Piecewise ARX Model Research Articles

Minimizing multistep-ahead prediction error for piecewise ARX model identification

This paper presents a new approach for piecewise auto-regressive with exogenous inputs (ARX) model identification by minimizing the multistep-ahead prediction error. A piecewise ARX model can approximate a nonlinear process within a wide operating range, and thus minimizing its long-term prediction error is of importance for the successful application of model predictive control (MPC). The traditional MPC relevant identification (MRI) methods rely on tuning a noise model with structures known a priori, but its application for the piecewise ARX model is non-trivial. Instead, we design an algorithm to directly minimize the multistep-ahead prediction error by solving a mixed-integer nonlinear program (MINLP) without incorporating a noise model. The proposed solution method is tested on datasets from a simulated fermenter and a real heat exchanger, respectively. The results show that our approach yields models with smaller prediction error than the compared method on both training and testing datasets.

A data-driven methodology to predict thermal behavior of residential buildings using piecewise linear models

Nowadays, data-driven approaches are a good way to estimate very efficient black box models for different engineering systems. This class of model is well recognized by its outstanding performances to describe the overall behavior of one system based on its input-output relationships without any physical knowledge. In the context of building modeling, this approach is particularly well suited to predict future temperatures or energy consumption in a building. This paper presents an innovative method that uses input-output data to establish reliable and suitable thermal behavior models for residential buildings, especially for existing buildings where only measurements are available and no numerical models are at the disposal of the facility managers. The main paper contributions consist in the design of a new methodology based on the adaptation of a switched model estimation technique and in its validation to model accurately building thermal behaviors. The paper describes different stages needed to reproduce faithfully complex behaviors: data collection, PieceWise affine Auto-Regressive eXogenous (PWARX) identification technique, sensitivity analysis … It also explains how the procedure and the data-driven estimation algorithm are efficient in extracting sub-model parameters and sequence that give an outstanding ability to reproduce thermal dynamics of buildings, requiring the only collection of available data. The effectiveness of our methodology is discussed through experiments on different buildings located in the North of France. Indeed, through a comparative study between the piecewise ARX model and other existing models such as nonlinear ARX, indexed ARX and ARX models, the PWARX model gives good results in terms of indoor temperature estimation with 78.48% accuracy.

Modeling and Analysis of Interactive Driving Behavior Based on Piecewise ARX Model

Modeling and Analysis of Interactive Driving Behavior Based on Piecewise ARX Model

Identification of cascade water tanks using a PWARX model

Abstract In this paper we consider the identification of a discrete-time nonlinear dynamical model for a cascade water tank process. The proposed method starts with a nominal linear dynamical model of the system, and proceeds to model its prediction errors using a model that is piecewise affine in the data. As data is observed, the nominal model is refined into a piecewise ARX model which can capture a wide range of nonlinearities, such as the saturation in the cascade tanks. The proposed method uses a likelihood-based methodology which adaptively penalizes model complexity and directly leads to a computationally efficient implementation.

Parameter design of switched assist controller for man–machine cooperative system with human behavior model based on hybrid system

AbstractRecently, the demand for man–machine cooperative systems has been growing in many industrial fields, particularly in cell production and in flexible manufacturing systems. In the design of man–machine cooperative systems, the characteristics of human behavior must be considered. This paper presents a new design strategy for a switched assist controller for a man–machine cooperative positioning task that takes into consideration a human behavior model based on a continuous/discrete hybrid dynamical system. First, the human behavior model is identified as a piecewise ARX model using k‐means clustering and a support vector machine. Second, the switched assist system is designed as a switched impedance controller based on the identified hybrid human behavior model with optimization. The optimization was solved by performing a forward calculation of the closed loop response of the human behavior model and controller with a criterion reflecting the task time and the force effort. The results show that one can find the optimal parameters for a switched impedance controller. © 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 177(1): 55–64, 2011; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/eej.20932

