Method for predicting aviation material demand by fusing multi-level decomposition and dynamic time-lag causal spectrum learning

Abstract

The application relates to the technical field of aviation material management, and discloses an aviation material demand prediction method fusing multi-stage decomposition and dynamic time-lag causal spectrum learning, which comprises the following steps: acquiring multivariate aviation material time series data, extracting a plurality of trend components of different scales and a high-frequency seasonal residual component layer by layer in a descending smooth window scale through a multi-stage recursive residual decomposition module; inputting the trend components of each scale into a time-lag perception causal graph structure learning module, learning a probability time-lag distribution, constructing a dynamic causal adjacency matrix, and outputting trend prediction of each scale after adaptive fusion of a linear baseline branch and a graph correction branch through bidirectional graph convolution propagation; inputting the high-frequency seasonal residual component into a frequency domain spectrum attention module, modeling spectrum interdependence with frequency points as tokens, and reconstructing seasonal prediction; and finally, aggregating the trend prediction of each scale and the seasonal prediction, and outputting the final aviation material demand prediction value through inverse normalization. The application effectively improves the precision of aviation material demand prediction.

Description

Technical Field

[0001] This application relates to the field of aircraft material management technology, and in particular to an aircraft material demand forecasting method that integrates multi-level decomposition and dynamic time-delay causal spectrum learning. Background Technology

[0002] Forecasting demand for aircraft parts is a core technological support for airlines and maintenance companies to achieve accurate inventory management and reduce the risks of spare parts backlog and shortages. Currently, existing technologies mainly cover traditional statistical methods, such as ARIMA and exponential smoothing; machine learning methods, such as random forests and XGBoost; and deep learning methods, such as graph neural networks and frequency domain prediction models. Traditional statistical methods can only characterize univariate linear trends and have limited responsiveness to sudden demand and external driving factors; machine learning methods are insensitive to time series order and lack the ability to explicitly model time dependencies; while deep learning methods have made breakthroughs in nonlinear fitting, they still generally suffer from the following shortcomings.

[0003] Most existing methods employ a single fixed-window moving average decomposition, which cannot simultaneously satisfy the dual requirements of long-term trend smoothness and high-frequency peak fidelity. This leads to the overlapping of multi-frequency features, weakening the model's ability to characterize complex aircraft material consumption patterns. Furthermore, existing graph neural network methods generally assume that the influence between variables is instantaneous, neglecting the real time lag effects in aircraft material consumption. For example, the impact of increased flight hours on spare parts consumption often lags by several days or even weeks, which not only introduces spurious correlations but also loses crucial historical driving information. In addition, frequency domain prediction methods directly fit phase values ​​when optimizing complex spectra. However, phase exhibits periodic numerical jumps at boundaries, easily leading to gradient instability and making it difficult to robustly model the multi-period superposition patterns of aircraft material demand triggered by periodic maintenance such as A-checks, C-checks, and D-checks.

[0004] Therefore, existing technologies lack a method for forecasting aircraft material demand that can simultaneously address the three major challenges of multi-scale trend aliasing, dynamic time-delay variable dependence, and stable modeling of high-frequency seasonal characteristics. Summary of the Invention

[0005] This application provides a method for predicting aircraft material demand that integrates multi-level decomposition and dynamic time-delay causal spectrum learning. This method addresses the technical problems of multi-scale trend aliasing, neglect of time delay effects between variables, and instability of frequency domain phase optimization in existing aircraft material demand prediction methods, thereby improving the accuracy of aircraft material demand prediction.

[0006] Firstly, this application provides a method for predicting aircraft material demand that integrates multi-level decomposition and dynamic time-delay causal spectrum learning, the method comprising: Step S1: Obtain multivariate time series data of aircraft materials, apply the moving average operator layer by layer according to the decreasing smooth window scale through the multi-level recursive residual decomposition module, extract the trend component of the corresponding scale from the upper residual and pass the remaining residual level by level, and finally obtain multiple trend components of different scales and a high-frequency seasonal residual component. Step S2: Input the trend components at each scale into the time-delay-aware causal graph structure learning module. The time-delay-aware causal graph structure learning module learns the probability time-delay distribution for each pair of directed variable nodes. Based on the probability time-delay distribution, it performs inner product calculation on the current node features and the time-delay-weighted historical node features to construct a dynamic causal adjacency matrix. It then performs bidirectional graph convolution propagation on the dynamic causal adjacency matrix to update the node representation. Finally, it adaptively weights and fuses the linear baseline branch and the graph correction branch to output the trend prediction results at each scale. Step S3: Input the high-frequency seasonal residual component into the frequency domain spectrum attention module. The frequency domain spectrum attention module performs a real-number fast Fourier transform on the high-frequency seasonal residual component to obtain a complex spectrum. Each frequency point is treated as an independent token and superimposed with a learnable frequency domain position code before being fed into a multi-head self-attention network to model the inter-spectral dependency in the frequency dimension. Then, the time-domain seasonal sequence is reconstructed by the inverse real-number fast Fourier transform and linearly mapped to the prediction step size, and the seasonal prediction result is output. Step S4: Aggregate the trend forecast results at each scale with the seasonal forecast results to obtain standardized forecast results, and then output the final aircraft material demand forecast value through inverse normalization transformation.

