Black-box Identification Of Nonlinear Systems Research Articles

Hybrid gray and black-box nonlinear system identification of an elastomer joint flexible robotic manipulator

Series elastic actuators possess several properties that make them widely used in collaborative robots, which play a major role in the current paradigm of industry 4.0. However, the compliant element responsible for those desired properties can also be responsible for the addition of unmodeled nonlinearities in the system. Therefore, the aim of this paper is to propose a novel hybrid model approach and apply it in the modeling of an elastomer-based series elastic joint. The proposed hybrid model combines a phenomenological gray-box model with a black-box Nonlinear Auto-regressive model with Exogenous inputs, which is able to provide the desired physical insight while enhancing accuracy by addressing the unknown nonlinearities. The results showed that the proposed hybrid model is more than 60% more accurate than the phenomenological model, considering the mean square error, and obtained a multiple correlation coefficient up to 0.97, indicating its capacity to be used in the construction of a digital twin of the system.

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

A new tool for black-box non-linear system identification of multi-input multi-output systems is presented in this paper. The new structure extends the conventional linear state-space model into a non-linear framework, where each parameter is a non-linear function of the inputs or the states. 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 the system eigenvalues and the dominant modes. This structure is a completely black-box system, which requires no physical understanding of the process for successful identification, and it is possible to expand easily the order and the complexity of non-linearities, while ensuring good parameter conditioning. A simple non-linear example illustrates the method, and identification of a highly non-linear brake model is also presented. These examples show that the method can be applied as a mechanism for model order reduction; it is equally very suitable as a tool for non-linear 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.

Robust Estimation of Balanced Simplicity-Accuracy Neural Networks-Based Models

Neural networks are powerful tools for black box system identification. However, their main drawback is the large number of parameters usually required to deal with complex systems. Classically, the model's parameters minimize a L2-norm-based criterion. However, when using strongly corrupted data, namely, outliers, the L2-norm-based estimation algorithms become ineffective. In order to deal with outliers and the model's complexity, the main contribution of this paper is to propose a robust system identification methodology providing neuromodels with a convenient balance between simplicity and accuracy. The estimation robustness is ensured by means of the Huberian function. Simplicity and accuracy are achieved by a dedicated neural network design based on a recurrent three-layer architecture and an efficient model order reduction procedure proposed in a previous work (Romero-Ugalde et al., 2013, “Neural Network Design and Model Reduction Approach for Black Box Nonlinear System Identification With Reduced Number of Parameters,” Neurocomputing, 101, pp. 170–180). Validation is done using real data, measured on a piezoelectric actuator, containing strong natural outliers in the output data due to its microdisplacements. Comparisons with others black box system identification methods, including a previous work (Corbier and Carmona, 2015, “Extension of the Tuning Constant in the Huber's Function for Robust Modeling of Piezoelectric Systems,” Int. J. Adapt. Control Signal Process., 29(8), pp. 1008–1023) where a pseudolinear model was used to identify the same piezoelectric system, show the relevance of the proposed robust estimation method leading balanced simplicity-accuracy neuromodels.

Computational cost improvement of neural network models in black box nonlinear system identification

Models play an important role in many engineering fields. Therefore, the goal in system identification is to find the good balance between the accuracy, complexity and computational cost of such identification models. In a previous work (Romero-Ugalde et al., 2013 [1]), we focused on the topic of providing balanced accuracy/complexity models by proposing a dedicated neural network design and a model complexity reduction approach. In this paper, we focus on the reduction of the computational cost required to achieve these balanced models. More precisely, the improvement of the preceding method presented here leads to a significantly computational cost reduction of the neural network training phase. Even if this reduction is achieved by a convenient choice of the activation functions and the initial conditions of the synaptic weights, the proposed architecture leads to a wide range of models among the most encountered in the literature assuring the interest of such a method. To validate the proposed approach, two different systems are identified. The first one corresponds to the unavoidable Wiener–Hammerstein system proposed in SYSID2009 as a benchmark. The second system is a flexible robot arm. Results show the interest of the proposed reduction methods.

