Optimal Detection of Exponential Component in Autoregressive Models

Abstract. In this article, the problem of detecting the eventual existence of an exponential component in an AR(1) model, that is, the problem of testing ordinary AR(1) dependence against the alternative of an exponential autoregression [EXPAR(1)] model, was considered. A local asymptotic normality property was established for EXPAR(1) models in the vicinity of AR(1) ones. Two problems arose in this context, which were quite typical in the study of nonlinear time‐series models. The first was a problem of parameter identification in the EXPAR(1) model. A special parameterization was developed so as to overcome this technical problem. The second problem was related to the fact that the underlying innovation density had to be treated as a nuisance. The problem at hand, indeed, appeared to be nonadaptive. These problems were solved using semi‐parametrically efficient pseudo‐Gaussian methods (which did not require Gaussian observations).     

多流股换热器网络综合方法在原油预热系统中的应用

以原油常减压蒸馏装置原油预热网络为研究对象,进行了多流股换热器网络的实例综合. 基于超结构物理模型建立了改进的多流股换热器网络综合数学模型,提出将该网络综合问题由混合整数非线性规划问题转化为简单的非线性规划问题的求解策略,并利用改进的遗传/模拟退火新算法进行了原油预热网络的综合. 与Hextran软件的综合结果以及现场换热网络的对比表明,本模型和求解策略可以应用于工业规模的多流股换热器网络综合,有可能取得较好的经济效益.     

炼厂生产计划优化模型

This article addresses a production planning optimization problem of overall refinery. The authors formulated the optimization problem as mixed integer linear programming. The model considers the main factors for optimizing the production plan of overall refinery related to the use of run-modes of processing units. The aim of this planning is to decide which run-mode to use in each processing unit in each period of a given horizon, to satisfy the demand, such as the total cost of production and inventory is minimized. The resulting model can be regarded as a generalized lot-sizing problem where a run-mode can produce and consume more than one product. The resulting optimization problem is large-sized and NP-hard. The authors have proposed a column generation-based algorithm called branch-and-price （BP） for solving the interested optimization problem. The model and implementation of the algorithm are described in detail in this article. The computational results verify the effectiveness of the proposed model and the solution method.     

Optimal design of reverse-osmosis networks for wastewater treatment

An optimization study of reverse-osmosis networks (RON) for wastewater treatment has been carried out by describing the system as a nonconvex mixed-integer nonlinear problem (MINLP). A mixed-integer linear problem (MILP) is derived from the original nonlinear problem by the convex relaxation of the nonconvex terms in the MINLP to provide bounds for the global optimum. The MILP model is solved iteratively to supply different initial guesses for the nonconvex MINLP model. It is found that such a procedure is effective in finding local optimum solutions in reasonable time and overcoming possible convergence difficulties associated with MINLP local search methods. Examples of water desalination and wastewater treatment from the pulp and paper industry are considered as case studies to illustrate the proposed solution strategy.     

考虑能耗影响的多产品间歇化工过程优化排序

提出一种用于间歇生产的多产品化工厂排序的多目标优化的混合整数非线性规划(MINLP)模型,其目标函数同时考虑了总生产时间最短和能耗最小的影响,定义了关于过程能耗的影响因子及决策因子,用以对总生产时间和能耗的影响进行权衡。采用改进的模拟退火算法(SA)对具有不同决策因子和能耗影响因子情况下的算例进行了求解,结果表明,该模型能够较好地反映能耗因素在多产品厂排序问题中的影响,使排序结果达到生产时间和能耗影响的综合最优。     

Comparison of certain MINLP algorithms when applied to a model structure determination and parameter estimation problem

The maximum likelihood method is frequently used in parameter estimation. If the structure of the model is unknown, the maximization of the likelihood function can be replaced by minimizing an information criterion. One criterion that allows this to be done is Akaike’s information criterion (AIC). Minimizing the AIC is a mixed integer non-linear programming (MINLP) problem. In this paper, three different MINLP algorithms are compared in the solution of a simultaneous model structure determination and parameter estimation problem by minimizing the AIC criterion. The problem considered appears in quantitative Fourier transformed infra red (FTIR) spectroscopy where concentration estimates of certain gas components are to be obtained from measured absorbances at different wave numbers. The resulting problem is a large MINLP problem containing several hundreds, or even thousands, of variables including a huge number of possible model structures. It is, however, found that the studied algorithms solve the considered problem in quite a small number of iterations and a reasonable CPU-time.     

