Sodium boiling Detection in a LMFBR Using Autoregressive Models and SVM

International audienceThis paper deals with acoustic detection of sodium boiling in a Liquid Metal Fast Breeder Reactor (LMFBR) cooled by liquid sodium. As sodium boiling induces acoustic emission, the method consists in real time analysis of acoustic signals measured through wave guides. AutoRegressive (AR) models are estimated on sliding windows and are classified in boiling or non-boiling models using Support Vector Machines (SVM). One of the difficulties to cope with is disturbances due to the influence of some environment noises like the liquid coolant cavitation, vortex flow, shaft vibration and mechanical pump noise. These disturbances can generate false alarms or mask the boiling. The proposed method is designed to be robust toward these disturbances. Furthermore, the SVM are designed to be robust toward the operating mode changing. The application for online monitoring is made on data obtained from French nuclear power plant Phenix and boiling sound signals generated from Laboratory experiments. Different acoustic boiling sound levels are used and the effectiveness of the method is shown by the good detection rate and its low false alarm rate even for low acoustic boiling sound level

A propos de la consistance d’un estimateur du maximum de vraisemblance utilisé dans la modélisation de données d’accidents

L'ensemble des méthodes statistiques utilisées dans la modélisation de données nécessite la recherche de solutions optimales locales mais aussi l’estimation de la précision (écart-type) liée à ces solutions. Ces méthodes consistent à optimiser, par approximations itératives, la fonction de vraisemblance ou une version approchée. Classiquement, on utilise des versions adaptées de la méthode de Newton-Raphson ou des scores de Fisher. Du fait qu'elles nécessitent des inversions matricielles, ces méthodes peuvent être complexes à mettre en œuvre numériquement en grandes dimensions ou lorsque les matrices impliquées ne sont pas inversibles. Pour contourner ces difficultés, des procédures itératives ne nécessitant pas d’inversion matricielle telles que les algorithmes MM (Minorization-Maximization) ont été proposées et sont considérés comme pertinents pour les problèmes en grandes dimensions et pour certaines distributions discrètes multivariées. Parmi les nouvelles approches proposées dans le cadre de la modélisation en sécurité routière, figure un algorithme nommé algorithme cyclique itératif (CA). Cette thèse a un double objectif. Le premier est d'étudier l'algorithme CA des points de vue algorithmique et stochastique; le second est de généraliser l'algorithme cyclique itératif à des modèles plus complexes intégrant des distributions discrètes multivariées et de comparer la performance de l’algorithme CA généralisé à celle de ses compétiteurs.Most of the statistical methods used in data modeling require the search for local optimal solutions but also the estimation of standard errors linked to these solutions. These methods consist in maximizing by successive approximations the likelihood function or its approximation. Generally, one uses numerical methods adapted from the Newton-Raphson method or Fisher’s scoring. Because they require matrix inversions, these methods can be complex to implement numerically in large dimensions or when involved matrices are not invertible. To overcome these difficulties, iterative procedures requiring no matrix inversion such as MM (Minorization-Maximization) algorithms have been proposed and are considered to be efficient for problems in large dimensions and some multivariate discrete distributions. Among the new approaches proposed for data modeling in road safety, is an algorithm called iterative cyclic algorithm (CA). This thesis has two main objectives: (a) the first is to study the convergence properties of the cyclic algorithm from both numerical and stochastic viewpoints and (b) the second is to generalize the CA to more general models integrating discrete multivariate distributions and compare the performance of the generalized CA to those of its competitors

On the maximum likelihood estimator for a discrete multivariate crash frequencies model

In this paper, we study the maximum likelihood estimator (MLE) of the parameter vector of a discrete multivariate crash frequencies model used in the statistical analysis of the effectiveness of a road safety measure. We derive the closed-form expression of the MLE afterwards we prove its strong consistency and we obtain the exact variance of the components of the MLE except one component whose variance is approximated via the delta method. Dans cet article, nous etudions l’estimateur du maximum de vraisem- ´ blance (EMV) du vecteur de parametres d’un mod ` ele discret  multivari ` e utilis ´ e´ dans l’analyse statistique de l’efficacite d’une mesure de s ´ ecurit ´ e routi ´ ere. Nous ` obtenons l’expression analytique exacte de l’EMV apres quoi nous prouvons sa ` forte consistance et nous obtenons la variance exacte des composantes de l’EMV, sauf pour une composante dont la variance est approximee par la m ´ ethode delta. ´ Key words: Maximum likelihood; parameter estimation; strong consistency; almost sure convergence; variance estimatio

An approximation method for a maximum likelihood equation system and application to the analysis of accidents data

