Mahmoud El-Kafafy

A Frequency-Domain Maximum Likelihood Implementation using the modal model formulation

Abstract In this paper, a multivariable frequency-domain maximum likelihood estimator based on a modal model formulation is proposed. The proposed approach is mainly introduced to improve the accuracy of the modal parameters estimated by the poly-reference least squares complex frequency-domain (i.e. pLSCF) estimator and to have their confidence intervals as well. In that approach, a 3-step procedure is introduced to improve the estimates accuracy while taking the advantage of the very clear stabilization diagram of pLSCF estimator. The proposed approach has been optimized to reduce the computation time as well as the memory requirements. The algorithm is evaluated and compared with two other published algorithms by means of Monte-Carlo simulations.

Advanced Frequency-Domain Modal Analysis for Dealing with Measurement Noise and Parameter Uncertainty

The poly-reference Least Squares Complex Frequency-domain (pLSCF) estimator –commercially known as the LMS PolyMAX method- has introduced an improvement in the field of modal analysis. The main advantages are its computational speed and the very clear stabilization diagrams it yields even in the case of highly damped systems and noisy FRF measurements. Moreover, the numerical stability of the algorithm allows for a large-bandwidth and high-model order analysis and makes it suitable both for lowly- and highly-damped structures.

Uncertainty propagation in Experimental Modal Analysis

As all experimental procedures, Experimental Modal Analysis (EMA) is subject to a wide range of potential testing and processing errors. The modal identification methods are sensitive to these errors, yielding modal results which are uncertain up to certain error bounds. The question hence is what these error bounds on test data and modal parameters are. In this paper, the studied source of uncertainty is related to the variance (noise) on the Frequency Response Function (FRF) measurements. Under the H1 assumptions and in single-input cases, the FRF variances can be computed from the coherences and the FRFs. In multiple-input cases, some more measurement functions are required. Advanced system identification methods like the Maximum Likelihood Estimator (MLE) and PolyMAX Plus have the possibility to take the uncertainty on the measurement data into account and to propagate the data uncertainty to (modal) parameter uncertainty. This paper will review FRF variance estimation techniques, including some pragmatic approaches. The basic concepts of Maximum Likelihood Estimation and the calculation of confidence bounds will be discussed. Some typical structural testing and modal analysis cases will be used as illustration of the discussed concepts.

Evaluating Different Automated Operational Modal Analysis Techniques for the Continuous Monitoring of Offshore Wind Turbines

This paper will evaluate different automated operational modal analysis techniques for the continuous monitoring of offshore wind turbines. The experimental data has been obtained during a long-term monitoring campaign on an offshore wind turbine in the Belgian North Sea. State-of-the art operational modal analysis techniques and the use of appropriate vibration measurement equipment can provide accurate estimates of natural frequencies, damping ratios and mode shapes of offshore wind turbines. To allow a proper continuous monitoring the methods have been automated and their reliability improved. The advanced modal analysis tools, which will be used, include the poly-reference Least Squares Complex Frequency-domain estimator (pLSCF), commercially known as PolyMAX, the polyreference maximum likelihood estimator (pMLE), and the frequency-domain subspace identification (FSSI) technique. The robustness of these estimators with respect to a possible change in the implementation options that could be defined by the user (e.g. type of polynomial coefficients used, parameter constraint used…) will be investigated. In order to improve the automation of the techniques, an alternative representation for the stabilization charts as well as robust cluster algorithms will be presented.

Monitoring Changes in the Soil and Foundation Characteristics of an Offshore Wind Turbine Using Automated Operational Modal Analysis

This paper will show the first results of a long term monitoring campaign on an offshore wind turbine in the Belgian North Sea. It will focus on the vibration levels and resonant frequencies of the fundamental modes of the support structure. These parameters will be crucial to minimize O&M costs and to extend the lifetime of offshore wind turbine structures. For monopile foundations for example, scouring and reduction in foundation integrity over time are especially problematic because they reduce the fundamental structural resonance of the support structure, aligning that resonance frequency more closely to the lower frequencies. Since both the broadband wave energy and the rotating frequency of the turbine are contained in this low frequency band, the lower natural frequency can create resonant behavior increasing fatigue damage. Continuous monitoring of the effect of scour on the dynamics of the wind turbine will help to optimize the maintenance activities on the scour protection system. To allow a proper continuous monitoring during operation, reliable state-of-the-art operational modal analysis techniques should be used and these are presented in this paper. The methods are also automated, so that no human-interaction is required and the system can track the natural frequencies and damping ratios in a reliable manner.

