A two-stage algorithm for identification of nonlinear dynamic systems

This paper investigates the two-stage stepwise identification for a class of nonlinear dynamic systems that can be described by linear-in-the-parameters models, and the model has to be built from a very large pool of basis functions or model terms. The main objective is to improve the compactness of the model that is obtained by the forward stepwise methods, while retaining the computational efficiency. The proposed algorithm first generates an initial model using a forward stepwise procedure. The significance of each selected term is then reviewed at the second stage and all insignificant ones are replaced, resulting in an optimised compact model with significantly improved performance. The main contribution of this paper is that these two stages are performed within a well-defined regression context, leading to significantly reduced computational complexity. The efficiency of the algorithm is confirmed by the computational complexity analysis, and its effectiveness is demonstrated by the simulation results.     

A methodology for control-relevant nonlinear system identification using restricted complexity models

A broadly-applicable, control-relevant system identification methodology for nonlinear restricted complexity models (RCMs) is presented. Control design based on RCMs often leads to controllers which are easy to interpret and implement in real-time. A control-relevant identification method is developed to minimize the degradation in closed-loop performance as a result of RCM approximation error. A two-stage identification procedure is presented. First, a nonlinear ARX model is estimated from plant data using an orthogonal least squares algorithm; a Volterra series model is then generated from the nonlinear ARX model. In the second stage, a RCM with the desired structure is estimated from the Volterra series model through a model reduction algorithm that takes into account closed-loop performance requirements. The effectiveness of the proposed method is illustrated using two chemical reactor examples.     

Rapid Analysis of Interval Value Ordering

Two models of ranking the interval-defined objects were described. They are based on the principles of domination in probability and utility. Proposed was a two-stage ranking procedure where the objects are first ranked according to the model of domination in probability and then this ranking is corrected using the model of domination in utility.     

A virtual try-on system in augmented reality using RGB-D cameras for footwear personalization

This paper presents a system for design evaluation of footwear using commercial depth-sensing technologies. In a mixed reality environment, the system allows users to virtually try on 3D shoe models in a live video stream. A two-stage object tracking algorithm was developed to correctly align shoe models to moving feet during the try-on process. Color markers on the user's foot enabled markerless tracking. Tracking was driven by an iterative closest point (ICP) algorithm that superimposed the captured depth data and predefined reference foot models. Test data showed that the two-stage approach resulted in increased positional accuracy compared with tracking using only surface registration. Trimming the reference model using the instant view angle increased the computational efficiency of the ICP algorithm. The proposed virtual try-on function is an effective tool for realizing human-centered design. This study also demonstrated a new application of RGB-D cameras to product design.     

Locally regularised two-stage learning algorithm for RBF network centre selection

Nonlinear system models constructed from radial basis function (RBF) networks can easily be over-fitted due to the noise on the data. While information criteria, such as the final prediction error (FPE), can provide a trade-off between training error and network complexity, the tunable parameters that penalise a large size of network model are hard to determine and are usually application dependent. This article introduces a new locally regularised, two-stage stepwise construction algorithm for RBF networks. The main objective is to produce a parsimonious network that generalises well over unseen data. This is achieved by utilising Bayesian learning within a two-stage stepwise construction procedure to penalise centres that are mainly interpreted by the noise. Specifically, each output layer weight is assigned a hyperparameter, a large value of such a parameter forcing the associated output layer weight to be near to zero. Sparsity is achieved by removing irrelevant RBF centres from the network. The efficacy of proposed algorithm from the original two-stage construction method is retained. Numerical analysis shows that this new method only needs about half of the computation involved in the locally regularised orthogonal least squares (LROLS) alternative. Results from two simulation examples are presented to show that the nonlinear system models resulting from this new approach are superior in terms of both sparsity and generalisation capability.     

