  There are many advantages to use probability method for nonlinear system
identification, such as the noises and outliers in the data set do not affect
the probability models significantly; the input features can be extracted in
probability forms. The biggest obstacle of the probability model is the
probability distributions are not easy to be obtained. In this paper, we form
the nonlinear system identification into solving the conditional probability.
Then we modify the restricted Boltzmann machine (RBM), such that the joint
probability, input distribution, and the conditional probability can be
calculated by the RBM training. Binary encoding and continue valued methods are
discussed. The universal approximation analysis for the conditional probability
based modelling is proposed. We use two benchmark nonlinear systems to compare
our probability modelling method with the other black-box modeling methods. The
results show that this novel method is much better when there are big noises
and the system dynamics are complex.
