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algorithm unrolling Network With Learnable Sparse Regularization for Interpretable Mechanical Anomaly Detection

IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 2025年第5期21卷 3786-3795页

作者： Chen, Xiyue Wang, Shibin Wang, Shi-ao Ding, Baoqing Yan, Ruqiang Chen, Xuefeng Xi An Jiao Tong Univ Natl Key Lab Aerosp Power Syst & Plasma Technol Xian 710049 Peoples R China Xi An Jiao Tong Univ Sch Mech Engn Xian 710049 Peoples R China

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.

关键词： Convolution Encoding Feature extraction Anomaly detection Dictionaries Convolutional codes Analytical models Predictive models Neural networks Signal processing algorithms algorithm unrolling anomaly detection convolutional dictionary learning (CDL) interpretable neural network

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Wasserstein Distributionally Robust Graph Learning via algorithm unrolling

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2025年 73卷 676-690页

作者： Zhang, Xiang Xu, Yinfei Shao, Mingjie Eldar, Yonina C. Southeast Univ Sch Informat Sci & Engn Nanjing 210096 Peoples R China Chinese Acad Sci Inst Syst Sci Acad Math & Syst Sci AMSS Key Lab Syst & Control Beijing 100149 Peoples R China Weizmann Inst Sci Fac Math & Comp Sci IL-7610001 Rehovot Israel

In this paper, we consider inferring the underlying graph topology from smooth graph signals. Most existing approaches learn graphs by minimizing a well-designed empirical risk using the observed data, which may be prone to data uncertainty that arises from noisy measurements and limited observability. Therefore, the learned graphs may be unreliable and exhibit poor out-of-sample performance. To enhance the robustness to data uncertainty, we propose a smoothness-based graph learning framework from a distributionally robust perspective, which is equivalent to solving an inf - sup problem. However, learning graphs directly in this way is challenging since (i) the inf - sup problem is intractable, and (ii) many parameters need to be manually determined. To address these issues, we first reformulate the inf - sup problem into a tractable one, where robustness is achieved via a regularizer. Theoretically, we show that the regularizer can improve generalization of the proposed graph estimator by bounding the out-of-sample risks. We then propose an algorithm based on the ADMM framework to solve the induced problem and further unroll it into a neural network. All parameters are determined automatically and simultaneously by training the unrolled network. Extensive experiments on both synthetic and real-world data demonstrate that our approach can achieve superior and more robust performance than existing models on different observed signals.

关键词： Graph learning graph signal processing distributionally robust optimization Wasserstein distance algorithm unrolling Graph learning graph signal processing distributionally robust optimization Wasserstein distance algorithm unrolling

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An interpretable algorithm unrolling network inspired by general convolutional sparse coding for intelligent fault diagnosis of machinery

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MEASUREMENT 2025年 244卷

作者： Yuan, Menghan Zeng, Ming Rao, Fengpei He, Zhiyi Cheng, Yiwei China Univ Geosci Sch Mech Engn & Elect Informat Wuhan 430074 Peoples R China China Univ Geosci Shenzhen Res Inst Shenzhen 518057 Peoples R China Changsha Univ Sci & Technol Coll Automot & Mech Engn Changsha 410114 Peoples R China

When applied in Intelligent Fault Diagnosis (IFD) of machinery, most of generic deep learning models lack interpretability in architecture design. From a signal processing perspective, we unroll the Alternating Direction Method of Multipliers (ADMM), the iterative algorithm for a general convolutional sparse coding denoising problem, into a deep neural network called the General ADMM Network (GADMM-Net) using algorithm unrolling. GADMM-Net has an encoder-decoder architecture where the encoder extracts signal features (i.e., sparse coefficients) and the decoder reconstructs denoised signals. As the encoder-decoder architecture is derived from the denoising algorithm, GADMM-Net is interpretable in its backbone architecture and inherits the prior domain knowledge behind the signal denoising problem. Compared with conventional and state-of-the-art IFD models, GADMM-Net performs more excellently in diagnostic accuracy, number of parameters, training set size requirement, and noise robustness. In the IFD task across different operating conditions, GADMM-Net shows domain generalization capabilities, without using any transfer learning strategy.

