The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

The Regularity of Solutions to Mixed Boundary Value Problems of Second-Order Elliptic Equations with Small Angles

This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.

Convergence analysis on Browder-Tikhonov regularization for second-order evolution hemivariational inequality

This paper studies the Browder-Tikhonov regularization of a second-order evolution hemivariational inequality （SOEHVI） with non-coercive operators. With duality mapping, the regularized formulations and a derived first-order evolution hemivariational inequality （FOEHVI） for the problem considered are presented. By applying the Browder-Tikhonov regularization method to the derived FOEHVI, a sequence of regularized solutions to the regularized SOEHVI is constructed, and the strong convergence of the whole sequence of regularized solutions to a solution to the problem is proved.

Efficient anti-aliasing and anti-leakage Fourier transform for high-dimensional seismic data regularization using cube removal and GPU

Seismic data is commonly acquired sparsely and irregularly, which necessitates the regularization of seismic data with anti-aliasing and anti-leakage methods during seismic data processing. We propose a novel method of 4D anti-aliasing and anti-leakage Fourier transform using a cube-removal strategy to address the combination of irregular sampling and aliasing in high-dimensional seismic data. We compute a weighting function by stacking the spectrum along the radial lines, apply this function to suppress the aliasing energy, and then iteratively pick the dominant amplitude cube to construct the Fourier spectrum. The proposed method is very efficient due to a cube removal strategy for accelerating the convergence of Fourier reconstruction and a well-designed parallel architecture using CPU/GPU collaborative computing. To better fill the acquisition holes from 5D seismic data and meanwhile considering the GPU memory limitation, we developed the anti-aliasing and anti-leakage Fourier transform method in 4D with the remaining spatial dimension looped. The entire workflow is composed of three steps: data splitting, 4D regularization, and data merging. Numerical tests on both synthetic and field data examples demonstrate the high efficiency and effectiveness of our approach.

Balance Sparse Decomposition Method with Nonconvex Regularization for Gearbox Fault Diagnosis

As an important part of rotating machinery,gearboxes often fail due to their complex working conditions and harsh working environment.Therefore,it is very necessary to effectively extract the fault features of the gearboxes.Gearbox fault signals usually contain multiple characteristic components and are accompanied by strong noise interference.Traditional sparse modeling methods are based on synthesis models,and there are few studies on analysis and balance models.In this paper,a balance nonconvex regularized sparse decomposition method is proposed,which based on a balance model and an arctangent nonconvex penalty function.The sparse dictionary is constructed by using Tunable Q-Factor Wavelet Transform(TQWT)that satisfies the tight frame condition,which can achieve efficient and fast solution.It is optimized and solved by alternating direction method of multipliers(ADMM)algorithm,and the non-convex regularized sparse decomposition algorithm of synthetic and analytical models are given.Through simulation experiments,the determination methods of regularization parameters and balance parameters are given,and compared with the L1 norm regularization sparse decomposition method under the three models.Simulation analysis and engineering experimental signal analysis verify the effectiveness and superiority of the proposed method.

SECOND-ORDER INTERACTION OF IRREGULAR WAVES WITH A TRUNCATED COLUMN

A complete semi-analytical solution is obtained for second-order diffraction of plane bichromatic waves by a fixed truncated circular column.The fluid domain is divided into interior and exterior regions.In the exterior region,the second-order velocity potential is expressed in terms of‘locked-wave’and‘free-wave’ components,both are solved using Fourier and eigenfunction expansions.The re- sulting‘locked wave’potential is expressed by one-dimensional Green's integrals with oscillating integrands.In order to increase computational efficiency,the far-field part of the integrals are carried out analytically.Solutions in both regions are matched on the interface by the potential and its normal derivative continuity conditions.Based on the present approach,the sum-and difference-frequency potentials are efficiently evaluated and are used to generate the quadratic transfer functions which correlates the incident wave spectrum with second-order forcing spectrum on the column.The sum-frequency QTFs for a TLP column are present,which are compared for some frequency pairs with those from a fully numerical procedure.Satisfactory agreement has been obtained.QTF spectra for a case study TLP column,generated using the semi-analytical solution are presented.Also given are the results for nonlinear wave field around the column.

