Time representations and mathematical models for process scheduling problems

During the last 15 years, many mathematical models have been developed in order to solve process operation scheduling problems, using discrete or continuous-time representations. In this paper, we present a unified representation and modeling approach for process scheduling problems. Four different time representations are presented with corresponding strengthened formulations that rely on exploiting the non-overlapping graph structure of these problems through maximum cliques and bicliques. These formulations are compared, and applied to single-stage and multi-stage batch scheduling problems, as well as crude-oil operations scheduling problems. We introduce three solution methods that can be used to achieve global optimality or obtain near-optimal solutions depending on the stopping criterion used. Computational results show that the multi-operation sequencing time representation is superior to the others as it allows efficient symmetry-breaking and requires fewer priority-slots, thus leading to smaller model sizes.     

A comparative study of different data representations under CNN and a novel integrated FDD architecture

In recent years, deep-learning-based fault detection and diagnosis (FDD) methods have received extensive attention. As we all know, different input forms have a great impact on the final performance. In this paper, three categories and seven representation methods are discussed: numeric representations, image mapping representations (radar chart mapping and Gramian angular summation field (GASF) mapping), and signal transforming representations (fast Fourier transform (FFT) and wavelet). The tests on the Tennessee Eastman process (TEP) dataset prove that the FFT method has achieved the best performance on average. Based on this, a general FDD integration framework is proposed to integrate multiple base learners together to make decisions by weighted voting or maximum voting. Finally, the comparison between our proposed method and other five typical models (FFT, a GASF and a multi-scale neural network (GASF–MSNN), convolutional neural network (CNN), Long Short-Term Memory (LSTM), and Support Vector Machine (SVM)) illustrates the effectiveness of our method for FDD on the TEP. The proposed integrated method provides an effective platform for deep-learning-based FDD.     

Impact of shape representation schemes used in discrete element modelling of particle packing

In different computer models, shape is represented using different methodologies, to varying degrees of precision. This paper examines two approaches to shape representation, and their effects on accuracy in the context of cylindrical particle packing. Two discrete element method (DEM) based software packages are used. A X-ray CT scan of a packed bed provides the experimental measurements for comparison. Eight sphere-composite representations of the same cylindrical pellet were tested. Two of these gave results that quantitatively follow experimental measurements. A range of factors that in theory could affect accuracy of the simulation results are examined, including edge roundedness, surface roughness and restitutional behaviour as a function of sphere-composite representations. The conclusion is that, for packing at least, matching the object's overall shape and dimensions is not enough. Only when a high enough resolution is applied to corners and edges, could the sphere-composite approach possibly match the experimental data quantitatively.     

UNIT ROOTS IN PERIODIC AUTOREGRESSIONS

Abstract. This paper analyzes the presence and consequences of a unit root in periodic autoregressive models for univariate quarterly time series. First, we consider various representations of such models, including a new parametrization which facilitates imposing a unit root restriction. Next, we propose a class of likelihood ratio tests for a unit root, and we derive their asymptotic null distributions. Likelihood ratio tests for periodic parameter variation are also proposed. Finally, we analyze the impact on unit root inference of misspecifying a periodic process by a constant-parameter model.     

Structural solvability analysis of dynamic process models

The variable structure of dynamic process models is represented by a directed graph termed as the representation graph for the purpose of solvability analysis in this paper. Structural solvability analysis, the determination of the structural differential index and the structural decomposition of the differential–algebraic equations (DAE) model set can be performed using the representation graph. The characteristic features of the representation graph for both index 1 and high index semi-explicit DAE models are presented. Based on the above a novel index reduction procedure for high index models is proposed. The notions and methods are illustrated on simple process examples.     

