A real-time early warning method for oscillating combustion of a turbofan afterburner

Abstract

The application discloses a real-time early warning method for oscillation combustion of a afterburner. The method adopts a network structure of Kolmogorov-Arnold Networks (KAN) by introducing a simplified Fourier series, proposes Cosine Kolmogorov-Arnold Networks (CosKAN), and combines an anomaly detection idea to propose a new algorithm named Anomaly Detection Kolmogorov-Arnold Networks (AD-KAN). Specifically, the algorithm can learn the feature distribution of all normal sample points unsupervisedly, is mapped into a high-dimensional space, and learns a warning boundary autonomously through a minimum enclosing ellipsoid to realize early warning of oscillation combustion of the afterburner. In order to verify the feasibility of the method, an experiment is conducted on a ground test bench of a certain type of turbofan aero-engine, and the result shows that the AD-KAN method has superior performance in accuracy, real-time performance, early warning performance and robustness. Therefore, the method has good early warning performance and can effectively realize real-time early warning of oscillation combustion of the afterburner of the aero-engine.

Description

Technical Field

[0001] This invention relates to a deep neural network that combines Fourier series and anomaly detection concepts and its application in oscillating combustion in afterburners of aero-engines, and relates to the field of intelligent fault diagnosis technology. Background Technology

[0002] As the core component of an aircraft propulsion system, the aircraft engine operates for extended periods in extreme and harsh environments, including high temperature, high pressure, and high speed. Its operational safety is crucial to its performance. Afterburners are widely used in military jet and turbofan engines. Afterburners can rapidly increase engine thrust, improving the takeoff, climb, and combat performance of military aircraft, enhancing flight maneuverability, and even enabling supersonic cruise.

[0003] The layout of turbofan engine components and the location of the afterburner are as follows: Figure 1 As shown, the airflow first enters the fan through the inlet and is split into two streams: one flows through the bypass duct, and the other flows through the core engine. The main airflow is pressurized by the high-pressure and low-pressure compressors before ignition and combustion in the combustion chamber. The exhaust gas then enters the high-pressure and low-pressure turbines. In the mixer, the two airflows are mixed to improve the inlet flow field of the afterburner, allowing the airflow to diffuse and slow down, which is beneficial for combustion and increases propulsion efficiency. When the turbofan engine engages afterburner, the mixed airflow ignites in the afterburner, increasing the total thrust by 70% compared to the maximum thrust. Finally, the exhaust gas exits from the exhaust nozzle.

[0004] Oscillatory combustion refers to an unstable combustion phenomenon caused by the resonance between the periodic changes in combustion rate and thermal efficiency resulting from the pulsation of the exothermic combustion reaction and the acoustic characteristics of the combustion chamber. Oscillatory combustion occurs because when a disturbance wave of a certain frequency is applied to the combustion system, the system cannot reduce its amplitude but instead rapidly increases it, leading to oscillatory combustion. Because the afterburner is located after the turbine, its combustion conditions are extremely harsh. The afterburner has a low inlet total pressure, high inlet airflow velocity, and low oxygen content in the combustion gas, all of which significantly reduce its combustion efficiency and flame stability. Compared to the main combustion chamber, the afterburner is more prone to oscillatory combustion.

[0005] like Figure 2As shown. Oscillating combustion can be mainly divided into detonation, low-frequency oscillation, medium-frequency oscillation, and high-frequency oscillation. Detonation occurs at frequencies less than 10 Hz and is extremely destructive during ignition failure or compressor surge. Low-frequency oscillating combustion occurs at frequencies of 10-200 Hz and mainly occurs during high-altitude, low-Mach-number flight. High-frequency oscillating combustion occurs at frequencies of 800-2000 Hz and mainly occurs during low-altitude, high-Mach-number flight, with a pulsation amplitude of 10%-20%, and generally does not cause engine failure. Oscillating combustion with frequencies between 200-800 Hz is 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-walled vibration and cracking, loosening and detachment of connecting parts, and may even cause engine failure.

