Appropriate search techniques to estimate Weibull function parameters in a Pinus spp. plantation
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ORIGINAL PAPER
Appropriate search techniques to estimate Weibull function parameters in a Pinus spp. plantation Laís Almeida Araújo1 · Rafael Menali Oliveira1 · Mário Dobner Jr2 · Carolina Souza Jarochinski e Silva1 · Lucas Rezende Gomide1
Received: 11 August 2020 / Accepted: 24 September 2020 © Northeast Forestry University 2020
Abstract The Weibull function, a continuous probability distribution, is widely used for diameter distribution modelling, in which parameter estimation performance is affected by stand attributes and fitting methods. The Weibull cumulative distribution function is nonlinear, and classical fitting methods may provide a not optimal solution. Invoking the use of artificial intelligence by metaheuristics is reasonable for this optimisation task. Therefore, aimed and compared (1) the metaheuristics genetic algorithm and simulated annealing performance over the moment and percentile methods; (2) the hybrid strategy merging the metaheuristics tested and the percentile method and, (3) the metaheuristics fitness functions under basal area and density errors. A long-term experiment in a Pinus taeda stand subjected to crown thinning was used. According to our findings, all methods have a similar performance, independent of the thinning regimes and age. The pattern of the estimated parameters tends to be acceptable, as b increases over time and c increases after thinning. Overall, our findings suggest that methods based on metaheuristics have a higher Project funding: This work was supported financially by agency CAPES (Coordination for the Improvement of Higher Education Personnel) (Finance Code 001). The online version is available at https://www.springerlink.com. Corresponding editor: Zhu Hong. * Laís Almeida Araújo [email protected] 1
Department of Forest Sciences, Federal University of Lavras, Lavras, Minas Gerais, Brazil
2
Department of Agriculture, Biodiversity and Forests, Federal University of Santa Catarina, Curitibanos, Santa Catarina, Brazil
precision than classical methods for estimating Weibull parameters. According to the classification test, the methods that involved simulated annealing stood out. The hybrid method involving this metaheuristic also stood out, with accurate estimates. Classical methods showed the poorest performance, and we therefore suggest the use of simulated annealing due to its faster processing time and high-quality solution. Keywords Forest management · Diameters distribution · Weibull function · Genetic algorithm · Simulated annealing
Introduction Forest stand dynamics is characterised by a complex biological interaction between individual trees. Spatial distribution and resource availability change dramatically over time, resulting in altered tree growing space conditions (Li et al. 2013; Aakala et al. 2013). As a result, growth rate is affected by inter-tree competition and also influenced by tree size (diameter, height and crown area), age, site, stand density, thinning, diseases, pests, natural disturbances and genetic characteristics, amon
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