关键词： Fault diagnosis Interpretable neural network algorithm unrolling General convolutional sparse coding Signal denoising Alternating direction method of multipliers

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algorithm unrolling for Massive Access via Deep Neural Networks With Theoretical Guarantee

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2022年第2期21卷 945-959页

作者： Shi, Yandong Choi, Hayoung Shi, Yuanming Zhou, Yong ShanghaiTech Univ Sch Informat Sci & Technol Shanghai 201210 Peoples R China Chinese Acad Sci Shanghai Inst Microsyst & Informat Technol Shanghai 200050 Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China Kyungpook Natl Univ Dept Math Daegu 41566 South Korea Yoke Intelligence Shanghai 201210 Peoples R China

Massive access is a critical design challenge of Internet of Things (IoT) networks. In this paper, we consider the grant-free uplink transmission of an IoT network with a multiple-antenna base station (BS) and a large number of single-antenna IoT devices. Taking into account the sporadic nature of IoT devices, we formulate the joint activity detection and channel estimation (JADCE) problem as a group-sparse matrix estimation problem. This problem can be solved by applying the existing compressed sensing techniques, which however either suffer from high computational complexities or lack of algorithm robustness. To this end, we propose a novel algorithm unrolling framework based on the deep neural network to simultaneously achieve low computational complexity and high robustness for solving the JADCE problem. Specifically, we map the original iterative shrinkage thresholding algorithm (ISTA) into an unrolled recurrent neural network (RNN), thereby improving the convergence rate and computational efficiency through end-to-end training. Moreover, the proposed algorithm unrolling approach inherits the structure and domain knowledge of the ISTA, thereby maintaining the algorithm robustness, which can handle non-Gaussian preamble sequence matrix in massive access. With rigorous theoretical analysis, we further simplify the unrolled network structure by reducing the redundant training parameters. Furthermore, we prove that the simplified unrolled deep neural network structures enjoy a linear convergence rate. Extensive simulations based on various preamble signatures show that the proposed unrolled networks outperform the existing methods in terms of the convergence rate, robustness and estimation accuracy.

关键词： Deep learning Convergence Estimation Training Robustness Internet of Things Approximation algorithms Massive access joint activity detection and channel estimation group-sparse matrix estimation algorithm unrolling deep learning

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algorithm-unrolling-Based Distributed Optimization for RIS-Assisted Cell-Free Networks

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IEEE INTERNET OF THINGS JOURNAL 2024年第1期11卷 944-957页

作者： Xu, Wangyang An, Jiancheng Li, Hongbin Gan, Lu Yuen, Chau Univ Elect Sci & Technol China Sch Informat & Commun Engn Chengdu 611731 Sichuan Peoples R China Singapore Univ Technol & Design Engn Prod Dev Pillar Singapore 487372 Singapore Stevens Inst Technol Dept Elect & Comp Engn Hoboken NJ 07030 USA Yibin Inst UESTC Sch Informat & Commun Engn Yibin 644000 Peoples R China Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

The user-centric cell-free network has emerged as an appealing technology to improve the wireless communication's capacity of the Internet of Things (IoT) networks thanks to its ability to eliminate intercell interference effectively. However, the cell-free network inevitably brings in higher hardware cost and backhaul overhead as a larger number of base stations (BSs) are deployed. Additionally, severe channel fading in high-frequency bands constitutes another crucial issue that limits the practical application of the cell-free network. In order to address the above challenges, we amalgamate the cell-free system with another emerging technology, namely reconfigurable intelligent surface (RIS), which can provide high spectrum and energy efficiency with low hardware cost by reshaping the wireless propagation environment intelligently. To this end, we formulate a weighted sum-rate (WSR) maximization problem for RIS-assisted cell-free systems by jointly optimizing the BS precoding matrix and the RIS reflection coefficient vector. Subsequently, we transform the complicated WSR problem to a tractable optimization problem and propose a distributed cooperative alternating direction method of multipliers (ADMMs) to fully utilize parallel computing resources. Inspired by the model-based algorithm unrolling concept, we unroll our solver to a learning-based deep distributed ADMM (D2-ADMM) network framework. To improve the efficiency of the D2-ADMM in distributed BSs, we develop a monodirectional information exchange strategy with a small signaling overhead. In addition to benefiting from domain knowledge, D2-ADMM adaptively learns hyperparameters and nonconvex solvers of the intractable RIS design problem through data-driven end-to-end training. Finally, numerical results demonstrate that the proposed D2-ADMM achieves around 210% improvement in capacity compared with the distributed noncooperative algorithm and almost 96% compared with the centralized algorithm.