[0006] Therefore, this invention aims to propose a neural network that can accurately analyze and predict oscillating combustion in afterburners, thereby adjusting operating parameters to avoid oscillating combustion and enabling next-generation aero engines to achieve higher thrust-to-weight ratios and other better performance. Summary of the Invention

[0007] Technical issues:

[0008] To address the problems of severe skewness in afterburner signal data, insufficient sample size, inability to provide early warning, and high false diagnosis rate in existing afterburner oscillation combustion early warning missions for aero-engines, this invention aims to propose a method for accurately analyzing and predicting afterburner oscillation combustion. This method can achieve efficient and highly sensitive detection of afterburner oscillation combustion and improve accuracy.

[0009] Technical solution:

[0010] This invention simplifies Fourier series and introduces it into the KAN network structure, proposing the CosKAN network. Combined with anomaly detection, it achieves real-time afterburner oscillation combustion early warning and proposes a real-time early warning method for afterburner oscillation combustion in aero-engines (AD-KAN). The AD-KAN method can unsupervisedly learn the feature distribution of all normal sample points, mapping it to a high-dimensional space. It then autonomously learns the early warning boundary through a minimum bounding ellipsoid, achieving early warning of afterburner oscillation combustion.

[0011] First, a brief introduction to the preliminary knowledge of neural networks such as KAN and CosKAN involved in this invention will be given, and then the process of using the AD-KNN method proposed in this invention for early warning of oscillating combustion in afterburners will be described in detail.

[0012] 1) Neural networks KAN and CosKAN

[0013] The KAN (Kolmogorov-Arnold Networks) proposed in this invention is a novel type of fully connected neural network. Its basic principle is derived from the Kolmogorov-Arnold theorem, and its structure diagram is shown below. Figure 3 As shown. Vladimir Arnold and Andrey Kolmogorov determined that if f is a multivariate continuous function on a bounded domain, then f can be written as a finite combination of addition operations of univariate continuous functions and bivariate continuous functions. More specifically, for a smooth mapping f:

[0014]

[0015] Where, φ q,p and Φ q It is a univariate function mapping of the input variables. In the KAN network, φ q,p For input x∈[0,1] to the real number field univariate mapping, Φ q It is the field of real numbers arrive The mapping.

[0016] The structure of the KAN network optimizes the fit of y. i =f(x) i f in ) completes the process from input x i To output y i Supervised learning mapping. According to the KA theorem, the above problem can be simplified to finding a single-variable function φ. q,p and Φ q To construct a multivariate continuous function f.

[0017] A KAN network consists of L layers, each containing multiple nodes and edges. Each node receives the input signal from the previous layer and applies a nonlinear transformation to these signals using learnable univariate functions on the edges. Typically, 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 The function matrix of the l-th layer is represented as follows:

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

[0021] Where the activation function φ q,p It contains learnable parameters, 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 These are learnable parameters.

[0026] Next, we introduce CosKAN. Most afterburner sensors transmit dynamic pressure, temperature, and vibration signals, exhibiting certain periodic characteristics. These signals can all be considered as combinations of various simple harmonic vibrations. A simple harmonic vibration is often characterized as displacement x being a cosine function of time t:

[0027]

[0028] The activation function in the original KAN network essentially fits the target mapping by superimposing multiple nonlinear functions, B-splines. However, B-spline functions currently suffer from high training complexity and poor fitting performance for periodic oscillation functions. This invention further improves the activation function in the original KAN network by introducing a Fourier series to replace the B-spline.

[0029]

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

[0031] In the formula for calculating Fourier series, for each fixed value of k, sin(kx) i Both can be cos(kx) i They are characterized by phase shifts. Therefore, a phase shift is introduced. To enhance the representational power of the cosine function, the sine function term is removed, further simplifying the activation function. This invention proposes the following activation function for CosKAN:

[0032]

[0033] Where d is the dimension of the feature; a ik and b ik These are trainable parameters, representing coefficient weights; This represents the mesh phase shift; g is the mesh size.

[0034] The target curve is fitted by the Cos activation function as follows: Figure 4 As shown, the activation function is learned through phase and frequency transformations performed on 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 represented as...

[0038]

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

[0040] 2) AD-KNN

[0041] This invention addresses the characteristics of afterburner oscillating combustion early warning tasks by proposing the AD-KAN framework based on CosKAN, such as... Figure 5 As shown.

