Sparse representation-based interpretable algorithm unrolling is one of promising techniques for mechanical anomaly detection. In order to enhance the learning and representation capabilities of the algorithm unrolling model, this article proposes a learnable sparse regularization network (LSR-Net). Instead of imposing explicit regularization constraints on the encoding and dictionary during modeling, two subnetworks are designed to learn prior information:$\mathbf{Net}_{\mathbf{X}}$and$\mathbf{Net}_{\mathbf{D}}$. The model is solved using the half quadratic splitting algorithm, and further unrolls the process of iterative computation into the form of a network. The architecture for encoding learning is structured as input convex neural networks, ensuring LSR-Net can learn meaningful encoding priors. Through the analysis of simulated and experimental data, it has been demonstrated that LSR-Net has strong feature extraction and noise resistance capabilities, and the design of its prior learning architecture is both reasonable and effective. In addition, the visualization of LSR-Net's overall reconstruction and the reconstruction of different dictionary atoms allows for both global and local interpretation of the learning results, thereby providing post hoc interpretability to LSR-Net. The visualization results confirm that LSR-Net is capable of learning features that align with mechanical vibration characteristics.

Lithium-ion batteries are widely used in modern society. Accurate modeling and prognosis are fundamental to achieving reliable operation of lithium-ion batteries. Accurately predicting the end-of-discharge (EOD) is critical for operations and decision-making when they are deployed to critical missions. Existing data-driven methods have large model parameters, which require a large amount of labeled data and the models are not interpretable. Model-based methods need to know many parameters related to battery design, and the models are difficult to solve. To bridge these gaps, this study proposes a physics-informed neural network (PINN), called battery neural network (BattNN), for battery modeling and prognosis. Specifically, we propose to design the structure of BattNN based on the equivalent circuit model (ECM). Therefore, the entire BattNN is completely constrained by physics. Its forward propagation process follows the physical laws, and the model is inherently interpretable. To validate the proposed method, we conduct the discharge experiments under random loading profiles and develop our dataset. Analysis and experiments show that the proposed BattNN only needs approximately 30 samples for training, and the average required training time is 21.5 s. Experimental results on three datasets show that our method can achieve high prediction accuracy with only a few learnable parameters. Compared with other neural networks, the prediction MAEs of our BattNN are reduced by 77.1%, 67.4%, and 75.0% on three datasets, respectively. Our data and code will be available at: https://github.com/wang-fujin/BattNN.

Anomaly detection is a task of identifying samples that significantly differ from the majority. However, most typical anomaly detection methods often prioritize accuracy over interpretability. To address this limitation, we propose an explainable anomaly detection approach using a deep learnable M-band wavelet packet network constructed from the frequency perspective. This network could flexibly decompose a signal into different frequency bands and learn its frequency representation. Then the learnable threshold function is designed to learn the distribution of the normal signal in each frequency band and corrupt the abnormal representation. As a result, the abnormal signal can not be reconstructed from its corrupted representation. We evaluate the proposed method on both simulation data and real acoustic data.

In mechanical anomaly detection, algorithms with higher accuracy, such as those based on artificial neural networks, are frequently constructed as black boxes, resulting in opaque interpretability in architecture and low credibility in results. This article proposes an adversarial algorithm unrolling network (AAU-Net) for interpretable mechanical anomaly detection. AAU-Net is a generative adversarial network (GAN). Its generator, composed of an encoder and a decoder, is mainly produced by algorithm unrolling of a sparse coding model, which is specially designed for feature encoding and decoding of vibration signals. Thus, AAU-Net has a mechanism-driven and interpretable network architecture. In other words, it is ad hoc interpretable. Moreover, a multiscale feature visualization approach for AAU-Net is introduced to verify that meaningful features are encoded by AAU-Net, helping users to trust the detection results. The feature visualization approach enables the results of AAU-Net to be interpretable, i.e., post hoc interpretable. To verify AAU-Net's capability of feature encoding and anomaly detection, we designed and performed simulations and experiments. The results show that AAU-Net can learn signal features that match the dynamic mechanism of the mechanical system. Considering the excellent feature learning ability, unsurprisingly, AAU-Net achieves the best overall anomaly detection performance compared with other algorithms.

Currently, the results of makeup transfer are generally satisfactory in most scenarios. However, the transfer results show that the transfer makeup details is not accurate, such as in blush and lip corners. To this end, we propose a variant model of generative adversarial networks (GAN) based on the embedded block search and the mask attention, called EmAGAN, in which we use a latent space module to supplement the detail information for makeup transfer. The latent space module is a randomly initialized Embedded Block. We quantify the transferred image matrix as a discrete probability value and fill the details of different regions by the closest image information found in the Embedded Block. Another, we propose a novel makeup alignment module, which divides the facial feature regions of the source and reference image into blocks by transformer and extracts the mask of makeup area by image segmentation approach. After that we can perform the makeup alignment by matching the similarity relationship learned from the mask of reference image through attention mechanism. Extensive experiments demonstrate that our proposed method can accurately transfer the makeup details. We use the Frechet Inception Distance (FID) and Peak Signal-to-noise Ratio (PSNR) to qualitatively evaluate the quality and similarity of the generated image. Compared with other related schemes, our method achieves better scores, which are 60.12 and 23.226 respectively.

Evolutionary algorithms (EAs) possess strong problem-solving abilities and have been applied in a wide range of applications. However, they still suffer from a high computational burden and poor generalization ability. To overcome the limitations, numerous studies consider conducting knowledge extraction across distinct optimization task domains. Among these research strands, one representative tributary is evolutionary multitask optimization (EMTO) that aims to resolve multiple optimization tasks simultaneously. The underlying attribute of implicit parallelism for EAs can well incorporate with the framework of EMTO, giving rise to the ascending EMTO studies. This review is intended to present a detailed exposition on the research in the EMTO area. We reveal the core components for designing the EMTO algorithms. Subsequently, we organize the works lying in the fusions between EMTO and traditional EAs. By analyzing the associations for diverse strategies in different branches of EMTO, this review uncovers the research trends and the potentially important directions, with additional interesting real-world applications mentioned.

In recent years, a significant amount of research work has been undertaken to address the problem about prognostic and health management (PHM) systems. Performance degradation assessment, an essential part of PHM systems, is still a challenge. Subspaces, forming a non-Euclidean and curved manifold that is known as Grassmann manifold, are able to capture dynamic behaviors and accommodate the effects of variations. In this paper, we propose a novel local subspace model for performance degradation assessment termed locally linear embedding on Grassmann manifold (GM-LLE), where subspaces are treated as points on Grassmann manifold. Due to the nonstationary property of vibration signal, second generation wavelet package is used to decompose the vibration signal into different levels. Subspaces are modeled by optimal statistical features of different frequency bands, and then GM-LLE is used to assess bearing performance degradation by embedding the subspaces into reproducing kernel Hilbert spaces. Finally, simulated and experimental vibration signals are used to validate the effectiveness of the proposed method. The results show that the proposed method can assess the bearing's degradation effectively, and performs better compared with locally linear embedding.

Many clustering methods have been adopted by personalized e-learning system to find interested groups or common characteristics of members within the same group. However, hard boundary during discretization on collected data or subjective influences was introduced, and corresponding methods were utilized. Aiming at this problem, a fuzzy clustering method based on fuzzy statistic is proposed to cluster the learners according to their personality and learning strategy data collected from an online system. Then, an analysis method based on frequent pattern is introduced to testify the result of the proposed unsupervised clustering methods. The clustering results correspond with viewpoints of pedagogy.