A small sample prediction method for performance degradation of an aero-engine

Abstract

This invention discloses a small-sample prediction method for aero-engine performance degradation, relating to the field of artificial intelligence technology. The key technical solution includes the following steps: acquiring small-sample performance degradation monitoring data of key aero-engine components; preprocessing the monitoring data to obtain a degradation data sequence; constructing a basic prediction model based on variational mode decomposition and real-domain grey generation operators; decomposing the degradation data sequence into at least two intrinsic mode components according to variational mode decomposition; performing real-domain grey generation processing on each intrinsic mode component to construct a sub-prediction model; and fusing the sub-prediction models to obtain the basic prediction result. The effect is to effectively enhance the trend characteristics and regularity of small-sample degradation data, solving the problems of insufficient model fitting and weak generalization ability in small-sample scenarios during the initial service phase of new aircraft and extreme operating condition testing, and significantly improving the prediction stability and accuracy under weak sample conditions.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence technology, and more specifically, to a small-sample prediction method for the performance degradation of aero-engines. Background Technology

[0002] As the core power unit of an aircraft, the operating status of an aero-engine directly determines flight safety and mission reliability. Under extreme and complex operating conditions of long-term high temperature, high pressure, and high speed, critical engine components are prone to fatigue, creep, and oxidation, leading to performance degradation. Failure to accurately predict degradation trends in a timely manner may result in engine failure, unplanned outages, or even serious flight accidents. With the rapid development of domestically produced aviation equipment, higher requirements have been placed on the full life-cycle health management of engines. Performance degradation prediction, as a core component of health management, provides a scientific basis for optimizing maintenance decisions and rationally allocating resources by accurately predicting the remaining service life of critical components. It is a key technological support for achieving independent engine maintenance and improving the reliability of aviation equipment.

[0003] Among existing data-driven prediction methods, grey prediction methods have been widely used due to their suitability for modeling small sample data. Their core principle is to enhance the trend of sequences through data generation and processing. However, traditional grey prediction methods are poorly adapted to the nonlinear and non-stationary characteristics of aero-engine degradation data, making it difficult to effectively capture the complex fluctuation patterns in engine performance degradation, resulting in limited prediction accuracy. Furthermore, existing prediction methods generally only focus on constructing the basic prediction model, failing to fully consider the residual patterns between the basic prediction results and the actual degradation data. The systematic biases and random fluctuations contained in the residuals cannot be effectively corrected, further reducing prediction accuracy. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a small-sample prediction method for the performance degradation of aero-engines.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A small-sample prediction method for aircraft engine performance degradation, the method comprising the following steps:

[0007] Acquire small sample performance degradation monitoring data of key components of aero-engines, and preprocess the monitoring data to obtain degradation data sequences;

[0008] Based on variational mode decomposition and real-domain gray generation operators, a basic prediction model is constructed. According to variational mode decomposition, the degenerate data sequence is decomposed into at least two intrinsic mode sub-quantities. Real-domain gray generation processing is performed on each intrinsic mode sub-quantity to construct a sub-prediction model. The basic prediction result is obtained by fusing the sub-prediction models.

[0009] An error dynamic correction model is constructed based on Markov chains. The initial state probability and state transition probability matrix of the Markov chain are optimized according to the basic prediction results and the residual data of the degraded data sequence. The basic prediction correction results are obtained by predicting the residual data according to the error dynamic correction model.

[0010] The optimal parameter set is obtained by jointly optimizing the number of decomposition layers, penalty factor, gray generation operator order and Markov chain state of the basic prediction model.

[0011] By combining the optimal parameter set with the dynamic error correction model and the degradation data sequence, accurate predictions of aero-engine performance degradation can be obtained.

[0012] Preferably, the monitoring data is preprocessed to obtain a degraded data sequence, including:

[0013] Identify and remove outliers from the monitoring data to obtain data without abnormal degradation.

[0014] Normalize the data without abnormal degradation, mapping it to the [0,1] interval. The calculation formula is as follows:

[0015]

[0016] Where x represents data without abnormal degradation, x min x is the minimum value of the data. max x represents the maximum value of the data. ∗ The data is after normalization;

[0017] The normalized data is sorted by time dimension to obtain the degraded data sequence.

[0018] Preferably, a basic prediction model is constructed based on variational mode decomposition and real-domain gray generation operators. The degenerate data sequence is decomposed into at least two intrinsic mode components according to variational mode decomposition. Real-domain gray generation processing is then performed on each intrinsic mode component to construct a sub-prediction model. The basic prediction result is obtained by fusing the sub-prediction models, including:

[0019] The initial number of decomposition layers and the penalty factor of variational mode decomposition are set, and the degraded data sequence is decomposed to obtain at least two independent intrinsic mode subquantities. Each intrinsic mode subquantity represents a different fluctuation characteristic of performance degradation.

