Generic flame extension model development based on machine learning for NPPs fire hazard analysis (FHA)

Pavan K. Sharma

doi:10.1515/kern-2023-0097

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Generic flame extension model development based on machine learning for NPPs fire hazard analysis (FHA)

Pavan K. Sharma

Published/Copyright: February 19, 2024

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From the journal Kerntechnik Volume 89 Issue 1

Abstract

In enclosed fire situations, the flame interacts with ceiling and its length extension take place, altering the fire severity significantly. Fire safety analysis demand a generic flame extension model. A generic reliable model is not available as the construct of flame itself had wide variation in literature. The present paper aims to develop a Machine Learning (ML) based generic model of non-dimensional flame extension as a function of non-dimensional Heat Release Rate (HRR). The non-dimensional scaling reduces the number of parameter and also provide a generic nature. Literature review was utilized to collect the data from various open literature sources. This eliminates the limitations of individual correlations and gives a best optimized model which is valid for a wide range of flow regimes and conditions as compared to a specific correlation. Various simple ML models are compared for their performance against test data and a MARS based model was finally recommended. The MARS model was tested against the data which was not used in training and also against the other reported correlation. The developed model has performed well against the test data and marked improvement over other reported correlation as a better optimized performance over an extended range of non-dimensional range. The results of the model were also conservative as compared to another model in the most of the practical requirement of NPPs. A Large Eddy Simulation (LES) based CFD code FDS was also used to generate the flame extension data for demonstrating conservative nature of the ML model.

Keywords: flame extension; CFD; fire hazard analysis; machine learning

Corresponding author: Pavan K. Sharma, Reactor Safety Division, Bhabha Atomic Research Centre, Mumbai, India, E-mail: pksharma@barc.gov.in

Nomenclature

C _p: thermal capacity of air kJ/Kg
D: Equivalent fire diameter, m
∂x: Maximum of domain size in x, y, z direction/grid number in x, y, z direction
g: acceleration due to gravity, m/s²
H: Vertical height of ceiling, m
R*: Resolution index
T _∞: Ambient temperature

Greek Symbol

ρ _∞: Density of air, kg/m³

Subscripts or Superscripts

nondim: Non dimensional

Abbreviations

BARC: Bhabha Atomic Research Centre
CFD: Computation Fluid Dynamics
CV: Cross-validation
FDS: Fire Dynamics Simulator
FHA: Fire Hazard Analysis
GCV: Generalized Cross-validation
HRRPUL: Heat Release Rate Per Unit length
LES: Large Eddy Simulation
MARS: Multivariate Adaptive Regression Splines
ML: Machine Learning
NPPs: Nuclear Power Plants
OLS: Ordinary Least Square
RANS: Reynolds-averaged Navier–Stokes

Research ethics: Not applicable.
Author contributions: The author has accepted responsibility for the entire content of this manuscript and approved its submission.
Competing interests: The author states no conflict of interest.
Research funding: None declared.
Data availability: Not applicable.

Appendix

Step 0: Problem Analysis

Variables considered in the model are (i) non-dimensional HRR (ii) flame extension. In this problem, various models are utilized i.e. Linear regression, Decision Tree regression, Lasso regression, Ridge regression, Random Forests regression and finally MARS regression which will study the correlation between the non-dimensional HRR and flame extension.

Step 1: Importing the libraries

The first step will always consist of importing the libraries that are needed to develop the ML model. The NumPy, matplotlib and the Pandas libraries are imported.

import numpy as np

import matplotlib.pyplot as plt

import pandas as pd

Step 2: Preparing and Importing the Dataset

Before importing the data, the data was prepared using the digitisation of graphs available in open literature data. The objective of the present work is to prepare a safe and reasonably conservative correlation for regulatory application. In this step, we shall use pandas to store the data prepared and store it as a Pandas DataFrame using the function ‘pd.read_csv’. In this, we assign the independent variable (X) to the ‘non-dimensional HRR’ column and the dependent variable (y) to the ‘flame extension’ column.

Step 3: Splitting the dataset into the Training set and Test set

In the next step, dataset is splitted as usual into the training set and the test set. In present study, 75 % flame extension data (as a function of non-dimensional HRR) for training and remaining 25 % flame extension data for ML testing.

from sklearn.model_selection import train_test_split

train, test=train_test_split(gdpdata)

Step 4, 5, 6, 7, 8, 9: Training for Various Models

Linear regression, Decision Tree regression, Lasso regression, Ridge regression, Random Forests regression and finally MARS regression model were used on the training set. The DecisionTreeRegressor class imported from sklearn.tree and assigned it to the variable ‘regressor’. Then X_train and the y_train have been fit to the model by using the regressor.fit function.

#:Linear Regression

from sklearn.linear_model import LinearRegression

model=LinearRegression().fit(train.iloc[:,:1],train.iloc[:,1:])

Step 10: Predicting the Results

In this step, the results predicated of the test set with the model trained on the training set values using the regressor.predict function and assign it to ‘y_pred’.

y_pred=regressor.predict(X_test.reshape(-1,1))

Step 11: Comparing the Real Values with Predicted Values

In this step, comparison and display of the values of y_test as ‘Real Values’ and y_pred as ‘Predicted Values’ is to be carried out in a Pandas dataframe. In all graphs, the Real values are plotted with “Red” color and the Predicted values are plotted with “Blue” color.

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Received: 2023-09-18

Accepted: 2024-01-17

Published Online: 2024-02-19

Published in Print: 2024-02-26

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https://doi.org/10.1515/kern-2023-0097

Keywords for this article

flame extension; CFD; fire hazard analysis; machine learning