Application of nonlinear partial least square in catalyst modeling

The neural network partial least square (NNPLS) method was used to establish a robust reaction model for a multi-component catalyst of methane oxidative coupling. The details, including the learning algorithm, the number of hidden units of the inner network, activation function, initialization of the network weights and the principal components, are discussed. The results show that the structural organizations of inner neural network are 1-10-5-1, 1-8-4-1, 1-8-5-1, 1-7-4-1, 1-8-4-1, 1-8-6-1, respectively. The Levenberg-Marquardt method was used in the learning algorithm, and the central sigmoidal function is the activation function. Calculation results show that four principal components are convenient in the use of the multi-component catalyst modeling of methane oxidative coupling. Therefore a robust reaction model expressed by NNPLS succeeds in correlating the relations between elements in catalyst and catalytic reaction results. Compared with the direct network modeling, NNPLS model can be adjusted by experimental data and the calculation of the model is simpler and faster than that of the direct network model.

Further Extension on a Theorem of the Value Distribution of f′f^n

By using small function method, the following result is obtained. If f（z） is transcendental meromorphic and that ψ（z） is non-zero meromorphic and that T（r,ψ） = S（r, f）, then（n＋1）T（r,f）≤N^-（r,1/f＇f^n-ψ）＋2N^-（r,1/f）＋N^-（r,f）＋S（r,f）.

Genetic algorithm-based evaluation of spatial straightness error

A genetic algorithm(GA)-based approach is proposed to evaluate the straightness error of spatial lines. According to the mathematical definition of spatial straightness, a verification model is established for straightness error, and the fitness function of GA is then given and the implementation techniques of the proposed algorithm is discussed in detail. The implementation techniques include real number encoding,adaptive variable range choosing, roulette wheel and elitist combination selection strategies,heuristic crossover and single point mutation schemes etc.An applicatin example is quoted to validate the proposed algorithm. The computation result shows that the GA-based approach is a superior nonlinear parallel optimization method. The performance of the evolution population can be improved through genetic operations such as reproduction,crossover and mutation until the optimum goal of the minimum zone solution is obtained. The quality of the solution is better and the efficiency of computation is higher than other methods.

Notes on the Scaling Function

Two properties are given in this paper about the scaling function: suppose Vj; j ∈ Z is a multiresolution analysis with a continuous scaling function φ which have compact support set and that φ the Fourier transform of φ is a continuous real function, compactly supported, then φ(0) ≠ 0 and when supp φ = [a1,b1]∪[a2,b2](b1 < a2,0 < a2), then we havea1 ≤ 0, 0 < b1, a1 < b2/2 ≤ b1, 2π < b2 - a1 ≤ 8π.

Filtering detecting signal of rockbolt with harmonic wavelet

Harmonic wavelets not only possess the traditional advantages of a wavelet function,they also have other merits such as clear expressions,more flexible time-frequency divisions,a simple transformation algorithm,a finer box-like frequency spectrum and others.Given the frequency distribution characteristics of the nondestructive testing signals from a rockbolt support system and based on the discrete harmonic wavelet transformation theory,we have effectively abstracted signals from frequency ranges concerned by removing useless high and low frequency signals from the testing signals of the rockbolt support system and obtained filtered signals with a reconstruction algorithm of harmonic wavelets.Finally,we applied the harmonic wavelet transformation in filtering analog signals and measured response signals of rockbolts.The results indicate that harmonic wavelets also have excellent filtering characteristics.

Construction of Compactly Supported Bivariate Orthogonal Wavelets

For a given compactly supported scaling fun ct ion supported over [0,3]×[0,3], we present an algorithm to construct compac t ly supported orthogonal wavelets. By this algorithm, the symbol function of the associated wavelets can be constructed explicitly.

Balance of multi-wavelets

The discrete scalar data need prefiltering when transformed by discrete multi-wavelet, but prefiltering will make some properties of multi-wavelets lost. Balanced multi-wavelets can avoid prefiltering. The sufficient and necessary condition of p-order balance for multi-wavelets in time domain, the interrelation between balance order and approximation order and the sampling property of balanced multi-wavelets are investigated. The algorithms of 1-order and 2-order balancing for multi-wavelets are obtained. The two algorithms both preserve the orthogonal relation between multi-scaling function and multi-wavelets. More importantly, balancing operation doesnt increase the length of filters, which suggests that a relatively short balanced multi-wavelet can be constructed from an existing unbalanced multi-wavelet as short as possible.

Method and application of wavelet shrinkage denoising based on genetic algorithm

Genetic algorithm (GA) based on wavelet transform threshold shrinkage (WTS) and translation-invariant threshold shrinkage (TIS) is introduced into the method of noise reduction, where parameters used in WTS and TIS, such as wavelet function, decomposition levels, hard or soft threshold and threshold can be selected automatically. This paper ends by comparing two noise reduction methods on the basis of their denoising performances, computation time, etc. The effectiveness of these methods in-troduced in this paper is validated by the results of analysis of the simulated and real signals.