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

[0043]

[0044] Construct a normal sample dataset by collecting sufficient normal sample points. The optimization objective is to train a high-dimensional MEE containing all normal sample points. Train CosKAN, optimizing the network weight parameters and the center c of the high-dimensional ellipsoid. Minimize the distance from all normal sample points to the center of the ellipsoid. The optimization terms and loss function of AD-KAN can be defined as follows:

[0045]

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

[0047] Training is complete when the loss function converges or the maximum number of training epochs is reached. In the normal sample dataset, D... c The sample point with the largest (x) value is considered the support vector x. s In high-dimensional space, support vectors lie on the boundaries of the MEE. The anomaly detection threshold 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 based on the anomaly score at each 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 a normal sample, and "Abnormal" represents an abnormal sample.

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

[0056] In the AD-KAN method, the CosKAN network, due to the introduction of the cosine activation function, can effectively map and fit dynamic signals such as rotational speed, air pressure, and oil pressure in the afterburner, extracting the correlation and important features between the signals. The construction of a high-dimensional ellipsoid can more tightly enclose all normal sample points, greatly improving the model's sensitivity to abnormal samples, thereby enabling earlier warning of oscillating combustion in the afterburner.

[0057] An afterburner oscillating combustion early warning framework based on AD-KAN is constructed, as shown in the figure. The trained AD-KAN consists of parameters ψ={ψ1,…,ψ} from CosKAN. l} and MEEER,c Characterization. The original time-series signal is first reconstructed in real time into sample points within a sliding time window. Then, a Fast Fourier Transform (FFT) is used to transform the one-dimensional dynamic signal of the sample points within the time window into a frequency domain signal. The sample points are input into CosKAN and mapped to MEEE. R,c In the high-dimensional space, a position vector is formed. This position vector is used in MEE to calculate the distance to the sphere's center, yielding an anomaly score. Based on this score, sample points are classified to determine the occurrence of oscillating combustion. Finally, the oscillating combustion classifications for all sample points are continuously output, constructing an oscillating combustion early warning signal. This completes the construction of AD-KAN.

[0058] This invention, based on the proposed AD-KAN network, constructs a real-time early warning method for oscillating combustion in the afterburner of an aero-engine. A real-time oscillating combustion early warning model for the afterburner of an aero-engine is also established. The system mainly consists of three modules: a training module, a testing and comparison module, and a real-time execution module, including the following steps:

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

[0060] Step 2: Use FFT (Fast Fourier Transform) to convert the one-dimensional dynamic pressure signal into a frequency domain signal. Determine whether oscillating combustion occurs in the dataset based on the oscillation combustion warning threshold set by expert experience, determine the label, and divide the dataset into training and test datasets according to the ratio to complete the data preprocessing.

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

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

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

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

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

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

[0067] (4) The AD-KAN method can be regarded as a general method for constructing early warning modeling of minor faults in key components of aero-engines, and can be applied to similar problems in the aerospace field or other anomaly detection fields. Attached Figure Description

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

[0069] Figure 2 This is a schematic diagram of the oscillating combustion zone within the flight envelope.

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

[0071] Figure 4 This is a schematic diagram of the CosKAN activation function.

[0072] Figure 5 A frame for AD-KAN real-time afterburner oscillation combustion warning.

[0073] Figure 6 This is a signal graph collected in Case 1.

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

[0075] Figure 8 This is a diagram showing the average AUC values ​​of the five methods across 10 cases.

[0076] Figure 9 This is a graph showing the early warning results for AD-KAN in Case 1.

[0077] Figure 10 This is a graph showing the early warning results for AD-KAN in Case 10.

[0078] Figure 11 The following diagram shows 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] Figure 12 The image shows the early warning timeline for the five methods.

[0080] Figure 13 The curve representing the advance warning time relative to λ.

[0081] Figure 14 The curve representing the early warning time relative to L.

[0082] Figure 15 The curve representing the early warning time relative to g. Detailed Implementation

[0083] First, ten ground test runs were conducted under different operating conditions. In each run, the operator controlled the flight until oscillating combustion occurred. Two oil pressure sensors were positioned at the fuel supply inlet to measure oil pressure. Two pressure sensors were positioned 15° and 165° off the longitudinal axis behind the flame stabilizer to measure air pressure. Additionally, experimental data included the high-pressure and low-pressure compressor speeds during engine testing. All sensors were sampled at a frequency of 10000Hz. For each case, six sensor signals were recorded: 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] Prior to this invention, the warning signal was based on frequency domain analysis of two pressure signals, ABP1 and ABP2: real-time FFT transformation was performed on the original dynamic pressure signals, and their dominant frequency and amplitude were recorded. An oscillating combustion warning threshold was set based on expert experience. When the pressure signal amplitude exceeded the threshold for more than 3 seconds, oscillating combustion was determined to have occurred, and the operator would perform a de-energization operation. No further energization was initiated until the end of the experiment; that is, for each experiment, only one energization and de-energization operation was performed. The oscillating combustion judgment threshold determined by expert experience is shown in Table 2.

