A novel leak detection approach in water distribution networks

© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksThis paper proposes a novel leak monitoring framework aims to improve the operation of water distribution network (WDN). To do that, an online statistical hypothesis test based leak detection is proposed. The main advantages of the developed method are first to deal with the higher required computational time for detecting leaks and then, to update the KPCA model according to the dynamic change of the process. Thus, this can be performed to massive and online datasets. Simulation results obtained from simulated WDN data demonstrate the effectiveness of the proposed technique.Peer ReviewedPostprint (author's final draft

Prediction

This chapter first presents a rather personal view of some different aspects of predictability, going in crescendo from simple linear systems to high-dimensional nonlinear systems with stochastic forcing, which exhibit emergent properties such as phase transitions and regime shifts. Then, a detailed correspondence between the phenomenology of earthquakes, financial crashes and epileptic seizures is offered. The presented statistical evidence provides the substance of a general phase diagram for understanding the many facets of the spatio-temporal organization of these systems. A key insight is to organize the evidence and mechanisms in terms of two summarizing measures: (i) amplitude of disorder or heterogeneity in the system and (ii) level of coupling or interaction strength among the system's components. On the basis of the recently identified remarkable correspondence between earthquakes and seizures, we present detailed information on a class of stochastic point processes that has been found to be particularly powerful in describing earthquake phenomenology and which, we think, has a promising future in epileptology. The so-called self-exciting Hawkes point processes capture parsimoniously the idea that events can trigger other events, and their cascades of interactions and mutual influence are essential to understand the behavior of these systems.Comment: 44 pages with 16 figures and 167 references, chapter in "Epilepsy: The Intersection of Neurosciences, Mathematics, and Engineering",Taylor & Francis Group, Ivan Osorio, Mark G. Frei, Hitten Zaveri, Susan Arthurs, eds (2010

Fault Diagnosis Via Univariate Frequency Analysis Monitoring: A Novel Technique Applied to a Simulated Integrated Drive Generator

The purpose of this research was to develop a fault detection and diagnostic method that would be able to detect and isolate seeded faults in data that was generated from a simulated integrated drive generator. The approach to the solution for this problem is summarized below. A novel approach for the detection and diagnoses of an anomaly due the occurrence of a fault within a system has been developed. This innovative technique uses specific characteristics of the frequency spectrum of a univariate signal to monitor system health for abnormal behavior due to previously characterized component failure. A fault detection and diagnostic scheme was developed that used dual heteroassociative kernel regression models. The first of these empirical models estimates selected features from the analytical redundant spectrum characteristic profile of the exciter current using power demand, a stressor, placed on the system as input query. The predicted spectrum features were compared to the actual characteristic features, which resulted in the generation of a residual signal. This signal was then analyzed in order to determine if they were the result of normal system disturbances or a predefined fault. If a fault was detected, the residual signal was passed to the second model, which isolated, and given enough information, identified the specific component of components causing the anomaly. Two case studies are presented to illustrate the capability to detect, isolate, and identify a system anomaly. As demonstrated, the monitoring of the frequency spectrum of a single variable can provide adequate indication of equipment health. With the availability of the appropriate data, as in the first case, it is possible for the development of three-layer detection and diagnostic systems that provides fault detection, isolation, and identification. A three-layer detection and diagnostic system is essential in the development of more advance health monitoring and prognostic systems. Despite some shortcomings in the simulated data made available for this work, this method is believed to be applicable to data that more realistically captures real-world relationships, including sensor noise and faults that grow with time

An Integrated Fuzzy Inference Based Monitoring, Diagnostic, and Prognostic System

