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Machine learning algorithm has brought the augmenting change in the field of artificial intelligence which espoused human discerning power in a splendid manner. The algorithm has various categories among which classification is the most popular part. Support vector machine algorithm, logistic regression, naïve bays algorithm, decision tree, boosted tree, random forest and k nearest neighbour algorithm all are under classification algorithms. Classification process needs some pre-defined method which leads the method for choosing the train data from the sample data given by the user. Decision making is the heart of any classification algorithm as supervised learning stands out on the decision of users. So the strong mathematical model based on conditional probability lies behind each algorithm. This paper is the study of those mathematical models and logic behind various classification algorithms which help to create a strong decision for users to make the training dataset based on which machine can predict the proper output. Markov chain model Markov chain model is a statistical and mathematical setup which has some hidden layers and can be represented as the simple Basyian network which is directly visible to the observer. This model has a remarkable contribution in the field of supervised and reinforcement learning and for pattern recognition. If any example is considered for two classes i.e. A and B and it has 4 transitions when the system is in A then it can be considered as a transition of B similarly when a system is in B it can be considered as a transition of A (Fig1). In that way, a transition matrix will be formed which will define the probability of transition of the state. In that way not only in two classes but also with n no of classes or states the model can be built up.

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Vibration failure in the pumping system is a significant issue for industries that rely on the pump as a critical device which requires regular maintenance. To save energy and money, a new automated system must be developed that can detect anomalies at an early stage. This paper presents a case study of a machine learning (ML)-based computational technique for automatic fault detection in a cascade pumping system based on variable frequency drive (VFD). Since the intensity of the vibrational effect depends on which axis has the most significant effect, a three-axis accelerometer is used to measure it in the pumping system. The emphasis is on determining the vibration effect on different axes. For experiment, various ML algorithms are investigated on collected vibratory data through Matlab software in x, y, z axes and performances of the algorithms are compared based on accuracy rate, prediction speed and training time. Based on the proposed research results, the multiclass support vector machine (MSVM) is found to be the best suitable algorithm compared to other algorithms. It has been demonstrated that ML algorithms can detect faults automatically rather than conventional methods. MSVM is used for the proposed work because it is less complex and produces better results with a limited data set.

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