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Stochastic stem bucking using mixture density neural networks

Simon Schmiedel

TL;DR

This work tackles the challenge of optimizing stem bucking decisions under uncertainty by conditioning predictions of the unmeasured stem portion on previously measured diameters. It introduces a conditional mixture-density LSTM that predicts Gaussian parameters for the unknown portion, enabling multiple stem-profile samples, which are then optimized via a stochastic longest-path bucking algorithm. Across four conifer species from eastern Canada, the stochastic LSTM consistently yields better bucking decisions than a deterministic LSTM and polynomial benchmarks, highlighting the value of modeling uncertainty and conditioning on multiple measurements. The approach has practical potential to improve log value in forest operations and motivates future integration with sawmill optimization and broader species testing.

Abstract

Poor bucking decisions made by forest harvesters can have a negative effect on the products that are generated from the logs. Making the right bucking decisions is not an easy task because harvesters must rely on predictions of the stem profile for the part of the stems that is not yet measured. The goal of this project is to improve the bucking decisions made by forest harvesters with a stochastic bucking method. We developed a Long Short-Term Memory (LSTM) neural network that predicted the parameters of a Gaussian distribution conditioned on the known part of the stem, enabling the creation of multiple samples of stem profile predictions for the unknown part of the stem. The bucking decisions could then be optimized using a novel stochastic bucking algorithm which used all the stem profiles generated to choose the logs to generate from the stem. The stochastic bucking algorithm was compared to two benchmark models: A polynomial model that could not condition its predictions on more than one diameter measurement, and a deterministic LSTM neural network. All models were evaluated on stem profiles of four coniferous species prevalent in eastern Canada. In general, the best bucking decisions were taken by the stochastic LSTM models, demonstrating the usefulness of the method. The second-best results were mostly obtained by the deterministic LSTM model and the worst results by the polynomial model, corroborating the usefulness of conditioning the stem curve predictions on multiple measurements.

Stochastic stem bucking using mixture density neural networks

TL;DR

This work tackles the challenge of optimizing stem bucking decisions under uncertainty by conditioning predictions of the unmeasured stem portion on previously measured diameters. It introduces a conditional mixture-density LSTM that predicts Gaussian parameters for the unknown portion, enabling multiple stem-profile samples, which are then optimized via a stochastic longest-path bucking algorithm. Across four conifer species from eastern Canada, the stochastic LSTM consistently yields better bucking decisions than a deterministic LSTM and polynomial benchmarks, highlighting the value of modeling uncertainty and conditioning on multiple measurements. The approach has practical potential to improve log value in forest operations and motivates future integration with sawmill optimization and broader species testing.

Abstract

Poor bucking decisions made by forest harvesters can have a negative effect on the products that are generated from the logs. Making the right bucking decisions is not an easy task because harvesters must rely on predictions of the stem profile for the part of the stems that is not yet measured. The goal of this project is to improve the bucking decisions made by forest harvesters with a stochastic bucking method. We developed a Long Short-Term Memory (LSTM) neural network that predicted the parameters of a Gaussian distribution conditioned on the known part of the stem, enabling the creation of multiple samples of stem profile predictions for the unknown part of the stem. The bucking decisions could then be optimized using a novel stochastic bucking algorithm which used all the stem profiles generated to choose the logs to generate from the stem. The stochastic bucking algorithm was compared to two benchmark models: A polynomial model that could not condition its predictions on more than one diameter measurement, and a deterministic LSTM neural network. All models were evaluated on stem profiles of four coniferous species prevalent in eastern Canada. In general, the best bucking decisions were taken by the stochastic LSTM models, demonstrating the usefulness of the method. The second-best results were mostly obtained by the deterministic LSTM model and the worst results by the polynomial model, corroborating the usefulness of conditioning the stem curve predictions on multiple measurements.
Paper Structure (27 sections, 4 equations, 10 figures, 5 tables)

This paper contains 27 sections, 4 equations, 10 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Research context
  3. Literature review
  4. Research objectives
  5. Materials and methods
  6. Stem taper data
  7. Predictive taper model
  8. Architecture
  9. Loss function
  10. Benchmark models
  11. Stochastic bucking optimization
  12. Experimental design
  13. Hyper-parameter tuning for stochastic bucking
  14. Training the deterministic LSTM model
  15. Hyper-parameter tuning for the polynomial model
  16. ...and 12 more sections

Figures (10)

  • Figure 1: Sample of 26 stem profiles from the data set
  • Figure 2: Stochastic bucking as a longest path problem using multiple predictions of the same stem profile. The dotted red lines indicate where the cuts maximizing the value of the products generated will be made, the arrows depict the corresponding longest path and the grey dotted lines are the cuts that were not chosen.
  • Figure 3: Mean difference in value of products generated on the validation data between the optimal bucking decisions and the decisions taken by stochastic bucking, according to the species, prediction sample size, and $\lambda$ value.
  • Figure 4: Mean difference in value of products generated on the validation data between the optimal bucking decisions and the decisions taken by the polynomial models, according to the species and maximum order of the polynomial terms. 95% confidence intervals over the estimates of the means are displayed.
  • Figure 5: Bias of the predictions made by the stochastic LSTM models according to the height up to which the steam measurements were known and the height at which the predictions were made.
  • ...and 5 more figures