Automated modal parameter estimation for coupled rotor–foundation systems using seal forces as excitation source

Modal analysis has developed into a major technology for the study of structural dynamics in the past several decades. Through it, complex structural dynamics phenomena can be represented in terms of structural invariants, i.e., the modal parameters: natural frequencies, damping ratios and mode shapes. Operational Modal Analysis (OMA) deals with the estimation of modal parameters on vibration data measured for operational conditions, when the excitation on the structure is not measured. In this work, OMA is performed on a wind turbine blade undergoing wind tunnel testing. These tests included different wind speeds, pitch angles and also different health conditions of the blade, where masses of different magnitude were fixed to the blade on different locations to emulate damage conditions. In order to monitor the modal parameters across multiple days of varied tests in the wind tunnel, the Polymax modal parameter estimator was implemented, coupled with an Automated Modal Analysis methodology. This methodology included an automatic modal parameter selection technique, using a Machine Learning (ML) clustering algorithm, coupled with a modal tracking procedure which applied statistical thresholds on the modal parameters’ values. The tracking procedure searches for modes similar to the ones calculated for healthy conditions. The results show how the modal parameters of the wind turbine blade vary with the different measured conditions in the wind tunnel. Moreover, a damage detection methodology is implemented to differentiate between the healthy and damaged conditions on the blade, by leveraging an anomaly detection algorithm using the Multivariate Gaussian Distribution (MGD). This algorithm takes as input the modal parameters calculated by the previous Automated Modal Analysis methodology and detects statistical deviations among them which could indicate the presence of damage. All steps of this work contribute to developing an automatic framework able to detect damages on a wind turbine blade, and therefore perform Structural Health Monitoring (SHM) for different operational conditions.

Modal tracking plays a vital role in structural health monitoring since changes in modal parameters help us understand a structure’s dynamic characteristics and may reflect the potential deterioration of structural performance. Although numerous modal parameter estimation (MPE) methods exist, it is not guaranteed that an MPE process will exclude all spurious modes and not lose any physical modes every time over a long-term monitoring period. Relatively large damping of a structure, poor data quality, and significant changes in structural modal parameters may make the estimated modal parameters spurious, missing, or misclassified. It makes long-term modal tracking semiautomated or manual, which constrains timely downstream applications such as anomaly detection, condition assessment, and decision making. This research aims to propose a long-term continuous automatic modal tracking algorithm based on Bayesian inference even when the modal parameters, damping, and data quality change significantly. Bayesian inference is used to determine the physical modes from the results of existing MPE methods. Both the modes identified from the most recent response set and the modal probability model from multiple previous response sets are considered in the Bayesian model to better determine the physical modes from the results of MPE. Moreover, the proposed algorithm requires only three extra hyperparameters compared to general modal tracking algorithms, and they can be quickly determined by a grid search method. The performance of the proposed algorithm is verified by a numerical example and a real-world civil structure Z24 Bridge benchmark.

This paper investigates the use of conventional operational modal analysis (OMA) techniques for modal parameters identification of a rotating system supported by roller bearings. Although largely applied in civil engineering, in-depth studies on different types of systems are still limited in the literature. The novel of the paper is to address such issue by applying conventional OMA methods, such as enhanced frequency domain decomposition (EFDD) and stochastic subspace identification (SSI-data), to identify the modal parameters of a rotating machine, investigating the challenging particularities of these systems due to their inherent operating conditions, especially regarding the presence of harmonic forces, eventually closed-spaced modes, and non-proportional damping due to the bearings. The results presented in the experimental tests showed that, with the use of specific tools, in comparison with traditional experimental modal analysis (EMA), the used OMA methods have managed to successfully identify the modal parameters of a roller bearing supported rotor.

The crankshaft is a very crucial part in an internal combustion engine. This paper presents the findings of the mode shape and natural frequency of 3 cylinder 4 stroke engine crankshafts. Both experimental and computational methods were carried out to determine the modal parameter or dynamic characteristics, which are natural frequency, damping factor and mode shape. The prediction of the dynamic properties of the chassis is of great significance in determining the natural frequencies of the structure. The experiment is done by using an impact hammer to excite the crankshaft and data is recorded using a data acquisition system (DAS) connected to a sensor located on the crankshaft. Computational modal analysis on the crankshaft structure is simulated using finite element software. It can be seen from the results that there is a good agreement between the experimental and computational results in terms of modal parameter with a small discrepancy. The modal analysis techniques are essential for automotive crankshaft structure design.