关键词： Precoding Internet of Things Optimization Neural networks Massive MIMO Wireless communication Iterative methods Cell-free system Internet of Things (IoT) reconfigurable intelligent surface (RIS) distributed cooperative design algorithm unrolling

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Adversarial algorithm unrolling Network for Interpretable Mechanical Anomaly Detection

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2024年第5期35卷 6007-6020页

作者： An, Botao Wang, Shibin Qin, Fuhua Zhao, Zhibin Yan, Ruqiang Chen, Xuefeng Xi An Jiao Tong Univ Sch Mech Engn Xian 710049 Peoples R China

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.

关键词： Anomaly detection Encoding Feature extraction Decoding Vibrations Codes Training Adversarial training algorithm unrolling anomaly detection interpretable neural network representation learning

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Low-Light Image Enhancement by Retinex-Based algorithm unrolling and Adjustment

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2024年第11期35卷 15758-15771页

作者： Liu, Xinyi Xie, Qi Zhao, Qian Wang, Hong Meng, Deyu Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Shaanxi Peoples R China Tencent Jarvis Lab Shenzhen 518020 Peoples R China Xi An Jiao Tong Univ Minist Educ Key Lab Intelligent Networks & Network Secur Xian 710049 Shaanxi Peoples R China Pazhou Lab Huangpu Guangzhou 510555 Guangdong Peoples R China Macau Univ Sci & Technol Macau Inst Syst Engn Taipa Macao Peoples R China

Low-light image enhancement (LIE) has attracted tremendous research interests in recent years. Retinex theory-based deep learning methods, following a decomposition-adjustment pipeline, have achieved promising performance due to their physical interpretability. However, existing Retinex-based deep learning methods are still suboptimal, failing to leverage useful insights from traditional approaches. Meanwhile, the adjustment step is either oversimplified or overcomplicated, resulting in unsatisfactory performance in practice. To address these issues, we propose a novel deep-learning framework for LIE. The framework consists of a decomposition network (DecNet) inspired by algorithm unrolling and adjustment networks considering both global and local brightness. The algorithm unrolling allows the integration of both implicit priors learned from data and explicit priors inherited from traditional methods, facilitating better decomposition. Meanwhile, considering global and local brightness guides the design of effective yet lightweight adjustment networks. Moreover, we introduce a self-supervised fine-tuning strategy that achieves promising performance without manual hyperparameter tuning. Extensive experiments on benchmark LIE datasets demonstrate the superiority of our approach over existing state-of-the-art methods both quantitatively and qualitatively. Code is available at https://***/Xinyil256/RAUNA2023.

关键词： Lighting Reflectivity Deep learning Brightness Pipelines Image enhancement Degradation algorithm unrolling deep learning low-light image enhancement (LIE) Retinex theory

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MIMO Radar Beampattern Design via algorithm unrolling

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2024年第6期60卷 9204-9220页

作者： Metwaly, Kareem Kweon, Junho Alhujaili, Khaled Gini, Fulvio Greco, Maria Sabrina Rangaswamy, Muralidhar Monga, Vishal Alexandria Univ Alexandria 5424041 Egypt Penn State Univ Dept Elect Engn University Pk PA 16801 USA Taibah Univ Medina Saudi Arabia Univ Pisa I-56126 Pisa Italy US Air Force Res Lab Dayton OH 45433 USA Dept Elect Engn Medina 344 Saudi Arabia Energy Ind & Adv Technol Res Ctr Medina 344 Saudi Arabia