[0085] All sensor signals from the 10 cases were recorded and stored as a dataset. The moments of force application and retraction in each experimental group were recorded, as shown in Table 3. This invention uses the results of FFT frequency domain analysis as a tag set to evaluate the accuracy of each comparative method. The retraction moment T obtained from FFT frequency domain analysis... FTT This serves as a reference point for early warning by various comparative methods.

[0086] A sliding time window method was used to reconstruct the acquired signals to adapt to the discretized input format of the anomaly detection algorithm. The sliding time window width was 1000 (0.1s), and the step size was 100 (0.01s). After reconstruction, each sample point was represented as a 1000×6 matrix. The reconstructed dataset was then Z-score normalized. The signals from each experimental group were reconstructed into an afterburner oscillating combustion dataset. Sample points in the first three seconds before de-energization were marked as anomalous sample points, while all other sample points were marked as normal sample points (even if their frequency domain exceeded the threshold).

[0087] For each data set, the initial 2 seconds before afterburner activation, the 3 seconds afterburner activation, and the 1 second afterburner deactivation were used as the training dataset, totaling 600 sample points, to construct the normal sample training set. The specific distribution of these sample points is shown in Table 4. Since there were fewer than 200 data points for case 2 without afterburner activation, 40 sample points without afterburner activation, 460 sample points with afterburner activation, and 100 sample points after afterburner deactivation were used to construct the dataset. The model learns the signal patterns of normal operation of the afterburner combustion chamber under different states.

[0088] This invention compares the proposed AD-KAN with four commonly used anomaly detection machine learning algorithms to evaluate and validate its performance. These algorithms are Isolation Forest (IF), Support Vector Data Description (SVDD), Deep Ellipsoid Support Vector Data Description (DeepESVDD), and KAN. The AUC value (AUC is an important performance metric in anomaly detection, referring to the area under the Receiver Operating Characteristic curve (ROC curve), used to compare the performance of different models under different threshold settings. Especially in cases of imbalanced data, AUC is a more reliable performance measure than accuracy) and early warning time are compared and evaluated on an afterburner oscillating combustion dataset to validate the performance of the proposed method.

[0089] The advance warning time is the most direct performance indicator of the model in the task of early warning of oscillating combustion in afterburners. The longer the advance warning time, the earlier and more accurately the model can predict the occurrence of oscillating combustion, giving the operator more time to implement preventive measures. The advance warning time is related to the model's anomaly detection performance, its sensitivity to anomalies, and its execution speed.

[0090] The optimal settings of hyperparameters for each comparative method are optimized based on published papers and grid search.

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

[0092] SVDD is a kernel-based unsupervised anomaly detection method. In this 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, and its structure diagram is as follows: Figure 7 The anomaly score is defined as the distance from a sample point to the hyperplane. An MLP (Multi-Level Processing) deep neural network is used, and the network parameters are optimized using a grid search algorithm. The training run consists of 150 epochs with a learning rate of 10^5. -4 The Adam optimizer was chosen to train the model.

[0094] DeepESVDD uses the sample space All normal sample points are mapped Mapping to Markovian space In the middle. Construct a MEEE in a high-dimensional space. Q,μ This ensures that it includes all normal sample points. All sample points are passed through... Projected into higher dimensions In this context, it is represented in vector form. It is contained within the ellipsoid E. Q,μ Points inside the ellipsoid are normal sample points, points outside the ellipsoid are outliers, and points on the ellipsoid are called support vectors.

[0095] In DeepESVDD From a multilayer perceptron (MLP) W = {W 1 ,...,W L The system consists of several parts, responsible for projecting sample points into a high-dimensional space. In high-dimensional space, Euclidean distance is no longer applicable to the distance between sample points. Mahalanobis distance, representing the covariance distance of the data, is an efficient method for calculating the similarity between two sample points in high-dimensional space. It can be seen as a modification of Euclidean distance that considers the relationship between characteristics in high-dimensional space.

