Optimal experimental design in structural dynamics.

Theoretical and computational issues arising in experimental design for model identification and parameter estimation in structural dynamics are addressed. The objective is to optimally locate sensors in a structure such that the resulting measured data are most informative for estimating the parameters of a family of mathematical model classes used for structural modeling. The information entropy, measuring the uncertainty in the parameters of a structural model class, is used as a performance measure of a sensor configuration. For a single model class, the optimal sensor location problem is formulated as an information entropy minimization problem. For model class selection and/or damage detection applications, the problem is formulated as a multi-objective optimization problem of finding the Pareto optimal sensor configurations that simultaneously minimize appropriately defined information entropy indices related to multiple model classes and/or probable damage scenarios. Asymptotic estimates for the information entropy, valid for large number of measured data, are presented that rigorously justify that the selection of the optimal experimental design can be based solely on the nominal structural model from a class, ignoring the details of the measured data that are not available in the experimental design stage. The effect of the measurement and model prediction error variances on the optimal sensor location design is examined. Finally, heuristic algorithms are proposed for constructing effective sensor configurations that are superior, in terms of accuracy and computational efficiency, to the sensor configurations provided by genetic algorithms

Structural model updating using vibration measurements

A multi-objective optimization framework is presented for updating finite element models of structures based on vibration measurements. The method results in multiple Pareto optimal structural models that are consistent with the measured data and the residuals used to measure the discrepancies between the measured and the finite element model predicted characteristics. The relation between the multi-objective identification method, Bayesian in-ference method, and conventional single-objective weighted residuals methods for model up-dating is discussed. Computational algorithms for the efficient and reliable solution of the resulting optimization problems are presented. The algorithms are classified to gradient-based, evolutionary strategies and hybrid techniques. In particular, efficient algorithms are introduced for reducing the computational cost involved in estimating the gradients of the ob-jective functions representing the modal residuals. Specifically, a formulation requiring the solution of the adjoint problem is presented, avoiding the explicit estimation of the gradients of the modal characteristics. The adjoint method is also extended to carry out efficiently the estimation of the Hessian of the objective function. The computational cost for estimating the gradients and Hessian is shown to be independent of the number of structural model parame-ters. The methodology is particularly efficient to system with several number of model param-eters and large number of DOFs where repeated gradient and Hessian evaluations are computationally time consuming. Component mode synthesis methods dividing the structure to linear substructural components with fixed properties and linear substructural components with uncertain properties are incorporated into the methodology to further reduce the compu-tational effort required in optimization problems. The linear substructures with fixed proper-ties are represented by their lower contributing modes which remain unchanged during the model updating process. The method is particular effective for finite element models with large number of DOF and for parameter estimation in localized areas of a structure. Theoret-ical and computational developments are illustrated by updating finite element models of a laboratory building using impact hammer measurements and multi-span reinforced concrete bridges using ambient vibration measurements

Finite element model updating of an experimental vehicle model using measured modal characteristics

Methods for modal identification and structural model updating are employed to develop high fidelity finite element models of an experimental vehicle model using acceleration measurements. The identification of modal characteristics of the vehicle is based on ac-celeration time histories obtained from impulse hammer tests. An available modal identification software is used to obtain the modal characteristics from the analysis of the various sets of vibration measurements. A high modal density modal model is obtained. The modal characteristics are then used to update an increasingly complex set of finite element models of the vehicle. A multi-objective structural identification method is used for estimating the parameters of the finite element structural models based on minimizing the modal residu-als. The method results in multiple Pareto optimal structural models that are consistent with the measured modal data and the modal residuals used to measure the discrepancies between the measured modal values and the modal values predicted by the model. Single objective structural identification methods are also evaluated as special cases of the proposed multi-objective identification method. The multi-objective framework and the corresponding compu-tational tools provide the whole spectrum of optimal models and can thus be viewed as a gen-eralization of the available conventional methods. The results indicate that there is wide variety of Pareto optimal structural models that trade off the fit in various measured quanti-ties. These Pareto optimal models are due to uncertainties arising from model and measure-ment errors. The size of the observed variations depends on the information contained in the measured data, as well as the size of model and measurement errors. The effectiveness of the updated models and the predictive capabilities of the Pareto vehicle models are assessed

Fatigue lifetime estimation in structures using ambient vibration measurements

A methodology is proposed for estimating damage accumulation due to fatigue in the entire body of a metallic structure using output-only vibration measurements from a sensor network installed at a limited number of structural locations. Available frequency domain stochastic fatigue methods based on Miner’s damage rule, S-N fatigue cycle curves and Dirlik’s probability distribution of the stress range are used to predict the expected fatigue accumulation of the structure in terms of the power spectral density of the stress processes. In predicting the damage and fatigue lifetime, it is assumed that the unmeasured excitations can be modeled by stationary stochastic processes. The power spectral densities of stresses at unmeasured locations are estimated from the response time history measurements available at the limited measured locations using Kalman filter and a model of the structure. The proposed formulation is demonstrated using a MDOF spring-mass chain model arising from structures that consist of members with uniaxial stress states

Identification of dynamic models of Metsovo (Greece) Bridge using ambient vibration measurements

