Detection In Dynamic Systems Research Articles

Early warning signals for bifurcations embedded in high dimensions

Recent work has highlighted the utility of methods for early warning signal detection in dynamic systems approaching critical tipping thresholds. Often these tipping points resemble local bifurcations, whose low dimensional dynamics can play out on a manifold embedded in a much higher dimensional state space. In many cases of practical relevance, the form of this embedding is poorly understood or entirely unknown. This paper explores how measurement of the critical phenomena that generically precede such bifurcations can be used to make inferences about some properties of their embeddings, and, conversely, how prior knowledge about the mechanism of bifurcation can robustify predictions of an oncoming tipping event. These modes of analysis are first demonstrated on a simple fluid flow system undergoing a Hopf bifurcation. The same approach is then applied to data associated with the West African monsoon shift, with results corroborated by existing models of the same system. This example highlights the effectiveness of the methodology even when applied to complex climate data, and demonstrates how a well-resolved spatial structure associated with the onset of atmospheric instability can be inferred purely from time series measurements.

Robust probabilistic predictable feature analysis and its application for dynamic process monitoring

Dynamic process monitoring with multivariate statistical methods has been widely researched and applied for anomaly detection in dynamic systems. However, most of them are designed under the assumption that the measurement noise follows a Gaussian distribution, which usually contradicts the actual situations. Alternatively, in this paper, a novel mixture of Gaussian and Student’s t distributions is designed to account for the system noise, and a robust probabilistic predictable feature analysis (RPPFA) algorithm is proposed to capture both the process dynamics and the characteristic of the heavy tail from multivariate temporal data. Moreover, an improved Expectation–Maximization algorithm and a modified Kalman filter method are proposed for parameter optimization. Three monitoring statistics are designed to identify abnormal conditions, which are Hotelling’s T2, squared prediction error and dynamic index. The superiority of RPPFA is demonstrated through two case studies, namely, a simulated three phase flow facility and an industrial medium speed coal mill.

Symbolic Time Series Analysis for Anomaly Detection in Measure-Invariant Ergodic Systems

Abstract This paper presents a novel framework of symbolic time series analysis (STSA) for anomaly detection in dynamical systems. The core concept is built upon a property of measure-preserving transformation (MPT) sequence, acting on a probability space with ergodic measure, that the eigenfunctions of these transformations would be time-invariant. As a result, unlike a standard STSA that is required to generate time-homogeneous Markov chains, the proposed MPT-based STSA is allowed to have time-inhomogeneous Markov chains, where the (possibly time-varying) state transition probability matrices have time-invariant eigenvectors. Such a time-invariance facilitates analysis of the dynamical system by using short-length time series of measurements. This is particularly important in applications, where the underlying dynamics and process anomalies need fast monitoring and control actions in order to mitigate any potential structural damage and/or to avoid catastrophic failures. The MPT-based STSA has been applied for low-delay detection of fatigue damage, which is a common source of failures in mechanical structures and which is known to have uncertain dynamical characteristics. The underlying algorithm has been validated with experimental data generated from a laboratory apparatus that uses ultrasonic sensors to detect fatigue damage in polycrystalline–alloy specimens. The performance of the proposed MPT-based STSA is evaluated by comparison with those of a standard STSA and a hidden Markov model (HMM) on the same experimental data. The results consistently show superior performance of the MPT-based STSA.

Outlier Detection in Dynamic Systems with Multiple Operating Points and Application to Improve Industrial Flare Monitoring

In chemical industries, process operations are usually comprised of several discrete operating regions with distributions that drift over time. These complexities complicate outlier detection in the presence of intrinsic process dynamics. In this article, we consider the problem of detecting univariate outliers in dynamic systems with multiple operating points. A novel method combining the time series Kalman filter (TSKF) with the pruned exact linear time (PELT) approach to detect outliers is proposed. The proposed method outperformed benchmark methods in outlier removal performance using simulated data sets of dynamic systems with mean shifts. The method was also able to maintain the integrity of the original data set after performing outlier removal. In addition, the methodology was tested on industrial flaring data to pre-process the flare data for discriminant analysis. The industrial test case shows that performing outlier removal dramatically improves flare monitoring results through Partial Least Squares Discriminant Analysis (PLS-DA), which further confirms the importance of data cleaning in process data analytics.

