Identifying algorithm for Markov network parameters

By | 14.02.2018

To solve the problems with forecasting of plane crashes periodicity Markov networks can be used. Recent researches made in different fields (from psychology to diagnostics and forecasting in complex technical systems) show that such models can be adapted to solve a wide range of technical (engineering) problems. Terminologically using Markov networks can be considered as an analog of neural network model.

Elements in these networks perform the variety of states of Markov processes and are analogs of traditional neurons. Neuron transformations that are usually set using activation functions are described in ordinary Kolmogorov differential equations. These transformations determine the dynamics of changes in probability of staying in network states. The intensities of event streams is used as the weights, and the probabilities of staying in corresponding states are the inputs and the outputs.

To determine the intensity of an event flow the identification of parameters of network transition from one state to another can be done. The identification process involves transition intensity values selection. The intensity values should in the best way correspond to observational data.

Specialists of “PAWLIN Technologies” company developed the algorithm of finding the optimal intensity values for transitions from one state to another for Markov networks. This algorithm is designed for networks of random architecture uses as input data the table of observational data about staying in different states. The optimization functional of this algorithm is the value of square of x statistics. The video on YouTube presents the work of the algorithm. We can see how the value in the Ch-sq cell gradually approaches the minimum statistics value in the Ch-sq MIN cell. In real time on the central diagram, graphs of the probabilities of staying in Markov networks states are displayed. The values in Opt par cells show current values of the intensities. Target cells show true values that are known from the test case. The values in Ration prob cells show the ratio of the known intensity values to the values found at this step of the algorithm.