<div class="htmlview paragraph">Operational Modal Analysis also known as Output Only Modal Analysis has in the recent years been used for extracting modal parameters of civil engineering structures and is now becoming popular for mechanical structures. The advantage of the method is that no artificial excitation needs to be applied to the structure or force signals to be measured. All the parameter estimation is based upon the response signals, thereby minimising the work of preparation for the test. This test case is a controlled lab set-up enabling different parameter estimation methods techniques to be used and compared to the Operational Modal Analysis. For Operational Modal Analysis two different estimation techniques are used: a non-parametric technique based on Frequency Domain Decomposition (FDD), and a parametric technique working on the raw data in time domain, a data driven Stochastic Subspace Identification (SSI) algorithm. These are compared to other methods such as traditional Modal Analysis. In the paper the method is illustrated by practical examples.</div>

<div class="htmlview paragraph">Traditionally, vibration analysis in operating conditions (on the road or on a bench) had to be combined with experimental modal analysis in controlled laboratory conditions in order to understand the modal behaviour of the structure. This requires additional measurements, costs and time. However, in many applications, the real operating conditions may differ significantly from those applied during the modal test and hence the vibration modes from the modal test might not be representative for the active modes in operation conditions. The need for a capability of doing a modal analysis on data from operating conditions is obvious.</div> <div class="htmlview paragraph">Over the last years, several modal parameter estimation techniques have been proposed and studied for modal parameter extraction from output-only data. Each method needs to make a number of assumptions and has some limitations. In this paper, the capabilities and limitations of the Least Squares Complex Exponential and two subspace techniques, referred to as the Balanced Realization (BR) and the Canonical Variate Analysis, are evaluated for its applicability to industrial cases.</div>

The present paper deals with the novel approach of filtering technique using hybrid of empirical mode decomposition technique with stabilization diagram, that autonomously implemented within Matlab. Noise or unwanted signal is always present in the data and a bad signal-to-noise can cause a severe error in modal parameter extraction. With the recent developments of automated procedures without user interaction for the operational modal analysis (OMA), the corrupted input signals turn out to be a big issue in obtaining reliable results of automated modal parameter identification. The appearance of noise or unwanted modes due to environmental effects could affect the actual structural modes selection. There is a significant issue regarding “noise” (or spurious) modes and eliminating them from the raw signal remains to be solved and requires a lot of interaction with an expert user. In the parametric modal analysis, oversizing of a modal model is usually performed to minimize the bias on modal estimates by getting all physical modes in the frequency range of interest and help to obtain a good model fit to the data. However, this will introduce noise modes. Thus, authors take advantage of tools, such as the stabilization diagram, to illustrate, and decide, if a mode is physical or not. This selection is not a trivial task, but it may be difficult and time consuming depending on the quality of data, the performance of the estimator and the experience of the user. Since the extensive interaction between tools and user is inappropriate for monitoring purposes, image clustering tool is introduced to separate the physical poles from the others with short response time and low computational efforts compared to the available clustering algorithm. Meanwhile, Empirical mode decomposition (EMD) is then introduced to break down a signal into various components without leaving the time domain and purposely used for filtering. These are a great combination as well as an effective procedure in producing a good input signal that free from unwanted modes which can cause disruptive decision making for the actual modes selection.

Automated modal parameter estimation using correlation analysis and bootstrap sampling

Experimental modeling of Wiener filters estimated on an operating diesel engine

Modal analysis, which provides modal parameters including frequencies, damping ratios, and mode shapes, is essential for assessing structural safety in structural health monitoring. Automated operational modal analysis (AOMA) offers a promising alternative to traditional methods that depend heavily on human intervention and engineering judgment. However, estimating structural dynamic properties and managing spurious modes remain challenging due to uncertainties in practical application conditions. To address this issue, we propose an automated modal identification approach comprising three key aspects: (1) identification of modal parameters using covariance-driven stochastic subspace identification; (2) automated interpretation of the stabilization diagram; (3) an improved self-adaptive algorithm for grouping physical modes based on ordering points to identify the clustering structure (OPTICS) combined with k-nearest neighbors (KNN). The proposed approach can play a crucial role in enabling real-time structural health monitoring without human intervention. A simulated 10-story shear frame was used to verify the methodology. Identification results from a cable-stayed bridge demonstrate the practicality of the proposed method for conducting AOMA in engineering practice. The proposed approach can automatically identify modal parameters with high accuracy, making it suitable for a real-time structural health monitoring framework.

Damping inter-area oscillations using virtual generator based power system stabilizer

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.

Modal parameters of a transmission tower considering the coupling effects between the tower and lines

The three-dimensional finite element model of 600 Wh energy storage flywheel rotor system supported by active magnetic bearing (AMB) was built with the commercial software ANSYS to carry out the modal analysis. The modeling method of the AMB and their effect on the rotor system are explored. Modal analysis was performed, and the modal shapes of the rotor system were obtained. The Campbell diagram calculated by ANSYS was gained to be compared with the one calculated by the theoretical dynamics model. This research provides a theoretical basis for the rotor system design. The ideas and methods can be used as a reference for the study of dynamic characteristics of the rotor system and direct the flywheel prototype future design.

Decentralized PID neural network control for five degree-of-freedom active magneticbearing