Uncertainty Quantification and Management in Ambient Modal Identification

Lead Research Organisation: University of Liverpool
Department Name: Civil Engineering and Industrial Design


The modal properties of a structure include primarily its natural frequencies, damping ratios and mode shapes. Their information is indispensable for design against dynamic loads such as wind, earthquake and human excitation. Uncertainty arises due to the lack of knowledge and modelling limitations and this generally increases project risk. Modal identification has long been recognised as an effective means for uncertainty mitigation in structural dynamics. Theoretically it is possible to identify the modal properties based on only the 'output' vibration response of structures without knowing the 'input' excitation. This type of test, called 'ambient vibration test', has now become the primary and most sustainable means for its high implementation feasibility, robustness and economy. In the absence of loading information and with data collected under uncontrolled field environment, however, the identification results have significant variability and low repeatability. This has limited the economic benefit of ambient vibration tests and undermined the scientific significance of their identification results. This has been well-recognised but there has been no quantitative account for its origin or how to control it.

This project aims at developing a comprehensive fundamental methodology for quantifying and managing the uncertainties of the modal properties of civil engineering structures identified from ambient vibration data. At the scientific core is a set of 'uncertainty laws', analogous to the laws of large numbers of data in classical probability, that expresses fundamentally the identification uncertainty of modal properties explicitly and quantitatively in terms of test configurations such as measurement noise, environmental load intensity and the number and location of sensors. Due to complexity of the problem, it is unlikely to obtain insightful results for general situations. The project aims at fundamental expressions with insights governing the dominant behaviour of the remaining identification uncertainty under realistic situations. The project objective is achieved through a comprehensive programme comprising fundamental theory development, extensive verification with synthetic, laboratory and field data, and knowledge transfer with industry. A practical guide for planning and performing ambient vibration test shall be produced incorporating scientific findings of the project and experience of the team members with input from industry partners.

Planned Impact

The beneficiaries of this project are instrumentation consultants and vibration specialists (better field tests), structural design consultants (better design) and infrastructure owners (better structures and utilisation of health monitoring resources).

1. Improving field test quality and economy. The project leads to scientific guidance for planning and performing ambient vibration tests. This will improve the competitiveness of instrumentation contractors and vibration specialists in bidding and carrying out projects. Consultants with access to this expertise will be able to improve performance-based vibration serviceability design of tall buildings, long span bridges, stadia, etc. Currently field tests are planned and budgeted primarily based on experience. Low data quality directly translates into poor identification results and remedial measures (e.g. retesting) are costly or impossible. Over-conservatism on the other hand impairs project economy.

2. Better sensor utilisation. Sensors used in the aerospace/automotive industry under laboratory environment do not necessarily perform well in ambient vibration test of civil structures. It is commonly accepted that servo-accelerometers (originally used in seismic applications) consistently out-perform miniature piezoelectric/capacitive sensors (common in laboratory) in field tests, although the former tend to be heavier and more expensive. It is premature to exclude the latter, however, as recent progress in MEMS technology has revealed the opportunity for light-weight sensors with improving quality. The scientific account of sensor quality and configuration on identification precision in the project shall allow one to make suitable use of the whole spectrum of sensors, from low-cost MEMS sensors on smart phones to state-of-the-art servo-accelerometers.

3. Better efficiency in tall building design. The project resolves the precision and hence improves the scientific significance of modal identification results. This will have a positive impact on many application areas currently challenged by questionable identification precision. Tall building design is an example of frontier technological and high economic relevance. Governed by wind effects, multi-fold increase in design forces can result due to dynamic amplification, which is inversely proportional to structural damping. There is currently no accepted method for predicting damping. Values used in design are based on rule of thumb or historical databases derived from old generation estimation methods having questionable reliability. Uncertainty in damping directly carries over to design forces and hence a risk premium in the structural cost and reduced floor area (e.g. due to over-sized columns) when the only prudent choice is a conservative damping estimate. Field data abound but identified damping values show big scatter with low repeatability and there is a lack of information or understanding about their uncertainty. This project shall resolve the identification precision, in the long run contributing to establishing an engineering model for predicting damping in tall buildings.

4. Wind tunnel tests allow realistic estimation of wind load based on scaled-down models/terrains and they are regularly performed for tall building and long bridge designs. Aeroelastic models are recent advance that allow aerodynamic damping to be investigated, although they are more expensive than conventional high-frequency base-balance model tests. Aerodynamic damping values are identified under turbulent wind conditions and so they are subjected to the same uncertainty in ambient vibration tests. The project shall contribute to the advance of aeroelastic model tests by improving their planning, identification precision and enhancing their scientific value.


