Two-Parameter Vector-Valued Martingales and Geometrical Properties of Banach Spaces

We obtained a number of inequalities and laws of large numbers for two parameter vector valued martingales.In the other direction we characterized p smoothness and q convexity of Banach spaces by using these inequalities and laws of large numbers for two parameter vector valued martingales.

Solving chemical dynamic optimization problems with ranking-based differential evolution algorithms

Dynamic optimization problems(DOPs) described by differential equations are often encountered in chemical engineering. Deterministic techniques based on mathematic programming become invalid when the models are non-differentiable or explicit mathematical descriptions do not exist. Recently, evolutionary algorithms are gaining popularity for DOPs as they can be used as robust alternatives when the deterministic techniques are invalid. In this article, a technology named ranking-based mutation operator(RMO) is presented to enhance the previous differential evolution(DE) algorithms to solve DOPs using control vector parameterization. In the RMO, better individuals have higher probabilities to produce offspring, which is helpful for the performance enhancement of DE algorithms. Three DE-RMO algorithms are designed by incorporating the RMO. The three DE-RMO algorithms and their three original DE algorithms are applied to solve four constrained DOPs from the literature. Our simulation results indicate that DE-RMO algorithms exhibit better performance than previous non-ranking DE algorithms and other four evolutionary algorithms.

A New Texture Analysis Approach

A new texture analysis approach by using Gibbs random field model is discussed. A parameter vector is defined in order to compute potentials of textures. It is found that texture features can be provided by its corresponding parameter vector, and the vector can be estimated in terms of maximum potential. Conclusions can be inferred that this new method based on the maximum potential is valid.

Combined forecast method of HMM and LS-SVM about electronic equipment state based on MAGA

For the deficiency that the traditional single forecast methods could not forecast electronic equipment states, a combined forecast method based on the hidden Markov model（HMM） and least square support vector machine（LS-SVM） is presented. The multi-agent genetic algorithm（MAGA） is used to estimate parameters of HMM to overcome the problem that the Baum-Welch algorithm is easy to fall into local optimal solution. The state condition probability is introduced into the HMM modeling process to reduce the effect of uncertain factors. MAGA is used to estimate parameters of LS-SVM. Moreover, pruning algorithms are used to estimate parameters to get the sparse approximation of LS-SVM so as to increase the ranging performance. On the basis of these, the combined forecast model of electronic equipment states is established. The example results show the superiority of the combined forecast model in terms of forecast precision,calculation speed and stability.

Inflatable Wing Design Parameter Optimization Using Orthogonal Testing and Support Vector Machines

The robust parameter design method is a traditional approach to robust experimental design that seeks to obtain the optimal combination of factors/levels. To overcome some of the defects of the inflatable wing parameter design method, this paper proposes an optimization design scheme based on orthogonal testing and support vector machines （SVMs）. Orthogonal testing design is used to estimate the appropriate initial value and variation domain of each variable to decrease the number of iterations and improve the identification accuracy and efficiency. Orthogonal tests consisting of three factors and three levels are designed to analyze the parameters of pressure, uniform applied load and the number of chambers that affect the bending response of inflatable wings. An SVM intelligent model is established and limited orthogonal test swatches are studied. Thus, the precise relationships between each parameter and product quality features, as well the signal-to-noise ratio （SNR）, can be obtained. This can guide general technological design optimization.

A NEW METHOD OF CHANNEL FRICTION INVERSION BASED ON KALMAN FILTER WITH UNKNOWN PARAMETER VECTOR

Channel friction is an important parameter in hydraulic analysis. A channel friction parameter inversion method based on Kalman Filter with unknown parameter vector is proposed. Numerical simulations indicate that when the number of monitoring stations exceeds a critical value, the so lution is hardly affected. In addition, Kalman Filter with unknown parameter vector is effective only at unsteady state. For the nonlinear equations, computations of sensitivity matrices are time-costly. Two simplified measures can reduce computing time, but not influence the results. One is to reduce sensitivity matrix analysis time, the other is to substitute for sensitivity matrix.

Uncertainty analysis and visualization of geological subsurface and its application in metro station construction

To visualize and analyze the impact of uncertainty on the geological subsurface,on the term of the geological attribute probabilities(GAP),a vector parameters-based method is presented.Perturbing local data with error distribution,a GAP isosurface suite is first obtained by the Monte Carlo simulation.Several vector parameters including normal vector,curvatures and their entropy are used to measure uncertainties of the isosurface suite.The vector parameters except curvature and curvature entropy are visualized as line features by distributing them over their respective equivalent structure surfaces or concentrating on the initial surface.The curvature and curvature entropy presented with color map to reveal the geometrical variation on the perturbed zone.The multiple-dimensional scaling(MDS)method is used to map GAP isosurfaces to a set of points in lowdimensional space to obtain the total diversity among these equivalent probability surfaces.An example of a bedrock surface structure in a metro station shows that the presented method is applicable to quantitative description and visualization of uncertainties in geological subsurface.MDS plots shows differences of total diversity caused by different error distribution parameters or different distribution types.