# Optimisation of Segregation Distances between Electric Cable Bundles Embedded in a Structure
## 1 Introduction  
To avoid electromagnetic (EM) compatibility problems, the allocation of elementary electrical cables in a bundle and the installation of cable harnesses in structures must be controlled and respect the segregation rules set today by the integrators. To this extent, in aeronautics, the wiring, named the Electrical Wiring Interconnection System (EWIS), is now considered as a system as a whole, which must fulfil the Certification Specifications for Large Aeroplanes (CS25 subpart H).  
Consequently, these constraints must be considered early in the upstream phase of a program, when cable harnesses are defined while most input data are not completely mastered or are even unknown (as cable lengths, relative location of harnesses, location versus the structure, etc.). This is the reason why only some routes in which harnesses can be grouped to run together are predefined. With respect to the signal nature and the electrical power on cables, distances between routes are imposed to secure the EM inter-compatibility between cables. Moreover, once these installation rules are defined, it is necessary to validate them for certification purposes. However the update of the computer-aided design (CAD) mock-up because of modifications of the structure or the installation of the harnesses in the structure can lead to deviations from the installation rules, by reducing for example the distance between two harnesses to a distance lower than the recommended segregation distance. In this case, one must be able to evaluate the potential risk brought by this deviation in order to justify it and to obtain the derogation.  
The objective of this article was thus to develop a modelling strategy to evaluate the optimal segregation distance between two electric cable bundles connecting two equipment, which will ensure their EM inter-compatibility. Therefore, we wanted here to minimise the distance between two bundles to save space for the installation of harnesses provided that the electromagnetic compatibility (EMC) constraints are respected with a given probability. We show in this article that this problem is in fact similar to a stochastic optimisation with probabilistic constraints [1]. Different methods have been proposed for this range of problems, and we particularly concentrate here on surrogate models and stochastic sampling.  
Besides, a recent review of this class of algorithms for optimisation under probabilistic constraint was performed with application to reliability in [2]. In this article, we also focus on the joint approach between Monte Carlo and Kriging surrogate models where the Monte Carlo sampling enables estimating the probability that the EM constraint is fulfilled and the Kriging model mimics the objective and the constraint function in an augmented space. The difficulty lies here in the nonlinearity of the constraint function, notably at high frequency, which can make the surrogate model unsuitable. Due to industrial constraints to provide a converged result in a reasonable time, whatever the use-case, we propose here to switch from the Kriging surrogate model with Monte Carlo sampling to classical Monte Carlo sampling when the surrogate model is not efficient. This question has been addressed in the Clean Sky 2 ANALYsis Statistical Techniques in aeronautics (EMC ANALYST) project (CFP07 GA 821128), gathering two Italian (Ingegneria dei Sistemi (IDS) and University of L'Aquila) and two French (AxesSim and ONERA) partners to answer the topic manager's (Safran Electrical & Power) requirements.  
In this article, we first describe the problem of segregation distance between cable bundles in Section 2. In Section 3, we show that this issue is in fact an optimisation problem under a probabilistic constraint where the constraint function is nonlinear due to the physics. Section 4 is dedicated to the statistical process we propose to solve this optimisation, and the last section develops the obtained results on the considered use-case.