Two Nonlinear Optimization Methods for Black Box Identification Compared

Mulders, Anne Van; Schoukens, Johan; Volckaert, Marnix; Diehl, Moritz

doi:10.3182/20090706-3-fr-2004.00180

Cited by 16 publications

(9 citation statements)

References 4 publications

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“…In addition to this the derivatives with respect to the objective function and the constraints are very simple. However, the application of constrained NLS for black box identification in [VMSVD10] does not show that it is advantageous with respect to computational speed for that application. However, it has the advantage that it can address unstable models.…”

Section: Numerical Implementationmentioning

confidence: 99%

Maximum likelihood estimation of Gaussian models with missing data—Eight equivalent formulations

Hansson

Wallin

2012

Automatica

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In this paper we derive the maximum likelihood problem for missing data from a Gaussian model. We present in total eight different equivalent formulations of the resulting optimization problem, four out of which are nonlinear least squares formulations. Among these formulations are also formulations based on the expectation-maximization algorithm. Expressions for the derivatives needed in order to solve the optimization problems are presented. We also present numerical comparisons for two of the formulations for an ARMAX model.

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Section: Numerical Implementationmentioning

confidence: 99%

Maximum likelihood estimation of Gaussian models with missing data—Eight equivalent formulations

Hansson

Wallin

2012

Automatica

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“…The need for a general nonlinear system identification technique that can represent many classes of nonlinear systems led to the development of state‐space nonlinear system identification techniques based on input/output data. The polynomial nonlinear state‐space (PNLSS) approach is a system identification method for MIMO systems that leads to a model of a multivariable nonlinear system based purely on input/output data . PNLSS is a promising all‐purpose nonlinear system identification method that can be used for many different types of systems, including those that are described by bilinear models, Wiener‐Hammerstein models, and models with nonlinearities appearing in the states or inputs, or appearing in both …”

Section: Introductionmentioning

confidence: 99%

“…In the PNLSS approach, a linear state‐space model is first obtained and it is then extended to a nonlinear model for the system using polynomial nonlinear terms with coefficients identified through an optimization problem . The linear part can be obtained using the best linear fit or least‐squares, or using subspace system identification . The linear model is determined first so that the nonlinear model subsequently identified will achieve a performance at least as good as that of the linear model in a small neighborhood of the measured process states used in the identification process .…”

Section: Introductionmentioning

confidence: 99%

On identification of well‐conditioned nonlinear systems: Application to economic model predictive control of nonlinear processes

2015

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The focus of this work is on economic model predictive control (EMPC) that utilizes well-conditioned polynomial nonlinear state-space (PNLSS) models for processes with nonlinear dynamics. Specifically, the article initially addresses the development of a nonlinear system identification technique for a broad class of nonlinear processes which leads to the construction of PNLSS dynamic models which are well-conditioned over a broad region of process operation in the sense that they can be correctly integrated in real-time using explicit numerical integration methods via time steps that are significantly larger than the ones required by nonlinear state-space models identified via existing techniques. Working within the framework of PNLSS models, additional constraints are imposed in the identification procedure to ensure well-conditioning of the identified nonlinear dynamic models. This development is key because it enables the design of Lyapunov-based EMPC (LEMPC) systems for nonlinear processes using the well-conditioned nonlinear models that can be readily implemented in real-time as the computational burden required to compute the control actions within the process sampling period is reduced. A stability analysis for this LEMPC design is provided that guarantees closed-loop stability of a process under certain conditions when an LEMPC based on a nonlinear empirical model is used. Finally, a classical chemical reactor example demonstrates both the system identification and LEMPC design techniques, and the significant advantages in terms of computation time reduction in LEMPC calculations when using the nonlinear empirical model.

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“…More recently, Van Mulders et al [11] have employed polynomial-based black-box nonlinear state-space systems, where the parameters are identified by the leastsquares method. This structure consists of a linear state-space model with polynomials added to the process and measurement equations.…”

Section: *Corresponding Author: Department Of Aeronautical and Automomentioning

confidence: 99%

A new structure for non-linear black-box system identification using the extended Kalman filter

Bogdanski

Best

2017

Proceedings of the Institution of Mechanical Engineers, Part D:

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The method works iteratively in the time domain using an Extended Kalman Filter. The model retains a state space structure in modal canonical form, which ensures that a minimal number of parameters need to be identified and also produces additional information in terms of system eigenvalues and dominant modes. This structure is completely black-box, requiring no physical understanding of the process for successful identification, and it is possible to easily expand the order and complexity of nonlinearities, whilst ensuring good parameter conditioning. A simple nonlinear example illustrates the method, and identification of a highly nonlinear brake model is also presented. These examples show the method can be applied as a mechanism for model order reduction; it is equally well suited as a tool for nonlinear plant system identification. In both capacities this new method is valuable, particularly as the generation of simplified models for the whole vehicle and its subsystems is an increasingly important aspect of modern vehicle design.

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Two Nonlinear Optimization Methods for Black Box Identification Compared

Cited by 16 publications

References 4 publications

Maximum likelihood estimation of Gaussian models with missing data—Eight equivalent formulations

Maximum likelihood estimation of Gaussian models with missing data—Eight equivalent formulations

On identification of well‐conditioned nonlinear systems: Application to economic model predictive control of nonlinear processes

A new structure for non-linear black-box system identification using the extended Kalman filter

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