Two-Stage Method for Diagonal Recurrent Neural Network Identification of a High-Power Continuous Microwave Heating System

This paper proposes a diagonal recurrent neural network (DRNN) based identification scheme to handle the complexity and nonlinearity of high-power continuous microwave heating system (HPCMHS). The new DRNN design involves a two-stage training process that couples an efficient forward model selection technique with gradient-based optimization. In the first stage, an impact recurrent network structure is obtained by a fast recursive algorithm in a stepwise forward procedure. To ensure stability, update rules are further developed using Lyapunov stability criterion to tune parameters of reduced size model at the second stage. The proposed approach is tested with an experimental regression problem and a practical HPCMHS identification, and the results are compared with four typical network models. The results show that the new design demonstrates improved accuracy and model compactness with reduced computational complexity over the existing methods.

     

基于词条之间关联关系的文档聚类

针对现有的空间向量模型在进行文档表示时忽略词条之间的语义关系的不足,提出了一种新的基于关联规则的文档向量表示方法。在广义空间向量模型中分析词条的频繁同现关系得到词条同现语义,根据关联规则分析词条之间的关联相关性,挖掘出文档中词条之间的潜在关联语义关系,将词条同现语义和关联语义线性加权对文档进行表示。实验结果表明,与BOW模型和GVSM模型相比,采用关联规则文档向量表示的文档聚类结果更准确。     

Deep convolutional learning for general early design stage prediction models

Designers rely on performance predictions to direct the design toward appropriate requirements. Machine learning (ML) models exhibit the potential for rapid and accurate predictions. Developing conventional ML models that can be generalized well in unseen design cases requires an effective feature engineering and selection. Identifying generalizable features calls for good domain knowledge by the ML model developer. Therefore, developing ML models for all design performance parameters with conventional ML will be a time-consuming and expensive process. Automation in terms of feature engineering and selection will accelerate the use of ML models in design.Deep learning models extract features from data, which aid in model generalization. In this study, we (1) evaluate the deep learning model’s capability to predict the heating and cooling demand on unseen design cases and (2) obtain an understanding of extracted features. Results indicate that deep learning model generalization is similar to or better than that of a simple neural network with appropriate features. The reason for the satisfactory generalization using the deep learning model is its ability to identify similar design options within the data distribution. The results also indicate that deep learning models can filter out irrelevant features, reducing the need for feature selection.     

Control relevant estimation of plant and disturbance dynamics

Estimating models for both plant and disturbance dynamics is important in control design applications that focus on disturbance rejection. Several methods for low-order approximate model estimation on the basis of closed-loop data exist in the literature, but fail to address the simultaneous estimation of low-order approximate models of both plant and disturbance dynamics. In this paper a new extended two-stage methodology is proposed that allows for low-order approximate disturbance model estimation. In the proposed extended two-stage method the first stage is used to estimate high-order models for filtering purposes. In the second stage, filtered signals are used to provide the means for low-order approximate model estimation of both plant and disturbance dynamics.     

Dynamics modeling for a rigid-flexible coupling system with nonlinear deformation field

In this paper, a moving flexible beam, which incorporates the effect of the geometrically nonlinear kinematics of deformation, is investigated. Considering the second-order coupling terms of deformation in the longitudinal and transverse deflections, the exact nonlinear strain-displacement relations for a beam element are described. The shear strains formulated by the present modeling method in this paper are zero, so it is reasonable to use geometrically nonlinear deformation fields to demonstrate and simplify a flexible beam undergoing large overall motions. Then, considering the coupling terms of deformation in two dimensions, finite element shape functions of a beam element and Lagrange’s equations are employed for deriving the coupling dynamical formulations. The complete expression of the stiffness matrix and all coupling terms are included in the formulations. A model consisting of a rotating planar flexible beam is presented. Then the frequency and dynamical response are studied, and the differences among the zero-order model, first-order coupling model and the new present model are discussed. Numerical examples demonstrate that a ‘stiffening beam’ can be obtained, when more coupling terms of deformation are added to the longitudinal and transverse deformation field. It is shown that the traditional zero-order and first-order coupling models may not provide an exact dynamic model in some cases.     