To date the majority of the research related to the development and application of monitoring, diagnostic, and prognostic systems has been exclusive in the sense that only one of the three areas is the focus of the work. While previous research progresses each of the respective fields, the end result is a variable grab bag of techniques that address each problem independently. Also, the new field of prognostics is lacking in the sense that few methods have been proposed that produce estimates of the remaining useful life (RUL) of a device or can be realistically applied to real-world systems. This work addresses both problems by developing the nonparametric fuzzy inference system (NFIS) which is adapted for monitoring, diagnosis, and prognosis and then proposing the path classification and estimation (PACE) model that can be used to predict the RUL of a device that does or does not have a well defined failure threshold. To test and evaluate the proposed methods, they were applied to detect, diagnose, and prognose faults and failures in the hydraulic steering system of a deep oil exploration drill. The monitoring system implementing an NFIS predictor and sequential probability ratio test (SPRT) detector produced comparable detection rates to a monitoring system implementing an autoassociative kernel regression (AAKR) predictor and SPRT detector, specifically 80% vs. 85% for the NFIS and AAKR monitor respectively. It was also found that the NFIS monitor produced fewer false alarms. Next, the monitoring system outputs were used to generate symptom patterns for k-nearest neighbor (kNN) and NFIS classifiers that were trained to diagnose different fault classes. The NFIS diagnoser was shown to significantly outperform the kNN diagnoser, with overall accuracies of 96% vs. 89% respectively. Finally, the PACE implementing the NFIS was used to predict the RUL for different failure modes. The errors of the RUL estimates produced by the PACE-NFIS prognosers ranged from 1.2-11.4 hours with 95% confidence intervals (CI) from 0.67-32.02 hours, which are significantly better than the population based prognoser estimates with errors of ~45 hours and 95% CIs of ~162 hours

Particle Filter-Based Fault Diagnosis of Nonlinear Systems Using a Dual Particle Filter Scheme

In this paper, a dual estimation methodology is developed for both time-varying parameters and states of a nonlinear stochastic system based on the Particle Filtering (PF) scheme. Our developed methodology is based on a concurrent implementation of state and parameter estimation filters as opposed to using a single filter for simultaneously estimating the augmented states and parameters. The convergence and stability of our proposed dual estimation strategy are shown formally to be guaranteed under certain conditions. The ability of our developed dual estimation method is testified to handle simultaneously and efficiently the states and time-varying parameters of a nonlinear system in a context of health monitoring which employs a unified approach to fault detection, isolation and identification is a single algorithm. The performance capabilities of our proposed fault diagnosis methodology is demonstrated and evaluated by its application to a gas turbine engine through accomplishing state and parameter estimation under simultaneous and concurrent component fault scenarios. Extensive simulation results are provided to substantiate and justify the superiority of our proposed fault diagnosis methodology when compared with another well-known alternative diagnostic technique that is available in the literature

