A LOW-COST OPTIMIZATION APPROACH FOR SOLVING MINIMUM NORM LINEAR SYSTEMS AND LINEAR LEAST-SQUARES PROBLEMS

Recently,the authors proposed a low-cost approach,named Optimization Approach for Linear Systems(OPALS)for solving any kind of a consistent linear system regarding the structure,characteristics,and dimension of the coefficient matrix A.The results obtained by this approach for matrices with no structure and with indefinite symmetric part were encouraging when compare with other recent and well-known techniques.In this work,we proposed to extend the OPALS approach for solving the Linear Least-Squares Problem(LLSP)and the Minimum Norm Linear System Problem(MNLSP)using any iterative low-cost gradient-type method,avoiding the construction of the matrices AT A or AAT,and taking full advantage of the structure and form of the gradient of the proposed nonlinear objective function in the gradient direction.The combination of those conditions together with the choice of the initial iterate allow us to produce a novel and efficient low-cost numerical scheme for solving both problems.Moreover,the scheme presented in this work can also be used and extended for the weighted minimum norm linear systems and minimum norm linear least-squares problems.We include encouraging numerical results to illustrate the practical behavior of the proposed schemes.

DMPFIT: A Tool for Atomic-Scale Metrology via Nonlinear Least-Squares Fitting of Peaks in Atomic-Resolution TEM Images

Despite the wide availability and usage of Gatan’s DigitalMicrograph software in the electron microscopy community for image recording and analysis, nonlinear least-squares fitting in DigitalMicrograph is less straightforward. This work presents a ready-to-use tool, the DMPFIT software package, written in DigitalMicrograph script and C++ language, for nonlinear least-squares fitting of the intensity distribution of atomic columns in atomic-resolution transmission electron microscopy (TEM) images with a general two-dimensional (2D) Gaussian model. Applications of the DMPFIT software are demonstrated both in atomic-resolution conventional coherent TEM (CTEM) images recorded by the negative spherical aberration imaging technique and in high angle annular dark field (HAADF) scanning TEM (STEM) images. The implemented peak-finding algorithm based on the periodicity of 2D lattices enables reliable and convenient atomic-scale metrology as well as intuitive presentation of the resolved atomic structures.

Least-squares reverse time migration in visco-acoustic media based on symplectic stereo-modeling method

The authors proposed a symplectic stereo-modeling method(SSM)in the Birkhoffian dynam-ics and apply it to the visco-acoustic least-squares reverse time migration(LSRTM).The SSM adopts ste-reo-modeling operator in space and symplectic Runge-Kutta scheme in time,resulting in great ability in suppressing numerical dispersion and long-time computing.These advantages are further confirmed by numerical dispersion analysis,long-time computation test and computational efficiency comparison.After these theoretical analyses and experiments,acoustic and visco-acoustic LSRTM are tested and compared between SSM method and the conventional symplectic method(CSM)using the fault and marmousi models.Meanwhile,dynamic source encoding and exponential decay moving average gradients method are adopted to reduce the computation cost and improve the convergence rate.The imaging results show that LSRTM based on visco-acoustic wave equations effectively takes into account the influence of viscosity can therefore compensate for the amplitude attenuation.Besides,SSM method not only has high numerical accuracy and computational efficiency,but also performs effectively in LSRTM.

Nonlinear total least-squares variance component estimation for GM(1,1)model

The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.

PCR ALGORITHM FOR PARALLEL COMPUTING MINIMUM-NORM LEAST-SQUARES SOLUTION OF INCONSISTENT LINEAR EQUATIONS

This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obtained in T = n(log2m + log2(n - r + 1) + 5) + log2m + 1 steps with P=mn processors when m × 2(n - 1) and with P = 2n(n - 1) processors otherwise.