[0020] For each intrinsic mode sub-quantum, perform real-domain gray generation processing to obtain the generation sequence corresponding to each sub-quantum. Generate a sequence based on the nearest neighbor mean of each generation sequence and establish a sub-prediction model.

[0021] Each sub-prediction model is optimized to obtain the sub-prediction results of each intrinsic mode sub-quantity. All sub-prediction results are then fused to obtain the basic prediction results of the basic prediction model.

[0022] Preferably, an error dynamic correction model is constructed based on the Markov chain. Based on the residual data of the basic prediction results and the degraded data sequence, the initial state probability and state transition probability matrix of the Markov chain are optimized. The basic prediction correction results are obtained by predicting the residual data using the error dynamic correction model, including:

[0023] The residual data between the basic prediction results and the degraded data sequence is calculated. The residual data is divided into multiple observation sequences according to a preset step size. The initial state probability and state transition probability matrix of the Markov chain are optimized to obtain the improved Markov chain.

[0024] Based on the distribution characteristics of the residual data, the hidden states of the improved Markov chain are divided, and the number of hidden states and the characteristic intervals of each state are determined to obtain the residual observation sequence.

[0025] The residual observation sequence is input into the improved Markov chain to obtain the predicted value of the residual. The predicted value of the residual is then superimposed with the basic prediction result to obtain the basic prediction correction result.

[0026] Preferably, the residual data between the basic prediction results and the degraded data sequence is calculated, and the residual data is divided into multiple observation sequences according to a preset step size. The initial state probability and state transition probability matrix of the Markov chain are optimized to obtain an improved Markov chain, including:

[0027] Based on the fluctuation range and trend of the residual data, different observation sequences are grouped into the same trend set, and the frequency of occurrence of residual states is selected by using the same trend set as the unit to obtain the initial probability of the state.

[0028] Based on the actual distribution characteristics of the residual data, the boundaries of the state interval are dynamically adjusted to obtain the state transition probability matrix;

[0029] Based on the temporal correlation of the residual data, the probability values ​​of low-frequency transition paths in the state transition probability matrix are corrected to obtain the corrected set of the state transition probability matrix;

[0030] An improved Markov chain is obtained by adjusting the weight allocation of the initial state probability and the state transition probability matrix based on the modified set of the state transition probability matrix.

[0031] Preferably, the optimal parameter set is obtained by jointly optimizing multiple parameters, including the number of decomposition layers, penalty factor, gray generation operator order, and Markov chain state number of the basic prediction model, as well as the number of decomposition layers, penalty factor, gray generation operator order, and Markov chain state number.

[0032] A multi-dimensional parameter space is constructed, with the number of decomposition layers, penalty factor, gray generation operator order, and Markov chain state number as independent dimensions to form a continuous parameter search interval;

[0033] The accuracy change value is obtained by obtaining the prediction accuracy change during the optimization process. The search step size and search range of each parameter search interval are dynamically adjusted based on the accuracy change value to obtain the parameter interval.

[0034] Based on the parameter range, the core parameter range is obtained by coarse-grained optimization of the number of decomposition layers and the penalty factor.

[0035] Based on the accuracy variation value, the target state prediction value is obtained by fine-grained optimization of the gray generation operator order and the number of Markov chain states.

[0036] The parameter combination is obtained by filtering the predicted values ​​of the target state based on prediction accuracy, complexity and computational efficiency;

[0037] The degraded data sequence is divided into a training set and a validation set. The parameter set is optimized based on the training set to obtain a candidate parameter set. The candidate parameter set is then filtered based on the validation set to obtain the optimal parameter set.

[0038] Preferably, the energy percentage of each intrinsic mode subquantum is calculated using the following formula:

[0039]

[0040] Among them, w k E represents the weight of the k-th intrinsic mode subquantum. k Let n be the energy of the k-th eigenmode subquantum, and n be the total number of eigenmode subquantums.

[0041] The energy calculation formula for the intrinsic modal quantum is as follows:

[0042]

[0043] Where, x kj Let be the j-th data of the k-th intrinsic mode component, and m be the data length of a single component.

[0044] Preferably, the small sample performance degradation monitoring data of the key components of the aero-engine includes aero-engine blade vibration, bearing temperature, bolt torque, or fuel nozzle flow rate.

[0045] Compared with existing technologies, this invention has the following advantages: By combining variational mode decomposition with gray generation operators in the real domain, the trend characteristics and regularity of small sample degradation data are effectively enhanced, solving the problems of insufficient fitting and weak generalization ability of prediction models in small sample scenarios during the initial service of new aircraft and the extreme operating condition test phase, and significantly improving the prediction stability and accuracy under weak sample conditions; by decomposing the degradation data sequence into multiple stationary intrinsic mode subquantities through variational mode decomposition, the mode aliasing problem that is prone to occur in single mode decomposition methods is effectively suppressed, and the complex fluctuation law in the performance degradation process of aero-engines can be accurately captured, greatly improving the adaptability and modeling rationality of nonlinear and non-stationary degradation data; based on Markov chains, an error dynamic correction model is constructed. By optimizing the initial state probability and state transition probability matrix, the residual law between the basic prediction results and the true values ​​is fully utilized to accurately predict and superimpose corrections on the residuals, effectively reducing the systematic bias and random fluctuations of the basic prediction model, and significantly improving the accuracy of the final prediction results. Attached Figure Description