Fault detection in dynamic systems using the Kullback–Leibler divergence

This paper proposes detecting incipient fault conditions in complex dynamic systems using the Kullback–Leibler or KL divergence. Subspace identification is used to identify dynamic models and the KL divergence examines changes in probability density functions between a reference set and online data. Gaussian distributed process variables produce a simple form of the KL divergence. Non-Gaussian distributed process variables require the use of a density-ratio estimation to compute the KL divergence. Applications to recorded data from a gearbox and two distillation processes confirm the increased sensitivity of the proposed approach to detect incipient faults compared to the dynamic monitoring approach based on principal component analysis and the statistical local approach.

An improved methodology for outlier detection in dynamic datasets

A time series Kalman filter (TSKF) is proposed that successfully handles outlier detection in dynamic systems, where normal process changes often mask the existence of outliers. The TSKF method combines a time series model fitting procedure with a modified Kalman filter to deal with additive outlier and innovational outlier detection problems in dynamic process dataset. Compared with current outlier detection methods, the new method enjoys the following advantages: (a) no prior knowledge of the process model is needed; (b) it is easy to tune; (c) it can be applied to both univariate and multivariate outlier detection; (d) it is applicable to both on‐line and off‐line operation; (e) it cleans outliers while maintains the integrity of the original dataset. © 2014 American Institute of Chemical Engineers AIChE J, 61: 419–433, 2015

Fault detection in dynamic systems by a Fuzzy/Bayesian network formulation

In this paper the fault detection problem is solved using an alternative methodology based on a fuzzy/Bayesian strategy combining a Bayesian network and the fuzzy set theory. The new important issue in this proposed methodology is to address uncertainties in the input of the Bayesian Network. This contribution is possible since the fuzzy set theory is used as the knowledge representation. To illustrate the technique, the fault detection problem in induction machine stator-winding is considered. Specifically, the faults in the induction machine stator-winding are detected by a state change of stator current. Simulation results are presented to illustrate the advance of the proposed methodology when compared to standard Bayesian network.

Fuzzy/Bayesian change point detection approach to incipient fault detection

This study presents a novel approach for incipient fault detection in dynamical systems which is based on a two-step fuzzy/Bayesian formulation for change point detection in time series. The first step consists of a fuzzy-based clusterisation to transform the initial data, with arbitrary distribution, into a new one that can be approximated with a beta distribution. The second step consists in using the Metropolis–Hastings algorithm to the change point detection in the transformed time series. The incipient fault is detected as long as it characterises a change point in such transformed time series. The problem of incipient fault detection in the RTN DAMADICS is analysed.

A Perturbative Approach to Novelty Detection in Autoregressive Models

We propose a new method to perform novelty detection in dynamical systems governed by linear autoregressive models. The method is based on a perturbative expansion to a statistical test whose leading term is the classical F-test, and whose O(1/n) correction can be approximated as a function of the number of training points and the model order alone. The method can be justified as an approximation to an information theoretic test. We demonstrate on several synthetic examples that the first correction to the F-test can dramatically improve the control over the false positive rate of the system. We also test the approach on some real time series data, demonstrating that the method still retains a good accuracy in detecting novelties.

Online Implementation of Inequality Constraints Monitoring in Dynamical Systems

This paper deals with fault detection in dynamical systems where the state variables evolutions are constrained by inequality constraints. The latter corresponds either to physical limitations or to safety specification. Two classical residual generation approaches are studied, namely, parity space and unknown input observer approaches, and are extended to monitor the inequality constraints. A practical implementation on a real process is performed and permits to validate the relevance of the proposed methods.

