Algorithm 1
Algorithm of the proposed framework for simultaneousfault diagnosis of timedependent ignition patterns.
Given a training dataset TRAIN_F of singlefault patterns only, a validation dataset VALID_F and a test dataset TEST_F of single  fault and simultaneousfault patterns (all datasets have been preprocessed by the combination of DK and WPT and PCA, as  presented in Figure 7(a)):  (i) Train the probabilistic classifier  includes pairwise classifiers as shown in Figure 6(b).  (ii) f VALID_F, prepare the probability vector  Calculate (f) = = (Figure 7(c)).  (iii) For k = 1 to Run a direct search technique, such as GA or PSO, M times  Produce an initial population for the decision threshold  (a) , find the classification vector y(f) = y = = according to (1).  (b) Calculate the measure with y(f) and l(f) using (12), that is, find over VALID_F,  where l(f) = [] is the true classification vector for input f provided from VALID_F.  (c) Produce next generation of  Until convergence or matching stopping criteria, return the best solution ε as the .  (iv) Among all , k = 1 to M, choose the one producing the highest Fmeasure as the optimal decision threshold .  (v) Return the trained probabilistic classifier and the optimized decision threshold as the main components of the  intelligent diagnostic system.  (vi) The performance of and can be evaluated with TEST_F and as illustrated in Figure 7(d). 
