Structural reliability methods are nowadays a cornerstone for the design of robustly performing structures, thanks to advancements in modeling and simulation tools. Monte Carlo-based simulation tools have been shown to provide the necessary accuracy and flexibility. While standard Monte Carlo estimation of the probability of failure is not hindered in its applicability by approximations or limiting assumptions, it becomes computationally unfeasible when small failure probability needs to be estimated, especially when the underlying numerical model evaluation is time consuming. In this case, variance reduction techniques are commonly employed, allowing for the estimation of small failure probabilities with a reduced number of samples and model calls. As a competing approach to variance reduction techniques, surrogate models can be used to substitute the computationally expensive model and performance function with an easy to evaluate numerical function calibrated through a supervised learning procedure. Both these tools provide accurate results for structural application. However, particular care should be taken into account when the reliability problems deal with high-dimensional or strongly nonlinear structural performances since the accuracy of the estimate is largely dependent on choices made during the surrogate modeling process. In this work, we compare the performance of the most recent state-of-the-art advance Monte Carlo techniques and surrogate models when applied to strongly nonlinear performance functions. This will provide the analysts with an insight to the issues that could arise in these challenging problems and help to decide with confidence on which tool to select in order to achieve accurate estimation of the failure probabilities within feasible times with their available computational capabilities.

In this paper we attempt to build upon past work on Interval Neural Networks, and provide a robust way to train and quantify the uncertainty of Deep Neural Networks. Specifically, we propose a back propagation algorithm for Neural Networks with constant width predictions. In order to maintain numerical stability we propose minimising the maximum of the batch of errors at each step. Our approach can accommodate incertitude in the training data, and therefore adversarial examples from a commonly used attack model can be trivially accounted for. We present preliminary results on a test function example. The reliability of the predictions of these networks are guaranteed by the non-convex Scenario approach to chance constrained optimisation. A key result is that, by using minibatches of size M , the complexity of our approach scales as O(M Niter), and does not depend upon the number of training data points as with other Interval Predictor Model methods.

This paper proposes numerical strategies to robustly and efficiently propagate probability boxes through expensive black box models. An interval is obtained for the system failure probability, with a confidence level. The three proposed algorithms are sampling based, and so can be easily parallelised, and make no assumptions about the functional form of the model. In the first two algorithms, the performance function is modelled as a function with unknown noise structure in the aleatory space and supplemented by a modified performance function. In the third algorithm, an Interval Predictor Model is constructed and a re-weighting strategy used to find bounds on the probability of failure. Numerical examples are presented to show the applicability of the approach. The proposed method is flexible and can account for epistemic uncertainty contained inside the limit state function. This is a feature which, to the best of the authors' knowledge, no existing methods of this type can deal with.

Abstract. Computer-aided modelling and simulation is now widely recognised as the third 'leg' of scientific method, alongside theory and experimentation. Many phenomena can be studied only by using computational processes such as complex simulations or analysis of experimental data. In addition, in many engineering fields computational approaches and virtual prototypes are used to support and drive the design of new components, structures and systems.A general purpose software for uncertainty quantification and risk assessment, named COS-SAN, is under continuous development. This is a multi-disciplinary software that satisfies industry requirements regarding numerical efficiency and analysis of detailed models that can be used to solve a wide range of industrial and scientific problems. The main aim of the COSSAN software is to allow the inclusion of non-deterministic analyses as a practice standard routing in scientific computing. This paper presents two recent toolboxes added to the OPENCOSSAN: Credal Networks and Interval Predictive model.

This paper presents probabilistic analysis of structural capacity of pre-stressed concrete containments subjected to internal pressure. The conventional design methods for containments are based on allowable stress codes which ensure certain factor of safety between expected load and expected structural strength. Such an approach may give different values of structural reliability in different situations. In recent years, two international round robin exercises have been conducted aimed at predicting the capacity of lined and unlined pre-stressed concrete containments used in nuclear industry. These exercises involved experimental testing and numerical analysis of the models. The first exercise involved ¼ scale steel-lined Pre-stressed Concrete Containment Vessel (PCCV) which was tested at Sandia National Laboratories (SNL) in USA. The second used an unlined containment being tested by the Bhabha Atomic Research Centre (BARC), Tarapur, India. These studies are essentially deterministic studies that have helped validate the analysis methodology and modelling techniques that can be used to predict pre-stressed concrete containment capacity and failure modes. The paper uses these two examples to apply structural reliability method to estimate the probability of failure of the containment. 2 coefficients of variation of the applied pressure and containment radius are the most important parameters. The variability of the probability of failure is decreased at higher pressures, but the coefficients of variation still play an important role.

In this paper a novel approach is presented for history matching models without making assumptions about the measurement error. Interval Predictor Models are used to robustly model the observed data and hence a novel figure of merit is proposed to quantify the quality of matches in a frequentist probabilistic framework. The proposed method yields bounds on the p-values from frequentist inference. The method is first applied to a simple example and then to a realistic case study (the Imperial College Fault Model) in order to evaluate its applicability and efficacy. When there is no modelling error the method identifies a feasible region for the matched parameters, which for our test case contained the truth case. When attempting to match one model to data from a different model, a region close to the truth case was identified. The effect of increasing the number of data points on the history matching is also discussed.

There has been increasing interest in characterising the error behaviour of systems which contain deep learning models before deploying them into any safety-critical scenario. However, characterising such behaviour usually requires large-scale testing of the model that can be extremely computationally expensive for complex real-world tasks. For example, tasks involving compute intensive object detectors as one of their components. In this work, we propose an approach that enables efficient large-scale testing using simplified low-fidelity simulators and without the computational cost of executing expensive deep learning models. Our approach relies on designing an efficient surrogate model corresponding to the compute intensive components of the task under test. We demonstrate the efficacy of our methodology by evaluating the performance of an autonomous driving task in the Carla [8] simulator with reduced computational expense by training efficient surrogate models for PIXOR [40] and CenterPoint [41] LiDAR detectors, whilst demonstrating that the accuracy of the simulation is maintained.Preprint. Under review.

Achieving safe and robust autonomy is the key bottleneck on the path towards broader adoption of autonomous vehicles technology. This motivates going beyond extrinsic metrics such as miles between disengagement, and calls for approaches that embody safety by design. In this paper, we address some aspects of this challenge, with emphasis on issues of motion planning and prediction. We do this through description of novel approaches taken to solving selected sub-problems within an autonomous driving stack, in the process introducing the design philosophy being adopted within Five. This includes safe-by-design planning, interpretable as well as verifiable prediction, and modelling of perception errors to enable effective sim-to-real and real-to-sim transfer within the testing pipeline of a realistic autonomous system.