Identification of Wiener–Hammerstein models: Two algorithms based on the best split of a linear model applied to the SYSID'09 benchmark problem

This paper describes the identification of Wiener–Hammerstein models and two recently suggested algorithms are applied to the SYSID'09 benchmark data. The most difficult step in the identification process of such block-oriented models is to generate good initial values for the linear dynamic blocks so that local minima are avoided. Both of the considered algorithms obtain good initial estimates by using the best linear approximation (BLA) which can easily be estimated from data. Given the BLA, the two algorithms differ in the way the dynamics are separated into two linear parts. The first algorithm simply considers all possible splits of the dynamics. Each of the splits is used to initialize one Wiener–Hammerstein model using linear least-squares and the best performing model is selected. In the second algorithm, both linear blocks are initialized with the entire BLA model using basis function expansions of the poles and zeros of the BLA. This gives over-parameterized linear blocks and their order is decreased in a model reduction step. Both algorithms are explained and their properties are discussed. They both give good, comparable models on the benchmark data.     

A multiple model filtering approach to transmission line fault diagnosis

This paper provides justification and implementation for a multiple model filtering approach to diagnosis of transmission line three-phase short to ground faults in the presence of protection misoperations. This approach utilizes the electric network dynamics and wide area measurements to provide diagnosis outcomes. A second focus of this paper is on the reduction of computational complexity of the diagnosis algorithm. This issue is addressed by a two-step heuristic. The first step designs subsystem models through measurement selection. The second step reduces the dynamic model order. The performance of the diagnosis algorithms are evaluated on a simulated WSCC 9-bus system.     

Identification of cohesive crack fracture parameters by evolutionary search

This paper is concerned with the application and performance of two evolutionary search techniques to identify the parameters characterizing mode I cohesive crack models. In particular, genetic-based heuristic schemes, implemented via a classical genetic algorithm and also as a differential evolution process, are considered. Actual experimental data are used to assess the schemes for both piecewise linear and nonlinear softening models. The results of these two adaptive algorithms are also compared with the performance of a previously proposed local optimization approach involving formulation of the inverse problem as a mathematical program with equilibrium constraints.     

基于局部先验模型的单目视频人体运动跟踪

在基于模型的单目视频人体运动跟踪中,视频图像信息往往不足以恢复人体姿态,通常需要加入对姿态的先验约束才能得到合理的解.为了有效地刻画人体运动过程的时变动态特征,提出局部先验模型,其中包括局部动态过程和局部姿态分布密度,通过在样本空间中检索出相似姿态的集合,并利用该集合学习模型参数来比较精确地刻画人体的运动规律.实验结果表明,与全局动态模型相比,局部先验模型有效地克服了肢体自遮挡和肢体混淆等问题,取得了更好的跟踪结果.     

Model predictive control of plant transitions using a new identification technique for interpolating nonlinear models

This paper presents a model based controller design approach for plants that operate in several distinct operating regimes and make transitions between them. Often it is difficult to identify a single global model that describes plant behavior in all the regimes. In the present work we propose an identification method that builds linear models for the individual regimes, and then interpolates nonlinear models in between these local models to match plant dynamics during transitions. The identification technique is shown to work well with transition data which lack excitation. A model predictive controller based on the local and the transition models is then presented and applied to a reactor.     

Dynamic modelling and stabilization of a new configuration of two-wheeled machines

This paper presents a novel design of two-wheeled vehicles and an associated stabilization approach. The proposed design provides the vehicle with more flexibility in terms of increased degrees of freedom which enable the vehicle to enlarge its working space. The additional translational degree of freedom (DOF), offered by the linear actuator, assists an attached payload to reach different levels of height as and when required. The model of the system mimics the scenario of the double inverted pendulum on a moving base, with the added DOF. Lagrangian dynamic formulation is used to derive the system dynamics. Joints frictions based on the Coulomb friction model are considered so as to retain nonlinear characteristics of the system. A PD-PID robust control approach is derived for the stabilization of the system. An investigation of the impact of damping associated with joints on the stability of the system is carried out. Simulation results validating the model and the control approach are presented and discussed.     

