Graph Construction Method for GNN-Based Multivariate Time-Series Forecasting

Multivariate time-series forecasting(MTSF)plays an important role in diverse real-world applications.To achieve better accuracy in MTSF,time-series patterns in each variable and interrelationship patterns between variables should be considered together.Recently,graph neural networks(GNNs)has gained much attention as they can learn both patterns using a graph.For accurate forecasting through GNN,a well-defined graph is required.However,existing GNNs have limitations in reflecting the spectral similarity and time delay between nodes,and consider all nodes with the same weight when constructing graph.In this paper,we propose a novel graph construction method that solves aforementioned limitations.We first calculate the Fourier transform-based spectral similarity and then update this similarity to reflect the time delay.Then,we weight each node according to the number of edge connections to get the final graph and utilize it to train the GNN model.Through experiments on various datasets,we demonstrated that the proposed method enhanced the performance of GNN-based MTSF models,and the proposed forecasting model achieve of up to 18.1%predictive performance improvement over the state-of-the-art model.

Multivariate Time Series Forecasting with Transfer Entropy Graph

Multivariate Time Series(MTS)forecasting is an essential problem in many fields.Accurate forecasting results can effectively help in making decisions.To date,many MTS forecasting methods have been proposed and widely applied.However,these methods assume that the predicted value of a single variable is affected by all other variables,ignoring the causal relationship among variables.To address the above issue,we propose a novel end-to-end deep learning model,termed graph neural network with neural Granger causality,namely CauGNN,in this paper.To characterize the causal information among variables,we introduce the neural Granger causality graph in our model.Each variable is regarded as a graph node,and each edge represents the casual relationship between variables.In addition,convolutional neural network filters with different perception scales are used for time series feature extraction,to generate the feature of each node.Finally,the graph neural network is adopted to tackle the forecasting problem of the graph structure generated by the MTS.Three benchmark datasets from the real world are used to evaluate the proposed CauGNN,and comprehensive experiments show that the proposed method achieves state-of-the-art results in the MTS forecasting task.

Machining Error Control by Integrating Multivariate Statistical Process Control and Stream of Variations Methodology

For aircraft manufacturing industries, the analyses and prediction of part machining error during machining process are very important to control and improve part machining quality. In order to effectively control machining error, the method of integrating multivariate statistical process control （MSPC） and stream of variations （SoV） is proposed. Firstly, machining error is modeled by multi-operation approaches for part machining process. SoV is adopted to establish the mathematic model of the relationship between the error of upstream operations and the error of downstream operations. Here error sources not only include the influence of upstream operations but also include many of other error sources. The standard model and the predicted model about SoV are built respectively by whether the operation is done or not to satisfy different requests during part machining process. Secondly, the method of one-step ahead forecast error （OSFE） is used to eliminate autocorrelativity of the sample data from the SoV model, and the T2 control chart in MSPC is built to realize machining error detection according to the data characteristics of the above error model, which can judge whether the operation is out of control or not. If it is, then feedback is sent to the operations. The error model is modified by adjusting the operation out of control, and continually it is used to monitor operations. Finally, a machining instance containing two operations demonstrates the effectiveness of the machining error control method presented in this paper.