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

[0097]

[0098] Here, 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-axis.

[0099] Mahalanobis distance can represent the degree of difference between two variables that follow the same distribution. Therefore, D M (x) can be represented as the degree to which sample point x deviates from the normal sample cluster, thus achieving anomaly detection. In the DeepESVDD method, the covariance matrix Q can be characterized by the weights W of the multilayer perceptron, defined as follows:

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

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

[0102]

[0103] The optimization objective of DeepESVDD, namely, to compress a high-dimensional ellipsoid containing all normal sample points as much as possible, can be defined as follows:

[0104]

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

[0106]

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

[0108]

[0109] Where x t This represents a test sample point, which has the same size as the training sample points.

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

[0111] For the proposed AD-KAN, for the equilibrium parameter λ∈{0,10} -4 10 -3 10 -2 10 -1 The three hyperparameters, namely the number of network layers L∈{1,2,4,8} and the grid size g∈{2,4,8,16} of CosKAN, were used for grid search based on anomaly detection accuracy. The final hyperparameter was set to λ=10. -2 L=2, g=16. The training epochs are 500. A fixed-step decaying learning rate is used. The initial learning rate is set to 10. -3The decay step size is 50, and the decay rate is 0.5. The Adam optimizer was selected to train the model.

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

[0113] All comparison methods used training datasets containing only normal sample points. For each comparison method, training was performed sequentially on the training set of each group of data, and evaluation and validation were conducted on an additional 9 groups of data. All experiments were repeated 5 times with different random seeds. The final experimental results were averaged.

[0114] All experiments were conducted on an NVIDIA RTX 4060 8G graphics card. The programming language was Python, and the deep learning framework was PyTorch 2.0.

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

[0116] Plot the AUC values ​​of each comparison method on a radar chart, such as... Figure 8 AD-KAN achieved the highest AUC value across all datasets. This indicates that the proposed AD-KAN method has the best anomaly detection performance on the afterburner oscillating combustion dataset. This is attributed to the CosKAN activation function constructed in AD-KAN, which can better fit the dynamic pressure signal in the afterburner by constructing a mapping of the input signal through multiple Cos functions. Simultaneously, the introduction of the high-dimensional MEE space also makes AD-KAN more sensitive to anomalies, improving its anomaly detection performance.

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

[0118] Among the five comparison methods, IF and SVDD have faster training and execution times because they do not involve deep neural networks. Among the three deep learning methods, DeepESVDD has the shortest training time due to the fewest training epochs. KAN and AD-KAN both have 500 training epochs, resulting in longer training times. It is worth noting that AD-KAN, due to the introduction of the CosKAN activation function, has fewer learnable parameters compared to KAN's B-spline activation function. Furthermore, AD-KAN's loss function, represented by Mahalanobis distance in a high-dimensional space, also offers faster computation and gradient optimization. Therefore, the training time per epoch of AD-KAN is significantly shorter than that of KAN, validating AD-KAN's advantage over the original KAN in terms of network lightweighting.

[0119] It's also worth noting that AD-KAN's execution time is shorter than DeepESVDD. This is because, for the same task, AD-KAN has far fewer network layers after grid search than MLP. Although CosKAN needs to compute multiple activation functions for each layer, while MLP only needs to compute them once, the advantages of GPU computing allow multiple activation functions in a single layer of CosKAN to be computed in parallel, significantly saving execution time per layer. Therefore, fewer network layers are more advantageous in improving model real-time performance.

[0120] In the afterburner oscillating combustion early warning task, an offline training and real-time execution strategy was adopted. The model's execution time directly affects the early warning performance and deserves more attention. Among the three deep learning methods, AD-KAN achieved the shortest average execution time, indicating that AD-KAN's real-time performance is the most suitable among deep learning methods for the afterburner oscillating combustion early warning task.

[0121] Early warning time is the most important performance indicator in the afterburner oscillation combustion early warning mission. The earlier the early warning of oscillation combustion is issued, the sooner operators can be reminded to take appropriate measures to avoid oscillation combustion, thereby improving the safety and reliability of aero engines.