Interval regression analysis using quadratic loss support vector machine

Support vector machines (SVMs) have been very successful in pattern recognition and function estimation problems for crisp data. This paper proposes a new method to evaluate interval linear and nonlinear regression models combining the possibility and necessity estimation formulation with the principle of quadratic loss SVM. This version of SVM utilizes quadratic loss function, unlike the traditional SVM. For data sets with crisp inputs and interval outputs, the possibility and necessity models have been recently utilized, which are based on quadratic programming approach giving more diverse spread coefficients than a linear programming one. The quadratic loss SVM also uses quadratic programming approach whose another advantage in interval regression analysis is to be able to integrate both the property of central tendency in least squares and the possibilistic property in fuzzy regression. However, this is not a computationally expensive way. The quadratic loss SVM allows us to perform interval nonlinear regression analysis by constructing an interval linear regression function in a high dimensional feature space. The proposed algorithm is a very attractive approach to modeling nonlinear interval data, and is model-free method in the sense that we do not have to assume the underlying model function for interval nonlinear regression model with crisp inputs and interval output. Experimental results are then presented which indicate the performance of this algorithm.     

A parallel Hamiltonian formulation for forward dynamics of closed-loop multibody systems

This paper presents a novel recursive divide-and-conquer formulation for the simulation of complex constrained multibody system dynamics based on Hamilton’s canonical equations (HDCA). The systems under consideration are subjected to holonomic, independent constraints and may include serial chains, tree chains, or closed-loop topologies. Although Hamilton’s canonical equations exhibit many advantageous features compared to their acceleration based counterparts, it appears that there is a lack of dedicated parallel algorithms for multi-rigid-body system dynamics based on the Hamiltonian formulation. The developed HDCA formulation leads to a two-stage procedure. In the first phase, the approach utilizes the divide and conquer scheme, i.e., a hierarchic assembly–disassembly process to traverse the multibody system topology in a binary tree manner. The purpose of this step is to evaluate the joint velocities and constraint force impulses. The process exhibits linear \(O(n)\) (\(n\) – number of bodies) and logarithmic \(O(\log_{2}{n})\) numerical cost, in serial and parallel implementations, respectively. The time derivatives of the total momenta are directly evaluated in the second parallelizable step of the algorithm. Sample closed-loop test cases indicate very small constraint violation errors at the position and velocity level as well as marginal energy drift without any additional form of constraint stabilization techniques involved in the solution process. The results are comparatively set against more standard acceleration based Featherstone’s DCA approach to indicate the performance of the HDCA algorithm.     

Multivariable frequency-response curve fitting with application to modal parameter estimation

This paper presents a computational approach for the frequency-domain identification of multivariable, discrete-time transfer function models based on a cost function minimization. The algorithm is optimized for the parametric characterization of complex high-order multivariable systems requiring a large number of model parameters, including sparse matrix methods and QR-projections for the reduction of computation time and memory requirements. The algorithm supports a multivariable frequency-dependent weighting, which generally improves the quality of the transfer function model estimate. The overall approach is successfully demonstrated for a typical case encountered in experimental structural dynamics modelling (using modal analysis) and compared with related algorithms in order to assess the gain in computational efficiency.     

Robust model predictive control of Wiener systems

Block-oriented models (BOMs) have shown to be appealing and efficient as nonlinear representations for many applications. They are at the same time valid and simple models in a more extensive region than time-invariant linear models. In this work, Wiener models are considered. They are one of the most diffused BOMs, and their structure consists in a linear dynamics in cascade with a nonlinear static block. Particularly, the problem of control of these systems in the presence of uncertainty is treated. The proposed methodology makes use of a robust identification procedure in order to obtain a robust model to represent the uncertain system. This model is then employed to design a model predictive controller. The mathematical problem involved in the controller design is formulated in the context of the existing linear matrix inequalities (LMI) theory. The main feature of this approach is that it takes advantage of the static nature of the nonlinearity, which allows to solve the control problem by focusing only in the linear dynamics. This formulation results in a simplified design procedure, because the original nonlinear model predictive control (MPC) problem turns into a linear one.     

