Time-dependent Capacity Research Articles

Estimating resilience of manufacturing plants to physical disruptions: Model and application

The concept of Resilience is gaining an increasing importance in industrial systems, service networks and supply chains, as it extends traditional risk assessment methods by capturing both shortterm and long-term effects of accidents and disruptions. Resilience is, in fact, both a qualitative property and a performance indicator that measures the system's ability to survive disruptive events, and rapidly restore its functionality after the disruptive event has occurred. However, while literature about systems resilience is ample, comparatively scarce attention has been devoted to the evaluation of production systems resilience. As a contribution to fill this gap, in this paper a quantitative method for resilience estimation specifically aimed at manufacturing plants is developed. The method focuses on computing resilience of the manufacturing process, according to its structure, when resources are subjected to physical damage resulting from disruptive events such as sabotage, technical accidents or natural disasters. Overall, the paper allows to assess the economic loss and duration of production interruption in any kind of manufacturing plant when subjected to damage produced by the above causes. In particular, the method enables direct assessment of the initial capacity loss following a prescribed disruptive event, and explicit estimation of the time-dependent capacity recovery path based on the actual process structure and sequence of resources restoration tasks, also allowing the quantification of resulting economic losses. In the paper, after model development, an application example is provided to show model capabilities. Facility designers and emergency managers can use this model as a decision support tool for risk assessment, and to plan emergency actions and plant refurbishment aimed at resilience enhancement.

Exploring the Impact of Oligomerization on Redox Flow Cell Performance

The redox flow battery (RFB) is a promising stationary energy storage technology due to its inherent decoupling of energy and power, long service lifetime, and potential for low-cost manufacturing.1 While current embodiments are constrained by high upfront cost, nonaqueous RFBs may offer a pathway to cost-competitive energy storage systems through higher energy densities;2 however, this concept is at an early stage and several challenges must be overcome. In particular, the development of stable, high-voltage redox chemistries in conjunction with low-cost, selective membranes is needed to mitigate difficult-to-reverse capacity fade and reduced efficiencies. As such, a range of redox-active organic macrostructures, including oligomers (RAOs),3 polymers (RAPs),4 and colloids (RACs),5 have been described in the peer-reviewed literature. Of specific interest are RAOs, which, like the other macrostructures, can be paired with size-exclusion membranes but exhibit electrochemical and fluid dynamic properties that more closely align with monomers. While this proof-of-concept has been demonstrated,6,7 to our knowledge, few studies have systematically evaluated how the molecular properties of RAOs influence their performance in flow cells.In this presentation, we will describe our efforts to understand how the molecular properties of different oligomers influence their behavior in redox flow cells. To this end, we synthesize and characterize a set of model compounds, ranging from monomers to tetramers, that utilize TEMPO as the redox-active unit. We then assess the thermodynamic, kinetic, and transport properties of these compounds using a suite of voltammetric techniques. Subsequently, we characterize the performance and durability of these compounds in symmetric flow cells via electrochemical impedance spectroscopy, DC polarization, and durational cycling. We perform post-test characterization after the cycling experiments to disaggregate molecular- and cell-level sources of capacity fade. We find that, in general, oligomers with increased size exhibit lower diffusivities while maintaining the facile charge transfer characteristics afforded by the appended monomer. These size-dependent variations in mass transport rates directly translate to differences in cell polarization and cycling performance. Time-dependent capacity fade observed during cycling is confirmed by post-mortem analysis. Broadly, these results align with previously developed relationships between molecular size, electrochemical properties, and flow cell performance; we posit that the principles for functionalization and testing utilized here can be applied to other RAOs with improved stability. Acknowledgements This work was supported as part of the Joint Center for Energy Storage Research, an Energy Innovation Hub funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences. B.J.N gratefully acknowledges the NSF Graduate Research Fellowship Program under Grant Number 1122374. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF. The authors thank Jeffrey Kowalski and Katharine Greco of the Brushett Group as well as Yu Cao and Jeffrey Moore of the Moore Group at the University of Illinois for their contributions to conceptualizing the framework and preliminary testing for this work.