Linearized waveform inversion for vertical transversely isotropic elastic media:Methodology and multi-parameter crosstalk analysis

Seismic migration and inversion are closely related techniques to portray subsurface images and identify hydrocarbon reservoirs.Seismic migration aims at obtaining structural images of subsurface geologic discontinuities.More specifically,seismic migration estimates the reflectivity function(stacked average reflectivity or pre-stack angle-dependent reflectivity)from seismic reflection data.On the other hand,seismic inversion quantitatively estimates the intrinsic rock properties of subsurface formulations.Such seismic inversion methods are applicable to detect hydrocarbon reservoirs that may exhibit lateral variations in the inverted parameters.Although there exist many differences,pre-stack seismic migration is similar with the first iteration of the general linearized seismic inversion.Usually,seismic migration and inversion techniques assume an acoustic or isotropic elastic medium.Unconventional reservoirs such as shale and tight sand formation have notable anisotropic property.We present a linearized waveform inversion(LWI)scheme for weakly anisotropic elastic media with vertical transversely isotropic(VTI)symmetry.It is based on two-way anisotropic elastic wave equation and simultaneously inverts for the localized perturbations(ΔVp_(0)/Vp_(0)/Vs_(0)/Vs_(0)/,Δ∈,Δδ)from the long-wavelength reference model.Our proposed VTI-elastic LWI is an iterative method that requires a forward and an adjoint operator acting on vectors in each iteration.We derive the forward Born approximation operator by perturbation theory and adjoint operator via adjoint-state method.The inversion has improved the quality of the images and reduces the multi-parameter crosstalk comparing with the adjoint-based images.We have observed that the multi-parameter crosstalk problem is more prominent in the inversion images for Thomsen anisotropy parameters.Especially,the Thomsen parameter is the most difficult to resolve.We also analyze the multi-parameter crosstalk using scattering radiation patterns.The linearized waveform inversion for VTI-elastic media presented in this article provides quantitative information of the rock properties that has the potential to help identify hydrocarbon reservoirs.

Optimization Algorithms of PERT/CPM Network Diagrams in Linear Diophantine Fuzzy Environment

The idea of linear Diophantine fuzzy set(LDFS)theory with its control parameters is a strong model for machine learning and optimization under uncertainty.The activity times in the critical path method(CPM)representation procedures approach are initially static,but in the Project Evaluation and Review Technique(PERT)approach,they are probabilistic.This study proposes a novel way of project review and assessment methodology for a project network in a linear Diophantine fuzzy(LDF)environment.The LDF expected task time,LDF variance,LDF critical path,and LDF total expected time for determining the project network are all computed using LDF numbers as the time of each activity in the project network.The primary premise of the LDF-PERT approach is to address ambiguities in project network activity timesmore simply than other approaches such as conventional PERT,Fuzzy PERT,and so on.The LDF-PERT is an efficient approach to analyzing symmetries in fuzzy control systems to seek an optimal decision.We also present a new approach for locating LDF-CPM in a project network with uncertain and erroneous activity timings.When the available resources and activity times are imprecise and unpredictable,this strategy can help decision-makers make better judgments in a project.A comparison analysis of the proposed technique with the existing techniques has also been discussed.The suggested techniques are demonstrated with two suitable numerical examples.

Numerical studies for plasmas of a linear plasma device HIT-PSI with geometry modified SOLPS-ITER

The HIT-PSI is a linear plasma device built for physically simulating the high heat flux environment of future reactor divertors to test/develop advanced target plate materials.In this study,the geometry-modified SOLPS-ITER program is employed to examine the effects of the magnetic field strength and neutral pressure in the device on the heat flux experienced by the target plate of the HIT-PSI device.The findings of the numerical simulation indicate a positive correlation between the magnetic field strength and the heat flux density.Conversely,there is a negative correlation observed between the heat flux density and the neutral pressure.When the magnetic field strength at the axis exceeds 1 tesla and the neutral pressure falls below 10 Pa,the HIT-PSI has the capability to attain a heat flux of 10 MW·m-2 at the target plate.The simulation results offer a valuable point of reference for subsequent experiments at HIT-PSI.

