Static Problem Research Articles

The static voltage stability analysis of photovoltaic energy storage systems based on NPU algorithm

Although the data-driven static voltage stability problems have been widely studied, most of the classical algorithms focus more on improving the accuracy of the system prediction, ignoring the error classification errors generated during the prediction process. Furthermore, current research ignores the utilization of data-driven voltage stability assessment of energy storage systems. Therefore, this paper proposes a static voltage stability assessment method for photovoltaic energy storage systems based on considering the error classification constraint algorithm using Neyman-Pearson umbrella algorithms. Firstly, the Spearman Correlation Coefficient is employed in the feature selection phase. Secondly, an updated voltage stability assessment (VSA) model is proposed. Compared with the existing data-driven prediction of system static voltage stability in the literature, it can realize voltage stability assessment more quickly. Furthermore, on the basis of rapid voltage stability assessment, the umbrella NP classifier can also effectively limit the first-class error and attenuate the effect of error classification by mirroring the control of the number of cycle splits and the type I classification error threshold. Finally, the simulation and experimental results show that the effectiveness and robustness of the scheme proposed in this paper in grid-connected photovoltaic energy farms.

Basic Principles of Deformed Objects with Methods of Analytical Mechanics

Analytical mechanics is the most fundamental discipline in this field. The basic principles of analytical mechanics should also be applicable to deformed objects. However, the virtual displacement principle proposed by analytical mechanics is only applicable to particle systems and rigid body systems, and not to general deformed objects. In this study, the basic principle, which includes the virtual displacement principle and d’Alembert–Lagrange principle (also called the virtual displacement principle of dynamics), of general deformed objects (such as, elastic, plastic, elasto-plastic, and flexible objects) is derived using analytical mechanics. First of all, according to the method of analytical mechanics, the external force, internal force, constraint reaction force and elastic recovery force of the deformed object system under the equilibrium state are analyzed, and the concepts of virtual displacement, ideal constraint and virtual work are introduced, and the virtual displacement principle (also called virtual work principle) of deformed objects is proposed; secondly, vector form, coordinate component form and generalized coordinate form of generalized virtual displacement principle of deformed object are given; thirdly, Introduce inertial force and use analytical mechanics to derive the d’Alembert–Lagrange principle of dynamic systems; fourthly, as application of the principle, the virtual displacement principle of deformed objects in plane polar coordinate system, space cylindrical coordinate system and spherical coordinate system are given; fifthly, the constitutive relationship between the gravitational strain of elastic–plastic materials was introduced, and an example of the application of the d'Alembert–Lagrange principle in elastic–plastic objects was given; finally, a brief conclusion is drawn. This study unifies the virtual displacement principle of elastic objects, plastic, elastoplastics, deformed object systems and rigid object systems using the basic analytical mechanics method. This is a basic principle for dealing with the static problems of deformed objects. This work also lays the foundation for further study of the dynamics of deformed object systems.

ROBUST OUTPUT FEEDBACK CONTROL FOR HETEROGENEOUS AUTONOMOUS VEHICLE PLATOONS

An heterogeneous vehicle platoon controller for autonomous vehicles is proposed in this paper. The traction force of each vehicle is controlled according to the state of the predecessor vehicle, which can be known by LiDAR/RADAR, and the state of the leader vehicle, which is received by vehicle-to-vehicle (V2V) communication. Platoon string stability is evaluated under Lyapunov and H8 conditions. An iterative procedure is proposed in order to deal with the non-convexity of the static output feedback control design problem. Simulation results demonstrate that the proposed heterogeneous vehicle platoon controller achieves a good overall performance without compromising the safety of any vehicle. The separation between each follower and its predecessor is kept in appropriate ranges, always close to the desired reference. Furthermore, the transient errors are not amplificated when propagated downstream the platoon, therefore string stability is assured. Keywords: Autonomous vehicles, heterogeneous vehicle platoon, vehicle platoon control, string stability, output feedback control, robust control, Linear Matrix Inequality

Using collocation with radial basis functions in a pseudospectral framework to the analysis of laminated plates by the Reissner’s mixed variational theorem

Abstract In order to predict the static deformations and free vibration behaviour of thin and thick cross-ply laminated plates, we integrate Carrera’s unified formulation with a radial basis function collocation technique on a pseudospectral framework, using Reissner’s mixed variational theorem. Numerical examples illustrate the precision and effectiveness of this collocation technique for static and vibration problems.

