A NEW GLOBAL OPTIMIZATION ALGORITHM FOR MIXED-INTEGER QUADRATICALLY CONSTRAINED QUADRATIC FRACTIONAL PROGRAMMING PROBLEM

The mixed-integer quadratically constrained quadratic fractional programming(MIQCQFP)problem often appears in various fields such as engineering practice,management science and network communication.However,most of the solutions to such problems are often designed for their unique circumstances.This paper puts forward a new global optimization algorithm for solving the problem MIQCQFP.We first convert the MIQCQFP into an equivalent generalized bilinear fractional programming(EIGBFP)problem with integer variables.Secondly,we linearly underestimate and linearly overestimate the quadratic functions in the numerator and the denominator respectively,and then give a linear fractional relaxation technique for EIGBFP on the basis of non-negative numerator.After that,combining rectangular adjustment-segmentation technique and midpointsampling strategy with the branch-and-bound procedure,an efficient algorithm for solving MIQCQFP globally is proposed.Finally,a series of test problems are given to illustrate the effectiveness,feasibility and other performance of this algorithm.

基于迁移QCNN的孪生网络轴承故障诊断方法

轴承故障诊断对于降低旋转机械的损坏风险,进一步提高经济效益具有重要意义;深度学习在轴承故障诊断中应用广泛,但是深度学习模型在训练与测试时容易受到噪声的干扰导致性能下降;并且轴承的工况变化频繁,不同工况下的数据采集困难;对此,提出了一种基于迁移QCNN的孪生网络轴承故障诊断方法,先预训练QCNN获取具有较强判别性的模型参数,将预训练的参数迁移到QCNN作为子网络的孪生网络中,然后正常训练孪生网络获取模型,最后将测试数据与故障数据组成数据对输入模型,即可得到测试数据的故障类型;该方法将QCNN与孪生网络相结合,QCNN中的Quadratic神经元具有强大的特征提取能力,孪生网络共享权重和相对关系的训练方式,使得模型可以缓解噪声和工况数据不平衡问题的影响;实验结果显示,相较与传统机器学习模型和QCNN等模型,所提出方法在面对噪声和工况数据不平衡问题表现更好。

Global Optimization of a Class of Nonconvex Quadratically Constrained Quadratic Programming Problems

In this paper we study a Class of nonconvex quadratically constrained quadratic programming problems generalized from relaxations of quadratic assignment problems. We show that each problem is polynomially solved. Strong duality holds if a redundant constraint is introduced. As an application, a new lower bound is proposed for the quadratic assignment problem.

Dynamic Event-Triggered Quadratic Nonfragile Filtering for Non-Gaussian Systems:Tackling Multiplicative Noises and Missing Measurements

This paper focuses on the quadratic nonfragile filtering problem for linear non-Gaussian systems under multiplicative noises,multiple missing measurements as well as the dynamic event-triggered transmission scheme.The multiple missing measurements are characterized through random variables that obey some given probability distributions,and thresholds of the dynamic event-triggered scheme can be adjusted dynamically via an auxiliary variable.Our attention is concentrated on designing a dynamic event-triggered quadratic nonfragile filter in the well-known minimum-variance sense.To this end,the original system is first augmented by stacking its state/measurement vectors together with second-order Kronecker powers,thus the original design issue is reformulated as that of the augmented system.Subsequently,we analyze statistical properties of augmented noises as well as high-order moments of certain random parameters.With the aid of two well-defined matrix difference equations,we not only obtain upper bounds on filtering error covariances,but also minimize those bounds via carefully designing gain parameters.Finally,an example is presented to explain the effectiveness of this newly established quadratic filtering algorithm.

Global dust density in two-dimensional complex plasma

The driven-dissipative Langevin dynamics simulation is used to produce a two-dimensional(2D) dense cloud, which is composed of charged dust particles trapped in a quadratic potential. A 2D mesh grid is built to analyze the center-to-wall dust density. It is found that the local dust density in the outer region relative to that of the inner region is more nonuniform,being consistent with the feature of quadratic potential. The dependences of the global dust density on equilibrium temperature, particle size, confinement strength, and confinement shape are investigated. It is found that the particle size, the confinement strength, and the confinement shape strongly affect the global dust density, while the equilibrium temperature plays a minor effect on it. In the direction where there is a stronger confinement, the dust density gradient is bigger.