Advanced motion as a hybrid system

AbstractThis paper presents a modeling and analysis strategy for advanced complex human motion based on a hybrid system framework. The motion modeling problem is addressed as a parameter estimation problem under the piecewise ARX model, which is a class of hybrid dynamical system. The advantages of motion modeling based on hybrid dynamics are: (1) complex dynamical behavior can be represented in terms of dynamical primitives together with the mechanism of switching between them; (2) the resulting model may be useful for various applications, such as the design of assist controllers, recognition of human behavior, and so on. Finally, the newly developed strategy is applied to a driver's vehicle following task and a peg‐in‐hole task, which represent two typical classes of complex human motion. The results obtained show the usefulness of hybrid dynamics for representing complex human motion. © 2010 Wiley Periodicals, Inc. Electron Comm Jpn, 93(12): 35–43, 2010; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/ecj.10236

人間行動のハイブリッドシステムモデルに基づいた人間—機械協調型ロボットシステムの切替型制御器設計

Recently, the demand for man–machine cooperative systems has been growing in many industrial fields, particularly in cell production and in flexible manufacturing systems. In the design of man–machine cooperative systems, the characteristics of human behavior must be considered. This paper presents a new design strategy for a switched assist controller for a man–machine cooperative positioning task that takes into consideration a human behavior model based on a continuous/discrete hybrid dynamical system. First, the human behavior model is identified as a piecewise ARX model using k-means clustering and a support vector machine. Second, the switched assist system is designed as a switched impedance controller based on the identified hybrid human behavior model with optimization. The optimization was solved by performing a forward calculation of the closed loop response of the human behavior model and controller with a criterion reflecting the task time and the force effort. The results show that one can find the optimal parameters for a switched impedance controller. © 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 177(1): 55–64, 2011; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/eej.20932

区分的ＡＲＸモデルの同定におけるデータ分類の改良

A piecewise ARX model is a typical model for identification of hybrid dynamical systems. This model consists of several ARX submodels which switch in accordance with the value of the regression vector. There have recently been reported many methods for piecewise ARX model identification based on data classification techniques. This approach first categorizes the observed data into several data sets and then estimates the parameters of the submodels and the switching hyperplanes based on the classification result. However, the result of the data classification procedure contains misclassified data in general, and they may have an adverse effect on the accuracy of the identified model. This paper presents two methods for refining the data classification by re-classifying the candidate for misclassified data based on piecewise linear separability or linear separability of the true data classification on the regression space, respectively. A numerical example also demonstrates the effectiveness of the present methods.

ハイブリッドシステムと高次モーション

This paper presents a modeling and analysis strategy of advanced complex human motion based on a hybrid system framework. The motion modeling problem is addressed as a parameter estimation problem of the piecewise ARX model which is a class of the hybrid dynamical systems. The advantages of motion modeling based on the hybrid dynamics are: (1) The complex dynamical behavior can be represented by underlying some primitive dynamics together with switching mechanism between them. (2) The obtained model could be useful for various application, such as, design of assist controller, recognition of the human behavior, and so on. Finally, the developed strategy is applied to a driver's vehicle following task and a peg-in-hole task which represent two typical classes of the complex human motion. The obtained results show the usefulness of the hybrid dynamics for representing complex human motion.

1A1-N07 人間行動モデルを用いた人間-機械協調ロボット制御系の応用(人間機械協調)

Recently, the demand for a man-machine cooperative system is rapidly growing in industrial fields. To meet this demand, the human model has been required to design the suitable assist controller in the man-machine cooperative system. We have already presented a human behavior model based on the hybrid system. In this paper, we apply to design the man-machine cooperative robot controller of the human behavior model. At first, the human behavior model is constructed as the piece-wise ARX model by using the hierarchal clustering, the support vector machine and the least square method. Then, we obtain the responses by computing the derived human model and the robot controller dynamics. Finally, we evaluate the responses and the experimental results with the evaluate function and confirm the usefulness of the proposed modeling method.

1A2-E08 PWARXモデルによる動作推定を用いた筋電位駆動型テレオペレーション(感覚・運動・計測)

When the human muscle is activated, we can observed a voltage called electromyogram (EMG). The EMG signal is expected to be used for the power assist system, motion estimation, and so on since it reflects human intention in the most direct manner. This paper presents a modeling strategy of the relation between human joint angle and the EMG. In particular, the relation between the wrist angle and the EMG of Extensor carpi radialis longus muscle is modeled based on the piecewise ARX model. By estimating the wrist angle using the identified model and observed EMG signal, the effectiveness of the proposed modeling strategy is verified.