Time-dependent Constraints Research Articles

A Variational Formulation of Nonequilibrium Thermodynamics for Discrete Open Systems with Mass and Heat Transfer.

We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for systems with time-dependent nonlinear nonholonomic constraints and time-dependent Lagrangian. For discrete open systems, the time-dependent nonlinear constraint is associated with the rate of internal entropy production of the system. We show that this constraint on the solution curve systematically yields a constraint on the variations to be used in the action functional. The proposed variational formulation is intrinsic and provides the same structure for a wide class of discrete open systems. We illustrate our theory by presenting examples of open systems experiencing mechanical interactions, as well as internal diffusion, internal heat transfer, and their cross-effects. Our approach yields a systematic way to derive the complete evolution equations for the open systems, including the expression of the internal entropy production of the system, independently on its complexity. It might be especially useful for the study of the nonequilibrium thermodynamics of biophysical systems.

On the structure of multifactor optimal portfolio strategies

The paper studies problem of optimal portfolio selection. It is shown that, under some mild conditions, near optimal strategies for investors with different performance criteria can be constructed using a limited number of fixed processes (mutual funds), for a market with a larger number of available risky stocks. This implies dimension reduction for the optimal portfolio selection problem: all rational investors may achieve optimality using the same mutual funds plus a saving account. This result is obtained under mild restrictions for the utility functions without any assumptions on regularity of the value function. The proof is based on the method of dynamic programming applied indirectly to some convenient approximations of the original problem that ensure certain regularity of the value functions. To overcome technical difficulties, we use special time dependent and random constraints for admissible strategies such that the corresponding HJB (Hamilton–Jacobi–Bellman) equation admits “almost explicit” solutions generating near optimal admissible strategies featuring sufficient regularity and integrability.

Anticipated backward stochastic variational inequalities with generalized reflection

We study the existence and uniqueness of the strong solution for the following anticipated backward stochastic variational inequality with oblique subgradients, written under differential form: [Formula: see text] The generalized multivalued product term [Formula: see text] loses the maximal monotony property of its constituent subdifferential operator and, as a consequence, some specific techniques when approaching the above problem are mandatory. The univalued anticipated BSDE addressed in Peng and Yang [19] highlights the duality between these types of equations and stochastic differential delay equations, in order to solve a stochastic control problem. We also provide an example of an anticipated BSDE with time-dependent convex constraints, which can be reduced to our equation.

An analytical and numerical approach to multiscale ductility constraint based model to predict uniaxial/multiaxial creep rupture and cracking rates

Uniaxial damage modelling use constituent components of the stress/strain measured data which have inherent scatter. Models developed for this purpose have also attempted to address the issues related to failure mechanisms within a multiaxial stress state context. This paper presents the multiscale approach to constraint by using the relationship between Monkman-Grant (MG) uniform failure strain and local sub-grain stress state to predict creep damage and rupture under uniaxial/multiaxial conditions. In essence, a global geometric constraint and a time-dependent local sub-grain constraint is defined with the latter controlling the failure response of the geometry. The model compliments and is in agreement with the established NSW model is also used to predict the lower/upper bound of cracking rates in crack dominated geometries. The model is employed into a finite element (FE) to assess its capability to numerically predict the rupture of plain and multiaxial notched bar specimens based on appropriate void growth models. For verification, creep constitutive properties of long term data from uniaxial and multiaxial tests on Grade 92 martensitic steels from various databases, where available, are used to establish the procedure. Given the level of scatter in the data and fabrication and testing uncertainties that cannot be accounted for in such databases, it is shown that the model is sufficiently simple and robust to be developed for use in conservatively predicting very long term failure times.

Operational optimization of an integrated solar combined cycle under practical time-dependent constraints

Abstract Integrated solar combined cycles (ISCCs) need to be able to handle some of the most dynamic operating conditions of any power generation system in order to provide the flexibility of a natural gas combustion turbine while simultaneously utilizing variable incident solar irradiation. Yet to date, most work on ISCC design has focused on high-level treatments of system viability and potential impact, without thorough consideration of system operations. In this work, a computationally efficient ISCC model is constructed that includes detailed modeling of the heat recovery steam generator that links the natural gas and solar thermal systems. The model is validated against a model in the literature, and then used to perform computational optimization of the facility operations. Critically, a wide variety of practical system constraints are considered at each time step evaluated in order to ensure system feasibility under realistic conditions. It is shown that under different operating modes the ISCC design examined displays similar emission rates, yet significantly different profit ranges. A marked increase in the operating flexibility of the ISCC is observed when the outlet temperature of the solar heat transfer fluid is allowed to vary over the course of the day.

