Costas Papadimitriou

Entropy-Based Optimal Sensor Location for Structural Model Updating

A statistical methodology is presented for optimally locating the sensors in a structure for the purpose of extracting from the measured data the most information about the parameters of the model used to represent structural behavior. The methodology can be used in model updating and in damage detection and localization applications. It properly handles the unavoidable uncertainties in the measured data as well as the model uncertainties. The optimality criterion for the sensor locations is based on information entropy, which is a unique measure of the uncertainty in the model parameters. The uncertainty in these parameters is computed by a Bayesian statistical methodology, and then the entropy measure is minimized over the set of possible sensor configurations using a genetic algorithm. The information entropy measure is also extended to handle large uncertainties expected in the pretest nominal model of a structure. In experimental design, the proposed entropy-based measure of uncertainty is also well-suited for making quantitative evaluations and comparisons of the quality of the parameter estimates that can be achieved using sensor configurations with different numbers of sensors in each configuration. Simplified models for a shear building and a truss structure are used to illustrate the methodology.

Design Optimization of Quarter-car Models with Passive and Semi-active Suspensions under Random Road Excitation

A methodology is presented for optimizing the suspension damping and stiffness parameters of nonlinear quarter-car models subjected to random road excitation. The investigation starts with car models involving passive damping with constant or dual-rate characteristics. Then, we also examine car models where the damping coefficient of the suspension is selected so that the resulting system approximates the performance of an active suspension system with sky-hook damping. For the models with semi-active or passive dual-rate dampers, the value of the equivalent suspension damping coefficient is a function of the relative velocity of the sprung mass with respect to the wheel subsystem. As a consequence, the resulting equations of motion are strongly nonlinear. For these models, appropriate methodologies are first employed for obtaining the second moment characteristics of motions resulting from roads with a random profile. This information is next utilized in the definition of a vehicle performance index, which is optimized to yield representative numerical results for the most important suspension parameters. Special attention is paid to investigating the effect of road quality as well as on examining effects related to wheel hop. Finally, a critical comparison is performed between the results obtained for vehicles with passive linear or bilinear suspension dampers and those obtained for cars with semi-active shock absorbers.

A probabilistic approach to structural model updating

The problem of updating a structural model and its associated uncertainties by utilizing measured dynamic response data is addressed. A Bayesian probabilistic formulation is followed to obtain the posterior probability density function (PDF) of the uncertain model parameters for given measured data. The present paper discusses the issue of identifiability of the model parameters and reviews existing asymptotic approximations for identifiable cases. The focus of the paper is on the treatment of the general unidentifiable case where the earlier approximations are not applicable. In this case the posterior PDF of the parameters is found to be concentrated in the neighborhood of an extended and extremely complex manifold in the parameter space. The computational difficulties associated with calculating the posterior PDF in such cases are discussed and an algorithm for an efficient approximate representation of the above manifold and the posterior PDF is presented. Numerical examples involving noisy data are presented to demonstrate the concepts and the proposed method.

Leakage detection in water pipe networks using a Bayesian probabilistic framework

A Bayesian system identification methodology is proposed for leakage detection in water pipe networks. The methodology properly handles the unavoidable uncertainties in measurement and modeling errors. Based on information from flow test data, it provides estimates of the most probable leakage events (magnitude and location of leakage) and the uncertainties in such estimates. The effectiveness of the proposed framework is illustrated by applying the leakage detection approach to a specific water pipe network. Several important issues are addressed, including the role of modeling error, measurement noise, leakage severity and sensor configuration (location and type of sensors) on the reliability of the leakage detection methodology. The present algorithm may be incorporated into an integrated maintenance network strategy plan based on computer-aided decision-making tools.

Bayesian uncertainty quantification and propagation in molecular dynamics simulations: A high performance computing framework

We present a Bayesian probabilistic framework for quantifying and propagating the uncertainties in the parameters of force fields employed in molecular dynamics (MD) simulations. We propose a highly parallel implementation of the transitional Markov chain Monte Carlo for populating the posterior probability distribution of the MD force-field parameters. Efficient scheduling algorithms are proposed to handle the MD model runs and to distribute the computations in clusters with heterogeneous architectures. Furthermore, adaptive surrogate models are proposed in order to reduce the computational cost associated with the large number of MD model runs. The effectiveness and computational efficiency of the proposed Bayesian framework is demonstrated in MD simulations of liquid and gaseous argon.

