Statistical analysis and simulation matrices were developed for the systematic examination of how various parameters affect both the peak HRR and time-to-peak HRR on fire behavior within the cabinet.
Figure 1a–f present histograms of key cabinet parameters, providing an overview of the dataset used for subsequent simulations, and analysis lies in their ability to provide critical input parameters for fire behavior simulations, ensuring realistic modeling. Datapoint distributions for cabinet volume (height, width, and depth) based on cabinet width, ventilation area, HRRPUA, burning duration, ignition source, and ignition source elevation were developed using data from [
1,
2,
4,
10,
11,
12]. The HRRPUA and burning duration of the combustible materials were quantified using reported cone calorimeter test data [
11,
13,
14,
15]. The geometric details of the cabinets were derived from experimental studies [
2,
6,
11], including the height, width, depth, and total ventilation area of the cabinets, along with their combustible surface area. A series of 41 experimental tests were identified, each featuring unique geometric characteristics in
Figure 1a–c, which also illustrate the distribution of cabinet heights, widths, and depths, respectively. The average depth and width of the cabinets used in the fire experiments were 0.6 m and 0.8 m, respectively. The height of the electrical cabinets ranged from 1.2 m to 2.4 m, and this variation was utilized to adjust the cabinet volume in the simulations. Using this information, the cabinet volume in the simulations will be fixed and vary between 0.72 and 1.25 m
3. For variable and fixed configurations, the width will change from 0.6 to 0.9 m, and the height will be set at 2 m for the simulations. The ventilation area considered includes both the bottom and top vents of the cabinet. In some cases, the total ventilation area also accounts for doors open, doors closed, and holes in the cabinet’s ceiling [
6,
16] ranging from 0.05 to 0.25 m
2. Based on the data in
Figure 1a–c, the ventilation areas considered ranged from 0.04 to 0.16 m
2. The combustible surface area was determined from the surface area of the cables and computer board located inside the cabinet during the experiments. The combustible surface area data were determined from 36 experiments, with the distribution shown in
Figure 1d. The range in the total combustible surface area was taken as 0.6–1.8 m
2, which represented 64% of the data.
Data from electrical cabinet fire experiments [
6,
11] were combined to obtain detailed combustible burning information. These experiments provided data on heat release rate per unit area (HRRPUA), burning duration, heat flux, and ignition time. A total of 56 unique experiments were recorded. A majority of the cone calorimeter tests were conducted at a heat flux of 50 kW/m
2, whereas some were performed at 25, 35, 75, and 100 kW/m
2. Using these data, parameter levels for HRRPUA and burning duration were established from the 50 kW/m
2 experiments.
Figure 1e,f display the distributions of burning duration and HRRPUA. For the 10th to 90th percentile range, HRRPUA levels ranged from 90 to 200 kW/m
2, while burning duration ranged from 300 to 1800 s. Most cabinet fire experiments in the literature used an ignition source in the form of the initial HRR, ranging from 10 to 50 kW, which was used in this research.
2.2. Cabinet Parameter Study
The cabinet parameter study used a comprehensive approach that allows for a systematic investigation of how these variables affect fire dynamics. The cabinet volume was modified by altering its width, using three distinct values: 0.6, 0.75, and 0.9 m. The overall height of the cabinet remained constant throughout the simulations. The ANOVA method utilized in this research offers a more effective way to determine the significance of parameters impacting on peak HRR. The peak HRR and time-to-peak HRR are affected in cabinets by varying parameters, such as cabinet width, surface area of combustibles (wall and ceiling), ignition source, HRRPUA, ignition source elevation, ventilation area, and combustible burning duration. A random forest ML model was used to analyze past electrical cabinet fire experiments relevant to nuclear power plants [
17]. The developed model identified the most critical fire parameters and provided a computationally efficient framework to support probabilistic risk assessments. Unlike traditional methods that rely on Monte Carlo simulations [
18], the predictive approach directly quantifies the influence of key parameters on HRR, leading to a reduction in uncertainty during fire risk evaluations. Compared to traditional methods [
19], the ML approach better captured complex parameter interactions. Advancements in ML-based regression techniques [
20] allow for a better way to address intricate nonlinear behaviors, including fire dynamics, by capturing complex relationships and enabling more accurate predictions.
2.3. Combustible Configuration Study
In the configuration study, we set constant parameter values. While our study may resemble a cabinet parameter study, only the location of combustibles and the ignition source are varied to assess their impact on peak HRR, as shown in
Table 2.
Previous experimental studies have demonstrated that the configuration of combustible materials and the placement of the ignition source within the cabinet influence the HRR. However, past electrical cabinet fire experiments did not methodically examine the effects of combustible arrangement and the ignition-source location (bottom, corner, and top) on HRR [
2,
6]. The corresponding models are shown in
Figure 3,
Figure 4,
Figure 5 and
Figure 6, and the results of the combustible configuration study are summarized in
Section 3.2. To address this, a series of twelve distinct electrical cabinet configurations were carried out by varying the position of combustibles, as outlined in
Table 3. In fire experiments [
6], one common combustible setup involves loosely bundled cables running along the side walls of the electrical cabinet, spanning the entire length of the cabinet and igniting at either one end or both ends, terminating inside a burner.
In Configuration 1 (
Figure 3a), combustible panels are situated along the lateral walls, with the ignition source positioned at the bottom of the wall. In Configuration 2 (
Figure 3b), the ignition source is positioned at the bottom of both combustible panels to ensure it directly impacts the panels from the lowest point, influencing the fire’s spread. Configuration 3 (
Figure 3c) was designed to study an upward flame spread on the circuit boards. The circuit boards are mounted vertically on the back wall of the cabinet, and the ignition source is placed directly below them [
11]. This setup exposes one side of the combustible to fire, providing insight into how flames and combustion products may interact with critical electrical components.
In Configuration 4 (
Figure 4a), combustibles are positioned on the side wall and ceiling, along with the ignition source, which is placed at the bottom. In Configuration 5 (
Figure 4b), the ignition source is at mid-height (0.6 m), and in Configuration 6 (
Figure 4c), the ignition source is at the top (1.2 m) from the bottom. This setup is considered one of the conservative configurations. This variation in burner placement was intended to evaluate how the elevation of ignition source influences both the peak HRR and time-to-peak HRR, shedding light on the sensitivity of fire growth to ignition location within electrical cabinets.
In Configuration 7 (
Figure 5a), combustible panels are arranged along both lateral walls and the posterior wall, with a single ignition source placed at the bottom of the wall. In Configuration 8 (
Figure 5b), combustibles with three ignition sources are located at the base of the walls. In Configuration 9 (
Figure 5c), the combustibles are along one lateral wall, and the ignition source is at the base.
In Configuration 10 (
Figure 6a), combustible materials are placed along the rear wall, with the ignition source placed at the base. The results indicate a significant increase in peak HRR for this configuration, highlighting the critical role of material arrangement in cabinet fires. In Configuration 11 (
Figure 6b), combustibles are positioned parallel to the lateral wall. This arrangement allows air to circulate around the combustibles both vertically and horizontally, while also allowing the upward movement of air through the upper vent. Configuration 12 (
Figure 6c) is a mirror image of Configuration 3, with combustibles on both sides.