Multi-Agent Second Order Average Consensus With Prescribed Transient Behavior

The problem of consensus reaching with prescribed transient behavior for a group of double-integrator agents is addressed. The information exchange of the multi-agent system is described by a static communication network. We initially set time-dependent constraints on the transient response of the relative positions between neighboring agents and we propose a distributed control law consisting of a proportional term of the transformed error and an additional damping term based on absolute velocities measurements. We also design an agreement protocol that can additionally achieve prescribed performance for a combined error of positions and velocities. Under a sufficient condition for the damping gains, the proposed nonlinear time-dependent distributed controllers guarantee that the predefined constraints are not violated and that consensus is achieved with a convergence rate independent of the underlying communication graph. Furthermore, connectivity maintenance can be ensured by appropriately designing the performance bounds. Theoretical results are supported by simulations.

Demo abstract: a building energy management system in the context of the smart grid traffic light concept

The BDEW smart grid traffic light concept is a framework to tackle some of the challenges posed by the transition of the energy system. In the project grid-control a system based on this concept has been implemented. This paper gives an overview of the system and outlines the building energy management system (BEMS) that will be installed and tested in a district battery storage system and five households as a part of this system. The BEMS utilizes a generic interface for exchanging and scheduling flexibility. The interface is based on an ideal battery model with time dependent constraints for power and energy. Daily, a schedule forecast for the following day is created by maximizing self-consumption utilizing consumption and production forecasts and locally available flexibility. An aggregated flexibility is then derived from this schedule forecast. The aggregated flexibility combined with the schedule forecast serve as basis for the actual schedule that is issued to the BEMS. Goal of the BEMS is schedule compliance while permitted by the traffic light phase.

Gradient flow formulation and longtime behaviour of a constrained Fokker–Planck equation

We consider a Fokker–Planck equation which is coupled to an externally given time-dependent constraint on its first moment. This constraint introduces a Lagrange-multiplier which renders the equation nonlocal and nonlinear.In this paper we exploit an interpretation of this equation as a Wasserstein gradient flow of a free energy F on a time-constrained manifold. First, we prove existence of solutions by passing to the limit in an implicit Euler scheme obtained by minimizing hF(ϱ)+W22(ϱ0,ϱ) among all ϱ satisfying the constraint for some ϱ0 and time-step h>0.Second, we provide quantitative estimates for the rate of convergence to equilibrium when the constraint converges to a constant. The proof is based on the investigation of a suitable relative entropy with respect to minimizers of the free energy chosen according to the constraint. The rate of convergence can be explicitly expressed in terms of constants in suitable logarithmic Sobolev inequalities.

Adaptive multilevel trust-region methods for time-dependent PDE-constrained optimization

We present a class of adaptive multilevel trust-region methods for the efficient solution of optimization problems governed by time-dependent nonlinear partial differential equations with control constraints. The algorithm is based on the ideas of the adaptive multilevel inexact SQP-method from \[26], \[27]. It is in particular well suited for problems with time-dependent PDE constraints. Instead of the quasi-normal step in a classical SQP method which results in solving the linearized PDE sufficiently well, in this algorithm a (nonlinear) solver is applied to the current discretization of the PDE. Moreover, different discretizations and solvers for the PDE and the adjoint PDE may be applied. The resulting inexactness of the reduced gradient in the current discretization is controlled within the algorithm. Thus, highly efficient PDE solvers can be coupled with the proposed optimization framework. The algorithm starts with a coarse discretization of the underlying optimization problem and provides during the optimization process implementable criteria for an adaptive refinement strategy of the current discretization based on error estimators. We prove global convergence to a stationary point of the infinite-dimensional problem. Moreover, we illustrate how the adaptive refinement strategy of the algorithm can be implemented by using a posteriori error estimators for the state and the adjoint equation. Numerical results for a semilinear parabolic PDE-constrained problem with pointwise control constraints are presented.

An adaptive large neighborhood search metaheuristic for agile satellite scheduling with time-dependent transition time

Agile satellites belong to the new generation of satellites with three degrees of freedom for acquiring images on the Earth. As a result, they have longer visible time windows for the requested targets. An image shot can be conducted at any time in the window if and only if the time left is sufficient for the fulfillment of the imaging process. For an agile satellite, a different observation time means a different image angle, thus defining a different transition time from its neighboring tasks. Therefore, the setup time for each imaging process depends on the selection of its observation start time, making the problem a time-dependent scheduling problem. To solve it, we develop a metaheuristic, called adaptive large neighborhood search (ALNS), thus creating a conflict-free observational timeline. ALNS is a local search framework in which a number of simple operators compete to modify the current solution. In our ALNS implementation, we define six removal operators and three insertion operators. At each iteration, a pair of operators is selected to destroy the current solution and generate a new solution with a large collection of variables modified. Time slacks are introduced to confine the propagation of the time-dependent constraint of transition time. Computational experiments show that the ALNS metaheuristic performs effectively, fulfilling more tasks with a good robustness.

