Minas D. Spiridonakos

A Data-Driven Diagnostic Framework for Wind Turbine Structures: A Holistic Approach

The complex dynamics of operational wind turbine (WT) structures challenges the applicability of existing structural health monitoring (SHM) strategies for condition assessment. At the center of Europe’s renewable energy strategic planning, WT systems call for implementation of strategies that may describe the WT behavior in its complete operational spectrum. The framework proposed in this paper relies on the symbiotic treatment of acting environmental/operational variables and the monitored vibration response of the structure. The approach aims at accurate simulation of the temporal variability characterizing the WT dynamics, and subsequently at the tracking of the evolution of this variability in a longer-term horizon. The bi-component analysis tool is applied on long-term data, collected as part of continuous monitoring campaigns on two actual operating WT structures located in different sites in Germany. The obtained data-driven structural models verify the potential of the proposed strategy for development of an automated SHM diagnostic tool.

Vibration-based experimental damage detection of a small-scale wind turbine blade

Structural health monitoring offers an attractive tool for condition assessment, fault prognosis and life-cycle management of wind turbine components. However, owing to the intense loading conditions, geometrical nonlinearities, complex material properties and the lack of real-time information on induced structural response, damage detection and characterization of structural components comprise a challenging task. This study is focused on the problem of damage detection for a small-scale wind turbine (Sonkyo Energy Windspot 3.5 kW) experimental blade. To this end, the blade is dynamically tested in both its nominal (healthy) condition and for artificially induced damage of varying types and intensities. The response is monitored via a set of accelerometers; the acquired signals serve for damage detection via the use of appropriate statistical and modal damage detection methods. The former rely on extraction of a characteristic statistical quantity and establishment of an associated statistical hypothesis test, while the latter rely on tracking of damage-sensitive variations of modal properties. The results indicate that statistical-based methods outperform modal-based ones, succeeding in the detection of induced damage, even at low levels.

Data-driven polynomial chaos basis estimation

A non-intrusive uncertainty quantification scheme based on Polynomial Chaos (PC) basis constructed from available data is introduced. The method uses properly parametrized basis functions in order to let them adapt to the given input-output data instead of predefining them based on the probability density function of the uncertain input variable. Model parameter estimation is effectively dealt with through a Separable Non-linear Least Squares (SNLS) procedure that allows the simultaneous estimation of both the PC basis and the corresponding coefficients of projection. Method’s effectiveness is demonstrated through its application to the uncertainty propagation modelling in two examples: a nonlinear differential equation with uncertain initial conditions and a nonlinear single degree-of-freedom system with an uncertain parameter. Comparisons with classical PC expansion modelling based on the Wiener-Askey scheme are used to illustrate the method’s performance and potential advantages. Polynomial Chaos (PC) expansion has been demonstrated to effectively model uncertainty propagation in a number of engineering problems. The main advantage of the PC representation is its low computational cost, compared to that of traditional approaches such as the classical MonteCarlo, and its ease of use for model-based analysis, e.g. for the purposes of statistical characterization of the output, reliability and global sensitivity analysis. Nevertheless, PC expansion for uncertainty quantification in real applications remains challenging mainly due to problems arising from the statistical characterization of the input variables, as well as the process of determining a sparse PC basis, in the sense of including only a small number of basis functions which may still provide high approximation accuracy. With regard to the first problem, although Xiu and Karniadakis (2002) have extended the initially proposed PC of Gaussian processes on Hermite polynomials proposed by Wiener, to a number of common continuous and discrete Probability Density Functions (PDFs) through the Wiener-Askey scheme, estimating the statistical distribution of input variables may be a nontrivial task since bounded, multi-modal, or discontinuous PDFs may be found to best fit given measured data (Oladyshkin and Nowak (2012)). In such cases, fitting the given data to a common PDF may significantly reduce the accuracy of the expansion, while on the other hand transformations to standard PDFs normally lead to slower convergence rates. The crucial problem of selecting specific PC subspaces is also an open problem that has been treated in a number of recent studies (for example see Blatman and Sudret (2011)), with a common approach being the forward selection procedure which builds up the PC model by adding bases till no further improvement is achieved, according to a predetermined criterion. In most cases however, such approaches require the estimation of a large number of candidate models. Moreover, potential limitations of the WienerAskey expansion scheme arise in situations where discontinuities or complex relationships characterize the dependency of the output variable on the random input data (Le Maître et al. (2004)).

Online State and Parameter Estimation of a Nonlinear Gear Transmission System

This study aims at modeling the nonlinear dynamic response of a gear transmission system, based on substructuring techniques. More specifically, a finite element (FE) model is introduced for the housing of the gearbox, while the essential effects of the gear-pair, the bearings and the shafts are described by a lumped parameter model. The latter is characterized by strongly nonlinear characteristics that account for gear backlash, meshing stiffness, transmission error properties and bearing stiffness nonlinearities. Accordingly, a joint state and parameter estimation (JS&PE) problem is formulated on the basis of the lumped model. The proposed framework uses vibration acceleration measurements from sensors attached on the housing and, through their propagation to the lumped nonlinear model via the FE substructure, an Unscented Kalman Filter (UKF) is activated for the solution of the JS&PE problem. In contrast to other alternatives (e.g., the Extended Kalman Filter), the UKF features a number of advantages in treating nonlinear systems, including a derivative free calculation and a capacity for higher order nonlinearities. The method’s performance is examined using both numerical simulations and experimental tests.

Implementation of Parametric Methods for the Treatment of Uncertainties in Online Identification

This chapter aims to provide an overview of the treatment of uncertainty in vibration-based monitoring and identification problems. This is delivered by means of an exemplary overview of methods that are structured in the time domain, and are of a parametric class, and which may or may not necessitate an assumption of an a priori system structure. In this respect, two main classes are herein demonstrated, namely (i) models formulated in the state-space domain, and (ii) models of the autoregressive type. The goal lies in tackling diverse sources of uncertainties including the identification of (i) linear system models from ambient sources, (ii) unmeasured system states under known excitation, (iii) potentially unknown a priori parameters, (iv) unmeasured input sources or (v) nonlinear response characteristics. A metamodeling approach able to account for the uncertainties in simulating nonlinear, dynamically evolving engineered systems is also touched upon herein.

Vibration-based Damage Detection on a Blade of a Small Scale Wind Turbine

The present study focuses on the damage detection problem applied for the case of a blade of a small wind turbine (Sonkyo Energy Windspot 3.5 kW). To this end, the blade is dynamically tested under a number of structural states, including both its nominal (healthy) condition and various damaged states. The collected vibration responses are then used for the estimation of appropriate nonparametric and parametric models of the structure, and the extraction of a characteristic statistical quantity. Damage detection is the performed by the means of simple hypothesis testing. Comparisons with standard vibration-based feature methods, such as ones relying on changes of modal properties, provide significant indications of superior performance. Overall, the results show excellent performance especially for the parametric based method. doi: 10.12783/SHM2015/351

Dispersion–Corrected, Operationally Normalized Stabilization Diagrams for Robust Structural Identification

This study aims at incorporating a certain degree of formalization to stabilization diagrams by integrating two additional features: the former introduces a new quantity, the modal dispersion metric, which expresses a certain part of the total stochastic vibration energy, and it is attributed to each vibration mode. The latter implements a polynomial chaos expansion framework for quantifying the effect of the operational conditions into the modal dispersion index. By combining these two features, a vibration mode is deemed as a structural one when it appears stabilized, i.e., comes with a high modal dispersion index and is operationally normalized. The proposed method is characterized by global applicability, thus also serving as a common measure of effectiveness among diverse parametric identification methods.