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

Hybrid System Identification of Manual Tracking Submovements in Parkinson\u27s Disease

Seemingly smooth motions in manual tracking, (e.g., following a moving target with a joystick input) are actually sequences of submovements: short, open-loop motions that have been previously learned. In Parkinson\u27s disease, a neurodegenerative movement disorder, characterizations of motor performance can yield insight into underlying neurological mechanisms and therefore into potential treatment strategies. We focus on characterizing submovements through Hybrid System Identification, in which the dynamics of each submovement, the mode sequence and timing, and switching mechanisms are all unknown. We describe an initialization that provides a mode sequence and estimate of the dynamics of submovements, then apply hybrid optimization techniques based on embedding to solve a constrained nonlinear program. We also use the existing geometric approach for hybrid system identification to analyze our model and explain the deficits and advantages of each. These methods are applied to data gathered from subjects with Parkinson\u27s disease (on and off L-dopa medication) and from age-matched control subjects, and the results compared across groups demonstrating robust differences. Lastly, we develop a scheme to estimate the switching mechanism of the modeled hybrid system by using the principle of maximum margin separating hyperplane, which is a convex optimization problem, over the affine parameters describing the switching surface and provide a means o characterizing when too many or too few parameters are hypothesized to lie in the switching surface

Model predictive control techniques for hybrid systems

This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.Ministerio de Eduación y Ciencia DPI2007-66718-C04-01Ministerio de Eduación y Ciencia DPI2008-0581

Realization of multi-input/multi-output switched linear systems from Markov parameters

This paper presents a four-stage algorithm for the realization of multi-input/multi-output (MIMO) switched linear systems (SLSs) from Markov parameters. In the first stage, a linear time-varying (LTV) realization that is topologically equivalent to the true SLS is derived from the Markov parameters assuming that the submodels have a common MacMillan degree and a mild condition on their dwell times holds. In the second stage, zero sets of LTV Hankel matrices where the realized system has a linear time-invariant (LTI) pulse response matching that of the original SLS are exploited to extract the submodels, up to arbitrary similarity transformations, by a clustering algorithm using a statistics that is invariant to similarity transformations. Recovery is shown to be complete if the dwell times are sufficiently long and some mild identifiability conditions are met. In the third stage, the switching sequence is estimated by three schemes. The first scheme is based on forward/backward corrections and works on the short segments. The second scheme matches Markov parameter estimates to the true parameters for LTV systems and works on the medium-to-long segments. The third scheme also matches Markov parameters, but for LTI systems only and works on the very short segments. In the fourth stage, the submodels estimated in Stage~2 are brought to a common basis by applying a novel basis transformation method which is necessary before performing output predictions to given inputs. A numerical example illustrates the properties of the realization algorithm. A key role in this algorithm is played by time-dependent switching sequences that partition the state-space according to time, unlike many other works in the literature in which partitioning is state and/or input dependent

Structural Health Monitoring and Application of Wireless Sensor Networks

Different elements of structural health monitoring (SHM) can benefit from the application of wireless sensor Networks (WSNs), as advanced sensing systems. While WSNs can significantly enhance the SHM by facilitating deployment of scalable and dense monitoring systems, challenges in the power consumption and data communication, and concerns regarding the possible impacts of their associated quality on the results have restricted their broad application. This research contributes in addressing the limitation associated with the prohibitive data communication delay and power consumption by introducing a novel time- and energy-efficient distributed algorithm for modal identification, and also addressing the concerns regarding the possible effects of their sensing quality by development of quality assessment approaches for modal identification and damage detection practices. The onboard processing techniques attempt to reduce the communication and power consumption by pushing the computation into the network. Efforts in developing onboard processing algorithms are restricted by the topology and algorithms, and their efficiency is not high enough to alleviate the challenge. A novel approach for modal identification of structural systems in a distributed scheme is developed which assigns the entire computational task of modal identification to remote nodes and limits the communication to transmission of only system\u27s parameters. The algorithm is based on estimation-updating steps at remote nodes and iterations by passing the results through the network for convergence of estimation. The algorithm is first developed for input-output scenarios and then is further expanded to address output-only systems as well. Development of approaches such as Cumulative System Formation for providing initial estimates of the system (as starting point of iteration) and also a novel AR-ARX approach for expediting the convergence also further enhanced the developed algorithm. Experiments and implementations have proved the functionality and performance of the algorithm. While the focus of the research is on development of algorithms for enhancing the application of wireless sensors in modal identification, other aspects of data-driven SHM such as damage detection, and performance evaluation through field-testing of real-life structures are also studied. A framework for damage detection algorithm including accuracy indicators and statistical approaches for change point detection is developed and validated through implementation on different experimental models. Moreover, the state of the art in structural monitoring and vibration evaluation is presented in two field deployments

Piecewise smooth system identification in reproducing kernel Hilbert space

International audienceThe paper extends the recent approach of Ohlsson and Ljung for piecewise affine system identification to the nonlinear case while taking a clustering point of view. In this approach, the problem is cast as the minimization of a convex cost function implementing a trade-off between the fit to the data and a sparsity prior on the number of pieces. Here, we consider the nonlinear case of piecewise smooth system identification without prior knowledge on the type of nonlinearities involved. This is tackled by simultaneously learning a collection of local models from a reproducing kernel Hilbert space via the minimization of a convex functional, for which we prove a representer theorem that provides the explicit form of the solution. An example of application to piecewise smooth system identification shows that both the mode and the nonlinear local models can be accurately estimated

