Aero-engine afterburner oscillation combustion real-time early warning method

Abstract

The invention discloses a real-time early warning method for oscillation combustion of an afterburner, and the method comprises the steps: employing a network structure in which Fourier series is simplified and then the Fourier series is introduced into a Kolmogorov-Arnold network (Kolmogorov-ArnoldNetworks, KAN), proposing a Cosine Kolmogorov-Arnold network (CosKAN), and in combination with an anomaly detection idea, proposing a new algorithm which is named as an anomaly detection Kolmogorov-Arnold network (AD-KAN). Specifically, the algorithm can learn feature distribution of all normal sample points in an unsupervised manner, map the feature distribution to a high-dimensional space, and autonomously learn an early warning boundary through a minimum surrounding ellipsoid to realize early warning of afterburner oscillation combustion. In order to verify the feasibility of the method, a test is carried out on a certain type of turbofan aero-engine ground test bench, and the result shows that the AD-KAN method has excellent performance in precision, real-time performance, early warning performance and robustness. Therefore, the method has good early warning performance, and real-time early warning of aero-engine afterburner oscillation combustion can be effectively achieved.

Description

Technical Field

[0001] The present invention relates to a deep neural network combining Fourier series and anomaly detection ideas and its application in oscillating combustion of afterburner chamber of an aircraft engine, and relates to the technical field of intelligent fault diagnosis. Background Art

[0002] As the core component of the aviation power system, aircraft engines work in extremely harsh environments such as high temperature, high pressure, and high speed for a long time. Its operating safety is crucial to its performance. Afterburners are widely used in military jet engines and turbofan engines. Afterburners can increase engine thrust in a short period of time, improve the take-off, climb and combat performance of military aircraft, increase flight maneuverability, and make supersonic cruise possible.

[0003] Turbofan engine component layout and afterburner location Figure 1 As shown. The airflow first enters the fan from the air inlet and is divided into two streams, one stream flows from the outer duct and the other flows from the core engine. After the main airflow is pressurized by the high-pressure compressor and the low-pressure compressor, it is ignited and burned in the combustion chamber. After combustion, the tail flow enters the high-pressure turbine and the low-pressure turbine. In the mixer, the inner and outer airflows are mixed to improve the inlet flow field of the afterburner combustion chamber, so that the airflow expansion and deceleration are conducive to organizing combustion and improving propulsion efficiency. When the turbofan engine starts the afterburner state, the mixed airflow is ignited in the afterburner combustion chamber, and the total thrust is increased by 70% compared with the original maximum state thrust. Finally, the exhaust gas flows out from the tail nozzle.

[0004] Oscillating combustion refers to the unstable combustion phenomenon caused by the periodic changes in combustion speed and thermal efficiency caused by the pulsation of the combustion exothermic reaction and the resonance of the acoustic characteristics of the combustion chamber. The reason for oscillating combustion is that after a disturbance wave of a certain frequency is added to the combustion system, the system cannot reduce its amplitude, but increases it rapidly, resulting in oscillating combustion. Since the afterburner is located after the turbine, its combustion conditions are poor. The afterburner has a low inlet total pressure, a high inlet air flow velocity, and a low oxygen content in the fuel gas, which greatly reduces the combustion efficiency and flame stability of the afterburner. Compared with the main combustion chamber, the afterburner is more prone to oscillating combustion.

[0005] like Figure 2As shown. Oscillating combustion can be mainly divided into detonation, low-frequency oscillation, medium-frequency oscillation and high-frequency oscillation. The frequency of detonation is less than 10Hz, which occurs when ignition is turned off or compressor surges, and is extremely destructive. The frequency of low-frequency oscillating combustion is 10-200Hz, and it mainly occurs during high-altitude and low-Mach number flight. The frequency of high-frequency oscillating combustion is 800-2000Hz, which mainly occurs during low-altitude and high-Mach number flight. The pulsation amplitude is 10%-20%, and generally does not cause flameout. Oscillation frequencies of 200-800Hz are called medium-frequency oscillating combustion. The pulsation amplitude of low-frequency and medium-frequency oscillating combustion exceeds 20%, which may cause changes in engine speed, thin-wall vibration and cracking, loosening and falling of connectors, and may even cause engine flameout.

[0006] Therefore, the present invention hopes to propose a neural network that can accurately analyze and predict the oscillating combustion in the afterburner, and then adjust the operating parameters to avoid oscillating combustion, so that the new generation of aircraft engines can achieve higher thrust-to-weight ratio and other better performance. Summary of the invention

[0007] Technical issues:

[0008] In order to improve the problems of serious skewness of afterburner signal data, too small sample size, inability to provide early warning, and high misdiagnosis rate in the existing aircraft engine afterburner oscillation combustion warning task, the present invention aims to propose a method that can accurately analyze and predict the afterburner oscillation combustion, which can achieve efficient and highly sensitive detection of the afterburner oscillation combustion and improve accuracy.

