Raimondo Betti

A Hybrid Optimization Algorithm with Bayesian Inference for Probabilistic Model Updating

A hybrid optimization methodology is presented for the probabilistic finite element model up- dating of structural systems. The model updating pro- cess is formulated as an inverse problem, analyzed by Bayesian inference, and solved using a hybrid optimiza- tion algorithm. The proposed hybrid approach is a com- bination of a modified artificial bee colony (MABC) algorithm and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. The MABC includes four modifica- tions compared to the standard ABC algorithm, which basically improve the global convergence of ABC in the solution phases of initialization, updating, selection, and rebirth. The BFGS is inserted to improve the finer solu- tion search ability aiming at a higher solution accuracy. In brief, a probabilistic framework based on Bayesian in- ference is first derived so to get a regularized objective function for optimization. Then the proposed MABC- BFGS algorithm is applied to determine the unknown system parameters by minimizing the newly defined objective function. System parameters as well as the pre- diction error covariance are updated iteratively in the optimization process. Posterior distributions of the iden- tified system parameters are determined using a weighted sum of Gaussian distributions. Finally, the effectiveness of the proposed approach is illustrated by the numer- ical data sets of the Phase I IASC-ASCE benchmark model and the experimental data sets of a three-storey frame structure (from the Los Alamos National Labo- ratory (LANL), New Mexico, United States).

Wind Analysis of a Suspension Bridge: Identification and Finite-Element Model Simulation

A framework for numerically predicting the wind-excited response of suspension bridges with a certain level of confidence is established by means of output only system identification, model updating, wind-response simulation, and input-output comparison. A real case study represented by the identification and analysis of a newly built suspension bridge is considered. In system identification, the estimates of the modal parameters of the structure are provided with uncertainty bounds that take into account variations in identified modal features arising from different selections of the main parameters in the implementation of the identification technique. Based on the identified modal parameters, a finite-element model of the bridge is updated via an optimization technique. The updated model is then employed for numerically predicting the wind-excited structural response. Comparison with recorded data allows to check the accuracy of the model’s predictions as well as to indicate possible strategies for ref...

On the Uniqueness of Solutions for the Identification of Linear Structural Systems

This work tackles the problem of global identifiability of an undamped, shear-type, N degrees of freedom linear structural system under forced excitation without any prior knowledge of its mass or stiffness distributions. Three actuator/sensor schemes are presented, which guarantee the existence of only one solution for the mass and stiffness identification problem while requiring a minimum amount of instrumentation (only I actuator and 1 or 2 sensors). Through a counterexample for a 3DOF system it is also shown that fewer measurements than those suggested result invariably in non-unique solutions.

Elastic composite beams

Abstract In this paper, an application of the model of the analog-beam for the analysis of composite beams is presented for the case of a simply-supported beam with a uniformly distributed load. These beams are composed of an upper slab and a lower beam, connected at the interface by shear transmitting studs. The sixth-order differential equation of equilibrium for the vertical displacement is solved for two different sets of boundary conditions: (1) with rigid shear restraints at both the end sections of the beam and (2) with no shear restraints. The results (displacements, rotations, normal stresses and internal shear forces) are compared with those obtained using an equivalent classical Navier beam. The importance of the effectiveness of the interaction between the upper slab and the lower beam is emphasized. By imposing perfect bonding between the two subbeams, the analog-beam model presents the same behavior as the equivalent Navier beam.

New Stochastic Subspace Approach for System Identification and Its Application to Long-Span Bridges

This paper investigates the model order determination problem in the identification of dynamic characteristics of long-span bridges subjected to ambient excitation. Based on a stochastic state-space model framework, a new approach for state variable estimation is proposed, which is developed for the purpose of properly determining the order of a mathematical model of the structure under consideration. Comparing the newly developed approach with existing ones, their performances for system identification are evaluated with respect to their ability to highlight structural properties against noise ones in terms of the solution of a singular value problem, from a theoretical point of view and in applications to numerical and field measurements of a suspension bridge. From these applications, it is demonstrated that the newly developed approach is the most effective among the existing ones in discriminating structural modes, including weakly excited and closely spaced modes, from noise ones in terms of singular values, even when dealing with low signal-to-noise ratio signals and nonwhite wind excitation.