Reliability of uncertain dynamical systems with multiple design points

Asymptotic approximations and importance sampling methods are presented for evaluating a class of probability integrals with multiple design points that may arise in the calculation of the reliability of uncertain dynamical systems. An approximation based on asymptotics is used as a first step to provide a computationally efficient estimate of the probability integral. The importance sampling method utilizes information of the integrand at the design points to substantially accelerate the convergence of available importance sampling methods that use information from one design point only. Implementation issues related to the choice of importance sampling density and sample generation for reducing the variance of the estimate are addressed. The computational efficiency and improved accuracy of the proposed methods is demonstrated by investigating the reliability of structures equipped with a tuned mass damper for which multiple design points are shown to contribute significantly to the value of the reliability integral.

Multi-Criteria Optimal Structural Design Under Uncertainty

A general framework for multi-criteria optimal design is presented which is well suited for performance-based design of structural systems operating in an uncertain dynamic environment. A decision theoretic approach is used which is based on aggregation of preference functions for the multiple, possibly conflicting, design criteria. This allows the designer to trade off these criteria in a controlled manner during the optimization. Reliability-based design criteria are used to maintain user-specified levels of structural safety by properly taking into account the uncertainties in the modeling and seismic loads that a structure may experience during its lifetime. Code-based requirements are also easily incorporated into this optimal design process. The methodology is demonstrated with a simple example involving the design of a three-story steel-frame building for which the ground motion uncertainty is characterized by a probabilistic response spectrum which is developed from available attenuation formulas and seismic hazard models.

Optimal Sensor Placement Methodology for Identification with Unmeasured Excitation

A methodology is presented for designing cost-effective optimal sensor configurations for structural model updating and health monitoring purposes. The optimal sensor configuration is selected such that the resulting measured data are most informative about the condition of the structure. This selection is based on an information entropy measure of the uncertainty in the model parameter estimates obtained using a statistical system identification method. The methodology is developed for the uncertain excitation case encountered in practical applications for which data are to be taken either from ambient vibration tests or from other uncertain excitations such as earthquake and wind. Important issues related to robustness of the optimal sensor configuration to uncertainties in the structural model are addressed. The theoretical developments are illustrated by designing the optimal configuration for a simple 8-DOF chain-like model of a structure subjected to an unmeasured base excitation and a 40-DOF truss model subjected to wind/earthquake excitation. @DOI: 10.1115/1.1410929#

Fault Detection and Optimal Sensor Location in Vehicle Suspensions

A statistical system identification methodology is applied for performing parametric identification and fault detection studies in nonlinear vehicle systems. The vehicle nonlinearities arise due to the function of the suspension dampers, which assume a different damping coefficient in tension than in compression. The suspension springs may also possess piecewise linear characteristics. These lead to models with parameter discontinuities. Emphasis is put on investigating issues of unidentifiability arising in the system identification of nonlinear systems and the importance of sensor configuration and excitation characteristics in the reliable estimation of the model parameters. A methodology is proposed for designing the optimal sensor configuration (number and location of sensors) so that the corresponding measured data are most informative about the condition of the vehicle. The effects of excitation characteristics on the quality of the measured data are systematically explored. The effectiveness of the system identification and the optimal sensor configuration design methodologies is confirmed using simulated test data from a classical two-degree-of-freedom quartercar model as well as from more involved and complete vehicle models, including four-wheel vehicles with flexible body.

π4U: A high performance computing framework for Bayesian uncertainty quantification of complex models

We present ?4U, an extensible framework, for non-intrusive Bayesian Uncertainty Quantification and Propagation (UQ+P) of complex and computationally demanding physical models, that can exploit massively parallel computer architectures. The framework incorporates Laplace asymptotic approximations as well as stochastic algorithms, along with distributed numerical differentiation and task-based parallelism for heterogeneous clusters. Sampling is based on the Transitional Markov Chain Monte Carlo (TMCMC) algorithm and its variants. The optimization tasks associated with the asymptotic approximations are treated via the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). A modified subset simulation method is used for posterior reliability measurements of rare events. The framework accommodates scheduling of multiple physical model evaluations based on an adaptive load balancing library and shows excellent scalability. In addition to the software framework, we also provide guidelines as to the applicability and efficiency of Bayesian tools when applied to computationally demanding physical models. Theoretical and computational developments are demonstrated with applications drawn from molecular dynamics, structural dynamics and granular flow.