[0046] Figure 1 This is a schematic diagram illustrating the steps of a small-sample prediction method for aero-engine performance degradation according to an embodiment of the present invention;

[0047] Figure 2 This is a schematic diagram illustrating the steps of obtaining an improved Markov chain in a small-sample prediction method for aero-engine performance degradation provided in an embodiment of the present invention. Detailed Implementation

[0048] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0049] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0050] Secondly, the term "an embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places throughout this specification does not necessarily refer to the same embodiment, nor is it a single embodiment or an embodiment selectively excluded from other embodiments.

[0051] Reference Figures 1-2 As shown.

[0052] This embodiment further illustrates the small-sample prediction method for aero-engine performance degradation proposed in this invention.

[0053] A small-sample prediction method for aircraft engine performance degradation, the method comprising the following steps:

[0054] Acquire small sample performance degradation monitoring data of key components of aero-engines, and preprocess the monitoring data to obtain degradation data sequences;

[0055] Based on variational mode decomposition and real-domain gray generation operators, a basic prediction model is constructed. According to variational mode decomposition, the degenerate data sequence is decomposed into at least two intrinsic mode sub-quantities. Real-domain gray generation processing is performed on each intrinsic mode sub-quantity to construct a sub-prediction model. The basic prediction result is obtained by fusing the sub-prediction models.

[0056] An error dynamic correction model is constructed based on Markov chains. The initial state probability and state transition probability matrix of the Markov chain are optimized according to the basic prediction results and the residual data of the degraded data sequence. The basic prediction correction results are obtained by predicting the residual data according to the error dynamic correction model.

[0057] The optimal parameter set is obtained by jointly optimizing the number of decomposition layers, penalty factor, gray generation operator order and Markov chain state of the basic prediction model.

[0058] By combining the optimal parameter set with the dynamic error correction model and the degradation data sequence, accurate predictions of aero-engine performance degradation can be obtained.

[0059] Preprocessing the monitoring data yields a degraded data sequence, including:

[0060] Identify and remove outliers from the monitoring data to obtain data without abnormal degradation.

[0061] Normalize the data without abnormal degradation, mapping it to the [0,1] interval. The calculation formula is as follows:

[0062]

[0063] Where x represents data without abnormal degradation, x min x is the minimum value of the data. max x represents the maximum value of the data. ∗ The data is after normalization;

[0064] The normalized data is sorted by time dimension to obtain the degraded data sequence.

[0065] During the performance degradation monitoring of critical components of aero-engines, outliers deviating from the normal degradation trend may be mixed into the monitoring data due to sensor noise, instantaneous operating condition fluctuations, or measurement errors. These outliers can interfere with the model's capture of the true degradation pattern, so they need to be identified and removed first. Statistical tests or threshold judgment methods can be used for identification. For example, setting three times the standard deviation as the outlier threshold, data exceeding this range are judged as outliers and removed, thus obtaining data without abnormal degradation and ensuring the authenticity and reliability of the data.

[0066] After removing outliers, to eliminate the differences in dimensions and numerical ranges between different monitoring indicators, it is necessary to normalize the non-degrading data, mapping it to a unified interval of 0 to 1. First, extract the minimum and maximum values ​​from the non-degrading data. Then, divide the difference between each original data point and the minimum value by the difference between the maximum and minimum values ​​to obtain the normalized data. For example, if the monitoring data sequence is 5, 10, 15, 20, with a minimum value of 5 and a maximum value of 20, then the normalized value of the original data 10 is: x ∗ = (10-5) / (20-5)≈0.333, the normalized value of the original data 15 is: x ∗ = (15-5) / (20-5)≈0.667. Normalization unifies degraded data from different dimensions to the same numerical scale, facilitating subsequent model training and prediction.

[0067] After normalization, all normalized data are arranged in chronological order according to their corresponding monitoring time to form a continuous degradation data sequence. This facilitates the restoration of the temporal correlation of the data and ensures that the position of each data point in the sequence accurately reflects the degradation process of the aero-engine performance over time. This provides an orderly input basis for subsequent time-series-based predictive analysis, and facilitates the transformation of the original monitoring data into a degradation data sequence without anomalies, standardized, and with a clear temporal order. This lays a solid data foundation for subsequent steps such as variational mode decomposition, grey prediction, and Markov chain error correction.

[0068] Based on variational mode decomposition and real-domain grey generation operators, a basic prediction model is constructed. The degenerate data sequence is decomposed into at least two intrinsic mode components according to variational mode decomposition. Real-domain grey generation processing is then applied to each intrinsic mode component to construct sub-prediction models. The basic prediction results are obtained by fusing these sub-prediction models, including:

[0069] The initial number of decomposition layers and the penalty factor of variational mode decomposition are set, and the degraded data sequence is decomposed to obtain at least two independent intrinsic mode subquantities. Each intrinsic mode subquantity represents a different fluctuation characteristic of performance degradation.