Protein Sub-Nuclear Localization Based on Effective Fusion Representations and Dimension Reduction Algorithm LDA

An effective representation of a protein sequence plays a crucial role in protein sub-nuclear localization. The existing representations, such as dipeptide composition (DipC), pseudo-amino acid composition (PseAAC) and position specific scoring matrix (PSSM), are insufficient to represent protein sequence due to their single perspectives. Thus, this paper proposes two fusion feature representations of DipPSSM and PseAAPSSM to integrate PSSM with DipC and PseAAC, respectively. When constructing each fusion representation, we introduce the balance factors to value the importance of its components. The optimal values of the balance factors are sought by genetic algorithm. Due to the high dimensionality of the proposed representations, linear discriminant analysis (LDA) is used to find its important low dimensional structure, which is essential for classification and location prediction. The numerical experiments on two public datasets with KNN classifier and cross-validation tests showed that in terms of the common indexes of sensitivity, specificity, accuracy and MCC, the proposed fusing representations outperform the traditional representations in protein sub-nuclear localization, and the representation treated by LDA outperforms the untreated one.     

Supply chain planning and scheduling integration using Lagrangian decomposition in a knowledge management environment

The integration of planning and scheduling decisions in rigorous mathematical models usually results in large scale problems. In order to tackle the problem complexity, decomposition techniques based on duality and information flows between a master and a set of subproblems are widely applied. In this sense, ontologies improve information sharing and communication in enterprises and can even represent holistic mathematical models facilitating the use of analytic tools and providing higher flexibility for model building. In this work, we exploit this ontologies’ capability to address the optimal integration of planning and scheduling using a Lagrangian decomposition approach. Scheduling/planning sub-problems are created for each facility/supply chain entity and their dual solution information is shared by means of the ontological framework. Two case studies based on a STN representation of supply chain planning and scheduling models are presented to emphasize the advantages and limitations of the proposed approach.     

Pyrolysis of polyurethane foam: optimized search for kinetic properties via simultaneous K–K method,genetic algorithm and elemental analysis

This study focuses on the determination of kinetic properties for non‐fire retardant (NFR) and fire retardant (FR) polyurethane foams. Based on the experimental thermogravimetric (TG) curves, this paper describes the application of an in‐depth mathematical analysis and genetic algorithm (GA) to produce the kinetic properties. A recent developed technique, K–K method, is used for calculating kinetic properties and determining the search regions of these properties for GA. Elemental analysis is also used to study the pyrolysis mechanism. Three decomposition models were investigated for comparison, and the results show that the decomposition model with three sub‐reactions achieves the closest representation with experimental results. In the model, two sub‐reactions capture the foam and melt decompositions, and another sub‐reaction with relatively lower activation energy captures the early onset of foam decomposition. The kinetic properties of melt decomposition are found similar because of the similarity of melt chemical formulas and decomposition of NFR and FR foams. The kinetic properties of foam decomposition between NFR and FR foams are different because of the mechanism of FR additives. Validation of the successive and parallel reaction schemes shows no noticeable difference between the two schemes in the modelling decomposition. Copyright © 2015 John Wiley & Sons, Ltd.     

Assessing Persistence In Discrete Nonstationary Time‐Series Models

Abstract. The aim of this paper is to examine the application of measures of persistence in a range of time‐series models nested in the framework of Cramer (1961) . This framework is a generalization of the Wold (1938) decomposition for stationary time‐series which, in addition to accommodating the standard I(0) and I(1) models, caters for a broad range of alternative processes. Two measures of persistence are considered in some detail, namely the long‐run impulse‐response and variance‐ratio functions. Particular emphasis is given to the behaviour of these measures in a range of non‐stationary models specified in discrete time. We document the conflict that arises between different measures, applied to the same model, as well as conflict arising from the use of a given measure in different models. Precisely which persistence measures are time dependent and which are not, is highlighted. The nature of the general representation used also helps to clarify which shock the impulse‐response function refers to in the case of models where more than one random disturbance impinges on the time series.     

Enhanced Deep-Learning Prediction of Molecular Properties via Augmentation of Bond Topology

Deep learning has made great strides in tackling chemical problems, but still lacks full-fledged representations for three-dimensional (3D) molecular structures for its inner working. For example, the molecular graph, commonly used in chemistry and recently adapted to the graph convolutional network (GCN), is inherently a 2D representation of 3D molecules. Herein we propose an advanced version of the GCN, called 3DGCN, which receives 3D molecular information from a molecular graph augmented by information on bond direction. While outperforming state-of-the-art deep-learning models in the prediction of chemical and biological properties, 3DGCN has the ability to both generalize and distinguish molecular rotations in 3D, beyond 2D, which has great impact on drug discovery and development, not to mention the design of chemical reactions.     

