Integration Scheme For Systems Research Articles

Thermal evaluation of different integration schemes for solar-nuclear hybrid systems

Solar-nuclear hybrid systems have been proposed to meet the growing energy demand and mitigate the effects of global warming caused by fossil fuels. To achieve optimal design for these systems, an appropriate integration scheme is crucial. This article proposes three integration schemes to couple the solar system with the nuclear power plant and evaluates their performance based on energy and exergy evaluations. A reference design of the hybrid system is used, consisting of a 77.04 MWth solar tower system coupled with a 330 MWth System-Integrated Modular Advanced Reactor. Numerical results show that heating partial feedwater and saturated steam with solar energy is the best-integrated scheme, resulting in the maximum thermal efficiency and exergy efficiency for the solar-nuclear hybrid system. Comparing the standalone reactor power system to the solar-nuclear hybrid system reveals that using solar energy to heat the feedwater and saturated steam can greatly improve the energy efficiency of the power plant, increasing it to 34.97%. The solar heat to nuclear heat ratio is 25.01%, while the solar power to nuclear power ratio is as high as 44.42%, indicating effective utilization of solar heat contribution. Exergy loss distributions of the solar-nuclear hybrid system reveal that exergy losses mainly occur within the nuclear reactor and solar field, taking possession of 70% of all exergy losses.

A time-marching procedure based on a sub-step explicit time integration scheme for non-viscous damping systems

A time-marching procedure based on a sub-step explicit time integration scheme for non-viscous damping systems

Symplectic Integration Schemes for Systems With Nonlinear Dissipation

In previous work a variational integration scheme for mechanical systems containing linear dissipation was developed (Limebeer et al., 2020). The key idea is to use a transmission line as the solution to a power-balancing control problem—in the physics literature controllers of this type are known as “heat baths.” The power-balanced closed-loop system is thereby made amenable to analysis with Hamilton's principle. As a consequence, variational principles can be used to find symplectic integration schemes for dissipative systems. The outcome of this work is a coherent physical explanation as to why variational/symplectic integration algorithms for the open dissipative system can perform as well as their conservative counterparts. An important application of these integration algorithms is the solution of long-time-horizon optimal control problems. In this article, these ideas are extended to systems with smooth memoryless nonlinear dissipation. This extension employs a nonlinear lossless transmission line, which is again the solution to a power-balancing control problem. As in the case of linear dissipation, the resulting variational integration schemes are demonstrated to have excellent numerical properties, which are significantly less demanding computationally than their implicit nonvariational counterparts.

A computational framework for mean square responses of bidirectional nonlinear systems under correlated stochastic excitation

A mathematical framework using Ito–Taylor expansion based stochastic integration scheme for planar structural systems subjected to correlated bidirectional excitation at the base is presented. The bidirectional excitation is modeled using correlated Wiener processes. Instead of simple lumped mass representation of structural systems, a more realistic planar multidirectional model is adopted here. Such assumption adequately captures the behavior of systems under real ground excitation which are often multidimensional in nature. The bidirectional excitation model is developed using a mathematically rigorous framework of correlated Wiener derivatives, exploiting the relationship between Wiener and white noise processes, something that is rarely adopted in literature. An Ito–Taylor expansion based Taylor 1.5 integration scheme is developed first for generating system responses, and, the same Ito–Taylor based scheme is utilized to create an automated framework for the evolution of mean-square responses, a manually difficult exercise otherwise. The proposed framework facilitates the development and simultaneous evaluation of n+nC2 (where, n is the number of system states) mean square equations after obtaining the mean square terms using Kronecker product. Extensive simulation studies are carried out for a torsionally coupled linear bidirectional frame, stochastic bidirectional duffing system and a Bouc–Wen hysteretic system at the base. The results for each of the case studies show that non-accounting of correlation in the bidirectional excitation leads to as much as 30% error in the estimation of displacement mean square responses.