New indices to balanceα-diversity against tree size inequality

The number and composition of species in a community can be quantified withα-diversity indices,including species richness(R),Simpson’s index(D),and the Shannon-Wiener index(H΄).In forest communities,there are large variations in tree size among species and individu-als of the same species,which result in differences in eco-logical processes and ecosystem functions.However,tree size inequality(TSI)has been largely neglected in studies using the available diversity indices.The TSI in the diameter at breast height(DBH)data for each of 99920 m×20 m forest census quadrats was quantified using the Gini index(GI),a measure of the inequality of size distribution.The generalized performance equation was used to describe the rotated and right-shifted Lorenz curve of the cumulative proportion of DBH and the cumulative proportion of number of trees per quadrat.We also examined the relationships ofα-diversity indices with the GI using correlation tests.The generalized performance equation effectively described the rotated and right-shifted Lorenz curve of DBH distributions,with most root-mean-square errors(990 out of 999 quadrats)being<0.0030.There were significant positive correlations between each of threeα-diversity indices(i.e.,R,D,and H’)and the GI.Nevertheless,the total abundance of trees in each quadrat did not significantly influence the GI.This means that the TSI increased with increasing spe-cies diversity.Thus,two new indices are proposed that can balanceα-diversity against the extent of TSI in the com-munity:(1−GI)×D,and(1−GI)×H’.These new indices were significantly correlated with the original D and H΄,and did not increase the extent of variation within each group of indices.This study presents a useful tool for quantifying both species diversity and the variation in tree sizes in forest communities,especially in the face of cumulative species loss under global climate change.

Predictive active control of building structures using LQR and artificial intelligence

This study presents a neural network-based model for predicting linear quadratic regulator(LQR)weighting matrices for achieving a target response reduction.Based on the expected weighting matrices,the LQR algorithm is used to determine the various responses of the structure.The responses are determined by numerically analyzing the governing equation of motion using the state-space approach.For training a neural network,four input parameters are considered:the time history of the ground motion,the percentage reduction in lateral displacement,lateral velocity,and lateral acceleration,Output parameters are LQR weighting matrices.To study the effectiveness of an LQR-based neural network(LQRNN),the actual percentage reduction in the responses obtained from using LQRNN is compared with the target percentage reductions.Furthermore,to investigate the efficacy of an active control system using LQRNN,the controlled responses of a system are compared to the corresponding uncontrolled responses.The trained neural network effectively predicts weighting parameters that can provide a percentage reduction in displacement,velocity,and acceleration close to the target percentage reduction.Based on the simulation study,it can be concluded that significant response reductions are observed in the active-controlled system using LQRNN.Moreover,the LQRNN algorithm can replace conventional LQR control with the use of an active control system.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures.These structures,commonly encountered in engineering applications,often involve complex objective and constraint functions that cannot be readily expressed as explicit functions of the design variables.As a result,sequential approximation techniques have emerged as the preferred strategy for addressing a wide array of topology optimization challenges.Over the past several decades,topology optimization methods have been advanced remarkably and successfully applied to solve engineering problems incorporating diverse physical backgrounds.In comparison to the large-scale equation solution,sensitivity analysis,graphics post-processing,etc.,the progress of the sequential approximation functions and their corresponding optimizersmake sluggish progress.Researchers,particularly novices,pay special attention to their difficulties with a particular problem.Thus,this paper provides an overview of sequential approximation functions,related literature on topology optimization methods,and their applications.Starting from optimality criteria and sequential linear programming,the other sequential approximate optimizations are introduced by employing Taylor expansion and intervening variables.In addition,recent advancements have led to the emergence of approaches such as Augmented Lagrange,sequential approximate integer,and non-gradient approximation are also introduced.By highlighting real-world applications and case studies,the paper not only demonstrates the practical relevance of these methods but also underscores the need for continued exploration in this area.Furthermore,to provide a comprehensive overview,this paper offers several novel developments that aim to illuminate potential directions for future research.