Diabetes Mellitus Glucose Prediction by Linear and Bayesian Ensemble Modeling

Diabetes Mellitus is a chronic disease of impaired blood glucose control due to degraded or absent bodily-specific insulin production, or utilization. To the affected, this in many cases implies relying on insulin injections and blood glucose measurements, in order to keep the blood glucose level within acceptable limits. Risks of developing short- and long-term complications, due to both too high and too low blood glucose concentrations are severalfold, and, generally, the glucose dynamics are not easy too fully comprehend for the affected individual—resulting in poor glucose control. To reduce the burden this implies to the patient and society, in terms of physiological and monetary costs, different technical solutions, based on closed or semi-closed loop blood glucose control, have been suggested. To this end, this thesis investigates simplified linear and merged models of glucose dynamics for the purpose of short-term prediction, developed within the EU FP7 DIAdvisor project. These models could, e.g., be used, in a decision support system, to alert the user of future low and high glucose levels, and, when implemented in a control framework, to suggest proactive actions. The simplified models were evaluated on 47 patient data records from the first DIAdvisor trial. Qualitatively physiological correct responses were imposed, and model-based prediction, up to two hours ahead, and specifically for low blood glucose detection, was evaluated. The glucose raising, and lowering effect of meals and insulin were estimated, together with the clinically relevant carbohydrate-to-insulin ratio. The model was further expanded to include the blood-to-interstitial lag, and tested for one patient data set. Finally, a novel algorithm for merging of multiple prediction models was developed and validated on both artificial data and 12 datasets from the second DIAdvisor trial

Fault Detection, Diagnosis and Fault Tolerance Approaches in Dynamic Systems based on Black-Box Models

In this dissertation new contributions to the research area of fault detection and diagnosis in dynamic systems are presented. The main research effort has been done on the development of new on-line model-based fault detection and diagnosis (FDD) approaches based on blackbox models (linear ARX models, and neural nonlinear ARX models). From a theoretical point of view a white-box model is more desirable to perform the FDD tasks, but in most cases it is very hard, or even impossible, to obtain. When the systems are complex, or difficult to model, modelling based on black-box models is usually a good and often the only alternative. The performance of the system identification methods plays a crucial role in the FDD methods proposed. Great research efforts have been made on the development of linear and nonlinear FDD approaches to detect and diagnose multiplicative (parametric) faults, since most of the past research work has been done focused on additive faults on sensors and actuators. The main pre-requisites for the FDD methods developed are: a) the on-line application in a real-time environment for systems under closed-loop control; b) the algorithms must be implemented in discrete time, and the plants are systems in continuous time; c) a two or three dimensional space for visualization and interpretation of the fault symptoms. An engineering and pragmatic view of FDD approaches has been followed, and some new theoretical contributions are presented in this dissertation. The fault tolerance problem and the fault tolerant control (FTC) have been investigated, and some ideas of the new FDD approaches have been incorporated in the FTC context. One of the main ideas underlying the research done in this work is to detect and diagnose faults occurring in continuous time systems via the analysis of the effect on the parameters of the discrete time black-box ARX models or associated features. In the FDD methods proposed, models for nominal operation and models for each faulty situation are constructed in off-line operation, and used a posteriori in on-line operation. The state of the art and some background concepts used for the research come from many scientific areas. The main concepts related to data mining, multivariate statistics (principal component analysis, PCA), linear and nonlinear dynamic systems, black-box models, system identification, fault detection and diagnosis (FDD), pattern recognition and discriminant analysis, and fault tolerant control (FTC), are briefly described. A sliding window version of the principal components regression algorithm, termed SW-PCR, is proposed for parameter estimation. The sliding window parameter estimation algorithms are most appropriate for fault detection and diagnosis than the recursive algorithms. For linear SISO systems, a new fault detection and diagnosis approach based on dynamic features (static gain and bandwidth) of ARX models is proposed, using a pattern classification approach based on neural nonlinear discriminant analysis (NNLDA). A new approach for fault detection (FDE) is proposed based on the application of the PCA method to the parameter space of ARX models; this allows a dimensional reduction, and the definition of thresholds based on multivariate statistics. This FDE method has been combined with a fault diagnosis (FDG) method based on an influence matrix (IMX). This combined FDD method (PCA & IMX) is suitable to deal with SISO or MIMO linear systems. Most of the research on the fault detection and diagnosis area has been done for linear systems. Few investigations exist in the FDD approaches for nonlinear systems. In this work, two new nonlinear approaches to FDD are proposed that are appropriate to SISO or MISO systems. A new architecture for a neural recurrent output predictor (NROP) is proposed, incorporating an embedded neural parallel model, an external feedback and an adjustable gain (design parameter). A new fault detection and diagnosis (FDD) approach for nonlinear systems is proposed based on a bank of neural recurrent output predictors (NROPs). Each neural NROP predictor is tuned to a specific fault. Also, a new FDD method based on the application of neural nonlinear PCA to ARX model parameters is proposed, combined with a pattern classification approach based on neural nonlinear discriminant analysis. In order to evaluate the performance of the proposed FDD methodologies, many experiments have been done using simulation models and a real setup. All the algorithms have been developed in discrete time, except the process models. The process models considered for the validation and tests of the FDD approaches are: a) a first order linear SISO system; b) a second order SISO model of a DC motor; c) a MIMO system model, the three-tank benchmark. A real nonlinear DC motor setup has also been used. A fault tolerant control (FTC) approach has been proposed to solve the typical reconfiguration problem formulated for the three-tank benchmark. This FTC approach incorporates the FDD method based on a bank of NROP predictors, and on an adaptive optimal linear quadratic Gaussian controller