Hybrid Machine Learning-Based Fault-Tolerant Sensor Data Fusion and Anomaly Detection for Fire Risk Mitigation in IIoT Environment

. 2025 Mar 28;25(7):2146. doi: 10.3390/s25072146

Algorithm 2: Adjusted prediction for faulty sensors and dynamic belief mass for final fire prediction

Input: Multi Sensor fusion pre-processed data {S₁DP, S₂DP, S₃DP, S₄DP, S₅DP}
Output: the final prediction of fire based on belief and plausibility values considering normal and faulty sensors
Process:

#Train machine learning Model, MobileNet on RGB pre-processed sensor Data, EfficientNet on IR pre-processed #sensor #Data, RandomForest on Smoke pre-processed sensor Data, SVM on Gas pre-processed sensor

#Data, DecisionTree on Flame pre-processed sensor Data

#Get Class probabilities prediction from each Model for 5 different multi sensor for fire and NoFire.

      ML₁ = MobileNet(S₁DP)

      ML₂ = EfficientNet(S₂DP)

      ML₃ = Randomforest(S₃DP)

      ML₄ = SVM(S₄DP)

      ML₅ = DecisionTree (S₅DP)
#adjusted prediction based on sensor status and model output is calculated.

$C o m b i n e d W e i g h t f a c t o r (C W F) = P W C \times F R + P W C \times C S + P W C \times S S N R + P W C \times P S M + P W C \times E I F$

#Percentage of weight (%) for calculating combined weight factor(PWC), Failure rate based on #historical data(FR), Calibration of sensors(CS), Sensor signal to Noise Ratio(SSNR), #performance of sensor by metrics(PSM), environmental impacted factors(EIF)

#Probabilistic model adjustment based on sensor reliability. each Model, gives probabilities for #fire and no fire:

If S_iAD = 0 then--# If Si(sensor) is normal,

$({m (f i r e)}_{K} = P_{k} (f i r e| S_{i})$

${m (n o f i r e)}_{K} = P_{k} (n o f i r e| S_{i})$

Else --# if Si(Sensor) is faulty

${m (n o f i r e)}_{K} = P_{k} (n o f i r e| S_{i}) x C W F$

${m (f i r e)}_{K} = P_{k} (f i r e| S_{i}) x C W F$

#where CWF< 1 is to reduce the confidence from faulty sensors.

# Si where i ranges from 1 to 5 of sensors S₁, S₂ … S₅ which are RGB, IR, Gas, Smoke and Flame

#sensors and PK is a particular machine learning model respective to that sensor which are ML₁, ML₂, ML₃, #ML₄, ML₅ from where probability is derived for fire and no fire.
#Combine the confidence score from all models (both normal and faulty sensors), Ensemble Fusion with Weighted #Confidence Scores

$T o t l C o n f = \sum_{K = 1}^{n} {m (f i r e)}_{K} + \sum_{K = 1}^{n} {m (n o f i r e)}_{K}$
#Convert the class probabilities mi(fire), mi(no fire),mi(Θ)from each machine learning models into belief masses. #Fusion-Weighted Belief Mass Calculation

#Belief mass for fire

$m (f i r e) = \sum_{K = 1}^{n} \frac{P_{k} (f i r e| S_{K}) X {w e i g h t f a c t o r}_{K}}}{T o t l C o n f}$

#Belief mass for no fire

$m (n o f i r e) = \sum_{K = 1}^{n} \frac{P_{k} (n o f i r e| S_{K}) X {w e i g h t f a c t o r}_{K}}}{T o t l C o n f}$

#Where for Normal sensors weight factor will be set to 1, while faulty sensors factor is set less than 1 to reduce #their impact.

#Belief mass for entire hypothesis

$m (Θ) = 1 - (m (f i r e) - m (n o f i r e))$
#Dynamically Belief is calculated, the new belief is based on the latest sensor readings.

$M_{N e w} (f i r e) = α \cdot M_{P r e v i o u s} (f i r e) + (1 - α) \cdot P_{k} (f i r e ∣ S_{k})$

      #Where α is a weighting factor between 0 and 1 that determines how much influence the previous

      #belief mass has compared to the new evidence from the current sensor reading. 0.5 is used for

      #Balanced approach as the IoT environment is assumed to be stable environments
#calculate the Hellinger Distance H(m_i,m_j) between each pair of belief masses

$H D (m_{i}, m_{j}) = \frac{1}{\sqrt{2}} \sqrt{\sum_{k = 1}^{n} {(\sqrt{m_{i} (k)} - \sqrt{m_{j} (k)})}^{2}}$
#Deng Entropy DE(mi) is calculated for each machine learning model of sensors, the belief masses are adjusted

$D E (m i) = - \sum_{\{k = 1\}}^{\{n\}} m_{i} (k) l o g (m_{i} (k))$

$w_{i} = \frac{1}{1 + α \cdot H D (m_{i}, m_{j}) + β \cdot D E (m_{i})}$

#α controls how much weight the Hellinger Distance has in adjusting the belief mass.
#β controls how much weight the Deng Entropy has in adjusting belief mass.

8.
#Apply Dempster’s Rule of Combination iteratively for all pairs of belief masses

$m_{C o m b i n e d} (A) = \frac{\sum_{\{B \cap C = A\}} w_{1} m_{1} (B) . w_{2} m_{2} (C)}{(1 - \sum_{B \cap C = \emptyset} w_{1} m_{1} (B) {. w}_{2} m_{2} (C))}$
9.
#After combining the belief masses, compute the belief and plausibility for each class, The final belief mass mcombined #provides the combined evidence,

$B e l i e f (A) = \sum_{B \cap C = A} m_{c o m b i n e d} (B)$

$P l a u s i b i l i t y (A) = \sum_{B \cap A \neq \emptyset} m_{c o m b i n e d} (B)$
10.
#Dempster’s Rule is applied to combine belief masses mcombined(A) from all models, Repeated this combination #iteratively for all pairs of machine learning models of every multi sensors inputs
11.
#After combining the BPAs, calculated the belief and plausibility for each class Belief(A) and Plausibility(A)
12.
Determined the final prediction of fire based on belief and plausibility values

The final prediction was made based on the calculated belief and plausibility values:

I f B e l i e f (f i r e) > t h r e s h o l d, P r e d i c t = “ f i r e ”

I f B e l i e f (n o f i r e) > t h r e s h o l d, P r e d i c t = “ n o f i r e . ”

Otherwise, predict “undefined” or “uncertain”.

13.
#When fire predicted, API is called for SMS(POST/alert/sms), email (POST/alert/email),

#Push notification (POST/alert/push), and also API called for auto showdown (POST/alert/shutdown) of devices.
14.
#Send the final prediction to cloud/central server by calling the API (POST/models/update). Global Update #centralized model training received from all the remote sites through secured and authenticated API. Periodically #this global model will be updated back in the machine learning model in every remote sites edge server using API #(POST/models/update-global).

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