[0122] The models trained using various comparison methods were used to simulate early warning of oscillating combustion. Reconstructed afterburner sensor signals were input into the model in real time, and the model output anomaly scores for each sample point in real time. To avoid false diagnosis and improve the robustness of the warning, the warning signal was given after identifying 10 consecutive abnormal sample points. For each case, 10 experiments were performed, and the average value was taken.

[0123] Record the warning time T of AD-KAN AD-KAN And the warning time T of the FFT method FTT Compare and record the early warning time as follows:

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

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

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

[0127] Figure 11 The warning results for the remaining 8 cases are shown.

[0128] The warning times and early warning times for 10 cases are recorded in the table. As shown in Table 7, the proposed AD-KAN method can provide earlier warning signals under different operating conditions compared to traditional time-frequency analysis methods. The results indicate that the early warning performance of the AD-KAN method is superior to the traditional FFT frequency domain analysis method and can be used as a replacement for the FFT method.

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

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

[0131] The IF and SVDD methods exhibited the worst performance across all cases. This is because the IF and SVDD methods do not incorporate a deep neural network structure, resulting in weak fitting ability and low accuracy for high-dimensional, large-scale data, making them insensitive to anomaly detection. Although the SVDD method has the shortest execution time, its inferior accuracy makes it less effective in early warning compared to other anomaly detection methods that incorporate deep neural networks.

[0132] Both the IF and SVDD methods exhibit instances where the warning time is later than that of time-frequency analysis. The afterburner oscillating combustion warning task places extremely high demands on the stability of the warning. If the model cannot achieve performance exceeding that of time-frequency analysis in all cases, it is not suitable as an effective alternative to the FFT time-frequency analysis method.

[0133] DeepESVDD and KAN both achieved positive early warning times in all 10 cases, outperforming time-frequency analysis methods and suggesting they could be considered effective alternatives to FFT. However, in case 2, KAN only achieved an early warning time of 0.142s, indicating that the early warning performance of the KAN network is significantly affected under certain engine operating conditions, reflecting insufficient generalization ability of the model. In contrast, AD-KAN achieved an early warning time of 0.691s in case 2, far exceeding that of KAN and DeepESVDD models. This demonstrates that AD-KAN has a stronger generalization ability for afterburner signals compared to DeepESVDD and KAN, exhibiting better stability and applicability in early warning tasks.

[0134] Although DeepESVDD has a higher average warning time than KAN, DeepESVDD only surpasses KAN in 6 cases, indicating that DeepESVDD's performance is not superior to KAN in all aspects, and the two have their own advantages and disadvantages in terms of warning capabilities.

[0135] The AD-KAN method achieved the longest early warning time in all 10 cases, with an average early warning time of 3.208 seconds, far exceeding the other four comparative methods. The results indicate that the AD-KAN method achieves the best early warning performance among all comparative methods and can be considered a novel early warning method for oscillating combustion in afterburners.

[0136] This section investigates 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, the hyperparameters λ, L, and g are changed respectively, and the changes in their early warning time are observed.

[0137] With L = 2 and g = 16 fixed, the value of λ is changed. The result is as follows: Figure 13 As shown, the early warning time initially increases with increasing λ. However, after exceeding an optimal value, the early warning time decreases significantly with further increases in λ. This is because during training, λ primarily controls the regularization of the network's loss function to suppress overfitting. A larger λ results in stronger gradient optimization and greater sensitivity to anomalies. However, when λ exceeds a certain value, the model may underfit to some extent, leading to a decrease in anomaly detection accuracy. In the AD-KAN model, for different values ​​of λ, the error in early warning time remains within 3%, indicating that the value of λ has a limited impact on warning performance.

[0138] With g = 16 and λ = 10 fixed, -2 Changing the value of L yields the following result: Figure 14As shown, the early warning time first increases and then decreases with increasing L. This indicates that in AD-KAN, a larger number of network layers is not necessarily better. For the afterburner oscillating combustion dataset in this work, the sample points have 6-channel time series. An excessively large number of network layers can lead to overfitting during model training, thus reducing model performance. In addition, when L is too large, the model's training time and execution time will increase significantly, which will also affect the model's early warning time.

