Forward and Inverse Modelling Approaches for Prediction of Light Stimulus from Electrophysiological Response in Plants

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.In this paper, system identification approach has been adopted to develop a novel dynamical model for describing the relationship between light as an environmental stimulus and the electrical response as the measured output for a bay leaf (Laurus nobilis) plant. More specifically, the target is to predict the characteristics of the input light stimulus (in terms of on-off timing, duration and intensity) from the measured electrical response - leading to an inverse problem. We explored two major classes of system estimators to develop dynamical models - linear and nonlinear - and their several variants for establishing a forward and also an inverse relationship between the light stimulus and plant electrical response. The best class of models are given by the Nonlinear Hammerstein-Wiener (NLHW) estimator showing good data fitting results over other linear and nonlinear estimators in a statistical sense. Consequently, a few set of models using different functional variants of NLHW has been developed and their accuracy in detecting the on-off timing and intensity of the input light stimulus are compared for 19 independent plant datasets (including 2 additional species viz. Zamioculcas zamiifolia and Cucumis sativus) under similar experimental scenario.The work reported in this paper was supported by project PLants Employed As SEnsor Devices (PLEASED), EC grant agreement number 296582

Identification of nonlinear interconnected systems

This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University.In this work we address the problem of identifying a discrete-time nonlinear system composed of a linear dynamical system connected to a static nonlinear component. We use linear fractional representation to provide a united framework for the identification of two classes of such systems. The first class consists of discrete-time systems consists of a linear time invariant system connected to a continuous nonlinear static component. The identification problem of estimating the unknown parameters of the linear system and simultaneously fitting a math order spline to the nonlinear data is addressed. A simple and tractable algorithm based on the separable least squares method is proposed for estimating the parameters of the linear and the nonlinear components. We also provide a sufficient condition on data for consistency of the identification algorithm. Numerical examples illustrate the performance of the algorithm. Further, we examine a second class of systems that may involve a nonlinear static element of a more complex structure. The nonlinearity may not be continuous and is approximated by piecewise a±ne maps defined on different convex polyhedra, which are defined by linear combinations of lagged inputs and outputs. An iterative identification procedure is proposed, which alternates the estimation of the linear and the nonlinear subsystems. Standard identification techniques are applied to the linear subsystem, whereas recently developed piecewise affine system identification techniques are employed for the estimation of the nonlinear component. Numerical examples show that the proposed procedure is able to successfully profit from the knowledge of the interconnection structure, in comparison with a direct black box identification of the piecewise a±ne system.Funding was obtained as a Marie Curie Early Stage Researcher Training fellowship, under the NET-ACE project (MEST-CT-2004-6724)

A combined B-Spline-Neural-Network and ARX Model for Online Identi cation of Nonlinear Dynamic Actuation Systems

This paper presents a block oriented nonlinear dynamic model suitable for online identi cation.The model has the well known Hammerstein architecture where as a novelty the nonlinear static part is represented by a B-spline neural network (BSNN), and the linear static one is formalized by an auto regressive exogenous model (ARX). The model is suitable as a feed-forward control module in combination with a classical feedback controller to regulate velocity and position of pneumatic and hydraulic actuation systems which present non stationary nonlinear dynamics. The adaptation of both the linear and nonlinear parts is taking place simultaneously on a patterby- patter basis by applying a combination of error-driven learning rules and the recursive least squares method. This allows to decrease the amount of computation needed to identify the model's parameters and therefore makes the technique suitable for real time applications. The model was tested with a silver box benchmark and results show that the parameters are converging to a stable value after 1500 samples, equivalent to 7.5s of running time. The comparison with a pure ARX and BSNN model indicates a substantial improvement in terms of the RMS error, while the comparison with alternative non linear dynamic models like the NNOE and NNARX, having the same number of parameters but greater computational complexity, shows comparable performances

A combined B-Spline-Neural-Network and ARX Model for Online Identi cation of Nonlinear Dynamic Actuation Systems

This paper presents a block oriented nonlinear dynamic model suitable for online identi cation.The model has the well known Hammerstein architecture where as a novelty the nonlinear static part is represented by a B-spline neural network (BSNN), and the linear static one is formalized by an auto regressive exogenous model (ARX). The model is suitable as a feed-forward control module in combination with a classical feedback controller to regulate velocity and position of pneumatic and hydraulic actuation systems which present non stationary nonlinear dynamics. The adaptation of both the linear and nonlinear parts is taking place simultaneously on a patterby- patter basis by applying a combination of error-driven learning rules and the recursive least squares method. This allows to decrease the amount of computation needed to identify the model's parameters and therefore makes the technique suitable for real time applications. The model was tested with a silver box benchmark and results show that the parameters are converging to a stable value after 1500 samples, equivalent to 7.5s of running time. The comparison with a pure ARX and BSNN model indicates a substantial improvement in terms of the RMS error, while the comparison with alternative non linear dynamic models like the NNOE and NNARX, having the same number of parameters but greater computational complexity, shows comparable performances

A New Hammerstein Model for Non-Linear System Identification

In the present work a newer type of black box nonlinear model in Hammerstein structure is proposed. The model has Wavelet Network coupled with Orthonormal Basis Functions which is capable of modeling a class of non-linear systems with acceptable accuracy. Wavelet basis functions have the property of localization in both the time and frequency domains which enables wavelet networks to approximate severe non-linearities using few number of parameters. Orthonormal Basis functions possess the ability to approximate any linear time invariant system using appropriate basis functions. The efficacy of the model in modeling is demonstrated using numerical examples

A comparative study of surrogate musculoskeletal models using various neural network configurations

Title from PDF of title page, viewed on August 13, 2013Thesis advisor: Reza R. DerakhshaniVitaIncludes bibliographic references (pages 85-88)Thesis (M.S.)--School of Computing and Engineering. University of Missouri--Kansas City, 2013The central idea in musculoskeletal modeling is to be able to predict body-level (e.g. muscle forces) as well as tissue-level information (tissue-level stress, strain, etc.). To develop computationally efficient techniques to analyze such models, surrogate models have been introduced which concurrently predict both body-level and tissue-level information using multi-body and finite-element analysis, respectively. However, this kind of surrogate model is not an optimum solution as it involves the usage of finite element models which are computation intensive and involve complex meshing methods especially during real-time movement simulations. An alternative surrogate modeling method is the use of artificial neural networks in place of finite-element models. The ultimate objective of this research is to predict tissue-level stresses experienced by the cartilage and ligaments during movement and achieve concurrent simulation of muscle force and tissue stress using various surrogate neural network models, where stresses obtained from finite-element models provide the frame of reference. Over the last decade, neural networks have been successfully implemented in several biomechanical modeling applications. Their adaptive ability to learn from examples, simple implementation techniques, and fast simulation times make neural networks versatile and robust when compared to other techniques. The neural network models are trained with reaction forces from multi-body models and stresses from finite element models obtained at the interested elements. Several configurations of static and dynamic neural networks are modeled, and accuracies close to 93% were achieved, where the correlation coefficient is the chosen measure of goodness. Using neural networks, the simulation time was reduced nearly 40,000 times when compared to the finite-element models. This study also confirms theoretical concepts that special network configurations--including average committee, stacked generalization, and negative correlation learning--provide considerably better results when compared to individual networks themselves.Introduction -- Methods -- Results -- Conclusion -- Future work -- Appendix A. Various linear and non-linear modeling techniques -- Appendix B. Error analysi