[0070] For each intrinsic mode sub-quantum, perform real-domain gray generation processing to obtain the generation sequence corresponding to each sub-quantum. Generate a sequence based on the nearest neighbor mean of each generation sequence and establish a sub-prediction model.

[0071] Each sub-prediction model is optimized to obtain the sub-prediction results of each intrinsic mode sub-quantity. All sub-prediction results are then fused to obtain the basic prediction results of the basic prediction model.

[0072] The variational mode decomposition (VMD) stage requires setting the initial decomposition level and penalty factor. The initial decomposition level determines how many independent eigenmode sub-quantities the degraded data sequence is decomposed into, while the penalty factor constrains the bandwidth of each sub-quantity to avoid over-decomposition or under-decomposition. Taking the temperature degradation data sequence of an aero-engine turbine blade as an example, assuming an initial decomposition level of 3 and a penalty factor of 2000, inputting the degradation data sequence into the VMD algorithm yields three independent eigenmode sub-quantities. These three sub-quantities characterize the fluctuation features at different scales during the performance degradation process. For example, the first sub-quantity reflects the high-frequency rapid fluctuations caused by operating condition switching, the second sub-quantity reflects the slow mid-frequency changes caused by material fatigue accumulation, and the third sub-quantity represents the low-frequency trend of overall performance degradation. Through this decomposition, the originally complex and coupled degradation process is broken down into several relatively simple and easy-to-model sub-processes, laying the foundation for subsequent accurate prediction.

[0073] In the real-domain grey generation processing and sub-prediction model construction stage, for each intrinsic modal subquantity, real-domain grey generation processing is required to obtain the corresponding generation sequence. The real-domain grey generation operator extends the generation order to any real number, thereby more accurately capturing the nonlinear evolution law of the subquantity. For example, for the first high-frequency fluctuating subquantity mentioned above, a generation order of 0.5 can be selected, and it can be processed by the real-domain cumulative generation operator to obtain the corresponding generation sequence. Subsequently, a sub-prediction model is established based on the nearest neighbor mean generation sequence of each generation sequence. Taking the generation sequence as an example, the calculation method of its nearest neighbor mean generation sequence is to use the average of two adjacent data in the generation sequence as the corresponding element of the new sequence. This processing can effectively smooth the random fluctuations of the generation sequence and highlight its inherent trend. Based on the nearest neighbor mean generation sequence, the corresponding sub-prediction model can be constructed to predict the future evolution trend of the subquantity.

[0074] Each sub-prediction model is optimized using a particle swarm optimization (PSO) algorithm. With prediction accuracy as the objective, the evolution coefficient and grey action parameter of the model are optimized to obtain the optimal sub-prediction results for each intrinsic mode sub-quantity. For example, the sub-prediction model for the first high-frequency fluctuation sub-quantity can be optimized to obtain its predicted values ​​for the next three time steps. Subsequently, all sub-prediction results are fused to obtain the basic prediction results of the basic prediction model. The fusion method can employ weighted summation, with weights determined based on the contribution of each sub-quantity to the overall degradation trend. For example, a higher weight is assigned to the third low-frequency sub-quantity, which reflects the overall trend, while a lower weight is assigned to the high-frequency fluctuation sub-quantity. Through this fusion, the prediction results of each sub-quantity are integrated into a unified whole, reconstructing the comprehensive trend of aero-engine performance degradation and forming the basic prediction results, providing reliable initial prediction values ​​for subsequent dynamic error correction.

[0075] A dynamic error correction model is constructed based on Markov chains. Based on the basic prediction results and the residual data of the degraded data sequence, the initial state probability and state transition probability matrix of the Markov chain are optimized. The basic prediction correction results are obtained by predicting the residual data using the dynamic error correction model, including:

[0076] The residual data between the basic prediction results and the degraded data sequence is calculated. The residual data is divided into multiple observation sequences according to a preset step size. The initial state probability and state transition probability matrix of the Markov chain are optimized to obtain the improved Markov chain.

[0077] Based on the distribution characteristics of the residual data, the hidden states of the improved Markov chain are divided, and the number of hidden states and the characteristic intervals of each state are determined to obtain the residual observation sequence.

[0078] The residual observation sequence is input into the improved Markov chain to obtain the predicted value of the residual. The predicted value of the residual is then superimposed with the basic prediction result to obtain the basic prediction correction result.