Nonlinear thermo-mechanical static stability analysis of FG-TPMS shallow spherical shells

An analytical solution for the nonlinear static stability problem of functionally graded triply periodic minimal surface (FG-TPMS) shallow spherical shells is studied in the current research for the first time. Three common TPMS structures including Primitive (P), Gyroid (G), and I-graph and Wrapped Package-graph (IWP) with three models of functionally graded porosity distribution along the thickness are considered. The shallow spherical shells (shallow SSs) are subjected to combined thermo-mechanical loadings and rested on a nonlinear elastic foundation. The fundamental formulas are expressed based on the higher-order shear deformation theory (HSDT) and von Kármán's geometrical nonlinearities. Employing the Ritz energy minimization method, the explicit relationship between load and deflection is derived. Subsequently, the static stability behavior of FG-TPMS shallow SSs is investigated. Numerical illustrations are investigated to show the superior thermo-mechanical load-carrying performance of the FG-TPMS SSs compared to corresponding isotropic structures of the same weight. The significant effects of geometric parameters, nonlinear elastic foundation parameters, and the type of FG-TPMS structures on the nonlinear static stability behavior of shallow SSs are further considered.

Bilinear branch and check for unspecified parallel machine scheduling with shift consideration

This paper tackles the complex challenge of team formations, assignments, and job schedules within the static Unspecified Parallel Machine Flexible Resource Scheduling problem, specifically incorporating shift considerations. In existing literature, teams are often simplified as machines that operate continuously throughout the day without any interruptions. However, in reality, teams require breaks between shifts and cannot work continuously within a day. Therefore, we introduce shift considerations to ensure that teams do not work in consecutive shifts. We consider flexible workers, capable of performing any job, who are distributed among different teams in different shifts to undertake various jobs. The number of teams in each shift is a decision variable. The duration of each job is determined by the number of workers in a team assigned to it. The objective function is to minimize the makespan, representing the overall schedule completion time, while adhering to precedence constraints. We formulate an integer linear programming model for the proposed problem and develop a novel bilinear branch and check algorithm that introduces valid bilinear inequalities to accelerate convergence. The numerical results confirm that our algorithm’s performance optimally solves problems up to 35 jobs within a reasonable timeframe, surpassing the efficiency of the branch and cut method of IBM CPLEX and the classical branch and check algorithm.

Coupling Phase Field Crystal and Field Dislocation Mechanics for a consistent description of dislocation structure and elasticity

This work addresses differences in predicted elastic fields created by dislocations either by the Phase Field Crystal (PFC) model, or by static Field Dislocation Mechanics (FDM). The PFC order parameter describes the topological content of the lattice, but it fails to correctly capture the elastic distortion. In contrast, static FDM correctly captures the latter but requires input about defect cores. The case of a dislocation dipole in two dimensional, isotropic, elastic medium is studied, and a weak coupling is introduced between the two models. The PFC model produces compact and stable dislocation cores, free of any singularity, i.e., diffuse. The PFC predicted dislocation density field (a measure of the topological defect content) is used as the source (input) for the static FDM problem. This coupling allows a critical analysis of the relative role played by configurational (from PFC) and elastic (from static FDM) fields in the theory, and of the consequences of the lack of elastic relaxation in the diffusive evolution of the PFC order parameter.

Irreversible reinsurance: minimization of capital injections in presence of a fixed cost

AbstractWe propose a model in which, in exchange to the payment of a fixed transaction cost, an insurance company can choose the retention level as well as the time at which subscribing a perpetual reinsurance contract. The surplus process of the insurance company evolves according to the diffusive approximation of the Cramér-Lundberg model, claims arrive at a fixed constant rate, and the distribution of their sizes is general. Furthermore, we do not specify any particular functional form of the retention level. The aim of the company is to take actions in order to minimize the sum of the expected value of the total discounted flow of capital injections needed to avoid bankruptcy and of the fixed activation cost of the reinsurance contract. We provide an explicit solution to this problem, which involves the resolution of a static nonlinear optimization problem and of an optimal stopping problem for a reflected diffusion. We then illustrate the theoretical results in the case of proportional and excess-of-loss reinsurance, by providing a numerical study of the dependency of the optimal solution with respect to the model’s parameters.