머신 러닝 기법과 정보 이론을 이용한 데이터 기반 이상 감지 및 진단

학위논문(박사) -- 서울대학교대학원 : 공과대학 화학생물공학부, 2021.8. 문경빈.공정 모니터링 시스템은 효과적이고 안전한 공정 운전을 위한 필수적인 요소이다. 공정 이상은 목표 생성물의 품질에 영향을 주거나 공정의 정상 가동을 방해하여 생산성을 저해할 수 있다. 폭발성 및 인화성 물질을 주로 다루는 화학공정의 경우 공정 이상은 가장 중요한 요소인 공정의 안전을 위협하는 요소로 작용할 수 있다. 한편, 현대의 공정의 범위가 확장되고 자동화와 고도화가 진행됨에 따라 점점 더 신뢰도 높은 모니터링 시스템이 요구되고 있다. 공정 모니터링은 크게 세 단계로 구분될 수 있다. 실시간으로 공정의 이상 여부를 판단하는 공정 이상 감지, 다음으로 감지된 이상의 원인을 파악하는 이상 진단, 마지막으로 공정 이상의 원인을 제거하고 정상 상태로 회복시키는 복원으로 나뉘어진다. 특히 공정 이상 감지와 진단 시스템을 위해 다양한 방법론들이 제안되어왔으며, 그 방법론들은 크게 세 가지로 구분할 수 있다. 물리 이론을 기반으로 한 모델 분석 방법과 특정 분야의 경험 지식을 바탕으로 한 지식 기반 방법론에 비해 범용적인 적용 가능성과 현대 공정의 풍부한 공정 데이터가 제공되는 조건의 충족으로 인해 데이터 기반 방법론이 널리 활용되어지고 있다. 또한, 데이터 기반 공정 모니터링 방법론들은 공정의 규모와 복잡도가 증가함에 따라 그 장점이 더욱 극대화되는 특징을 갖는다. 본 연구에서는 기존의 데이터 기반 공정 모니터링 방법론들의 성능을 개선하기 위한 공정 이상 감지 방법론과 이상 진단 방법론을 제안한다. 전통적인 공정 이상 감지 시스템은 차원 축소방법들을 기반으로 개발되었다. 차원 축소를 기반으로 한 공정 이상 감지 모델은 공정 데이터에 내재되어 있는 특징으로 정의되는 저차원의 잠재 공간을 정의하고, 이를 기준으로 모니터링을 수행한다. 대표적인 방법으로는 전통적인 다변량 공정 모니터링 방법인 주 성분 분석과 머신 러닝 기법인 오토인코더가 있다. 최근 풍부한 학습 데이터와 우수한 성능 덕분에 다양한 머신 러닝 기법을 사용한 이상 감지 시스템이 널리 활용되고 있지만, 앞서 소개한 현대 공정의 다양한 특징으로 인해 더욱 향상된 성능의 모니터링 기법의 개발이 요구되어지고 있다. 이러한 데이터 기반 모니터링 시스템의 성능 향상을 위해서 모델의 구조를 변경하거나 모델의 학습 절차를 변형하는 접근법들이 주로 제안되었다. 하지만, 데이터 기반 방법론들은 궁극적으로 학습 데이터의 품질에 의존적이라는 특성은 여전히 남아있다. 즉, 학습 데이터의 부족한 정보를 보완함으로써 모니터링 시스템의 완성도를 높일 수 있는 방법론이 요구된다. 따라서, 본 연구는 첫 번째 주제로 데이터 증강 기법을 결합한 공정 이상 감지 방법론을 제안한다. 데이터 증강 기법은 여러 집합을 구분하는 분류기 모델링시에 특정 집합의 학습 데이터가 부족한 경우에 주로 활용되었다. 이러한 경우 데이터 증강을 통해 학습 데이터의 균형을 맞춤으로써 모델의 학습 효율을 증진시킬 수 있다. 반면에, 본 연구에서의 데이터 증강은 한 집합 내에서의 불균형을 완화하기 위한 목적으로 사용되었다. 정상 조건의 공정 데이터는 정상과 이상의 경계에 분포하는 데이터가 희박하게 존재하는 특징을 갖는다. 이상 감지 시스템이 정상 상태의 저차원 특징 공간을 학습하고, 이를 통해 정상과 이상을 구분하는 모델이라는 점을 고려하면 경계 영역의 데이터의 증강이 특징 공간 학습에 긍정적으로 작용할 것을 기대해 볼 수 있다. 이와 같은 맥락에서 제안된 방법론은 다음과 같다. 먼저, 기존의 학습 데이터를 이용하여 인공 데이터를 생성하기위한 생성모델인 변분 오토인코더를 학습한다. 생성 모델로 학습한 정상 운전 데이터의 저차원 분포의 경계영역에 해당하는 데이터들을 인공 데이터로 생성하여 학습데이터에 증강시킨다. 이렇게 증강된 학습 데이터를 기반으로 이상 감지 모델을 위한 머신 러닝 기반 차원 축소 방법인 오토인코더를 학습하여 이상 감지 시스템을 구축한다. 증강된 학습 데이터를 사용함으로써 오토인코더의 잠재 공간 학습이 더 효과적으로 수행될 수 있고, 이는 곧 정상과 이상 상태를 구분하는 이상 감지 시스템의 성능 개선으로 이어질 수 있다. 차원 축소 기법은 전통적인 이상 진단 방법으로도 활용되었다. 하지만, 이는 차원 축소시의 정보의 손실로 인해 저조하고 일관성이 부족한 성능을 보였다. 전통적인 방법의 한계점을 개선하기 위해 공정 변수 간의 인과 관계를 직접적으로 분석하는 기법들이 개발되었다. 그 중 하나인 정보 이론 기반의 전달 엔트로피는 특정 모델이나 선형 가정을 기반으로 하지 않기 때문에 비선형 공정의 이상 진단에 대해 일반적으로 우수한 성능을 보인다고 알려져 있다. 하지만, 전달 엔트로피를 이용한 인과관계 분석 방법은 고비용의 밀도 추정을 필요로 한다는 단점으로 인해 소규모 공정에 대해서만 제한적으로 적용되어 왔다. 이러한 한계점을 개선하기 위한 방안으로 그래프 라쏘라는 조정 방법을 전달 엔트로피와 결합한 방법론을 제안하였다. 그래프 라쏘는 비 방향성 그래프 모델에서 성긴 구조를 학습하기 위한 방법론으로 전체 공정 그래프로부터 상관 관계가 높은 부분 그래프를 추출해낼 수 있다. 가장 높은 상관 관계를 갖는 부분 그래프와 독립된 나머지 변수들이 그래프 라쏘의 출력으로 제시되기 때문에, 나머지 변수들에 대한 반복적인 적용을 통해 전체 공정 변수들을 연관성이 높은 몇몇의 부분 그래프로 변환할 수 있다. 연관성이 낮은 관계를 사전에 배제함으로써 인과 관계 분석의 대상을 크게 축소할 수 있다. 즉, 이 단계를 통해 고비용의 전달 엔트로피의 한계점을 완화하고, 그 적용 가능성을 확장할 수 있도록 한다. 두 방법을 결합하여 다음과 같은 이상 진단 방법론을 제안하였다. 먼저, 공정 이상이 발생한 데이터를 대상으로 반복적 그래프 라쏘를 적용하여 전체 공정 변수들을 연관성이 높은 5개의 부분 집합으로 구분한다. 구분된 각각의 부분 집합을 대상으로 전달 엔트로피를 이용한 인과관계 척도를 계산하고, 가장 유력한 원인 변수를 판별해낸다. 즉, 그래프 라쏘를 통해 효과적으로 인과관계 분석의 대상을 축소함으로써 불필요한 전달 엔트로피 계산으로 발생하는 비용을 크게 절감할 수 있다. 따라서, 제안된 방법론은 대규모 산업 공정에 대해서도 전달 엔트로피를 이용한 이상 진단 기법의 적용을 가능하게 했다는 점에서 의의가 있다. 본 연구에서 제안된 방법론의 성능을 검증하기 위하여 산업 규모의 벤치마크 공정 모델인 테네시 이스트만 공정에 이를 적용하고 결과를 분석하였다. 벤치마크 공정 모델은 다수의 단위 공정을 포함하고, 재순환 흐름과 화학 반응을 포함하고 있어 실제 공정과 같은 복잡도를 갖는 공정 모델로서 제안한 방법론들의 성능을 시험해보기에 적합했다. 성능 테스트는 테네시 이스트만 공정 모델에 포함되어 있는 사전에 정의된 28개 종류의 공정 이상에 대하여 수행하였다. 제안한 데이터 증강을 접목한 공정 이상 감지 방법론은 기존 방법론 대비 높은 이상 감지율을 보였다. 일부의 경우 이상 감지 지연측면에서도 개선을 확인할 수 있었다. 또한, 이상 진단을 위해 전달 엔트로피와 그래프 라쏘를 결합한 제안한 방법론은 전체 공정에 전달 엔트로피를 직접 적용한 기존의 방법론 대비 약 20%의 계산 비용만으로도 효과적으로 이상의 원인을 파악해내는 것을 확인할 수 있었다. 또한, 성능 테스트 결과는 일부 공정 이상의 경우 제안한 방법론이 기존의 방법보다 더 정확한 이상 진단 결과를 제시할 수 있음을 보였다.Process monitoring system is an essential component for efficient and safe operation. Process faults can affect the quality of the product or interfere with the normal operation of the process, hindering productivity. In the case of chemical processes dealing with explosive and flammable materials, process fault can act as a threat to the process safety which should be the top priority. Meanwhile, modern processes demand a more advanced monitoring system as the scope of the process expands and the process automation and intensification progress. The framework of the process monitoring system can be classified into three stages. It is divided into process fault detection that determines the existence of process faults in a system in real-time, fault diagnosis