[0139] With L = 2 and λ = 10 fixed, -2 Change the value of g, and the result is as follows Figure 15 As shown in the figure, the early warning time increases with the increase of the value of g across the entire range g∈{2,4,8,16}. In AD-KAN, g is the number of grids in the CosKAN activation function; a larger g indicates that the model uses more univariate Cos functions to fit the CosKAN activation function of each layer. The results in the figure illustrate that the hyperparameter g can improve the model's ability to fit the training dataset. However, an excessively large g will cause the model's training time and execution time to increase exponentially, which is reflected in the increased model execution time in the early warning of oscillating combustion in afterburners, thus affecting the actual deployment of the model.

[0140] Different hyperparameter settings affect the early warning performance of the AD-KAN method. However, generally, parameter selection within a reasonable range has a limited impact on model performance, reflected in an impact of less than 5% on early warning time. The results indicate that the AD-KAN model exhibits good robustness in terms of hyperparameter selection.

[0141] In summary, the proposed AD-KAN outperforms all comparative methods in both theoretical and practical oscillatory combustion early warning performance, and can serve as a novel real-time afterburner oscillatory combustion early warning method. Furthermore, the work presented in this invention can be considered a general workflow for early fault diagnosis in the aerospace field. In the future, it can be considered for application to other intelligent fault diagnosis tasks with problems such as severe sample skewness and insufficient data volume.

[0142] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

[0143] Table 1 Training Process of AD-KAN

[0144]

[0145] Table 2 Oscillation Combustion Warning Thresholds

[0146]

[0147] Table 3 shows the unloading time analyzed by FFT frequency domain.

[0148]

[0149] Table 4. Distribution of sampling quantity in each case

[0150]

[0151] Table 5. Average AUC values ​​of 5 methods in 510 cases

[0152]

[0153] Table 65 shows the time consumption of each method.

[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 for different methods

[0158]

Claims

1. A method for real-time warning of oscillatory combustion in an aircraft engine afterburner, characterized in that, The method comprises the following steps: Step 1: Perform an oscillating combustion experiment of the afterburner, and complete dynamic signal acquisition of the rotation speed, air pressure and oil pressure in the afterburner; Step 2: Convert the dynamic signal into a frequency domain signal, determine whether oscillating combustion occurs in a data set constituted by the frequency domain signal according to a set oscillating combustion early warning threshold, determine a label, and proportionally divide a training data set and a test data set, wherein the training data set is a normal sample, and the test data set contains normal samples and abnormal samples; Step 3: Initialize parameters of the KAN network, and complete training of the KAN network based on the data set, wherein an activation function of the KAN network is: ， wherein, is a dimension of a feature; is a trainable parameter representing a coefficient weight; represents a grid phase shift; is a grid size; Step 4: Perform the KAN network using real-time acquisition signals, and output an early warning signal by the KAN network when the afterburner is about to have an oscillating combustion condition; Function matrix of each layer of the KAN network To ， wherein L is the number of layers of the KAN network, is an input feature latitude of the KAN network, is an output feature latitude of the KAN network; The output of the KAN network is represented as ， An optimization target of the KAN network is to train a high-dimensional space MEE containing all normal sample points, and an optimization item and a loss function of the KAN network are defined as ， wherein, is a KAN network weight decay regularization parameter, is a high-dimensional space ellipsoid center of sphere vector, is a number of samples; The steps of training the KAN network in Step 3 comprise: the distance from the center of the ball the sample point with the largest value is considered as a support vector ; ； In high dimensional MEE, support vectors fall on the boundary of MEE, defining the anomaly detection threshold For ； For anomaly detection of test sample points in the test data set , according to the anomaly score of the test sample point , the criterion is as follows: ； 2. The method of claim 1, wherein, The oscillating combustion early warning threshold is set according to expert experience in Step 2.

3. The method of claim 1, wherein, When the oscillating combustion experiment of the afterburner is performed, if the air pressure signal amplitude exceeds the threshold for more than 3s, it is determined that oscillating combustion occurs, and a power reduction operation is performed; the sample points in the last three seconds before the power reduction operation are marked as abnormal sample points, and the remaining sample points are marked as normal sample points; a data set of 2s before the afterburner is started, 3s after the afterburner is started and 1s after the afterburner is stopped is taken to construct a normal sample training set.

4. The method of claim 1, wherein, The oscillating combustion experiment of the afterburner is performed on an aero-engine ground test bench.

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