Конечно-элементное моделирование нелинейных задач упругости в абсолютных узловых координатах на неструктурированных шестигранных сетках

We consider a finite element approach to solving the problem of elasticity theory in terms of absolute nodal coordinate formulation (ANCF), in which large body displacements are described in a global reference frame without using any local coordinate system. The main feature of the method is the absence of gyroscopic effects and, as a result, constancy of the mass matrix and the vector of the generalized force of gravity. In contrast to the traditional ANCF approach, the sets of nodal degrees of freedom of the finite element are formed only on the basis of absolute coordinates of nodes, which allows us to solve the problem using, in particular, unstructured hexahedral meshes. To construct the stiffness matrix, we apply a second-order automatic differentiation algorithm, which ensures its symmetrical form (Hessian matrix) and is analytically accurate in calculating the derivative. This approach also makes it possible to carry out calculations for models of hyperelastic materials without the corresponding Piola-Kirchhoff tensor. It has been shown that within the framework of discretization of the equation of motion, along with the well-known Newmark numerical integration scheme, it is possible to use the HTT-α scheme, which is unconditionally stable, second-order accurate and dissipative for high frequencies. We present several examples of solving static and dynamic elasticity problems for compressible and incompressible models of hyperelastic materials, in which the functions of internal energy density of the body are specified in terms of the deformation gradient.

Nonlinear elastic general integral equations in micromechanics of random structure composites

We consider static problems for composite materials (CMs) with either locally elastic or peridynamic constitutive properties. The general integral equation (GIE) is the exact integral equationWe consider static problems for composite materials connecting the random fields at the point being considered and the surrounding points. There is a very long and colored history of the development of GIE which goes back to Lord Rayleigh. Owing to the new GIE (forming the second background of micromechanics also called the computational analytical micromechanics, CAM), one proved that local micromechanics (LM) and peridynamic micromechanics (PM) are formally similar to each other for CM of random structures. By now, the GIEs are generalized to CMs (of statistically homogeneous and inhomogeneous structures) with the phases described by local models, strongly nonlocal models (strain type and displacement type, peridynamics), and weakly nonlocal models (strain-gradient theories, stress-gradient theories, and higher-order models). However, a fundamental restriction of all mentioned GIEs is their linearity with respect to a primary unknown variable. The goal of this study is obtaining nonlinear GIEs for PM, and, in a particular case, for LM. For the presentation of PM as a unified theory, we describe PM as the formalized schemes of blocked (or modular) structures so that the experts developing one block need not be experts in the underlying another block (this is a good background for effective collaborations of different teams in so many multidisciplinary areas as PM). The opportunity for the creation of this blocked structure of the PM is supported by a critical generalization of CAM which is extremely flexible, robust, and general.

An incremental learning approach to dynamic parallel machine scheduling with sequence-dependent setups and machine eligibility restrictions

Minimizing the tardiness of a parallel machine scheduling problem has been actively studied in modern manufacturing systems. In particular, dynamic parallel machine scheduling problems (DPMSPs) have gained much attention since rescheduling is required to address unpredictable events such as unexpected job arrivals and machine breakdowns, which usually occur in real-world manufacturing systems. To deal with such unpredictable events, many researchers have employed deep supervised learning (SL). However, it is still challenging to solve a DPMSP since SL requires a large number of high-quality schedules for the training neural networks. In this paper, we propose an incremental learning-based scheduling method (ILS) in which neural networks (NNs) are periodically trained by utilizing schedules built from the updated NNs in previous training intervals. Furthermore, to perform training without reducing solution space within a dynamic environment, the proposed method is designed to consider the dependency between consecutive allocations on a machine for the sum of setup time and tardiness. To verify the effectiveness of the proposed method, extensive experiments are carried out in static and dynamic scheduling problems. The experiment results demonstrate that ILS outperforms the existing methods such as dispatching rules, metaheuristics, and DRL-based methods. Additionally, we show that the proposed input features are effective in appropriately selecting job-machine pairs for assigning jobs on eligible machines through deep Shapley additive explanations analysis.

Physics‐informed neural operator solver and super‐resolution for solid mechanics

AbstractPhysics‐Informed Neural Networks (PINNs) have solved numerous mechanics problems by training to minimize the loss functions of governing partial differential equations (PDEs). Despite successful development of PINNs in various systems, computational efficiency and fidelity prediction have remained profound challenges. To fill such gaps, this study proposed a Physics‐Informed Neural Operator Solver (PINOS) to achieve accurate and fast simulations without any required data set. The training of PINOS adopts a weak form based on the principle of least work for static simulations and a strong form for dynamic systems in solid mechanics. Results from numerical examples indicated that PINOS is capable of approximating solutions notably faster than the benchmarks of PINNs in both static an dynamic systems. The comparisons also showed that PINOS reached a convergence speed of over 20 times faster than finite element software in two‐dimensional and three‐dimensional static problems. Furthermore, this study examined the zero‐shot super‐resolution capability by developing Super‐Resolution PINOS (SR‐PINOS) that was trained on a coarse mesh and validated on fine mesh. The numerical results demonstrate the great performance of the model to obtain accurate solutions with a speed up, suggesting effectiveness in increasing sampling points and scaling a simulation. This study also discusses the differentiation methods of PINOS and SR‐PINOS and suggests potential implementations related to forward applications for promising machine learning methods for structural designs and optimization.

