Definition and mathematical expression on instability domain of safety event and safety structure

Abstract

Dynamic risk assessment is a main research task of process safety. One of the main methods of dynamic risk assessment is to measure the distance between the real-time state and its threshold (dangerous state). Due to the influence of temperature, pressure and other factors, the dangerous state will often be expanded into a “dangerous range” of states. At present, most of the “dangerous range” are determined subjectively or according to experiences. Based on the safety structure theory, instability domain as the scientific term of "dangerous range" is proposed, and then its mathematical expression is developed in this paper. The safety structure composed of an atomic activity factor (AAF) and an atomic environmental factor (AEF) is regarded as the smallest unit to analyze safety issues in safety structure theory. When the state of a safety structure falls into its instability domain, the state of intrinsic factor will fall into the instability domain of the safety event. This is a sufficient condition to cause an accident. In this paper, the attribute of intrinsic factor about a safety event is determined by developing the performance extension membership function of the intrinsic factor, thus the mathematical expression on instability domain of the safety event is established. Taking the instability domain of safety event as the domain of the inverse mapping of state relationship functions among environmental factors, and then the mathematical expression on atomic environmental instability domain (AEID) of safety structure is established. Taking AEID as domain of the inverse mapping of state relationship function between AAF and AEF, thus the mathematical expression on atomic activity instability domain (AAID) of safety structure is established. The instability domain of safety structure is composed of AEID and AAID together. The mathematical expression on instability domains can provide theoretical basis for the dynamic risk assessment, prediction and active control of safety accidents.