Modelling the qualitative structure of Scots pine trunks using a random process

Abstract

The study highlights a method for predicting the volume of qualitative categories of trunk wood for timber trunks of Scots pine, using a model of distribution of various qualitative zones along the trunk. The study is based on empirical material collected in the main-use cutting area, where the length of various qualitative wood zones from the butt to the top was determined for 245 model trees. The paper uses a semi-Markov probabilistic model to generalise the order of appearance and length of zones of timber wood, firewood, and waste, which was determined by three parameters: 1) input probabilities of the appearance of the corresponding qualitative zone in the butt part of the trunk (initial state); 2) matrix of distribution of zone lengths; 3) matrix of probabilities of changes in qualitative zones at different heights of the trunk. According to research data, it is generally accepted that pine trunks begin with timber wood. The beta distribution function is used to model the length of qualitative trunk zones, the parameters of which are selected depending on the relative height of the beginning of the corresponding trunk zone. The probabilities of changes in qualitative zones are calculated based on empirical data. The study identified that the distribution of timber and firewood lengths depends on the absolute height of the trunk location and the height of the trunk. For a mathematical generalisation of this process, the paper defines four zones within which the distribution of the length of the timber part of the trunk can be described by a single function. The probabilities of changes in qualitativ e zones are modelled depending on the relative height of trunks. On this basis, the method of simulation modelling of initial data sets has been developed, which can be used to develop tables of dimensional and qualitative wood structure for trunks of different diameters, heights, and categories of technical suitability. The study applies only to timber pine trunks, so other patterns are probable for trunks of other tree species, semi-timber, and firewood trunks. The developed methodology is appropriate to use when updating the tables of trunk volume distribution by variable-quality categories, which now need to be updated by introducing new requirements for the classification of timber wood in Ukraine

Keywords

• merchantable wood
• distribution function
• semi-markov probability model
• volume tables