Design of an artificial immune system based on Danger Model for fault detection

This paper presents a methodology that enables fault detection in dynamic systems based on recent immune theory. The fault detection is a challenging problem due to increasing complexity of processes and agility necessary to avoid malfunction or accidents. The fault detection central challenge is determining the difference between normal and potential harmful activities at dynamic systems. A promising solution is emerging in the form of Artificial Immune Systems (AIS). The Danger Model (DM) proposes that the immune system reacts not against self or non-self but by threats generated into the organism: the danger signals. DM-based fault detection system proposes a new formulation for a fault detection system. A DM-inspired methodology is applied to a fault detection benchmark provided by DAMADICS to compare its relative performance to others algorithms. The results show that the strategy developed is promising for incipient and abrupt fault detection in dynamic systems.

A wavelet-based multivariable approach for fault detection in dynamic systems

This paper presents a multivariable extension to a recently proposed wavelet-based technique for fault detection. In the original formulation, the Discrete Wavelet Transform is used to carry out dynamic consistency checks between pairs of signals within frequency subbands. For this purpose, moving average models with an integrative term are employed to reproduce the dynamics of the system in each subband under consideration. The present work introduces a new architecture allowing the use of subband models with more general multivariable structures. More specifically, a multivariable ARX (autoregressive with exogenous input) structure is adopted for each subband model. The proposed technique is illustrated in a case study involving a nonlinear simulation model for an aircraft with a sensor fault. The results show that the multivariable approach outperforms the original formulation in terms of residue amplification following the fault onset.

Robust Detection and Estimation in Dynamic Systems and Statistical Signal Processing: Intersections, Parallel Paths and Applications

Algorithms for Robust Fault Detection and Identification (RFDI) in dynamic systems strive to be sensitive to faults in plant components, while being insensitive to plant and noise model uncertainties. In the field of signal detection with applications such as radar and medical images, sensitivity to signals of interest is also an objective, while robustness is concerned with undesirable interferences residing in unknown or partially known subspaces, and uncertainties in the signal and learned interference models. In this review article, we present the similarities and differences in the game theoretic, stochastic, and geometric subspace formulations and solution approaches to robust detection in dynamic systems and in signal processing. We illustrate how innovative formulations are successfully addressing challenging problems by briefly describing results from two examples, one in functional Magnetic Resonance Imaging (fMRI) of the brain, and the other in non-invasive image based classification of stem cells.

Some Optimal CUSUM Rule Extensions in Dynamic Model Parameter Change-point Detection Problems

This paper proposes three extensions of the usual CUSUM rule for change point detection in dynamic systems, in situations where the application of the rule is problematic. The first two ones concern the case of nonlinear state-space systems indirectly observed and the case of uncertain systems. The third one improves the performance of the usual rule when applied to nonstationary systems, by ensuring a constant rate of false alarms. They all rely on kernel-based nonparametric estimation approaches.

Statistical Kernel Estimators for Design of a Fault Detection, Diagnosis, and Prognosis System

This paper presents the concept of a fault detection system covering detection, diagnosis, and prognosis associ- ated with them. To this aim procedures of data analysis and exploration, based on the nonparametric method of kernel es- timators were applied. This method allows the useful characterization of probability distributions without arbitrary as- sumptions regarding their membership to a fixed class. The investigated system was proved to be effective with respect to both abrupt as well as slowly progressing symptoms of arising anomalies. This work has been aimed at the problem of fault detection in dynamical systems as objects of automatic control, although the general formula is universal and can be used for a wide range of tasks, also outside of engineering.

