Generalized Minimax-concave Penalty Research Articles

Accelerated generalized minimax-concave sparse regularization for impact force reconstruction and localization

Impact force identification has always been of significance for structure health monitoring especially on the applications involving composite materials. As a typical inverse problem, impact force reconstruction and localization is undoubtedly a challenging task. The well-known ℓ1 sparse regularization has a tendency to underestimate the amplitude of impact forces. To alleviate this limitation, we propose an accelerated generalized minimax-concave (AGMC) for sparse regularization that employs a non-convex generalized minimax-concave (GMC) penalty as the regularizer and incorporates an acceleration technique to expedite the attainment of the global minimum. Compared with the classic ℓ1-norm penalty, the GMC penalty can not only induce sparsity in the estimation, but also maintain the convexity of the cost function, so that the global optimal solution can be obtained through convex optimization algorithms. This method is applied to solve the impact force identification problem with unknown force locations to simultaneously reconstruct and localize impact forces in the under-determined case utilizing a limited number of sensors. Meanwhile, K-sparsity criterion is used to adaptively select regularization parameters by taking advantage of the sparse prior knowledge on impact forces. Simulations and experiments are conducted on a composite plate to verify the computational efficiency and robustness of the AGMC method in terms of impact force reconstruction and localization, particularly in the presence of noise. Results demonstrate that the proposed AGMC method achieves faster convergence and provides more accurate and sparse reconstruction and localization of impact forces compared to other state-of-the-art sparse regularization methods.

Robust seismic attenuation compensation based on generalized minimax concave penalty sparse representation

Abstract Deep hydrocarbon resources have become more and more important nowadays. However, owing to the affection of long-distance propagation and stratigraphic absorption, seismic data coming from deep beds generally suffer from weak energy, low resolution, and low signal-to-noise ratio (SNR), which seriously influence the reliability of seismic interpretation. Generally, inverse Q (quality factor) filtering (IQF) is used for absorption compensation, but it may amplify noise at the same time. Although compensation methods based on inversion overcomes the instability, it is still difficult to obtain high-SNR results. To address this issue, under the framework of sparse representation theory, we proposed a single-channel attenuation compensation method constrained by generalized minimax concave (GMC) penalty function. It takes the modified Kolsky model to describe seismic absorption and combines sparse representation theory to create objective function. Furthermore, a GMC penalty function is utilized to promote sparsity. It allows more accurate estimates of sparse coefficients from noise-contaminated seismic data. Although the GMC penalty itself is concave, the objective function remains strictly convex. Therefore, globally optimal sparse solutions can be obtained through an operator-splitting algorithm. Even in the presence of noise, this method can obtain stable and accurate compensation results through reconstruction. Synthetic data tests and field seismic data application showed that this method has high robustness to noise. It can stably and effectively compensate for the energy loss of seismic data, as well as maintain high SNR.

Sparse representation learning for fault feature extraction and diagnosis of rotating machinery

Early fault feature extraction and fault diagnosis are of great importance for predictive maintenance of rotating machinery. To accurately extract early fault features from original noisy signals, a novel joint sparse representation learning method is developed in this paper, this method is based on the proposed nonlocal generalized minimax-concave (GMC) penalty and generalized fraction-order total variation (FTV) regularization. The motivation for this research is to leverage the benefits of joint regularizations. The proposed nonlocal GMC penalty regularization tends to preserve weak fault features, promote sparsity and avoid underestimating the amplitude of periodic fault impulses. Simultaneously, the proposed generalized FTV regularization tends to remove fault irrelevant noise and reduce staircase artifacts. Therefore, the proposed model can effectively extract early fault features from original noisy signals. The performance of the proposed model is verified by a series of experiments. In two fault diagnosis tasks, the peak signal-to-noise ratio (PSNR) of the proposed method reaches − 5 dB and − 8 dB, respectively. Compared with state-of-the-art methods, the PSNR has been improved by at least 2 dB, comparison results show that the proposed model has superior performance for early fault feature extraction.