An Artificial Neural Network approximation based decomposition approach for parameter estimation of system of ordinary differential equations

In this work a new approach for parameter estimation which is based upon decomposing the problem into two subproblems is proposed, the first subproblem generates an Artificial Neural Network (ANN) model from the given data and then the second subproblem uses the ANN model to obtain an estimate of the parameters. The analytical derivates from the ANN model obtained from the first subproblem are used for obtaining the differential terms in the formulation of the second subproblem. This greatly simplifies the parameter estimation problem. The key advantage of the proposed approach is that solution of a large optimization problem requiring high computational resources is avoided and instead two smaller problems are solved. This approach is particularly useful for large and noisy data sets and nonlinear models where ANN models are known to perform quite well and therefore plays an important role in the solution of the overall parameter estimation problem.     

基于信赖域算法的精馏塔优化

从结构优化角度建立精馏塔优化的混合整数非线性规划(MINLP)模型,为了消除整数变量,引入绕流效率将MINLP问题转化为非线性规划(NLP)问题。针对得到的NLP问题提出一种优化方法,在该方法中采用结构优化中常用的信赖域优化算法进行求解,并应用虚拟瞬态连续性方程辅助优化中的稳态模拟。采用提出的优化方法对3个精馏系统进行设计优化,以不同初始值开始,均可得到令人满意的优化结果,表明所提优化方法具有良好的稳健性,对于较复杂的部分热耦合精馏过程仍然可以有效优化求解;信赖域算法在精馏塔优化中也表现出良好的收敛性。     

Optimization issues of the broke management system in papermaking

This paper presents an optimization strategy for the design and operation of a broke management system in a papermaking process. A stochastic model based on a two-state Markov process is presented for the broke system and a multiobjective and bi-level stochastic optimization model is developed featuring (i) a multiobjective operational subproblem for the optimization of the broke dosage and (ii) a multiobjective design problem formulation. An efficient optimization strategy is proposed for the operational subproblem along with a simulation based Pareto optimal solution for the design problem, and illustrated with a detailed case study.     

多产品间歇过程的分层次在线调度--一种数学规划与遗传算法的混合算法

In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant. The overall mixed integer nonlinear programming (MINLP) problem is hierarchically structured into a mixed integer linear programming (MILP) problem first and then a reduced dimensional MINLP problem, which are optimized by mathematical programming (MP) and genetic algorithm (GA) respectively. The basis idea relies on combining MP with GA to exploit their complementary capacity. The key features of the hierarchical model are explained and illustrated with some real world cases from the multiproduct batch plants.     

Using surrogate models for efficient optimization of simulated moving bed chromatography

A new approach of using computationally cheap surrogate models for efficient optimization of simulated moving bed (SMB) chromatography is presented. Two different types of surrogate models are developed to replace the detailed but expensive full-order SMB model for optimization purposes. The first type of surrogate is built through a coarse spatial discretization of the first-principles process model. The second one falls into the category of reduced-order modeling. The proper orthogonal decomposition (POD) method is employed to derive cost-efficient reduced-order models (ROMs) for the SMB process. The trust-region optimization framework is proposed to implement an efficient and reliable management of both types of surrogates. The framework restricts the amount of optimization performed with one surrogate and provides an adaptive model update mechanism during the course of optimization. The convergence to an optimum of the original optimization problem can be guaranteed with the help of this model management method. The potential of the new surrogate-based solution algorithm is evaluated by examining a separation problem characterized by nonlinear bi-Langmuir adsorption isotherms. By addressing the feed throughput maximization problem, the performance of each surrogate is compared to that of the standard full-order model based approach in terms of solution accuracy, CPU time and number of iterations. The quantitative results prove that the proposed scheme not only converges to the optimum obtained with the full-order system, but also provides significant computational advantages.     