Available methods for structural model updating are employed to develop high fidelity models of the Metsovo bridge using ambient vibration measurements. The Metsovo bridge, the highest bridge of the Egnatia Odos Motorway, is a two-branch balanced cantilever ravine bridge. It has a total length of 357m, a very long central span of 235m, and a height of 110m for the taller pier. Ambient vibration measurements are available during different construction phases of the bridge for both bridge branches, as well as after the completed construction phases of the bridge. Operational modal analysis software is used to obtain the modal characteristics of the bridge for the various sets of vibration measurements. The modal characteristics are then used to update an increasingly complex set of finite element models of the bridge. These models are based on beam and solid elements. A multi-objective structural identification method is used for estimating the parameters of the finite element structural models based on minimising the modal residuals. The method results in multiple Pareto optimal structural models that are consistent with the measured modal data and the modal residuals used to measure the discrepancies between the measured modal values and the modal values predicted by the model. Single objective structural identification methods are also evaluated as special cases of the proposed multi-objective identification method. The effectiveness of the updated models and their predictive capabilities are assessed. In particular, the variability of the Pareto optimal models and their associated response prediction variability are explored. It is demonstrated that the Pareto optimal structural models may vary, depending on the fidelity of the model class employed and the size of measurement errors. The developed high fidelity finite element models are used for checking design assumptions and for carrying out more accurate predictions of structural response

Bridge monitoring system based on vibration measurements

This work outlines the main algorithms involved in a proposed bridge monitoring system based on ambient and earthquake vibration measurements. The monitoring system can be used to predict the existence, location and size of structural modifications in the bridge by monitoring the changes in the modal characteristics and updating the finite element model of the bridge based on the modal characteristics. Sophisticated system identification methods, combining information from a sensor network with the theoretical information built into a fi-nite element model for simulating structural behaviour, are incorporated into the monitoring system in order to track structural changes and identify the location, type and extent of these changes. Emphasis in this work is given on presenting theoretical and computational issues relating to structural modal identification and structural model updating methods. Specifical-ly, the proposed work outlines the algorithms and software that has been developed for com-puting the modal properties using ambient and earthquake data, as well as recent methodologies and software for finite element model updating using the modal characteristics. Various issues encountered in the optimization problems involved in model updating are demonstrated, including the existence of multiple local optima and the effects of weight values in conventional weighted modal residual methods for selecting the optimal finite element model. Selected features are demonstrated using vibration measurements from a four-span bridge of the Egnatia Odos motorway in Greece

Multi-objective optimization framework for finite element model updating and response prediction variability.

A multi-objective optimization framework based on modal data is presented for finite element model updating in structural dynamics. The framework results in multiple Pareto optimal structural models that are consistent with the measured data and the norms used for reconciling finite element models with data. Computationally efficient methods for estimating the gradients and Hessians of the objective functions with respect to the model parameters are proposed and shown to significantly reduce the computational effort for solving the single or multi-objective optimization problems. Theoretical and computational developments are addressed and demonstrated by updating the finite element model of a concrete bridge structure using modal data identified from ambient acceleration time history measurements. The results clearly indicate that there is wide variety of Pareto optimal structural models that trade off the fit in various measured quantities. The variability in Pareto models affect the variability in response predictions

Multi-Objective Optimisation Algorithms for Finite Element Model Updating.

<p>PhD Thesis.</p> <p>Submitted to the Department of Mechanical Engineering, University of Thessaly.</p> <p>Deffended December 2009.</p> <p>Division of Mechanics, Materials & Manufacturing Processes, System Dynamics Laboratory.</p> <p>In English.</p

Multi-objective framework for structural modeling consistent with data.

A generalized multi-objective framework for structural model updating is proposed and demonstrated using experimental data from a small scale laboratory structure. Multiple Pareto optimal structural models are obtained that are consistent with the measured data and the norms used for reconciling finite element models with data. The relation between the mul-ti-objective identification framework and conventional weighted residuals methods that mini-mize a weighted sum of the residuals between the structural model and the measured data is investigated. The Pareto models contain the optimal models obtained from conventional weighted residuals methods. Theoretical and computational issues involved in estimating the Pareto optimal models are addressed. Conventional methods use arbitrary assumptions to select a single optimal model among the multiple alternative ones. The proposed multi-objective framework and corresponding computational tools provide the whole spectrum of optimal models and can thus be viewed as a generalization of the available conventional methods. Multi-objective and conventional single-objective model updating methods are com-pared and their effectiveness is demonstrated using experimental results from a three-story laboratory structure. The results clearly indicate that there is wide variety of Pareto optimal structural models consistent with the measured data and the norms used for reconciling finite element models with data. It is shown that the response and reliability predictions from these data-consistent Pareto optimal models can vary considerably. The size of observed variations depends on the information contained in the measured data, as well as the size of model and measurement errors always present in structural modeling and data processing techniques

Data Driven, Predictive Molecular Dynamics for Nanoscale Flow Simulations under Uncertainty

For over five decades, molecular dynamics (MD) simulations have helped to elucidate critical mechanisms in a broad range of physiological systems and technological innovations. MD simulations are synergetic with experiments, relying on measurements to calibrate their parameters and probing “what if scenarios” for systems that are difficult to investigate experimentally. However, in certain systems, such as nanofluidics, the results of experiments and MD simulations differ by several orders of magnitude. This discrepancy may be attributed to the spatiotemporal scales and structural information accessible by experiments and simulations. Furthermore, MD simulations rely on parameters that are often calibrated semiempirically, while the effects of their computational implementation on their predictive capabilities have only been sporadically probed. In this work, we show that experimental and MD investigations can be consolidated through a rigorous uncertainty quantification framework. We employ a Bayesian probabilistic framework for large scale MD simulations of graphitic nanostructures in aqueous environments. We assess the uncertainties in the MD predictions for quantities of interest regarding wetting behavior and hydrophobicity. We focus on three representative systems: water wetting of graphene, the aggregation of fullerenes in aqueous solution, and the water transport across carbon nanotubes. We demonstrate that the dominant mode of calibrating MD potentials in nanoscale fluid mechanics, through single values of water contact angle on graphene, leads to large uncertainties and fallible quantitative predictions. We demonstrate that the use of additional experimental data reduces uncertainty, improves the predictive accuracy of MD models, and consolidates the results of experiments and simulations