Kernel-based system identification from noisy and incomplete input-output data

In this contribution, we propose a kernel-based method for the identification of linear systems from noisy and incomplete input-output datasets. We model the impulse response of the system as a Gaussian process whose covariance matrix is given by the recently introduced stable spline kernel. We adopt an empirical Bayes approach to estimate the posterior distribution of the impulse response given the data. The noiseless and missing data samples, together with the kernel hyperparameters, are estimated maximizing the joint marginal likelihood of the input and output measurements. To compute the marginal-likelihood maximizer, we build a solution scheme based on the Expectation-Maximization method. Simulations on a benchmark dataset show the effectiveness of the method.Comment: 16 pages, submitted to IEEE Conference on Decision and Control 201

NEW FAST RECURSIVE ALGORITHMS FOR SIMULTANEOUS RECONSTRUCTION AND IDENTIFICATION OF AR PROCESSES WITH MISSING OBSERVATIONS

This paper deals with the problem of adaptive reconstruction and identification of AR processes with randomly missing observations. The performances of a previously proposed real time algorithm are studied. Two new alternatives, based on other predictors, are proposed. They offer an unbiased estimation of the AR parameters. The first algorithm, based on the h-step predictor, is very simple but suffers from a large reconstruction error. The second one, based on the incomplete past predictor, offers an optimal reconstruction error in the least mean square sense

NEW FAST ALGORITHM FOR SIMULTANEOUS IDENTIFICATION AND OPTIMAL RECONSTRUCTION OF NON STATIONARY AR PROCESSES WITH MISSING OBSERVATIONS

International audienceThis paper deals with the problem of adaptive reconstruction and identification of AR processes with randomlymissing observations. A new real time algorithm is proposed. It uses combined pseudo-linear RLS algorithm and Kalman filter. It offers an unbiased estimation of the AR parameters and an optimal reconstruction error in the least mean square sense. In addition, thanks to the pseudo-linear RLS identification, this algorithm can be used for the identification of non stationary AR signals. Moreover, simplifications of the algorithm reduces the calculation time, thus this algorithm can be used in real time applications

Identification and Optimal Linear Tracking Control of ODU Autonomous Surface Vehicle

Autonomous surface vehicles (ASVs) are being used for diverse applications of civilian and military importance such as: military reconnaissance, sea patrol, bathymetry, environmental monitoring, and oceanographic research. Currently, these unmanned tasks can accurately be accomplished by ASVs due to recent advancements in computing, sensing, and actuating systems. For this reason, researchers around the world have been taking interest in ASVs for the last decade. Due to the ever-changing surface of water and stochastic disturbances such as wind and tidal currents that greatly affect the path-following ability of ASVs, identification of an accurate model of inherently nonlinear and stochastic ASV system and then designing a viable control using that model for its planar motion is a challenging task. For planar motion control of ASV, the work done by researchers is mainly based on the theoretical modeling in which the nonlinear hydrodynamic terms are determined, while some work suggested the nonlinear control techniques and adhered to simulation results. Also, the majority of work is related to the mono- or twin-hull ASVs with a single rudder. The ODU-ASV used in present research is a twin-hull design having two DC trolling motors for path-following motion. A novel approach of time-domain open-loop observer Kalman filter identifications (OKID) and state-feedback optimal linear tracking control of ODU-ASV is presented, in which a linear state-space model of ODU-ASV is obtained from the measured input and output data. The accuracy of the identified model for ODU-ASV is confirmed by validation results of model output data reconstruction and benchmark residual analysis. Then, the OKID-identified model of the ODU-ASV is utilized to design the proposed controller for its planar motion such that a predefined cost function is minimized using state and control weighting matrices, which are determined by a multi-objective optimization genetic algorithm technique. The validation results of proposed controller using step inputs as well as sinusoidal and arc-like trajectories are presented to confirm the controller performance. Moreover, real-time water-trials were performed and their results confirm the validity of proposed controller in path-following motion of ODU-ASV

Sooty blotch and flyspeck of apple: assessment of an RFLP-based identification technique and adaptation of a warning system for the Upper Midwest

