Bayesian MCMC estimation of the limiting oxygen concentrations for laboratory electrical wires in various gravity levels

Scaling analysis offers a promising approach for predicting the flammability of electrical wires in manned space missions, yet determining the high-dimensional model parameter vector remains challenging, particularly when extrapolating to unknown gravities. This study introduces an effective method for predicting the limiting oxygen concentration (LOC) of electrical wires across different gravities, by integrating physical flame spread modeling with the data-driven technique and ground-based experimental data. A flame spread model for thin wires was developed based on the energy conservation law, and the LOC is determined by the existence of a stable-physical solution to the resulting nonlinear equation. Model parameters were estimated using a Bayesian approach, specifically the Markov Chain Monte Carlo (MCMC) method, trained on experimental LOC data under various hypergravity and opposed flow conditions. The results demonstrate the model’s capability to predict LOC curves accurately across gravity levels, providing fire safety margins based on uncertainties in model parameters and experimental measurements. The physics underlying the inferred parameter values was discussed, showing the important role of boundary layer effect and structure of the flame front. The interdependence of model parameters governing the blowoff or quenching branches allows for their values to be inferred via posterior distributions or inherent correlations. Interestingly, despite notable variations in quenching and blowoff branches, the predicted minimum LOC (MLOC) remains largely unchanged from 0 g to 4 g, thus it appears feasible to consider MLOC as a quasi-intrinsic property of the tested wire itself. Stable flame spread cannot be sustained in low-speed, low-gravity environments, even in oxygen-enriched atmospheres, due to the significant radiative heat loss. This “physics-informed data-driven” modelling approach bridges the gap between uncertainties in scaling analysis and practical flammability evaluations, thereby offering a more reliable methodology for screening spacecraft materials using ground-based facilities that support fire safety for space missions to Moon and Mars.