Determining the propagation path of a disturbance in multi-rate systems

© 2015, IF AC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.Several methods to derive the propagation path of a disturbance in process plants are applicable only to systems whose measurements are all available with the same sampling rate. This paper proposes a multi-rate method to identify the propagation path when measurements have different sampling rates. This is relevant for including in the analysis fast-sampled measurements from electromechanical equipment. The method is based on non-linear mutual prediction, which yields the directionality in the relationship between two time series. The method was demonstrated and validated, giving the expected outcome in an experimental case study, in which the root cause and propagation path of the disturbance were known

Adapting nearest neighbors-based monitoring methods to irregularly sampled measurements

Prognostics and Health Management Society. All rights reserved.Irregularly spaced measurements are a common quality problem in real data and preclude the use of several feature extraction methods, which were developed for measurements with constant sampling intervals. Feature extraction methods based on nearest neighbors of embedded vectors are an example of such methods. This paper proposes the use of a timebased construction of embedded vectors and a weighted similarity metric within nearest neighbor-based methods in order to extend their applicability to irregularly sampled measurements. The proposed idea is demonstrated within a method of univariate detection of transient or spiky disturbances. The result obtained with an irregularly sampled measurement is benchmarked by the original regularly sampled measurement. Although the method was originally implemented for off-line analysis, the paper also discusses modifications to enable its on-line implementation

Non-stationary discrete convolution kernel for multimodal process monitoring

Data-driven process monitoring has benefited from the development and application of kernel transformations, especially when various types of nonlinearity exist in the data. However, when dealing with the multimodality behavior which is frequently observed in process operations, the most widely used Radial Basis Function kernel has limitations in describing process data collected from multiple normal operating modes. In this paper, we highlight this limitation via a synthesized example. In order to account for the multimodality behavior and improve fault detection performance accordingly, we propose a novel Non-stationary Discrete Convolution kernel, which derives from the convolution kernel structure, as an alternative to the RBF kernel. By assuming the training samples to be the support of the discrete convolution, this new kernel can properly address these training samples from different operating modes with diverse properties, and therefore can improve the data description and fault detection performance. Its performance is compared with RBF kernels under a standard kernel PCA framework and with other methods proposed for multimode process monitoring via numerical examples. Moreover, a benchmark data set collected from a pilot-scale multiphase flow facility is used to demonstrate the advantages of the new kernel when applied to an experimental data set

Anomaly detection and mode identification in multimode processes using the field Kalman filter

A process plant can have multiple modes of operation due to varying demand, availability of resources or the fundamental design of a process. Each of these modes is considered as normal operation. Anomalies in the process are characterised as deviations away from normal operation. Such anomalies can be indicative of developing faults which, if left unresolved, can lead to failures and unplanned downtime. The Field Kalman Filter (FKF) is a model-based approach, which is adopted in this paper for monitoring a multimode process. Previously, the FKF has been applied in process monitoring to differentiate normal operation from known faulty modes of operation. This paper extends the FKF so that it may detect occurrences of anomalies and differentiate them from the various normal modes of operation. A method is proposed for offline training an FKF monitoring model and on-line monitoring. The off-line part comprises training an FKF model based on Multivariate Autoregressive State-Space (MARSS) models fitted to historical process data. A monitoring indicator is also introduced. On-line monitoring, on the basis of the FKF for anomaly detection and mode identification, is demonstrated using a simulated multimode process. The performance of the proposed method is also demonstrated using data obtained from a pilot scale multiphase flow facility. The results show that the method can be applied successfully for anomaly detection and mode identification

Fault detection and identification combining process measurements and statistical alarms

Classification-based methods for fault detection and identification can be difficult to implement in industrial systems where process measurements are subject to noise and to variability from one fault occurrence to another. This paper uses statistical alarms generated from process measurements to improve the robustness of the fault detection and identification on an industrial process. Two levels of alarms are defined according to the position of the alarm threshold: level-1 alarms (low severity threshold) and level-2 alarms (high severity threshold). Relevant variables are selected using the minimal-Redundancy-Maximal-Relevance criterion of level-2 alarms to only retain variables with large variations relative to the level of noise. The classification-based fault detection and identification fuses the results of a discrete Bayesian classifier on level-1 alarms and of a continuous Bayesian classifier on process measurements. The discrete classifier offers a practical way to deal with noise during the development of the fault, and the continuous classifier ensures a correct classification during later stages of the fault. The method is demonstrated on a multiphase flow facility

Search for Gravitational Waves from Primordial Black Hole Binary Coalescences in the Galactic Halo

We use data from the second science run of the LIGO gravitational-wave detectors to search for the gravitational waves from primordial black hole (PBH) binary coalescence with component masses in the range 0.2--$1.0 M_\odot$. The analysis requires a signal to be found in the data from both LIGO observatories, according to a set of coincidence criteria. No inspiral signals were found. Assuming a spherical halo with core radius 5 kpc extending to 50 kpc containing non-spinning black holes with masses in the range 0.2--$1.0 M_\odot$, we place an observational upper limit on the rate of PBH coalescence of 63 per year per Milky Way halo (MWH) with 90% confidence.Comment: 7 pages, 4 figures, to be submitted to Phys. Rev.

Self-force: Computational Strategies

Building on substantial foundational progress in understanding the effect of a small body's self-field on its own motion, the past 15 years has seen the emergence of several strategies for explicitly computing self-field corrections to the equations of motion of a small, point-like charge. These approaches broadly fall into three categories: (i) mode-sum regularization, (ii) effective source approaches and (iii) worldline convolution methods. This paper reviews the various approaches and gives details of how each one is implemented in practice, highlighting some of the key features in each case.Comment: Synchronized with final published version. Review to appear in "Equations of Motion in Relativistic Gravity", published as part of the Springer "Fundamental Theories of Physics" series. D. Puetzfeld et al. (eds.), Equations of Motion in Relativistic Gravity, Fundamental Theories of Physics 179, Springer, 201

Monitoring statistics and tuning of kernel principal component analysis with radial basis function kernels

Kernel Principal Component Analysis (KPCA) using Radial Basis Function (RBF) kernels can capture data nonlinearity by projecting the original variable space to a high-dimensional kernel feature space and obtaining the kernel principal components. This article examines the tuning of the kernel width when using RBF kernels in KPCA, showing that inappropriate kernel widths result in RBF-KPCA being unable to capture nonlinearity present in data. The paper also considers the choice of monitoring statistics when RBF-KPCA is applied to anomaly detection. Linear PCA requires two monitoring statistics. The Hotelling’s T2 monitoring statistic detects when a sample exceeds the healthy operating range, while the Squared Prediction Error (SPE) monitoring statistic detects the case when the sample does not follow the model of the training data. The analysis in this article shows that SPE for RBF-KPCA can detect both cases. Moreover, unlike the case of linear PCA, the T2 monitoring statistic for RBF-KPCA is non-monotonic with respect to the magnitude of the anomaly, making it not optimal as a monitoring statistic. The paper presents examples to illustrate these points. The paper also provides a detailed mathematical analysis which explains the observations from a theoretical perspective. Tuning strategies are proposed for setting the kernel width and the detection threshold of the monitoring statistic. The performance of optimally tuned RBF-KPCA for anomaly detection is demonstrated via numerical simulation and a benchmark dataset from an industrial-scale facility