A Hybrid Exact–Local Search Approach for One-Machine Scheduling with Time-Dependent Capacity

Machine scheduling is a hard combinatorial problem having many manifestations in real life. Due to the schedule followed, the possibility of installations of machines operating sub-optimally is high. In this work, we examine the problem of a single machine with time-dependent capacity that performs jobs of deterministic durations, while for each job, its due time is known in advance. The objective is to minimize the aggregated tardiness in all tasks. The problem was motivated by the need to schedule charging times of electric vehicles effectively. We formulate an integer programming model that clearly describes the problem and a constraint programming model capable of effectively solving it. Due to the usage of interval variables, global constraints, a powerful constraint programming solver, and a heuristic we have identified, which we call the “due times rule”, the constraint programming model can reach excellent solutions. Furthermore, we employ a hybrid approach that exploits three local search improvement procedures in a schema where the constraint programming part of the solver plays a central role. These improvement procedures exhaustively enumerate portions of the search space by exchanging consecutive jobs with a single job of the same duration, moving cost-incurring jobs to earlier times in a consecutive sequence of jobs or even exploiting periods where capacity is not fully utilized to rearrange jobs. On the other hand, subproblems are given to the exact constraint programming solver, allowing freedom of movement only to certain parts of the schedule, either in vertical ribbons of the time axis or in groups of consecutive sequences of jobs. Experiments on publicly available data show that our approach is highly competitive and achieves the new best results in many problem instances.

Approximation algorithms for the generalized incremental knapsack problem

We introduce and study a discrete multi-period extension of the classical knapsack problem, dubbed generalized incremental knapsack. In this setting, we are given a set of n items, each associated with a non-negative weight, and T time periods with non-decreasing capacities \(W_1 \le \dots \le W_T\). When item i is inserted at time t, we gain a profit of \(p_{it}\); however, this item remains in the knapsack for all subsequent periods. The goal is to decide if and when to insert each item, subject to the time-dependent capacity constraints, with the objective of maximizing our total profit. Interestingly, this setting subsumes as special cases a number of recently-studied incremental knapsack problems, all known to be strongly NP-hard. Our first contribution comes in the form of a polynomial-time \((\frac{1}{2}-\epsilon )\)-approximation for the generalized incremental knapsack problem. This result is based on a reformulation as a single-machine sequencing problem, which is addressed by blending dynamic programming techniques and the classical Shmoys–Tardos algorithm for the generalized assignment problem. Combined with further enumeration-based self-reinforcing ideas and new structural properties of nearly-optimal solutions, we turn our algorithm into a quasi-polynomial time approximation scheme (QPTAS). Hence, under widely believed complexity assumptions, this finding rules out the possibility that generalized incremental knapsack is APX-hard.

One-Machine Scheduling with Time-Dependent Capacity via Efficient Memetic Algorithms

This paper addresses the problem of scheduling a set of jobs on a machine with time-varying capacity, with the goal of minimizing the total tardiness objective function. This problem arose in the context scheduling the charging times of a fleet of electric vehicles and it is NP-hard. Recent work proposed an efficient memetic algorithm for solving the problem, combining a genetic algorithm and a local search method. The local search procedure is based on swapping consecutive jobs on a C-path, defined as a sequence of consecutive jobs in a schedule. Building on it, this paper develops new memetic algorithms that stem from new local search procedures also proposed in this paper. The local search methods integrate several mechanisms to make them more effective, including a new condition for swapping pairs of jobs, a hill climbing approach, a procedure that operates on several C-paths and a method that interchanges jobs between different C-paths. As a result, the new local search methods enable the memetic algorithms to reach higher-quality solutions. Experimental results show significant improvements over existing approaches.

Multi-criteria analysis of the efficiency of scenarios for the development of the Russian nuclear industry in view of the uncertain prospects for the future

Multi-criteria analysis is used in many areas of research where it is required to compare several alternatives according to a selected set of criteria. Of particular interest is the application of this method for a comparative assessment of the efficiency of scenarios for the development of innovative nuclear systems. The article proposes an approach to the computational substantiation of the step-by-step transfer of the Russian nuclear industry to a two-component nuclear energy system (NES) with a centralized closed nuclear fuel cycle (NFC) based on the multi-criteria analysis method. At the same time, consideration is given to options for the development of the domestic nuclear industry in view of the uncertain prospects for the future. Taking into account various trends in the nuclear energy development, the authors identify the following three groups of possible scenarios. The first group includes ‘growing’ scenarios in which the number of units and their total installed capacity grow over time. The second group assumes that after a certain time of growth of the installed capacities, the stationary level will be reached, in which there will be no time-dependent capacity changes. The third group simulates a decrease in the installed nuclear energy capacities in the country after some growth. To select the most preferable ways of technological development and assess the efficiency of a nuclear energy system, a limited set of selection criteria and performance indicators are used, covering the economy, export potential, competitiveness, efficient SNF and RW management, natural uranium consumption, and innovative development potential. An important part of this work was a detailed analysis of the uncertainties in the weights and input data used to derive the criteria.