A Novel Extension of Kernel Partial Least Squares Regression

Based on continuum power regression(CPR) method, a novel derivation of kernel partial least squares(named CPR-KPLS) regression is proposed for approximating arbitrary nonlinear functions.Kernel function is used to map the input variables(input space) into a Reproducing Kernel Hilbert Space(so called feature space),where a linear CPR-PLS is constructed based on the projection of explanatory variables to latent variables(components). The linear CPR-PLS in the high-dimensional feature space corresponds to a nonlinear CPR-KPLS in the original input space. This method offers a novel extension for kernel partial least squares regression(KPLS),and some numerical simulation results are presented to illustrate the feasibility of the proposed method.

Robust structured total least squares algorithm for passive location

A new approach called the robust structured total least squares(RSTLS) algorithm is described for solving location inaccuracy caused by outliers in the single-observer passive location. It is built within the weighted structured total least squares(WSTLS)framework and improved based on the robust estimation theory.Moreover, the improved Danish weight function is proposed according to the robust extremal function of the WSTLS, so that the new algorithm can detect outliers based on residuals and reduce the weights of outliers automatically. Finally, the inverse iteration method is discussed to deal with the RSTLS problem. Simulations show that when outliers appear, the result of the proposed algorithm is still accurate and robust, whereas that of the conventional algorithms is distorted seriously.

Implementing single-scale wavelet transform processor with magnetostatic surface wave device

When the envelope of the conducting strips for the input transducer of magnetostatic surface wave(MSSW) device is designed according to the wavelet-function envelope,the impulse-response function of the input transducer for MSSW device is equal to the wavelet function,so that single-scale wavelet-transform processor of MSSW type is fabricated.First,according to the envelope function of the wavelet,the length function of the conducting strips is defined,then,the lengths of the conducting strips can be calculated from the length function of the conducting strips,finally,the input transducer can be designed according to the lengths and widths for the conducting strips.The compensation method of the insertion loss for single-scale wavelet trans-form processor of MSSW type is also given in the paper.When the output end of single-scale wavelet transform processor of MSSW type is connected to the amplifier,its insertion loss can be compensated.

VARIABLE SELECTION FOR COVARIATE ADJUSTED REGRESSION MODEL

This paper employs the SCAD-penalized least squares method to simultaneously select variables and estimate the coefficients for high-dimensional covariate adjusted linear regression models.The distorted variables are assumed to be contaminated with a multiplicative factor that is determined by the value of an unknown function of an observable covariate.The authors show that under some appropriate conditions,the SCAD-penalized least squares estimator has the so called "oracle property".In addition,the authors also suggest a BIC criterion to select the tuning parameter,and show that BIC criterion is able to identify the true model consistently for the covariate adjusted linear regression models.Simulation studies and a real data are used to illustrate the efficiency of the proposed estimation algorithm.

A proximal alternating linearization method for minimizing the sum of two convex functions

In this paper, we develop a novel alternating linearization method for solving convex minimization whose objective function is the sum of two separable functions. The motivation of the paper is to extend the recent work Goldfarb et al.(2013) to cope with more generic convex minimization. For the proposed method,both the separable objective functions and the auxiliary penalty terms are linearized. Provided that the separable objective functions belong to C1,1(Rn), we prove the O(1/?) arithmetical complexity of the new method. Some preliminary numerical simulations involving image processing and compressive sensing are conducted.

Improved single image dehazing using dark channel prior

An improved single image dehazing method based on dark channel prior and wavelet transform is proposed. This proposed method employs wavelet transform and guided filter instead of the soft matting procedure to estimate and refine the depth map of haze images. Moreover, a contrast enhancement method based on just noticeable difference(JND) and quadratic function is adopted to enhance the contrast for the dehazed image, since the scene radiance is usually not as bright as the atmospheric light,and the dehazed image looks dim. The experimental results show that the proposed approach can effectively enhance the haze image and is well suitable for implementing on the surveillance and obstacle detection systems.

Wave interaction with a two-layer porous breakwater in the presence of step-type bottom

Oblique wave interaction with a two-layer breakwater consisting of perforated front and back wall in the presence of bottom undulations is analyzed.Wave characteristics are studied in the framework of small-amplitude wave theory,and Darcy’s law is used for flow past porous structures.The varying bottom topography spanned over a finite interval connected by two semi-infinite intervals of uniform water depths.Eigenfunction expansion method is used to handle the solution in the regions of uniform bottom and a modified mild-slope equation along with jump conditions is employed for varying bottom topography.Reflection,transmission,and wave energy dissipation coefficients are obtained numerically by applying the matrix method to understand the effects of several physical quantities such as wavenumber,porosity,and angle of incidence.The transmission coefficient reduces significantly and the wave energy dissipation is high for the present model.Also,Bragg scattering is analyzed in the presence of step-type rippled bottom and presented in this paper.