Uncertainty law in ambient modal identification---Part II: Implication and field verification

This paper presents a qualitative analysis of the uncertainty laws for the modal parameters identified in a Bayesian approach using ambient vibration data, based on the theory developed in the companion paper. The uncertainty laws are also appraised using field test data. The paper intends to provide insights for planning ambient vibration tests and managing the uncertainties of the identified modal parameters. Some typical questions that shall be addressed are: to estimate the damping ratio to within 30% of posterior coefficient of variation (c.o.v), what is the minimum data duration? Will deploying an additional accelerometer significantly improve the accuracy in damping (or frequency)? Answers to these questions based on this work can be found in the Conclusions. As the Bayesian approach allows full use of information in the data for given modeling assumptions, the uncertainty laws obtained in this work represent the lower limit of uncertainty (estimation error) that can be achieved by any method (Bayesian or non-Bayesian)

Uncertainty law in ambient modal identification. Part I: theory

Ambient vibration test has gained increasing popularity in practice as it provides an economical means for modal identification without artificial loading. Since the signal-to-noise ratio cannot be directly controlled, the uncertainty associated with the identified modal parameters is a primary concern. From a scientific point of view, it is of interest to know on what factors the uncertainty depends and what the relationship is. For planning or specification purposes, it is desirable to have an assessment of the test configuration required to achieve a specified accuracy in the modal parameters. For example, what is the minimum data duration to achieve a 30% coefficient of variation (c.o.v.) in the damping ratio? To address these questions, this work investigates the leading order behavior of the ‘posterior uncertainties’ (i.e., given data) of the modal parameters in a Bayesian identification framework. In the context of well-separated modes, small damping and sufficient data, it is shown rigorously that, among other results, the posterior c.o.v. of the natural frequency and damping ratio are asymptotically equal to and , respectively; where is the damping ratio; is the data length as a multiple of the natural period; and are data length factors that depend only on the bandwidth utilized for identification, for which explicit expressions have been derived. As the Bayesian approach allows full use of information contained in the data, the results are fundamental characteristics of the ambient modal identification problem. This paper develops the main theory. The companion paper investigates the implication of the results and verification with field test data

Asymptotic identification uncertainty of close modes in Bayesian operational modal analysis

This is the final version. Available on open access from Elsevier via the DOI in this recordClose modes are not typical subjects in operational modal analysis (OMA) but they do occur in structures with modes of similar dynamic properties such as tall buildings and towers. Compared to well-separated modes they are much more challenging to identify and results can have significantly higher uncertainty especially in the mode shapes. There are algorithms for identification (ID) and uncertainty calculation but the value itself does not offer any insight on ID uncertainty, which is necessary for its management in ambient test planning. Following a Bayesian approach, this work investigates analytically the ID uncertainty of close modes under asymptotic conditions of long data and high signal-to-noise ratio, which are nevertheless typical in applications. Asymptotic expressions for the Fisher Information Matrix (FIM), whose inverse gives the asymptotic ‘posterior’ (i.e., given data) covariance matrix of modal parameters, are derived explicitly in terms of governing dynamic properties. By investigating analytically the eigenvalue properties of FIM, we show that mode shape uncertainty occurs in two characteristic types of mutually uncorrelated principal directions, one perpendicular (Type 1) and one within the ‘mode shape subspace’ spanned by the mode shapes (Type 2). Uncertainty of Type 1 was found previously in well-separated modes. It is uncorrelated from other modal parameters (e.g., frequency and damping), diminishes with increased data quality and is negligible in applications. Uncertainty of Type 2 is a new discovery unique to close modes. It is potentially correlated with all modal parameters and does not vanish even for noiseless data. It reveals the intrinsic complexity and governs the achievable precision limit of OMA with close modes. Theoretical findings are verified numerically and applied with field data. This work has not reached the ultimate goal of ‘uncertainty law’, i.e., explicitly relating ID uncertainty to test configuration for understanding and test planning, but the analytical expressions of FIM and understanding about its eigenvalue properties shed light on possibility and provide the pathway to it.Engineering and Physical Sciences Research Council (EPSRC

Bayesian modal identification method based on general coherence model for asynchronous ambient data

© 2019 Elsevier Ltd A Bayesian frequency domain method for modal identification using asynchronous ambient data has been proposed previously. It provides a flexible and economical way to conduct ambient vibration tests as time synchronisation among data channels is not required. To simplify computation, zero coherence among synchronous data groups is assumed in the method, which inevitably introduces modelling error and lacks the ability of quantifying the synchronisation degree among different groups. To address these issues, a Bayesian modal identification method with a general coherence assumption among synchronisation groups is proposed in this paper. Computational difficulties are addressed and an efficient algorithm for determining the most probable values of modal properties is proposed. Synthetic and laboratory data examples are presented to validate the proposed method. It is also applied to modal identification of a full-scale ambient test, which illustrates the feasibility of the proposed method to real asynchronous data under field test configurations. For the cases investigated the proposed method does not lead to significant improvement in the identification accuracy of modal parameters compared to the method with zero coherence assumption. This is consistent with previous experience regarding the robustness of the zero coherence assumption and is now verified in this work. One may use the latter in practice for computational efficiency if the synchronisation degree among different groups is not demanded

Protective Relay Studies for the Nigerian National Electric 330 KV Transmission System