[0009] Technical solution:

[0010] The present invention introduces the network structure of KAN after simplifying the Fourier series, proposes the CosKAN network, and combines the idea of ​​abnormal detection to realize real-time afterburner combustion oscillation warning, and proposes a real-time warning method for afterburner combustion oscillation of an aircraft engine (AD-KAN). The AD-KAN method can learn the feature distribution of all normal sample points unsupervised, map them to high-dimensional space, and autonomously learn the warning boundary through the minimum enclosing ellipsoid to realize early warning of afterburner combustion oscillation.

[0011] First, the preliminary knowledge of the neural network KAN and CosKAN involved in the present invention is briefly introduced, and then the process of performing afterburner oscillation combustion warning using the AD-KNN method proposed in the present invention is specifically described.

[0012] 1) Neural Network KAN and CosKAN

[0013] The KAN (Kolmogorov-Arnold Networks) proposed in this invention is a new type of fully connected neural network. Its basic principle comes from the Kolmogorov-Arnold theorem. The structure diagram is as follows Figure 3 Vladimir Arnold and Andrey Kolmogorov determined that if f is a multivariate continuous function over a bounded domain, then f can be written as a finite combination of single-variable continuous functions and binary continuous functions. More specifically, for a smooth mapping f:

[0014]

[0015] Among them, φ q,p and Φ q is a univariate function mapping of the input variable. In the KAN network, φ q,p For input x∈[0,1] to the real number domain The univariate mapping, Φ q is the field of real numbers arrive 's mapping.

[0016] The structure of the KAN network is optimized by fitting y i =f(x i ) in f, complete the i To output y i According to the KA theorem, the above problem can be simplified to find the single variable function φ q,p and Φ q , to construct a multivariate continuous function f.

[0017] The KAN network consists of L layers, each containing multiple nodes and edges. Each node receives input signals from the previous layer and applies nonlinear transformations to these signals through learnable univariate functions on the edges. Usually, these univariate functions are parameterized as spline functions to ensure smoothness and stability during data processing. Given an input vector The output of KAN is

[0018]

[0019] Φ l Represents the function matrix of the lth layer, expressed as

[0020] Φ l ={φ l,q,p},l=0,1,2,…,L,p=1,2,…,n in ,q=1,2…,n out #(3)

[0021] The activation function φ q,p Contains learnable parameters and is located between nodes.

[0022] Define the activation function φ(x) as

[0023] φ(x)=w(b(x)+spline(x))#(4)

[0024]

[0025] Among them, c i is a learnable parameter.

[0026] Next, let's introduce CosKAN. Afterburner sensors are mostly dynamic pressure, temperature, and vibration signals with certain periodic characteristics. These signals can be regarded as a combination of multiple simple harmonic vibrations. A simple harmonic vibration is often characterized as a displacement x being a cosine function of time t:

[0027]

[0028] The essence of the activation function in the original KAN network is to fit the target mapping by superimposing multiple nonlinear functions B-spline. The B-spline function currently has problems such as high training complexity and poor fitting effect on periodic vibration functions. The present invention further improves the activation function in the original KAN network and introduces Fourier series to replace B-spline.

[0029]

[0030] Among them, d is the dimension of the feature, a ik and b ik is a trainable parameter, and g is the grid size, which controls the number of terms used in the Fourier series expansion. Specifically, g determines how many different sine and cosine terms are contained in the Fourier coefficients corresponding to each input dimension. The introduction of Fourier series can greatly improve the computational efficiency compared to the B-spline in the original KAN, and is more suitable for periodic signals such as combustion chamber sensor signals.

[0031] In the Fourier series calculation formula, for each fixed value of k, sin(kx i ) can be combined with cos(kx i ) are characterized by phase shift. Therefore, the phase shift is introduced To enhance the representation ability of the cosine function, the sine function term is deleted to further simplify the activation function. The activation function of CosKAN proposed in this invention is:

[0032]

[0033] Among them, d is the dimension of the feature; a ik and b ik is a trainable parameter, representing the coefficient weight; represents the grid phase shift; g is the grid size.

[0034] The target curve is fitted by the Cos activation function as follows Figure 4 The activation function is learned by performing a phase and frequency transformation via the weight matrix of the cosine function.

[0035] Based on the proposed CosKAN activation function, construct the function matrix Ψ of each layer of CosKAN l for

[0036] Ψ l ={ψ l,q,p},l=0,1,2,…,L,p=1,2,…,n in ,q=1,2…,n out #(10)

[0037] The output of CosKAN can be expressed as

[0038]

[0039] Thanks to the better fitting ability of Fourier function for periodic data, for the same modeling, CosKAN can be implemented with lower g, which further improves the performance and efficiency of KAN.

