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.

动态风险评估是过程安全的一项主要研究任务。动态风险评估的主要方法之一是测量实时状态与其阈值（危险状态）之间的距离。由于温度、压力等因素的影响，危险状态往往会扩大为“危险范围”的状态。目前，大部分“危险范围”都是主观或根据经验确定的。本文基于安全结构理论，提出了作为“危险范围”科学术语的失稳域，并建立了其数学表达式。由原子活性因子（AAF）和原子环境因子（AEF）组成的安全结构被视为安全结构理论中分析安全问题的最小单位。当安全结构的状态落入其不稳定域时，内因状态将落入安全事件的不稳定域。这是造成事故的充分条件。本文通过开发内在因素的性能扩展隶属函数来确定安全事件内在因素的属性，从而建立安全事件不稳定域的数学表达式。将安全事件不稳定域作为环境因素间状态关系函数的逆映射域，建立了安全结构原子环境不稳定域(AEID)的数学表达式。将AEID作为AAF和AEF状态关系函数逆映射的域，从而建立了安全结构原子活性不稳定域(AAID)的数学表达式。安全结构不稳定域由AEID和AAID共同组成。不稳定域的数学表达式可为安全事故的动态风险评估、预测和主动控制提供理论依据。