  Machine learning-based methods have achieved successful applications in
machinery fault diagnosis. However, the main limitation that exists for these
methods is that they operate as a black box and are generally not
interpretable. This paper proposes a novel neural network structure, called
temporal logic neural network (TLNN), in which the neurons of the network are
logic propositions. More importantly, the network can be described and
interpreted as a weighted signal temporal logic. TLNN not only keeps the nice
properties of traditional neuron networks but also provides a formal
interpretation of itself with formal language. Experiments with real datasets
show the proposed neural network can obtain highly accurate fault diagnosis
results with good computation efficiency. Additionally, the embedded formal
language of the neuron network can provide explanations about the decision
process, thus achieve interpretable fault diagnosis.