that identifies the root cause of the faults, and finally, process recovery that removes the cause of the fault and normalizes the process. In particular, various methodologies for fault detection and diagnosis have been proposed, and they can be categorized into three approaches. Data-driven methodologies are widely utilized due to the general applicability and the conditions under which abundant process data are provided compared to analytical methods based on the detailed first-principle models and knowledge-based methods on the specific domain knowledge. Furthermore, the advantage of the data-driven methods can be prominent as the scale and complexity of the process increase. In this thesis, fault detection and diagnosis methodologies to improve the performance of existing data-driven methods are proposed. Conventional data-driven fault detection systems have been developed based on dimensionality reduction methods. The fault detection models using dimensionality reduction identify the low dimensional latent space defined by features inherent in process data, performing process monitoring based on it. As the representative methods, there are principal component analysis which is the conventional multivariate process monitoring approach, and autoencoder which is one of the machine learning techniques. Although the monitoring systems using various machine learning techniques have been widely utilized thanks to sufficient process data and good performance, a monitoring scheme that improves the performance of up-to-date methods is required due to the aforementioned factors. To improve the performance of such a data-driven monitoring system, approaches that change the structure of the model or learning procedure have been mainly discussed. Meanwhile, the nature that data-driven methods are ultimately dependent on the quality of the training dataset still remains. In other words, a methodology to enhance the completeness of the monitoring system by supplementing the insufficient information in the training dataset is required. Thus, a process fault detection method that combines data augmentation techniques is proposed in the first part of the thesis. Data augmentation has been mostly employed to manage the deficiency of certain classes, between-class imbalance, in a classification problem. In this case, data augmentation can be effectively applied to improve the training performance by balancing the amount of each class. Data augmentation in this study, on the other hand, is applied to alleviate the with-in-class imbalance. The process data in normal operation has characteristics that the data samples in the borderline of normal and abnormal state are relatively sparse. Given that the modeling of the fault detection system corresponds to defining the low-dimensional feature space and monitoring the system in it, it can be expected that the supplement of the samples on the boundary of the normal state would positively affect the training process. In this context, the proposed method is as follows. First, variational autoencoder which is a generative model is constructed to generate the synthetic data using the original training data. The sample vector corresponding to the boundary region of the low-dimensional distribution of the normal state learned by the generative model is generated as the synthetic data and augmented to the original training data. Based on the augmented training data the fault detection system is established using autoencoder, a machine learning algorithm for feature extraction. The feature learning of autoencoder can be performed more effectively by using the augmented training data, which can lead to the improvement of the fault detection system that distinguishes between normal and abnormal states. The dimensionality reduction methods have been also utilized as the fault isolation method known as the contribution charts. However, the approaches showed limited performance and inconsistent analysis results due to the information loss during the dimension reduction process. To resolve the limitations of the conventional method, the approaches that directly figure out the causal relationships between process variables have been developed. As one of them, transfer entropy, an information-theoretic causality measure, is generally known to have good fault isolation performance in the fault isolation of nonlinear processes because it is neither linearity assumption