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In order to enhance the performance of Transformer models for long-term multivariate forecasting while minimizing computational demands, this paper introduces the Joint Time-Frequency Domain Transformer (JTFT). JTFT combines time and frequency domain representations to make predictions. The frequency domain representation efficiently extracts multi-scale dependencies while maintaining sparsity by utilizing a small number of learnable frequencies. Simultaneously, the time domain (TD) representation is derived from a fixed number of the most recent data points, strengthening the modeling of local relationships and mitigating the effects of non-stationarity. Importantly, the length of the representation remains independent of the input sequence length, enabling JTFT to achieve linear computational complexity. Furthermore, a low-rank attention layer is proposed to efficiently capture cross-dimensional dependencies, thus preventing performance degradation resulting from the entanglement of temporal and channel-wise modeling. Experimental results on six real-world datasets demonstrate that JTFT outperforms state-of-the-art baselines in predictive performance.

Atmospheric powered descent guidance can be solved by successive convexification; however, its onboard application is impeded by the sharp increase in computation caused by nonlinear aerodynamic forces. The problem has to be converted into a sequence of convex subproblems instead of a single convex problem when aerodynamic forces are ignored. Besides, each subproblem is significantly more complicated, which increases computation. A fast real-time interior point method was presented to solve the correlated convex subproblems onboard in the work. The main contributions are as follows: Firstly, an algorithm was proposed to accelerate the solution of linear systems that cost most of the computation in each iterative step by exploiting the specific problem structure. Secondly, a warm-starting scheme was introduced to refine the initial value of a subproblem with a rough approximate solution of the former subproblem, which lessened the iterative steps required for each subproblem. The method proposed reduced the run time by a factor of 9 compared with the fastest publicly available solver tested in Monte Carlo simulations to evaluate the efficiency of solvers. Runtimes on the order of 0.6 s are achieved on a radiation-hardened flight processor, which demonstrated the potential of the real-time onboard application., Comment: The paper is accepted by IEEE Transactions on Aerospace and Electronic Systems, 2023

Traditional supervised bearing fault diagnosis methods rely on massive labelled data, yet annotations may be very time-consuming or infeasible. The fault diagnosis approach that utilizes limited labelled data is becoming increasingly popular. In this paper, a Wavelet Transform (WT) and self-supervised learning-based bearing fault diagnosis framework is proposed to address the lack of supervised samples issue. Adopting the WT and cubic spline interpolation technique, original measured vibration signals are converted to the time-frequency maps (TFMs) with a fixed scale as inputs. The Vision Transformer (ViT) is employed as the encoder for feature extraction, and the self-distillation with no labels (DINO) algorithm is introduced in the proposed framework for self-supervised learning with limited labelled data and sufficient unlabeled data. Two rolling bearing fault datasets are used for validations. In the case of both datasets only containing 1% labelled samples, utilizing the feature vectors extracted by the trained encoder without fine-tuning, over 90\% average diagnosis accuracy can be obtained based on the simple K-Nearest Neighbor (KNN) classifier. Furthermore, the superiority of the proposed method is demonstrated in comparison with other self-supervised fault diagnosis methods., Comment: 20 pages, 9 figures, 6 tables

This paper studies the worst case iteration complexity of an infeasible interior point method (IPM) for seconder order cone programming (SOCP), which is more convenient for warmstarting compared with feasible IPMs. The method studied bases on the homogeneous and self-dual model and the Monteiro-Zhang family of searching directions. Its worst case iteration complexity is $O\left(k^{1/2}\log\left(\epsilon^{-1}\right)\right)$, to reduce the primal residual, dual residual, and complementarity gap by a factor of $\epsilon$, where $k$ is the number of cone constraints. The result is the same as the best known result for feasible IPMs. The condition under which warmstarting improves the complexity bound is also studied.

Fault diagnosis of rotating machinery is an important engineering problem. In recent years, fault diagnosis methods based on the Convolutional Neural Network (CNN) and Recurrent Neural Network (RNN) have been mature, but Transformer has not been widely used in the field of fault diagnosis. To address these deficiencies, a new method based on the Time Series Transformer (TST) is proposed to recognize the fault mode of bearings. In this paper, our contributions include: Firstly, we designed a tokens sequences generation method which can handle data in 1D format, namely time series tokenizer. Then, the TST combining time series tokenizer and Transformer was introduced. Furthermore, the test results on the given dataset show that the proposed method has better fault identification capability than the traditional CNN and RNN models. Secondly, through the experiments, the effect of structural hyperparameters such as subsequence length and embedding dimension on fault diagnosis performance, computational complexity and parameters number of the TST is analyzed in detail. The influence laws of some hyperparameters are obtained. Finally, via t-Distributed Stochastic Neighbor Embedding (t-SNE) dimensionality reduction method, the feature vectors in the embedding space are visualized. On this basis, the working pattern of TST has been explained to a certain extent. Moreover, by analyzing the distribution form of the feature vectors, we find that compared with the traditional CNN and RNN models, the feature vectors extracted by the method in this paper show the best intra-class compactness and inter-class separability. These results further demonstrate the effectiveness of the proposed method., Comment: 17 pages, 10 figures

We present the remote stochastic gradient (RSG) method, which computes the gradients at configurable remote observation points, in order to improve the convergence rate and suppress gradient noise at the same time for different curvatures. RSG is further combined with adaptive methods to construct ARSG for acceleration. The method is efficient in computation and memory, and is straightforward to implement. We analyze the convergence properties by modeling the training process as a dynamic system, which provides a guideline to select the configurable observation factor without grid search. ARSG yields $O(1/\sqrt{T})$ convergence rate in non-convex settings, that can be further improved to $O(\log(T)/T)$ in strongly convex settings. Numerical experiments demonstrate that ARSG achieves both faster convergence and better generalization, compared with popular adaptive methods, such as ADAM, NADAM, AMSGRAD, and RANGER for the tested problems. In particular, for training ResNet-50 on ImageNet, ARSG outperforms ADAM in convergence speed and meanwhile it surpasses SGD in generalization., Comment: The generalization is improved by modifying the preconditioner. For training ResNet-50 on ImageNet, ARSG outperforms ADAM in convergence speed and meanwhile it surpasses SGD in generalization. We also present a convergence bound in non-convex settings