Explicit dynamics of space free-flyers with multiple manipulators via SPACEMAPLE

This paper focuses on the dynamics of a multiple manipulator space free-flying robot (SFFR) with rigid links and issues relevant to the development of appropriate control algorithms. To develop an explicit dynamics model of such complex systems, the Lagrangian formulation is applied. First, the system kinetic energy is derived based on a developed kinematics approach. Then, through vigorous mathematical analyses, three formats are obtained which describe the contribution of each term of kinetic energy to the equations of motion. Next, explicit derivations of a system's mass matrix, and of the vectors of non-linear velocity terms and generalized forces are introduced for the first time. The obtained dynamics model is very useful for dynamics analyses, design and development of control algorithms for such complex systems. The explicit SFFR dynamics can be implemented either numerically or symbolically. Following the latter approach, the developed symbolic code for dynamics modeling, i.e. SPACEMAPLE, and its verification procedure are described, and issues relevant to the development and computation of dynamics models in control algorithms are briefly discussed. Specific dynamic characteristics of SFFRs compared to fixed-base manipulators are pointed out.     

Stable Adaptive Fuzzy Control with TSK Fuzzy Friction Estimation for Linear Drive Systems

This paper considers the control of a linear drive system with friction and disturbance compensation. A stable adaptive controller integrated with fuzzy model-based friction estimation and switching-based disturbance compensation is proposed via Lyapunov stability theory. A TSK fuzzy model with local linear friction models is suggested for real-time estimation of its consequent local parameters. The parameters update law is derived based on linear parameterization. In order to compensate for the effects resulting from estimation error and disturbance, a robust switching law is incorporated in the overall stable adaptive control system. Extensive computer simulation results show that the proposed stable adaptive fuzzy control system has very good performances, and is potential for precision positioning and trajectory tracking control of linear drive systems.     

Editorial

A fundamental physical understanding of the properties and structure of dynamic robot models is the basis of controller design for robotic manipulators. This paper focuses on the estimation of different parameters which appear in the dynamics models of robots. By introducing candidate functions and a statistical approach to analyze these functions it is possible to identify the significant parameters in the dynamics model of the manipulator. This generalized method is also capable of considering Coloumb and viscous friction effects. Modeling based on candidate functions does not require symbolic calculation for the dynamics of the manipulator and can easily be applied to manipulators with more than 6 d.o.f. Parameter estimation is especially appropriate for modeling manipulators with many degrees of freedom prior to developing control algorithms, where otherwise the computation of such models is overwhelming. It is also demonstrated that this type of modeling is equivalent to the conventional symbolic calculation of dynamics of manipulators.     

Swarm intelligence algorithms for macroscopic traffic flow model validation with automatic assignment of fundamental diagrams

This paper is concerned with the problem of macroscopic road traffic flow model calibration and verification. Thoroughly validated models are necessary for both control system design and scenario evaluation purposes. Here, the second order traffic flow model METANET was calibrated and verified using real data.A powerful optimisation problem formulation is proposed for identifying a set of model parameters that makes the model fit to measurements. For the macroscopic traffic flow model validation problem, this set of parameters characterise the aggregate traffic flow features over a road network. In traffic engineering, one of the most important relationships whose parameters need to be determined is the fundamental diagram of traffic, which models the non-linear relationship between vehicular flow and density. Typically, a real network does not exhibit the same traffic flow aggregate behaviour everywhere and different fundamental diagrams are used for covering different network areas. As a result, one of the initial steps of the validation process rests on expert engineering opinion assigning the spatial extension of fundamental diagrams. The proposed optimisation problem formulation allows for automatically determining the number of different fundamental diagrams to be used and their corresponding spatial extension over the road network, simplifying this initial step. Although the optimisation problem suffers from local minima, good solutions which generalise well were obtained.The design of the system used is highly generic and allows for a number of evolutionary and swarm intelligence algorithms to be used. Two UK sites have been used for testing it. Calibration and verification results are discussed in detail. The resulting models are able to capture the dynamics of traffic flow and replicate shockwave propagation.A total of ten different algorithms were considered and compared with respect to their ability to converge to a solution, which remains valid for different sets of data. Particle swarm optimisation (PSO) algorithms have proven to be particularly effective and provide the best results both in terms of speed of convergence and solution generalisation. An interesting result reported is that more recently proposed PSO algorithms were outperformed by older variants, both in terms of speed of convergence and model error minimisation.     

