A hybrid global optimization method for inverse estimation of hydraulic parameters: Annealing‐Simplex Method

Abstract

Abstract. Inverse estimation of unsaturated hydraulic parameters is often a highly nonlinear optimization problem with multiple parameters. The objective functions involved are often topographically complex and may contain many local minima. Because of these reasons, the inverse solutions are commonly very sensitive to the initial guess of the parameters when conventional optimizers are used. This paper presents an annealingsimplex method that incorporates simulated annealing strategies into a classical downhill simplex method. An upward infiltration experiment was used as an example of inverse estimation to test the method. Numerical experiments of both minimizing an algebraic function and inversion of upward infiltration data showed that the new method successfully converged to the global minimum in all cases, irrespective of the initial hydraulic parameter estimates, while the classical downhill method often converged to unfavorable local minima. The CPU times needed for the annealing-simplex method to estimate 5 and 7 hydraulic parameters simultaneously are about a half hour and 1 hour on a PC, respectively. Additionally, no special requirements are imposed on the objective function, and the method is independent of the details of the simulation submodel. Therefore the proposed method should be applicable to other optimization problems in water resources when it is important to have a robust global search capability. IntroductionKnowledge of unsaturated soil hydraulic properties is essential for prediction of water flow and contaminant transport through the vadose zone. Specifically, the hydraulic properties are the water retention and hydraulic conductivity functions, both of which are highly nonlinear functions of the soil water pressure head. As opposed to more classical direct method, inverse estimation of the hydraulic properties from transient flow experiments has recently become more popular because of its flexibility in considering various data types, availability of more powerful computers, and the presence of increasingly accurate flow simulators [Kool and Parker, 1988 Hence, like many other geophysical inverse problems, the inverse estimation of hydraulic parameters of soils is a strongly nonlinear and multiparameter optimization problem that often involves finding the global minimum in between many local minima. The simulated annealing method, first incorporated into numerical calculations by Metropolis et al. The objective of this paper is to develop an effective and efficient inverse parameter estimator that can be used to find unique and stable parameter estimation given that the experiment is well designed to ensure identifiability. We will apply the estimation to the upward infiltration experiment described by Hudson et al. [1996]. A key step in our work is the development of a new technique of combining the classical downhill simplex method with the simulated annealing method in order to find the global minimum of the objective function in an efficient and effective manner. Being different ...

Estimation of reservoir properties using transient pressure data: An asymptotic approach

“…ods attempt to estimate parameters using stochastic optimization methods such as simulated annealing [Mauldon et al, 1993] or hybrid schemes such as simplex annealing [Pan and Wu, 1998]. More commonly, a linearized inversion technique is used iteratively to estimate parameter values.…”

On the use of surrogate-based modeling for the numerical analysis of Low Impact Development techniques

“…However, these methods are sensitive to the initial values of optimized parameters and the algorithm often remains trapped in local minima, especially when the response surface exhibits a multimodal behavior. These considerations inspired researchers to develop and use global optimization techniques such as the annealing-simplex method (Pan and Wu, 1998), genetic algorithms (Ines and Droogers, 2002), shuffled complex methods (Vrugt et al, 2003), and ant-colony optimization (Abbaspour et al, 2001), among many others.…”

A novel fault diagnosis method for rotating machinery based on S transform and morphological pattern spectrum

“…Based on an inverse estimation approach [38], these parameters were obtained with reference to online speed, current and voltage measurements under different external loads. Solving Equation (29) obtains the electrical current and then provides the voltage prediction Upre(kV,i,Rin,j) across the external resistances under a number of incremental voltage constants kV,i and internal resistances Rin,j.…”