A MODIFIED ITERATIVE METHOD FOR NONLINEAR CHEMICAL CONCENTRATION IN CYLINDRICAL AND SPHERICAL PELLETS

In a previous paper a transform (spectral)-iterative method, with a new mode of iteration, was introduced for solving a variety of nonlinear problems including nonlinear (quadratic) or variable coefficient chemical reactions in planar catalyst pellets with reference to its possible application to other geometries. In this paper we further develop the method, with more general modifications of the iteration, and where we also use the Green's function for a nonlinear integral equation representation of the problem in the physical space. Such a representation offers a more direct way of involving general nonlinearities besides the quadratic one of the last paper. In addition, the modified iteration for both this (physical space) and the transform (spectral) representations can now be supported by a simple test or condition, that can explain its better convergence. The method is illustrated here for cylindrical and spherical pellets, with various relevant nonlinearities and, for reference most of these results are compared with those done by a well known method like the shooting method.     

浅谈钢帘线附胶率判定

钢帘线最重要的性能之一是与橡胶的粘合性能,它是影响轮胎寿命的主要因素。粘合性能有两种表示方法,一是粘合力表示法,二是附胶率表示法,粘合力表示法有相应的等级判定,而附胶率表示法无相应的等级判定标准。依据大量实验,结合实际情况,制定了相应判定图谱。     

Continuous-time approaches for short-term scheduling of network batch processes: Small-scale and medium-scale problems

Two time representation approaches, discrete-time and continuous-time approaches, have been developed for short-term scheduling of batch process in small-scale and medium-scale during the last two decades. As usually establishing advantages over discrete-time approaches in the scheduling problems, continuous-time approaches have gained increasing attention in the last 10 years. The reported continuous-time approaches can be divided into four categories: global event-based, unit-specific event-based, slot-based and precedence-based models. In this paper, more complex processes, network batch processes in small and medium scales, are considered. Six models based on different continuous-time representations are compared in several benchmark examples from the literature. The compared items include problem size, computational times and model convergence. Moreover, two intermediate storage policies (limited and unlimited intermediate storage) and two objective functions (maximization of profit and minimization of makespan) are addressed.     

Discrete-time mixed-integer programming models and solution methods for production scheduling in multistage facilities

We address the problem of production scheduling in multi-product multi-stage batch plants. Unlike most of the previous works, which propose continuous-time models, we study discrete-time mixed-integer programming models and solution methods. Specifically, we discuss two models based on network representations of the facility and develop two new models inspired by the Resource-Constrained Project Scheduling Problem. Furthermore, we propose different solution methods, including tightening methods based on processing unit availability, a reformulation based on processing unit occupancy, and an algorithm to refine approximate solutions for large-scale instances. Finally, we present a comprehensive computational study which shows that speedups of up to four orders of magnitude in are observed when our models and methods are compared to existing approaches.     

Hybrid modelling of yeast production processes – combination of a priori knowledge on different levels of sophistication

Process models are used to formulate knowledge about process behaviour. They are applied, e.g., to predict the process' future behaviour and for state estimation when reliable on-line measuring techniques to monitor the key variables of the process are not available. There are different sources of information available for modelling, which provide process knowledge in different representations. Some elements or aspects may be described by physically based mathematical models and others by heuristically obtained rules of thumb, while some information may still be hidden in the process data recorded during previous runs of the process. Heuristic rules are conveniently processed with fuzzy expert systems, while artificial neural networks present themselves as a powerful tool for uncovering the information within the process data without the need to transform the information into one of the other representations. Artificial neural networks and fuzzy technology are increasingly being employed for modelling biotechnological processes, thus extending the traditional way of process modelling by mathematical equations. However, a sufficiently comprehensive combination of all these techniques has not yet been put forward. Here, we present a simple way of combining all the available knowledge relating to a given process. In a case study, we demonstrate the development of a hybrid model for state estimation and prediction on the example of a yeast production process. The model was validated during a cultivation performed in a standard pilot-scale fermenter.     

