from all combinations of N health parameters, and taking the remaining combinations as candidate health parameter combinations; Step 3, for each candidate health parameter combination, taking the matrix composed of the feature vectors of the N health parameters in the candidate health parameter combination as the feature matrix of the candidate health parameter combination, and selecting the N health parameters in the candidate health parameter combination with the minimum condition number of the feature matrix as the N optimal health parameters.

2. The method of modeling an aeroengine performance degradation estimation model of claim 1, wherein, The Pearson correlation coefficient is used as the measure of the correlation.

3. The method of claim 1, wherein: The preset degradation amount is 1% to 20%.

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