Free-Decay Nonlinear System Identification via Mass-Change Scheme

Methods for nonlinear system identification of structures generally require input-output measured data to estimate the nonlinear model, as a consequence of the noninvariance of the FRFs in nonlinear systems. However, providing a continuous forcing input to the structure may be difficult or impracticable in some situations, while it may be much easier to only measure the output. This paper deals with the identification of nonlinear mechanical vibrations using output-only free-decay data. The presented method is based on the nonlinear subspace identification (NSI) technique combined with a mass-change scheme, in order to extract both the nonlinear state-space model and the underlying linear system. The technique is tested first on a numerical nonlinear system and subsequently on experimental measurements of a multi-degree-of-freedom system comprising a localized nonlinearity

External condition removal in bearing diagnostics through EMD and One-Class SVM

The removal of the running conditions influencing data acquisitions in rotating machinery is a very important task because it could avoid some misunderstandings when diagnostic techniques are applied. This paper introduces a new parameter that could be able to identify damage in a rotating element of a roller bearing removing the effect of speed and external load. The parameter proposed in this paper is evaluated through Empirical Mode Decomposition (EMD). Our algorithm proposes firstly the decomposition of the acceleration vibration signals into a finite number of Intrinsic Mode Functions (IMFs) and then the evaluation of the energy for each one of these. Data are acquired both for a healthy bearing and for one with a 450 μm large indentation on a rolling element. Three different speeds and three radial loads are monitored for both cases, so nine conditions can be evaluated for each type of bearing overall. The parameters obtained, namely energy evaluated for a certain number of IMFs, are then used to train a One-Class Support Vector Machine (OCSVM). Healthy data belonging to the nine different conditions are taken into account and OCSVM is trained while other acquisitions are given to the classifier as test object. Since the real class membership is known, we consider how many errors the labelling produces. We compare these results with those obtained by considering a wavelet decomposition. Energies are evaluated for each level of decomposition and the previous approach is then applied to these parameter

Nonlinear dynamics of a negative stiffness oscillator: experimental identification and model updating

Systems exhibiting a negative stiffness region are often used as vibration isolators, due to their enhanced damping properties. The device tested in this paper is part of a damping system and it acts like an asymmetric double-well Duffing oscillator, with two stable and one unstable equilibrium positions. The range of motion can either be bounded around one stable position (in-well oscillations) or include all the three positions (cross-well oscillations). Depending on the input amplitude, the oscillator can exhibit linear and nonlinear dynamics, and chaotic motion as well. Due to its asymmetrical design, the two linearized systems associated to small-amplitude oscillations around one stable equilibrium position are different. In this work, the dynamical behavior of the system is first investigated in the case of linear and nonlinear in-well oscillations and then in the case of cross-well oscillations with chaotic motion. To accomplish this task, the device is mounted on a shaking table and it is driven through several excitation levels with both harmonic and random inputs. An experimental bifurcation tracking analysis is also carried out to understand the possible response scenarios. Afterwards, the nonlinear identification is performed using nonlinear subspace algorithms to extract the restoring force of the system. Eventually, the physically-based model of the device is updated to match the identified characteristics via genetic algorithms

New Separation Techniques for Output-Only Modal Analysis

The paper is devoted to the problem of discriminating between operational and natural modes of structures excited by generic inputs. This case often occurs when the system under analysis holds rotating parts and is contemporary excited by ambient noise; in this case the output-only techniques may fail being easily trapped in a misinterpretation of the system eigenvalues. A survey of the methods available in literature is given, together with the explanation of their failures. To solve this problem, two new techniques are introduced and their capabilities are checked with numerical and experimental data from a paper machine

Big Data management: A Vibration Monitoring point of view

Vibration Monitoring is a particular kind of Condition Monitoring meant to infer the state of health of a machine from accelerometric measurements. From a practical point of view, the scope is then to extract from the acceleration data some valuable diagnostic information which could be used to detect the presence of possible damages (i.e., to produce knowledge about the state of health). When the monitoring is implemented online, in a continuous way, the raw accelerometric data sets can be very large and complex to be dealt with, as usually involve multiple channels (i.e., multiple locations and directions) and high sample rates (i.e., order of ksps - 103 samples per second), but the final knowledge about the state of health can, in principle, be summarized by a single binary information (i.e., healthy – 0 vs damaged – 1). This is commonly called Damage Detection. In this work, the big data management challenge is tackled from the point of view of statistical signal processing, so as to aggregate the multivariate data and condense them into single information of distance with respect to a healthy reference condition (i.e., the Novelty). When confounding influences (such as the work condition or the environmental condition) can be disregarded, the novelty information has a direct correspondence to the health information, so that an alarm indicating the detection of damage can be triggered upon exceeding a selected threshold for the limit novelty. Many different ways of solving such a binary classification problem can be found in the literature. Starting from the simplest, some of the more effective are compared in the present analysis, to finally select a reliable procedure for the big data management in vibration monitoring