nor model-based method. However, it has been limitedly applied to the small-scale process because of the drawback that the causal analysis using transfer entropy requires costly density estimation. To resolve the limitation, the method that combines graphical lasso which is a regularization method with transfer entropy is proposed. Graphical lasso is a sparse structure learning algorithm of the undirected graph model, which can be used to sort out the most relevant sub-group in the entire graph model. As graphical lasso algorithm presents the output as a highly correlated subgroup with the rest of the variables, the iterative application of graphical lasso can substitute the entire process into several subgroups. This process can greatly reduce the subject of causal analysis by excluding relationships with little relevance in advance. Accordingly, the limitation of demanding cost of transfer entropy can be mitigated and thus the applicability of fault isolation using transfer entropy can be expanded through this process. Combining the two methods, the following fault isolation method is proposed. First of all, the entire process variables are divided into the five most relevant subgroups based on the data when the fault has occurred. The root cause variable can be isolated from the most significant relationship by calculating the causality measure using transfer entropy only within each subgroup. It is possible to significantly reduce the computational cost due to transfer entropy by efficiently decreasing the subject of causal analysis through graphical lasso. Therefore, the proposed method is noteworthy in that it enables the application of fault isolation using transfer entropy for industrial-scale processes. The proposed methodologies in each stage are verified by applying them to the industrial-scale benchmark process model, the Tennessee Eastman process (TEP). The benchmark process model is suitable to test the performance of the proposed methods because it is a process model with similar complexity as a real chemical process involving multiple unit operations, recycle stream, and chemical reactions in it. The performance test is performed with respect to the 28 predefined process faults scenarios in TEP model. Application results of the proposed fault detection method performed better than the case using the conventional approach in terms of the fault detection rate. In some fault cases, the fault detection delay, the time required to first detect a fault since it occurred, also showed improvement. Fault isolation results by the proposed method integrating transfer entropy with graphical lasso showed that it could effectively identify the cause of the process fault with only about 20% of the computational cost compared to the base case that directly applied the transfer entropy to the entire process for fault isolation. In addition, the demonstration results suggested that the proposed method could outperform the base case in terms of accuracy in some particular cases.Chapter 1 Introduction -2 1.1. Research Motivation -2 1.2. Research Objectives 5 1.3. Outline of the Thesis 7 Chapter 2 Backgrounds and Preliminaries 8 2.1. Autoencoder 8 2.2. Variational Autoencoder 3 2.3. Transfer Entropy 7 2.4. Graphical Lasso 11 Chapter 3 Process Fault Detection Using Autoencoder with Data Augmentation via Variational Autoencoder 23 3.1. Introduction 23 3.2. Process Fault Detection Model Integrated with Data Augmentation 28 3.2.1. Info-Variational Autoencoder for Data Augmentation 31 3.2.2. Autoencoder for Process Monitoring 33 3.3. Case study and Discussion 34 3.3.1. Tennessee Eastman Process 35 3.3.2. Implementation of the Proposed Methodology 39 3.3.3. Discussion of the Results 64 Chapter 4 Process Fault Isolation using Transfer Entropy and Graphical Lasso 80 4.1. Introduction 80 4.2. Fault Isolation using Transfer Entropy Integrated with Graphical Lasso 86 4.2.1. Graphical Lasso for Sub-group Modeling 89 4.2.2. Transfer Entropy for Fault Isolation 90 4.3. Case study and Discussion 1 92 4.3.1. Selective Catalytic Reduction Process 92 4.3.2. Implementation of the Proposed Methodology 97 4.3.3. Discussion of the Results 99 4.4. Case study and Discussion 2 102 4.4.1. Tennessee Eastman Process 102 4.4.2. Implementation of the Proposed Methodology 108 4.4.3. Discussion of the Results 109 Chapter 5 Concluding Remarks 130 5.1. Summary of the Contributions 130 5.2. Future Work 133 Bibliography 135박