Long-Term Automatic Tracking of the Modal Parameters of an Offshore Wind Turbine Drivetrain System in Standstill Condition

Modal behavior of a wind turbine is an important design aspect for tackling noise, vibration, and harshness (NVH) issues and validating complex simulation models. This paper focusses long-term modal analysis on an offshore wind turbine (OWT) in stand still conditions. It presents the results of an automated procedure to track the variation of the modal parameters of the drivetrain system of the OWT. The tracking focuses on the continuous monitoring of the resonant frequencies and damping values of the most dominant modes of the drivetrain unit during more than half a day of stand still. The long-term tracking of the natural frequencies and modal damping of the drivetrain vibration modes under distinct ambient conditions allows to better understand the dynamics of the drivetrain by gaining confidence in modal parameters estimated over multiple measurement blocks and helps in gaining understanding in the dynamics of the OWT. The used automatic tracking procedure is based on the well-known parametric operational modal analysis algorithm, pLSCF estimator. The experimental data used in this paper has been obtained during a long-term measurement campaign lasting 6 months on an offshore wind turbine with instrumentation directly mounted on the drivetrain. Both eigenfrequencies and damping values are of particular interest.

Influence of the Harmonics on the Modal Behavior of Wind Turbine Drivetrains

In the last decades, noise, vibration and harshness (NVH) problems became critical issues to be tackled by the wind industry. They have been caused by the upscaling trend that has imposed bigger (not quasi-static) loads on turbine subcomponents: the dynamic loads are significantly influencing the fatigue life of the wind turbine components and the tonalities generated. To validate complex simulation models, it is of high interest to continuously track the modal parameters of the fundamental modes of a wind turbine during operating conditions. At this purpose, operational modal analysis (OMA) represents a powerful tool.

Efficient Use of the Output Information to Improve Modal Parameter Estimation

In modal identification, the value of the model parameters and the associated uncertainty depends on the quality of the measurements. The maximum likelihood estimator (mle) is a consistent and efficient estimator. This means that the value of the parameters trends asymptotically close to the true value, while the variance of such parameters is the lowest possible with the associated data. The mle implementation and application can be complex and generally need strong computational requirements. In applications where the number of inputs and outputs are elevated (as in modal analysis) is common to reduce the covariance matrix to a diagonal one where only the variances are considered. This implementation is still consistent but not efficient. However, it generates acceptable results. The current work shows that using efficiently the output information as complement to the input–output relations, it is possible to improve the model identification reaching similar levels than the mle, while reducing the execution time and the computational load.

Modal Parameters Estimation of an Offshore Wind Turbine Using Measured Acceleration Signals from the Drive Train

Offshore Wind Turbine (OWT) is complex structure that consists of different parts (e.g. foundation, tower, drivetrain, blades, …). The last decade there is a continuous trend towards larger machines with the goal of cost reduction. Modal behavior is an important design aspect. For tackling NVH issues and validating complex simulation models it is of high interest to continuously track the vibration levels and the evolution of the modal parameters (resonance frequencies, damping ratios, mode shapes) of the fundamental modes of the turbine. Wind turbines are multi-physical machines with significant interaction between their subcomponents. This paper will exploit this and present the possibility of identifying and tracking consistently the structural vibration modes of the drivetrain of the instrumented offshore wind turbine by using signals (e.g. acceleration responses) measured on the drivetrain system. The experimental data has been obtained during a measurement campaign on an offshore wind turbine in the Belgian North Sea where the OWT was in standstill condition. The drivetrain, more specifically the gearbox, is instrumented with a dedicated measurement set-up consisting of 17 sensor channels with the aim to continuously track the vibration modes. The consistency of modal estimates made at consequent 10-min intervals is validated, and the dominant drivetrain modal behavior is identified.

Optimal Modal Parameter Estimation for Highly Challenging Industrial Cases

In this paper, the recently-developed MLMM method (Maximum Likelihood estimation of a Modal Model) will be introduced and applied to challenging industrial cases. Specific about the method is that the well-established statistical concept of maximum likelihood estimation is applied to estimate directly a modal model based on measured Frequency Response Functions (FRFs). Due to the nature of this model, the optimal modal parameters are estimated using an iterative Gauss-Newton minimization scheme. The method is able to tackle some of the remaining challenges in modal analysis. For instance, in highly-damped cases (e.g. acoustic cavity modal analysis, trimmed body modal analysis) where it is needed to use a large amount of excitation locations to sufficiently excite the modes and to obtain a reliable modal model, the more classical modal parameter estimation methods sometimes fail to achieve a high-quality curve-fit of the measured FRF data. Due to the iterative minimization of the cost function, MLMM is able to estimate a model that very closely represents the measurements. Another benefit of the method is that additional constraints can be imposed to the model. For instance, it is possible to impose that real modes and participation factors are estimated and/or to impose that the estimated modal model is reciprocal (as prescribed by the modal theory). More classical modal parameter estimation methods have rarely the possibly to fully integrate these constraints and the obtained modal parameters are typically altered in a subsequent step to satisfy the desired realness and reciprocity constraints. It is obvious that this may lead to sub-optimal results, as for instance evidenced by a degradation of the quality of the fit between the identified modal model and the measurements. The applicability of MLMM to estimate a constrained modal model will be demonstrated using challenging industrial applications.