Determination of Dynamic Coefficients of Air-Ring Bearings

An externally-pressurized journal air bearing (AB) with an air-ring (AR), or air-ring bearing (ARB), for a balanced, rigid and light-weight rotor is studied. An elastic structure in the form of an AR is provided between the bearing-bushing and the casing. The ARB is analyzed to determine the dynamic coefficients (DC) at various angular velocities and angular frequencies of vibration of the journal in its range of operation. These DC can then be used to predict the dynamic stability of the rotor ARB system against self-excited (SE) vibration. A numerical simulation procedure is followed to determine the DC. The ARB is modeled as a two-degrees of freedom system. During the simulation, the journal follows a prescribed harmonic motion. Self-exciting forces due to flow dynamics inside an ARB induce this motion. Three-dimensional (3-D) flow equations are solved on a moving/deformable grid using ANSYS®, to compute the pressure (p) distribution in the ARB. Unlike in previous studies, in this study the bushing displacement is determined by the instantaneous p-distribution in the ARB. DC of both AB and AR are determined simultaneously by considering the interaction between the AR and the AB regions through the feed-holes in the bushing. Time-dependent displacement, velocity, and load-carrying capacity obtained by numerical simulation are used to evaluate the DC. Incorporation of an AR around an AB can prevent SE vibration due to positive values of direct damping coefficients of AR. A 3-D flow analysis can reveal the realistic nature of flow in an ARB.

Time-Dependent Structural Behavior of Repaired Corroded RC Columns Located in a Marine Site

The chloride corrosion of reinforcing steel in reinforced concrete (RC) structures is a significant reason for premature deterioration and failure of RC structures in aggressive environments such as the Persian Gulf region. This is one of the major sources of engineering and economic problems in developed countries. On that account, modeling chloride permeation and investigating different methods for the repair and maintenance of RC structures exposed to corrosive environments are considered to be essential for optimizing the service life and life cycle cost of these structures. In this research, a finite element model is applied to assess the time-dependent capacity of corroded RC structures applying nonlinear analysis; this includes the impact of corrosion on inelastic buckling and low-cycle fatigue degradation of reinforcements. In this analysis, the influence of shotcrete repair after the initial cracking of concrete cover as a rehabilitation method on the performance of a corroded square RC column due to chloride-induced corrosion is investigated.

Joint pricing and lot-sizing problem with variable capacity

Abstract This paper presents an extension to the classical capacitated lot-sizing problem. Demand for the products is price-dependent and modelized as an isoelastic function. The capacity is not considered as a parameter anymore, it becomes a decision variable for the company as the production, inventory and pricing decisions. This variable capacity leads to two variants of the problem: one with a time-dependent capacity and the other one a uniform capacity over the periods. We propose heuristic methods, which are based on Lagrangian multipliers, to solve variations of the problem. The methods provide high-quality results.

A methodology to estimate resilience of manufacturing plants

Abstract Resilience is a performance measure representing the system ability to survive disruptive events, and the rapidity in restoring system capacity after the disruptive event has occurred. Given the significant impact that disruptive events have in the current strictly interconnected and globalized economy, resilience is gaining an increasing relevance in the supply chain sector. Nevertheless, research on resilience estimation of single production plants has been much scarcer. In order to contribute to fill this gap, in this paper a quantitative method to compute plant resilience is developed with reference to manufacturing plants. The method is presented in a deterministic context but it is easily extended to a probabilistic setting. It allows a direct assessment of the initial capacity loss following a disruptive event, as well as the time-dependent capacity recovery path and the connected economic loss due to capacity reconstruction and business interruption. The model can act as a decision support tools for facility designers and emergency managers, and may constitute a building block for more extended models aimed at estimating resilience of whole supply chains.