[0040] 2) AD-KNN

[0041] Aiming at the characteristics of afterburner oscillation combustion warning task, this paper proposes AD-KAN framework based on CosKAN, such as Figure 5 shown.

[0042] The output vector of CosKAN is used as the position vector of the sample point in the high-dimensional space. An ellipsoid is constructed in the high-dimensional space, represented as E R,c , where R is the radius and c is the center vector. The distance between the sample point and the center can be expressed as

[0043]

[0044] Take enough normal sample points to build a normal sample data set. The optimization goal is to train a high-dimensional space MEE containing all normal sample points. Train CosKAN to optimize the network weight parameters and the center c of the high-dimensional space ellipsoid. Minimize the distance from all normal sample points to the center of the ellipsoid. The optimization term and loss function of AD-KAN can be defined as

[0045]

[0046] Among them, λ is the neural network weight decay regularization parameter, which is used to control the regularization strength to avoid overfitting.

[0047] When the loss function converges or reaches the maximum number of training rounds, the training is completed. c The sample point with the largest value (x) is considered as the support vector x s In high-dimensional space, the support vector falls on the boundary of MEE. The anomaly detection critical value R is defined as

[0048] R=||(CosKAN(x s )-c) T ·(CosKAN(x s )-c) T || 2 #(14)

[0049] All normal samples satisfy

[0050] s(x)≤R#(15)

[0051] For a test sample point x t Anomaly detection can be determined based on the anomaly score of the test point. The criteria are as follows:

[0052] s(x t )=||CosKAN(x t -c) T ·CosKAN(x t -c)|| 2 #(16)

[0053]

[0054] Normal represents normal samples, and Abnormal represents abnormal samples.

[0055] The training process of AD-KAN is shown in Table 1.

[0056] In the AD-KAN method, the CosKAN network can map and fit the dynamic speed, air pressure, oil pressure and other signals in the afterburner well due to the introduction of the cosine activation function, and extract the correlation and important features between the signals. The construction of the high-dimensional space ellipsoid can more tightly surround all normal sample points, greatly improving the sensitivity of the model to abnormal samples, thereby achieving earlier warning of the oscillating combustion of the afterburner.

[0057] The AD-KAN-based afterburner oscillation combustion warning framework is constructed as shown in the figure. The trained AD-KAN is composed of CosKAN parameters ψ={ψ1,…,ψ l} and MEEER,c The original time series signal is first reconstructed into sample points in the time window in real time through a sliding time window, and then the one-dimensional dynamic signal of the sample points in the time window is converted into a frequency domain signal through fast Fourier transform. The sample points are input into CosKAN and mapped to MEEE R,c The position vector is formed in the high-dimensional space where the position vector is located. The distance between the position vector and the center of the sphere is calculated in MEE to obtain the anomaly score. The sample points are classified according to the anomaly score to determine the occurrence of oscillating combustion. Finally, the oscillating combustion classification of all sample points is continuously output to construct an oscillating combustion warning signal. At this point, the construction of AD-KAN is completed.

[0058] Based on the proposed AD-KAN network, the present invention constructs a real-time early warning method for oscillating combustion in the afterburner of an aircraft engine. And establishes a real-time oscillating combustion early warning model for the afterburner of an aircraft engine. The system is mainly divided into three modules: a training module, a test and comparison module, and a real-time execution module, including the following steps:

[0059] Step 1: Conduct an afterburner combustion oscillation experiment on a certain type of aircraft engine ground test bench and collect dynamic signals such as engine speed, air pressure and oil pressure through various types of sensors;

[0060] Step 2: Use FFT to transform the one-dimensional dynamic pressure signal into a frequency domain signal. Use the oscillation combustion warning threshold set by expert experience to determine whether oscillation combustion occurs in the data set to determine the label and divide it into training data set and test data set in proportion to complete data preprocessing.

[0061] Step 3: Initialize the parameters of AD-KAN;

[0062] Step 4: Use the preprocessed training data set to train the parameters of AD-KAN to obtain the parameters of the AD-KAN model.

[0063] Step 5: Compare the obtained AD-KAN model with several other methods in the test set and draw conclusions.

[0064] Beneficial effects: (1) AD-KAN can effectively reduce the impact of severe skewness of afterburner signal data and too small sample size;

[0065] (2) The AD-KAN model can provide early warning of afterburner combustion oscillations in real time through the afterburner sensor signals, and accurately give early warning signals;

[0066] (3) AD-KAN has good robustness. The results show that AD-KAN has excellent performance in terms of real-time, accuracy and robustness in the afterburner oscillation combustion early warning task;

[0067] (4) The AD-KAN method can be regarded as a general method for constructing early warning modeling of minor faults in key aircraft engine components and can be applied to similar problems in the aerospace field or other anomaly detection fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 This is a schematic diagram of the layout of a turbofan engine.