[0007] Compared with the prior art, the beneficial effects of the present invention are at least as follows: This application uses a multi-level recursive residual decomposition module to peel off the time series data of aircraft materials layer by layer from coarse to fine. This can simultaneously preserve the smoothness of long-term trends and the high-frequency peak fidelity of sudden demands, fundamentally eliminating the multi-frequency feature aliasing phenomenon that is difficult to avoid with single-scale decomposition. As a result, it significantly improves the prediction accuracy under complex conditions where fleet size growth, flight season switching and sudden fault disturbances coexist.

[0008] This application employs a time-delay-aware causal graph structure learning module. By learning the probability time-delay distribution for each pair of variables and constructing a dynamic causal adjacency matrix, it explicitly characterizes the lag response characteristics of aircraft material consumption to external driving factors. This effectively avoids the introduction of spurious correlations and completes key historical driving information. Furthermore, by combining an adaptive weighted fusion strategy of linear baseline branch and graph correction branch, the model can maintain stable trend prediction capabilities even under sparse sample conditions.

[0009] The frequency domain spectral attention module designed in this application uses frequency points as independent tokens and models the inter-spectral dependencies through a multi-head self-attention network. This avoids the gradient discontinuity problem caused by directly optimizing the wrapper phase in traditional frequency domain methods. It can reconstruct the high-frequency seasonal patterns formed by the superposition of multiple scheduled maintenance cycles such as A-check, C-check, and D-check with high fidelity. With the addition of graph structure sparse regularization constraints, the learned causal topology has the physical interpretability of aviation maintenance, and finally achieves a comprehensive improvement in the accuracy, robustness, and reliability of aviation material demand prediction. Attached Figure Description

[0010] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 This is a diagram illustrating the overall design framework of the aircraft material demand forecasting model in the embodiments of this application. Figure 2 This is a flowchart of the prediction process for the aircraft material demand prediction model in the embodiments of this application; Figure 3 This is a flowchart illustrating the steps of the aircraft material demand forecasting method that integrates multi-level decomposition and dynamic time-delay causal spectrum learning in the embodiments of this application. Detailed Implementation

[0012] This application provides a method for predicting aircraft material demand by integrating multi-level decomposition and dynamic time-delay causal spectrum learning. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data used can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0013] To facilitate understanding, in conjunction with, for example Figure 1 The overall design framework of the aircraft material demand forecasting model of this application is shown below. The specific process of the embodiments of this application is described below, as follows: Figure 2 and Figure 3 The embodiment of this application shows a method for predicting aircraft material demand that integrates multi-level decomposition and dynamic time-delay causal spectrum learning, including:

[0014] Step S1: Obtain multivariate time series data of aircraft materials, apply the moving average operator layer by layer according to the decreasing smooth window scale through the multi-level recursive residual decomposition module, extract the trend component of the corresponding scale from the upper residual and pass the remaining residual level by level, and finally obtain multiple trend components of different scales and a high-frequency seasonal residual component.

[0015] The calculation process of the multi-level recursive residual decomposition module is as follows: Let the initial residual be... Equal to the input sequence For the first The layers are calculated sequentially according to the following formula: , ;in, Represents the input sequence. Presentation layer, with values ​​ranging from 1 to... Positive integers between Indicates the number of decomposition layers. Indicates the first The length of the moving average window used in multi-level recursive residual decomposition, i.e., the smoothing scale. Indicates the window length is The moving average operator, Indicates the first Scale trend components, This represents the updated residual, and the smoothing window scales for each layer satisfy the following: The final high-frequency seasonal residual is: .

[0016] Among them, the number of decomposition layers The range of values ​​for is: The smoothing window size decreases proportionally for each layer, by default: .