[0079] In the error dynamic correction stage of small-sample prediction of aero-engine performance degradation, it is first necessary to calculate the residual data between the basic prediction results and the true values ​​of the degradation data sequence. This residual data can effectively characterize the systematic bias and random fluctuations of the basic prediction model. To adapt to the modeling requirements of Markov chains, the residual data needs to be divided into multiple observation sequences according to a preset step size, thereby constructing the initial state probability and state transition probability matrix of the Markov chain, resulting in an improved Markov chain. The initial state probability can be calculated by the frequency of the first occurrence of each state in the residual observation sequence, using the following formula: , where P i Let N be the initial probability of the i-th state. iLet be the number of times the i-th state first appears in the observation sequence, and N be the total length of the observation sequence. The state transition probability matrix is ​​obtained by statistically analyzing the transition frequencies between states, as shown in the formula: , where P ij M is the probability of transitioning from state i to state j. ij Let n be the frequency of transition from state i to state j, and n be the total number of hidden states.

[0080] Based on the distribution characteristics of the residual data, the hidden states of the improved Markov chain are divided. Specifically, the residual value range can be divided into several non-overlapping feature intervals according to the minimum, maximum, and distribution density of the residual data. Each interval corresponds to a hidden state, thereby determining the number of hidden states and the feature intervals of each state, and obtaining the residual observation sequence. For example, if the residual data range is [−0.5, 0.5], it can be divided into four state intervals: [−0.5, −0.25], [−0.25, 0], [0, 0.25], and [0.25, 0.5]. Each interval corresponds to a hidden state, and the residual data falling into the corresponding interval is marked as that state.

[0081] Subsequently, the residual observation sequence is input into the improved Markov chain. The residual state at the next time step is predicted using the state transition probability matrix, and then the predicted residual value is obtained by combining the median or mean of the characteristic interval of each state. Finally, the predicted residual value is superimposed and corrected with the basic prediction result to obtain the basic prediction correction result, as shown in the formula: , where Y 修正 Based on the revised prediction results, Y 基础 Based on the prediction results, e 预测 These are the residual prediction values. This correction process effectively reduces the systematic bias and stochastic fluctuations of the basic prediction model, significantly improving the accuracy and robustness of aero-engine performance degradation prediction.

[0082] The residual data between the base prediction results and the degraded data sequence is calculated. The residual data is then divided into multiple observation sequences according to a preset step size. The initial state probability and state transition probability matrix of the Markov chain are optimized to obtain an improved Markov chain, including:

[0083] Based on the fluctuation range and trend of the residual data, different observation sequences are grouped into the same trend set, and the frequency of occurrence of residual states is selected by using the same trend set as the unit to obtain the initial probability of the state.

[0084] Based on the actual distribution characteristics of the residual data, the boundaries of the state interval are dynamically adjusted to obtain the state transition probability matrix;

[0085] Based on the temporal correlation of the residual data, the probability values ​​of low-frequency transition paths in the state transition probability matrix are corrected to obtain the corrected set of the state transition probability matrix;

[0086] An improved Markov chain is obtained by adjusting the weight allocation of the initial state probability and the state transition probability matrix based on the modified set of the state transition probability matrix.

[0087] In constructing a dynamic error correction model for small-sample prediction of aero-engine performance degradation, improving the optimization process of the Markov chain is a core step in enhancing the accuracy of residual prediction. First, the residual data between the basic prediction results and the actual values ​​of the degradation data sequence is calculated. This residual data effectively characterizes the systematic bias and random fluctuations of the basic prediction model. To construct a more targeted Markov chain, the residual data needs to be divided into multiple observation sequences according to a preset step size. Then, based on the fluctuation amplitude and trend of the residual data, different observation sequences are grouped into similar trend sets. For example, observation sequences with fluctuation amplitudes less than a preset threshold and consistent trends can be grouped into the same trend set. The frequency of occurrence of residual states is then statistically analyzed using similar trend sets as units to obtain the initial state probability.

[0088] Based on the actual distribution characteristics of the residual data, the boundaries of the state intervals are dynamically adjusted to construct a state transition probability matrix that better reflects the data patterns. Specifically, the boundaries of each state interval can be determined using methods such as kernel density estimation or quantile partitioning, making the residual data distribution within each state interval more uniform and avoiding distortion of state transition probabilities caused by unreasonable interval partitioning.

[0089] Based on the temporal correlation of the residual data, the probability values ​​of low-frequency transition paths in the state transition probability matrix are corrected to obtain a corrected set of state transition probability matrices. For example, if a certain state transition path occurs with extremely low frequency in the time series data, its probability value can be corrected by introducing temporal weights or smoothing coefficients to avoid distortion of transition probabilities caused by sample sparsity. The correction formula can be expressed as: , where P ij ′ represents the corrected state transition probability, α is the smoothing coefficient, ranging from 0 to 1, and n is the total number of hidden states.

[0090] By adjusting the weights of the initial state probability and the state transition probability matrix based on the modified set of the state transition probability matrix, an improved Markov chain is obtained. For example, the optimal weights of the initial state probability and the state transition probability matrix can be determined through cross-validation or Bayesian optimization methods, enabling the Markov chain to simultaneously consider the distribution characteristics of the initial state and the temporal transition patterns in residual prediction. Through this optimization step, the improved Markov chain can more accurately capture the dynamic changes in residual data, providing a reliable basis for subsequent residual prediction and result correction.