[0069] Figure 2 Schematic diagram of the oscillating combustion area within the flight envelope.

[0070] Figure 3 This is the network structure of KAN.

[0071] Figure 4 Schematic diagram of CosKAN activation function.

[0072] Figure 5 Real-time afterburner oscillation combustion warning framework for AD-KAN.

[0073] Figure 6 This is the signal diagram collected in Case 1.

[0074] Figure 7 This is the network structure of DeepSVDD.

[0075] Figure 8 Schematic diagram of the average AUC values ​​of 5 methods in 10 cases.

[0076] Fig. 9 This is the warning result diagram of AD-KAN in Case 1.

[0077] Fig.10 This is the warning result diagram of AD-KAN in Case 10.

[0078] Fig.11 The following are the early warning results of AD-KAN in other cases. (a), (b), (c), (d), (e), (f), (g), and (h) represent Case 2, Case 3, Case 4, Case 5, Case 6, Case 7, Case 8, and Case 9, respectively.

[0079] Fig.12 This is a diagram of the early warning time of the five methods.

[0080] Fig.13 is the curve of the advance warning time relative to λ.

[0081] Fig.14 is the curve of advance warning time relative to L.

[0082] Fig.15 is the curve of advance warning time relative to g. DETAILED DESCRIPTION

[0083] First, 10 groups of ground test experiments were carried out under different working conditions. In each group of experiments, the flight status was controlled by the operator until oscillating combustion occurred. Two oil pressure sensors were arranged at the inlet of the fuel supply device to measure the oil pressure. Two pressure sensors were respectively arranged at 15° and 165° deflected from the longitudinal axis behind the flame stabilizer to measure the air pressure. In addition, the experimental data also included the high-pressure compressor speed and the low-pressure compressor speed during the engine test. The sampling frequency of all sensors is 10000 Hz. For each case, 6 sensor signals were recorded, namely oil pressure 1, oil pressure 2 (OP), afterburner air pressure 1, afterburner air pressure 2 (ABP), high-pressure speed (NH), and low-pressure speed (NL). Figure 6 .

[0084] Before the present invention was proposed, the warning signal was given based on the frequency domain analysis of the two air pressure signals ABP1 and ABP2: the original dynamic pressure signal was subjected to real-time FFT transformation, and its main frequency and amplitude were recorded. The oscillation combustion warning threshold was set according to expert experience. When the amplitude of the air pressure signal exceeded the threshold for more than 3 seconds, it was determined that oscillation combustion occurred, and the operator performed the de-energizing operation. Until the end of this group of experiments, the boost was no longer started, that is, for each experiment, only one boost in and boost out operation was completed. The oscillation combustion judgment threshold analyzed by expert experience is shown in Table 2.

[0085] All sensor signals in 10 cases were recorded and stored as data sets. The boost time and de-boost time in each group of experiments were recorded, as shown in Table 3. The present invention uses the results of FFT frequency domain analysis as a label set to evaluate the accuracy of each comparison method. The de-boost time T obtained by FFT frequency domain analysis FTT Serves as a reference time for early warning of various comparison methods.

[0086] The collected signals are reconstructed using the sliding time window method to adapt to the discretized input form of the anomaly detection algorithm. The window width of the sliding time window is 1000 (0.1s) and the step size is 100 (0.01s). After reconstruction, each sample point is represented as a 1000×6 matrix. The reconstructed data set is Z-score normalized. The signals of each group of experiments are reconstructed into an afterburner oscillation combustion data set. The sample points three seconds before de-energization are marked as abnormal sample points, and the remaining sample points are marked as normal sample points (even if their frequency domain exceeds the threshold).

[0087] For each set of data, the initial 2s without afterburner, 3s after afterburner, and 1s after afterburner were used as training data sets, with a total of 600 sample points to construct a normal sample training set. The specific quantity distribution is shown in Table 4. Since the number of data points without afterburner in case 2 is less than 200, 40 sample points without afterburner, 460 sample points with afterburner, and 100 sample points after afterburner were used to construct the data set. The model learns the signal patterns of the normal operation of the afterburner combustion chamber under different states.