[0017] Among them, the smooth window scale of each layer The determination follows these principles: First-level smooth window scale The longest period length of the input sequence is set, which includes the sampling length corresponding to the annual trend; the scales of subsequent smoothing windows are proportionally proportional. Decreasing, that is: ,in: ,default ;common ratio The value of ensures sufficient frequency bandwidth separation between adjacent layer scales to suppress mode aliasing between trend components at different scales.

[0018] Specifically, one of the technical problems to be solved by this application is that the single-scale time series decomposition strategy commonly used in existing aircraft material demand forecasting methods cannot simultaneously meet the dual requirements of long-term trend smoothness and peak fidelity of sudden demand, resulting in the overlapping of multi-frequency features and thus reducing forecast accuracy.

[0019] To this end, this application provides a time-series structured separation mechanism based on multi-level recursive residual decomposition as the first step in the overall prediction method. Specifically, after acquiring multivariate aircraft material time-series data, the standardized input sequence is first sent to the multi-level recursive residual decomposition module. The core idea of ​​the multi-level recursive residual decomposition module is to apply a moving average operation to the sequence layer by layer according to a smooth window scale that decreases from large to small, thereby separating the trend components of different frequency bands from coarse to fine, and retaining the remaining high-frequency components as seasonal residuals.

[0020] In engineering implementation, the initial residual is set to equal the original input sequence. For the first level of decomposition, a larger smoothing window scale is selected. This scale is usually determined based on the longest periodicity in the aircraft material consumption sequence, such as the sampling length corresponding to the consumption baseline drift caused by annual fleet growth. Applying a moving average operator at this scale to the residuals of this level extracts the smoothest long-term trend component, which reflects the slowly changing baseline such as fleet expansion and overall maintenance workload increase. Subsequently, this trend component is subtracted from the current residuals to obtain the updated residuals, which have eliminated the slowest drift component. Then, the second level of decomposition is entered. At this time, the smoothing window scale used is significantly smaller than that of the first level, usually decreasing by about half. A moving average is applied again to the residuals of the previous level to extract the trend component at the mid-frequency scale, which corresponds to structural migration characteristics such as flight season switching and mid-term adjustment of maintenance strategies.

[0021] Repeat the above recursive process, with each layer removing a finer-scale trend from the residual of the previous layer, until the preset number of decomposition layers is completed; through this layer-by-layer stripping, the final remaining high-frequency residual is the seasonal component containing characteristics such as scheduled maintenance triggering cycles and sudden fault disturbances.

[0022] It should be noted that the smoothing window scales of each layer should maintain a decreasing relationship, and the window size should be selected so that the frequency passbands of adjacent layers maintain an appropriate interval as much as possible, thereby suppressing mode aliasing between trend components of different scales. In the preferred embodiment of this application, the number of decomposition layers can be selected between two and five, with a three-layer structure adopted by default. The window scales of each layer decrease by a common ratio of approximately 0.5. The output of the above-mentioned multi-level recursive residual decomposition module includes multiple trend components of different scales and a single high-frequency seasonal residual component. The former is sent to the subsequent time-delay-aware causal graph structure learning module for trend modeling, while the latter is sent to the frequency domain spectral attention module for fine reconstruction of seasonal features.

[0023] Therefore, this application eliminates the mutual interference between different frequency components from a structural perspective through multi-level recursive residual decomposition, providing a clean and hierarchical input for subsequent dedicated modeling channels, thereby effectively improving the accuracy of aerospace material demand forecasting under complex dynamic conditions.

[0024] Step S2: Input the trend components at each scale into the time-delay-aware causal graph structure learning module. The time-delay-aware causal graph structure learning module learns the probability time-delay distribution for each pair of directed variable nodes. Based on the probability time-delay distribution, it performs inner product calculation on the current node features and the time-delay-weighted historical node features to construct a dynamic causal adjacency matrix. It then performs bidirectional graph convolution propagation on the dynamic causal adjacency matrix to update the node representation. Finally, it adaptively weights and fuses the linear baseline branch and the graph correction branch to output the trend prediction results at each scale.

