Generalized Minimax-concave Research Articles

Loose particle Detection: The optimal detection condition and weak loose particle impulse extraction

To achieve effective detection of loose particles within small cavities in microelectronic devices, this paper proposes the optimal detection conditions of loose particles in ceramic packaging for microelectronic devices based on simulation, and presents a method for weak signal reconstruction using weighted sparse representation. To address the challenge of ineffective detection of loose particles under recommended vibration conditions, a particle-cavity collision dynamics model is established. Subsequently, the detection laws of loose particles under different accelerations, frequencies, and cavity heights are studied through simulation, leading to the establishment of optimal detection conditions for microelectronic devices with varying cavity heights. To address the issue of weak impulses being submerged in background noise under optimal detection conditions, sparse representation is utilized for signal reconstruction. First, a Laplace wavelet dictionary is constructed according to the impulse characteristics. Second, the generalized minimax-concave (GMC) penalty function is applied as a sparse regularization term to preserve signal amplitude. Meanwhile, a weight matrix based on kurtosis and singular value is designed to threshold sparse coefficients. The results demonstrate that the proposed optimal detection conditions and signal reconstruction method effectively detect loose particles. Compared with other algorithms, the proposed method reduces background noise in the particle impact noise detection (PIND) signals while maintaining impulse amplitude; it also improves signal reconstruction accuracy and offers valuable insights into effective loose particle detection in microelectronic packaging devices.

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.

Sparse Low-Rank Matrix Estimation With Nonconvex Enhancement for Fault Diagnosis of Rolling Bearings

The diagnosis of bearing early fault is significant and fundamental in the machine condition monitoring. The accurate and effective diagnosis is of great importance to avoid further serious accidents. However, existing sparse low-rank (SLR) methods for bearing fault diagnosis suffer from underestimation of amplitude and inaccurate approximation of singular values. Therefore, in this paper, a novel sparse low-rank matrix estimation method with nonconvex enhancement (SLRNE) is proposed, extracting the fault transients from observed noisy signal. Specifically, fault transients have both sparse and low-rank properties in time-frequency domain. Based on this, a SLR optimization model is proposed to simultaneously promote the above two properties via truncated nuclear norm (TNN) and generalized minimax concave (GMC) penalty function. The two nonconvex functions aim to promote low-rank property and sparsity respectively. Then, based on derived convexity conditions of the optimization problem, convex optimization algorithm, alternating direction method of multipliers (ADMM) and forward-and-backward splitting (FBS) algorithm, are applied to obtain global optimal solution. In the iterative algorithm, a weighting strategy is designed for the singular value threshold operator to enhance the effect of fault feature extraction. Simulated and experimental signals verify the effectiveness of SLRNE and contrast experiments verify its superiority.

Group-Sparse Feature Extraction via Ensemble Generalized Minimax-Concave Penalty for Wind-Turbine-Fault Diagnosis

Extracting weak fault features from noisy measured signals is critical for the diagnosis of wind turbine faults. In this paper, a novel group-sparse feature extraction method via an ensemble generalized minimax-concave (GMC) penalty is proposed for machinery health monitoring. Specifically, the proposed method tackles the problem of formulating large useful magnitude values as isolated features in the original GMC-based sparse feature extraction method. To accurately estimate group-sparse fault features, the proposed method formulates an effective unconstrained optimization problem wherein the group-sparse structure is incorporated into non-convex regularization. Moreover, the convex condition is proved to maintain the convexity of the whole formulated cost function. In addition, the setting criteria of the regularization parameter are investigated. A simulated signal is presented to verify the performance of the proposed method for group-sparse feature extraction. Finally, the effectiveness of the proposed group-sparse feature extraction method is further validated by experimental fault diagnosis cases.

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.

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.

Compressed feature reconstruction for localized fault diagnosis with generalized minimax-concave penalty

Compressed sensing can effectively relieve the burden of data storage and transmission for mechanical condition monitoring. However, feature reconstruction from compressed observations has always been a challenge. A novel compressed feature reconstruction method for the impulse response signal caused by localized damage is proposed based on the generalized minimax-concave (GMC) penalty. To improve the efficiency of compression and reconstruction, the fault signal is divided into several segments before compression, and the segmented sparse coefficient is obtained by solving a GMC problem. The fault-caused impulse signal is obtained by combining all the reconstructed segments together. Furthermore, a strategy of regularization parameter selection based on the sparse coefficient proxy is presented. Compared with the commonly used l1 regularization-based reconstruction method, the proposed method can better preserve the amplitudes of impulse features. The effectiveness of the proposed method is further verified by simulation and experimental data.

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.