Driving Fatigue Monitoring via Kernel Sparse Representation Regression With GMC Penalty

Automatic monitoring technology for fatigued driving can greatly reduce traffic accidents caused by drivers due to decreased attention. The use of monitoring algorithms based on physiological signal sensors is of great significance for objective monitoring. In this paper, a novel algorithm with excellent performance and strong generalization ability, kernel sparse representation regression based on generalized minimax-concave (GMC-KSRR), is proposed to identify fatigue physiological signals. Specifically, in the proposed algorithm, the training samples of physiological features are mapped in reproducing kernel Hilbert space (RKHS) for linear separability. Then, in RKHS, the sparse coefficients of the test samples are obtained by generalized minimax-concave (GMC) penalty-based sparse representation (SR). Different from the traditional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{{1}}$ </tex-math></inline-formula> -norm, the GMC penalty we used does not underestimate the high-amplitude component of sparsity coefficients, resulting in a more accurate regression result. Finally, the regression decision is performed in the label subspace according to the obtained sparse coefficients. Meanwhile, a multimodality algorithm based on GMC-KSRR has also been proposed that weighs each modality according to quality for robust fatigue monitoring. Eventually, competitive experimental results on the well-known SEED-VIG dataset against the state-of-the-art methods demonstrate the efficacy of the proposed algorithms in identifying fatigue physiological signals, indicating its powerful application potential in driving fatigue monitoring.

Transient-extracting transform based on non-convex sparse regularization: A useful scheme for bearing fault feature enhancement

Periodic transient shocks of vibration signals often reflect the failure of mechanical components. With the time-frequency (TF) distribution (TFD), Transient-extracting transform (TET) can descript and extract the fault-related transient component effectively. Nevertheless, vibrations collected from practical sources are always contaminated by strong background noise, thus the transient shocks are often submerged by noise components. Therefore, how to effectively extract the weak transient component from noise is an important task to achieve the bearing fault diagnosis. Considering the above issue, this paper developed a generalized mini-max concave (GMC) penalty based TET (GMCTET) for bearing fault feature enhancement. Specifically, the GMC penalty based-sparse regularization is firstly applied to the raw signal. Benefiting from the good ability of GMC penalty-based sparse regularization in both sparsity and signal fidelity. The transient shocks are initially presented, and the loss of energy amplitude of the raw signal during the processing is reduced simultaneously. Next, TET can well characterize these transient shocks via a highly readable TFD, and the transient component is extracted based on the TF coefficients. The shock structures in transient component are further highlighted after TET treatment. Finally, the bearing fault frequencies are identified through the spectrum of the extracted transient component. The effectiveness of GMCTET is verified from the comparative analysis results of the simulation and experimental studies.

Revisiting convexity-preserving signal recovery with the linearly involved GMC penalty

• A new method for setting the matrix parameter in the linearly involved GMC is proposed. • An alternative algorithm is presented to solve the linear involved convexity-preserving model. • Two properties of the solution path are proved to help with tuning parameter selection. The generalized minimax concave (GMC) penalty is a newly proposed regularizer that can maintain the convexity of the objective function. This paper deals with signal recovery with the linearly involved GMC penalty. First, we propose a new method to set the matrix parameter in the penalty via solving a feasibility problem. The new method possesses appealing advantages over the existing method. Second, we recast the linearly involved GMC model as a saddle-point problem and use the primal-dual hybrid gradient (PDHG) algorithm to compute the solution. Another important work in this paper is that we provide guidance on the tuning parameter selection by proving desirable properties of the solution path. Finally, we apply the linearly involved GMC penalty to 1-D signal recovery and matrix regression. Numerical results show that the linearly involved GMC penalty can obtain better recovery performance and preserve the signal structure more successfully in comparison with the total variation (TV) regularizer.