Heat exchanger network design using geometric mean temperature difference

The work presents a model which solves the heat exchanger network (HEN) synthesis problem using geometric mean temperature difference (GMTD) in place of the logarithmic mean temperature difference (LMTD). With the aid of logarithmic transformation and piecewise linearization, the problem is stated in a linear form and thus global optimality can be assured for the model. The accuracy of the approximation is discussed and the results obtained for three known case problems show that the usage of GMTD instead of LMTD can be justified. The GMTD-based model produces designs that are sufficiently accurate and comparable with the ones obtained using the LMTD.     

Temporal clustering for order reduction of nonlinear parabolic PDE systems with time‐dependent spatial domains: Application to a hydraulic fracturing process

A temporally‐local model order‐reduction technique for nonlinear parabolic partial differential equation (PDE) systems with time‐dependent spatial domains is presented. In lieu of approximating the solution of interest using global (with respect to the time domain) empirical eigenfunctions, low‐dimensional models are derived by constructing appropriate temporally‐local eigenfunctions. Within this context, first of all, the time domain is partitioned into multiple clusters (i.e., subdomains) by using the framework known as global optimum search. This approach, a variant of Generalized Benders Decomposition, formulates clustering as a Mixed‐Integer Nonlinear Programming problem and involves the iterative solution of a Linear Programming problem (primal problem) and a Mixed‐Integer Linear Programming problem (master problem). Following the cluster generation, local (with respect to time) eigenfunctions are constructed by applying the proper orthogonal decomposition method to the snapshots contained within each cluster. Then, the Galerkin's projection method is employed to derive low‐dimensional ordinary differential equation (ODE) systems for each cluster. The local ODE systems are subsequently used to compute approximate solutions to the original PDE system. The proposed local model order‐reduction technique is applied to a hydraulic fracturing process described by a nonlinear parabolic PDE system with the time‐dependent spatial domain. It is shown to be more accurate and computationally efficient in approximating the original nonlinear system with fewer eigenfunctions, compared to the model order‐reduction technique with temporally‐global eigenfunctions. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3818–3831, 2017     

Robust supply chain performance via Model Predictive Control

This paper presents a novel robust Model Predictive Control (MPC) method for real-time supply chain optimization under uncertainties. This method optimizes the closed-loop economic performance of supply chain systems and addresses different sources of uncertainties located external to and within the feedback loop. The future system behavior is predicted by a closed-loop model, which includes both the open-loop system model and a controller model described by an optimization problem. The robust MPC formulation involves the solution of a constrained, bi-level stochastic optimization problem, which is transformed into a tractable problem involving a limited number of deterministic conic optimization problems solved reliably using an interior point method. The robust controller is applied to a real industrial multi-echelon supply chain optimization problem, and its performance is shown to reduce stock-outs without excessive inventories.     

Scheduling of displacement batch digesters using discrete time formulation

This paper provides mathematical programming based optimization model and computational results for short-term scheduling of displacement batch digesters in a pulp industry. The scheduling problem involves development of an optimal solution that yields the best sequence of operations in each of the parallel batch digesters sharing common resources. The constraints are imposed on meeting the demand of pulp of different qualities within a specified time horizon. The problem comprises of both fixed-time and variable time durations of the tasks, different storage policies, zero-wait and finite wait times, and handling of shared resources. The scheduling problem is formulated using a state-task-network (STN) representation of production recipes, based on discrete time representation resulting in a mixed-integer linear programming (MILP) problem which is solved using GAMS software. The basic framework is adapted from the discrete-time model of Kondili et al. (Comput. Chem. Eng., 1993, 17, 211–227). Different case studies involving parallel digesters in multiple production lines are considered to demonstrate the effectiveness of the proposed formulation using two different objective functions.     