Optimal Cooperative Secondary Control for Islanded DC Microgrids via a Fully Actuated Approach

DC-DC converter-based multi-bus DC microgrids(MGs) in series have received much attention, where the conflict between voltage recovery and current balancing has been a hot topic. The lack of models that accurately portray the electrical characteristics of actual MGs while is controller design-friendly has kept the issue active. To this end, this paper establishes a large-signal model containing the comprehensive dynamical behavior of the DC MGs based on the theory of high-order fully actuated systems, and proposes distributed optimal control based on this. The proposed secondary control method can achieve the two goals of voltage recovery and current sharing for multi-bus DC MGs. Additionally, the simple structure of the proposed approach is similar to one based on droop control, which allows this control technique to be easily implemented in a variety of modern microgrids with different configurations. In contrast to existing studies, the process of controller design in this paper is closely tied to the actual dynamics of the MGs. It is a prominent feature that enables engineers to customize the performance metrics of the system. In addition, the analysis of the stability of the closed-loop DC microgrid system, as well as the optimality and consensus of current sharing are given. Finally, a scaled-down solar and battery-based microgrid prototype with maximum power point tracking controller is developed in the laboratory to experimentally test the efficacy of the proposed control method.

Highly Accurate Golden Section Search Algorithms and Fictitious Time Integration Method for Solving Nonlinear Eigenvalue Problems

This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.

Reduced-Order Observer-Based LQR Controller Design for Rotary Inverted Pendulum

The Rotary Inverted Pendulum(RIP)is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge.Despite the implementation of various control strategies to maintain equilibrium,optimally tuning control gains to effectively mitigate uncertain nonlinearities in system dynamics remains elusive.Existing methods frequently rely on extensive experimental data or the designer’s expertise,presenting a notable drawback.This paper proposes a novel tracking control approach for RIP,utilizing a Linear Quadratic Regulator(LQR)in combination with a reduced-order observer.Initially,the RIP system is mathematically modeled using the Newton-Euler-Lagrange method.Subsequently,a composite controller is devised that integrates an LQR for generating nominal control signals and a reduced-order observer for reconstructing unmeasured states.This approach enhances the controller’s robustness by eliminating differential terms from the observer,thereby attenuating unknown disturbances.Thorough numerical simulations and experimental evaluations demonstrate the system’s capability to maintain balance below50Hz and achieve precise tracking below1.4 rad,validating the effectiveness of the proposed control scheme.

Nonparametric Statistical Feature Scaling Based Quadratic Regressive Convolution Deep Neural Network for Software Fault Prediction

The development of defect prediction plays a significant role in improving software quality. Such predictions are used to identify defective modules before the testing and to minimize the time and cost. The software with defects negatively impacts operational costs and finally affects customer satisfaction. Numerous approaches exist to predict software defects. However, the timely and accurate software bugs are the major challenging issues. To improve the timely and accurate software defect prediction, a novel technique called Nonparametric Statistical feature scaled QuAdratic regressive convolution Deep nEural Network (SQADEN) is introduced. The proposed SQADEN technique mainly includes two major processes namely metric or feature selection and classification. First, the SQADEN uses the nonparametric statistical Torgerson–Gower scaling technique for identifying the relevant software metrics by measuring the similarity using the dice coefficient. The feature selection process is used to minimize the time complexity of software fault prediction. With the selected metrics, software fault perdition with the help of the Quadratic Censored regressive convolution deep neural network-based classification. The deep learning classifier analyzes the training and testing samples using the contingency correlation coefficient. The softstep activation function is used to provide the final fault prediction results. To minimize the error, the Nelder–Mead method is applied to solve non-linear least-squares problems. Finally, accurate classification results with a minimum error are obtained at the output layer. Experimental evaluation is carried out with different quantitative metrics such as accuracy, precision, recall, F-measure, and time complexity. The analyzed results demonstrate the superior performance of our proposed SQADEN technique with maximum accuracy, sensitivity and specificity by 3%, 3%, 2% and 3% and minimum time and space by 13% and 15% when compared with the two state-of-the-art methods.

High-Order Decoupled and Bound Preserving Local Discontinuous Galerkin Methods for a Class of Chemotaxis Models

In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.