Sparsity-enhanced equivalent source method for acoustic source reconstruction via the Generalized Minimax-Concave penalty

The Equivalent Source Method (ESM) is a powerful technique for acoustic source reconstruction, which has been widely used in noise control and machinery fault detection. Because the inverse acoustic source reconstruction problem is typically ill-conditioned, regularization techniques are often adopted in ESM to achieve meaningful solutions. Based on the sparse distribution assumption of acoustic sources, sparse regularization can be utilized in ESM to promote the spatial resolution of reconstructed results. Existing sparse ESMs often adopt convex l1 norm or nonconvex lp norm as the regularization terms. However, l1 norm-regularized ESM suffers from an insufficient sparsity-inducing problem, which decreases the spatial resolution and reconstruction accuracy. Meanwhile, reconstructed results of lp norm-regularized ESM are often unstable due to multiple local minimas. In this paper, a sparsity-enhanced ESM is proposed, which introduces a nonconvex Generalized Minimax-Concave (GMC) penalty into ESM as the regularization term. The GMC penalty can enhance the sparsity of solutions and simultaneously maintain the convexity of the overall objective function in acoustic source reconstruction. Consequently, the GMC penalty-regularized ESM can improve the spatial resolution and reconstruction accuracy of the reconstructed results. To solve the acoustic source reconstruction problem rapidly, a computation framework based on Alternating Direction Method of Multipliers (ADMM) is derived. Simulation studies indicate that the proposed method can improve the acoustic source reconstruction accuracy in a wide frequency band, compared with existing l1 and lp norm-regularized ESMs. Two experimental cases further verify that the proposed sparsity-enhanced ESM can effectively reconstruct the acoustic sources with high spatial resolution and reconstruction accuracy at higher frequencies.

Sparse reconstruction for blade tip timing signal using generalized minimax-concave penalty

Rotor blade health monitoring based on the non-contact blade tip timing (BTT) technique has already been proved to be an alternative method to the classical contact strain measurement method. However, the signal sampled by the BTT system is usually undersampled due to the limited BTT sensors. Sparse regularization in the framework of ℓ1-norm has been introduced to identify the blade vibration parameter from the undersampled BTT data. However, the standard sparse regularization based onℓ1-norm penalty generally generates an underestimated solution. Compared with ℓ1-norm penalty, generalized minimax-concave (GMC) penalty as a non-convex penalty has the promising property of amplitude improvement. In this paper, a non-convex optimization model based on GMC penalty is developed for reconstructing the undersampled BTT signal to obtain the accurate blade-tip displacement and blade natural frequency. The optimization model based on GMC penalty is presented to find the global optimal solution for the sparse representation of the BTT signal even if GMC penalty turns out to be a non-convex regularizer. Additionally, the strategy of regularization parameter selection is provided through the blade tip timing simulator. The relationship between the noise level and the regularization parameter is established to provide the strategy of regularization parameter selection in experiment. Finally, the blade spin testing is carried out for measuring the blade vibration by BTT and strain gauge systems. Amplitudes and frequencies of reconstructed BTT signals are compared with the measurements of the strain gauge, which are transferred from the strain at the blade root to the displacement at the blade tip by using the conversion coefficient obtained from the finite element model. Both simulation and experiment demonstrate that compared with the ℓ1-norm penalty, GMC penalty can reconstruct the blade-tip displacement and blade natural frequency with high accuracy.

A generalized minimax-concave penalty based compressive beamforming method for acoustic source identification

Acoustic source identification using compressive beamforming has been extensively investigated and applied in numerous fields. In this paper, a generalized minimax-concave (GMC) penalty based compressive beamforming method is proposed. The method solves acoustic inverse problems using the GMC penalty, by which the capacity of sound field reconstruction in low-frequency and low-signal-to-noise ratio environments can be enhanced. In addition, the problem of systematic underestimation of source strength can be relieved with the benefit of penalty homogeneity, and a balance can be reached between the sparsity-induced capacity and computing complexity. Moreover, the convergence of the proposed method and parameter influences were studied through numerical simulations. The results show that the method is robust within a relatively wide range of parameters, and the computational efficiency is within the limits of acceptability. Furthermore, the performance of the proposed method was compared with two other methods using simulated and experimental data. The results indicate that the proposed method performs better than existing algorithms under low-frequency and strong-noise conditions, and the spatial resolution in acoustic maps and the capacity of source strength estimation can be improved.