Segmentation of Fault Networks Determined from Spatial Clustering of Earthquakes

We present a new method of data clustering applied to earthquake catalogs, with the goal of reconstructing the seismically active part of fault networks. We first use an original method to separate clustered events from uncorrelated seismicity using the distribution of volumes of tetrahedra defined by closest neighbor events in the original and randomized seismic catalogs. The spatial disorder of the complex geometry of fault networks is then taken into account by defining faults as probabilistic anisotropic kernels, whose structures are motivated by properties of discontinuous tectonic deformation and previous empirical observations of the geometry of faults and of earthquake clusters at many spatial and temporal scales. Combining this a priori knowledge with information theoretical arguments, we propose the Gaussian mixture approach implemented in an Expectation-Maximization (EM) procedure. A cross-validation scheme is then used and allows the determination of the number of kernels that should be used to provide an optimal data clustering of the catalog. This three-steps approach is applied to a high quality relocated catalog of the seismicity following the 1986 Mount Lewis ($M_l=5.7$) event in California and reveals that events cluster along planar patches of about 2 km$^2$, i.e. comparable to the size of the main event. The finite thickness of those clusters (about 290 m) suggests that events do not occur on well-defined euclidean fault core surfaces, but rather that the damage zone surrounding faults may be seismically active at depth. Finally, we propose a connection between our methodology and multi-scale spatial analysis, based on the derivation of spatial fractal dimension of about 1.8 for the set of hypocenters in the Mnt Lewis area, consistent with recent observations on relocated catalogs

