复杂机械系统时变不确定性设计方法

Evolution-Based Uncertainty Design for Complex Mechanical Systems

考虑机械系统参数随时间的演化,基于连续时间模型和伊藤引理,推导建立了多参数复杂机械系统时变不确定性计算模型,将系统整体时变不确定性由其漂移函数和波动函数表达,系统漂移函数和波动函数则由底层时变参数的漂移率和波动率决定,从而解析了机械系统时变不确定性设计的原理。与传统方法相比,该多参数复杂机械系统时变不确定性设计方法既可以针对各零件(或子系统)进行时变不确定性设计,也可以建立统一的系统状态方程,针对复杂机械系统进行不确定性设计,并且算得的系统可靠度是动态的,可以预测未来任意时刻的可靠度,从而为系统的未来发展趋势提供先期预警,为设备维护提供指导。通过具体算例,说明了该设计方法的应用。该设计方法具有普适性,可以推广应用于城市公交系统、城市给排水系统、燃气系统、核电系统等的时变不确定性设计和可靠性分析。

Considering the evolution of mechanical system parameters, and based on the continuous-time model and Ito Lemma, a time-varying reliability calculation model of multi-parameter complex mechanical system is established. In this model the systems＇ time-varying uncertainty can be expressed by drift functions and volatility functions, which are dependent on the drift rate and volatility rate known from basic design parameters. Thus the principle of evolution-based uncertainty design （EBUD） for complex mechanical systems is expounded. Compared with the traditional methods, this method can be applied to either the evolution-based uncertainty design of the elements （or subsystems）, or the uncertainty design for complex mechanical systems by establishing uniform system state equations. By this means, the dynamic system reliability can be obtained, and the reliability at any time in the future can be calculated. Thereby the time- varying reliability calculation model can forecast the system＇ s future development trend and offer early warnings, giving proper advice for the equipment maintenance. Taking the design of bolt group as an example and with the model applied, the time-varying reliabilities of screws in different positions are calculated and compared. In this example, the basic time-varying parameters include the turning torque M, the pre-load Fp, the minor diameter dl and the yield strength [S] of the screws. This method can also be used in other fields, such as evolution-based uncertainty design and reliability analysis of urban traffic control system, urban water-supply and drainage system, urban gas supply system, and so on.