Nonlinear Identification With Local Model Networks Using GTLS Techniques and Equality Constraints

Institute of Mechanics and Mechatronics, Division of Control and Process Automation, Vienna University of Technology, Vienna, Austria.
IEEE Transactions on Neural Networks (Impact Factor: 2.95). 07/2011; 22(9):1406-18. DOI: 10.1109/TNN.2011.2159309
Source: PubMed


Local model networks approximate a nonlinear system through multiple local models fitted within a partition space. The main advantage of this approach is that the identification of complex nonlinear processes is alleviated by the integration of structured knowledge about the process. This paper extends these concepts by the integration of quantitative process knowledge into the identification procedure. Quantitative knowledge describes explicit dependences between inputs and outputs and is integrated in the parameter estimation process by means of equality constraints. For this purpose, a constrained generalized total least squares algorithm for local parameter estimation is presented. Furthermore, the problem of proper integration of constraints in the partitioning process is treated where an expectation-maximization procedure is combined with constrained parameter estimation. The benefits and the applicability of the proposed concepts are demonstrated by means of two illustrative examples and a practical application using real measurement data.

10 Reads
  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper proposes a local model network (LMN) for measurement-based modeling of the nonlinear aggregate power system loads. The proposed LMN approach requires no pre-defined standard load model and uses measurement data to identify load dynamics. Furthermore, due to the interesting characteristics of the proposed approach, the LMN is able to have separate and independent linear and nonlinear inputs, determined by the use of prior knowledge. Trained by the newly developed hierarchical binary tree (HBT) learning algorithm, the proposed LMN attains maximum generalizability with the best linear or nonlinear structure. The previous values of the power system voltage and active and reactive powers are considered as the inputs of the LMN. The proposed approach is applied to the artificially generated data and IEEE 39-bus test system. Work on the field measurement real data is also provided to verify the method. The results of modeling for artificial data, the test system and real data confirm the ability of the proposed approach in capturing the dynamics of the power system loads.
    IEEE Transactions on Power Systems 01/2012; DOI:10.1109/TPWRS.2012.2234142 · 2.81 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, advanced concepts for the identification of complex nonlinear systems are discussed. Three major problems are addressed: The nonlinearity of the system, noise in the data upon which the model has to be built, and the potential to incorporate qualitative and quantitative prior knowledge about the system. As an integrated solution approach, local model networks (LMNs) with appropriate parameter estimation schemes are proposed. LMNs generally offer a versatile structure for the identification of nonlinear dynamic systems. In order to account for a realistic situation when noise is present both in input and output data, an equality constrained generalised total least squares algorithm for the local model parameter estimation of the LMN is presented; the incorporation of equality constraints allows to mathematically enforce desired system properties. As an application and benchmark problem, the vertical dynamics of a vehicle is considered. After training the LMN on a rough road, excellent predictions of the behaviour of the vehicle at crossing a single obstacle are obtained, thus proving the effectiveness of the proposed algorithm. It is illustrated how both the application of a proper parameter estimation scheme and the integration of system constraints systematically improve the performance of the model.
    Acta Mechanica 08/2012; 223(8). DOI:10.1007/s00707-012-0638-8 · 1.47 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Local modeling approaches, owing to their ability to model different operating regimes of nonlinear systems and processes by independent local models, seem appealing for modeling, identification, and prediction applications. In this paper, we propose a local neuro-fuzzy (LNF) approach based on the least-squares support vector machines (LSSVMs). The proposed LNF approach employs LSSVMs, which are powerful in modeling and predicting time series, as local models and uses hierarchical binary tree (HBT) learning algorithm for fast and efficient estimation of its parameters. The HBT algorithm heuristically partitions the input space into smaller subdomains by axis-orthogonal splits. In each partitioning, the validity functions automatically form a unity partition and therefore normalization side effects, e.g., reactivation, are prevented. Integration of LSSVMs into the LNF network as local models, along with the HBT learning algorithm, yield a high-performance approach for modeling and prediction of complex nonlinear time series. The proposed approach is applied to modeling and predictions of different nonlinear and chaotic real-world and hand-designed systems and time series. Analysis of the prediction results and comparisons with recent and old studies demonstrate the promising performance of the proposed LNF approach with the HBT learning algorithm for modeling and prediction of nonlinear and chaotic systems and time series.
    IEEE transactions on neural networks and learning systems 02/2013; 24(2):207-218. DOI:10.1109/TNNLS.2012.2227148 · 4.29 Impact Factor
Show more