A Branch and Bound Algorithm for Agile Earth Observation Satellite Scheduling

The agile earth observing satellite scheduling (AEOSS) problem consists of scheduling a subset of images among a set of candidates that satisfy imperative constraints and maximize a gain function. In this paper, we consider a new AEOSS model which integrates a time-dependent temporal constraint. To solve this problem, we propose a highly efficient branch and bound algorithm whose effective ingredients include a look-ahead construction method (for generating a high quality initial lower bound) and a combined use of three pruning strategies (which help to prune a large portion of the search space). We conducted computational experiments on a set of test data that were generated with information from real-life scenarios. The results showed that the proposed algorithm is efficient enough for engineering application. In particular, it is able to solve instances with 55 targets to optimality within 164 seconds on average. Furthermore, we carried out additional experiments to analyze the contribution of each key algorithm ingredient.

Variational inequalities of Navier–Stokes type with time dependent constraints

We consider a class of parabolic variational inequalities with time dependent obstacle of the form |u(x,t)|≤p(x,t), where u is the velocity field of a fluid governed by the Navier–Stokes variational inequality. The obstacle function p=p(x,t), imposed on u, consists of three parts, which are respectively: the degenerate part p(x,t)=0, the finitely positive part 0<p(x,t)<∞ and the singular part p(x,t)=∞. In this paper, we shall propose a sequence of approximate obstacle problems with everywhere finitely positive obstacles, and prove an existence result for the original problem by discussing convergence of the approximate problems. The crucial step is to handle the nonlinear convection term. In this paper we propose a new approach to it.

Analysis of non-EEG evidence for preparatory activity in the human brain: pre-contraction impedance changes in skeletal muscles

Precontraction impedance changes (PICs) are known to occur during isometric contractions of the human forearm finger flexors. Without reliance on electroencephalogical data these are construed as evidence for the construction of a ‘template of instructions’ in the brain for muscle contractions to be performed once a ‘go’ instruction is received, as widely expected from EEG measurements A model is proposed to explain earlier impedance results, based on a PIC-associated time-dependent inhibitory constraint and a modified role for the ‘go’ command. A principal result is that (for appropriate choice of parameters) the time difference between occurrence of a PIC and the onset of force generation can be independent of the timing of the ‘go’ command, as has in fact been reported earlier. Independent of the detailed model, it is argued that there is no reproducible relationship between the time of occurrence of a PIC and the emergence of force, even for repeat tests on the same subject. However, we propose that results for a wide range of circumstances are nevertheless governed by a common probability distribution, based on data for 1200 PICs in a cohort of 11 healthy young subjects.

Maximum probable life time analysis under the required time-dependent failure probability constraint and its meta-model estimation

Time-dependent reliability (failure probability) aims at measuring the probability of the normal (abnormal) operation for structure/mechanism within the given time interval. To analyze the maximum probable life time under a required time-dependent failure probability (TDFP) constraint, an inverse process corresponding to the time-dependent reliability is proposed by taking the randomness of the input variables into consideration. The proposed inverse process employs the monotonicity between the TDFP and the upper boundary of the given time interval which reflects the life time, and an adaptive single-loop sampling meta-model for the time-dependent limit state function is presented to estimate the TDFP at the given time interval flexibly. Since the TDFP is generally monotonic to the upper boundary of the given time interval, thus by adjusting the probable upper and lower boundaries of the time interval in which the corresponding TDFPs include the required TDFP constraint, the proposed approach can always search the maximum probable life time at the required TDFP by the dichotomy. By introducing the time variable as an input which is the same level as the input random variables and constructing the adaptive single-loop sampling meta-model for the time-dependent limit state function in a longer time interval with the TDFP bigger than the required TDFP, the TDFP in any subintervals of the time interval involved in the constructed meta-model can be estimated as a byproduct of the constructed meta-model without any additional actual limit state evaluations. Then the efficiency for analyzing the maximum probable life time is improved by the dichotomy and the unified meta-model of the time-dependent limit state function. Two examples are employed to illustrate the accuracy and the efficiency of the proposed approach.

Subdifferential inclusions with unbounded perturbation: Existence and relaxation theorems

The paper studies an evolution inclusion in a separable Hilbert space whose right-hand side contains the subdifferential of a proper convex lower semicontinuous function of time and a set-valued perturbation. Together with this inclusion, an inclusion with convexified perturbation values is considered. The existence and density of the solution set of the initial inclusion in the closure of the solution set of the inclusion with convexified perturbation are proved. This property is usually called relaxation. Traditional assumptions for relaxation theorems are the compactness property of the convex function and the boundedness of the perturbation. In the present paper, such assumptions are not made. Assumptions for subdifferential inclusions described by polyhedral sweeping processes and variational inequalities with time-dependent obstacles and constraints are specified.