Optimizing a transmit multiple-input-multiple-output (MIMO) radar waveform subject to the nonconvex constant modulus constraint (CMC) remains a problem of enduring interest. The past decade has seen a variety of tailored iterative approaches with various performance-complexity tradeoffs. Despite promising work, iterative algorithms have a speed handicap and require meticulous parameter tuning. Deep learning has recently been proposed for MIMO radar waveform design, where iterative optimization is replaced by a neural network that regresses from the problem specification to the desired waveform. Once trained, a deep network can quickly regress the desired waveform coefficients, but it is a black box and may excel only when generous training is available. We present a fast, learned, and explainable deep (FLED) learning approach by unrolling a state-of-the-art iterative algorithm. We particularly leverage the recently proposed projection-descent-retraction (PDR) algorithm and design a neural network where each PDR iteration is mapped to a step of the network while preserving the CMC. Alongside an interpretable network architecture, we propose learning of key algorithm parameters such as the direction of descent, while introducing learning of FLED initialization and solution refinement through trainable prune-expand blocks. By enforcing appropriate regularizers in the learning of these parameters, FLED breaks the tradeoff between computational speed and performance. Compared to the state-of-the-art alternatives, it is near real time with boosted performance-fidelity to the desired beampattern. Crucially, the benefits of FLED over competing deep learning techniques are enhanced in the regime of limited training, i.e., FLED exhibits superior generalizability.

关键词： Iterative methods Training MIMO radar Radar Interference Aerospace and electronic systems Signal to noise ratio algorithm unrolling constant modulus deep learning (DL) multiple-input multiple-output (MIMO) radar waveform design

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Photon Limited Non-Blind Deblurring Using algorithm unrolling

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IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING 2022年 8卷 851-864页

作者： Sanghvi, Yash Gnanasambandam, Abhiram Chan, Stanley H. Purdue Univ Sch Elect & Comp Engn W Lafayette IN 47907 USA Purdue Univ W Lafayette IN 47907 USA

Image deblurring in photon-limited conditions is ubiquitous in a variety of low-light applications such as photography, microscopy and astronomy. However, the presence of the photon shot noise due to the low illumination and/or short exposure makes the deblurring task substantially more challenging than the conventional deblurring problems. In this paper, we present an algorithm unrolling approach for the photon-limited deblurring problem by unrolling a Plug-and-Play algorithm for a fixed number of iterations. By introducing a three-operator splitting formation of the Plug-and-Play framework, we obtain a series of differentiable steps which allows the fixed iteration unrolled network to be trained end-to-end. The proposed algorithm demonstrates significantly better image recovery compared to existing state-of-the-art deblurring approaches. We also present a new photon-limited deblurring dataset for evaluating the performance of algorithms.

关键词： Photon limited poisson deconvolution deblurring plug-and-play algorithm unrolling

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A Novel Interpretable Model via algorithm unrolling for Intelligent Fault Diagnosis of Machinery

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IEEE SENSORS JOURNAL 2024年第1期24卷 495-505页

作者： Rao, Fengpei Zeng, Ming Cheng, Yiwei China Univ Geosci Sch Mech Engn & Elect Informat Wuhan 430074 Peoples R China China Univ Geosci Shenzhen Res Inst Shenzhen 518057 Peoples R China

Identifying the health state of machinery using sensor information is one of the key tasks for intelligent operation and maintenance of machinery. In recent years, deep learning models have been widely used in this field. However, these models usually lack interpretability. To this end, we use the algorithm unrolling technique to unroll the convolutional version of iterative shrinkage-thresholding algorithm (CISTA) into a neural network called CISTA-Net. The CISTA-Net's structure is determined by the iterative algorithm and thus has a clear theoretical basis. By adding a classification module and a reconstruction module in parallel to its output end, the CISTA-Net is interpretable in terms of both its structure and output. Interpretability analysis through the well-known bearing dataset from the Case Western Reserve University (CWRU) shows that the reconstruction module can enhance the interpretability. In addition, a simple residual block can be optionally added to the input end of the CISTA-Net for feature pre-extraction, resulting in an alternative CISTA-Net called ResCISTA-Net. The ResCISTA-Net is compared with some conventional and interpretable fault diagnosis models on another two mechanical fault diagnosis tasks. Experimental results suggest that: 1) the residual block can not only improve diagnostic accuracy but also prevent performance degradation for some tasks;2) the reconstruction module can also improve diagnostic accuracy;and 3) the ResCISTA-Net performs excellently in terms of diagnostic accuracy, training sample size requirement, and noise robustness.

关键词： Convolution Convolutional codes Feature extraction Encoding Kernel Signal processing algorithms Fault diagnosis algorithm unrolling convolutional sparse coding intelligent fault diagnosis interpretable neural network

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