[0088] The present invention will compare with four commonly used anomaly detection machine learning algorithms to evaluate and verify the performance of the proposed AD-KAN. They are Isolation Forest (IF), support vector data description (SVDD), deep ellipsoid support vector data description (DeepESVDD) and KAN. The AUC value (AUC value is an important performance indicator in anomaly detection, which refers to the area under the receiver operating characteristic curve (ROC curve), which is used to compare the performance of different models under different threshold settings. Especially in the case of data imbalance, the AUC value is a more reliable performance metric than the accuracy rate.) and the advance warning time of each comparison method on the afterburner oscillation combustion data set are compared and evaluated to verify the performance of the proposed method.

[0089] The advance warning time is the most intuitive performance indicator of the model in the afterburner oscillation combustion warning task. The longer the advance warning time, the earlier the model can accurately warn of the occurrence of oscillation combustion, giving the operator more time to take preventive measures. The advance warning time is related to the model's anomaly detection performance, sensitivity to anomalies, and the execution speed of the model.

[0090] The best settings of hyperparameters for each compared method were optimized based on published papers and grid search.

[0091] Isolation forest is a tree-based unsupervised anomaly detection method. Anomaly detection is achieved by building a series of randomly constructed sub-detectors, isolating trees, and fusing them. The anomaly score is defined as the average of the lengths of all paths from the sample point. In this paper, the number of isolation trees (iTree) is set to 200.

[0092] SVDD is a kernel-based unsupervised anomaly detection method. In the present invention, a Gaussian kernel function is selected and the distance from the sample point to the hyperplane is defined as the anomaly score.

[0093] DeepESVDD is an unsupervised deep anomaly detection method. Its structure is shown in the figure Figure 7 The distance from the sample point to the hyperplane is defined as the anomaly score. The deep neural network selects MLP, and the network parameters are optimized by grid search method. The training rounds are 150 rounds, and the learning rate is 10 -4 The Adam optimizer was chosen to train the model.

[0094] DeepESVDD transforms the sample space into All normal sample points in are mapped Mapping to Mahalanobis space Constructing a MEEE in a high-dimensional space Q,μ So that it contains all normal sample points. All sample points are passed Projected into high-dimensional space , expressed as a vector. Contained in the ellipsoid E Q,μ The points inside are normal sample points, the points outside the ellipsoid are abnormal points, and the points on the ellipsoid surface are called support vectors.

[0095] In DeepESVDD, A multi-layer perceptron (MLP) W = {W 1 ,...,W L}, responsible for projecting sample points into high-dimensional space. In high-dimensional space, the distance between sample points is no longer applicable to Euclidean distance. Mahalanobis distance represents the covariance distance of data and is an effective method for calculating the similarity of two sample points in high-dimensional space. It can be regarded as a modification of Euclidean distance in high-dimensional space to consider the relationship between features.

[0096] The Mahalanobis distance from a sample point x to the center μ of the ellipsoid in high-dimensional space is defined as

[0097]

[0098] where Q is the covariance matrix of μ, which is a symmetric positive definite matrix whose eigenvectors define the axes of the ellipsoid and the corresponding eigenvalues ​​λ are the squares of the semi-axes.

[0099] The Mahalanobis distance can represent the difference between two variables that follow the same distribution. M (x) can be expressed as the degree to which the sample point x deviates from the normal sample cluster, thereby achieving anomaly detection. In the DeepESVDD method, the covariance matrix Q can be represented by the weight W of the multi-layer perceptron, defined as

[0100] Q=W T W#(19)

[0101] All normal sample points X={x1,…,x n The sum of the distances from the center point μ of MEE can be expressed as

[0102]

[0103] The optimization goal of DeepESVDD, which is to compress the high-dimensional space ellipsoid containing all normal sample points as much as possible, can be defined as

[0104]

[0105] Among all training samples, D Q,μ The sample point with the largest value is the support vector x s In high-dimensional space, the support vector falls on the boundary of MEE. The anomaly detection critical value R is defined as

[0106]

[0107] The anomaly score s(x) of DeepESVDD t ) is defined as

[0108]

[0109] where x t Represents the test sample point, which has the same size as the training sample point.

[0110] When s(x t )>R, the test sample point falls outside the boundary of MEE and is an outlier. t )≤R, the test sample point falls within the boundary of MEE and is a normal point. The anomaly detection idea of ​​DeepESVDD can be applied to the present invention.

[0111] For the proposed AD-KAN, the balance parameter λ∈{0,10 -4 ,10 -3 ,10 -2 ,10 -1 ,1}, the number of network layers L∈{1,2,4,8} and the grid size g∈{2,4,8,16} of CosKAN are grid searched by anomaly detection accuracy. The final hyperparameter is set to λ=10 -2 , L = 2, g = 16. The training round is 500 rounds. The learning rate is decayed with a fixed step size. The initial learning rate is set to 10 -3, the decay step size is 50, and the decay rate is 0.5. Adam optimizer is selected to train the model.