Fast interference detection between geometric models

We present efficient algorithms for interference detection between geometric models described by linear or curved boundaries and undergoing rigid motion. The set of models include surfaces described by rational spline patches or piecewise algebraic functions. In contrast to previous approaches, we first describe an efficient algorithm for interference detection between convex polytopes using coherence and local features. Then an extension using hierarchical representation to concave polytopes is presented. We apply these algorithms along with properties of input models, local and global algebraic methods for solving polynomial equations, and the geometric formulation of the problem to devise efficient algorithms for convex and nonconvex curved objects. Finally, a scheduling scheme to reduce the frequency of interference detection in large environments is described. These algorithms have been successfully implemented and we discuss their performance in various environments.     

Intelligent control of DC motor driven mechanical systems: a robust learning control approach

A robust learning controller is presented for DC motor driven mechanical systems with friction. The proposed controller takes advantage of both robust and learning control approaches to learn and compensate periodic and non‐periodic uncertain dynamics. In the learning controller, a set of learning rules is implemented in which three types of learnings occur: one is direct learning of desired inverse dynamics input and the other two learning of unknown linear parameters and nonlinear bounding functions in the models of system dynamics and friction. The global asymptotic stability of learning control system is shown by using the Lyapunov stability theory. Experimental data demonstrate the effectiveness of developed learning approach to tracking of DC motor driven mechanical systems. Copyright © 2002 John Wiley & Sons, Ltd.     

Improving the interpretability of TSK fuzzy models by combiningglobal learning and local learning

The fuzzy inference system proposed by Takagi, Sugeno, and Kang, known as the TSK model in fuzzy system literature, provides a powerful tool for modeling complex nonlinear systems. Unlike conventional modeling where a single model is used to describe the global behavior of a system, TSK modeling is essentially a multimodel approach in which simple submodels (typically linear models) are combined to describe the global behavior of the system. Most existing learning algorithms for identifying the TSK model are based on minimizing the square of the residual between the overall outputs of the real system and the identified model. Although these algorithms can generate a TSK model with good global performance (i.e., the model is capable of approximating the given system with arbitrary accuracy, provided that sufficient rules are used and sufficient training data are available), they cannot guarantee the resulting model to have a good local performance. Often, the submodels in the TSK model may exhibit an erratic local behavior, which is difficult to interpret. Since one of the important motivations of using the TSK model (also other fuzzy models) is to gain insights into the model, it is important to investigate the interpretability issue of the TSK model. We propose a new learning algorithm that integrates global learning and local learning in a single algorithmic framework. This algorithm uses the idea of local weighed regression and local approximation in nonparametric statistics, but remains the component of global fitting in the existing learning algorithms. The algorithm is capable of adjusting its parameters based on the user's preference, generating models with good tradeoff in terms of global fitting and local interpretation. We illustrate the performance of the proposed algorithm using a motorcycle crash modeling example     

Continuous-time decentralized smoothers based on two-filter form: identical local and global models

This paper proposes some decentralized smoothing algorithms for a continuous-time linear estimation structure consisting of a central processor and of two local processors, in which the local models are assumed to be identical to the global model. The philosophy of the paper is to solve the problem in terms of the local forward and backward information (or Kalman) filters. The resulting algorithms are somewhat different from those based on the local smoothing estimates which have been studied by some other authors. Smoothing update and real-time smoothing algorithms are also presented, ft is shown that the present algorithms have some advantages: the global filtered estimates can be obtained in the course of computing the decentralized smoothing estimates and the central and local processors can be derived in a completely parallel fashion