[0025] In the time-delay-aware causal graph structure learning module, each pair of directed variable nodes... Learning probability time delay distribution The method is as follows: using two learnable low-rank matrices: Build node-based basic interaction scores: Learnable time-delay embedding vectors Projected onto the time-delay space and normalized using Softmax, we obtain: Dynamic causal edge connection strength The calculation formula is: ; in, and Represents a node. Represents a discrete time offset index. Represents a learnable time-delay embedding vector. This represents the number of variables in a multivariate time series. The embedding dimension represents the node feature. These are static, trainable, low-level interaction parameters prior to learning the time-delay distribution; they reflect the variables. For variables The overall potential impact and Representing nodes respectively exist Time and Node exist Characteristics of time, The inner product is represented by the causal adjacency matrix: ,in, This represents the Sigmoid activation function.

[0026] Among them, the maximum time delay step size of the probability time delay distribution The value is set according to the lag period of the external driving factors of aviation material demand response, and the range is 3 to 30.

[0027] The adaptive weighted fusion method of the linear baseline branch and the graph correction branch is as follows: Let the causal enhancement feature be: Then the linear baseline branch output is: ,in: This represents a fully connected layer; the graph correction branch performs a linear projection of the causal enhancement features to obtain the correction term. ; final The scale trend prediction is as follows: ;in, This indicates the batch size, which is the number of samples processed in one forward propagation. This indicates the prediction step size, which is the number of future time steps that need to be predicted. This represents the weight matrix of the fully connected layer in the linear baseline branch, with dimension 1. , This represents a learnable fusion vector. This represents element-wise product; where lin represents the linear baseline branch, graph represents the graph correction branch, and trend represents the trend component.

[0028] Specifically, another technical problem that this application aims to solve is that existing graph neural network methods generally assume that the influence between variables is instantaneous, which cannot characterize the lag response effect that is common in the consumption of aircraft materials. For example, the increase in flight hours often only manifests as an increase in spare parts demand after several days or even weeks. Ignoring this time lag will not only introduce spurious correlations, but also lose key historical driving information.

[0029] To this end, this application constructs a dynamic causal graph with time-lag information for each scale's trend component in the time-lag-aware causal graph structure learning module, thereby achieving explicit modeling of lag dependencies. Specifically, the input to the time-lag-aware causal graph structure learning module is a node feature matrix formed by linear projection of a trend component at a certain scale obtained from multi-level recursive residual decomposition. Each variable node represents a type of aviation material or external driving factor, and the feature dimension is a preset embedding size. To learn the directed causal dependencies between variables and their lag steps, the time-lag-aware causal graph structure learning module first maintains a learnable low-level interaction parameter for each pair of nodes. This parameter reflects the overall influence potential of the source node on the target node and is independent of the specific lag time. Simultaneously, for each possible lag step... The time-delay-aware causal graph structure learning module employs a learnable scalar parameter that encodes the importance of the lag step. For a given pair of nodes, the underlying interaction parameters are multiplied by the scalar parameter corresponding to each lag step, and then normalized to obtain a discrete probability distribution. This distribution represents the probability that the historical state of the source node will causally influence the current state of the target node at different lag steps. Next, the time-delay-aware causal graph structure learning module uses this probability distribution to perform weighted aggregation of the historical features of the source node: for each candidate lag step, the inner product similarity between the features of the target node at the current moment and the features of the source node at the corresponding past moment is calculated, and then weighted and summed using the probability value corresponding to that lag step, thus obtaining the dynamic causal edge connection strength.

[0030] After performing the above operations on all node pairs, the causal adjacency matrix at the current time is formed, and its value is then limited to a reasonable range by a nonlinear activation function. On this basis, the time-delay-aware causal graph structure learning module performs bidirectional graph convolutional propagation: using row-normalized and column-normalized adjacency matrices respectively, it simulates two information flows: driving others and being driven by others, and aggregates the features of neighboring nodes to the current node, thereby obtaining enhanced features that integrate time-delay causal dependencies.

[0031] The specific mathematical definition of bidirectional graph convolution propagation is: Let the input node feature matrix be: The dynamic causal adjacency matrix is ​​as follows: First, calculate the row-normalized adjacency matrix: Normalized adjacency matrix ,in, for A row-degree diagonal matrix, for Given a row-degree diagonal matrix, the bidirectional graph convolution propagation is defined as: Where row represents a row and col represents a column. and Let be a learnable weight matrix, and: , For non-linear activation functions, such as ReLU; This is a characteristic of causal reinforcement.

[0032] Subsequently, the time-delay-aware causal graph structure learning module employs a hybrid prediction strategy to output trend predictions at this scale. Specifically, on one hand, a linear baseline branch is set up to directly perform a fully connected linear mapping on the enhanced features. This branch does not introduce any nonlinear activation, and its output serves as a globally stable trend anchor, ensuring the robustness of the prediction under sparse sample conditions. On the other hand, a graph correction branch is set up to perform another linear projection on the enhanced features, outputting a correction term to compensate for local nonlinear biases. The outputs of the two branches are then element-wise weighted and summed through a learnable fusion vector to form the final trend prediction at this scale.