Magnitude-Dependent Omori Law: Empirical Study and Theory

We propose a new physically-based ``multifractal stress activation'' model of earthquake interaction and triggering based on two simple ingredients: (i) a seismic rupture results from activated processes giving an exponential dependence on the local stress; (ii) the stress relaxation has a long memory. The combination of these two effects predicts in a rather general way that seismic decay rates after mainshocks follow the Omori law 1/t^p with exponents p linearly increasing with the magnitude M of the mainshock and the inverse temperature. We carefully test the prediction on the magnitude dependence of p by a detailed analysis of earthquake sequences in the Southern California Earthquake catalog. We find power law relaxations of seismic sequences triggered by mainshocks with exponents p increasing with the mainshock magnitude by approximately 0.1-0.15 for each magnitude unit increase, from p(M=3) \approx 0.6 to p(M=7) \approx 1.1, in good agreement with the prediction of the multifractal model. The results are robust with respect to different time intervals, magnitude ranges and declustering methods. When applied to synthetic catalogs generated by the ETAS (Epidemic-Type Aftershock Sequence) model constituting a strong null hypothesis with built-in magnitude-independent $p$-values, our procedure recovers the correct magnitude-independent p-values. Our analysis thus suggests that a new important fact of seismicity has been unearthed. We discuss alternative interpretations of the data and describe other predictions of the model.Comment: latex 67 pages including 17 figures ep

Seleção de variáveis aplicada ao controle estatístico multivariado de processos em bateladas

A presente tese apresenta proposições para o uso da seleção de variáveis no aprimoramento do controle estatístico de processos multivariados (MSPC) em bateladas, a fim de contribuir com a melhoria da qualidade de processos industriais. Dessa forma, os objetivos desta tese são: (i) identificar as limitações encontradas pelos métodos MSPC no monitoramento de processos industriais; (ii) entender como métodos de seleção de variáveis são integrados para promover a melhoria do monitoramento de processos de elevada dimensionalidade; (iii) discutir sobre métodos para alinhamento e sincronização de bateladas aplicados a processos com diferentes durações; (iv) definir o método de alinhamento e sincronização mais adequado para o tratamento de dados de bateladas, visando aprimorar a construção do modelo de monitoramento na Fase I do controle estatístico de processo; (v) propor a seleção de variáveis, com propósito de classificação, prévia à construção das cartas de controle multivariadas (CCM) baseadas na análise de componentes principais (PCA) para monitorar um processo em bateladas; e (vi) validar o desempenho de detecção de falhas da carta de controle multivariada proposta em comparação às cartas tradicionais e baseadas em PCA. O desempenho do método proposto foi avaliado mediante aplicação em um estudo de caso com dados reais de um processo industrial alimentício. Os resultados obtidos demonstraram que a realização de uma seleção de variáveis prévia à construção das CCM contribuiu para reduzir eficientemente o número de variáveis a serem analisadas e superar as limitações encontradas na detecção de falhas quando bancos de elevada dimensionalidade são monitorados. Conclui-se que, ao possibilitar que CCM, amplamente utilizadas no meio industrial, sejam adequadas para banco de dados reais de elevada dimensionalidade, o método proposto agrega inovação à área de monitoramento de processos em bateladas e contribui para a geração de produtos de elevado padrão de qualidade.This dissertation presents propositions for the use of variable selection in the improvement of multivariate statistical process control (MSPC) of batch processes, in order to contribute to the enhacement of industrial processes’ quality. There are six objectives: (i) identify MSPC limitations in industrial processes monitoring; (ii) understand how methods of variable selection are used to improve high dimensional processes monitoring; (iii) discuss about methods for alignment and synchronization of batches with different durations; (iv) define the most adequate alignment and synchronization method for batch data treatment, aiming to improve Phase I of process monitoring; (v) propose variable selection for classification prior to establishing multivariate control charts (MCC) based on principal component analysis (PCA) to monitor a batch process; and (vi) validate fault detection performance of the proposed MCC in comparison with traditional PCA-based and charts. The performance of the proposed method was evaluated in a case study using real data from an industrial food process. Results showed that performing variable selection prior to establishing MCC contributed to efficiently reduce the number of variables and overcome limitations found in fault detection when high dimensional datasets are monitored. We conclude that by improving control charts widely used in industry to accomodate high dimensional datasets the proposed method adds innovation to the area of batch process monitoring and contributes to the generation of high quality standard products