[0091] The optimal parameter set is obtained by jointly optimizing the number of decomposition layers, penalty factor, gray generation operator order, and Markov chain state of the basic prediction model, including:

[0092] A multi-dimensional parameter space is constructed, with the number of decomposition layers, penalty factor, gray generation operator order, and Markov chain state number of the basic prediction model as independent dimensions, forming a continuous parameter search interval.

[0093] The accuracy change value is obtained by obtaining the prediction accuracy change during the optimization process. The search step size and search range of each parameter search interval are dynamically adjusted based on the accuracy change value to obtain the parameter interval.

[0094] Based on the parameter range, the core parameter range is obtained by coarse-grained optimization of the number of decomposition layers and the penalty factor.

[0095] Based on the accuracy variation value, the target state prediction value is obtained by fine-grained optimization of the gray generation operator order and the number of Markov chain states.

[0096] The parameter combination is obtained by filtering the predicted values ​​of the target state based on prediction accuracy, complexity and computational efficiency;

[0097] The degraded data sequence is divided into a training set and a validation set. The parameter set is optimized based on the training set to obtain a candidate parameter set. The candidate parameter set is then filtered based on the validation set to obtain the optimal parameter set.

[0098] In the small-sample prediction of aero-engine performance degradation, the multi-parameter joint optimization of the basic prediction model is carried out based on four key parameters: the number of decomposition layers, the penalty factor, the order of the grey generation operator, and the number of Markov chain states. Through hierarchical optimization and cross-validation, the optimal parameter set is finally obtained.

[0099] The number of decomposition layers, penalty factor, gray generation operator order, and Markov chain state number of the basic prediction model are used as independent dimensions to form a continuous parameter search interval. For example, based on engineering experience and preliminary experimental results, the search interval for the number of decomposition layers can be set to 2 to 10, the search interval for the penalty factor to 100 to 10000, the search interval for the gray generation operator order to 1 to 5, and the search interval for the Markov chain state number to 3 to 7. The initial step size of each dimension can be differentiated according to the degree of influence of the parameters on the model performance.

[0100] The accuracy change value is obtained by acquiring the change in prediction accuracy during the optimization process. Based on this accuracy change value, the search step size and search range of each parameter are dynamically adjusted to obtain the parameter range. When the accuracy change value is large, it indicates that the current parameters have a significant impact on model performance, and the search step size can be appropriately reduced to improve optimization accuracy. When the accuracy change value is small, the search range can be expanded to avoid getting trapped in local optima. The formula for calculating the accuracy change value can be expressed as: , where ΔA is the accuracy change value, Ak+1 is the prediction accuracy of the (k+1)th iteration, and Ak is the prediction accuracy of the kth iteration.

[0101] Based on the parameter range, a coarse-grained optimization of the decomposition level and penalty factor is performed to obtain the core parameter range. The decomposition level and penalty factor directly affect the effect of variational mode decomposition, determining the stationarity and effectiveness of the intrinsic mode components after the decomposition of the degenerate data sequence, which is crucial for the construction of subsequent sub-prediction models. Therefore, the core value range is first determined through coarse-grained optimization. For example, a grid search method can be used to traverse the combinations of decomposition level and penalty factor within the parameter range, selecting the top 20% of combinations with the highest prediction accuracy to form the core parameter range, providing a foundation for subsequent fine-grained optimization.

[0102] Based on the accuracy variation value, fine-grained optimization is performed on the order of the gray generation operator and the number of Markov chain states to obtain the target state prediction value. The order of the gray generation operator affects the enhancement effect of trend features of small sample degraded data; too high an order can easily lead to overfitting, while too low an order cannot fully explore the data patterns. The number of Markov chain states determines the state division accuracy of the error correction model; too many states increase computational complexity, while too few states make it difficult to characterize the dynamic changes of residuals. Therefore, based on the core parameter range, particle swarm optimization or genetic algorithm is used, with the accuracy variation value as the fitness function, to iteratively update the values ​​of the gray generation operator order and the number of Markov chain states until the convergence condition is met to obtain the target state prediction value.

[0103] Parameter combinations are obtained by filtering the predicted values ​​of the target state based on prediction accuracy, complexity, and computational efficiency. A comprehensive evaluation index can be constructed, which weights and integrates prediction accuracy, model complexity, and computational efficiency to select the parameter combination with the best overall performance. The formula for calculating the comprehensive evaluation index can be expressed as: Where S is the comprehensive evaluation index, A is the prediction accuracy, C is the model complexity, T is the computation time, ω1, ω2, and ω3 are the corresponding weights, and ω1+ω2+ω3=1.