[0033] It should be noted that the linear baseline branch provides a linear estimate based on the overall historical drift, while the graph correction branch focuses on capturing dynamic local adjustments caused by time-delay causality that are difficult for linear models to fit. The two work together to enable the model to maintain high-precision trend prediction capabilities even in complex scenarios where there is both long-term dependence on aircraft material demand and sudden disturbances.

[0034] Through the above mechanism, this application organically integrates time delay information into the graph structure learning and message passing process, thereby effectively eliminating spurious correlations and significantly improving the ability of aircraft material demand forecasting to model the characteristics of delayed response.

[0035] Step S3: Input the high-frequency seasonal residual components into the frequency domain spectrum attention module. The frequency domain spectrum attention module performs a real-number fast Fourier transform on the high-frequency seasonal residual components to obtain a complex spectrum. Each frequency point is treated as an independent token and superimposed with a learnable frequency domain position code before being fed into a multi-head self-attention network to model the inter-spectral dependencies in the frequency dimension. Then, the time-domain seasonal sequence is reconstructed by an inverse real-number fast Fourier transform and linearly mapped to the prediction step size, outputting the seasonal prediction result.

[0036] In the frequency domain spectral attention module, each frequency point is treated as an independent token by using the complex spectrum obtained from the real-number fast Fourier transform: Perform dimensional rearrangement, shifting the frequency axis to the sequence length dimension, and concatenate the real and imaginary parts to obtain a real tensor: Each frequency token corresponds to a token of length [length missing]. The spectral eigenvectors are, in order, the real parts of all variable channels, followed by the imaginary parts of all variable channels; the superimposed learnable frequency domain positional encoding: Sine / cosine encoding is used for initialization and set as learnable parameters; a multi-head self-attention network models the inter-spectral interactions of the token sequence along the frequency dimension, where... The input sequence represents the time length, i.e., the number of time steps for historical observations; tok represents the tokenized result; model represents the hidden dimension of the model; and freq represents the frequency domain. It is a learnable frequency domain position code.

[0037] Specifically, another technical problem that this application aims to solve is that existing frequency domain prediction methods directly optimize the wrapped phase of complex spectrum, while the phase value has numerical jumps near its periodic boundary. This discontinuity leads to inconsistent gradients or even a sudden increase in gradient magnitude, making it difficult to stably model the multi-period superposition characteristics triggered by regular maintenance such as A-check, C-check and D-check in the demand for aviation materials.

[0038] To address this, this application designs a frequency-domain spectral attention module. After transforming the high-frequency seasonal residuals to the frequency domain, each frequency point is used as an independent token. A multi-head self-attention network is used to model the inter-spectral dependencies in the frequency dimension, thus avoiding direct optimization of the phase value. In its implementation, the module first receives the high-frequency seasonal residual components output from the multi-level recursive residual decomposition module. This component is a three-dimensional tensor in the real number domain, corresponding to the batch dimension (multiple independent sequences processed at once), the variable dimension (different types of aviation materials or external driving factors), and the time dimension (historical observation time). The module performs real-number fast operations on this tensor along the time dimension. The rapid Fourier transform is used to obtain the complex spectrum. The frequency axis of this complex spectrum is approximately half the length of the original time plus one. Each frequency point corresponds to a specific vibration frequency and carries the complex results of all variable channels at that frequency. The real part represents the amplitude contribution of the cosine component, and the imaginary part represents the amplitude contribution of the sine component. Together, they determine the original phase information of the frequency component. In order to adapt the frequency domain data to the processing framework of the attention mechanism, the module performs dimensional rearrangement on the complex spectrum: the frequency axis is moved to the position of the sequence length dimension, and the real and imaginary parts of each variable at each frequency point are decomposed and concatenated into a real vector.