An indepth study and analysis has been performed on the 330KV transmission protective relay schemes of the National Electric Power Authority. Some of the basic considerations taken into account in the study to optimize the settings on the existing protective relay schemes are presented. Typical calculations are performed to illustrate the guidelines enumerated in the setting philosophy. These settings as calculated are presented and major defects existing in the protective schemes pointed out. The fundamental reasons for requiring these specific protective relaying features are also reviewed. Other protective relaying schemes that can accomplish the same basic protection objectives are presented. Based on the Nigerian special system characteristics, schemes to correct existing protection inadequacies are recommended

Quantifying and managing uncertainty in operational modal analysis

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Operational modal analysis aims at identifying the modal properties (natural frequency, damping, etc.) of a structure using only the (output) vibration response measured under ambient conditions. Highly economical and feasible, it is becoming a common practice in full-scale vibration testing. In the absence of (input) loading information, however, the modal properties have significantly higher uncertainty than their counterparts identified from free or forced vibration (known input) tests. Mastering the relationship between identification uncertainty and test configuration is of great interest to both scientists and engineers, e.g., for achievable precision limits and test planning/budgeting. Addressing this challenge beyond the current state-of-the-art that are mostly concerned with identification algorithms, this work obtains closed form analytical expressions for the identification uncertainty (variance) of modal parameters that fundamentally explains the effect of test configuration. Collectively referred as ‘uncertainty laws’, these expressions are asymptotically correct for well-separated modes, small damping and long data; and are applicable under non-asymptotic situations. They provide a scientific basis for planning and standardization of ambient vibration tests, where factors such as channel noise, sensor number and location can be quantitatively accounted for. The work is reported comprehensively with verification through synthetic and experimental data (laboratory and field), scientific implications and practical guidelines for planning ambient vibration tests.This work is funded by the UK Engineering and Physical Sciences Research Council (EP/N017897/1 & EP/N017803/1). The support is gratefully acknowledged

Derivative chromosome 9 deletions in chronic myeloid leukaemia: Interpretation of atypical D-FISH pattern

Background/Aims: New molecular cytogenetic techniques are increasingly applied as a routine investigative tool in haematological malignancies, both at diagnosis and subsequent monitoring. This report describes the interpretation of atypical signal patterns encountered using BCR-ABL dual colour dual fusion fluorescence in situ hybridisation (D-FISH) translocation probes in chronic myeloid leukaemia (CML). Methods: Interphase FISH experiments were carried out using BCR-ABL D-FISH probes in 46 patients with CML at diagnosis and during subsequent disease monitoring. Atypical hybridisation signal patterns were characterised by molecular cytogenetic techniques and correlated with conventional karyotyping. Results: Two patients showed atypical interphase D-FISH patterns with one orange, one green, and one fusion (1O1G1F) signal. The presence of BCR-ABL gene fusion was documented by a dual colour single fusion (S-FISH) probe. The submicroscopic deletion of the ABL-BCR fusion gene on the derivative chromosome 9 in these cases was subsequently characterised by metaphase FISH on relocated G banded metaphases. Conclusions: Atypical interphase D-FISH patterns should not be interpreted in isolation and should be considered in conjunction with other cytogenetic or molecular genetic investigations.published_or_final_versio

Optimised ambient vibration testing of long span bridges

Eurodyn 2017, 2017-09-10 - 2017-09-13, Rome,This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.Vibration testing of long span bridges is becoming a commissioning requirement. Long span bridges represent the extreme end of experimental capability, with challenges for logistics and access (due to length and location), instrumentation (due to frequency range, resolution and physical separation of accelerometers) and system identification (because of the extreme low frequencies). Similar challenges apply to other extreme structures such as tall buildings, masts, offshore lighthouses and extended geotechnical structures stretching technology requirements for both instrumentation and signal interpretation. A solution for instrumentation is autonomous ‘wireless’ recorders. The problem with signal interpretation is the reliability of the modal parameter estimates that is particularly challenged with low frequency modes, which ‘third generation’ operational modal analysis procedures offer using Bayesian approaches. The paper describes a preliminary exercise combining both these technologies in readiness for testing two very large bridges, one in China and one in Scotland.The research was funded by EPSRC grant EP/N017897/1 and EP/N01780

An expectation-maximization algorithm for Bayesian operational modal analysis with multiple (possibly close) modes

© 2019 Elsevier Ltd The Bayesian FFT method has gained attention in operational modal analysis of civil engineering structures. Not only the most probable value (MPV) of modal parameters can be computed efficiently, but also the identification uncertainty can be rigorously quantified in terms of posterior covariance matrix. A recently developed fast algorithm for general multiple (possibly close) modes was found to work well in most cases, but convergence could be slow or even fail in challenging situations. The algorithm is also tedious to computer-code. Aiming at resolving these issues, an expectation-maximization (EM) algorithm is developed by viewing the modal response as a latent variable. The parameter-expansion EM and the parabolic-extrapolation EM are further adopted, allowing mode shape norm constraints to be incorporated and accelerating convergence, respectively. A robust implementation is provided based on the QR and Cholesky decompositions, so that the computation can be done efficiently and reliably. Empirical studies verify the performance of the proposed EM algorithm. It offers a more efficient and robust (in terms of convergence) alternative that can be especially useful when the existing algorithm has difficulty to converge. In addition, it opens a way to compute the MPV in the Bayesian FFT method for other unexplored cases, e.g., multi-mode multi-setup problem