Mixed H2/H∞ fuzzy output feedbackcontrol design for nonlinear dynamic systems: an LMI approach

This study introduces a mixed H₂/H_∞ fuzzy output feedback control design method for nonlinear systems with guaranteed control performance. First, the Takagi-Sugeno fuzzy model is employed to approximate a nonlinear system. Next, based on the fuzzy model, a fuzzy observer-based mixed H₂/H_∞ controller is developed to achieve the suboptimal H₂ control performance with a desired H_∞ disturbance rejection constraint. A robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure. By the proposed decoupling technique and two-stage procedure, the outcome of the fuzzy observer-based mixed H₂/H_∞ control problem is parametrized in terms of the two eigenvalue problems (EVPs): one for observer and the other for controller. The EVPs can be solved very efficiently using the linear matrix inequality (LMI) optimization techniques. A simulation example is given to illustrate the design procedures and performances of the proposed method     

Supplier selection with an integrated methodology in unknown environment

This paper proposes an integrated methodology and its solution for supplier selection problem. A two-stage stochastic programming model and fuzzy TOPSIS methods are consolidated in this methodology. After pre-research phase, in the second part of the methodology, fuzzy TOPSIS is used for ranking potential suppliers considering qualitative data under fuzzy environment. In the third part of the methodology a group of ranked potential suppliers are included in a two-stage stochastic programming model for evaluation. In the two-stage stochastic programming model demand is assumed as uncertain and different scenarios are generated for this parameter. With this methodology, supplier evaluation procedure can be done in unknown environment. Our methodology is interested with a problem in multi-product, multi-period and multi-sourcing environment.     

Design of multi-product manufacturing lines with the consideration of product change dependent inter-task times,reduced changeover and machine flexibility

Traditional research work in manufacturing line design assumes that the times between manufacturing tasks performed on a workstation are independent of the task sequence on that station. Furthermore, such studies paid little attention to the sequence dependent inter-task times in multi-model production. Since the inter-task times related to product model changeover have significant impact on manufacturing line performance, it is necessary to take into account the inter-task times explicitly in multi-model manufacturing line design. The need for this consideration is growing as product variety increases. This paper presents mathematical models of manufacturing line design with the consideration of product change related inter-task times in evaluating station times for multi-model production. An optimization model is developed using mixed integer programming to minimize manufacturing line cost. The model takes into account the recurrence of manufacturing tasks in a station to determine the machine type in a station. This paper also presents a heuristic solution procedure developed for efficient calculation. This paper also investigates how product model build sequences and inter-task times affect manufacturing line performance. The developed models will help enhance task-station assignment in multi- and mixed-model production by increasing line cost effectiveness and reducing line changeover impact as well as shortening long re-balancing processes.     

Design of observer-based controllers for a class of discrete systems

Design of observers and observer-based controllers for linear, discrete control systems with fast and slow modes are considered in this paper. The time separation is expressed in terms of an inequality relating norms of system submatrices. It is shown that reconstruction of fast and slow states can be accomplished by a full-order observer, the gains of which are computed using a two-stage procedure. Then, provided that the fast subsystem is asymptotically stable, it is shown that a low-order observer-based controller can be designed with independent gain matrices to stabilize the original discrete system. The theoretical analysis is illustrated by a ninth-order boiler system model.     

