•Autonomous method learns how to perform modal analysis optimally.•Modal damping of test object automatically identified with high accuracy.•Automatic modal parameter identification method ...universally usable.•Autonomous implementation facilitates modal analysis quasi in real-time.
Safety-critical applications like the evaluation of aeroelastic stability during aircraft flight require modal parameters identified with high accuracy. Promising methods of automated modal identification exist. Nevertheless, these methods are not yet chosen for safety–critical applications. The reason is either insufficient accuracy of modal parameters or significant adaptions for each individual application. In this work, a new method is presented that not only enables fully automated modal analysis, but also learns an optimal way to analyze the data in a supervised manner. Based on the result of a single manual modal analysis, the self-learning method finds optimal parameters for the automated analysis. In an iterative process, new analysis parameters are chosen by Bayesian Optimization with a Gaussian Process as surrogate model and Expected Improvement as the acquisition function. With these parameters, the method can analyze additional datasets as accurately as a manual expert. The presented method is evaluated on ground vibration test data (i.e., experimental modal analysis) as well as flight vibration data (i.e., operational modal analysis) of an aircraft structure. In contrast to previous methods, the presented method can be easily used for various modal tests, since it can learn by itself to perform optimally with respect to a specific target function like for example the one provided in this work. Due to its robustness, the method is promising also for industrial test cases and safety–critical applications.
Transmissibility-based operational modal analysis (TOMA) is a recent research area that has seen its most significant developments over the last two decades. The advantage of this new approach is its ...independence from the excitation spectrum. All methods developed have been based on Response Transmissibility (RT) functions or Power Spectrum Density Transmissibility (PSDT) functions. The RT-based methods identify modal parameters from various load conditions and the PSDT-based methods use a single load condition by combining multiple reference outputs. This work proposes a unified concept for TOMA that relates the scalar RT and PSDT functions. This new concept shows that scalar PSDT functions combine n RT functions due to a single load. Two applications emerge from the unified concept: a) the matrix representation permits to identify modal parameters (natural frequencies, damping ratios and mode shapes) from PSDT functions in only one load condition, b) a procedure based on the joint diagonalization of matrices with PSDT functions from different load conditions allows the identification of RT functions. A numerical simulation and actual field data were used to assess the applications of unified concept. The results demonstrate the capacity of new concept to estimate modal parameters and RT functions of structures in operations conditions.
Summary
Structural health monitoring (SHM) is one of the main research topics in civil, mechanical and aerospace engineering. In this regard, modal parameters and their trends over time can be used ...as features and indicators of damage occurrence and growth. However, for practical reasons, output‐only techniques are particularly suitable for the system identification (SI) of large civil structures and infrastructures, as they do not require a controlled source of input force. In this context, these approaches are typically referred to as operational modal analysis (OMA) techniques. However, the interpretation of the OMA identifications is a labour‐intensive task, which could be better automated with artificial intelligence and machine learning (ML) techniques. In particular, clustering and cluster analysis can be used to group unlabelled datasets and interpret them. In this study, a novel multi‐stage clustering algorithm for automatic OMA (AOMA) is tested and validated for SHM applications—specifically, for damage detection and severity assessment—to a masonry arch bridge. The experimental case study involves a 1:2 scaled model, progressively damaged to simulate foundation scouring at the central pier.
•The impact of harmonic/random excitation amplitude ratios on OMA methods is studied.•Novel method AOBMA extends OBMA by scaling and (weighted) averaging of orders.•Comparing OMA estimation ...performances using a Monte-Carlo simulation study.•AOBMA reduces estimation errors compared to OBMA in simulation and operational data.•Order-based methods (AOBMA, OBMA) surpass traditional OMA in mode shape estimation.