A multi-scale second-order autoregressive recursive filter approach for the sea ice concentration analysis

To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.

Composition Analysis and Identification of Ancient Glass Products Based on L1 Regularization Logistic Regression

In view of the composition analysis and identification of ancient glass products, L1 regularization, K-Means cluster analysis, elbow rule and other methods were comprehensively used to build logical regression, cluster analysis, hyper-parameter test and other models, and SPSS, Python and other tools were used to obtain the classification rules of glass products under different fluxes, sub classification under different chemical compositions, hyper-parameter K value test and rationality analysis. Research can provide theoretical support for the protection and restoration of ancient glass relics.

Coordinated Control of Second-order Harmonic Voltage and Current Fluctuations in Cascaded H-bridge Inverter with Supercapacitor and DC-DC Stage at Variable Output Frequencies

In the cascaded H-bridge inverter(CHBI)with supercapacitor and dc-dc stage,inherent second-order harmonic power flows through each submodule(SM),causing fluctuations in both the dc-link voltage and the dc-dc current.There exist limitations in handling these fluctuations at variable output frequencies when employing proportional-integral(PI)control to the dc-dc stage.This paper aims to coordinately control these second-order harmonic voltage and current fluctuations in the CHBI.The presented method configures a specific second-order harmonic voltage reference,equipped with a maximum voltage fluctuation constraint and a suitable phase,for the dc-dc stage.A PI-resonant controller is used to track the configured reference.This allows for regulating the second-order harmonic fluctuation in the average dc-link voltage among the SMs within a certain value.Importantly,the second-order harmonic fluctuation in the dc-dc current can also be reduced.Simulation and experimental results demonstrate the effectiveness of the presented method.

Convergent Data-Driven Regularizations for CT Reconstruction

The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography(CT).As the(naive)solution does not depend on the measured data continuously,regularization is needed to reestablish a continuous dependence.In this work,we investigate simple,but yet still provably convergent approaches to learning linear regularization methods from data.More specifically,we analyze two approaches:one generic linear regularization that learns how to manipulate the singular values of the linear operator in an extension of our previous work,and one tailored approach in the Fourier domain that is specific to CT-reconstruction.We prove that such approaches become convergent regularization methods as well as the fact that the reconstructions they provide are typically much smoother than the training data they were trained on.Finally,we compare the spectral as well as the Fourier-based approaches for CT-reconstruction numerically,discuss their advantages and disadvantages and investigate the effect of discretization errors at differentresolutions.

Impact Force Localization and Reconstruction via ADMM-based Sparse Regularization Method

In practice,simultaneous impact localization and time history reconstruction can hardly be achieved,due to the illposed and under-determined problems induced by the constrained and harsh measuring conditions.Although l_(1) regularization can be used to obtain sparse solutions,it tends to underestimate solution amplitudes as a biased estimator.To address this issue,a novel impact force identification method with l_(p) regularization is proposed in this paper,using the alternating direction method of multipliers(ADMM).By decomposing the complex primal problem into sub-problems solvable in parallel via proximal operators,ADMM can address the challenge effectively.To mitigate the sensitivity to regularization parameters,an adaptive regularization parameter is derived based on the K-sparsity strategy.Then,an ADMM-based sparse regularization method is developed,which is capable of handling l_(p) regularization with arbitrary p values using adaptively-updated parameters.The effectiveness and performance of the proposed method are validated on an aircraft skin-like composite structure.Additionally,an investigation into the optimal p value for achieving high-accuracy solutions via l_(p) regularization is conducted.It turns out that l_(0.6)regularization consistently yields sparser and more accurate solutions for impact force identification compared to the classic l_(1) regularization method.The impact force identification method proposed in this paper can simultaneously reconstruct impact time history with high accuracy and accurately localize the impact using an under-determined sensor configuration.