Review of the exponential and Cayley map on SE(3) as relevant for Lie group integration of the generalized Poisson equation and flexible multibody systems

The exponential and Cayley maps on SE(3) are the prevailing coordinate maps used in Lie group integration schemes for rigid body and flexible body systems. Such geometric integrators are the Munthe–Kaas and generalized- α schemes, which involve the differential and its directional derivative of the respective coordinate map. Relevant closed form expressions, which were reported over the last two decades, are scattered in the literature, and some are reported without proof. This paper provides a reference summarizing all relevant closed-form relations along with the relevant proofs, including the right-trivialized differential of the exponential and Cayley map and their directional derivatives (resembling the Hessian). The latter gives rise to an implicit generalized- α scheme for rigid/flexible multibody systems in terms of the Cayley map with improved computational efficiency.

Variational Integrators for Dissipative Systems

This article uses physical arguments to derive variational integration schemes for dissipative mechanical systems. These integration algorithms find utility in the solution of the equations of motion and optimal control problems for these systems. Engineers usually represent dissipation effects using phenomenological devices such as “dampers.” In this article, we replace these dampers with a lossless transmission-line in order that the equations of motion are derivable from a variational principle. The associated system Lagrangian can then be discretized and used to develop low-order variational integration schemes that inherit the advantageous features of their conservative counterparts. The properties of a lossless spring-inerter based transmission system are analyzed in detail, with the resulting variational integration schemes shown to have excellent numerical properties. The article concludes with the analysis of a dissipative variant of the classical Kepler central force problem.

New high order symplectic integrators via generating functions with its application in many-body problem

A new family of high order one-step symplectic integration schemes for separable Hamiltonian systems with Hamiltonians of the form \(T(p) + U(q)\) is presented. The new integration methods are defined in terms of an explicitly defined generating function (of the third kind). They are implicit in q (but explicit in p and the internal states), and require the evaluation of the gradients of T(p) and U(q) and the actions of their Hessians on vectors (the later being relatively cheap in the case of many-body problems). A time-symmetric symplectic method is constructed that has order 10 when applied to Hamiltonian systems with quadratic kinetic energy T(p). It is shown by numerical experiments that the new methods have the expected order of convergence.

A new conservative/dissipative time integration scheme for nonlinear mechanical systems

We present a conservative/dissipative time integration scheme for nonlinear mechanical systems. Starting from a weak form, we derive algorithmic forces and velocities that guarantee the desired conservation/dissipation properties. Our approach relies on a collection of linearly constrained quadratic programs defining high order correction terms that modify, in the minimum possible way, the classical midpoint rule so as to guarantee the strict energy conservation/dissipation properties. The solution of these programs provides explicit formulas for the algorithmic forces and velocities which can be easily incorporated into existing implementations. Similarities and differences between our approach and well-established methods are discussed as well. The approach, suitable for reduced-order models, finite element models, or multibody systems, is tested and its capabilities are illustrated by means of several examples.

L^{p } (p>2)-strong convergence of multiscale integration scheme for jump-diffusion systems

In this paper we shall prove the L^{p} (p>2)-strong convergence of multiscale integration scheme for stochastic jump-diffusion systems with two-time-scale, which gives a numerical method for effective dynamical systems.

Automatically Selecting a Suitable Integration Scheme for Systems of Differential Equations in Neuron Models

On the level of the spiking activity, the integrate-and-fire neuron is one of the most commonly used descriptions of neural activity. A multitude of variants has been proposed to cope with the huge diversity of behaviors observed in biological nerve cells. The main appeal of this class of model is that it can be defined in terms of a hybrid model, where a set of mathematical equations describes the sub-threshold dynamics of the membrane potential and the generation of action potentials is often only added algorithmically without the shape of spikes being part of the equations. In contrast to more detailed biophysical models, this simple description of neuron models allows the routine simulation of large biological neuronal networks on standard hardware widely available in most laboratories these days. The time evolution of the relevant state variables is usually defined by a small set of ordinary differential equations (ODEs). A small number of evolution schemes for the corresponding systems of ODEs are commonly used for many neuron models, and form the basis of the neuron model implementations built into commonly used simulators like Brian, NEST and NEURON. However, an often neglected problem is that the implemented evolution schemes are only rarely selected through a structured process based on numerical criteria. This practice cannot guarantee accurate and stable solutions for the equations and the actual quality of the solution depends largely on the parametrization of the model. In this article, we give an overview of typical equations and state descriptions for the dynamics of the relevant variables in integrate-and-fire models. We then describe a formal mathematical process to automate the design or selection of a suitable evolution scheme for this large class of models. Finally, we present the reference implementation of our symbolic analysis toolbox for ODEs that can guide modelers during the implementation of custom neuron models.