Analysis of laminated shells using pseudospectrals and the Reissner-Mixed Variational Theorem

In this paper, we combine the Carrera’s Unified Formulation CUF and a pseudospectral technique for predicting the static deformations and free vibrations behaviour of thin and thick cross-ply laminated shells. For the first time, the Reissner-Mixed Variational Theorem is used together with pseudospectrals to achieve a highly accurate technique. The accuracy and efficiency of this numerical technique for static and vibration problems are demonstrated through numerical examples.

Optimal Neumann control of the wave equation with L 1-control cost: the finite-time turnpike property

The finite-time turnpike property describes a situation where the optimal state reaches a steady state after finite time. The steady state is a solution of a static optimal control problem. We study an optimal control problem where the objective functional is the sum of an L 1 -norm control cost with a weight γ > 0 and a differentiable tracking term. We consider a vibrating string with homogeneous Dirichlet conditions at one end and Neumann control action at the other end. The tracking term is defined by the squared L 2 -norm of a non-collocated Neumann-observation. We show that the problem has a unique solution and that due to the non-smoothness of the L 1 -norm for sufficiently large T the optimal state reaches the desired state after a finite time that is equal to the minimal time where exact controllability holds. We also study the effect of smoothing of the control cost on the structure of the optimal control and show that the finite-time turnpike property also holds in the smoothing limit in a strong L 2 -sense.

Fast Fourier Transform periodic interpolation method for superposition sums in a periodic unit cell

We propose a Fast Fourier Transform based Periodic Interpolation Method (FFT-PIM), a flexible and computationally efficient approach for computing the scalar potential given by a superposition sum in a unit cell of an infinitely periodic array. Under the same umbrella, FFT-PIM allows computing the potential for 1D, 2D, and 3D periodicities for dynamic problems involving the Helmholtz potential and static problems involving Coulomb potential, including problems with and without a periodic phase shift. The computational complexity of the FFT-PIM is of O(Nlog⁡N) for N spatially coinciding sources and observer points. The FFT-PIM uses rapidly converging series representations of the Green's function serving as a kernel in the superposition sum. Based on these representations, the FFT-PIM splits the potential into its near-zone component, which includes a small number of images surrounding the unit cell of interest, and far-zone component, which includes the rest of an infinite number of images. The far-zone component is evaluated by projecting the non-uniform sources onto a sparse uniform grid, performing superposition sums on this sparse grid, and interpolating the potential from the uniform grid to the non-uniform observation points. The near-zone component is evaluated using an FFT-based method, which is adapted to efficiently handle non-uniform source-observer distributions within the periodic unit cell. The FFT-PIM can be used for a broad range of applications, such as periodic problems involving integral equations for wave propagation in electromagnetics and acoustics, micromagnetic solvers, and density functional theory solvers.

An isogeometric analysis of solar panels with a bio-inspired substrate

We in this paper propose a high-performance design using bio-inspired metamaterials for multilayered perovskite solar cell (MPSC) plates. The static bending and free vibrational responses of the newly designed MPSC panels with the presence of the triply periodic minimal surface (TPMS) substrate are subsequently investigated numerically. The displacements of the present plate model are then approximated by five-variable higher-order shear deformation theories (HSDTs). The weak forms are established for both the static bending and free vibration problems and subsequently derive the discrete forms using the NURBS-based isogeometric approach. To enhance the operational efficiency of solar panels in challenging environments, we integrate advanced lightweight architectures based on bio-inspired TPMS structures as a substrate layer into the original solar panel design. In this research, three widely employed TPMS structures: Primitive, Gyroid, and I-graph and Wrapped Package-graph (IWP), are examined in conjunction with two functional grading patterns implemented through the thickness direction. For the first time, the static bending performance of MPSC plates integrated into a TPMS-based substrate layer and subjected to wind pressure as well as thermal conditions is comprehensively studied. In addition, the influence of several significant factors on the free vibration behavior of MPSC plates is also elucidated. The findings show a promising and intriguing design avenue, particularly in the application of high-performance metamaterials to address contemporary challenges in renewable energy usage and environmental protection.