Effect of Quadrat Shape on Spatial Point Pattern Performance of Haloxylon ammodendron

In this study, we investigated the natural growth of Haloxylon ammodendron forest in Moso Bay, southwest of Gurbantunggut Desert. Random sample analysis was used to analyze the spatial point pattern performance of Haloxylon ammodendron population. ArcGIS software was used to summarize and analyze the spatial point pattern response of Haloxylon ammodendron population. The results showed that: 1) There were significant differences in the performance of point pattern analysis among different random quadrants. The paired t-test for variance mean ratio showed that the P values were 0.048, 0.004 and 0.301 respectively, indicating that the influence of quadrat shape on the performance of point pattern analysis was significant under the condition of the same optimal quadrat area. 2) The comparative analysis of square shapes shows that circular square is the best, square and regular hexagonal square are the second, and there is no significant difference between square and regular hexagonal square. 3) The number of samples plays a decisive role in spatial point pattern analysis. Insufficient sample size will lead to unstable results. With the increase of the number of samples to more than 120, the V value and P value curves will eventually stabilize. That is, stable spatial point pattern analysis results are closely related to the increase of the number of samples in random sample square analysis.

Robust Parameter Identification Method of Adhesion Model for Heavy Haul Trains

A robust parameter identification method based on Kiencke model was proposed to solve the problem of the parameter identification accuracy being affected by the rail environment change and noise interference for heavy-duty trains. Firstly, a Kiencke stick-creep identification model was constructed, and the parameter identification task was transformed into a quadratic programming problem. Secondly, an iterative algorithm was constructed to solve the problem, into which a time-varying forgetting factor was added to track the change of the rail environment, and to solve the uncertainty problem of the wheel-rail environment. The Granger causality test was adopted to detect the interference, and then the weights of the current data were redistributed to solve the problem of noise interference in parameter identification. Finally, simulations were carried out and the results showed that the proposed method could track the change of the track environment in time, reduce the noise interference in the identification process, and effectively identify the adhesion performance parameters.

Semidefinite Relaxation for Two Mixed Binary Quadratically Constrained Quadratic Programs:Algorithms and Approximation Bounds

This paper develops new semidefinite programming(SDP)relaxation techniques for two classes of mixed binary quadratically constrained quadratic programs and analyzes their approximation performance.The first class of problems finds two minimum norm vectors in N-dimensional real or complex Euclidean space,such that M out of 2M concave quadratic constraints are satisfied.By employing a special randomized rounding procedure,we show that the ratio between the norm of the optimal solution of this model and its SDP relaxation is upper bounded by 54πM2 in the real case and by 24√Mπin the complex case.The second class of problems finds a series of minimum norm vectors subject to a set of quadratic constraints and cardinality constraints with both binary and continuous variables.We show that in this case the approximation ratio is also bounded and independent of problem dimension for both the real and the complex cases.

Robust Solutions of Uncertain Complex-valued Quadratically Constrained Programs

In this paper, we discuss complex convex quadratically constrained optimization with uncertain data. Using S-Lemma, we show that the robust counterpart of complex convex quadratically constrained optimization with ellipsoidal or intersection-of-two-ellipsoids uncertainty set leads to a complex semidefinite program. By exploring the approximate S-Lemma, we give a complex semidefinite program which approximates the NP-hard robust counterpart of complex convex quadratic optimization with intersection-of-ellipsoids uncertainty set.

Manifolds of positive Ricci curvature,quadratically asymptotically nonnegative curvature,and infinite Betti numbers

In a previous paper(Jiang and Yang(2021)),we constructed complete manifolds of positive Ricci curvature with quadratically asymptotically nonnegative curvature and infinite topological type but dimensions greater than or equal to 6.The purpose of the present paper is to use a different technique to exhibit a family of complete I-dimensional(I≥5)Riemannian manifolds of positive Ricci curvature,quadratically asymptotically nonnegative sectional curvature,and certain infinite Betti numbers bj(2≤j≤I-2).

Modelling Foot and Mouth Disease in the Context of Active Immigrants

This study employs mathematical modeling to analyze the impact of active immigrants on Foot and Mouth Disease (FMD) transmission dynamics. We calculate the reproduction number (R0) using the next-generation matrix approach. Applying the Routh-Hurwitz Criterion, we establish that the Disease-Free Equilibrium (DFE) point achieves local asymptotic stability when R0 α1 and α2) are closely associated with reduced susceptibility in animal populations, underscoring the link between immigrants and susceptibility. Furthermore, our findings emphasize the interplay of disease introduction with population response and adaptation, particularly involving incoming infectious immigrants. Swift interventions are vital due to the limited potential for disease establishment and rapid susceptibility decline. This study offers crucial insights into the complexities of FMD transmission with active immigrants, informing effective disease management strategies.