Symplectic spatial integration schemes for systems of balance equations

A method to generate geometric pseudo-spectral spatial discretization schemes for hyperbolic or parabolic partial differential equations is presented. It applies to the spatial discretization of systems of conservation laws with boundary energy flows and/or distributed source terms. The symplecticity of the proposed spatial discretization schemes is defined with respect to the natural power pairing (form) used to define the port-Hamiltonian formulation for the considered systems of balance equations. The method is applied to the resistive diffusion model, a parabolic equation describing the plasma dynamics in tokamaks. A symplectic Galerkin scheme with Bessel conjugated bases is derived from the usual Galerkin method, using the proposed method. Besides the spectral and energetic properties expected from the symplecticity of the method, it is shown that more accurate approximation of eigenfunctions and reduced numerical oscillations result from this choice of conjugated approximation bases. Finally, the obtained numerical results are validated against experimental data from the tokamak Tore Supra facility.

Linear Response Function of Bond-Order.

We present the linear response function of bond-orders (LRF-BO) based on a real space integration scheme for molecular systems. As in the case of the LRF of density, the LRF-BO is defined as the response of the bond order of the molecule for the virtual perturbation. Our calculations show that the LRF-BO enables us not only to detect inductive and resonating effects of conjugating systems, but also to predict pKa values on substitution groups via linear relationships between the Hammett constants and the LRF-BO values for meta- and para-substituted benzoic acids. More importantly, the LRF-BO values for the O-H bonds strongly depend on the sites to which the virtual perturbation is applied, implying that the LRF-BO values include essential information about reaction mechanism of the acid-dissociation of substituted benzoic acids.

An energy-consistent integration scheme for flexible multibody systems with dissipation

This work is concerned with the numerical solution of the equations of the dynamics of flexible multibody systems with dissipative physical mechanisms. Specifically, we consider systems composed of rigid and deformable bodies made of a viscoelastic continuum, that may experience large displacements and strains, connected by joints. Within this framework, we present a novel integration scheme for these types of systems that intrinsically satisfies the laws of thermodynamics and existing symmetries. The resulting solutions are physically accurate since they preserve the fundamental physical properties of the model. Furthermore, the method gives excellent performance with respect to robustness and stability. Justification of these claims as well as numerical examples that illustrate the performance of the scheme are provided.

Gene Expression in a 2D System

We designed a new integration scheme for artificial biological systems into solid materials. Inspired by the spatial patterns in morphogenesis and by microelectronics, we developed a biochip on which the protein synthesis and assembly is carried out in spatially segregated micro-compartments.

Flying Supercapacitors as Power Smoothing Elements in Wind Generation

This paper presents a capacitor-clamped three-level inverter-based supercapacitor direct integration scheme for wind energy conversion systems. The idea is to increase the capacitance of clamping capacitors with the use of supercapacitors and allow their voltage to vary within a defined range. Even though this unique approach eliminates the need of interfacing dc-dc converters for supercapacitors, the variable voltage operation brings about several challenges. The uneven distribution of space vectors is the major modulation challenge. A space vector modulation method is proposed in this paper to address this issue and to generate undistorted currents even in the presence of dynamic changes in supercapacitor voltages. A supercapacitor voltage equalization algorithm is also presented. Moreover, control strategies of the proposed system are discussed in detail. Simulation and experimental results are presented to verify the efficacy of the proposed system in suppressing short-term wind power fluctuations.

