Modal identification using optimization approach.

In this thesis, the modal identification problem is pursued using two different optimization approaches. The first approach is a deterministic optimization approach that minimizes the output model error in the time domain between a direct solution using the modal model and the measured response. Examples of single-input single-output identification are used to illustrate this method; it has been shown this approach is robust against noise and can be used to fine-tune the modal parameter, especially for the damping. The second approach is based on probabilistic optimization; the objective function is defined as the a posteriori probabilistic density of the parameters given observations/measurements. The conditional probability density is computed using the Bayesian theory of minimum-mean-square-error estimation. Examples of single-output under ambient excitation are simulated to demonstrate this approach. This methodology allows one to obtain not only the estimated parameters in the form of probabilistic mean but also the uncertainties in the form of covariance. The optimization approaches works though the minimization of an objective function which can be calculated from given set of modal/model parameters. Since there is no gradient or Hessian available for the objective functions defined in this thesis, two direct optimization methods: Nelder-Mead simplex and the Genetic Algorithm are adopted to search the minimum of defined objective functions and thus find the structural parameters. (Abstract shortened by UMI.)Dept. of Civil and Environmental Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2005 .L52. Source: Masters Abstracts International, Volume: 44-03, page: 1437. Thesis (M.A.Sc.)--University of Windsor (Canada), 2005

Operational modal analysis and continuous dynamic monitoring of footbridges

Tese de doutoramento. Engenharia Civil. Universidade do Porto. Faculdade de Engenharia. 201

Comparative review of methods for stability monitoring in electrical power systems and vibrating structures

This study provides a review of methods used for stability monitoring in two different fields, electrical power systems and vibration analysis, with the aim of increasing awareness of and highlighting opportunities for cross-fertilisation. The nature of the problems that require stability monitoring in both fields are discussed here as well as the approaches that have been taken. The review of power systems methods is presented in two parts: methods for ambient or normal operation and methods for transient or post-fault operation. Similarly, the review of methods for vibration analysis is presented in two parts: methods for stationary or linear time-invariant data and methods for non-stationary or non-linear time-variant data. Some observations and comments are made regarding methods that have already been applied in both fields including recommendations for the use of different sets of algorithms that have not been utilised to date. Additionally, methods that have been applied to vibration analysis and have potential for power systems stability monitoring are discussed and recommended. � 2010 The Institution of Engineering and Technology

Operational modal analysis - Theory and aspects of application in civil engineering

In recent years the demand on dynamic analyses of existing structures in civil engineering has remarkably increased. These analyses are mainly based on numerical models. Accordingly, the generated results depend on the quality of the used models. Therefore it is very important that the models describe the considered systems such that the behaviour of the physical structure is realistically represented. As any model is based on assumptions, there is always a certain degree of uncertainty present in the results of a simulation based on the respective numerical model. To minimise these uncertainties in the prediction of the response of a structure to a certain loading, it has become common practice to update or calibrate the parameters of a numerical model based on observations of the structural behaviour of the respective existing system. The determination of the behaviour of an existing structure requires experimental investigations. If the numerical analyses concern the dynamic response of a structure it is sensible to direct the experimental investigations towards the identification of the dynamic structural behaviour which is determined by the modal parameters of the system. In consequence, several methods for the experimental identification of modal parameters have been developed since the 1980ies. Due to various technical restraints in civil engineering which limit the possibilities to excitate a structure with economically reasonable effort, several methods have been developed that allow a modal identification form tests with an ambient excitation. The approach of identifying modal parameters only from measurements of the structural response without precise knowledge of the excitation is known as output-only or operational modal analysis. Since operational modal analysis (OMA) can be considered as a link between numerical modelling and simulation on the one hand and the dynamic behaviour of an existing structure on the other hand, the respective algorithms connect both the concepts of structural dynamics and mathematical tools applied within the processing of experimental data. Accordingly, the related theoretical topics are revised after an introduction into the topic. Several OMA methods have been developed over the last decades. The most established algorithms are presented here and their application is illustrated by means of both a small numerical and an experimental example. Since experimentally obtained results always underly manifold influences, an appropriate postprocessing of the results is necessary for a respective quality assessment. This quality assessment does not only require respective indicators but should also include the quantification of uncertainties. One special feature in modal testing is that it is common to instrument the structure in different sensor setups to improve the spacial resolution of identified mode shapes. The modal information identified from tests in several setups needs to be merged a posteriori. Algorithms to cope with this problem are also presented. Due to the fact that the amount of data generated in modal tests can become very large, manual processing can become extremely expensive or even impossible, for example in the case of a long-term continuous structural monitoring. In these situations an automated analysis and postprocessing are essential. Descriptions of respective methodologies are therefore also included in this work. Every structural system in civil engineering is unique and so also every identification of modal parameters has its specific challenges. Some aspects that can be faced in practical applications of operational modal analysis are presented and discussed in a chapter that is dedicated specific problems that an analyst may have to overcome. Case studies of systems with very close modes, with limited accessibility as well as the application of different OMA methods are described and discussed. In this context the focus is put on several types of uncertainty that may occur in the multiple stages of an operational modal analysis. In literature only very specific uncertainties at certain stages of the analysis are addressed. Here, the topic of uncertainties has been considered in a broader sense and approaches for treating respective problems are suggested. Eventually, it is concluded that the methodologies of operatinal modal analysis and related technical solutions have been well-engineered already. However, as in any discipline that includes experiments, a certain degree of uncertainty always remains in the results. From these conclusions has been derived a demand for further research and development that should be directed towards the minimisation of these uncertainties and to a respective optimisation of the steps and corresponding parameters included in an operational modal analysis