[0112] KAN is used as a single-classification network in this invention. KAN is trained to obtain a decision boundary around normal samples. The anomaly score is defined as the output loss value of the sample point in KAN. All hyperparameter settings of KAN are the same as those of AD-KAN.

[0113] All comparison methods use training data sets containing only normal sample points. For each comparison method, the training set of each group of data is sequentially trained, and the evaluation and verification are performed on another 9 groups of data. All experiments are repeated 5 times with different random seeds. The final experimental results are averaged.

[0114] All experiments were conducted on an NVIDIA RTX40608G graphics card. The programming language was Python and the deep learning framework was PyTorch2.0.

[0115] The average AUC values ​​of the five methods in different cases are shown in Table 5.

[0116] The AUC values ​​of the comparison methods are plotted on a radar chart, such as Figure 8 . AD-KAN achieved the highest AUC value on all data sets. This means that the proposed AD-KAN method has the best anomaly detection performance on the afterburner oscillation combustion data set. This is due to the CosKAN activation function constructed in AD-KAN, which can construct a mapping of the input signal through multiple Cos functions to better fit the dynamic pressure signal in the afterburner. At the same time, the introduction of high-dimensional space MEE also makes AD-KAN more sensitive to anomalies and improves the detection performance of anomalies.

[0117] The training time and execution time of each comparison method are tested to verify the real-time performance of the model. The average training time and average execution time of a single model of each comparison method are shown in Table 6.

[0118] Among the five comparison methods, IF and SVDD have faster training time and execution time because they do not involve deep neural networks. Among the three deep learning methods, DeepESVDD has the shortest training time because of the shortest training rounds. KAN and AD-KAN have 500 training rounds, so the training time is longer. It is worth noting that AD-KAN can have fewer learnable parameters compared to KAN's B-spline activation function due to the introduction of the CosKAN activation function. And AD-KAN's loss function is represented by the Mahalanobis distance in high-dimensional space, which also has faster computing speed and optimization gradient. Therefore, the training time per round of AD-KAN is much shorter than KAN, which verifies the advantage of AD-KAN in network lightweighting compared to the original KAN.

[0119] It is also worth noting that the execution time of AD-KAN is also shorter than that of DeepESVDD. This is because in the same task, the number of network layers of AD-KAN after grid search is much lower than that of MLP. Although CosKAN needs to calculate multiple activation functions for each layer of the network, while MLP only needs to calculate once, thanks to the advantages of GPU computing, multiple activation functions in one layer of CosKAN can be calculated in parallel, greatly saving the execution time of each layer of the network. Therefore, fewer network layers are more advantageous in improving the real-time performance of the model.

[0120] In the afterburner oscillation combustion warning task, the strategy of offline training and real-time execution is adopted. The execution time of the model directly affects the early warning performance and deserves more attention. Among the three deep learning methods, AD-KAN achieves the shortest average execution time, which shows that the real-time performance of AD-KAN is the most suitable for the afterburner oscillation combustion warning task among the deep learning methods.

[0121] The advance warning time is the most important performance indicator in the afterburner oscillation combustion warning task. The earlier the oscillation combustion warning is issued, the earlier the operator can be reminded to take corresponding measures to avoid the occurrence of oscillation combustion, thereby improving the safety and reliability of aircraft engines.

[0122] The models trained by the comparison methods are used to simulate the early warning of oscillating combustion. The reconstructed afterburner sensor signal is input to the model in real time, and the model outputs the abnormal score of each sample point in real time. In order to avoid misdiagnosis and improve the robustness of the warning, the warning signal will be given after 10 abnormal sample points are continuously identified. For each case, 10 experiments are performed and the average value is taken.

[0123] Record the warning time T of AD-KAN AD-KAN and the warning time T of the FFT method FTT For comparison, record the advance warning time as

[0124] T advance =T FTT -T AD-KAN #(twenty four)

[0125] Fig. 9 The early warning results of AD-KAN on case 1 are shown. The warning time of the FFT method is 19.050s, while AD-KAN gives a warning signal in 16.68s. Compared with the FFT method, AD-KAN has an early warning time of 2.37s.

[0126] Fig.10The early warning results of AD-KAN on case 10 are shown. The warning time of the FFT method is 22.599s, while AD-KAN gives a warning signal in 18.969s. Compared with the FFT method, AD-KAN has an early warning time of 3.63s.

[0127] Fig.11 The warning results on the remaining 8 cases are shown.

[0128] The warning time and advance warning time of the 10 cases are recorded in the table. As can be seen from Table 7, the proposed AD-KAN method can give early warning signals under different working conditions compared with the traditional time-frequency analysis method. The results show that the early warning performance of the AD-KAN method is better than the traditional FFT frequency domain analysis method and can be used as a substitute for the FFT method.