Machinery with rotating components poses a challenge to Operational Modal Analysis (OMA) due to its periodic inputs, i.e. orders. Transient (acceleration or deceleration) runs represent a relevant test condition for structures, which experience a low amount of broadband (noise) excitation during operation. In these cases, orders present themselves as a favourable source of excitation. However, this type of excitation can result in distortions of the response spectrum at the ending frequencies of individual orders. These “end-of-order” distortions can introduce spurious or biased modal estimations. Order-based Modal Analysis (OBMA) is an OMA method, which was developed specifically for the transient test case and is not affected by end-of-order distortions. However, some downsides are associated with OBMA because it performs modal analysis for each relevant order individually. In addition to the associated analysis effort, this produces multiple sets of modal estimations with ambiguous results. This paper introduces an extension of OBMA to address these issues. The proposed method, called Averaged Order-based Modal Analysis (AOBMA), applies scaling and (weighted) averaging to extracted orders prior to the modal estimation step. A Monte-Carlo simulation study is introduced to compare the modal estimation performance of traditional OMA, OBMA and AOBMA. Different ratios of harmonic and random excitation amplitudes are simulated to gauge the impact of the excitation's composition. In addition, all methods are also applied to operational measurements from a turbofan casing during run-up. The results indicate that AOBMA produces a lower variance in the estimated modal parameters compared to OBMA. Moreover, while OMA was more successful in the estimation of closely spaced modes, it was surpassed by AOBMA and OBMA regarding the accuracy of mode shape estimations.
The vibration and acoustic behavior of electric machines is an important criterion in the design phase. The impact of the winding and the insulation on the eigenfrequencies, the eigenmodes and the ...damping of the stator is one of the main uncertainties. Therefore, in this work, the influence of a hairpin winding, insulated with two different insulation types, is analyzed. Four different stator specimens are examined by performing an experimental modal analysis and a FE harmonic analysis. On the basis of the results, equivalent material parameters for the homogenized winding, consisting of copper conductors and insulation material, are derived by comparing the simulation and the measurement results. The Young 's modulus (also called the elastic modulus) is identified by performing a parameter fitting. A methodology for comparing and evaluating the measurement and the simulation results is presented. The resulting equivalent material parameters of the winding can be used for future calculations.
•We outline the historical development of the application of the cepstrum to modal analysis.•Most recent developments and current state-of-the-art also covered.•Use of the cepstrum to extract modal ...properties is explained, including MIMO applications.•Discussion on preprocessing applications of the cepstrum to improve conventional OMA.•Importance of cepstral methods is explained, especially in OMA with strong forcing functions.
The cepstrum has a very long history, since the first paper was published in 1963, two years before the publication of the FFT algorithm. The first application was to the determination of echo delay time, but it was quickly applied to speech analysis for two reasons. Firstly, it was able to detect voiced speech, and measure the voice pitch, and secondly it was able to separate the forcing and transfer function components in speech signals. These two properties apply equally to machine vibration signals, and the cepstrum can be used to detect and remove periodic discrete frequency components (harmonics and modulation sidebands) from the spectrum (and corresponding time signals) and also to extract the modal properties of a structure in the presence of the forcing function. This paper describes the development of these applications to structural modal analysis over many years, primarily to operational modal analysis (OMA), where the modal information is extracted from response signals, often with the structure in its normal operating environment. The cepstrum extracts the modal information in terms of pole/zero models, and requires compensation for the effects of unmeasured out-of-band modes, by an equalisation process, and overall scaling to obtain scaled mode shapes. Steady advances to achieve this have been made over the years. A recent development that has revolutionised the application has been the ability to edit stationary and slowly varying non-stationary signals using the real cepstrum (which does not contain the phase information of the original signals) but regenerating time signals by combining the edited amplitude spectra with the original phase spectra (with negligible error). There are currently two ways in which this can be used in operational modal analysis:1.Pre-processing of the response signals to remove most excitation components and other disturbances, and enhance the modal properties, before applying standard OMA procedures.2.Extracting the modal models from the pre-processed signals by curve-fitting pole/zero models to the cepstra, and applying compensation for equalisation and scaling.The paper describes the history, current situation and potential future development of the application of cepstral analysis to structural modal analysis, this seemingly being greatly under-utilised.
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