Time-dependent probabilistic capacity degradation assessment of prestressed concrete piles in marine environment

As coastal infrastructure systems are continuously exposed to deterioration, it is increasingly crucial to analyse their current and future serviceability performance. This paper investigates effects of chloride corrosion on the lateral force capacity and ductility of a wharf-supporting prestressed concrete marine pile and provides new insights into the state of marine structures. A probabilistically generated finite element modelling approach is developed for piles, which includes discrete concrete pile cross-sectional models connected to steel tendon non-linear elements via a series of non-linear springs that simulate bonding behaviour. Moreover, a prestressed material model is established that incorporates alternate failure modes including stress corrosion cracking and brittle failure to capture chloride-induced pitting corrosion in piles. It is shown that various failure modes cause an overall decrease in the maximum force capacity as piles age. Specifically, the alternate failure modes result in 31 and 56% reductions in the maximum capacity of the pile and associated top pile displacement, respectively, as the age of the pile increases from 25 years to 75 years. The presented methodology and results can greatly assist in decision-making for repair or replacement of wharves and aid in the design of new wharves considering their future performance.

Admissible Inertial Manifolds for Delay Equations and Applications to Fisher-Kolmogorov Model

For solutions to the delay equations of the form $\dot{u}(t) + Au(t) = f(t,u_{t}), t\in\mathbb{R}$ , we prove the existence of an admissible inertial manifold. Here, the linear differential operator $A$ is positive definite and self-adjoint with a discrete spectrum, and the nonlinear part $f$ is $\varphi$ -Lipschitz for $\varphi$ belonging to an admissible space of functions defined on the whole line. An application to Fisher-Kolmogorov model with time-dependent environmental capacity and finite delay is also given to illustrate our results. Our main method is based on Lyapunov-Perron’s equation in combination with admissibility and duality estimates.

Exploring the impact of chloride-induced corrosion on seismic damage limit states and residual capacity of reinforced concrete structures

A non-linear finite element (FE) framework for time-dependent capacity assessment of corroded rectangular reinforced concrete (RC) columns is developed. The proposed non-linear FE model includes the impact of corrosion on inelastic buckling and low-cycle fatigue degradation of longitudinal reinforcement. The proposed non-linear FE model is validated against a set of experimental data and then extended to evaluate the impact of corrosion on damage limit states to be used in seismic performance and evaluation of corroded structures. This is done through a parametric study on hypothetical RC columns, varied in axial force ratios, mass loss ratios, cover crack widths and confinement levels. Moreover, the application of the proposed model in seismic collapse capacity assessment of corroded structures is shown through non-linear dynamic analyses of prototype columns. Results show that, depending on the axial force ratio, corrosion changes the failure mechanism of the columns. The results of this study suggest that in seismic fragility analysis of corroded structures, the damage limit states should be considered as time-variant parameters.

Time-Dependent Capacity of Large Scale Deep Beams under Sus-tained Loads

Time-Dependent Capacity of Large Scale Deep Beams under Sus-tained Loads

Serviceability-related reliability for mainshock-damaged reinforced concrete piers considering the aftershock-induced seismic hazards

After the mainshock of an earthquake, the major concerns are their serviceability of damaged structures or safety when subjected aftershocks. How to choose the appropriate maintenance actions for damaged structures in their limited post-mainshock service periods is important. To consider the effect of aftershock events on the deterioration of structural performance, reduction factors of seismic capacity for specified damage states based on experimental data are used in the reliability analysis. Additionally, this work proposes an integral method that can analyze the time-dependent capacity of a mainshock-damaged RC pier and simulate aftershock events within a specified period after the mainshock of an earthquake, while at the same time considering cumulative damage induced by ground motions. To determine the post-mainshock service period for a mainshock-damaged RC pier located in a region with high seismic hazard induced by the aftershock, the proposed assessment method is applied to derive its reliability function of a specified damage state. Finally, the proposed procedure for the reliability function for a specified limit state is then applied to a case study of typical RC piers in Taiwan to demonstrate its applicability.

Consideration of time-evolving capacity distributions and improved degradation models for seismic fragility assessment of aging highway bridges

This paper presents a methodology to develop seismic fragility curves for deteriorating highway bridges by uniquely accounting for realistic pitting corrosion deterioration and time-dependent capacity distributions for reinforced concrete columns under chloride attacks. The proposed framework offers distinct improvements over state-of-the-art procedures for fragility assessment of degrading bridges which typically assume simplified uniform corrosion deterioration model and pristine limit state capacities. Depending on the time in service life and deterioration mechanism, this study finds that capacity limit states for deteriorating bridge columns follow either lognormal distribution or generalized extreme value distributions (particularly for pitting corrosion). Impact of column degradation mechanism on seismic response and fragility of bridge components and system is assessed using nonlinear time history analysis of three-dimensional finite element bridge models reflecting the uncertainties across structural modeling parameters, deterioration parameters and ground motion. Comparisons are drawn between the proposed methodology and traditional approaches to develop aging bridge fragility curves. Results indicate considerable underestimations of system level fragility across different damage states using the traditional approach compared to the proposed realistic pitting model for chloride induced corrosion. Time-dependent predictive functions are provided to interpolate logistic regression coefficients for continuous seismic reliability evaluation along the service life with reasonable accuracy.