Methods and Systems for Fault Diagnosis in Nuclear Power Plants

This research mainly deals with fault diagnosis in nuclear power plants (NPP), based on a framework that integrates contributions from fault scope identification, optimal sensor placement, sensor validation, equipment condition monitoring, and diagnostic reasoning based on pattern analysis. The research has a particular focus on applications where data collected from the existing SCADA (supervisory, control, and data acquisition) system is not sufficient for the fault diagnosis system. Specifically, the following methods and systems are developed. A sensor placement model is developed to guide optimal placement of sensors in NPPs. The model includes 1) a method to extract a quantitative fault-sensor incidence matrix for a system; 2) a fault diagnosability criterion based on the degree of singularities of the incidence matrix; and 3) procedures to place additional sensors to meet the diagnosability criterion. Usefulness of the proposed method is demonstrated on a nuclear power plant process control test facility (NPCTF). Experimental results show that three pairs of undiagnosable faults can be effectively distinguished with three additional sensors selected by the proposed model. A wireless sensor network (WSN) is designed and a prototype is implemented on the NPCTF. WSN is an effective tool to collect data for fault diagnosis, especially for systems where additional measurements are needed. The WSN has distributed data processing and information fusion for fault diagnosis. Experimental results on the NPCTF show that the WSN system can be used to diagnose all six fault scenarios considered for the system. A fault diagnosis method based on semi-supervised pattern classification is developed which requires significantly fewer training data than is typically required in existing fault diagnosis models. It is a promising tool for applications in NPPs, where it is usually difficult to obtain training data under fault conditions for a conventional fault diagnosis model. The proposed method has successfully diagnosed nine types of faults physically simulated on the NPCTF. For equipment condition monitoring, a modified S-transform (MST) algorithm is developed by using shaping functions, particularly sigmoid functions, to modify the window width of the existing standard S-transform. The MST can achieve superior time-frequency resolution for applications that involves non-stationary multi-modal signals, where classical methods may fail. Effectiveness of the proposed algorithm is demonstrated using a vibration test system as well as applications to detect a collapsed pipe support in the NPCTF. The experimental results show that by observing changes in time-frequency characteristics of vibration signals, one can effectively detect faults occurred in components of an industrial system. To ensure that a fault diagnosis system does not suffer from erroneous data, a fault detection and isolation (FDI) method based on kernel principal component analysis (KPCA) is extended for sensor validations, where sensor faults are detected and isolated from the reconstruction errors of a KPCA model. The method is validated using measurement data from a physical NPP. The NPCTF is designed and constructed in this research for experimental validations of fault diagnosis methods and systems. Faults can be physically simulated on the NPCTF. In addition, the NPCTF is designed to support systems based on different instrumentation and control technologies such as WSN and distributed control systems. The NPCTF has been successfully utilized to validate the algorithms and WSN system developed in this research. In a real world application, it is seldom the case that one single fault diagnostic scheme can meet all the requirements of a fault diagnostic system in a nuclear power. In fact, the values and performance of the diagnosis system can potentially be enhanced if some of the methods developed in this thesis can be integrated into a suite of diagnostic tools. In such an integrated system, WSN nodes can be used to collect additional data deemed necessary by sensor placement models. These data can be integrated with those from existing SCADA systems for more comprehensive fault diagnosis. An online performance monitoring system monitors the conditions of the equipment and provides key information for the tasks of condition-based maintenance. When a fault is detected, the measured data are subsequently acquired and analyzed by pattern classification models to identify the nature of the fault. By analyzing the symptoms of the fault, root causes of the fault can eventually be identified