Intelligent computationally efficient modelling of multi-input multi-output non-linear dynamical process plants: An industrial steam generator case study

Most of the process plants have intrinsic non-linear, time-varying, non-minimum phase and coupling characteristics that result in a highly time-consuming and tedious task to derive complicated non-linear dynamic equations governing on such types of processes. On the other hand, even though such equations can be analytically extracted, they have not worked out in most cases yet. To find a simple fix that can address these hurdles associated with analytical modelling, two types of non-analytical models, namely, simulator and predictor, are proposed based on a computationally efficient technique so-called locally linear neuro-fuzzy modelling. That is, a simulator model as well as a specially structured long-term predictor model that is built based on a sequential arrangement of single-stage predictor models is presented for multi-input multi-output non-linear dynamical process plants and feasibly applied to a real water-tube steam generator for the first time. An adaptive evolving algorithm named linear model tree contributes to estimate the parameters of neuro-fuzzy simulator and predictor models. Furthermore, an order selection method based on Lipschitz theory, whose merit is being totally independent from developing any model prior to commencing tedious modelling trials, is also proposed for the first time by defining a modified Lipschitz index to remedy the order determination problem within the very first steps of black-box non-linear system identification. The blend of such a fully modelling-independent order selection algorithm and a unique type of computationally inexpensive non-linear neuro-fuzzy model lessens the overall computational burden of modelling procedure that represents a great concern in a black-box system identification approach. The recorded data from a real water-tube steam generator operating at Abbot Power plant unit of Champaign, IL, were exploited to carry out experimental modelling in order to reveal the pros and cons of the presented models.

Neural network design and model reduction approach for black box nonlinear system identification with reduced number of parameters

In this paper a dedicated recurrent neural network design and a model reduction approach are proposed in order to improve the balance between complexity and quality of black box nonlinear system identification models. The proposed neural network design, based on a three-layers architecture, helps to reduce the number of parameters of the model after the training phase without any significant loss of estimation accuracy. Nevertheless, the proposed architecture remains sufficiently general to provide a wide range of models among the most encountered in the literature. This reduction, achieved by a convenient choice of the activation functions and the initial conditions of the synaptic weights, is developed in two steps. The first step is to train the proposed architecture under two reasonable assumptions. Then the recurrent three-layers neural network is transformed into a representation of two-layer with less number of neurons, that is, a significant reduced number of parameters. The constructed architecture provided models with reasonable reduced number of parameters with a convenient estimation accuracy. To validate the proposed approach, we identify the Wiener–Hammerstein benchmark nonlinear system proposed in SYSID2009 [1].

Stable Nonlinear System Identification: Convexity, Model Class, and Consistency

Recently a new approach to black-box nonlinear system identification has been introduced which searches over a convex set of stable nonlinear models for the one which minimizes a convex upper bound of long-term simulation error. In this paper, we further study the properties of the proposed model set and identification algorithm and provide two theoretical results: (a) we show that the proposed model set includes all quadratically stable nonlinear systems, as well as some more complex systems; (b) we study the statistical consistency of the proposed identification method applied to a linear system with noisy measurements. It is shown a modification related to instrumental variables gives consistent parameter estimates.

Multiple steps prediction with nonlinear ARX models

NLARX (NonLinear AutoRegressive with eXogenous inputs) models are frequently used in black-box nonlinear system identification. Though it is easy to make one step ahead prediction with such models, multiple steps prediction is far from trivial. The main difficulty is that in general there is no easy way to compute the mathematical expectation of an output conditioned by past measurements. An optimal solution would require intensive numerical computations related to nonlinear filtering. The purpose of this paper is to investigate simple non optimal prediction methods. It is shown that cautions must be paid when using such methods, since their prediction behaviors may be radically different, depending on some detailed choice.