[0104] The degraded data sequence is divided into a training set and a validation set. Parameter sets are optimized using the training set to obtain candidate parameter sets, and then further refined using the validation set to obtain the optimal parameter set. For example, the degraded data sequence can be divided into training and validation sets in a 7:3 ratio. Multiple rounds of parameter optimization are performed on the training set to obtain candidate parameter sets. These candidate parameter sets are then substituted into the basic prediction model and the dynamic error correction model, and tested on the validation set. The parameter set with the highest prediction accuracy on the validation set is selected as the optimal parameter set, ensuring the model's generalization ability and engineering reliability on unknown data.

[0105] Through a multi-parameter joint optimization process, parameter matching can be achieved in the decomposition, prediction, and correction stages, significantly improving the accuracy and robustness of the aero-engine performance degradation prediction model under small sample and high noise conditions, and providing strong support for the full life cycle health monitoring of aero-engines.

[0106] The formula for calculating the energy percentage of each intrinsic mode subquant is as follows:

[0107]

[0108] Among them, w k E represents the weight of the k-th intrinsic mode subquantum. k Let n be the energy of the k-th eigenmode subquantum, and n be the total number of eigenmode subquantums.

[0109] The energy calculation formula for the intrinsic modal quantum is as follows:

[0110]

[0111] Where, x kj Let be the j-th data of the k-th intrinsic mode component, and m be the data length of a single component.

[0112] First, calculate the energy of each eigenmode subquant. The formula for calculating the energy of an eigenmode subquant is: This formula effectively quantifies the signal energy contained in an intrinsic mode subquantity by summing the squared values ​​of all data points in the subquantity. The higher the energy value, the stronger the subquantity's ability to characterize the original degraded data sequence. For example, if a certain intrinsic mode subquantity contains the main trend characteristics of engine performance degradation, its energy value will be significantly higher than other subquantities.

[0113] Based on the energy values ​​of each intrinsic mode subquanta, their corresponding energy weights are calculated. The formula for calculating the energy weight of each intrinsic mode subquanta is as follows: This formula calculates the weight coefficient of a single quantum by comparing its energy to the total energy of all quantums. A larger weight value indicates a higher contribution of that quantum to the fusion process. For example, if variational mode decomposition yields three eigenmode quantums with energies of 100, 60, and 40, respectively, the total energy is 200, corresponding to weights of 0.5, 0.3, and 0.2. In fusing the quantum prediction results, the prediction result of the first quantum will dominate.

[0114] In practical applications, after calculating the weights of each intrinsic mode sub-quantity using the energy proportions described above, the outputs of each sub-prediction model can be weighted and summed with their corresponding weights to obtain the basic prediction result. The fusion formula can be expressed as: , where Y 基础 Based on the prediction results, yk This represents the sub-prediction result corresponding to the k-th intrinsic mode sub-quantum. This fusion method can fully utilize the feature information of each intrinsic mode sub-quantum, avoid the excessive influence of single sub-quantum prediction bias on the overall result, and improve the stability and accuracy of the basic prediction model.

[0115] By calculating the energy of intrinsic modal subquanta and allocating energy proportion weights, it is possible to accurately quantify and effectively fuse different characteristic components of degraded data sequences, laying a solid foundation for subsequent dynamic error correction and multi-parameter optimization, and ultimately improving the accuracy and reliability of aero-engine performance degradation prediction.

[0116] The small-sample performance degradation monitoring data of the key components of the aero-engine includes aero-engine blade vibration, bearing temperature, bolt torque, or fuel nozzle flow rate.

[0117] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A small-sample prediction method for aero-engine performance degradation, characterized in that, The method includes the following steps: Acquire small sample performance degradation monitoring data of key components of aero-engines, and preprocess the monitoring data to obtain degradation data sequences; Based on variational mode decomposition and real-domain gray generation operators, a basic prediction model is constructed. According to variational mode decomposition, the degenerate data sequence is decomposed into at least two intrinsic mode sub-quantities. Real-domain gray generation processing is performed on each intrinsic mode sub-quantity to construct a sub-prediction model. The basic prediction result is obtained by fusing the sub-prediction models. An error dynamic correction model is constructed based on Markov chains. The initial state probability and state transition probability matrix of the Markov chain are optimized according to the basic prediction results and the residual data of the degraded data sequence. The basic prediction correction results are obtained by predicting the residual data according to the error dynamic correction model. The optimal parameter set is obtained by jointly optimizing the number of decomposition layers, penalty factor, gray generation operator order and Markov chain state of the basic prediction model. By combining the optimal parameter set with the dynamic error correction model and the degradation data sequence, accurate predictions of aero-engine performance degradation can be obtained.

2. The small-sample prediction method for aero-engine performance degradation according to claim 1, characterized in that, Preprocessing the monitoring data yields a degraded data sequence, including: Identify and remove outliers from the monitoring data to obtain data without abnormal degradation. Normalize the data without abnormal degradation, mapping it to the [0,1] interval. The calculation formula is as follows: Where x represents data without abnormal degradation, x min x is the minimum value of the data. max x represents the maximum value of the data. ∗ The data is after normalization; The normalized data is sorted by time dimension to obtain the degraded data sequence.

