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

Probabilistic Anomaly Detection in Natural Gas Time Series Data

This paper introduces a probabilistic approach to anomaly detection, specifically in natural gas time series data. In the natural gas field, there are various types of anomalies, each of which is induced by a range of causes and sources. The causes of a set of anomalies are examined and categorized, and a Bayesian maximum likelihood classifier learns the temporal structures of known anomalies. Given previously unseen time series data, the system detects anomalies using a linear regression model with weather inputs, after which the anomalies are tested for false positives and classified using a Bayesian classifier. The method can also identify anomalies of an unknown origin. Thus, the likelihood of a data point being anomalous is given for anomalies of both known and unknown origins. This probabilistic anomaly detection method is tested on a reported natural gas consumption data set

Real-time flutter analysis

The important algorithm issues necessary to achieve a real time flutter monitoring system; namely, the guidelines for choosing appropriate model forms, reduction of the parameter convergence transient, handling multiple modes, the effect of over parameterization, and estimate accuracy predictions, both online and for experiment design are addressed. An approach for efficiently computing continuous-time flutter parameter Cramer-Rao estimate error bounds were developed. This enables a convincing comparison of theoretical and simulation results, as well as offline studies in preparation for a flight test. Theoretical predictions, simulation and flight test results from the NASA Drones for Aerodynamic and Structural Test (DAST) Program are compared

F-8C adaptive flight control extensions

An adaptive concept which combines gain-scheduled control laws with explicit maximum likelihood estimation (MLE) identification to provide the scheduling values is described. The MLE algorithm was improved by incorporating attitude data, estimating gust statistics for setting filter gains, and improving parameter tracking during changing flight conditions. A lateral MLE algorithm was designed to improve true air speed and angle of attack estimates during lateral maneuvers. Relationships between the pitch axis sensors inherent in the MLE design were examined and used for sensor failure detection. Design details and simulation performance are presented for each of the three areas investigated

Modeling XV-15 tilt-rotor aircraft dynamics by frequency and time-domain identification techniques

Models of the open-loop hover dynamics of the XV-15 Tilt-Rotor Aircraft are extracted from flight data using two approaches: frequency domain and time-domain identification. Both approaches are reviewed and the identification results are presented and compared in detail. The extracted models are compared favorably, with the differences associated mostly with the inherent weighing of each technique. Step responses are used to show that the predictive capability of the models from both techniques is excellent. Based on the results of this study, the relative strengths and weaknesses of the frequency and time-domain techniques are summarized and a proposal for a coordinated parameter identification approach is presented

Development of advanced techniques for rotorcraft state estimation and parameter identification

An integrated methodology for rotorcraft system identification consists of rotorcraft mathematical modeling, three distinct data processing steps, and a technique for designing inputs to improve the identifiability of the data. These elements are as follows: (1) a Kalman filter smoother algorithm which estimates states and sensor errors from error corrupted data. Gust time histories and statistics may also be estimated; (2) a model structure estimation algorithm for isolating a model which adequately explains the data; (3) a maximum likelihood algorithm for estimating the parameters and estimates for the variance of these estimates; and (4) an input design algorithm, based on a maximum likelihood approach, which provides inputs to improve the accuracy of parameter estimates. Each step is discussed with examples to both flight and simulated data cases

Aerodynamic parameter identification for an unmanned aerial vehicle

A dissertation submitted to the Faculty of Engineering and the Built Environment, School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, in fulfilment of the requirements for the degree of Master of Science in Engineering. Johannesburg, May 2016The present work describes the practical implementation of systems identification techniques to the development of a linear aerodynamic model for a small low-cost UAV equipped with a basic navigational and inertial measurement systems. The assessment of the applicability of the techniques were based on determining whether adequate aerodynamic models could be developed to aid in the reduction of wind tunnel testing when characterising new UAVs. The identification process consisted of postulating a model structure, flight test manoeuvre design, data reconstruction, aerodynamic parameter estimation, and model validation. The estimators that were used for the post-flight identification were the output error maximum likelihood method and an iterated extended Kalman filter with a global smoother. SIDPAC and FVSysID systems identification toolboxes were utilised and modified where appropriate. The instrumentation system on board the UAV consisted of three-axis accelerometers and gyroscopes, a three-axis vector magnetometer and GPS tracking while data was logged at 25 Hz. The angle of attack and angle of sideslip were not measured directly and were estimated using tailored data reconstruction methods. Adequate time domain lateral model correlation with flight data was achieved for the cruise flight condition. Adequacy was assessed against Theil’s inequality coefficients and Theil’s covariance. It was found that the simplified estimation algorithms based on the linearized equations of motion yielded the most promising model matches. Due to the high correlation between the pitch damping derivatives, the longitudinal analysis did not yield valid model parameter estimates. Even though the accuracy of the resulting models was below initial expectations, the detailed data compatibility analysis provided valuable insight into estimator limitations, instrumentation requirements and test procedures for systems identification on low-cost UAVs.MT201

The ROMES method for statistical modeling of reduced-order-model error

This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive `error indicators' to a distribution over the true error. The variance of this distribution can be interpreted as the (epistemic) uncertainty introduced by the reduced-order model. To model normed errors, the method employs existing rigorous error bounds and residual norms as indicators; numerical experiments show that the method leads to a near-optimal expected effectivity in contrast to typical error bounds. To model errors in general outputs, the method uses dual-weighted residuals---which are amenable to uncertainty control---as indicators. Experiments illustrate that correcting the reduced-order-model output with this surrogate can improve prediction accuracy by an order of magnitude; this contrasts with existing `multifidelity correction' approaches, which often fail for reduced-order models and suffer from the curse of dimensionality. The proposed error surrogates also lead to a notion of `probabilistic rigor', i.e., the surrogate bounds the error with specified probability