Visual inspections of large networks of bridges yield millions of data points scattered across thousands of structural elements. Alongside visual inspections, structural attributes such as age, location and traffic load provide contextual information about the deterioration patterns in the network. Leveraging this network-scale data for modeling deterioration is challenging, especially when each structural element has few inspections over a long period of time. Moreover, as new bridge information and inspections are added each year, it is strictly important for deterioration models to be scalable. This paper addresses these challenges by proposing a scalable probabilistic approach for modeling deterioration of large networks of bridges. The new framework consists of state-space models (SSM) for modeling the deterioration based on visual inspections and a Bayesian neural network (BNN) that factors-in information about structural attributes. The role of the BNN model is to learn the mapping between the initial distribution of the deterioration speed and the structural attributes of each bridge. The new framework is shown to be computationally efficient and can seamlessly incorporate a large number of structural attributes, which alleviates the need for feature selection. In addition, the proposed framework incorporates a new approach for learning the inspectors’ uncertainty parameters which is shown to provide better generalization. The experiments in this study are based on real data from the network of bridges in the province of Quebec, Canada. • Scalable probabilistic deterioration model for large networks of bridges. • Deterioration modeling is based on visual inspections while considering structural attributes. • A new approach for quantifying the uncertainty associated with each inspector. • Validation analyses on inspection data from the network of bridges in the Quebec province.

With few exceptions, neural networks have been relying on backpropagation and gradient descent as the inference engine in order to learn the model parameters, because closed-form Bayesian inference for neural networks has been considered to be intractable. In this paper, we show how we can leverage the tractable approximate Gaussian inference's (TAGI) capabilities to infer hidden states, rather than only using it for inferring the network's parameters. One novel aspect is that it allows inferring hidden states through the imposition of constraints designed to achieve specific objectives, as illustrated through three examples: (1) the generation of adversarial-attack examples, (2) the usage of a neural network as a black-box optimization method, and (3) the application of inference on continuous-action reinforcement learning. In these three examples, the constrains are in (1), a target label chosen to fool a neural network, and in (2 and 3) the derivative of the network with respect to its input that is set to zero in order to infer the optimal input values that are either maximizing or minimizing it. These applications showcase how tasks that were previously reserved to gradient-based optimization approaches can now be approached with analytically tractable inference.

In this paper, we propose an analytical method for performing tractable approximate Gaussian inference (TAGI) in Bayesian neural networks. The method enables the analytical Gaussian inference of the posterior mean vector and diagonal covariance matrix for weights and biases. The method proposed has a computational complexity of $\mathcal{O}(n)$ with respect to the number of parameters $n$, and the tests performed on regression and classification benchmarks confirm that, for a same network architecture, it matches the performance of existing methods relying on gradient backpropagation.

Rehabilitation of contaminated soils in urban areas is in high demand because of the appreciation of land value associated with the increased urbanization. Moreover, there are financial incentives to minimize soil characterization uncertainties. Minimizing uncertainty is achieved by providing models that are better representation of the true site characteristics. In this paper, we propose two new probabilistic formulations compatible with Gaussian Process Regression (GPR) and enabling (1) to model the experimental conditions where contaminant concentration is quantified from aggregated soil samples and (2) to model the effect of physical site discontinuities. The performance of approaches proposed in this paper are compared using a Leave One Out Cross-Validation procedure (LOO-CV). Results indicate that the two new probabilistic formulations proposed outperform the standard Gaussian Process Regression.