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Adamson L (2020) Receptance-based robust eigenstructure assignment in Mechanical Systems and Signal Processing

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Adamson L (2019) Pole placement in uncertain dynamic systems by variance minimisation in Mechanical Systems and Signal Processing

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Au S (2016) Model validity and frequency band selection in operational modal analysis in Mechanical Systems and Signal Processing

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Au S (2018) Posterior uncertainty, asymptotic law and Cramér-Rao bound in Structural Control and Health Monitoring

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Au S (2017) Calculation of Hessian under constraints with applications to Bayesian system identification in Computer Methods in Applied Mechanics and Engineering

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Au S (2018) Quantifying and managing uncertainty in operational modal analysis in Mechanical Systems and Signal Processing

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Brownjohn J (2018) Bayesian operational modal analysis of Jiangyin Yangtze River Bridge in Mechanical Systems and Signal Processing

Description As one of the key objectives of the project, a Bayesian probabilistic theory with an explicit formula has been developed that fundamentally relates the identification uncertainty of modal properties of well-separated modes to test configuration in an ambient vibration environment. Based on this, a method has been developed to allow the identification uncertainty in ambient vibration tests to be quantitatively managed, where factors such as data length, sensor quality and quantity can be assessed. This will allow practitioners to plan/budget ambient test campaigns in a risk-informed manner and improve efficiency by removing unnecessary conservatism previously applied due to lack of understanding of uncertainty. The method is being applied to test planning of full-scale structures (e.g., the Jiangyin Bridge in China, offshore lighthouses in UK, footbridge in Knowsley) and understanding their uncertainties.

A method has also been developed that allows sensor noise to be calibrated without precise alignment that is required by existing methods. In addition to improving the accuracy of calibration results and safe-guarding them from bias due to potential misalignment, this allows noise calibration tests to be conveniently and robustly performed in the laboratory as well as field environment.
Exploitation Route The methods and findings in the project will allow practitioners to plan/budget ambient test campaigns in a risk-informed manner and improve efficiency by removing unnecessary conservatism previously applied due to lack of understanding of uncertainty.
Sectors Aerospace, Defence and Marine,Construction,Energy

Title A new model and a Bayesian OMA method for stochastic asynchronous ambient vibration data 
Description A model has been proposed for stochastic ambient vibration data where different channels are 'asynchronous', i.e., not perfectly synchronised. Traditional models assume perfectly synchronised channels and lead to erroneous results with asynchronous data that can been encountered in practice. The proposed model allow the spectral characteristics of asynchronous data to be derived. Based on this model, a Bayesian method has been developed for modal identification using asynchronous ambient vibration data. 
Type Of Material Computer model/algorithm 
Year Produced 2017 
Provided To Others? Yes  
Impact The model and the OMA method have just been published in scholarly journals (Structural Control & Health Monitoring and Mechanical Systems & Signal Processing, respectively). Their impact has yet to be seen. As an example of potential impact, they allow modal identification to be performed using acceleration data measured on the MEMS of multiple smart phones without special provision for synchronisation. This lowers the overhead for obtaining in-situ property of civil engineering structures. 
Title Instrument noise calibration method for arbitrary sensor orientations 
Description A method has been developed for determining the instrument noise of sensors. While existing methods require precise alignment of sensor orientations, the proposed method is applicable for arbitrary sensor orientations. This allows sensor noise to be calibrated in a robust and accurate manner compared to existing methods that require precise orientation or else results will be biased. 
Type Of Material Data analysis technique 
Year Produced 2019 
Provided To Others? Yes  
Impact The method have just been published in scholarly journals (Mechanical Systems and Signal Processing). The impact has yet to be seen. As an example of potential impact, it eliminates the bias due to sensor misalignment during laboratory calibration that is often performed by researchers or sensor manufacturers. Not requiring precise orientation also means sensors can be calibrated much faster in the field environment. 
Description Research collaboration with Tongji 
Organisation Tongji University
Country China 
Sector Academic/University 
PI Contribution Various visits leading to visiting position, joint outputs, student exchange and proposal with China funding agency
Collaborator Contribution Various visits leading to visiting position, joint outputs, student exchange and proposal with China funding agency
Impact Two papers being written
Start Year 2014
Description Research collaboration with Waseda University (Japan) 
Organisation Waseda University
Department Department of Civil and Environmental Engineering
PI Contribution Operational modal analysis of RC columns subjected to different levels of damage
Collaborator Contribution Formulation of problem context, laboratory experiments, expertise in reinforced concrete
Impact No output yet
Start Year 2017
Description Summer School on Structural Vibrations and Testing 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Postgraduate students
Results and Impact A one-week Summer School on Structural Vibrations and Testing was held during 30 Jul - 3 Aug 2018. The school aims at disseminating basic concepts in structural vibrations, their relevance as well as the latest advance in field testing that allows cost-effective uncertainty mitigation and management. The event attracted undergraduate and postgraduate students from University College London the Universities of Exeter, Oxford, Liverpool, Aberdeen and Warwick, as well as an industry visitor from WSP Parsons Brinckerhoff. The course covered structures with single and multi-degrees of freedom, stochastic process and stochastic structural dynamics, power spectral density estimation, vibration testing and experimental modal analysis. As well as theoretical sessions, students carried out experimental modal analysis in the state of the art structures lab at the University of Exeter, which prepared them for a modal test of Baker Bridge at Sandy Park. The summer school has given participants both an important theoretical grounding, and some practical experience on vibrations and how to perform field tests and make use of the information produced.
Year(s) Of Engagement Activity 2018
URL https://veswordpresscom.wordpress.com/2018/08/06/students-from-all-over-the-uk-attend-structural-vib...