Operational modal analysis and prediction of remaining useful life for rotating machinery

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonThe significance of rotating machinery spans areas from household items to vital industry sectors, such as aerospace, automotive, railway, sea transport, resource extraction, and manufacturing. Hence, our technologised society depends on efficient and reliable operation of rotating machinery. To contribute to this aim, this thesis leverages measurable quantities during its operation for structural-mechanical evaluation employing Operational Modal Analysis (OMA) and the prediction of Remaining Useful Life (RUL). Modal parameters determined by OMA are central for the design, test, and validation of rotating machinery. This thesis introduces the first open parametric simulation dataset of rotating machinery during an acceleration run. As there is a lack of similar open datasets suitable for OMA, it lays a foundation for improved reproducibility and comparability of future research. Based on this, the Averaged Order-Based Modal Analysis (AOBMA) method is developed. The novel addition of scaling and weighted averaging of individual machine orders in AOBMA alleviates the analysis effort of the existing Order-Based Modal Analysis (OBMA) method by providing a unified set of modal parameters with higher accuracy. As such, AOBMA showed a lower mean absolute relative error of 0.03 for damping ratio estimations across compared modes while OBMA provided an error value of 0.32 depending on the processed order. At excitation with high harmonic contributions, AOBMA also resulted in the highest number of accurately identified modes among the compared methods. At a harmonic ratio of 0.8, for example, AOBMA identified an average of 11.9 modes per estimation, while OBMA and baseline OMA followed with 9.5 and 9 modes, respectively. Moreover, it is the first study, which systematically evaluates the impact of excitation conditions on the compared methods and finds an advantage of OBMA and AOBMA over traditional OMA regarding mode shape estimation accuracy. While OMA can be used to evaluate significant structural changes, Machine Learning (ML) methods have seen substantially greater success in condition monitoring, including RUL prediction. However, as these methods often require large amounts of time and cost- intensive training data, a novel data-efficient RUL prediction methodology is introduced, taking advantage of distinct healthy and faulty condition data. When the number of training sequences from an open dataset is reduced to 5%, an average prediction Root Mean Square Error (RMSE) of 24.9 operation cycles is achieved, outperforming the baseline method with an RMSE of 28.1. Motivated by environmental considerations, the impact of data reduction on the training duration of several method variants is quantified. When the full training set is utilised, the most resource-saving variant of the proposed approach achieves an average training duration of 8.9% compared to the baseline method

On the Sample Complexity of Multichannel Frequency Estimation via Convex Optimization

The use of multichannel data in line spectral estimation (or frequency estimation) is common for improving the estimation accuracy in array processing, structural health monitoring, wireless communications, and more. Recently proposed atomic norm methods have attracted considerable attention due to their provable superiority in accuracy, flexibility and robustness compared with conventional approaches. In this paper, we analyze atomic norm minimization for multichannel frequency estimation from noiseless compressive data, showing that the sample size per channel that ensures exact estimation decreases with the increase of the number of channels under mild conditions. In particular, given $L$ channels, order $K\left(\log K\right) \left(1+\frac{1}{L}\log N\right)$ samples per channel, selected randomly from $N$ equispaced samples, suffice to ensure with high probability exact estimation of $K$ frequencies that are normalized and mutually separated by at least $\frac{4}{N}$. Numerical results are provided corroborating our analysis.Comment: 14 pages, double column, to appear in IEEE Trans. Information Theor

Damage Detection in Largely Unobserved Structures under Varying Environmental Conditions: An AutoRegressive Spectrum and Multi-Level Machine Learning Methodology

Vibration-based damage detection in civil structures using data-driven methods requires sufficient vibration responses acquired with a sensor network. Due to technical and economic reasons, it is not always possible to deploy a large number of sensors. This limitation may lead to partial information being handled for damage detection purposes, under environmental variability. To address this challenge, this article proposes an innovative multi-level machine learning method by employing the autoregressive spectrum as the main damage-sensitive feature. The proposed method consists of three levels: (i) distance calculation by the log-spectral distance, to increase damage detectability and generate distance-based training and test samples; (ii) feature normalization by an improved factor analysis, to remove environmental variations; and (iii) decision-making for damage localization by means of the Jensen-Shannon divergence. The major contributions of this research are represented by the development of the aforementioned multi-level machine learning method, and by the proposal of the new factor analysis for feature normalization. Limited vibration datasets relevant to a truss structure and consisting of acceleration time histories induced by shaker excitation in a passive system, have been used to validate the proposed method and to compare it with alternate, state-of-the-art strategies