Enhanced Differentiable Architecture Search Based on Asymptotic Regularization

In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search space with different complexity according to various operations.Meanwhile rationalizing the search strategies to explore the well-defined search space will further improve the speed and efficiency of architecture search.With this in mind,we propose a faster and more efficient differentiable architecture search method,AllegroNAS.Firstly,we introduce a more efficient search space enriched by the introduction of two redefined convolution modules.Secondly,we utilize a more efficient architectural parameter regularization method,mitigating the overfitting problem during the search process and reducing the error brought about by gradient approximation.Meanwhile,we introduce a natural exponential cosine annealing method to make the learning rate of the neural network training process more suitable for the search procedure.Moreover,group convolution and data augmentation are employed to reduce the computational cost.Finally,through extensive experiments on several public datasets,we demonstrate that our method can more swiftly search for better-performing neural network architectures in a more efficient search space,thus validating the effectiveness of our approach.

Trigonometric Regularization and Continuation Method Based Time-Optimal Control of Hypersonic Vehicles

Aiming at the time-optimal control problem of hypersonic vehicles(HSV)in ascending stage,a trigonometric regularization method(TRM)is introduced based on the indirect method of optimal control.This method avoids analyzing the switching function and distinguishing between singular control and bang-bang control,where the singular control problem is more complicated.While in bang-bang control,the costate variables are unsmooth due to the control jumping,resulting in difficulty in solving the two-point boundary value problem(TPBVP)induced by the indirect method.Aiming at the easy divergence when solving the TPBVP,the continuation method is introduced.This method uses the solution of the simplified problem as the initial value of the iteration.Then through solving a series of TPBVP,it approximates to the solution of the original complex problem.The calculation results show that through the above two methods,the time-optimal control problem of HSV in ascending stage under the complex model can be solved conveniently.

Low-Rank Multi-View Subspace Clustering Based on Sparse Regularization

Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The significance of low-rank prior in MVSC is emphasized, highlighting its role in capturing the global data structure across views for improved performance. However, it faces challenges with outlier sensitivity due to its reliance on the Frobenius norm for error measurement. Addressing this, our paper proposes a Low-Rank Multi-view Subspace Clustering Based on Sparse Regularization (LMVSC- Sparse) approach. Sparse regularization helps in selecting the most relevant features or views for clustering while ignoring irrelevant or noisy ones. This leads to a more efficient and effective representation of the data, improving the clustering accuracy and robustness, especially in the presence of outliers or noisy data. By incorporating sparse regularization, LMVSC-Sparse can effectively handle outlier sensitivity, which is a common challenge in traditional MVSC methods relying solely on low-rank priors. Then Alternating Direction Method of Multipliers (ADMM) algorithm is employed to solve the proposed optimization problems. Our comprehensive experiments demonstrate the efficiency and effectiveness of LMVSC-Sparse, offering a robust alternative to traditional MVSC methods.

Enhanced Deep Reinforcement Learning Strategy for Energy Management in Plug-in Hybrid Electric Vehicles with Entropy Regularization and Prioritized Experience Replay

Plug-in Hybrid Electric Vehicles(PHEVs)represent an innovative breed of transportation,harnessing diverse power sources for enhanced performance.Energy management strategies(EMSs)that coordinate and control different energy sources is a critical component of PHEV control technology,directly impacting overall vehicle performance.This study proposes an improved deep reinforcement learning(DRL)-based EMSthat optimizes realtime energy allocation and coordinates the operation of multiple power sources.Conventional DRL algorithms struggle to effectively explore all possible state-action combinations within high-dimensional state and action spaces.They often fail to strike an optimal balance between exploration and exploitation,and their assumption of a static environment limits their ability to adapt to changing conditions.Moreover,these algorithms suffer from low sample efficiency.Collectively,these factors contribute to convergence difficulties,low learning efficiency,and instability.To address these challenges,the Deep Deterministic Policy Gradient(DDPG)algorithm is enhanced using entropy regularization and a summation tree-based Prioritized Experience Replay(PER)method,aiming to improve exploration performance and learning efficiency from experience samples.Additionally,the correspondingMarkovDecision Process(MDP)is established.Finally,an EMSbased on the improvedDRLmodel is presented.Comparative simulation experiments are conducted against rule-based,optimization-based,andDRL-based EMSs.The proposed strategy exhibitsminimal deviation fromthe optimal solution obtained by the dynamic programming(DP)strategy that requires global information.In the typical driving scenarios based onWorld Light Vehicle Test Cycle(WLTC)and New European Driving Cycle(NEDC),the proposed method achieved a fuel consumption of 2698.65 g and an Equivalent Fuel Consumption(EFC)of 2696.77 g.Compared to the DP strategy baseline,the proposed method improved the fuel efficiency variances(FEV)by 18.13%,15.1%,and 8.37%over the Deep QNetwork(DQN),Double DRL(DDRL),and original DDPG methods,respectively.The observational outcomes demonstrate that the proposed EMS based on improved DRL framework possesses good real-time performance,stability,and reliability,effectively optimizing vehicle economy and fuel consumption.

