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Stochastic models to Mitigate Sparse Sensor Attacks in Continuous-Time non-linear Cyber-Physical Systems

Computers, Materials & Continua 2023年第9期76卷 3189-3218页

作者： Borja Bordel Sánchez Ramón Alcarria Tomás Robles Information Technologies Department Universidad Politécnica de MadridMadrid28031Spain Geospatial Information Department Universidad Politécnica de MadridMadrid28031Spain

Cyber-Physical Systems are very vulnerable to sparse sensor attacks.But current protection mechanisms employ linear and deterministic models which cannot detect attacks precisely.Therefore,in this paper,we propose a new non-linear generalized model to describe Cyber-Physical Systems.This model includes unknown multivariable discrete and continuous-time functions and different multiplicative noises to represent the evolution of physical processes and randomeffects in the physical and computationalworlds.Besides,the digitalization stage in hardware devices is represented too.Attackers and most critical sparse sensor attacks are described through a stochastic process.The reconstruction and protectionmechanisms are based on aweighted stochasticmodel.Error probability in data samples is estimated through different indicators commonly employed in non-linear dynamics(such as the Fourier transform,first-return maps,or the probability density function).A decision algorithm calculates the final reconstructed value considering the previous error probability.An experimental validation based on simulation tools and real deployments is also carried out.Both,the new technology performance and scalability are studied.Results prove that the proposed solution protects Cyber-Physical Systems against up to 92%of attacks and perturbations,with a computational delay below 2.5 s.The proposed model shows a linear complexity,as recursive or iterative structures are not employed,just algebraic and probabilistic functions.In conclusion,the new model and reconstructionmechanism can protect successfully Cyber-Physical Systems against sparse sensor attacks,even in dense or pervasive deployments and scenarios.

关键词： Cyber-physical systems sparse sensor attack non-linear models stochastic models security

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Identification of non-linear autoregressive models with exogenous inputs for room air temperature modelling

能源与人工智能(英文)

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能源与人工智能(英文) 2022年第3期9卷 78-87页

作者： Christian Ankerstjerne Thilker Peder Bacher Davide Cali Henrik Madsen Technical University of Denmark Department of Applied Mathematics and Computer ScienceAsmussens AlléBuilding 303BDK-2800 Kgs.LyngbyDenmark

This paper proposes non-linear autoregressive models with exogenous inputs to model the air temperature ineach room of a Danish school building connected to the local district heating network. To obtain satisfactorymodels, the authors find it necessary to estimate the solar radiation effect as a function of the time of the dayusing a B-spline basis expansion. Furthermore, this paper proposes a method for estimating the valve positionof the radiator thermostats in each room using modified Hermite polynomials to ensure monotonicity of theestimated curve. The non-linearities require a modification in the estimation procedure: Some parametersare estimated in an outer optimisation, while the usual regression parameters are estimated in an inneroptimisation. The models are able to simulate the temperature 24 h ahead with a root-mean-square-errorof the predictions between 0.25℃ and 0.6℃. The models seem to capture the solar radiation gain in away aligned with expectations. The estimated thermostatic valve functions also seem to capture the importantvariations of the individual room heat inputs.

关键词： Time series analysis non-linear models District heating Smart energy systems

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