Model generation by domain refinement and rule reduction

The granularity and interpretability of a fuzzy model are influenced by the method used to construct the rule base. Models obtained by a heuristic assessment of the underlying system are generally highly granular with interpretable rules, while models algorithmically generated from an analysis of training data consist of a large number of rules with small granularity. This paper presents a method for increasing the granularity of rules while satisfying a prescribed precision bound on the training data. The model is generated by a two-stage process. The first step iteratively refines the partitions of the input domains until a rule base is generated that satisfies the precision bound. In this step, the antecedents of the rules are obtained from decomposable partitions of the input domains and the consequents are generated using proximity techniques. A greedy merging algorithm is then applied to increase the granularity of the rules while preserving the precision bound. To enhance the representational capabilities of a rule and reduce the number of rules required, the rules constructed by the merging procedure have multi-dimensional antecedents. A model defined with rules of this form incorporates advantageous features of both clustering and proximity methods for rule generation. Experimental results demonstrate the ability of the algorithm to reduce the number of rules in a fuzzy model with both precise and imprecise training information.     

A two-stage model for cost effective part family and machine cell formation

This research presents, implements and tests a two-stage procedure for cost effective part family and machine cell formation. First, the problem is formulated as a mixed integer mathematical model for simultaneous machine grouping and part family assignment. This model, which we refer to as the single-stage model, considers the cost trade-offs of cell configuration, machine procurement and salvage, subcontracting, inter-cell movement, and capital investment, all of which reflect the significance of real life planning aspects. To alleviate the computational burden of this single-stage model, we decompose it into two stages: the first stage is a heuristic for machine cell and part family formations; the second stage integrates the heuristic method with a mathematical program to optimize the various cost aspects. The efficacy of the proposed models is shown through a number of example problems. The results show that the two-stage procedure is powerful in the planing stages of large-size problems where the cost aspects are crucial.     

Micromachined III-V multimorph actuators for MOEMS applications - concept, design, and model

A multimorph configuration of III-V materials that is based on the global optimization method using the simulated annealing (SA) algorithm is proposed to enhance small intrinsic piezoelectric effect of such materials. In this paper, a novel piezoelectric multimorph microactuator design such as a five-layer multimorph is proposed and analyzed using both numerical and analytical methods for potential microoptoelectromechanical systems (MOEMS) applications. Previously published analytical multimorph models for MEMS, which have been shown to reduce to equivalent expressions, are also presented and used for design optimization. By imposing a set of "real-world" constraints on the designs, optimal device geometries, which are more realistic and visible, have been determined using the SA method. Design tradeoffs are also discussed in terms of potential utility for the multimorph actuator in MOEMS applications. Finally, the proposed multimorph models are verified by finite element simulations results.     

Automated modeling for structural analysis

The numerical computations required for structural analysis are well defined and easy to automate. If structural analysis is to be automated fully, however, the modeling process, as well as the numerical computations, must be automated. This paper outlines a procedure for the automation of the entire modeling and analysis sequence.Structural analysis is considered as one of several planning, design, and analysis applications to be included in a computerintegrated design system. An essential ingredient of such a system is a central data base that supports all applications. A data base using a hierarchicalcomponent-connection concept is first described. A procedure is then outlined by which a modeler program can extract analysis models from this data base. Whereas the central data base describes the structure in terms of its components and connections, the analysis model is in terms of nodes, elements, substructures, slaving constraints, and so on. The features required in a structural analysis program to analyze the resulting model are also described. This program follows well-established principles, but is substantially different in its arhitecture from conventional analysis programs.A simple frame building is used as an example. However, the procedure is believed to be applicable to structures of a variety of types.     

Component mode synthesis-based design optimization method for local structural modification

This research integrates component mode synthesis with a multilevel design optimization strategy to develop a design methodology for making the dynamical modification of complex structures simpler and tractable. The component mode synthesis formulates the eigenvalue equation of the entire structure in terms of vibration characteristics of local structure components. With this particular feature, the component mode synthesis helps to facilitate a two-stage procedure for the dynamic modification of a complex structure; the lower-level design optimization modifies the local structure components whose performances are prescribed by the optimal solution of the upper-level design optimization. The paper first discusses the formulation and the derivation of the Kuhn-Tucker necessary conditions for the proposed design optimization procedure and then presents numerical examples to demonstrate its numerical implementation and applicability.