A NOx Concentration Prediction Model Based on a Sparse Regularization Stochastic Configuration Network

For accurate prediction of nitrogen oxides(NOx) concentration during the municipal solid waste incineration(MSWI) process, in this paper, a prediction modeling method based on a sparse regularization stochastic configuration network is proposed. The method combines Drop Connect regularization with L1 regularization. Based on the L1 regularization constraint stochastic configuration network output weights, Drop Connect regularization is applied to the input weights to introduce sparsity. A probability decay strategy based on network residuals is designed to address situations where the Drop Connect fixed drop probability affects model convergence. Finally, the generated sparse stochastic configuration network is used to establish the model, and is validated through experiments with standard datasets and actual data from an MSWI plant in Beijing. The experimental results prove that this modeling method exhibits high-precision prediction and generalization ability while effectively simplifying the model structure, which enables accurate prediction of NOx concentration.

3D density inversion of gravity gradient data using the extrapolated Tikhonov regularization

We use the extrapolated Tikhonov regularization to deal with the ill-posed problem of 3D density inversion of gravity gradient data. The use of regularization parameters in the proposed method reduces the deviations between calculated and observed data. We also use the depth weighting function based on the eigenvector of gravity gradient tensor to eliminate undesired effects owing to the fast attenuation of the position function. Model data suggest that the extrapolated Tikhonov regularization in conjunction with the depth weighting function can effectively recover the 3D distribution of density anomalies. We conduct density inversion of gravity gradient data from the Australia Kauring test site and compare the inversion results with the published research results. The proposed inversion method can be used to obtain the 3D density distribution of underground anomalies.

Second-Order Raman Scattering from n- and p-Type 4H-SiC

The results of second-order Raman-scattering experiments on n- and p-type 4H-SiC are presented,covering the acoustic and the optical overtone spectral regions.Some of the observed structures in the spectra are assigned to particular phonon branches and the points in the Brillouin zone from which the scattering originates.There exists a doublet at 626/636cm -1 with energy difference about 10cm -1 in both n- and p-type 4H-SiC,which is similar to the doublet structure with the same energy difference founded in hexagonal GaN,ZnO, and AlN.The cutoff frequency at 1926cm -1 of the second-order Raman is not the overtone of the A 1(LO) peak of the n-type doping 4H-SiC,but that of the undoping one.The second-order Raman spectrum of 4H-SiC can hardly be affected by doping species or doping density.

Iterative regularization method for image denoising with adaptive scale parameter

In order to decrease the sensitivity of the constant scale parameter, adaptively optimize the scale parameter in the iteration regularization model （IRM） and attain a desirable level of applicability for image denoising, a novel IRM with the adaptive scale parameter is proposed. First, the classic regularization item is modified and the equation of the adaptive scale parameter is deduced. Then, the initial value of the varying scale parameter is obtained by the trend of the number of iterations and the scale parameter sequence vectors. Finally, the novel iterative regularization method is used for image denoising. Numerical experiments show that compared with the IRM with the constant scale parameter, the proposed method with the varying scale parameter can not only reduce the number of iterations when the scale parameter becomes smaller, but also efficiently remove noise when the scale parameter becomes bigger and well preserve the details of images.

Anti-periodic solutions to a class of second-order evolution equations

In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.