The Feasibility of Coordinating International Monetary Policy Strategies in the Context of Asymmetric Demand Shocks

In the context of the increasing interdependence of countries due to the development of international trade, a relevant question arises as to whether it is necessary to conduct independent monetary policies for each country or whether it is advisable to coordinate these policies. This question becomes a key in the debate on optimal monetary policy strategies in open economies. The aim of this study is to analyze the impact of asymmetric aggregate demand shocks on the appropriateness of monetary policy coordination in a simple stochastic model of two interacting countries. The analysis of equilibrium states of the monetary authorities’ interaction strategies under study was carried out analytically by minimizing the loss function and solving one-period static optimization problems. The equilibrium states of macroeconomics of interacting countries under coordination of monetary policy and in cases of lack of coordination (Nash and Stackelberg equilibrium) in the presence of asymmetric, serially uncorrelated demand shocks have been analyzed. It is proven that the response of inflation to asymmetric demand shocks is smaller in the case of coordinated policy than in the case of non-cooperative policy. The loss function analysis shows that the compensation of demand shocks is found to be more costly in Nash equilibrium than in the case of monetary authority coordination policy. The analysis of the monetary authorities’ interaction strategies showed that the real exchange rate plays an important role in balancing supply and demand in the two economies.

Stochastic optimization problems with nonlinear dependence on a probability measure via the Wasserstein metric

Nonlinear dependence on a probability measure has recently been encountered with increasing intensity in stochastic optimization. This type of dependence corresponds to many situations in applications; it can appear in problems static (one-stage), dynamic with finite (multi-stage) or infinite horizon, and single- and multi-objective ones. Moreover, the nonlinear dependence can appear not only in the objective functions but also in the constraint sets. In this paper, we will consider static one-objective problems in which the nonlinear dependence appears in the objective function and may also appear in the constraint sets. In detail, we consider “deterministic” constraint sets, whose dependence on the probability measure is nonlinear, constraint sets determined by second-order stochastic dominance, and sets given by mean-risk problems. The last mentioned instance means that the constraint set corresponds to solutions which guarantee acceptable values of both criteria. To obtain relevant assertions, we employ the stability results given by the Wasserstein metric, based on the L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {{\\mathcal {L}}}_{1} $$\\end{document} norm. We mainly focus on the case in which a solution has to be obtained on the basis of the data and of investigating a relationship between the original problem and its empirical version.

Analytical solution to some boundary value problems of elasticity in bipolar coordinates

Analytical solutions of two-dimensional statics problems of elasticity are presented in bipolar coordinates for homogeneous isotropic bodies bounded by the coordinate lines of a bipolar coordinate system. In particular, various boundary problems for an eccentric circular ring, a half-plane with circular holes, and others are considered. The equilibrium equations and Hooke’s law are expressed using bipolar coordinates. This paper does not address the static equilibrium requirement of the external load at each circular boundary of the study area. This requirement, which significantly limits the range of problems that can be solved, typically appears in papers dealing with the aforementioned problems. In addition, the proposed method for obtaining an exact (analytical) solution is much simpler compared to the traditional approach. The exact solutions are derived using the method of separation of variables. By utilizing MATLAB software, the numerical results of some boundary value problems for an eccentric semi-ring are obtained, and the corresponding diagrams are presented.

Dynamic and static fusion mechanisms of infrared and visible images

This paper propose a dynamic fusion mechanism of infrared and visible images, named DIFM, capable of solving the static fusion optimization problem. The DIFM correlates the image fusion quality with the image restoration quality to construct a unified optimization loss function. According to the DIFM, a dynamic image fusion network of infrared and visible images is constructed and is therefore denoted with DF-Net. Specifically, the DF-Net comprises two modules, i.e., the dynamic fusion module (DFM) and the self-learning dynamic restoration module (SLDRM). In order to solve the static fusion problem of existing methods, the DFM is proposed to learn the fusion weight dynamically. Specifically, the DFM comprises a classification module (CM) and an image fusion module (IFM), which determine whether and how to fuse source images. In addition, a unified fusion loss function is introduced to obtain more hidden features of infrared and visible images in complex environments. Therefore, the stumbling block of deep learning in image fusion, i.e., static fusion, is significantly mitigated. Extensive experiments demonstrate that the dynamic fusion optimization method neatly outperforms the state-of-the-art methods in most metrics.