A Study of the TPS Based Beam-Matching Concept for Medical Linear Accelerators at a Tertiary Hospital

The flexibility in radiotherapy can be improved if patients can be moved between any one of the department’s medical linear accelerators (LINACs) without the need to change anything in the patient’s treatment plan. For this to be possible, the dosimetric characteristics of the various accelerators must be the same, or nearly the same. The purpose of this work is to describe further and compare measurements and parameters after the initial vendor-recommended beam matching of the five LINACs. Deviations related to dose calculations and to beam matched accelerators may compromise treatment accuracy. The safest and most practical way to ensure that all accelerators are within clinical acceptable accuracy is to include TPS calculations in the LINACs matching evaluation. Treatment planning system (TPS) was used to create three photons plans with different field sizes 3 × 3 cm, 10 × 10 cm and 25 × 25 cm at a depth of 4.5 cm in Perspex. Calculated TPS plans were sent to Mosaiq to be delivered by five LINACs. TPS plans were compared with five LINACs measurements data using Gamma analyses of 2% and 2 mm. The results suggest that for four out of the five LINACs, there was generally good agreement, less than a 2% deviation between the planned dose distribution and the measured dose distribution. However, one specific LINAC named “Asterix” exhibited a deviation of 2.121% from the planned dose. The results show that all of the LINACs’ performance were within the acceptable deviation and delivering radiation dose consistently and accurately.

Linear dichroism transition and polarization-sensitive photodetector of quasi-one-dimensional palladium bromide

Perpendicular optical reversal of the linear dichroism transition has promising applications in polarization-sensitive optoelectronic devices. We perform a systematical study on the in-plane optical anisotropy of quasi-one-dimensional PdBr_(2) by using combined measurements of the angle-resolved polarized Raman spectroscopy(ARPRS) and anisotropic optical absorption spectrum. The analyses of ARPRS data validate the anisotropic Raman properties of the PdBr_(2) flake.And anisotropic optical absorption spectrum of PdBr_(2) nanoflake demonstrates distinct optical linear dichroism reversal. Photodetector constructed by PdBr_(2) nanowire exhibits high responsivity of 747 A·W^(-1) and specific detectivity of 5.8×10^(12) Jones. And the photodetector demonstrates prominent polarization-sensitive photoresponsivity under 405-nm light irradiation with large photocurrent anisotropy ratio of 1.56, which is superior to those of most of previously reported quasi-one-dimensional counterparts. Our study offers fundamental insights into the strong optical anisotropy exhibited by PdBr_(2), establishing it as a promising candidate for miniaturization and integration trends of polarization-related applications.

Feedback linearization and equivalent-disturbance compensation control strategy for piezoelectric stage

Piezoelectric stages use piezoelectric actuators and flexure hinges as driving and amplifying mechanisms,respectively.These systems have high positioning accuracy and high-frequency responses,and they are widely used in various precision/ultra-precision positioning fields.However,the main challenge with these devices is the inherent hysteresis nonlinearity of piezoelectric actuators,which seriously affects the tracking accuracy of a piezoelectric stage.Inspired by this challenge,in this work,we developed a Hammerstein model to describe the hysteresis nonlinearity of a piezoelectric stage.In particular,in our proposed scheme,a feedback-linearization algorithm is used to eliminate the static hysteresis nonlinearity.In addition,a composite controller based on equivalent-disturbance compensation was designed to counteract model uncertainties and external disturbances.An analysis of the stability of a closed-loop system based on this feedback-linearization algorithm and composite controller was performed,and this was followed by extensive comparative experiments using a piezoelectric stage developed in the laboratory.The experimental results confirmed that the feedback-linearization algorithm and the composite controller offer improved linearization and trajectory-tracking performance.

Linear magnetoresistance and structural distortion in layered SrCu_(4-x)P_(2) single crystals

We report a systematic study on layered metal SrCu_(4-x)P_(2) single crystals via transport, magnetization, thermodynamic measurements and structural characterization. We find that the crystals show large linear magnetoresistance without any sign of saturation with a magnetic field up to 30T. We also observe a phase transition with significant anomalies in resistivity and heat capacity at T_(p)~140 K. Thermal expansion measurement reveals a subtle lattice parameter variation near Tp, i.e.,?L_(c)/L_(c)~0.062%. The structural characterization confines that there is no structure transition below and above T_(p). All these results suggest that the nonmagnetic transition of SrCu_(4-x)P_(2) could be associated with structural distortion.