Effect of noise on chaos synchronization in time-delayed systems: Numerical and experimental observations

We discuss the constructive role of noise (white and colored) in chaos synchronization in time-delayed systems. We first numerically investigate noise-induced synchronization (NIS) between two identical uncoupled Ikeda and Mackey–Glass systems. We find that synchronization occurs above a critical noise intensity that differs for different colors of noise. Synchronization onset is characterized by the value of the maximum transverse Lyapunov exponent. We then discuss the enhancement of chaos synchronization between two time-delayed systems when they are coupled unidirectionally. The effect of parameter mismatch for NIS is described in detail. We provide experimental evidence of NIS for a Mackey–Glass-like system in an electronic circuit using different colors of noise. An integration scheme for time-delayed systems in the presence of additive white and colored noise is discussed.

Energy–work connection integration schemes for mechanico-electrical systems

This paper focuses on studying new energy–work relationship numerical integration schemes of mechanico-electrical systems. The single-stage numerical integration scheme, multi-stage scheme, and parallel composition numerical integration scheme are presented. The method is constructed by a parallel connection of n multi-stage schemes of order 2 and its order of accuracy is 2n. This work also shows that the connection between the change of energy and work of dissipative force is a discrete analogue of the usual case, and further that the error of the schemes becomes smaller when taking a larger number of stages. Finally, an applied example is discussed to illustrate these results.

Diode-Clamped Three-Level Inverter-Based Battery/Supercapacitor Direct Integration Scheme for Renewable Energy Systems

This paper describes a diode-clamped three-level inverter-based battery/supercapacitor direct integration scheme for renewable energy systems. The study is carried out for three different cases. In the first case, one of the two dc-link capacitors of the inverter is replaced by a battery bank and the other by a supercapacitor bank. In the second case, dc-link capacitors are replaced by two battery banks. In the third case, ordinary dc-link capacitors are replaced by two supercapacitor banks. The first system is supposed to mitigate both long-term and short-term power fluctuations while the last two systems are intended for smoothening long-term and short-term power fluctuations, respectively. These topologies eliminate the need for interfacing dc-dc converters and thus considerably improve the overall system efficiency. The major issue in aforementioned systems is the unavoidable imbalance in dc-link voltages. An analysis on the effects of unbalance and a space vector modulation method, which can produce undistorted current even in the presence of such unbalances, are presented in this paper. Furthermore, small vector selection-based power sharing and state of charge balancing techniques are proposed. Experimental results, obtained from a laboratory prototype, are presented to verify the efficacy of the proposed modulation and control techniques.

Une méthode de décomposition en temps avec des schémas dʼintégration réversible pour la résolution de système dʼéquations différentielles ordinaires

We propose a time domain decomposition method that breaks the sequentiality of the integration scheme for systems of ODE. Under the condition of differentiability of the flow, we transform the initial value problem into a well-posed boundary values problem using the symmetrization of the interval of time integration and time-reversible integration scheme. For systems of linear ODE, we explicitly construct the block tridiagonal system satisfied by the solutions at the time sub-intervals extremities. We then propose an iterative algorithm of Schwarz type for updating the interfaces conditions which can extend the method to systems of nonlinear ODE.

Stochastic direct integration schemes for dynamic systems subjected to random excitations

In this work, a stochastic version of direct integration schemes is constructed, based on a general recursive state space formulation. The technique is applicable to evaluating the second order response statistics of systems subjected to non-stationary random excitations, and is potentially able to handle non-proportional damping. A specific group of these algorithms obtained using one of the most frequently used families of time stepping schemes is introduced. It is shown that statistics obtained for two multi-degree of freedom (MDOF) dynamic systems using the proposed method are in close agreement with those obtained from Monte Carlo simulation when a proper time step is used. Stability of the proposed scheme is systematically investigated and it is concluded that, for the response statistics to be bounded, the time step used in the algorithm has to lie within certain limits.