Bearing vibration data are often contaminated with noise, which is detrimental to equipment fault diagnosis and predictive maintenance. Denoising bearing vibration data is crucial. Traditional denoising methods have certain limitations. For instance, when employing wavelet denoising, fixed basis functions may fail to perfectly match all signal structures, potentially compromising denoising accuracy. Similarly, when utilizing data-driven tight frame (DDTF) denoising, the learned basis, due to the lack of noise constraints, may incur a risk of overfitting. To optimize denoising performance in both scenarios, this paper proposes a method that combines wavelet transform and DDTF dictionary learning to extract noise based on a doubly sparse dictionary. The specific approach involves mutually cascading the wavelet transform and DDTF. After applying the wavelet transform to the noisy signal, multi-layer wavelet sparse coefficients are obtained. DDTF processing is then applied to each layer of wavelet sparse coefficients. Subsequent inverse transformation achieves noise suppression. This method integrates the structural constraint capability of wavelet decomposition with the learning capability of DDTF, thereby mitigating their respective limitations to some extent. The denoised data are fed into a residual network model, and training results confirm that the proposed method achieves the best classification performance. Experimental results from both data denoising and deep learning classification demonstrate that the proposed method exhibits superior denoising performance. Although the algorithm structure of this method is more complex compared to other approaches, it is meaningful in scenarios where high-precision denoising is required.

In this paper, the disjunctive and conjunctive lattice piecewise affine (PWA) approximations of explicit linear model predictive control (MPC) are proposed. Training data consisting of states and corresponding affine control laws are generated in a control invariant set, and redundant sample points are removed to simplify the construction of lattice PWA approximations. Resampling is proposed to guarantee the equivalence of lattice PWA approximations and optimal MPC control law at the sample points. Under certain conditions, the disjunctive lattice PWA approximation constitutes a lower bound, while the conjunctive version formulates an upper bound of the original optimal control law. The equivalence of the two lattice PWA approximations then guarantees error-free approximations in the domain of interest, which is tested through a statistical guarantee. The performance of the proposed approximation strategy is tested through two simulation examples, and the results show that error-free lattice PWA approximations can be obtained with low offline complexity and small storage requirements. Besides, the online complexity is less compared with the state-of-the-art method.

Audio magnetotelluric (AMT) is commonly used in mineral resource exploration. However, the weak energy of AMT signals makes them susceptible to being overwhelmed by noise, leading to erroneous geophysical interpretations. In recent years, deep learning has been applied to AMT denoising and has shown better denoising performance compared to traditional methods. However, current deep learning denoising methods overlook the characteristics of AMT signals, resulting in reduced denoising accuracy. To enhance the denoising performance of deep learning by better matching the features of AMT signals, we propose a convolutional block attention module (CBAM)-based method for AMT denoising. This method focuses on the features of AMT signals and improves the process from three aspects: 1) in the establishment of the sample set, we adopt a multicomponent form based on the correlation of noise to enable the neural network to explore the potential connections among the components of AMT during the training process, thus constructing a stronger network mapping relationship; 2) in the construction of the neural network, we have introduced the CBAM structure into the residual blocks of the ResNet to enhance the network's feature learning capability by focusing on the characteristics of noise; and 3) in the design of the denoising procedure, we adopt a process of identification before denoising to protect the noise-free data segments from being compromised during the denoising process. Finally, through synthetic, field data experiments, and comparative tests, we demonstrate that our proposed method achieves higher denoising accuracy than some traditional methods and conventional deep learning methods.

Traffic flow (TF) prediction is an important and yet a challenging task in transportation systems, since the TF involves high nonlinearities and is affected by many elements. Recently, neural networks have attracted much attention for TF prediction, but they are commonly black boxes with complex architectures and difficult to be interpreted, e.g., the contributions of specific traffic elements are not explicit, hardly providing informative guidance. In this paper, we aim at addressing more interpretable short-term TF prediction with joint consideration to high accuracy, and thus introduces a pragmatic method by applying the efficient hinging hyperplanes neural network (EHHNN) simply built upon sparse neuron connections. In the proposed method, different traffic factors are incorporated into the inputs, including their spatial-temporal information. Besides the pursuit of accuracy, we further extend the ANOVA decomposition of EHHNNs to the interpretation analysis with specifications to traffic data, in which the contributions concerning specific traffic variables are detected quantitatively. As such, the proposed method firstly applies the EHHNN to filter out more important traffic variables for dimensionality reduction while maintaining accurate prediction. Then, variable interpretation analysis is performed from different perspectives, e.g. to quantitatively investigate the influence of traffic factors and also their spatial-temporal impacts. Therefore, a predictor and an analyzing tool can both be attained for the TF by exerting the flexibility and extending the interpretability of EHHNNs, which is promising to provide informative guidance to future traffic control. Numerical experiments verify the effectiveness and potential of the proposed method in TF prediction and analysis.