Monitoring the performance of soft sensors used in WWTPs by means of formal verification

In Waste-Water Treatment Plant (WWTP) automation, "soft" sensors might be used in conjunction with "hard" sensors to improve the reliability of the measurements, or even to replace the latter when they would be too expensive or difficult to maintain. Unfortunately, many soft sensors are created using black-box data mining techniques such as neural networks or Bayesian networks. These algorithms approximate the relation between simpler, more easily available data and the desired "sensed" quantity. However, they are usually dependent on the training data and cannot always generalise correctly when processing completely different inputs. Like their hardware counterparts, then, soft sensors may have input validity ranges. Moreover, they may be subject to "failures" when analysing inputs for which the training algorithm could not capture the input-output relation correctly. Due to their black-box nature, it is quite difficult to obtain a 100% accurate soft sensor and even more to debug it. So, in our approach, we propose to deploy a soft sensor together with a dedicated monitoring sub-system that processes the inputs and the outputs of the sensor itself. This monitor, created using a specific type of rules supporting the concept of "expectation", applies some logic criteria to define whether a particular sensing is acceptable or not for the purpose of the application using the soft sensor. We will discuss different types of criteria, both qualitative and quantitative, and how they impact the confidence in the estimated measurements. As a use case, we will present a soft sensor for the estimation of the nitrogen compounds in the aeration tank of a 500 litres pilot scale WWTP. Its performance, both in presence and in absence of the monitoring system, will be compared to a real nitrogen sensor placed in the same tank