Monitoring the performance of Soft Sensors used in WWTPs by means of Formal Verification

In Waste-Water Treatment Plant (WWTP) automation, “soft” sensors might beused in conjunction with “hard” sensors to improve the reliability of the measurements, oreven 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 suchas neural networks or Bayesian networks. These algorithms approximate the relationbetween simpler, more easily available data and the desired “sensed” quantity. However,they are usually dependent on the training data and cannot always generalise correctlywhen processing completely different inputs. Like their hardware counterparts, then, softsensors may have input validity ranges. Moreover, they may be subject to “failures” whenanalysing inputs for which the training algorithm could not capture the input-output relationcorrectly. Due to their black-box nature, it is quite difficult to obtain a 100% accuratesoft sensor and even more to debug it. So, in our approach, we propose to deploy asoft sensor together with a dedicated monitoring sub-system that processes the inputsand the outputs of the sensor itself. This monitor, created using a specific type of rulessupporting the concept of “expectation”, applies some logic criteria to define whether aparticular sensing is acceptable or not for the purpose of the application using the softsensor. We will discuss different types of criteria, both qualitative and quantitative, andhow they impact the confidence in the estimated measurements. As a use case, we willpresent a soft sensor for the estimation of the nitrogen compounds in the aeration tankof a 500 litres pilot scale WWTP. Its performance, both in presence and in absence of themonitoring system, will be compared to a real nitrogen sensor placed in the same tank.