[0039] Specifically, for each frequency point, the real parts of all variable channels are arranged sequentially, and then the imaginary parts of all variable channels are concatenated to form a real feature vector with a length twice the number of variables. Each such vector represents a token for a frequency point. The dimension of the constructed token sequence is the batch size multiplied by the frequency axis length multiplied by twice the number of variables. Since the attention mechanism itself does not have the ability to perceive the token order, and the order on the frequency axis from low frequency to high frequency implies important physical priors, such as low frequency corresponding to long-term periods and high frequency corresponding to short-term fluctuations, the module additionally introduces a learnable frequency domain position encoding. The encoding is initialized using sine and cosine functions to provide initial sequence information, and is adaptively fine-tuned during model training. It is then superimposed on the aforementioned token sequence, enabling the model to distinguish the positional relationships of different frequency points. Next, the module maps the token sequence with positional encoding to a preset model hidden dimension through linear projection, and then feeds it into a multi-head self-attention network. This network calculates the attention weights between each frequency point along the frequency dimension, enabling each frequency point to aggregate information from other frequency points, thereby capturing complex frequency interaction patterns such as the coupling relationship between the fundamental frequency and its harmonics and cross-band energy redistribution.

[0040] It is important to emphasize that this attention network does not directly modify the phase value of each frequency point, but evolves the spectral structure by adjusting the mixing weights between different frequency points. Therefore, it fundamentally avoids the optimization difficulties caused by the discontinuity of the wrapping phase at the boundary. After one or more layers of self-attention processing, the module restores the evolved token sequence to the same feature dimension as the input through linear transformation and reorganizes it into the form of a complex spectrum. That is, it restores the complex value of each variable at each frequency point according to the arrangement of the real and imaginary parts, and then performs an inverse real fast Fourier transform to map it from the frequency domain back to the time domain to obtain the reconstructed seasonal sequence. Finally, the module applies a learnable linear mapping to the time-domain seasonal sequence, projects it onto the specified prediction step size, and outputs the final seasonal aircraft material prediction result.

[0041] Through the above mechanism, this application transforms the seasonal modeling problem in the frequency domain into a stable, attention-based sequence-to-sequence learning problem. This not only preserves the frequency domain's inherent ability to tightly represent periodic signals but also overcomes the instability of phase optimization in traditional frequency domain methods. As a result, it can reconstruct the high-frequency seasonal patterns formed by the superposition of multiple scheduled maintenance cycles in the demand for aviation materials with high fidelity.

[0042] Step S4: Aggregate the trend forecast results at each scale with the seasonal forecast results to obtain standardized forecast results, and then output the final aircraft material demand forecast value through inverse normalization transformation.

[0043] The method for aggregating trend forecast results at various scales with seasonal forecast results is as follows: ;in, This represents the learnable scale confidence vector. This represents element-wise multiplication; the inverse normalization transformation is: ,in, and represents the standard deviation and mean of the records in the preprocessing stage, respectively; season represents the seasonal component; norm and real represent the standardized predicted value and the denormalized real-scale predicted value, respectively.

[0044] The aircraft material demand forecasting method, which integrates multi-level decomposition and dynamic time-delay causal spectrum learning, also includes an aircraft material demand forecasting model training step, during which the following loss function is used: ,in, The regularization balance coefficient is represented by reg, and the regularization term is represented by reg. The graph structure regularization term is used to impose sparsity constraints on the causal adjacency matrix to suppress the generation of redundant causal edges.

[0045] Specifically, another technical problem that this application aims to solve is that the contribution of trend components at different scales to the final prediction results of aircraft materials varies. Simply adding them with equal weights cannot reflect the differences in importance of each scale under different operating conditions. At the same time, if the learned causal graph structure is not constrained, it is easy to generate a large number of redundant connections, which reduces the interpretability and generalization performance of the model.

[0046] To address this, this application introduces a learnable scale confidence vector into the multi-scale aggregation and output module and designs a loss function with sparse regularization to achieve adaptive weighting of the contributions of each component and physical interpretability constraints of the causal topology. In specific implementation, the multi-scale prediction aggregation and output module first receives the trend prediction results of each scale from the time-delay-aware causal graph structure learning module and the seasonal prediction results from the frequency domain spectral attention module. These prediction results have all been uniformly projected to the same prediction step size and variable channel number, so they can be directly combined element-wise. In order for the model to adaptively learn the importance of trend components at different scales, the module maintains a learnable scale confidence vector for each scale. The length of this vector is equal to the variable channel number, that is, different types of aerospace materials are assigned independent weights. During aggregation, the trend prediction result of each scale is multiplied element-wise with the confidence vector of that scale, and then the trend prediction results after weighting all scales are added element-wise with the seasonal prediction results to obtain the final prediction value under the standardized scale. Since the input data has already undergone mean and variance standardization during the preprocessing stage, the standardized predicted value does not reflect the actual demand for aircraft materials. Therefore, the module further performs an inverse normalization transformation: using the standard deviation and mean recorded in the preprocessing stage, the standardized predicted value is multiplied element by element by the standard deviation and then added back to the mean, thereby restoring the prediction result to the original data scale and outputting the final predicted value of actual aircraft material demand. The above process achieves adaptive fusion and dimensional recovery of multi-scale information. Based on this, to ensure the effectiveness of model training and the interpretability of the learned causal graph structure, this application further defines the model training steps. During training, the model uses an end-to-end approach for parameter optimization. The loss function consists of two parts: the first part is the main loss, i.e., the mean square error between the predicted and true values, used to measure the model's prediction accuracy; the second part is a graph structure regularization term, which acts on the causal adjacency matrix output by the time-delay-aware causal graph structure learning module, imposing sparsity constraints on it. This regularization term suppresses the generation of redundant causal edges, encouraging the model to retain only dependency edges between spare parts pairs with actual physical repair relationships. The regularization balance coefficient is used to adjust the relative weights of the two losses.

