Hydrologic frequency linear parameter estimation method

Abstract

The invention discloses a hydrologic frequency linear parameter estimation method, which combines a simulated annealing-genetic algorithm (SAGA) and a maximum likelihood (ML) method to establish an SAGA-ML method, namely an expression for solving a minimal value of an opposite number of a likelihood function is taken as a target function, a parameter numeric area is estimated by a moments method, and is taken as a constraint condition, and then the SAGA is applied to perform parameter estimation. Essentially different from the thought of the conventional ML method, the SAGA-ML method carries out parameter optimization through a genetic algorithm. Monte Carlo experiments verify that the SAGA-ML method has good accuracy in aspects of parameter estimation and different frequency design value estimation; simultaneously, the method is not limited to linear type, parameter number and the constraint condition, can avoid the conditions that the likelihood function has no solution and the like when the conventional ML method is applied; and the solving process is simple, convenient and quick, so that the ML method become an effective method theoretically and practically.

Description

technical field [0001] The invention relates to a hydrological frequency analysis method, in particular to a hydrological frequency linear parameter estimation method. Background technique [0002] Hydrological frequency analysis is to study the probability of different numerical values ​​of a hydrological random variable, and to provide probabilistic hydrological design values ​​for the construction of water conservancy and hydropower projects, water resources evaluation and management, etc. Hydrological frequency analysis mainly involves two problems, one is line type selection, and the other is parameter estimation. So far, more than 10 line types have been used at home and abroad (Sun Jiliang, Qin Dayong. Research on the general model of hydrological frequency analysis [J]. Journal of Hydraulic Engineering, 1989, (4): 1-10; Jin Guangyan. Review of hydrological frequency analysis [J]. ]. Advances in Water Science, 1999, 10(3): 319-327), but what kind of probability distr...

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Problems solved by technology

From a comprehensive analysis, it can be seen that the above-mentioned commonly used parameter estimation methods mainly have the following problems: ①Except for MOM, almost all methods are affected by the line type when solving parameters, that is, for different distribution line types, the parameter solution expressions need to be derived separately and / or equation(s)

Although it is more intuitive and convenient to use MOM to solve the parameters, it does not vary with the distribution line type, but there are large errors in the results (especially when solving C s In practice, it is generally used to initially estimate parameter values; ②The process of solving parameters with various methods is more complicated and difficult

Even the relatively good POME and ML methods usually need to solve a nonlinear equation system, and the equation contains non-explicit functions such as Digamma function, which makes the solution difficult; ③The difficulty of solving parameters of various methods is affected by The number of parameters has a great influence; ④Although theoretically speaking, the parameter estimation effect of the ML method is good and the accuracy is high, but because the conventional method is to estimate the parameters by calculating partial derivatives, it brings many problems, and there are many defects in practical applications: One is that the solution process is difficult; the other is that it is generally considered that C s When >2, there is no local extremum, the likelihood equation has no solution, and the ML method is invalid at this time; the third is that when estimating the parameters of the P-III distribution, the parameter estimation results are insensitive due to the application of three first-order moments (Jin Guangyan .Review of parameter estimation methods in hydrological frequency calculation[J].Anhui Water Resources Science and Technology, 2004, 3:38-40), etc.

It is generally believed that C s > 2, there is no solution, only in [0, X min ] optimal solution; ② even if C s <2, since the three equations in formula (7) are nonlinear equations, and the first equation contains Digamma function, the solution process is difficult; ③ because three first-order moments are used in the solution process, the sequence Small values ​​play a dominant role in the determination of parameters, which is inconsistent with the actual situation

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