Modelagem hipsométrica utilizando regressão simbólica e variável ambiental

Abstract

In planted forests, it is customary to measure the height of only a few trees in the plot and use the hypsometric relationship to estimate the remaining ones, thus reducing forest inventory costs. These estimates are usually made using regression models and artificial intelligence (AI) techniques. However, regression models are subject to dependence on statistical assumptions and sometimes a high number of equations, while AI techniques are concentrated only on ANN. Other techniques have emerged in the scientific community, but are still poorly studied, as is the case of symbolic regression (SR). In view of this, the present study aimed to verify the feasibility of using symbolic regression in the hypsometric modeling process. The data for perform the study come from a clonal plantation of Eucalyptus spp., located in the northern region of the state of Minas Gerais. The database is composed of 57 genetic materials, implanted in six spacings with ages ranging among 2 and 14 years. The database was partitioned into 70% for training and 30% for validation. For comparison, 5 traditional models (Curtis, Trorey, Simple Linear, Stoffels and Henricksen) and ANN were adjusted, then, to reach the best estimates of the data with SR, 5 different strategies were tested as input variables, being them E1: Dap; E2: Dap and Age; E3: Dap, project, species and spacing; E4: Dap, project, clone and spacing; E5: Dap, age, project and clone. For the inclusion test of environmental variables, a clone widely distributed throughout the area was selected and the variables pluviometric precipitation and average temperature obtained from meteorological stations were obtained. To assess the quality of the estimates were calculated correlation (r), mean absolute error (MAE) and square root of mean error in percentage (RMSE%). The main results were that the model generated by symbolic regression, with r of 0.7861, and RMSE% of 11.72%, proved to be more efficient than the other models and slightly inferior to the ANN. The E5 with mean absolute error of 1.44 m presented the best values for all presented statistics. With the qualitative variables the SR presented r of 0.8338, MAE of 1.53 m and RMSE of 9.96%. With the environmental variables, the SR presented r of 0.91 and RMSE of 5.49%, showing no gain in precision compared to the model without the variables. Symbolic regression proved to be a viable and efficient method for hypsometric estimates, presenting superiority to traditional hypsometric models, but when compared to ANN it achieved similar results, but not superior. The addition of dap, age, project and clone variables when used together in the symbolic regression model presented the best results. As this is an unprecedented topic within this approach to forest management, further studies are recommended so that the technique can be improved and consolidated.