Application of offset-free Koopman-based model predictive control to a batch pulp digester

This work presents the application of a Koopman operator approach to a batch pulp digester. To manufacture paper products with desired properties, it is essential to consider both macroscopic and microscopic attributes of pulp. However, the complexity of multiscale dynamics of pulping processes hinders proper control system design. Therefore, we utilize extended dynamic mode decomposition (EDMD), which is based on Koopman operator theory, to derive a global linear representation of a pulp digester. Then, we design an offset-free Koopman-based model predictive control (KMPC) system to regulate the Kappa number and cell wall thickness (CWT) of fibers at a batch pulp digester while compensating for the influence of plant-model mismatch and disturbance during operation. The numerical experiments demonstrate that the linear state-space model, obtained via EDMD, properly predicts the behavior of a batch pulp digester, and the designed offset-free KMPC system successfully drives the Kappa number and CWT to set-point values.     

A Lagrangean decomposition approach for oil supply chain investment planning under uncertainty with risk considerations

We present a scenario decomposition framework based on Lagrangean decomposition for the multi-product, multi-period, supply investment planning problem considering network design and discrete capacity expansion under demand uncertainty. We also consider a risk measure that allows to reduce the probability of incurring in high costs while preserving the decomposable structure of the problem. To solve the resulting large-scale two-stage mixed-integer stochastic linear programming problem we propose a novel Lagrangean decomposition scheme, and compare different formulations for the non-anticipativity conditions. In addition, we present a new hybrid algorithm for updating the Lagrangean multiplier set based on the combination of cutting-plane, subgradient and trust-region strategies. Numerical results suggest that different formulations of the non-anticipativity conditions have a significant impact on the performance of the algorithm. Moreover, we observe that the proposed hybrid approach has superior performance in terms of faster computational times when compared with the traditional subgradient algorithm.     

Comparison of Construction Method for DEM Simulation of Ellipsoidal Particles

Discrete element model was developed to simulate the ellipsoidal particles moving in the moving bed. Multi-element model was used to describe a ellipsoidal particle, the contact detection algorithm of ellipsoidal particle was developed, and both contact force and gravity force were considered in the models. The simulation results were validated by our experiment. Three algorithms for representing an ellipsoidal particle were compared in macro and micro aspects. The results show that there exists big difference in the microscopic parameters such as kinetic energy, rotational kinetic energy, deformation, contact force and collision number which leads to the difference of macroscopic parameters. The relative error in the discharge rate and tracer particle position is the largest between 3-tangent-element representation and experimental results. The flow pattern is similar for the 5-element and 3-intersection representations. The only difference is the discharge rate of 5-element representation is larger than the experimental value and that of the 3-intersection representation has the contrary result. Finally the 3-intersection- element representation is chosen in the simulation due to less computing time than that of the 5-element representation.     

Assessing robustness of hyperelastic models for describing nonlinearity of the mechanical response for pristine and swollen carbon black filled elastomers

We consider the hyperelastic response of semi-crystalline ethylene–co-butyl acrylate (EBA) samples filled with carbon black (CB) particles. Such material is structurally complex with its microstructure being characterized by many structural parameters including crosslink density, filler/matrix interfaces, crystallinity, filler network, and chain entanglement which have different degrees of influence on the effective mechanical properties. We evaluate the ability of a number of analytical models to correctly reproduce the non-linear elastic mechanical response of these samples. We do this by considering either dry samples, or samples which are swollen by a non-polar solvent (toluene) at equilibrium, and subjected to uniaxial tension at room temperature. As test cases, we focus on six physical models for the purpose of analyzing the stress–strain curves of samples with different cross-linking densities. Among these frameworks, we show that the Mooney–Rivlin (MR), Ogden, and eight-chain models accurately describe the stress–strain curves of both dry and swollen CB-EBA samples. These findings highlight the possibility of attaining a diverse set of mechanical properties of filled polymer samples by tailoring their structural parameters.