Identification of Linear Structural Systems With a Limited Set of Input-Output Measurements

In this paper, a methodology is presented for the identification of the complete mass, damping, and stiffness matrices of a dynamical system using a limited number of time histories of the input excitation and of the response output. Usually, in this type of inverse problems, the common assumption is that the excitation and the response are recorded at a sufficiently large number of locations so that the full-order mass, damping, and stiffness matrices can be estimated. However, in most applications, an incomplete set of recorded time histories is available and this impairs the possibility of a complete identification of a second-order model. In this proposed approach, all the complex eigenvectors are correctly identified at the instrumented locations (either at a sensor or at an actuator location). The remaining eigenvector components are instead obtained through a nonlinear least-squares optimization process that minimizes the output error between the measured and predicted responses at the instrumented locations. The effectiveness of this approach is shown through numerical examples and issues related to its robustness to noise polluted measurements and to uniqueness of the solution are addressed.

Optimal bilinear observers for bilinear state-space models by interaction matrices

This paper formulates optimal bilinear observers for bilinear state-space models. Observers in bilinear form, as opposed to other nonlinear forms, are required to develop an extension of observer/Kalman filter identification for simultaneous identification of a bilinear state-space model and an associated bilinear observer from noisy input–output measurements. The paper establishes the relationship between the bilinear observer gains and the interaction matrices which are used to convert the original bilinear state-space model to a form that simplifies the identification of such a model. Techniques to find the interaction matrices are developed. In the absence of noises, these matrices produce the gains of the fastest converging observer. In the presence of noises, they minimise the state estimation error in the same manner as a standard steady-state Kalman filter. Numerical examples illustrate both the theoretical and computational aspects of the proposed algorithms.

Experimental Analysis of a Nondestructive Corrosion Monitoring System for Main Cables of Suspension Bridges

Corrosion of high-strength steel wires in a suspension bridges main cable has been attributed to the environment within the cable wrapping. A sensor network was developed to monitor and provide information in order to indirectly assess the environmental conditions and the deterioration of the interior of suspension bridge main cables. The overall functionality of both the individual sensors and the monitoring system was tested on a full-scale mock-up cable. The cable mock-up was covered in aluminum wrapping and an environmental chamber was builtarounditinordertosubjectthetestspecimenandsensornetworktoanaggressivecorrosiveenvironmentcreatedbycyclictemperatureand humidity conditions. The temperature, relative humidity (RH), and corrosion rate levels were recorded by all sensors. The recorded data were analyzed in an attempt to determine general trends and correlations between the environmental variables themselves and their effects on corrosionrates.Therecordedtemperature fluctuationswerehighlydependentonthesensordepthwithinthecable;however,theRHlevelswere not.Duringcyclictesting,near-linear temperatureincreasesandRHdecreaseswererecordedclosetothecablescenter.Thebaselinecorrosion rate levels were affected by the RH levels, with significant increases in corrosion rates at RH levels greater than 50%. The temperature changes proved to impact the corrosion rates on a cyclic level, with high correlations between the temperature and corrosion rate readings recorded by linear polarization resistance corrosion rate sensors. DOI: 10.1061/(ASCE)BE.1943-5592.0000399.

OKID as a Unified Approach to System Identification

This paper presents a unified approach for the identification of linear state-space models from input-output measurements in the presence of noise. It is based on the established Observer/Kalman filter IDentification (OKID) method of which it proposes a new formulation capable of transforming a stochastic identification problem into a (simpler) deterministic problem, where the Kalman filter corresponding to the unknown system and the unknown noise covariances is identified. The system matrices are then recovered from the identified Kalman filter. The Kalman filter can be identified with any deterministic identification method for linear state-space models, giving rise to numerous new algorithms and establishing the Kalman filter as the unifying bridge from stochastic to deterministic problems in system identification.

Experimental studies on damage detection in frame structures using vibration measurements

This paper presents an experimental study of frequency and time domain identification algorithms and discusses their effectiveness in structural health monitoring of frame structures using acceleration input and response data. Three algorithms were considered: 1) a frequency domain decomposition algorithm (FDD), 2) a time domain Observer Kalman IDentification algorithm (OKID), and 3) a subsequent physical parameter identification algorithm (MLK). Through experimental testing of a four-story steel frame model on a uniaxial shake table, the inherent complications of physical instrumentation and testing are explored. Primarily, this study aims to provide a dependable first-order and second-order identification of said test structure in a fully instrumented state. Once the characteristics (i.e. the stiffness matrix) for a benchmark structure have been determined, structural damage can be detected by a change in the identified structural stiffness matrix. This work also analyzes the stability of the identified structural stiffness matrix with respect to fluctuations of input excitation magnitude and frequency content in an experimental setting.