[0047] Through joint optimization, the model can learn a sparse causal topology with interpretable physical properties of aerospace materials while pursuing high prediction accuracy, thereby improving the model's credibility and engineering deployability in aviation maintenance and support scenarios.

[0048] By coordinating the above steps, this application can effectively improve the accuracy of aircraft material demand forecasting. In summary, this application, through multi-scale adaptive weighted aggregation and sparse regularization constraints, enables the entire forecasting framework to output high-precision, interpretable aircraft material demand forecasting results under complex dynamic conditions, providing a reliable basis for subsequent spare parts procurement and maintenance planning decisions.

[0049] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the system and unit described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0050] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0051] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application 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. Such 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 this application.

Claims

1. A method for predicting aircraft material demand that integrates multi-level decomposition and dynamic time-delay causal spectrum learning, characterized in that, The method includes: Step S1: Obtain multivariate time series data of aircraft materials, apply the moving average operator layer by layer according to the decreasing smooth window scale through the multi-level recursive residual decomposition module, extract the trend component of the corresponding scale from the upper residual and pass the remaining residual level by level, and finally obtain multiple trend components of different scales and a high-frequency seasonal residual component. Step S2: Input the trend components at each scale into the time-delay-aware causal graph structure learning module. The time-delay-aware causal graph structure learning module learns the probability time-delay distribution for each pair of directed variable nodes. Based on the probability time-delay distribution, it performs inner product calculation on the current node features and the time-delay-weighted historical node features to construct a dynamic causal adjacency matrix. It then performs bidirectional graph convolution propagation on the dynamic causal adjacency matrix to update the node representation. Finally, it adaptively weights and fuses the linear baseline branch and the graph correction branch to output the trend prediction results at each scale. Step S3: Input the high-frequency seasonal residual component into the frequency domain spectrum attention module. The frequency domain spectrum attention module performs a real-number fast Fourier transform on the high-frequency seasonal residual component to obtain a complex spectrum. Each frequency point is treated as an independent token and superimposed with a learnable frequency domain position code before being fed into a multi-head self-attention network to model the inter-spectral dependency in the frequency dimension. Then, the time-domain seasonal sequence is reconstructed by the inverse real-number fast Fourier transform and linearly mapped to the prediction step size, and the seasonal prediction result is output. Step S4: Aggregate the trend forecast results at each scale with the seasonal forecast results to obtain standardized forecast results, and then output the final aircraft material demand forecast value through inverse normalization transformation.

2. The aircraft material demand forecasting method integrating multi-level decomposition and dynamic time-delay causal spectrum learning according to claim 1, characterized in that, The calculation process of the multi-level recursive residual decomposition module is as follows: Let the initial residuals be... Equal to the input sequence X, for the i-th The layers are calculated sequentially according to the following formula: , ; Where X represents the input sequence, m represents the layer, taking a positive integer between 1 and M, and M represents the number of decomposition layers. Indicates the first The length of the moving average window used in multi-level recursive residual decomposition, i.e., the smoothing scale. Indicates the window length is The moving average operator, Indicates the first Scale trend components, This represents the updated residual, and the smoothing window scale of each layer satisfies... Ultimately, high-frequency seasonal residuals .