[0129] In order to compare the performance of the proposed AD-KAN method with other machine learning anomaly detection methods, the same experiment was performed on the other four comparison methods, and the advance warning time of each warning method was recorded. The comparison is shown in Table 8.

[0130] Plot the lead time on a radar chart, such as Fig.12 .

[0131] The IF and SVDD methods showed the worst performance in all cases. This is because the IF and SVDD methods did not introduce the structure of deep neural networks, had weak fitting capabilities for high-dimensional, large-scale data, and had low accuracy, resulting in insensitivity to the detection of abnormal samples. Although the SVDD method had the shortest execution time, its accuracy disadvantage made it inferior to other anomaly detection methods that introduced deep neural networks in terms of early warning performance.

[0132] Both IF and SVDD methods have the problem that the warning time is later than that of time-frequency analysis. The afterburner oscillation combustion warning task has extremely high requirements for the stability of the warning. If the model cannot achieve performance that exceeds that of time-frequency analysis in all cases, it is not suitable as an effective substitute for the FFT time-frequency analysis method.

[0133] DeepESVDD and KAN achieved positive advance warning times in all 10 cases, outperforming the time-frequency analysis method and can be considered as an effective alternative to the FFT method. However, in case 2, KAN only had an advance warning time of 0.142s, indicating that the advance warning performance of the KAN network will be greatly affected under certain specific engine conditions, reflecting the insufficient generalization ability of the model. In contrast, AD-KAN achieved an advance warning time of 0.691s in case 2, far exceeding the KAN and DeepESVDD models. This shows that AD-KAN has a stronger generalization ability for afterburner signals than DeepESVDD and KAN, and can show better stability and applicability in warning tasks.

[0134] Although DeepESVDD has a higher average warning time than KAN, it only exceeds KAN in 6 cases, indicating that DeepESVDD's performance does not surpass KAN in all aspects, and the two have their own advantages and disadvantages in warning capabilities.

[0135] The AD-KAN method achieved the longest advance warning time in all 10 cases, with an average advance warning time of 3.208s, far exceeding the other four comparison methods. The results show that the AD-KAN method achieves the best advance warning performance among all comparison methods and can be used as a new afterburner oscillation combustion warning method.

[0136] In this section, we study the impact of different hyperparameter settings on the early warning performance of the AD-KAN method. Taking Case 3, Case 5, and Case 10 as examples, we change the hyperparameters λ, L, and g respectively to observe the changes in their early warning time.

[0137] Fix L = 2, g = 16, and change the value of λ. The results are as follows Fig.13 As shown in the figure. The advance warning time first increases with the increase of λ. When it exceeds an optimal value, the advance warning time decreases significantly with the increase of λ. This is because during the training process, λ mainly controls the regularization degree of the network's loss function to suppress the overfitting of the model. The larger the λ, the greater the regularization of the model gradient optimization and the greater the sensitivity of the model to anomalies. However, when λ exceeds a certain value, the model will be underfit to a certain extent, resulting in a decrease in the accuracy of anomaly detection. In the AD-KAN model, for different λ values, the error of the advance warning time is within 3%, indicating that the value of λ has limited impact on the warning performance.

[0138] Fixed g = 16, λ = 10 -2 , change the value of L, the result is as follows Fig.14As shown in the figure, the advance warning time increases first and then decreases with the increase of L. This shows that in AD-KAN, the larger the number of network layers, the better. For the afterburner oscillation combustion dataset in this work, the sample points are time series with 6 channels. Too large a number of network layers will cause overfitting in the model training process and reduce the performance of the model. In addition, when L is too large, the training time and execution time of the model will increase greatly, which will also affect the advance warning time of the model.

[0139] Fixed L = 2, λ = 10 -2 , change the value of g, the result is as follows Fig.15 As shown. In the entire range of g∈{2,4,8,16, the advance warning time increases with the increase of g value. In AD-KAN, g is the number of grids of the CosKAN activation function. The larger g means that the model uses more univariate Cos functions to fit the CosKAN activation function of each layer. The results in the figure show that the hyperparameter g can improve the model's ability to fit the training data set. However, too large g will cause the training time and execution time of the model to increase exponentially, which is reflected in the early warning of afterburner oscillation combustion as an increase in the model execution time, which in turn affects the actual deployment of the model.

[0140] Different hyperparameter settings will affect the warning performance of the AD-KAN method. However, in general, parameter selection within a reasonable range has limited impact on the performance of the model, and the impact on the early warning time is less than 5%. The results show that the AD-KAN model has good robustness in the selection of hyperparameters.