A Sparsity-Assisted Fault Diagnosis Method Based on Nonconvex Sparse Regularization

Sparse representation theory can be adopted for fault feature extraction and classification. Inspired by these two capabilities of sparse representation theory, this paper proposes a novel collaborative sparsity-assisted fault diagnosis (CSFD) method. Specifically, due to the repeatability and sparsity of fault feature signal in the whole signal, the feature extraction capability of sparse representation is utilized to extract fault features and construct a feature matrix. Subsequently, owing to the sparsity of fault classification problem itself, the classification capability of sparse representation is employed to achieve fault classification. Moreover, fault feature extraction is a key issue for fault diagnosis. Therefore, in order to improve the effectiveness of fault feature extraction, a RC-adjustment strategy with the ability to adaptively adjust regularization parameter is designed to assist the generalized minimax-concave (GMC) penalty for feature extraction. The advantage of the GMC penalty is that it can establish a nonconvex sparse regularization model with convex optimization solution. Finally, the proposed CSFD method is tested and verified by Case Western Reserve University (CWRU) bearing dataset and actual engineering dataset. Especially, the diagnostic accuracy of this method can reach 99.92%, which is nearly 7.68% higher than the traditional method based on L1 norm penalty. Enormous experiment results have thoroughly demonstrated the effectiveness of the proposed CSFD method for fault diagnosis.

Impact force identification via sparse regularization with generalized minimax-concave penalty

As a typical inverse problem, impact force identification tends to be a challenge owing to its ill-posedness. Recently, the sparse characteristic of the impact force in time domain are taken into consideration to convert the ill-posed problem into a sparse recovery task. The classic way to obtain sparse approximate solutions of impact force is to use the L1-norm regularization. However, underestimating the exact solution inevitably happens when applying the L1-norm regularization to impact force identification. In this paper, a novel sparse regularization method with generalized minimax-concave (GMC) penalty is proposed to deal with the impact force identification problem. Even if the GMC penalty turns out to be a nonconvex regularizer to promote sparsity in the sparse estimation, it retains the convexity of the sparsity-regularized least squares cost function and the global optimal solution can be found by convex optimization. Additionally, an approach to adaptively set regularization parameters is presented. Finally, simulations and experiments are conducted to verify the performances of the proposed method, and the results are compared with those of the L1-norm regularization method. Results demonstrate that the nonconvex sparse regularization based on GMC can produce more accurate estimations for impact force identification.

Ship Wake Detection in SAR Images via Sparse Regularization

In order to analyse synthetic aperture radar (SAR) images of the sea surface, ship wake detection is essential for extracting information on the wake generating vessels. One possibility is to assume a linear model for wakes, in which case detection approaches are based on transforms such as Radon and Hough. These express the bright (dark) lines as peak (trough) points in the transform domain. In this paper, ship wake detection is posed as an inverse problem, which the associated cost function including a sparsity enforcing penalty, i.e. the generalized minimax concave (GMC) function. Despite being a non-convex regularizer, the GMC penalty enforces the overall cost function to be convex. The proposed solution is based on a Bayesian formulation, whereby the point estimates are recovered using maximum a posteriori (MAP) estimation. To quantify the performance of the proposed method, various types of SAR images are used, corresponding to TerraSAR-X, COSMO-SkyMed, Sentinel-1, and ALOS2. The performance of various priors in solving the proposed inverse problem is first studied by investigating the GMC along with the L1, Lp, nuclear and total variation (TV) norms. We show that the GMC achieves the best results and we subsequently study the merits of the corresponding method in comparison to two state-of-the-art approaches for ship wake detection. The results show that our proposed technique offers the best performance by achieving 80% success rate.

Sparse ECG Denoising with Generalized Minimax Concave Penalty.

