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Di Tang - One of the best experts on this subject based on the ideXlab platform.
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Fuzzy Phase Partition and Hybrid Modeling Based Quality Prediction and Process Monitoring Methods for Multiphase Batch Processes
Industrial & Engineering Chemistry Research, 2016Co-Authors: Di TangAbstract:A novel fuzzy phase Partition Method and a hybrid modeling strategy are proposed for quality prediction and process monitoring in batch processes with multiple operation phases. The fuzzy phase Partition Method is proposed on the basis of a sequence-constrained fuzzy c-means (SCFCM) clustering algorithm. It divides the batch process into several fuzzy operation phases by performing the SCFCM algorithm on trajectory data of phase-sensitive process variables. This SCFCM-based Partition Method not only has high computation efficiency and good Partition accuracy but also is easy to implement and popularize. In addition, it generates “soft” Partition results, where a “transition” phase exists between two adjacent “steady” operation phases. A hybrid modeling strategy is developed to build appropriate models for all operation phases according to their own characteristics. Phase-based multiway PLS models are built for regular steady phases that have longer durations and stable process behaviors. Just-in-time PLS ...
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Phase Partition and Phase-Based Process Monitoring Methods for Multiphase Batch Processes with Uneven Durations
Industrial & Engineering Chemistry Research, 2016Co-Authors: Di TangAbstract:Integrated phase Partition, online phase identification, and phase-based monitoring Methods are proposed for multiphase batch processes with uneven durations. A new phase Partition Method is developed based on the warped K-means (WKM) clustering algorithm, which divides the entire batch into several operation phases by clustering the trajectory data of phase-sensitive process variables. This WKM-based phase Partition Method can efficiently cope with the sequentiality of batch data and, thus, ensures a reasonable phase Partition result. Besides, because only phase-sensitive variables are used for phase Partition, the phase Partition accuracy is improved. An online phase identification Method is proposed to identify the corresponding operation phase of a new sample according to a phase identification combination index (PICI). PICI quantifies the correlation of a new sample with each operation phase by calculating distance and time difference between the sample and the phase center. The PARAFAC2 and unfolded...
Victor Kowalenko - One of the best experts on this subject based on the ideXlab platform.
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Programming the Partition Method for a Power Series Expansion
The Partition Method for a Power Series Expansion, 2017Co-Authors: Victor KowalenkoAbstract:A programming Methodology is concerned with: (1) the analysis of a problem by developing algorithms based on modern programming techniques, (2) designing programs in appropriate languages and (3) implementation on a suitable platform. Chapter 5 completes the programming Methodology for the Partition Method for a power series expansion that began with the presentation of the BRCP algorithm in Chapter 3 and continued with the general theory of Partition Method for a power series expansion in the previous chapter. The results of these chapters are employed to produce two C/C++ codes, which generate the coefficients in a general symbolic form that can be introduced into Mathematica. Both programs are fully listed in Appendix B , where they appear as Programs 1 and 2. The first program calculates the coefficients D k D k and E k E k in Theorem 4.1 for k ranging from unity to a specified number, while the second calculates only one coefficient, which is useful when the number of Partitions becomes too large. By assigning values to the coefficients of the inner and outer power series, the coefficients of the resulting power series expansion can be calculated using either the integer arithmetic routines in Mathematica, thereby avoiding rounded-off decimal values, or they can be evaluated via the symbolic routines to yield polynomial coefficients.
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Chapter 4 – General Theory
The Partition Method for a Power Series Expansion, 2017Co-Authors: Victor KowalenkoAbstract:Chapter 4 presents the general theory behind the Partition Method for a power series expansion, which is required for the development of a programming Methodology appearing in the following chapter. The theory begins by introducing the pseudo-composite function g(af(x))g(af(x)), where a is arbitrary and the functions g(x)g(x) and f(x)f(x) are expressed as general power series expansions that are referred to as the outer and inner series, respectively. Then Theorem 4.1 presents general expressions for the coefficients of the resulting power series expansion for both the quotient of pseudo-composite functions and its inverted form in terms of sums over Partitions. Next it is shown that Faa di Bruno's formula or the Bell polynomial approach represents a special case of the Partition Method for a power series expansion. To demonstrate both the generality and versatility of the Partition Method for a power series expansion, Theorem 4.1 is used to determine the power series expansion for the function f(z)=exp(azνsinρz)f(z)=exp(azνsinρz). If the quotient of the pseudo-composite functions in Theorem 4.1 is smooth, then the coefficients of its Taylor/Maclaurin series can also be expressed in terms of a sum over the Partitions. In a second corollary the theory is extended by taking an arbitrary power ρ of the quotient of the pseudo-composite functions of Theorem 4.1. The chapter concludes by deriving the power series expansion for the exponentiated function of the second corollary to Theorem 4.1.
