OPTIMIZING RELIABILITY OF LINEAR FRACTIONAL DIFFERENCE SYSTEMS UNDER UNCERTAINTY AND RANDOMNESS

Some complex systems may suffer from failure processes arising from soft failures and hard failures. The existing researches have shown that the reliability of a dynamic system is not constant under uncertain random environments. First, two types of uncertain random optimization models are proposed where reliability index is quantified by chance measure based on whether soft and hard failures are independent or not. It is considered that internal degradation is driven by left Caputo fractional linear difference equation, while shocks are defined as discrete i.i.d. random variables. The shocks may generate additional uncertain degradation shifts when considering the competing dependent failure processes. Then, two proposed optimization reliability problems may be transformed into their equivalent deterministic forms on the basis of alpha-path, and improved gradient descent method is applied to obtain optimal solutions. Finally, the numerical example of a micro-engine indicates that the optimization models are beneficial to the reliability of engineering systems.