Stochastic Integral Equation Method Research Articles

Electromagnetic scattering of two-dimensional rough cylinder based on statistical integral equation

The study of electromagnetic scattering from Gaussian rough surface is of great significance in radar reconnaissance, target tracking and ocean remote sensing. The moment method (MOM) is a commonly used method with high accuracy. However, in the past research, Monte Carlo method is used to simulate the Gaussian rough surface. In this method, a large number of random simulation operations are carried out, and then a statistical convergence result is obtained by counting the results of all operations. In this paper, the stochastic integral equation method SIEM(Stochastic Integral Equation Method) is proposed to calculate the electromagnetic scattering of Gaussian rough surface. SIEM avoids the difficulty of high difficulty precise modeling and repeated calculation many times, and only single modeling and calculation are carried out for the target problem. In this paper, the electromagnetic scattering of two-dimensional cylinder with Gaussian rough surface is solved, and the effectiveness of SIEM is proved by comparing with mom.

A Stochastic Green’s Function for Solution of Wave Propagation in Wave-Chaotic Environments

We present a statistical, mathematical, and computational model for prediction and analysis of wave propagation through complex, wave-chaotic environments. These are generally enclosed environments that are many wavelengths in extent and are such that, in the geometric optics limit, ray trajectories diverge from each other exponentially with distance traveled. The wave equation solution is expressed in terms of a novel stochastic Green's function that includes both coherent coupling due to direct path propagation and incoherent coupling due to propagation through multiple paths of the scattering environment. The statistically fluctuating portion of the Green's function is characterized by random wave model and random matrix theory. Built upon the stochastic Green's function, we have derived a stochastic integral equation method, and a hybrid formulation to incorporate the component-specific attributes. The proposed model is evaluated and validated through representative experiments.

Development of confidence interval estimates for predictions from a rainfall-runoff model

In any rainfall-runoff model, there is uncertainty associated to prediction of runoff. The stochastic integral equation method is used in this paper to represent the history of the rainfall-runoff modeling error as a convolution of model input (effective rainfall in this paper) with a frequency-distribution of transfer function realizations. In prediction, the expected runoff estimate is quantified by use of a distribution of runoff error estimates, each estimate of error based upon a previous experience using the subject rainfall-runoff model. Although this paper focuses upon a simple unit-hydrograph rainfall-runoff model, the principles discussed apply, in generality, to other rainfall-runoff model structures.

Evaluation of rainfall-runoff performance using the stochastic integral equation method

The stochastic integral equation method (S.I.E.M.) is used to evaluate the relative performance of a set of both calibrated and uncalibrated rainfall-runoff models with respect to prediction errors. The S.I.E.M. is also used to estimate confidence (prediction) interval values of a runoff criterion variable, given a prescribed rainfall-runoff model, and a similarity measure used to condition the storms that are utilized for model calibration purposes. Because of the increasing attention given to the issue of uncertainty in rainfall-runoff modeling estimates, the S.I.E.M. provides a promising tool for the hydrologist to consider in both research and design.

Approximating rainfall-runoff modelling uncertainty using the stochastic integral equation method

Although the uncertainty in rainfall-runoff model predictions has been frequently demonstrated, little attention has been paid towards including uncertainty in rainfall-runoff models, or providing a methodology that not only accommodates the uncertainty, but can be readily integrated into most rainfall-runoff modelling structures. In this paper, the uncertainty problem is approached by providing a methodology which can be incorporated into almost all rainfall-runoff models. The methodology is based upon the standard theory of stochastic integral equations which has been successfully applied to several problems in the life sciences and chemical engineering. The stochastic integral formulation is used to represent the total variation between a record of measured runoff data and model estimates. Because of the simplicity of the technique, the stochastic integral equation method can be integrated into most currently available rainfall-runoff models. The method provides the capability to develop probability distributions of almost all criterion variable estimates as produced from almost any rainfall-runoff modelling approach.