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Developments from Programming the Partition Method for a Power Series Expansion
arXiv: Combinatorics, 2012Co-Authors: Victor KowalenkoAbstract:Recently, a novel Method based on coding Partitions [1]-[4] has been used to derive power series expansions to previously intractable problems. In this Method the coefficients at $k$ are determined by summing the contributions made by each Partition whose elements sum to $k$. These contributions are found by assigning values to each element and multiplying by an appropriate multinomial factor. This work presents a theoretical framework for the Partition Method for a power series expansion. To overcome the complexity due to the contributions, a programming Methodology is created allowing more general problems to be studied than envisaged originally. The Methodology uses the bi-variate recursive central Partition (BRCP) algorithm, which is based on a tree-diagram approach to scanning Partitions. Its main advantage is that Partitions are generated in the multiplicity representation. During the development of the theoretical framework, scanning over Partitions was seen as a discrete operation with an operator $L_{P,k}[ \cdot]$, whose summand depends on the coefficients of the two series when the original function is written as a pseudo-composite function. Simple modifications result in programs for other operators of specific types of Partitions such as: (1) only odd or even elements, (2) a fixed number of elements, (3) discrete elements, (4) specific elements and (5) those restricted by element size. Another modification generates conjugate Partitions by transposing Ferrers diagrams. The operator approach is then applied to the generating functions for both discrete and standard Partitions. The main generalisation introduces a parameter $\omega$, whose powers give the number of elements in the Partitions while the coefficients become polynomials in $\omega$. Finally, power series expansions for more advanced infinite products are derived, culminating in Heine's multi-parameter product.
Lu Jian - One of the best experts on this subject based on the ideXlab platform.
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Analysis of Thread Partition Method Oriented to Thread Level Speculation
Computer Science, 2006Co-Authors: Lu JianAbstract:A proper thread-Partition Method is the precondition wben extracting thread level parallelism.Thread level speculation can reduce the complexity of thread Partition and improve the performance of the system.In this paper,sev- eral thread Partition Methods supporting thread level speculation are discussed,and key techniques are issued base on the discussion.Then thread Partition Methods are analyzed with an automatic thread Partition algorithm in detail.At last,questions need to he studied fatherly are proposed.
Chen Jian-xin - One of the best experts on this subject based on the ideXlab platform.
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Application of Entropy-Based Partition Method in TCM Syndrome
Computer Simulation, 2009Co-Authors: Chen Jian-xinAbstract:A new approach(entropy-based Partition Method for complex system) for TCM syndrome diagdnosis was proposed.Firstly,a clinical epidemiology survey was carried out,400 patients of vascular endothelial dysfunction(ED) were chosen,and corresponding symptoms information was collected.Then the symptoms combination was reached according to the entropy-based Partition Method for complex system and the diagnostic threshold of "deficiency of Yin" in ED objectively was decided.Finally,an examination on this diagnostic criterion was conducted through three indexes:sensitivity,specificity and agreement rate.The result shows that the diagnostic criterion of "deficiency of Yin" in ED has a favorable diagnostic effect and the entropy-based Partition Method for complex system is suitable for study on the diagnosis of syndromes in TCM.It paves a new way for the research of syndromes in TCM.
Shu Lin - One of the best experts on this subject based on the ideXlab platform.
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a fast network Partition Method for large scale urban traffic networks
Journal of Control Theory and Applications, 2013Co-Authors: Zhao Zhou, Shu LinAbstract:In order to control the large-scale urban traffic network through hierarchical or decentralized Methods, it is necessary to exploit a network Partition Method, which should be both effective in extracting subnetworks and fast to compute. In this paper, a new approach to calculate the correlation degree, which determines the desire for interconnection between two adjacent intersections, is first proposed. It is used as a weight of a link in an urban traffic network, which considers both the physical characteristics and the dynamic traffic information of the link. Then, a fast network division approach by optimizing the modularity, which is a criterion to distinguish the quality of the Partition results, is applied to identify the subnetworks for large-scale urban traffic networks. Finally, an application to a specified urban traffic network is investigated using the proposed algorithm. The results show that it is an effective and efficient Method for Partitioning urban traffic networks automatically in real world.
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a dynamic network Partition Method for heterogenous urban traffic networks
International Conference on Intelligent Transportation Systems, 2012Co-Authors: Zhao Zhou, Shu LinAbstract:Recently, it has been shown that Macroscopic Fundamental Diagrams(MFDs) existing in large scale urban traffic networks paly an important role in dynamic traffic management, traffic signal control and mitigation of urban traffic congestion. A well defined MFD can be derived from a homogeneous urban traffic network with similar traffic conditions. In reality, however, most large scale traffic networks are usually heterogeneous networks with various road types and uneven distribution of congestion. In order to use the MFD concept for controlling the large scale urban traffic network through hierarchical or decentralized Methods, it is necessary to exploit a network Partition Method, which should be both effective in extracting homogeneous sub-networks and fast to compute. In this paper, a new approach to calculate the correlation degree, which describes the traffic conditions between two adjacent intersections quantitatively, is first proposed. Then, a fast network division approach by optimizing the modularity, which is a criterion to distinguish the quality of the Partition results, is applied to identify the homogeneous sub-networks for large scale urban traffic networks. Finally, an application to a specified urban traffic network is investigated by using the proposed algorithm. The results show that it is an effective and efficient Method for Partitioning heterogeneous urban traffic networks automatically.
