Table 11 Performance metrics of proposed JO-LSTM controller for PWM and HBO-LSTM for BMS.

From: Battery management in IoT hybrid grid system using deep learning algorithms based on crowd sensing and micro climatic data

Parameter

statistical test

Test statistic (value)

p-value

Interpretation

Energy generation (PV & Wind)

T-test/ANOVA

F = 5.62

0.014

Significant variation in energy output under different conditions (p < 0.05)

Environmental data impact

Pearson Correlation

r = 0.85

0.001

Strong correlation between solar irradiance and energy output (p < 0.05)

Grid stability (voltage/frequency variations)

F-test (Levene’s Test)

F = 2.15

0.087

No significant variance in grid stability (p > 0.05)

Battery performance (SOC, DOD, efficiency)

Paired T-test

t = 3.98

0.008

Significant improvement in battery performance after optimization (p < 0.05)

IoT-based monitoring accuracy

Wilcoxon Signed-Rank Test

W = 175

0.022

IoT-based monitoring accuracy improved significantly (p < 0.05)

Harmonic distortions in grid

Kruskal–Wallis Test

H = 10.21

0.018

Significant reduction in harmonic distortions post-filtering (p < 0.05)

Deep learning algorithm performance (JO-LSTM, HBO-LSTM, SCO-LSTM)

ANOVA (Post-hoc Tukey Test)

F = 7.89

0.004

Significant difference in algorithm accuracy, favoring SCO-LSTM (p < 0.05)

Crowd-sensing data reliability

Cohen’s Kappa/Fleiss’ Kappa

κ = 0.78

High agreement among crowd-sensing sources (κ > 0.75 is considered strong)

Overall system efficiency

Regression Analysis

R2 = 0.92

 < 0.001

Strong predictive power of key parameters affecting system optimization