Study For Multidisciplinary Design Optimization Based On Time-varying Uncertainty Analysis

Multidisciplinary design optimization(MDO)is widely recognized at an early stage by many on the cutting edge of engineering design as the key to the future.The conventional MDO is a deterministic method,which takes load,material properties,geometry dimensions,et al.as deterministic factors.However,uncertainties do exist through entire life cycle of mechanical system.Uncertainty analysis is a hot research topic in MDO for complex mechanical systems.Furthermore,degradation failure is one of main reasons for complex mechanical systems losing their functions.Research on MDO under uncertainties should shift from static uncertainties to time-varying uncertainties.Which eventually lead to a large number of product failure of time-varying uncertainty is the key of the MDO research work.Based on those factors,this paper make a series of beneficial preliminary research on the time-varying uncertainty MDO,the main research contents are as follows:(1)Due to the computational complexity of MDO problem,it is hard to find a suitable general algorithm for all problems.At present,the calculation method for MDO problem mainly has two types: traditional methods and modern intelligent optimization algorithm.Traditional optimization methods have many inherent defects,such as difficult to solve discontinuous functions,as well as into local optimum,therefore we propose an new algorithm based on improved artificial bee colony(ABC)to solve the multidisciplinary problem.Firstly,this paper discusses the application of intelligent algorithms in MDO,and by a detailed description of the characteristics and superiority of the ABC algorithm.Followed,this paper put forward an improved ABC algorithm based on augmented Lagrange multiplier method.Finally,both a mathematical example and a case study of a cylindrical spring are provided to illustrate the feasibility and validity of the proposed method.(2)Existing MDO works typically assume that uncertainties are uncorrelated of each other.In real-world engineering systems,however,correlations do exist between different uncertainties.The MDO methods without considering correlations between uncertainties may cause inaccurate and thus misleading optimization results.In this paper,we make contributions by proposing a new MDO approach based on the ellipsoidal set theory to investigate characteristics of correlated uncertainties and incorporate their effects in the MDO through an advanced collaborative optimization method,where the quantitative model of correlated uncertainties is transformed into constrains of subsystems.Both a mathematical example and a thin-walled pressure vessel design are provided to illustrate feasibility and validity of the proposed method.(3)Aiming at time-varying uncertainties in mechanical systems,we propose a multidisciplinary reliability design optimization method by using stochastic differential equation theory.Firstly,we investigate the characteristics of time-varying uncertainties in complex mechanical systems;then utilized stochastic differential equation theory to quantify time-varying uncertainties.Secondly,through combining the multidisciplinary simultaneous analysis and design(SAND)optimization method,the model of MDO under time-varying uncertainties is established.Moreover,a mathematical problem and a speed reducer design problem are provided to illustrate the accuracy and effectiveness of the proposed method.(4)The performance of a complex mechanical system often degrades over time.How to deal with time-varying uncertainties in MDO is a key factor to improve the design of complex mechanical systems.Considering time-varying uncertainties in mechanical systems,a multidisciplinary robust design optimization(MRDO)method is put forward based on time-varying sensitivity analysis.Firstly,time-varying reliability indexes of limit state functions by combining sensitivity analysis and empirical correction formula is calculated.Secondly,the propagation effects of these time-varying uncertainties are qualified through combining the simplified implicit uncertainty propagation(IUP)method and sequential quadratic programming(SQP)method,then robust design method is integrated into MDO method to reduce the impact of time-varying uncertainties.Finally,the illustration of the proposed method is provided with both of a mathematical problem and a four high rolling mill example.