3. The aircraft material demand forecasting method integrating multi-level decomposition and dynamic time-delay causal spectrum learning according to claim 1, characterized in that, In the time-delay-aware causal graph structure learning module, each pair of directed variable nodes... Learning probability time delay distribution The method is as follows: Using two learnable low-rank matrices Build node-to-basic interaction score Through learnable time-delay embedding vectors Projected onto the time-delay space and normalized using Softmax, we obtain: ; Dynamic causal edge connection strength The calculation formula is: ; in, and Represents a node. Represents a discrete time offset index. Let C represent the learnable time-delay embedding vector, C represent the number of variables in the multivariate time series, and d represent the embedding dimension of the node features. These are static, trainable, low-level interaction parameters prior to learning the time-delay distribution; they reflect the variables. For variables The overall potential impact Representing nodes respectively exist Time and Node exist Characteristics of time, Represents the inner product, causal adjacency matrix , This represents the Sigmoid activation function.

4. The aircraft material demand forecasting method integrating multi-level decomposition and dynamic time-delay causal spectrum learning according to claim 1, characterized in that, The adaptive weighted fusion method of the linear baseline branch and the graph correction branch is as follows: Let the causal enhancement feature be Then the linear baseline branch output ,in, This represents a fully connected layer; the graph correction branch performs a linear projection of the causal enhancement features to obtain the correction term. The final trend prediction at the m-th scale is: ; Where B represents the batch size, i.e. the number of samples processed in one forward propagation, and H represents the prediction step size, i.e. the number of future time steps to be predicted. This represents the weight matrix of the fully connected layer in the linear baseline branch, with dimension 1. ω represents the learnable fusion vector, and ⊙ represents the element-wise product; Wherein, lin represents the linear baseline branch, graph represents the graph correction branch, and trend represents the trend component.

5. The aircraft material demand forecasting method integrating multi-level decomposition and dynamic time-delay causal spectrum learning according to claim 1, characterized in that, In the frequency domain spectral attention module, each frequency point is treated as an independent token in the following way: Complex spectrum obtained by fast Fourier transform of real numbers Perform dimensional rearrangement, shifting the frequency axis to the sequence length dimension, and concatenate the real and imaginary parts to obtain a real tensor. Each frequency token corresponds to a spectral feature vector of length 2C; Superimposed learnable frequency domain position coding Sine / cosine encoding is used for initialization and set as learnable parameters. A multi-head self-attention network models the interspectral interactions of the token sequence along the frequency dimension, where L represents the time length of the input sequence, i.e., the number of time steps of historical observations, tok represents the tokenized result, model represents the hidden dimension of the model, and freq represents the frequency domain. It is a learnable frequency domain position code.

6. The aircraft material demand forecasting method integrating multi-level decomposition and dynamic time-delay causal spectrum learning according to claim 4, characterized in that, The method for aggregating trend forecasts at various scales with seasonal forecasts is as follows: ;in, This represents the learnable scale confidence vector. Represents element-wise product; inverse normalization transformation is , and represents the standard deviation and mean of the records in the preprocessing stage, respectively; season represents the seasonal component; norm and real represent the standardized predicted value and the denormalized real-scale predicted value, respectively.

7. The aircraft material demand forecasting method integrating multi-level decomposition and dynamic time-delay causal spectrum learning according to claim 3, characterized in that, The method also includes a training step for an aircraft material demand prediction model, during which the following loss function is used: ,in, The regularization balance coefficient is represented by reg, and the regularization term is represented by reg. The graph structure regularization term is used to impose sparsity constraints on the causal adjacency matrix to suppress the generation of redundant causal edges.

8. The aircraft material demand forecasting method integrating multi-level decomposition and dynamic time-delay causal spectrum learning according to claim 2, characterized in that, The range of values ​​for the number of decomposition layers M is: The window size of each layer decreases proportionally, by default. , , , .

9. The aircraft material demand forecasting method integrating multi-level decomposition and dynamic time-delay causal spectrum learning according to claim 3, characterized in that, Maximum time delay step size of probability time delay distribution The value is set according to the lag period of the external driving factors of aviation material demand response, and the range is 3 to 30.

10. The aircraft material demand forecasting method integrating multi-level decomposition and dynamic time-delay causal spectrum learning according to claim 2, characterized in that, Smooth window scale of each layer The determination follows these principles: First-level smoothing window scale The longest period is set according to the length of the longest period of the input sequence, where the longest period includes the sampling length corresponding to the annual trend; The scales of subsequent smoothing windows are proportionally proportional. Decreasing, that is ,in The default value is r=0.5; The value of the common ratio r ensures that there is sufficient frequency bandwidth separation between adjacent layer scales to suppress mode aliasing between trend components at different scales.

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