3. The small-sample prediction method for aero-engine performance degradation according to claim 2, characterized in that, Based on variational mode decomposition and real-domain grey generation operators, a basic prediction model is constructed. The degenerate data sequence is decomposed into at least two intrinsic mode components according to variational mode decomposition. Real-domain grey generation processing is then applied to each intrinsic mode component to construct sub-prediction models. The basic prediction results are obtained by fusing these sub-prediction models, including: The initial number of decomposition layers and the penalty factor of variational mode decomposition are set, and the degraded data sequence is decomposed to obtain at least two independent intrinsic mode subquantities. Each intrinsic mode subquantity represents a different fluctuation characteristic of performance degradation. For each intrinsic mode sub-quantum, perform real-domain gray generation processing to obtain the generation sequence corresponding to each sub-quantum. Generate a sequence based on the nearest neighbor mean of each generation sequence and establish a sub-prediction model. Each sub-prediction model is optimized to obtain the sub-prediction results of each intrinsic mode sub-quantity. All sub-prediction results are then fused to obtain the basic prediction results of the basic prediction model.

4. The small-sample prediction method for aero-engine performance degradation according to claim 3, characterized in that, A dynamic error correction model is constructed based on Markov chains. Based on the basic prediction results and the residual data of the degraded data sequence, the initial state probability and state transition probability matrix of the Markov chain are optimized. The basic prediction correction results are obtained by predicting the residual data using the dynamic error correction model, including: The residual data between the basic prediction results and the degraded data sequence is calculated. The residual data is divided into multiple observation sequences according to a preset step size. The initial state probability and state transition probability matrix of the Markov chain are optimized to obtain the improved Markov chain. Based on the distribution characteristics of the residual data, the hidden states of the improved Markov chain are divided, and the number of hidden states and the characteristic intervals of each state are determined to obtain the residual observation sequence. The residual observation sequence is input into the improved Markov chain to obtain the predicted value of the residual. The predicted value of the residual is then superimposed with the basic prediction result to obtain the basic prediction correction result.

5. The small-sample prediction method for aero-engine performance degradation according to claim 4, characterized in that, The residual data between the base prediction results and the degraded data sequence is calculated. The residual data is then divided into multiple observation sequences according to a preset step size. The initial state probability and state transition probability matrix of the Markov chain are optimized to obtain an improved Markov chain, including: Based on the fluctuation range and trend of the residual data, different observation sequences are grouped into the same trend set, and the frequency of occurrence of residual states is selected by using the same trend set as the unit to obtain the initial probability of the state. Based on the actual distribution characteristics of the residual data, the boundaries of the state interval are dynamically adjusted to obtain the state transition probability matrix; Based on the temporal correlation of the residual data, the probability values ​​of low-frequency transition paths in the state transition probability matrix are corrected to obtain the corrected set of the state transition probability matrix; An improved Markov chain is obtained by adjusting the weight allocation of the initial state probability and the state transition probability matrix based on the modified set of the state transition probability matrix.

6. The small-sample prediction method for aero-engine performance degradation according to claim 5, characterized in that, The optimal parameter set is obtained by jointly optimizing the number of decomposition layers, penalty factor, gray generation operator order, and Markov chain state of the basic prediction model, including: A multi-dimensional parameter space is constructed, with the number of decomposition layers, penalty factor, gray generation operator order, and Markov chain state number as independent dimensions to form a continuous parameter search interval; The accuracy change value is obtained by obtaining the prediction accuracy change during the optimization process. The search step size and search range of each parameter search interval are dynamically adjusted based on the accuracy change value to obtain the parameter interval. Based on the parameter range, the core parameter range is obtained by coarse-grained optimization of the number of decomposition layers and the penalty factor. Based on the accuracy variation value, the target state prediction value is obtained by fine-grained optimization of the gray generation operator order and the number of Markov chain states. The parameter combination is obtained by filtering the predicted values ​​of the target state based on prediction accuracy, complexity and computational efficiency; The degraded data sequence is divided into a training set and a validation set. The parameter set is optimized based on the training set to obtain a candidate parameter set. The candidate parameter set is then filtered based on the validation set to obtain the optimal parameter set.

7. The small-sample prediction method for aero-engine performance degradation according to claim 6, characterized in that, The formula for calculating the energy percentage of each intrinsic mode subquant is as follows: Among them, w k E represents the weight of the k-th intrinsic mode subquantum. k Let n be the energy of the k-th eigenmode subquantum, and n be the total number of eigenmode subquantums. The energy calculation formula for the intrinsic modal quantum is as follows: Where, x kj Let be the j-th data of the k-th intrinsic mode component, and m be the data length of a single component.

8. The small-sample prediction method for aero-engine performance degradation according to claim 7, characterized in that, The small-sample performance degradation monitoring data of the key components of the aero-engine includes aero-engine blade vibration, bearing temperature, bolt torque, or fuel nozzle flow rate.

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