Is there any way we can predict a crash from the system inputs?
The question arises from this discussion.
Yes, many aircraft are fitted with TCAS which predicts one type of crash - an aerial collision.
Many aircraft are fitted with GPWS which predicts another type of crash - controlled flight into terrain.
The ground based ATC have systems that predict a loss of separation, the Short-Term Conflict Alert [STCA]. See this question about separation and conflicts. In terms of predictions this would constitute a very high rate of false positives. But that is good.
Because of the predictions, many crashes are avoided.
In addition to the systems listed by RedGrittyBrick, it is also possible to let the aircraft detect itself, from its sensors, potential crashes.
This problem has been studied, and is pretty well documented in a report made by the BEA (the French equivalent of the NTSB) after the crash of the flight AF447. The full report is available in French and in English. I made a summary of their work in this answer.
The solution proposed in this report is a triggered transmission of flight data. The aircraft transmits them only if it detects a potentially dangerous situation from its sensors (this reduces the load on communication systems).
Two types of triggering criterion are proposed :
One base on binary logic
One based on Fuzzy logic
They both take into account several parameters (speed, pitch angle, pilot's inputs...) and verify some relations about them. For example, if
roll > 50° for more than 2s, something is probably wrong.
The criterion have been check against a database of real flight data recovered from crashed aircrafts, in order to assess their performances :
The robustness of the triggering criteria was evaluated using the following metrics:
False detection rate (or nuisance trigger rate): out of all the normal flights, how many are considered as containing an emergency situation
Nuisance transmission time that the nuisance triggers generate
Emergency situation detection rate: out of all the accident/incident flights, how many are considered as containing an emergency situation
For flights with a correctly detected emergency situation, what is the warning time between the time of detection and the time of impact with the surface
The conclusion of these tests is that accidents were almost always predicted (binary logic failed in only one case out of 44, fuzzy logic detected every case). On average, the problem was raised about 350s before the actual crash (the median is around 33s, minimum at 3s and maximum at 10,019s).
The second half of the report discusses different system to transmit these triggered alarms to infrastructures on the ground. It is also interesting and well written, but outside the scope of this question.