[0141] In summary, the proposed AD-KAN outperforms all the comparison methods in both theoretical and practical oscillation combustion warning performance, and can be used as a new real-time afterburner oscillation combustion warning method. In addition, the work proposed in this paper can be regarded as a general workflow for early fault diagnosis in the aerospace field. In the future, it can be considered to be applied to other intelligent fault diagnosis tasks with severe sample skewness and small data volume problems.

[0142] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

[0143] Table 1 Training process of AD-KAN

[0144]

[0145] Table 2 Oscillation combustion warning threshold

[0146]

[0147] Table 3 De-energizing time by FFT frequency domain analysis

[0148]

[0149] Table 4 Distribution of the number of samples in each case

[0150]

[0151] Table 5 Average AUC values ​​of 5 methods in 10 cases

[0152]

[0153] Table 6 Time consumption of 5 methods

[0154]

[0155] Table 7 Results of early warning time

[0156] Case FFT(s) AD-KAN(s) Early warning time (s) 1 19.050 16.68 2.37 2 26.651 25.96 0.691 3 24.803 20.849 3.954 4 25.820 18.94 6.88 5 17.999 14.179 3.82 6 14.583 12.52 2.063 7 19.325 16.43 2.895 8 17.100 12.95 4.15 9 20.267 18.64 1.627 10 22.599 18.969 3.63 average \ \ 3.208

[0157] Table 8 Early warning time of different methods

[0158]

Claims

1. A real-time early warning method for oscillating combustion in afterburner of an aircraft engine, characterized in that: The steps include: Step 1: Conduct an afterburner combustion oscillation experiment to complete the dynamic signal collection of the speed, air pressure and oil pressure in the afterburner; Step 2: Convert the dynamic signal into a frequency domain signal, and determine whether oscillation combustion occurs in the data set composed of the frequency domain signal according to the set oscillation combustion warning threshold to determine the label and divide the training data set and the test data set in proportion. The training data set contains normal samples, and the test data set contains normal samples and abnormal samples; Step 3: Initialize the parameters of the KAN network and complete the training of the KAN network based on the data set. The activation function of the KAN network is: Among them, d is the dimension of the feature; a ik and b ik is a trainable parameter, representing the coefficient weight; represents the grid phase shift; g is the grid size; Step 4: Use the real-time acquisition signal to execute the KAN network. When the afterburner is about to experience oscillating combustion, the KAN network outputs a warning signal.

2. The real-time early warning method for afterburner combustion oscillation of an aircraft engine according to claim 1, characterized in that: The function matrix ψ of each layer of the KAN network l for P l ={ψ l,q,p },l=0,1,2,…,L,p=1,2,…,n in ,q=1,2…,n out Where L is the number of layers in the KAN network, n in is the input feature dimension of the KAN network, n out is the output feature dimension of the KAN network; The output of the KAN network is expressed as 3. The real-time early warning method for oscillating combustion in afterburner of an aircraft engine according to claim 2, characterized in that: The optimization goal of the KAN network is to train a high-dimensional space MEE containing all normal sample points. Its optimization term and loss function are defined as Among them, λ is the KAN network weight decay regularization parameter, c is the center vector of the ellipsoid in high-dimensional space, and n is the number of samples.

4. The real-time early warning method for afterburner combustion oscillation of an aircraft engine according to claim 3, characterized in that: The steps for training the KAN network in step 3 include: The distance D between the training data set and the center of the sphere c The sample point with the largest value (x) is considered as the support vector x s ; In the high-dimensional space MEE, the support vector falls on the boundary of MEE, and the anomaly detection critical value R is defined as R = || (CosKAN (x s )-c) T ·(CosKAN(x s )-c) T || 2 For the test sample point x in the test data set t Anomaly detection, according to the anomaly score s(x t ) is judged according to the following criteria: s(x t )=||CosKAN( x t-c) T ·CosKAN( x t-c)|| 2 5. The real-time early warning method for afterburner combustion oscillation of an aircraft engine according to claim 1, characterized in that: In step 2, the oscillation combustion warning threshold is set based on expert experience.

6. The real-time early warning method for afterburner combustion oscillation of an aircraft engine according to claim 1, characterized in that: When conducting the afterburner oscillation combustion experiment, when the amplitude of the air pressure signal exceeds the threshold for more than 3 seconds, it is determined that oscillation combustion occurs and the afterburner deactivation operation is performed; the sample points three seconds before deactivation are marked as abnormal sample points, and the remaining sample points are marked as normal sample points; the data sets of 2 seconds when the afterburner is not turned on, 3 seconds after the afterburner is turned on, and 1 second after the afterburner is deactivated are taken to construct a normal sample training set.

7. The real-time early warning method for afterburner combustion oscillation of an aircraft engine according to claim 1, characterized in that: The afterburner oscillation combustion experiment is carried out on the aircraft engine ground test bench.

Images