Identification Of Complex Dynamic Systems Research Articles

On sparse identification of complex dynamical systems: A study on discovering influential reactions in chemical reaction networks

A wide variety of real life complex networks are prohibitively large for modeling, analysis and control. Understanding the structure and dynamics of such networks entails creating a smaller representative network that preserves its relevant topological and dynamical properties. While modern machine learning methods have enabled identification of governing laws for complex dynamical systems, their inability to produce white-box models with sufficient physical interpretation renders such methods undesirable to domain experts. In this paper, we introduce a hybrid black-box, white-box approach for the sparse identification of the governing laws for complex, highly coupled dynamical systems with particular emphasis on finding the influential reactions in chemical reaction networks for combustion applications, using a data-driven sparse-learning technique. The proposed approach identifies a set of influential reactions using species concentrations and reaction rates, with minimal computational cost without requiring additional data or simulations. The new approach is applied to analyze the combustion chemistry of H2 and C3H8 in a constant-volume homogeneous reactor. The influential reactions determined by the sparse-learning method are consistent with the current kinetics knowledge of chemical mechanisms. Additionally, we show that a reduced version of the parent mechanism can be generated as a combination of the significantly reduced influential reactions identified at different times and conditions and that for both H2 and C3H8 fuel, the reduced mechanisms perform closely to the parent mechanisms as a function of the ignition delay time over a wide range of conditions. Our results demonstrate the potential of the sparse-learning approach as an effective and efficient tool for dynamical system analysis and reduction. The uniqueness of this approach as applied to combustion systems lies in the ability to identify influential reactions in specified conditions and times during the evolution of the combustion process. This ability is of great interest to understand chemical reaction systems.

Online Identification of Aircraft Dynamics in the Presence of Actuator Faults

In this paper, a multiple model-based nonlinear identification approach is introduced for a conventional aircraft in the presence of different types of actuator faults. Occurrence of actuator faults can obviously reduce the validity of a predetermined dynamic model of nonlinear systems. In such cases, use of multi-model structures can be an effective choice. However, determining the optimal validity functions of the local models in a multi-model structure is still a challenging problem. This problem becomes even more challenging in case of unpredictable faults, which are not considered in training the local models. In this paper, two effective techniques are proposed for online determination of the validity functions of local models called the Error-based Gaussian validity functions (E-GVF) and the Online Sequential Extreme Learning Machine (OSELM)-based approach. Accordingly, there is no need to employ a separate Fault Detection and Isolation (FDI) block in the proposed identification approach. Also, due to great capabilities of neural networks for modeling complex nonlinear systems, recurrent neural networks are used as the local models of the proposed multi-model structure. The obtained simulation results indicate the capability of the proposed OSELM-based multi-model structure for nonlinear identification of complex dynamic systems in the presence of both predictable and unpredictable actuator faults.

Efficient online model-based design of experiments via parameter subset selection for batch dynamical systems

Model-based design of experiments (MBDOE) is being widely used for the efficient identification of complex dynamical systems. Given real-time measurements, online MBDOE can be formulated. However, conventional real-time MBDOE requires considerable computational time for finding a solution which makes real-time implementation impossible. Moreover, the optimality of experimental design and the accuracy of parameter estimates are not ensured. We propose a new algorithm that advances online MBDOE by focusing on the subset of parameters at each design instant. It considerably reduces the numerical complexity of the problem while almost completely preserving its optimality and allowing for faster and more accurate calculation. A case study is presented, wherein the proposed algorithm is applied to a fed-batch bioreactor model with 14 parameters.

Adaptable urban water demand prediction system

In this work, identification of 24-hours-ahead water demand prediction model based on historical water demand data is considered. As part of the identification procedure, the input variable selection algorithm based on partial mutual information is implemented. It is shown that meteorological data on a daily basis are not relevant for the water demand prediction in the sense of partial mutual information for the analysed water distribution systems of the cities of Tavira, Algarve, Portugal and Evanton East, Scotland, UK. Water demand prediction system is modelled using artificial neural networks, which offer a great potential for the identification of complex dynamic systems. The adaptive tuning procedure of model parameters is also developed in order to enable the model to adapt to changes in the system. A significant improvement of the prediction ability of such a model in relation to the model with fixed parameters is shown when a certain trend is present in the water demand profile.

A fast method for fuzzy neural network modelling and refinement

In the identification of complex dynamic systems using fuzzy neural networks, one of the main issues is the curse of dimensionality, which makes it difficult to retain a large number of system inputs or to consider a large number of fuzzy sets. Moreover, due to the correlations, not all possible network inputs or regression vectors in the network are necessary and adding them simply increases the model complexity and deteriorates the network generalisation performance. In this paper, the problem is solved by first proposing a fast algorithm for selection of network terms, and then introducing a refinement procedure to tackle the correlation issue. Simulation results show the efficacy of the method.

A New Rule Selection Procedure for Fuzzy-Neural Modelling

In identification of complex dynamic systems using fuzzy neural networks, one of the main issues is the curse-of-dimensionality. In the literature this issue has been addressed by the selection of either the inputs or the rules. Adding unnecessary inputs or rules increases the model complexity and worsens the network generalization performance. Selecting the best set of inputs or rules is a combinational problem and can be computationally expensive. In this paper, the problem is solved by first proposing a refinement procedure for rule selection. The algorithm is then adapted with prior input selection to further improve the model accuracy.

Methodology of effective structural identification of complex dynamic systems

Features of structural identification of models of dynamics of multidimensional objects are considered. The algorithms for determining the transfer functions of the identification object and the filter that generates the dynamic characteristics of the perturbation are proposed, and the method for determining the dynamic properties of a linear stationary dynamic object

Program system SIDYS: Simulation and parameter identification of dynamic systems

We describe a program SIDYS for simulation and parameter identification of complex dynamic systems. SIDYS is characterized by a combination of modeling, data handling, simulation and identification. Either continuous or time discrete processes can be simulated by SIDYS; a choice is offered among Euler, Runge—Kutta—Merson and Gear for the integration of systems of differential equations. Least squares or weighted least squares can be used for parameter evaluation. The nonlinear minimization can be carried out by random search, Rosenbrock, quasi-Newton, or lattice search. An optimal analysis of the residuals allows the quality of the parameter identification to be judged, thereby revealing specification errors in the model programming. The basic flow diagram of SIDYS is described. The use of SIDYS is illustrated by a spectroscopic-kinetic analysis of a reversible photoreaction of dihydroindolizines accompanied by thermal reaction. The evaluation shows that a differential absorbance equation can be used with a noisy experimental data set only if the rate constant of the thermal reaction is taken as known. An analysis of the residuals is provided and the significance of the parameters is discussed.