概率守恒原理的历史起源与发展现状

HISTORICAL ORIGIN AND CURRENT DEVELOPMENT OF THE PRINCIPLE OF PROBABILITY CONSERVATION

  • 摘要: 随机事件都遵循概率守恒原理,它是与能量守恒原理和质量守恒原理一样基本的、自然界遵守的普遍规律。随机力学涵盖随机结构分析、随机振动、可靠性评价、可靠性优化设计和随机最优控制等内容,而概率守恒原理在其中起着根本性、决定性的作用。随机静、动力系统的一对概率密度积分方程是刻画随机性传播与演化的统一基本方程。本文论述概率守恒原理的历史起源和发展现状,追溯其在统计物理中的起源,和在概率论、随机力学中的发展状况。然后,从概率守恒原理推导建立时间−空间域的概率密度积分方程,并介绍随机积分理论和直接概率积分法的基本思想,及其在静动力系统随机响应与可靠度分析和可靠性优化设计方面的研究进展,旨在推动随机力学的科研和教学。

     

    Abstract: Random events obey the principle of probability conservation, which is a fundamental and universal law of nature, paralleling the principles of energy conservation and mass conservation. Stochastic mechanics involves the aspects of stochastic structural analysis, random vibration, reliability assessment, reliability-based design optimization, and stochastic optimal control, in which the principle of probability conservation plays a fundamental and decisive role. A pair of probability density integral equations for stochastic static and dynamic systems are the unified and fundamental equations that represent the propagation and evolution of randomness. This paper describes the historical origin and current development of the principle of probability conservation, tracing its origin in statistical physics and its development in probability theory and stochastic mechanics. Then, the probability density integral equation in the time-space domain based on the principle of probability conservation is derived and established. Moreover, the theory of stochastic integral, basic idea of direct probability integral method and its recent developments in stochastic response analysis of static and dynamic systems, reliability evaluation and reliability-based optimum design are introduced, aiming to promote the advancement of research and teaching in stochastic mechanics.

     

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