PBL
Let me, however, tell you what the answer is. You need 5 sensors to detect reliably when two of them are failing-live. That is a hard constraint. And no avionics designer in hisher right mind would seriously try to implement the algorithm that lets you do it with 5.
Actually there is another more reasonable way to cue the crew (and the flight control computers) that something is amiss.
How did the BEA determine that the two AOA sensors were frozen? Simple-they were not changing after the aircraft reached altitude.
There are a multitude of ways to cross check instrument indications and to alert the crew that something is wrong. In the case of AOA, airspeed vs AOA checks, AOA variation over time, test control inputs, noise in the AOA signal, and no doubt many more checks that I haven't mentioned. In the old days with single indicating systems, a prudent pilot was always questioning what he was being presented.
These same methods can be used to check a whole range of indications for validity. Would AF447 have been lost if there were an expert system monitoring the airspeed indications and noting that all 3 indications appeared to be bonkers just from an energy balance standpoint? Suppose both the computers and aircrew were advised that something was wrong with all three airspeed signals? Would that have made a difference in the outcome? (I know, sheer speculation at this point).
Voting algorithms still have a place for sorting out the best information to use of 3 inputs on modern airliners but are essentially defenseless against common mode failures.
An expert system to monitor the system inputs would not be a part of the core flight control system. If it were, it would slow down the process and make the problems of certification of flight control software an order of magnitude more complicated.
The expert system would be an add-on system which would have to be integrated into the total aircraft system. Its purpose would be to look for anomalous input data using a wide range of screening methods. It would then apply a confidence factor to any critical information being input into the flight control system. If the confidence factor in any critical input was too low, it would not be used for flight control, and the system would degrade as necessary to maintain control.
I do not expect such an expert system to be retrofitted into present aircraft, at least not anytime soon, but I believe such an approach promises a reasonable way around the voting algorithm limitations problem.