Modeling the Two-Region, Two-Product Capacitated Production and Transportation Problem

In this paper, we examine the problem of establishing minimum cost production and transportation plans that satisfy known demands over a finite planning horizon. Two products, product 1 and 2, can be produced in each of two regions. Each region uses its own facility to supply the demands for two products. Demands for product 2 in one region can be satisfied either by its own production or by transportation from other region, while no transportation between two regions is allowed for product 1. Moreover, the transportation in each period is constrained by a time-dependent capacity bound. Production and transportation costs are assumed to be non-decreasing and concave. Using a network flow approach, properties of extreme points are identified. Then, a dynamic programming algorithm is developed to find an optimal plan.

Fluid Approximation of Point-queue Model

Point-queue model is widely used in the dynamic user equilibrium (DUE) analysis in discrete-time or continuous-time form. In this paper, a continuous time point queue is proposed. In the former studies, the negativity of the queue length of the original point-queue model is shown and some improvement has been made. Based on the observation that the original point-queue model is actually a queuing model with a server and a buffer with infinite capacity, a fluid approximation (FA) model is proposed to interpret the original point-queue model. Three essential components are a flow balance function, an exit flow function and a time-dependent capacity utilization ratio function, which are all in continuous form. During the analysis, the theoretical proof and numerical study of the non-negativity of queue length are accomplished. With the first-order Taylor expansion, this paper applies the Gronwall's inequality to prove the non-negativity of queue-length. Through numerical testing different specific FA models in the solution scheme, we can show that the negativity of the queue length in the FA model is overcome and some differences between the FA and former studies are discussed. Based on the testing, the capability of our model in approximating the point- queue model is demonstrated.

Regression versus artificial neural networks: Predicting pile setup from empirical data

Piles have been used as a deep foundation for both inland and offshore structures. After installation, pile capacity may increase with time. This time dependent capacity increase is known as setup, and was first mentioned in the literature in 1900 by Wendel. When accounted for accurately during the design stages, the integration of pile setup can lead to more cost-effective pile design as it will reduce pile length, pile section, and size of driving equipment. In this paper, Both Multiple Linear Regression (MLR) and Artificial Neural Networks (ANN) models were developed for predicting pile setup for three pile types (pipe, concrete, and H-pile) using 169 dynamic load tests obtained from the published literature and the authors’ files. In addition, the paper discusses the choice of variables that were examined to obtain the optimum model. Furthermore, the paper compares the predictions obtained by the developed MLR and the ANN models with those given by four traditional empirical formulae. It is concluded that the ANN model outperforms both the MLR model and the examined empirical formulae in predicting the measured pile setup. Finally, static load test data was used to further verify the developed models. It’s noted that the optimal ANN model overestimated pile capacity by 17% to 21% for the H-piles, and underestimated pile capacity by 12% to 17% for the pipe piles.

On the interdependency between multi-channel scheduling and tree-based routing for WSNs in smart grid environments

Field tests show that the link-quality of wireless links in different smart grid environments, such as outdoor substation, varies greatly both in space and time because of various factors, including multi-path, fading, node contentions, radio frequency (RF) interference, and noise. This leads to both time and location dependent capacity limitations of wireless links in smart grid environments. To improve network capacity in such environments, multichannel communication and the use of proper routing topologies emerge as efficient solutions to achieve simultaneous, interference-free transmissions over multiple channels. In this paper, we explore the impact of multi-channel communication and the selection of efficient routing topologies on the performance of wireless sensors networks in different smart grid spectrum environments. Particularly, we evaluate the network performance using a receiver-based channel selection method and using different routing trees, including routing trees constructed considering the link qualities, Capacitated Minimum Spanning Trees (CMSTs), capacitated minimum spanning tree considering link qualities and Minimum Hop Spanning Trees (MHSTs). We focus on performance measures such as delay and throughput that can benefit from the simultaneous parallel transmissions and show that the use multiple channels together with routing trees that consider network capacity and link quality, i.e., capacitated minimum spanning tree considering link qualities, substantially improve the network performance in harsh smart-grid environments compared to single-channel communication and minimum-hop routing trees.