Equivalent linear model for seismic damage evaluation of single-degree-of-freedom systems representing reinforced concrete structures considering cyclic degradation behavior

In this study,a novel equivalent damping ratio model that is suitable for reinforced concrete(RC)structures considering cyclic degradation behavior is developed,and a new equivalent linearization analysis method for implementing the proposed equivalent damping ratio model for use in seismic damage evaluation is presented.To this end,Ibarra’s peak-oriented model,which incorporates an energy-based degradation rule,is selected for representing hysteretic behavior of RC structure,and the optimized equivalent damping for predicting the maximum displacement response is presented by using the empirical method,in which the effect of cyclic degradation is considered.Moreover,the relationship between the hysteretic energy dissipation of the inelastic system and the elastic strain energy of the equivalent linear system is established so that the proposed equivalent linear system can be directly integrated with the Park-Ang seismic model to implement seismic damage evaluation.Due to the simplicity of the equivalent linearization method,the proposed method provides an efficient and reliable way of obtaining comprehensive insight into the seismic performance of RC structures.The verification demonstrates the validity of the proposed method.

Effects of the initiation position on the damage and fracture characteristics of linear-charge blasting in rock

To study the effects of the initiation position on the damage and fracture characteristics of linear-charge blasting, blasting model experiments were conducted in this study using computed tomography scanning and three-dimensional reconstruction methods. The fractal damage theory was used to quantify the crack distribution and damage degree of sandstone specimens after blasting. The results showed that regardless of an inverse or top initiation, due to compression deformation and sliding frictional resistance, the plugging medium of the borehole is effective. The energy of the explosive gas near the top of the borehole is consumed. This affects the effective crushing of rocks near the top of the borehole, where the extent of damage to Sections Ⅰ and Ⅱ is less than that of Sections Ⅲ and Ⅳ. In addition, the analysis revealed that under conditions of top initiation, the reflected tensile damage of the rock at the free face of the top of the borehole and the compression deformation of the plug and friction consume more blasting energy, resulting in lower blasting energy efficiency for top initiation. As a result, the overall damage degree of the specimens in the top-initiation group was significantly smaller than that in the inverse-initiation group. Under conditions of inverse initiation, the blasting energy efficiency is greater, causing the specimen to experience greater damage. Therefore, in the engineering practice of rock tunnel cut blasting, to utilize blasting energy effectively and enhance the effects of rock fragmentation, using the inverse-initiation method is recommended. In addition, in three-dimensional(3D) rock blasting, the bottom of the borehole has obvious end effects under the conditions of inverse initiation, and the crack distribution at the bottom of the borehole is trumpet-shaped. The occurrence of an end effect in the 3D linear-charge blasting model experiment is related to the initiation position and the blocking condition.

Linear paired electrolysis of furfural to furoic acid at both anode and cathode in a multiple redox mediated system

Implementing a new energy-saving electrochemical synthesis system with high commercial value is a strategy of the sustainable development for upgrading the bulk chemicals preparation technology in the future.Here,we report a multiple redox-mediated linear paired electrolysis system,combining the hydrogen peroxide mediated cathode process with the I2 mediated anode process,and realize the conversion of furfural to furoic acid in both side of the dividedflow cell simultaneously.By reasonably controlling the cathode potential,the undesired water splitting reaction and furfural reduction side reactions are avoided.Under the galvanostatic electrolysis,the two-mediated electrode processes have good compatibility,which reduce the energy consumption by about 22%while improving the electronic efficiency by about 125%.This system provides a green electrochemical synthesis route with commercial prospects.

Underdetermined direction of arrival estimation with nonuniform linear motion sampling based on a small unmanned aerial vehicle platform

Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.

A review of linear friction welding of Ni -based superalloys

Ni-based superalloys are one of the most important materials employed in high-temperature applications within the aerospace and nuclear energy industries and in gas turbines due to their excellent corrosion,radiation,fatigue resistance,and high-temperature strength.Linear friction welding(LFW)is a new joining technology with near-net-forming characteristics that can be used for the manu-facture and repair of a wide range of aerospace components.This paper reviews published works on LFW of Ni-based superalloys with the aim of understanding the characteristics of frictional heat generation and extrusion deformation,microstructures,mechanical proper-ties,flash morphology,residual stresses,creep,and fatigue of Ni-based superalloy weldments produced with LFW to enable future optim-um utilization of the LFW process.

