Convolutional Non-Homogeneous Poisson Process and its Application to Wildfire Ignition Risk Quantification for Power Delivery Networks

Abstract

To quantify wildfire ignition risks on power delivery networks, the current practice predominantly relies on the empirically calculated fire danger indices, which may not well capture the effects of dynamically changing environmental factors. This article proposes a spatio-temporal point process model, known as the Convolutional Non-homogeneous Poisson Process (cNHPP), and applies the model to quantify wildfire ignition risks for power delivery networks. The proposed model captures both the current (i.e., instantaneous) and cumulative (i.e., historical) effects of key environmental processes (i.e., covariates) on wildfire risks, as well as the spatio-temporal dependency among different segments of the power delivery network. The computation and interpretation of the intensity function are thoroughly investigated. We apply the proposed approach to estimate wildfire ignition risks on major transmission lines in California, using historical fire data, meteorological and vegetation data obtained from the National Oceanic and Atmospheric Administration and National Aeronautics and Space Administration. A comprehensive comparison study is performed to show the applicability and predictive capability of the proposed approach.

Keywords:

• Non-homogeneous Poisson process
• Power delivery networks
• Spatio-temporal point process
• Wildfire ignition risks

Supplementary Materials

The online supplementary materials include: the derivation of long-term cumulative effects h(i, t) (Supplement A), representation of cNHPP using the architecture of a Recurrent Neural Network (Supplement B), as well as the parameter estimation results of the RNN for Section 3.3.1 (Supplement C). We also provide the Python code for reproducing Table 1, Figures 6–8 in this article.

Disclosure Statement

No potential conflict of interest was reported by the author(s).