The results indicate the dimensionless equation between the thickness of the frozen wall and the temperature distribution approximates linear,the dimensionless equation between the thickness of the frozen wall and the frozen time is quadratic polynomial.

In the paper,the quadratic polynomial function smoothing-method is used to smooth the sampling data,which is proved to be effective in filtering the high frequency noise.

The quadratic polynomial method and the artificial neural network (ANN) response surface method are in common use and belong to the local response surface methods, which only match the real limit state surface well in the area near the confirmatory calculation point.

Influenced by the integrality and weathering breakage degree of rock,the biggish different is existed between dynamic elastic modulus gained by dynamical method and static elastic modulus obtained by static method,and the relationship between dynamic and static value of elastic modulus is approximatively expressed as a relationship of quadratic polynomial function.

In this paper,the quadratic polynomial function is used to reconstruct the response surface in search of the possible breakdown point,and the BP neural network is adopted to reconstruct the response surface around the possible breakdown point,fitting the limit state function.

Based on the process and analysis of the data from orthogonal test, a series of the quadratic polynomial regression formula on the relations between the circle-crossing time or the differential coefficient of frozen wall and the four influencing factors have been obtained.

The velocity of the sheet is a quadratic polynomial of the distance from the slit and the sheet is subjected to a linear mass flux.

The interpolant is obtained patching together cubic with quadratic polynomial segments; it is co-monotone and/or co-convex with the data.

Cubic-spline and discrete-quadratic polynomial techniques are presented for reliably computing up to third-order derivatives of experimental information.

An algorithm to recover bit timing is proposed which maximises a quadratic polynomial approximation to the log-likelihood function.

The formulae are characterized by the presence of an infinite series whose general term consists of a linear recurrence damped by the central binomial coefficient and a certain quadratic polynomial.

On the base of studying on the mathematic model about the temperature field of the frozen wall used for protecting the deep foundation ditch and accounting for engineering factors, a series of model tests are completed for researching the dynamic temperature field of the frozen wall according to the simulation theory. The results indicate the dimensionless equation between the thickness of the frozen wall and the temperature distribution approximates linear,the dimensionless equation between the thickness of...

On the base of studying on the mathematic model about the temperature field of the frozen wall used for protecting the deep foundation ditch and accounting for engineering factors, a series of model tests are completed for researching the dynamic temperature field of the frozen wall according to the simulation theory. The results indicate the dimensionless equation between the thickness of the frozen wall and the temperature distribution approximates linear,the dimensionless equation between the thickness of the frozen wall and the frozen time is quadratic polynomial. The calculating methods about the average temperature and the thickness and the frozen time of the frozen wall are put forward based on the experimental results. It is convenient and available to keep the temperature of the frozen soil wall using the foam plate.

In the paper,the quadratic polynomial function smoothing-method is used to smooth the sampling data,which is proved to be effective in filtering the high frequency noise.Two data process methods both by Discrete Fourier Transform(DFT)and by Fast Fourier Transform(FFT)are compared.An algorithm used to analyse the leakage current and the reference voltage simultaneously in frequency domain is also provided.

The response surface method for structural reliability analysis is often used when the performance function is unknown. The paper points out that the response surface methods should be divided into the local response surface method and the whole response surface method. The quadratic polynomial method and the artificial neural network (ANN) response surface method are in common use and belong to the local response surface methods, which only match the real limit state surface well in the area near the...

The response surface method for structural reliability analysis is often used when the performance function is unknown. The paper points out that the response surface methods should be divided into the local response surface method and the whole response surface method. The quadratic polynomial method and the artificial neural network (ANN) response surface method are in common use and belong to the local response surface methods, which only match the real limit state surface well in the area near the confirmatory calculation point. The whole and the improved whole response surface methods of ANN and fuzzy neural network (FNN) put forward in this paper belong to the whole response surface methods which match the real limit state surface well in the whole area. Through illustrations and contrast analysis, it can be known that the improved whole response surface methods of ANN and FNN are the best among all above methods, by which the amount of calculation of finite element analysis can be reduced as well as the accuracy of calculation can be increased.