Risk-Informed Model-Free Safe Control of Linear Parameter-Varying Systems

This paper presents a risk-informed data-driven safe control design approach for a class of stochastic uncertain nonlinear discrete-time systems.The nonlinear system is modeled using linear parameter-varying(LPV)systems.A model-based probabilistic safe controller is first designed to guarantee probabilisticλ-contractivity(i.e.,stability and invariance)of the LPV system with respect to a given polyhedral safe set.To obviate the requirement of knowing the LPV system model and to bypass identifying its open-loop model,its closed-loop data-based representation is provided in terms of state and scheduling data as well as a decision variable.It is shown that the variance of the closedloop system,as well as the probability of safety satisfaction,depends on the decision variable and the noise covariance.A minimum-variance direct data-driven gain-scheduling safe control design approach is presented next by designing the decision variable such that all possible closed-loop system realizations satisfy safety with the highest confidence level.This minimum-variance approach is a control-oriented learning method since it minimizes the variance of the state of the closed-loop system with respect to the safe set,and thus minimizes the risk of safety violation.Unlike the certainty-equivalent approach that results in a risk-neutral control design,the minimum-variance method leads to a risk-averse control design.It is shown that the presented direct risk-averse learning approach requires weaker data richness conditions than existing indirect learning methods based on system identification and can lead to a lower risk of safety violation.Two simulation examples along with an experimental validation on an autonomous vehicle are provided to show the effectiveness of the presented approach.

A Weakly-Supervised Crowd Density Estimation Method Based on Two-Stage Linear Feature Calibration

In a crowd density estimation dataset,the annotation of crowd locations is an extremely laborious task,and they are not taken into the evaluation metrics.In this paper,we aim to reduce the annotation cost of crowd datasets,and propose a crowd density estimation method based on weakly-supervised learning,in the absence of crowd position supervision information,which directly reduces the number of crowds by using the number of pedestrians in the image as the supervised information.For this purpose,we design a new training method,which exploits the correlation between global and local image features by incremental learning to train the network.Specifically,we design a parent-child network(PC-Net)focusing on the global and local image respectively,and propose a linear feature calibration structure to train the PC-Net simultaneously,and the child network learns feature transfer factors and feature bias weights,and uses the transfer factors and bias weights to linearly feature calibrate the features extracted from the Parent network,to improve the convergence of the network by using local features hidden in the crowd images.In addition,we use the pyramid vision transformer as the backbone of the PC-Net to extract crowd features at different levels,and design a global-local feature loss function(L2).We combine it with a crowd counting loss(LC)to enhance the sensitivity of the network to crowd features during the training process,which effectively improves the accuracy of crowd density estimation.The experimental results show that the PC-Net significantly reduces the gap between fullysupervised and weakly-supervised crowd density estimation,and outperforms the comparison methods on five datasets of Shanghai Tech Part A,ShanghaiTech Part B,UCF_CC_50,UCF_QNRF and JHU-CROWD++.

Stability analysis of a liquid crystal elastomer self-oscillator under a linear temperature field

Self-oscillating systems abound in the natural world and offer substantial potential for applications in controllers,micro-motors,medical equipments,and so on.Currently,numerical methods have been widely utilized for obtaining the characteristics of self-oscillation including amplitude and frequency.However,numerical methods are burdened by intricate computations and limited precision,hindering comprehensive investigations into self-oscillating systems.In this paper,the stability of a liquid crystal elastomer fiber self-oscillating system under a linear temperature field is studied,and analytical solutions for the amplitude and frequency are determined.Initially,we establish the governing equations of self-oscillation,elucidate two motion regimes,and reveal the underlying mechanism.Subsequently,we conduct a stability analysis and employ a multi-scale method to obtain the analytical solutions for the amplitude and frequency.The results show agreement between the multi-scale and numerical methods.This research contributes to the examination of diverse self-oscillating systems and advances the theoretical analysis of self-oscillating systems rooted in active materials.