ON THE USE OF STOCHASTIC RESONANCE FOR FAULT DETECTION IN SPUR GEARBOXES

This study demonstrates how a time domain data based non-linear approach known as Stochastic Resonance (SR) can be effectively used for fault detection in spur gearboxes. SR has just been used recently for fault diagnosis in mechanical systems with a focus on faulty systems. This paper examines the behaviour of SR when it is applied to healthy systems, in particular a healthy gearbox and explores approaches like residual signal and filtered signal computations to aid in the containment of false alarms while improving overall results. Although SR is a time domain procedure, its results also extend to the frequency domai

Performance of Envelope Demodulation for Bearing Damage Detection on {CWRU} Accelerometric Data: Kurtogram and Traditional Indicators vs. Targeted a Posteriori Band Indicators

Envelope demodulation of vibration signals is surely one of the most successful methods of analysis for highlighting diagnostic information of rolling element bearings incipient faults. From a mathematical perspective, the selection of a proper demodulation band can be regarded as an optimization problem involving a utility function to assess the demodulation performance in a particular band and a scheme to move within the search space of all the possible frequency bands {f, Df} (center frequency and band size) towards the optimal one. In most of cases, kurtosis-based indices are used to select the proper demodulation band. Nevertheless, to overcome the lack of robustness to non-Gaussian noise, different utility functions can be found in the literature. One of these is the kurtosis of the unbiased autocorrelation of the squared envelope of the filtered signal found in the autogram. These heuristics are usually sufficient to highlight the defect spectral lines in the demodulated signal spectrum (i.e., usually the squared envelope spectrum (SES)), enabling bearings diagnostics. Nevertheless, it is not always the case. In this work, then, posteriori band indicators based on SES defect spectral lines are proposed to assess the general envelope demodulation performance and the goodness of traditional indicators. The CaseWestern Reserve University bearing dataset is used as a test case

ANOVA and other statistical tools for bearing damage detection

The aim of the paper is to exhaustively exploit and test some statistical tools, such as ANOVA and Linear Discriminant Analysis, to investigate a massive amounts of data collected over a rig available @DIRG Lab, specifically conceived to test high speed aeronautical bearings; the rig permits the control of rotational speed (6000 – 30000 RPM), radial load (0 to 1800 N) and temperature, and allows monitoring vibrations by means of 4 tri-axial accelerometers. Fifteen different damages have been realised on the bearing but, for simplicity, this papers only treats those cases where simple identification methods have failed or not demonstrated to be fully affordable. The damages have been inferred on rolls or on the internal ring, with different severities, which are reported as a function of their extension, i.e. 150, 250, 450 μm. A total number of 17 combinations of load and speed have been analysed per each damaged bearing. Although ANOVA rigorously applies when some conditions are respected on the probability distribution of the responses, such as Independence of observations, Normality (normal distribution of the residuals) and Homoscedasticity (homogeneity of variances – equal variances), the paper exploits the robustness of the technique even when data do not fully fall into the requisites. Analyses are focused on the best features to be taken into account, trying to seek for the most informative, but also trying to extract a “best choice” for the acceleration direction and the most informative point to be monitored over the simple structure. Wanting to focus on the classification of the single observation, Linear Discriminant Analysis has been tested, demonstrating to be quite effective as the number of misclassification is not very high, (at least considering the widest damages). All these classifications have unfortunately the limit of requiring labelled examples. Acquisitions in un- damaged and damaged conditions are in fact essential to guarantee their applicability, which is quite often impossible for real industrial plants. The target can be anyway reached by adopting distances from un-damaged conditions which, conversely, must be known as a reference. Advantages of the statistical methods are quickness, simplicity and full independence from human interaction

ON THE USE OF PCA FOR DIAGNOSTICS VIA NOVELTY DETECTION: INTERPRETATION, PRACTICAL APPLICATION NOTES AND RECOMMENDATION FOR USE

The Principal Component Analysis (PCA) is the simplest eigenvector-based multivariate data analysis tool and dates back to 1901 when Karl Pearson proposed it as a way for finding the best fitting d-1 hyperplane of a system of points in a d-dimensional (Euclidean) space. Over time, the PCA evolved in different fields with several different names and with different scopes, but, in its essence, it is always an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. Generalizing Pearson’s purpose, the knowledge derived by such an analysis is mostly used to find a subspace which effectively and efficiently summarizes the original system of points by losing a minimum amount of information. In the field of Diagnostics, the fundamental task of detecting damage is basically a binary classification problem which is in many cases tackled via Novelty Detection: an observation is classified as novel if it differs significantly from other observations. Novelty can, in principle, be assessed directly in the original space, but the effectiveness of the estimated novelty can be improved by taking advantage of the PCA. In this work, the traditional PCA will be compared to a robust modification that is commonly used in the field of diagnostics to face the issue of confounding influences which could affect the novelty-damage correspondence. Comparisons will be made to shed light on the main misleading aspects of PCA, and finally, define a unique, theoretically justified procedure for Diagnostics via Novelty Detection