Particle filter based hybrid prognostics of proton exchange membrane fuel cell in bond graph framework

This paper presents a holistic solution towards prognostics of industrial Proton Exchange Membrane Fuel Cell. It involves an efficient multi-energetic model suited for diagnostics and prognostics, developed using some specific properties of Bond Graph (BG) theory. The benefits of Particle Filters (PF) are integrated with the BG model derived fault indicators named Analytical Redundancy Relations, for prognostics of the Electrical-Electrochemical part. The hybrid prognostics involves statistical degradation model obtained using real degradation tests. Prognostics problem is formulated as the joint state-parameter estimation problem in PF framework where estimations of state of health (SOH) is obtained in probabilistic domain. This in turn is used for prediction of Remaining Useful Life (RUL) under constant current as well as dynamic current solicitations. The SOH estimation and RUL prediction is obtained with very high accuracy and precise confidence bounds. Moreover, a comparative analysis with Extended Kalman Filter demonstrates the usefulness of PF.     

用伪并行遗传/模拟退火算法进行多流股换热器网络综合的研究

The multi-stream heat exchanger network synthesis (HENS) problem can be formulated as a mixed integer nonlinear programming model according to Yee et al. Its nonconvexity nature leads to existence of more than one optimum and computational difficulty for traditional algorithms to find the global optimum. Compared with deterministic algorithms, evolutionary computation provides a promising approach to tackle this problem. In this paper, a mathematical model of multi-stream heat exchangers network synthesis problem is setup. Different from the assumption of isothermal mixing of stream splits and thus linearity constraints of Yee et al., non-isothermal mixing is supported. As a consequence, nonlinear constraints are resulted and nonconvexity of the objective function is added. To solve the mathematical model, an algorithm named GA/SA (parallel genetic/simulated annealing algorithm) is detailed for application to the multi-stream heat exchanger network synthesis problem. The performance of the proposed approach is demonstrated with three examples and the obtained solutions indicate the presented approach is effective for multi-stream HENS.     

Optimal multi-floor process plant layout

This paper presents a general mathematical programming formulation for the multi-floor process plant layout problem, which considers a number of cost and management/engineering drivers within the same framework thus resolving various trade-offs at an optimal manner. The proposed model determines simultaneously the number of floors, land area, floor allocation of each equipment item and detailed layout for each floor. The overall problem is formulated as a mixed integer linear programming (MILP) model based on a continuous domain representation. The applicability of the model is demonstrated by three illustrative examples.     

Calculation of the elastic-stressed state under concentrated loading in diamond-like–metal substrate system

A model is proposed which reduces the contact problem of a coating to that of an elastic semi-space with modified boundary conditions. The model takes into account mechanical (difference in elastic modulus of the coating and substrate) and geometric (ratio of contact area to coating thickness) properties of a coating–substrate system, and conditions of their interface conjugation. A comparison of the model outcomes with calculation results for the problem without a coating is carried out in a simple case of uniaxial load. Experiments on the shock action of corundum particles on the surface of two mechanically different metals (aluminium and steel) with diamond-like coating are considered.     

Optimization for the minimum reaction time of pet esterification

We have investigated the direct esterification reaction between terephthalic acid (TPA) and ethylene glycol (EG) in semi-batch reactors, the first stage process for making polyethylene terephthalate (PET), to get optimum conditions for the minimum reaction time. An independent-variable-minimization problem, i.e., a free-end-time/fixed-end-point problem, has been formulated for the system, and then converted to a dependent-variable-minimization (fixed-end-time/ free-end-point) problem by a coordinate transformation, for the latter problem readily yields to established solution methods. We have solved this reformulated problem to obtain the optimal temperature profiles in the reactor required for the minimum reaction time, by iteratively improving the temperature (manipulating variable) profile using the Pontryagin’s minimum principle. The results prove that the method employed here successfully finds an optimal solution for the PET esterification process. The reduction of the reaction time realized following this optimal temperature profile in the reactor was, however, found to be smaller than expected, due to the approximating assumptions of neglecting the solubility equation of TPA in the model. The results obtained using a more improved model of the system will be reported in the future.