Data-Driven Time-Frequency Method and Its Application in Detection of Free Gas Beneath a Gas Hydrate Deposit

The time-frequency (TF) analysis method plays a significant role in the detection of natural gas hydrates. As a data-driven method, compressed sensing (CS) has been widely used in the TF methods due to the sparsity of the TF representation. This study proposes a data-driven TF method based on the CS theory and a non-convex regularization. In the implementation, a continuous wavelet transform (CWT) with a generalized beta wavelet (GBW) is formulated as an inverse problem based on the CS theory. The selection of appropriate parameters enables the GBW to match the seismic wavelets better than the widely used Morlet wavelet. The GBW can constitute a tight frame to reduce calculation time, particularly for large-scale field data processing. Additionally, the proposed TF method introduces the generalized minimax concave (GMC) penalty function as a non-convex regularization term. Compared with the classical sparse approximation method with <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> regularization, the GMC regularization term can enhance the sparsity in sparse inverse problems and ensure the convexity of sparse inversions. This article also presents an exponentially decreasing threshold scheme to adaptively select the regularization parameters. Three synthetic examples are investigated to demonstrate the performance of the proposed sparse TF representation with GMC regularization. Finally, the proposed TF method’s performance in detecting free gas of gas hydrates is validated using field seismic data obtained from the Blake Ridge.

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.

Robust AOA-Based Source Localization in Correlated Measurement Noise via Nonconvex Sparse Optimization

This letter considers the problem of robust angle of arrival (AOA) source localization in the presence of correlated noise and outliers based on nonconvex sparse optimization. To maintain the total convexity of the cost function while using the nonconvex penalty, we propose to regularize the correlation matrix weighted cost by generalized minimax concave (GMC) function. Then the alternating direction forward-backward splitting algorithm (ADFBS) is proposed to estimate outliers and source position simultaneously. To counter the bias problem of ADFBS, a new ADFBS based instrumental-variable estimator (IVADFBS) is developed. The IVADFBS is observed to produce nearly unbiased estimates with lower mean squared errors.

Enhanced Sparse Regularization Based on Logarithm Penalty and Its Application to Gearbox Compound Fault Diagnosis

A vibration signal observed from a gearbox is normally composed of the vibrations of bearing and gear components as well as the strong background noise. Sparse regularization performs as an effective method to deal with vibration signal denoising and compound fault diagnosis for the gearbox. In this article, a multivariate and non-convex logarithm penalty based on the generalized infimal convolution smoothing (GICS) is deduced. To guarantee the global minimum of the overall cost function, we also derive a convexity condition to prescribe the non-convex penalty. In this way, the optimal sparse solution to the cost function can be calculated by a convex algorithm. Multiplied by respective transform matrices, all fault components in a compound signal can be simultaneously reconstructed, and then each fault characteristic frequency can be extracted. Numerical and experimental analyses demonstrate the effectiveness of the proposed method. Compared with the classical convex $L1$ norm and newly developed non-convex generalized minimax-concave (GMC) penalties, the proposed method is superior in terms of inducing sparsity effectively and enhancing the estimation accuracy of signal components.

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.

A novel dictionary learning method for sparse representation with nonconvex regularizations

In dictionary learning, sparse regularization is used to promote sparsity and has played a major role in the developing of dictionary learning algorithms. ℓ1-norm is of the most popular sparse regularization due to its convexity and the related tractable convex optimization problems. However, ℓ1-norm leads to biased solutions and provides inferior performance on certain applications compared with nonconvex sparse regularizations. In this work, we propose a generalized minimax-concave (GMC) sparse regularization, which is nonconvex, to promote sparsity to design dictionary learning model. Applying the alternate optimization scheme, we use the forward–backward splitting (FBS) algorithm to solve the sparse coding problem. As the improvement, we incorporate Nesterov’s acceleration technique and adaptive threshold scheme into the FBS algorithm to improve the convergence efficiency and performance. In the dictionary update step, we apply the difference of convex functions (DC) programming and the DC algorithm (DCA) to address the dictionary update. Two dictionary update algorithms are designed; one updates the dictionary atoms one by one, and the other one updates the dictionary atoms simultaneously. The presented dictionary learning algorithms perform robustly in dictionary recovery. Numerical experiments are designed to verify the performance of proposed algorithms and to compare with the state-of-the-art algorithms.

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.

Reweighted generalized minimax-concave sparse regularization and application in machinery fault diagnosis

The vibration signal of faulty rotating machinery tends to be a mixture of repetitive transients, discrete frequency components and noise. How to accurately extract the repetitive transients is a critical issue for machinery fault diagnosis. Inspired by reweighted L1 (ReL1) minimization for sparsity enhancement, a reweighted generalized minimax-concave (ReGMC) sparse regularization method is proposed to extract the repetitive transients. We utilize the generalized minimax-concave (GMC) penalty to regularize the weighted sparse representation model to overcome the underestimation deficiency of L1 norm penalty. Moreover, a new reweight strategy which is different from the reweight strategy in ReL1 for sparsity enhancement is proposed according to the statistical characteristic, i.e., squared envelope spectrum kurtosis. Then ReGMC is proposed by solving a series of weighted GMC minimization problems. ReGMC is utilized to process a simulated signal and the vibration signals of a hot-milling transmission gearbox and a run-to-failure bearing with incipient fault. The ReGMC analysis results and the comparison studies show that ReGMC can effectively extract the repetitive transients while suppressing the discrete frequency components and noise, and behaves better than GMC, improved lasso, and spectral kurtosis.