Especially, the combined ratio estimator of domain total is investigated under stratified complemental sampling when auxiliary information can be used.

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The numerical results indicate that the generalized Dirichlet distribution should be a reasonable prior, and the computation in forecasting coproduct output is relatively straightforward with respect to the approximation approach.

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Trimming correction is a way of using the area integral or Simpson to calculate the volume correction value.

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The Cholesky decomposition of cross spectral density matrix was approximated and reduced, and then the modified spectral representation method is efficient and requires less computer memory, which is suitable for simulating spatial wind fields of long span bridges.

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In static analysis, small deflection theory of circular plate and electrostatic actuating theory are adopted to simulate electrostatic-structural coupled process. In modal analysis, harmonic response analysis and nonlinear transient dynamic analysis of pump membrane, the fluid in the pump is regarded as an additional mass acting on the pump membrane to approximately substitute the effect of fluid field on pump membrane, which reduces the amount of calculation and improves simulation efficiency.

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The weight values in NLSM were adjusted automatically according to target data, which allowed the measured data with different dimensions or ranges to be treated at the same level, and thus the accuracy and stability of algorithm were improved accordingly. Derivative was replaced by the difference quotient in NLSM which further improved the algorithm speed.

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Adjacency search, double linked element list, random direction search, adjacency rotation, and heredity of geometrical quantities are applied to increase the efficiency of mesh generation. The relationship between the computing time and the number of generated elements is nearly linear and the time complexity is O(N^1.05), where N is the number of elements.

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In the feature selection stage,the computing approximate gains in parallel is adopted in order to solve the computational expensiveness of the model and system spending.

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As for the factitiously specified allowable values,such as allowable deflection,allowable amount of wear,and so on,their magnitudes,which are confirmed on the basis of empirical formula,often have an interval value or a limit value,therefore they can be described suitably by minor type membership function, As for various strength values of parts,such as tensile strength,compression strength,contact strength and so on,their magnitudes,which are often confirmed only by approximate mean,can be described suitably with middle type membership function.

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