Multivariate Statistical Process Control Charts: An Overview

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.quality control, process control, multivariate statistical process control, Hotelling's T-square, CUSUM, EWMA, PCA, PLS

Low Latency Anomaly Detection with Imperfect Models

The problem of anomaly detection deals with detecting abrupt changes/anomalies in the distribution of sequentially observed data in a stochastic system. This problem applies to many applications, such as signal processing, intrusion detection, quality control, medical diagnosis, etc. A low latency anomaly detection algorithm, which is based on the framework of quickest change detection (QCD), aims at minimizing the detection delay of anomalies in the sequentially observed data while ensuring satisfactory detection accuracy. Moreover, in many practical applications, complete knowledge of the post-change distribution model might not be available due to the unexpected nature of the change. Hence, the objective of this dissertation is to study low latency anomaly detection or QCD algorithms for systems with imperfect models such that any type of abnormality in the system can be detected as quickly as possible for reliable and secured system operations. This dissertation includes the theoretical foundations behind these low latency anomaly detection algorithms along with real-world applications. First, QCD algorithms are designed for detecting changes in systems with multiple post-change models under both Bayesian and non-Bayesian settings. Next, a QCD algorithm is studied for real-time detection of false data injection attacks in smart grids with dynamic models. Finally, a QCD algorithm for detecting wind turbine bearing faults is developed by analyzing the statistical behaviors of stator currents generated by the turbines. For all the proposed algorithms, analytical bounds of the system performance metrics are derived using asymptotic analysis and the simulation results show that the proposed algorithms outperform existing algorithms

Adaptive Estimation and Detection Techniques with Applications

Hybrid systems have been identified as one of the main directions in control theory and attracted increasing attention in recent years due to their huge diversity of engineering applications. Multiplemodel (MM) estimation is the state-of-the-art approach to many hybrid estimation problems. Existing MM methods with fixed structure usually perform well for problems that can be handled by a small set of models. However, their performance is limited when the required number of models to achieve a satisfactory accuracy is large due to time evolution of the true mode over a large continuous space. In this research, variable-structure multiple model (VSMM) estimation was investigated, further developed and evaluated. A fundamental solution for on-line adaptation of model sets was developed as well as several VSMM algorithms. These algorithms have been successfully applied to the fields of fault detection and identification as well as target tracking in this thesis. In particular, an integrated framework to detect, identify and estimate failures is developed based on the VSMM. It can handle sequential failures and multiple failures by sensors or actuators. Fault detection and target maneuver detection can be formulated as change-point detection problems in statistics. It is of great importance to have the quickest detection of such mode changes in a hybrid system. Traditional maneuver detectors based on simplistic models are not optimal and are computationally demanding due to the requirement of batch processing. In this presentation, a general sequential testing procedure is proposed for maneuver detection based on advanced sequential tests. It uses a likelihood marginalization technique to cope with the difficulty that the target accelerations are unknown. The approach essentially utilizes a priori information about the accelerations in typical tracking engagements and thus allows improved detection performance. The proposed approach is applicable to change-point detection problems under similar formulation, such as fault detection

Adaptive Estimation and Detection Techniques with Applications

Hybrid systems have been identified as one of the main directions in control theory and attracted increasing attention in recent years due to their huge diversity of engineering applications. Multiplemodel (MM) estimation is the state-of-the-art approach to many hybrid estimation problems. Existing MM methods with fixed structure usually perform well for problems that can be handled by a small set of models. However, their performance is limited when the required number of models to achieve a satisfactory accuracy is large due to time evolution of the true mode over a large continuous space. In this research, variable-structure multiple model (VSMM) estimation was investigated, further developed and evaluated. A fundamental solution for on-line adaptation of model sets was developed as well as several VSMM algorithms. These algorithms have been successfully applied to the fields of fault detection and identification as well as target tracking in this thesis. In particular, an integrated framework to detect, identify and estimate failures is developed based on the VSMM. It can handle sequential failures and multiple failures by sensors or actuators. Fault detection and target maneuver detection can be formulated as change-point detection problems in statistics. It is of great importance to have the quickest detection of such mode changes in a hybrid system. Traditional maneuver detectors based on simplistic models are not optimal and are computationally demanding due to the requirement of batch processing. In this presentation, a general sequential testing procedure is proposed for maneuver detection based on advanced sequential tests. It uses a likelihood marginalization technique to cope with the difficulty that the target accelerations are unknown. The approach essentially utilizes a priori information about the accelerations in typical tracking engagements and thus allows improved detection performance. The proposed approach is applicable to change-point detection problems under similar formulation, such as fault detection

A mathematical framework for new fault detection schemes in nonlinear stochastic continuous-time dynamical systems

n this work, a mathematical unifying framework for designing new fault detection schemes in nonlinear stochastic continuous-time dynamical systems is developed. These schemes are based on a stochastic process, called the residual, which reflects the system behavior and whose changes are to be detected. A quickest detection scheme for the residual is proposed, which is based on the computed likelihood ratios for time-varying statistical changes in the Ornstein–Uhlenbeck process. Several expressions are provided, depending on a priori knowledge of the fault, which can be employed in a proposed CUSUM-type approximated scheme. This general setting gathers different existing fault detection schemes within a unifying framework, and allows for the definition of new ones. A comparative simulation example illustrates the behavior of the proposed schemes

Diagnosis of airspeed measurement faults for unmanned aerial vehicles

Airspeed sensor faults are common causes for incidents with unmanned aerial vehicles with pitot tube clogging or icing being the most common causes. Timely diagnosis of such faults or other artifacts in signals from airspeed sensing systems could potentially prevent crashes. This paper employs parameter adaptive estimators to provide analytical redundancies and a dedicated diagnosis scheme is designed. Robustness is investigated on sets of flight data to estimate distributions of test statistics. The result is robust diagnosis with adequate balance between false alarm rate and fault detectability

Analysis of stochastic technical trading algorithms

We apply the well-known CUSUM, the Girshick-Rubin, the Graversen-Peskir-Shiryaev and an improved alteration of the Brodsky-Darkovsky algorithm as trading strategies involving only mutually exclusive long positions in cash and the DAX at Xetra intraday auction prices. We select optimal pairs of fixed thresholds for up- and downmovements from a pre-defined two-dimensional grid, hence, admitting asymmetric intervals. We show that under three different scenarios for transaction costs, the improved Brodsky-Darkovsky technique not only outperforms the passive investment in the DAX but also the other three presented algorithms