Bayesian neural networks for bridge integrity assessment

Abstract

In recent years, neural network models have been widely used in the Civil Engineering field. Interesting enhancements may be obtained by re-examining this model from the Bayesian probability logic viewpoint. Using this approach, it will be shown that the conventional regularized learning approach can be derived as a particular approximation of the Bayesian framework. Network training is only a first level where Bayesian inference can be applied to neural networks. It can also be utilized in another three levels in a hierarchical fashion: for the optimization of the regularization terms, for data-based model selection, and to evaluate the relative importance of different inputs. In this paper, after a historical overview of the probability logic approach and its application in the field of neural network models, the existing literature is revisited and reorganized according to the enunciated four levels. Then, this framework is applied to develop a two-step strategy for the assessment of the integrity of a long-suspension bridge under ambient vibrations. In the first step of the proposed strategy, the occurrence of damage is detected and the damaged portion of the bridge is identified. In the second step, the specific damaged element is recognized and the intensity of damage is evaluated. The Bayesian framework is applied in both steps and the improvements in the results are discussed.

Structural integrity monitoring for dependability

“…The optimal network model, that is the most efficient in terms of localisation and quantification of damage (Arangio and Beck 2010), is selected by the Bayesian approach on the base of the 370 patterns considered for training. It consists of three input variables, that is, the errors err evaluated at A, B, and C, five output variables, that is, the possible locations (coincident with a structural element) and intensities of damage, and two hidden layers with 11 units (obtained by the Bayesian selection process).…”

“…The case example: Results of the procedure for the integrity assessment 5.1. Results of step 1: Damage detection The optimal model for the prediction of the timehistories of the response parameters has been selected by considering the structural response in the undamaged condition, and exploiting the procedure for Bayesian model selection that is fully explained in Arangio and Beck (2010); it consists of 2, 2 and 1 units in, respectively, the input, hidden and output layers. The model optimised in this way is also the most efficient in terms of sensitivity to changes in structural behavior: it corresponds to the lowest error in the training phase and to the highest error in the approximation of the signal when anomalies are detected (Arangio 2008).…”

“…As a result, the selection of the neural network model class is mathematically rigorous and systematic; the Bayesian approach allows an objective comparison among alternative solutions and eliminates reliance on the judgment of the neural network designer (MacKay 1995). The mathematical approach for neural network model class selection is illustrated in detail in Arangio and Beck (2010), where the most plausible model class among a set of candidate ones is obtained by applying Bayes' Theorem and maximising the posterior probability of the model class given a set of training data. In this respect, let us remember that it is not correct to choose simply the model that better fits data: more complex models will always fit the data in a better way, but they may be over-parameterised and give poor prediction for new cases.…”

“…To individuate the actual cause of the anomaly, the intensity of De is checked in different test sections, according to the procedure that is schematically represented in the flow chart shown in Figure 8. In the left side of Figure 8, the start-up of the procedure is shown: given a data set, the optimal neural network model is selected according to the Bayesian approach, that is, the model with the highest posterior probability is chosen and trained (Arangio and Beck 2010). Then, as shown in the right side of Figure 8, the model is tested with new input data sets.…”

An efficient algorithm for architecture design of Bayesian neural network in structural model updating

“…For system identification and health monitoring of structures, the multi‐layer neural networks are widely utilized in the literature (Adeli, ; Adeli & Jiang, ; Arangio & Beck, ; Chang, Lin, & Chang, ; Hakim, Razak, & Ravanfar, ; Lam & Ng, ; Sirca & Adeli, ; Sohn et al., ; Yin & Zhu, ), and currently, deep learning neural networks have also begun to be applied in this area (Abdeljaber, Avci, Kiranyaz, Gabbouj, & Inmand, ; Cha, Choi, & Büyüköztürk, ; Grande, Castillo, Mora, & Lo, ; Lin, Nie, & Ma, ; Gao & Mosalam, ; Wang, Zhao, Li, Zhao, & Zhao, ; Yang et al., ). In this paper, the commonly used multi‐layer feedforward neural networks are investigated, and they have been confirmed to be able to approximate any functional relationship between inputs and outputs with a single hidden layer (Cybenko, ).…”