As industrial plants increase the number of wirelessly connected sensors for fault detection, a key problem is to identify and obtain data from the sensors. Due to the large number of sensors, random access protocols exploiting non-orthogonal multiple access (NOMA) are a natural approach. In this paper, we develop new algorithms based on approximate message passing for sensor identification and channel estimation accounting for correlation in the activity probability of each sensor and observations of physical variables (e.g., temperature) by the access point. These algorithms form the basis for data decoding, while also identifying faulty machines and estimating local values of the temperature, which can lead to a reduction in the amount of data required to be transmitted. Numerical results show that for an expected activity probability of 0.35, our algorithms improve the normalized mean-square error of the channel estimate by up to 5dB and reduce the rate of sensor identification errors by a factor of four.