A Wavelet Band-Limiting Filter Approach for Fault Detection in Dynamic Systems

This paper presents a wavelet-based analytical redundancy method for the detection of faults in dynamic systems. In the proposed approach, consistency checks are carried out after band-limiting the signals under consideration to specific frequency ranges. For this purpose, the discrete wavelet transform is used to establish the frequency bands of analysis and a finite impulse response filter is employed to check the dynamic consistency of the data within each band. The filter weights can be adjusted by a simple parametric identification procedure on the basis of data acquired under normal operating conditions. The proposed method is illustrated by using experimental fault data from an analog computer, which was adjusted to emulate the dynamic response of a servomechanism, as well as simulated data representing a sensor fault scenario in the operation of a Boeing 747 aircraft. For comparison, a standard Luenberger observer fault detection scheme is also employed. The results show that the wavelet method compares favorably with the observer-based scheme in terms of sensitivity to the fault effect, false alarms, and nondetected faults.

Fault detection in dynamic systems via decision fusion

Due to the growing demands for system reliability and availability of large amounts of data, efficient fault detection techniques for dynamic systems are desired. In this paper, we consider fault detection in dynamic systems monitored by multiple sensors. Normal and faulty behaviors can be modeled as two hypotheses. Due to communication constraints, it is assumed that sensors can only send binary data to the fusion center. Under the assumption of independent and identically distributed (1ID) observations, we propose a distributed fault detection algorithm, including local detector design and decision fusion rule design, based on state estimation via particle filtering. Illustrative examples are presented to demonstrate the effectiveness of our approach.

Using invariants to determine change detection in dynamical system with chaos

The problem of change detection in dynamical systems originated from ordinary differential equations and real world phenomena is covered. Until now suitable methods for detecting changes for linear systems and nonlinear systems have been elaborated but there are no such method for chaotic systems. In this paper we propose the method of change detection based on the fractal dimension, which is the one of characteristics dynamical system invariants. The application of the method is illustrated with simulations.

SIGEST

Many important practical problems require a control system to be able to automatically, efficiently, and accurately detect changes in dynamical systems that the control system is monitoring. In some instances, public safely is involved. Well-known examples include analysis of seismic data to detect earthquakes, analysis of radar data in aircraft navigation, and monitoring of activities in chemical plants. The SIGEST paper in this issue, “A Nonlinear Filtering Approach to Changepoint Detection Problems: Direct and Differential-Geometric Methods” by M. H. Vellekoop and J. M. C. Clark, from the SIAM Journal on Control and Optimization, significantly advances the state of the art in this area. In particular, it considers the problem of online detection of parameter changes in dynamical systems, when the data are noisy, and when both the time of the change and the size of the change are unknown a priori. The problem of changepoint detection in dynamical systems on the basis of noisy observations has been well studied in cases when only one of these two factors is unknown. It can be solved by the Shiryayev–Wonham equation if the value after the change is known a priori, or by a Kalman filter if the time of the change is known a priori. But when both are unknown, the problem turns out to be much more difficult. Vellekoop and Clark use differential-geometric methods to derive an approximate, suboptimal filter for solving this challenging changepoint detection problem. The method they derive draws upon both of the approaches mentioned above. In their words, their new nonlinear filter can be interpreted as an adaptive version of the Shiryayev–Wonham equation for the detection of a priori known changes, combined with a modified Kalman filer structure to generate estimates of the unknown size of the change. The paper includes excellent mathematics, as well as nicely presented and readily understandable simulation results that compare the performance of the proposed new filters to more exact but computationally expensive approaches. These results indicate that the proposed new filters may be quite useful in practice. We hope that SIAM Review readers enjoy this fascinating glimpse into state-of-the-art research in optimal control.

Symbolic dynamic analysis of complex systems for anomaly detection

This paper presents a novel concept of anomaly detection in complex dynamical systems using tools of Symbolic Dynamics, Finite State Automata, and Pattern Recognition, where time-series data of the observed variables on the fast time-scale are analyzed at slow time-scale epochs for early detection of (possible) anomalies. The concept of anomaly detection in dynamical systems is elucidated based on experimental data that have been generated from an active electronic circuit with a slowly varying dissipation parameter.