International audienceThere exist many iterative methods for computing the maximum likelihood estimator but most of them suffer from one or several drawbacks such as the need to inverse a Hessian matrix and the need to find good initial approximations of the parameters that are unknown in practice. In this paper, we present an estimation method without matrix inversion based on a linear approximation of the likelihood equations in a neighborhood of the constrained maximum likelihood estimator. We obtain closed-form approximations of solutions and standard errors. Then, we propose an iterative algorithm which cycles through the components of the vector parameter and updates one component at a time. The initial solution, which is necessary to start the iterative procedure, is automated. The proposed algorithm is compared to some of the best iterative optimization algorithms available on R and MATLAB software through a simulation study and applied to the statistical analysis of a road safety measure

Global convergence and ascent property of a cyclic algorithm used for statistical analysis of crash data

In this paper, we consider an estimation algorithm called cyclic iterative algorithm (CA) that is used in statistics to estimate the unknown vector parameter of a crash data model. We provide a theoretical proof of the global convergence of the CA that justifies the good numerical results obtained in early numerical studies of this algorithm. We also prove that the CA is an ascent algorithm, what ensures its numerical stability.Keywords: Iterative method, Maximum likelihood, cyclic algorithm, global convergence, road safetyAMS 2010 Mathematics Subject Classification : 62-04, 62F10, 62H12, 62P9

A Fast and Efficient Estimation of the Parameters of a Model of Accident Frequencies via an MM Algorithm

In this paper, we consider a multivariate statistical model of accident frequencies having a variable number of parameters and whose parameters are dependent and subject to box constraints and linear equality constraints. We design a minorization-maximization (MM) algorithm and an accelerated MM algorithm to compute the maximum likelihood estimates of the parameters. We illustrate, through simulations, the performance of our proposed MM algorithm and its accelerated version by comparing them to Newton-Raphson (NR) and quasi-Newton algorithms. The results suggest that the MM algorithm and its accelerated version are better in terms of convergence proportion and, as the number of parameters increases, they are also better in terms of computation time

Autoregressive model-based boiling detection in a Liquid Metal Fast Breeder Reactor

International audienceThis paper presents a new approach for acoustic detection of sodium boiling in a Liquid Metal Fast Breeder Reactor (LMFBR) based on Autoregressive (AR) models. The AR models are estimated on a sliding window and classified into boiling or non-boiling models by comparing the on-line estimated values of their components to the predictions of their components from the environment parameters using linear regression. In order to avoid false alarms the proposed approach takes into account operating mode information. Promising results are obtained on the background noise data collected from the French Phenix nuclear power plant provided by the French Commission of Atomic and Alternative Energies (CEA). © 2015, IF AC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved

Autoregressive model-based boiling detection in a Liquid Metal Fast Breeder Reactor

International audienceThis paper presents a new approach for acoustic detection of sodium boiling in a Liquid Metal Fast Breeder Reactor (LMFBR) based on Autoregressive (AR) models. The AR models are estimated on a sliding window and classified into boiling or non-boiling models by comparing the on-line estimated values of their components to the predictions of their components from the environment parameters using linear regression. In order to avoid false alarms the proposed approach takes into account operating mode information. Promising results are obtained on the background noise data collected from the French Phenix nuclear power plant provided by the French Commission of Atomic and Alternative Energies (CEA)

Acoustic monitoring of sodium boiling in a Liquid Metal Fast Breeder Reactor from autoregressive models

International audienceThis paper deals with acoustic monitoring of sodium boiling in a Liquid Metal Fast Breeder Reactor (LMFBR) based on Auto Regressive (AR) models which have low computational complexities. Some authors have used AR models for sodium boiling or sodium-water reaction detection. These works are based on the characterization of the difference between fault free condition and current functioning of the system. However, even in absence of faults, it is possible to observe a change in the AR models due to the change of operating mode of the LMFBR. This sets up the delicate problem of how to distinguish a change in operating mode in absence of faults and a change due to presence of faults. In this paper we propose a new approach for boiling detection based on the estimation of AR models on sliding windows. Afterwards, classification of the models into boiling or non-boiling models is made by comparing their coefficients by two statistical methods, multiple linear regression (LR) and Support Vectors Machines (SVM). The proposed approach takes into account operating mode informations in order to avoid false alarms. Experimental data include non-boiling background noise data collected from Phenix power plant (France) and provided by the CEA (Commissariat à l'Energie Atomique et aux énergies alternatives, France) and boiling condition data generated in laboratory. High boiling detection rates as well as low false alarms rates obtained on these experimental data show that the proposed method is efficient for boiling detection. Most importantly, it shows that the boiling phenomenon introduces a disturbance into the AR models that can be clearly detected