Modelling Soil Water Retention Using Support Vector Machines with Genetic Algorithm Optimisation

Abstract

This work presents point pedotransfer function (PTF) models of the soil water retention curve. The developed models allowed for estimation of the soil water content for the specified soil water potentials: –0.98, –3.10, –9.81, –31.02, –491.66, and –1554.78 kPa, based on the following soil characteristics: soil granulometric composition, total porosity, and bulk density. Support Vector Machines (SVM) methodology was used for model development. A new methodology for elaboration of retention function models is proposed. Alternative to previous attempts known from literature, the ν-SVM method was used for model development and the results were compared with the formerly used the C-SVM method. For the purpose of models' parameters search, genetic algorithms were used as an optimisation framework. A new form of the aim function used for models parameters search is proposed which allowed for development of models with better prediction capabilities. This new aim function avoids overestimation of models which is typically encountered when root mean squared error is used as an aim function. Elaborated models showed good agreement with measured soil water retention data. Achieved coefficients of determination values were in the range 0.67–0.92. Studies demonstrated usability of ν-SVM methodology together with genetic algorithm optimisation for retention modelling which gave better performing models than other tested approaches.

A Plant Propagation Algorithm for Constrained Engineering Optimisation Problems

“…, NP do (8) ← set of runners where both the size of the set and the distance for each runner (individually) are proportional to , the normalized objective value (9) Φ ← Φ ∪ {append to population}; (10) end for (11) ← Φ {new population}; (12) end for (13) Return , the population of solutions. for = 1 to do (14) if ≤ NP then (15) if rand ≤ then (16) Generate a new solution * according to (5); (17) Evaluate it and store it in Φ; (18) end if (19) if rand ≤ then (20) Generate a new solution * according to (6); (21) Evaluate it and store it in Φ; (22) end if (23) else (24) for = 1: do (25) if ( < 4) or (rand ≤ ) then (26) update the th entry of , = 1, 2, . .…”

“…In the exact category, one can name Branch-and-Bound, [7], Recursive Quadratic Programming, [8], the Cutting Plane Algorithm [9], Bender's decomposition [10]. Of the approximate variety, one can name Simulated Annealing, [11][12][13], the Genetic Algorithm [14][15][16], and the Particle Swarm Optimisation algorithm, [17,18], to name a few. The latter category is often referred to as the metaheuristic algorithms.…”

Assessment of the usefulness of particle size distribution measured by laser diffraction for soil water retention modelling

“…The developed models rely on one parameter—the penalty parameter C— with its value determined using a genetic algorithm by minimizing the aim function which is the root mean square error (RMSE) between measured values of water content and those approximated by the model. Details of this SVM modeling approach for PTF development are presented in Lamorski et al (2014).…”

Pedotransfer in soil physics: trends and outlook — A review —

“…The uncertainty in PTF estimates may be evaluated using replicated PTF development with data resampling by either the bootstrap (SCHAAP et al, 1998) or jackknife methods. Another technique to reduce over-fitting of PTFs is using cross validation (MARTIN et al, 2009;LAMORSKI et al, 2014;TÓTH et al, 2015).…”