Bayesian System Identification Research Articles

Embankment on sludge: predicted and observed performances

The case history of an embankment built over soft water-treatment sludge is presented. To assure that the sludge would consolidate and gain strength as predicted, a test embankment was built. The observed performance of the test embankment was compared with the predicted performance to verify and modify design assumptions. The results were used to design and construct the full-scale embankment. The finite element method and the critical state model were used to predict the performances of the test embankment and the full-scale embankment. Bayesian updating and system identification were used to update the material properties used in the prediction for the test embankment. The updated properties were then used to update the prediction for the test embankment and to predict the performance of the full-scale embankment. These predictions were compared with the observed performances to evaluate the accuracies of the predictions with different input data. Efforts were made to identify factors that cause differences between predicted and measured performances.Key words: Bayesian updating, consolidation, finite-element prediction, shear strength, stability, water-treatment sludge.

High frequency edges (but not contrast) predict where we fixate: A Bayesian system identification analysis

A Bayesian system identification technique was used to determine which image characteristics predict where people fixate when viewing natural images. More specifically an estimate was derived for the mapping between image characteristics at a given location and the probability that this location was fixated. Using a large database of eye fixations to natural images, we determined the most probable (a posteriori) model of this mapping. From a set of candidate feature maps consisting of edge, contrast and luminance maps (at two different spatial scales), fixation probability was dominated by high spatial frequency edge information. The best model applied compressive non-linearity to the high frequency edge detecting filters (approximately a square root). Both low spatial frequency edges and contrast had weaker, but inhibitory, effects. The contributions of the other maps were so small as to be behaviourally irrelevant. This Bayesian method identifies not only the relevant weighting of the different maps, but how this weighting varies as a function of distance from the point of fixation. It was found that rather than centre surround inhibition, the weightings simply averaged over an area of about 2 degrees.

Unified Probabilistic Approach for Model Updating and Damage Detection

A probabilistic approach for model updating and damage detection of structural systems is presented using noisy incomplete input and incomplete response measurements. The situation of incomplete input measurements may be encountered, for example, during low-level ambient vibrations when a structure is instrumented with accelerometers that measure the input ground motion and the structural response at a few instrumented locations but where other excitations, e.g., due to wind, are not measured. The method is an extension of a Bayesian system identification approach developed by the authors. A substructuring approach is used for the parameterization of the mass, damping and stiffness distributions. Damage in a substructure is defined as stiffness reduction established through the observation of a reduction in the values of the various substructure stiffness parameters compared with their initial values corresponding to the undamaged structure. By using the proposed probabilistic methodology, the probability of various damage levels in each substructure can be calculated based on the available dynamic data. Examples using a single-degree-of-freedom oscillator and a 15-story building are considered to demonstrate the proposed approach.

Two-Stage Structural Health Monitoring Approach for Phase I Benchmark Studies

This paper presents a two-stage structural health monitoring methodology and applies it to the Phase I benchmark study sponsored by the IASC-ASCE Task Group on Structural Health Monitoring. In the first stage, modal parameters are identified using measured structural response from the undamaged system and then from the (possibly) damaged system. In the second stage, these data are used to update a parametrized structural model of the system using Bayesian system identification. The approach allows one to obtain not only estimates of the stiffness parameters but also the probability that damage in any substructure exceeds any specified threshold expressed in terms of a fractional stiffness loss. It successfully identifies the location and severity of damage in all cases of the benchmark problem.

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 system identification

In Bayesian statistics the concept of probability is interpreted as a rational measure of belief which is used to describe mathematically the uncertain relation between the statistician and the external world. The statistical inference is understood as a correction of prior subjective probability distribution by objective data. The paper shows that on this Bayesian basis it is possible to build a consistent theory of system identification. The following problems are considered: one-shot and real-time identification, estimation and prediction in closed control loop, redundant and unidentifiable parameters, time-varying parameters and adaptivity.

Bayesian System Identification

In Bayesian statistics the concept of probability is interpreted as a rational measure of belief which is used to descri be mathemat ically the uncertain re lation between the statistician and the external world. The statistical inference is understood as a correction of prior subject ive probability distribution by objective data. The paper shows that on this Bayesian basis it is possible to build up a consistent theory of system identification. The following problems are considered: one-shot and real time identification, estimation and prediction in closed control loop, redundant and ~identifiable parameters, time-varying parameters and adaptivity.