Local Linear Model Tree Research Articles

Modelling a variable valve timing spark ignition engine using different neural networks

In this paper different neural networks (NN) are compared for modelling a variable valve timing spark-ignition (VVT SI) engine. The overall system is divided for each output into five neural multi-input single output (MISO) subsystems. Three kinds of NN, multilayer Perceptron (MLP), pseudo-linear radial basis function (PLRBF), and local linear model tree (LOLIMOT) networks, are used to model each subsystem. Real data were collected when the engine was under different operating conditions and these data are used in training and validation of the developed neural models. The obtained models are finally tested in a real-time online model configuration on the test bench. The neural models run independently of the engine in parallel mode. The model outputs are compared with process output and compared among different models. These models performed well and can be used in the model-based engine control and optimization, and for hardware in the loop systems.

Local Linear Model Tree (LOLIMOT) for Nonlinear System Identification of a Turbocharger with Variable Turbine Geometry (VTG)

This paper deals with nonlinear dynamic system identification by local basis function networks. A special kind of local basis function network generated by a tree construction algorithm is proposed. This local linear model tree (LOLIMOT) is applied for identification of a truck Diesel engine exhaust turbocharger with variable turbine geometry (VTG). The charging pressure is modelled as the output of a nonlinear second order multiple input system with engine speed, pulse width of injection and VTG control signal as inputs. The LOLIMOT approach was capable to identify the turbocharger with measured signals from engine test stand experiments and with fifteen local linear models in less than one minute on a Pentium PC.

Local Linear Model Trees (LOLIMOT) Toolbox for Nonlinear System Identification

The goal of the local linear model trees (LOLIMOT) toolbox for MATLAB® is to provide the industrial user and the research engineer with a fast and easy-to-use software package for nonlinear system identification. The emphasis is on shortening the overall modeling development time by reducing the number of required trial-and-error steps for identification, rather than on variability. In order to achieve this goal, the implemented algorithm has to converge in a reliable manner without any random influences (as they may be caused by random initializations for nonlinear optimization techniques). Furthermore, an appropriate problem dependent model complexity should be suggested to the user in order to avoid the requirement for tedious tuning. No (at least no non-interpretable) "fiddle" parameters should exist on which the identification results depend in a sensitive manner. The core of the LOLIMOT toolbox is a fast incremental construction algorithm for local linear neuro-fuzzy models also known as Takagi-Sugeno fuzzy models.

Structure Optimization of Takagi-Sugeno Fuzzy Models

A new approach for nonlinear system identification based on Takagi-Sugeno fuzzy models is presented. The premise structure and membership functions are optimized by the LOLIMOT (local linear model tree) algorithm, see [1]. This method is extended by a subset selection technique which automatically determines the structure of the local linear models in the rule consequents. This allows to select the significant input variables for static models and additionally the determination of the dynamic orders and dead times for dynamic models. The utilized subset selection technique is the orthogonal least-squares (OLS) algorithm. It exploits the linear regression structure of the problem and thus is very fast. The applicability of the proposed approach is illustrated by the identification of a transport delay process which has operating point dependent time constants and dead times.

Exploiting Prior Knowledge in Fuzzy Model Identification of a Heat Exchanger

Abstract Intelligent automation systems integrate a great variety of methods based on models of the controlled processes, e. g. model-based control or model-based supervision and fault diagnosis. Hence, there emerges a great demand for modeling techniques suitable for the identification of nonlinear dynamic systems. Besides classical approaches, neuro/fuzzy systems appear promising due to their approximation qualities. In this contribution, it is investigated how Takagi-Sugeno type fuzzy systems can be utilized for identification of a cross-flow water/air heat exchanger. On the one hand, these models provide transparency and interpretability which allows to incorporate qualitative and quantitative prior knowledge about the plant. On the other hand, Takagi-Sugeno models can also be identified from measurement data in order to compensate for incomplete system knowledge. Data gathering requires appropriate excitation of the system. It will be shown how elementary prior knowledge can be exploited for the design of identification signals. The concept of error bars is reviewed, and it is used to roughly evaluate the model quality depending on the properties of the excitation signal. For identification from training data the local linear model tree algorithm (LOLIMOT) is applied.

Automatic Model Selection in Local Linear Model Trees (LOLIMOT) for Nonlinear System Identification of a Transport Delay Process

In this paper a new method for nonlinear system identification is proposed. It is based on local linear models constructed by a tree algorithm in combination with a subset selection technique for determination of the local linear models’ structure. The local linear model tree can be interpreted as a Takagi-Sugeno fuzzy model, where the tree algorithm constructs the rule premises, the input membership functions and allows easy control of the model’s complexity (number of rules) while the subset selection technique determines the rule conclusions. The selection of the local linear model structure allows an automatic choice of different model orders and dead times in different operating regions. The capability of this approach to model a real world process with operating point dependent dead times and time constants is demonstrated.

Orthonormal Basis Functions for Nonlinear System Identification with Local Linear Model Trees (LOLIMOT)

A new approach for identification of nonlinear dynamic systems is proposed. It is based on a combination of generalized orthonormal basis functions and local linear model trees (LOLIMOT). The main idea is to approximate an unknown function from data by the interpolation of many local linear models. The number of local linear models and their validity regions are determined by a tree construction algorithm that partitions the input space by axisorthogonal cuts. The parameters of the local linear models are estimated by minimizing a equation error criterion (ARX models). These local parametric models are replaced by linear parameterized output error models based on generalized orthonormal basis functions. Thus, stability of the nonlinear dynamic model can be proven and the low bias property of output error models can be exploited. Furthermore, a subset selection technique may be applied for choosing the complexity of each local linear model. Since different basis functions may be constructed for each local linear model, processes with operating condition dependent dynamic behavior can be modeled efficiently.

Adaptive Predictive Control Based on Local Linear Fuzzy Models

Abstract In this paper, local linear fuzzy models are used for adaptive predictive control of nonlinear processes. First, an algorithm (LOLIMOT = local linear model tree algorithm) for off-line identification of Takagi-Sugeno type fuzzy models is briefly reviewed. In order to cope with time-variant nonlinear processes and also with the influence of non-measurable disturbances, an on-line adaptation of the model is performed. A recursive least-squares algorithm (RLS) is applied to update the linear parameters in the rule consequents locally. The local estimation results in low computational effort and avoids forgetting in non-active operating regimes. The effectiveness of the approach is demonstrated by simulations and by controlling the output temperature of a cross-flow heat exchanger.