Sooty blotch and flyspeck (SBFS) of apple, a disease caused by more than 30 species of fungi, reduces crop value by blemishing the fruit surface. This study investigated two research tools designed to improve identification of SBFS fungi and management of the disease.;The first objective was to validate a PCR-based method to identify SBFS pathogens. Members of the sooty blotch and flyspeck (SBFS) disease complex are challenging to identify by traditional mycological methods that rely on agar-plate isolation and morphological description. Identification using a PCR-RFLP assay was investigated as an alternative to culturing. The method involved amplification of the internal transcribed spacer region of ribosomal DNA using a Capnodiales order-specific reverse primer paired with a universal forward primer, followed by digestion using the HaeIII restriction enzyme. When applied to 24 SBFS species from a survey in the Midwest U.S., the PCR-RFLP assay produced 14 unique band patterns, all specific to genus. The technique also identified SBFS fungi from DNA extracted directly from colonies on apples. The PCR-RFLP assay streamlined the identification process by circumventing the requirement for culturing, and should be a valuable tool for further ecological studies of the SBFS disease complex.;The second objective was to adapt a SBFS warning system for the Upper Midwest. The Sutton-Hartman warning system, developed in the Southeast U.S., uses cumulative hours of leaf wetness duration (LWD) to predict the timing of the first appearance of SBFS signs. In the Upper Midwest, however, this warning system experienced sporadic control failures. To determine if other weather variables were useful predictors of SBFS appearance, hourly LWD, rainfall, relative humidity (RH), and temperature data were collected from orchards in IA, WI and NC. Timing of the first appearance of SBFS was determined by scouting weekly for disease signs. Receiver operating characteristic curve analysis revealed that cumulative hours of RH≥97% was a more conservative and accurate predictor than cumulative LWD for the Upper Midwest. The results suggest that the performance of the SBFS warning system in the Upper Midwest could be improved if cumulative hours of RH≥97% were substituted for cumulative hours of LWD to predict the first appearance of SBFS

Control Relevant System Identification Using Orthonormal Basis Filter Models

Models are extensively used in advanced process control system design and implementations. Nearly all optimal control design techniques including the widely used model predictive control techniques rely on the use of model of the system to be controlled. There are several linear model structures that are commonly used in control relevant problems in process industries. Some of these model structures are: Auto Regressive with Exogenous Input (ARX), Auto Regressive Moving Average with Exogenous Input (ARMAX), Finite Impulse Response (FIR), Output Error (OE) and Box Jenkins (BJ) models. The selection of the appropriate model structure, among other factors, depend on the consistency of the model parameters, the number of parameters required to describe a system with acceptable accuracy and the computational load in estimating the model parameters. ARX and ARMAX models suffer from inconsistency problem in most open-loop identification problems. Finite Impulse Response (FIR) models require large number of parameters to describe linear systems with acceptable accuracy. BJ, OE and ARMAX models involve nonlinear optimization in estimating their parameters. In addition, all of the above conventional linear models, except FIR, require the time delay of the system to be separately estimated and included in the estimation of the parameters. Orthonormal Basis Filter (OBF) models have several advantages over the other conventional linear models. They are consistent in parameters for most open-loop identification problems. They are parsimonious in parameters if the dominant pole(s) of the system are used in their development. The model parameters are easily estimated using the linear least square method. Moreover, the time delay estimation can be easily integrated in the model development. However, there are several problems that are not yet addressed. Some of the outstanding problems are: (i) Developing parsimonious OBF models when the dominant poles of the system are not known (ii) Obtaining a better estimate of time delay for second or higher order systems (iii) Including an explicit noise model in the framework of OBF model structures and determine the parameters and multi-step ahead predictions (iv) Closed-loop identification problems in this new OBF plus noise model frame work This study presents novel schemes that address the above problems. The first problem is addressed by formulating an iterative scheme where one or two of the dominant pole(s) of the system are estimated and used to develop parsimonious OBF models. A unified scheme is formulated where an OBF-deterministic model and an explicit AR or ARMA stochastic (noise) models are developed to address the second problem. The closed-loop identification problem is addressed by developing schemes based on the direct and indirect approaches using OBF based structures. For all the proposed OBF prediction model structures, the method for estimating the model parameters and multi-step ahead prediction are developed. All the proposed schemes are demonstrated with the help of simulation and real plant case studies. The accuracy of the developed OBF-based models is verified using appropriate validation procedures and residual analysis

Maximising Oil Production Through Data Modelling, Simulation and Optimisation.

The research work presented on this thesis provides an alternative tool for characterising oil fields under fluid injection by analysing historical production/injection rates. In particular polynomial and radial basis Non Linear Autoregressive with Exogenous Input Model (NARX) models were developed; these models were capable of capturing the dynamics of an operating field in the North Sea. A Greedy Randomised Adaptive Search Procedure (GRASP) heuristic optimisation method was applied for estimating a future injection strategy. This approach is combined with a risk analysis methodology, a popular approach in financial mathematics. As a result, it is possible to estimate how likely it is to reach a production goal. According to the simulations, it is possible to increase oil production by 10% in one year by implementing a smart injection strategy with low statistical uncertainty. Resulting from this research project, a computational tool was developed. It is now possible to estimate NARX models from any field under fluid injection as well as finding the best future injection scenario