Reduced Order Models for increased security and safety in cities
Computational simulations have been increasingly used in the last decades in order to reach high standards of security and safety in cities. The increasing number of urban explosions has brought attention to blast-wave simulations, pushing scientists to develop numerical methods and technologies with the purpose of facilitating the design of buildings, public transport infrastructures and improving urban planning.
The number of terrorist attacks, as well as the number of victims, has peaked since 2010, killing in the last decade an average of 24000 people worldwide each year [1]. A great fraction of the incidents has been carried out with explosives, bombs, and/or dynamite as weapons for mass destruction [2]. Blast waves in cities can also have an accidental cause such as the improper storage of explosive material. On the 4th of August 2020, an explosion occurred in the port of Beirut, destroying a large part of the city. The event originated a blast wave that could be perceived more than 240 km away and is considered one of the most powerful accidental non-nuclear explosions in history.
The European Commission’s effort
In 2017, the European Commission concretised the effort in an action plan aimed at supporting the development of methods and technologies to ensure the protection of public spaces. The subsequent studies brought large developments in terms of 3D numerical simulations of blast waves [3] and advanced software [4]. Numerical simulations play an essential role in the estimation of damage to infrastructures and the risk assessment for people.
Large-scale simulations and the need for Reduced Order Methods
This kind of problems involves solving non-linear and time-dependent Partial Differential Equations (PDEs) in a usually very large domain and often the interaction between fluid (air) and structure (e.g. buildings). In particular, blast waves can be seen as initially small regions of high pressure which then propagate in the surroundings. The high dimension of these systems makes the solution by means of a full-order method (FOM) prohibitively expensive in real-time and many-query contexts. Hence, Reduced Order Methods (ROMs) [5] come in handy to reduce the dimension of the system and speed-up the calculations. Since blast events are violent and extremely fast in nature, some of the traditional ROMs, such as the Proper Orthogonal Decomposition [6], are not very efficient. Thus, it is necessary to develop methods suitable to deal with fast and transient phenomena.
Deep-learning based ROMs
Our contribution to the cause, with the collaboration of the EC Joint Research Centre (JRC) in Ispra (Varese, Italy), consists in building a data-driven computational pipeline based on a combination of different non-linear ROMs [7]. As an example problem, we considered a virtual explosion happening in the vicinity of a building, specifically the SISSA building in Trieste.
In cases where the full-order solver is not easily accessible, such as this one, a data-driven approach is preferable. Therefore, the scheme is based on a collection of high-fidelity solutions computed using EUROPLEXUS [4], which is a software, developed jointly by JRC and CEA. The ROM we developed follows a local approach, where an approximation is sought by partitioning the solution space into sub-regions [8]. In each sub-region, a reduced-order basis is obtained by means of the Proper Orthogonal Decomposition, which is used to determine the main spacial characteristics, or modes. A second layer of compression is obtained by exploiting a powerful unsupervised deep-learning tool, such as Autoencoders (AE) [9]. An autoencoder is a type of neural network characterised by a “bottleneck”, which allows us to obtain an encrypted representation of the input data by applying the encoder function.
The fast recovery of an approximation to the full-order solution is obtained through the evaluation of a regression map previously trained (e.g. using Deep Forward Neural Networks) and reconstruction through the decoder function and a linear combination of the POD modes. In other words, it is possible to quickly obtain a ROM solution for values of the parameters that were not used for the training of the scheme.
Conclusions & Future perspectives
It is clear that data-driven non-linear Reduced Order Methods can play an important role in the 3D simulation of blast waves, with the potential of being game changers when applied to perform parametric studies and in many-query and real-time contexts. Future possible investigations could include the application of local deep-learning based ROMs, such as the one briefly presented in this article, to more complex problems and geometries. It would also be interesting to see how Optimisation techniques can help in answering questions like: where is the exact location and shape of a protective wall? what are the best materials, in terms of safety, for the different parts composing a building?
References
[1] Ritchie H., Hasell J., Mathieu E., Appel C. and Roser M. — “Terrorism”. Published online at OurWorldInData.org (2013). Retrieved from: https://ourworldindata.org/terrorism [Online Resource].
[2] Tin D., Margus C. and Ciottone G. Half-a-Century of Terrorist Attacks: Weapons Selection, Casualty Outcomes, and Implications for Counter-Terrorism Medicine. Prehospital and Disaster Medicine 36(5), 526–530 (2021).
[3] Valsamos G., Larcher M. and Casadei F. Beirut explosion 2020: A case study for a large-scale urban blast simulation. Safety Science 137, January (2021), 105190.
[4] EUROPLEXUS User’s Manual — A Computer Program for the Finite Element Simulation of Fluid-Structure Systems under Transient Dynamic Loading, 2016. https://europlexus.jrc.ec.europa.eu.
[5] Benner P., Grivet-Talocia S., Quarteroni A., Rozza G., Schilders, W., and Silveira L. M., Eds. Model Order Reduction: Volume 2: Snapshot-Based Methods and Algorithms. De Gruyter, 2020.
[6] Guo M. and Hesthaven J. S. Data-driven reduced order modeling for time-dependent problems. Computer Methods in Applied Mechanics and Engineering 345 (2019), 75–9.
[7] Cracco M., Stabile G., Lario. A, Larcher M., Casadei F., Valsamos G. and Rozza G. Deep-learning based ROMs for fast transient dynamics. Ready for submission, September (2022).
[8] Amsallem D., Zahr M. J. and Farhat C. Nonlinear model order reduction based on local reduced-order bases. International Journal for Numerical Methods in Engineering, February (2012), 1102–1119.
[9] Luo W., Li J., Yang J., Xu W. and Zhang J. Convolutional sparse autoencoders for image classification. IEEE Transactions on Neural Networks and Learning Systems 29, 7 (2018), 3289–3294.