New Geometric Restriction for the Displacement–Constraint Points in Discontinuous Deformation Analysis

A displacement-based seismic discontinuous deformation analysis (DDA) considers the influence of an earthquake by applying a time-dependent displacement constraint to simulate time-dependent ground movement of the base rock. However, unexpected variations of the base block stress and the block area in a seismic DDA may affect the block contacts with another block. This study theoretically clarifies the mechanism that causes unwanted base block distortion in a seismic DDA. A new geometric restriction is proposed for the assignment of displacement–constraint points to simulate the ground movement of two-dimensional (2D) and three-dimensional (3D) convex and concave blocks without changing the DDA algorithm. Additionally, the Daguangbao rock avalanche triggered by the Wenchuan earthquake in China is considered as a case study to demonstrate the capability of the new geometric restriction in a DDA to solve practical problems.

Generation of cubic power-law for high frequency intra-day returns: Maximum Tsallis entropy framework

A theoretical framework based on the maximum Tsallis entropy is proposed to explain the tail behavior of the intra-day stock returns, providing a rationale for the cubic law behavior for high frequency data. The specification of first two time-dependent moment constraints yields a q-Gaussian distribution for the intra-day stock returns. The value of the parameter q is estimated by minimizing appropriately modified Jensen–Shannon (JS) divergence in Tsallis entropy framework between q-Gaussian distribution and empirical NASDAQ 100 data. The estimated value of q yields the well-known empirically observed cubic law tail behavior of the intra-day stock returns which has been observed for high frequency data sets. To validate the cubic law stylized fact, five more data sets from high frequency NASDAQ 100, S&P 500 and NYSE index have been examined and it is found that the cubic law operates.

Real time experimental implementation of optimum energy management system in standalone Microgrid by using multi-layer ant colony optimization

In this paper, an algorithm for energy management system (EMS) based on multi-layer ant colony optimization (EMS-MACO) is presented to find energy scheduling in Microgrid (MG). The aim of study is to figure out the optimum operation of micro-sources for decreasing the electricity production cost by hourly day-ahead and real time scheduling. The proposed algorithm is based on ant colony optimization (ACO) method and is able to analyze the technical and economic time dependent constraints. This algorithm attempts to meet the required load demand with minimum energy cost in a local energy market (LEM) structure. Performance of MACO is compared with modified conventional EMS (MCEMS) and particle swarm optimization (PSO) based EMS. Analysis of obtained results demonstrates that the system performance is improved also the energy cost is reduced about 20% and 5% by applying MACO in comparison with MCEMS and PSO, respectively. Furthermore, the plug and play capability in real time applications is investigated by using different scenarios and the system adequate performance is validated experimentally too.

Shape and cross-section optimization of plane trusses subjected to earthquake excitation using gradient and Hessian matrix calculations

ABSTRACTThis article describes a second-order shape and cross-section optimization method of plane truss subjected to earthquake excitation. The method is based on gradient and Hessian matrix calculation. First, the first and second derivatives of dynamic response with respect to design variables are calculated based on the Newmark method. Second, the inequality time-dependent constraint problem is converted into a sequence of appropriately formed unconstrained problems using the integral interior penalty function method. Then, the gradient and Hessian matrix of the integral interior penalty function are computed. Third, Marquardt's method is employed to solve the unconstrained problems. Finally, the new approach is validated through several case studies. The results show that the new optimization method is an efficient and effective approach for minimum weight design of truss structures.

Time reversal invariance, entropy production and work dissipation in stochastic thermodynamics

We consider the work production in a mesosccopic Markov system obeying discrete stochastic dynamics with time-dependent constraints. Using asymmetry relations presented elsewhere, which result from time reversal invariance of the underlying microscopic system, we derive, beside known equalities in stochastic thermodynamics, a new result: the “Carnot equality”, that generalizes the Carnot relation for macroscopic bi-thermal engines. Such equalities, which extend the classical inequalities of thermodynamics, result from microscopic time reversal invariance only. On the other hand we show that, on the mesoscopic level, notions such as entropy production and power dissipation per transition cannot always be defined. In the absence of a precise mechanical model, such definitions are possible if, and only if, the asymmetry relations due to microscopic time reversal invariance are supplemented by space symmetry relations, equivalent to parity, which are not always satisfied. This article is supplemented with comments by J.M.R. Parrondo and L. Granger and a final reply by the authors.