Reliability assessment for serviceability limit states of stiffened deep cement mixing column-supported embankments

The reliability and deterministic analyses of wood-cored stiffened deep cement mixing and deep cement mixing column-supported embankments(referred to as WSCSE and DCSE,respectively)considering serviceability limit state requirements are presented in this paper.Random field theory was used to simulate the spatial variability of soil
cement mixing(SCM)material in which the adaptive Kriging Monte Carlo simulation was adopted to estimate the failure probability of a column
supported embankment(CSE)system.A new method for stochastically generating random values of unconfined compressive strength(qu)and the ratio(Ru)between the undrained elastic modulus and qu of SCM material based on statistical correlation data is proposed.Reliability performance of CSEs concerning changes in the mean(μ),coefficient of variation(CoV),and vertical spatial correlation length(θv)of qu and Ru are presented and discussed.The obtained results indicate that WSCSE can provide a significantly higher reliability level and can tolerate more SCM material spatial variability than DCSE.Some performance of DCSE and WSCSE,which can be considered satisfactory in a deterministic framework,cannot guarantee an acceptable reliability level from a probabilistic viewpoint.This highlights the importance and necessity of employing reliability analyses for the design of CSEs.Moreover,consideration of only μ and CoV of qu seems to be sufficient for reliability analysis of WSCSE while for DCSE,uncertainties regarding the Ru(i.e.both μ and CoV)and θv of qu cannot be ignored.

Measurement Uncertainty Evaluation of Conicity Error Inspected on CMM

The cone is widely used in mechanical design for rotation, centering and fixing. Whether the conicity error can be measured and evaluated accurately will directly influence its assembly accuracy and working performance. According to the new generation geometrical product specification（GPS）, the error and its measurement uncertainty should be evaluated together. The mathematical model of the minimum zone conicity error is established and an improved immune evolutionary algorithm（IlEA） is proposed to search for the conicity error. In the IIEA, initial antibodies are firstly generated by using quasi-random sequences and two kinds of affinities are calculated. Then, each antibody clone is generated and they are self-adaptively mutated so as to maintain diversity. Similar antibody is suppressed and new random antibody is generated. Because the mathematical model of conicity error is strongly nonlinear and the input quantities are not independent, it is difficult to use Guide to the expression of uncertainty in the measurement（GUM） method to evaluate measurement uncertainty. Adaptive Monte Carlo method（AMCM） is proposed to estimate measurement uncertainty in which the number of Monte Carlo trials is selected adaptively and the quality of the numerical results is directly controlled. The cone parts was machined on lathe CK6140 and measured on Miracle NC 454 Coordinate Measuring Machine（CMM）. The experiment results confirm that the proposed method not only can search for the approximate solution of the minimum zone conicity error（MZCE） rapidly and precisely, but also can evaluate measurement uncertainty and give control variables with an expected numerical tolerance. The conicity errors computed by the proposed method are 20%-40% less than those computed by NC454 CMM software and the evaluation accuracy improves significantly.

An Improved Measurement Uncertainty Calculation Method of Profile Error for Sculptured Surfaces

The current researches mainly adopt "Guide to the expression of uncertainty in measurement(GUM)" to calculate the profile error. However, GUM can only be applied in the linear models. The standard GUM is not appropriate to calculate the uncertainty of profile error because the mathematical model of profile error is strongly non-linear. An improved second-order GUM method(GUMM) is proposed to calculate the uncertainty. At the same time, the uncertainties in different coordinate axes directions are calculated as the measuring points uncertainties. In addition, the correlations between variables could not be ignored while calculating the uncertainty. A k-factor conversion method is proposed to calculate the converge factor due to the unknown and asymmetrical distribution of the output quantity. Subsequently, the adaptive Monte Carlo method(AMCM) is used to evaluate whether the second-order GUMM is better. Two practical examples are listed and the conclusion is drawn by comparing and discussing the second-order GUMM and AMCM. The results show that the difference between the improved second-order GUM and the AMCM is smaller than the difference between the standard GUM and the AMCM. The improved second-order GUMM is more precise in consideration of the nonlinear mathematical model of profile error.