{"title": "Support Vector Novelty Detection Applied to Jet Engine Vibration Spectra", "book": "Advances in Neural Information Processing Systems", "page_first": 946, "page_last": 952, "abstract": null, "full_text": "Support Vector Novelty Detection \n\nApplied to Jet Engine Vibration Spectra \n\nPaul Hayton \n\nDepartment of Engineering Science \n\nUniversity of Oxford, UK \n\npmh@robots.ox.ac.uk \n\nBernhard SchOlkopf \nMicrosoft Research \n\n1 Guildhall Street, Cambridge, UK \n\nbsc@scientist.com \n\nLionel Tarassenko \n\nDepartment of Engineering Science \n\nUniversity of Oxford, UK \nlionel@robots.ox.ac.uk \n\nPaul Anuzis \n\nRolls-Royce Civil Aero-Engines \n\nDerby, UK \n\nAbstract \n\nA system has been developed to extract diagnostic information from jet \nengine carcass vibration data. Support Vector Machines applied to nov(cid:173)\nelty detection provide a measure of how unusual the shape of a vibra(cid:173)\ntion signature is, by learning a representation of normality. We describe \na novel method for Support Vector Machines of including information \nfrom a second class for novelty detection and give results from the appli(cid:173)\ncation to Jet Engine vibration analysis. \n\n1 \n\nIntroduction \n\nJet engines have a number of rigorous pass-off tests before they can be delivered to the \ncustomer. The main test is a vibration test over the full range of operating speeds. Vibration \ngauges are attached to the casing of the engine and the speed of each shaft is measured \nusing a tachometer. The engine on the test bed is slowly accelerated from idle to full \nspeed and then gradually decelerated back to idle. As the engine accelerates, the rotation \nfrequency of the two (or three) shafts increases and so does the frequency of the vibrations \ncaused by the shafts. A tracked order is the amplitude of the vibration signal in a narrow \nfrequency band centered on a harmonic of the rotation frequency of a shaft, measured as \na function of engine speed. It tracks the frequency response of the engine to the energy \ninjected by the rotating shaft. Although there are usually some harmonics present, most \nof the energy in the vibration spectrum is concentrated in the fundamental tracked orders. \nThese therefore constitute the \"vibration signature\" of the jet engine under test. It is very \nimportant to detect departures from the normal or expected shapes of these tracked orders \nas this provides very useful diagnostic information (for example, for the identification of \nout-of-balance conditions). \n\nThe detection of such abnormalities is ideally suited to the novelty detection paradigm for \nseveral reasons. Usually, there are far fewer examples of abnormal shapes than normal \nones and often there may only be a single example of a particular type of abnormality in \n\n\fthe available database. More importantly, the engine under test may show up a type of \nabnormality which has never been seen before but which should not be missed. This is \nespecially important in our current work where we are adapting the techniques developed \nfor pass-off tests to in-flight monitoring. \n\nWith novelty detection, we first of all learn a description of normal vibration shapes by \nincluding only examples of normal tracked orders in the training data. Abnormal shapes \nin test engines are subsequently identified by testing for novelty against the description of \nnormality. \n\nIn our previous work [2], we investigated the vibration spectra of a two-shaft jet engine, \nthe Rolls-Royce Pegasus. In the available database, there were vibration spectra recorded \nfrom 52 normal engines (the training data) and from 33 engines with one or more unusual \nvibration feature (the test data). The shape of the tracked orders was encoded as a low(cid:173)\ndimensional vector by calculating a weighted average of the vibration amplitude over six \ndifferent speed ranges (giving an 18-D vector for three tracked orders). With so few engines \navailable, the K -means clustering algorithm (with K = 4) was used to construct a very \nsimple model of normality, following component-wise normalisation of the 18-D vectors. \n\nThe novelty of the vibration signature for a test engine was assessed as the shortest dis(cid:173)\ntance to one of the kernel centres in the clustering model of normality (each distance being \nnormalised by the width associated with that kernel). When cumulative distributions of \nnovelty scores were plotted both for normal (training) engines and test engines, there was \nlittle overlap found between the two distributions [2]. A significant shortcoming of the \nmethod, however, is the inability to rank engines according to novelty, since the shortest \nnormalised distance is evaluated with respect to different cluster centres for different en(cid:173)\ngines. In this paper, we re-visit the problem but for a new engine, the RB211-535. We argue \nthat the SVM paradigm is ideal for novelty detection, as it provides an elegant distribution \nof normality, a direct indication of the patterns on the boundary of normality (the support \nvectors) and, perhaps most importantly, a ranking of \"abnormality\" according to distance \nto the separating hyperplane in feature space. \n\n2 Support Vector Machines for Novelty Detection \n\nSuppose we are given a set of \"normal\" data points X = {Xl, ... , xL}. In most novelty \ndetection problems, this is all we have; however, in the following we shall develop an \nalgorithm that is slightly more general in that it can also take into account some examples \nof abnormality, Z = {Zl' ... ' zt} . Our goal is to construct a real-valued function which, \ngiven a previously unseen test point x, charaterizes the \"X -ness\" of the point x, i.e. which \ntakes large values for points similar to those in X. The algorithm that we shall present \nbelow will return such a function, along with a threshold value, such that a prespecified \nfraction of X will lead to function values above threshold. In this sense we are estimating \na region which captures a certain probability mass. \n\nThe present approach employs two ideas from support vector machines [6] which are cru(cid:173)\ncial for their fine generalization performance even in high-dimensional tasks: maximizing \na margin, and nonlinearly mapping the data into some feature .space F endowed with a dot \nproduct. The latter need not be the case for the input domain X which may be a general set. \nThe connection between the input domain and the feature space is established by a feature \nmap <1> : X -+ F, i.e. a map such that some simple kernel [1,6] \n\nsuch as the Gaussian \n\nk(x,y) = (<1>(x)\u00b7 <1>(y)), \n\nk(x,y) = e-llx-yIl2/c, \n\n(1) \n\n(2) \n\n\fprovides a dot product in the image of