The electrocardiogram (ECG) is an important diagnostic tool for cardiovascular diseases. However, ECG signals are susceptible to noise, which may degenerate waveform and cause misdiagnosis. In this paper, the ECG noise reduction techniques based on sparse recovery are investigated. A novel sparse ECG denoising framework combining low-pass filtering and sparsity recovery is proposed. Two sparsity recovery algorithms are developed based on the traditional -norm penalty and the novel generalized minimax concave (GMC) penalty, respectively. Compared with the -norm penalty, the non-differentiable non-convex GMC penalty has the potential to strongly promote sparsity while maintaining the convexity of the cost function. Moreover, the GMC punishes large values less severely than -norm, which is utilized to overcome the drawback of underestimating the high-amplitude components for the -norm penalty. The proposed methods are evaluated on ECG signals from the MIT-BIH Arrhythmia database. The results show that underestimating problem is overcome by the proposed GMC-based method. The GMC-based method shows significant improvement with respect to the average of output signal-to-noise ratio improvement (), the average of root mean square error (RMSE) and the percent root mean square difference (PRD) over almost any given SNR compared with the classical methods, thus providing promising approaches for ECG denoising.

Sparsity-enhanced signal decomposition via generalized minimax-concave penalty for gearbox fault diagnosis

Vibration signals arising from faulty gearboxes are often a mixture of the meshing component and the periodic transient component, and simultaneously contaminated by noise. Sparsity-assisted signal decomposition is an effective technique to decompose a signal into morphologically distinct components based on sparse representation and optimization. In this paper, we propose a sparsity-enhanced signal decomposition method which uses the generalized minimax-concave (GMC) penalty as a nonconvex regularizer to enhance sparsity in the sparse approximation compared to classical sparsity-assisted signal decomposition methods, and thus to improve the decomposition accuracy for gearbox fault diagnosis. Even though the GMC penalty itself is nonconvex, it maintains the convexity of the GMC regularized cost function to be minimized. Hence, similar to the classical L1-norm regularization methods, the global optimal solution can be guaranteed via convex optimization. Moreover, we present and validate a straight-forward way to choose transforms and set parameters for the proposed method. Through simulation studies, it is demonstrated that the proposed sparsity-enhanced signal decomposition method can effectively decompose the simulated faulty gearbox signal into the meshing component and the periodic transient component. Comparisons with the classical L1-norm regularized signal decomposition method and spectral kurtosis show that the proposed method can accurately preserve the amplitude of the periodic transient component and provide a more accurate estimation result. Experiment and engineering case studies further verify that the proposed method can accurately estimate the periodic transient component from vibration signals, which demonstrate that the proposed method is a promising tool for gearbox fault diagnosis.

A Novel Fault Diagnosis Method for Rolling Bearing Based on Improved Sparse Regularization via Convex Optimization

Structural health monitoring and fault state identification of key components, such as rolling bearing, located in the mechanical main drive system, have a vital significance. The acquired fault signal of rolling bearing always presents the obvious nonlinear and nonstationary characteristics. Moreover, the concerned features are submerged in strong background noise. To handle this difficulty, a novel fault signal denoising scheme based on improved sparse regularization via convex optimization is proposed to extract the fault feature of rolling bearing. In this paper, the generalized minimax-concave (GMC) penalty is firstly researched to promote the sparsity of signal, which is based on traditional L1-norm and Huber function. It is designed to estimate the sparse solutions more accurately and maintain the convexity of the cost function. Then, the GMC penalty is extended to 1-D first-order total variation (TV) as nonseparability and nonconvex regularizer. Thus, a convex optimization problem, which involves a quadratic data fidelity term and a convex regularization term, is developed in this paper. To accelerate the convergence of the algorithm, it is solved by forward-backward (FB) iterative algorithm and thus the denoised signal can be obtained. In order to demonstrate its performance, the proposed method is illustrated for numerical simulation signal and applied in the feature extraction of the measured rolling bearing vibration signal.