Back toAbstract, Chapter 4.3.
Parameter estimation has been proven to follow the parameters of a time varying system. Parameter prediction for the linear parameter drift has been proven possible.
As shown in the simulation of online estimation, the model parameter follows the simulated plant's parameter, in this case the dominant pole.
Parameter estimation of plant parameters is a reliable method of fault detection, even if predictive trend analysis does not yield a fault prediction. For example, a prediction of no faults could be immediately followed by a sudden fault. In this situation, the parameter estimation is the best detection available.
Fault prediction was proven possible by figure 12. This figure shows the estimated parameter p1, and the prediction of the parameter as it experienced slow linear drift. Note that both sides of the confidence interval pass through the threshold on the graph, determining the lead time (min and max) for the failure to occur.
Obviously, the prediction procedure can't predict everything. A sudden change in the system can occur at any time, causing the predictions to be invalid. However, the sine-wave prediction simulation proves that the prediction routine can follow more than just a linear trend.
Prediction of failure is certainly possible for some failures. The fact that not all failures can be predicted should not prevent the use of a prediction technique. Prediction of just 1 fault could pay for the whole cost of implementation.
It was demonstrated in section 2.3.4 that monitoring a plant parameter to be within 10% of it's nominal value is not a valid fault criteria. Rather, it is necessary to consider the performance of the entire plant. Otherwise, the fault estimation/prediction would make nuisance declarations of faults.
The comparison of fault prediction models shows that a higher order AR model out-performs an ARMA(1,1) model significantly.
The predictions of figures 12-15 demonstrate that the confidence interval is good but not perfect. Since the model of the time series is estimated, there can be more to the time series than the form or the order of the model can represent. When this occurres, the prediction and the confidence intervals can deviate quite significantly from the model. The solution to this problem is to select a better model. However, in on-line applications, computer resources are limited.
Therefore, it is not feasible to try many different models until the best one is found. Therefore, it seems that the best model to use is the AR(n) model, where n is chosen to maximize performance of the predictions while fitting with the resources available.
An important factor in prediction is that the skip factor can be used to extend the prediction over a wider time-span while reducing the computation requirements. The range of the prediction is directly related to range of the historical estimates. Thus, the skip factor is used to reduce the computer computations wile increasing the time-span of the estimation input to the prediction routine. For example, it is possible to predict a failure several years in advance if several years of estimates are available. To extend the time-span, the estimated parameter time series must also cover a wider time-span. One way to accomplish this, would be for the flight control computer to save the last parameter estimate before power down in the computer's non-volatile memory (NVM). Then during initiated self test(Initiated Built In Test, IBIT), the computer could perform the prediction procedure. By storing the last parameter estimated during power down, a large skip factor is automatically introduced.
A design decision is necessary for the use of the NVM. As system ages and the NVM space becomes filled, the two design options are
1. replace the oldest estimate with each new estimate, or
2. keep the oldest estimate, and discard every other estimate in the NVM.
By discarding the oldest estimate to make space for each new estimate, the time span of the predictive diagnostics remains fixed. If the goal for prediction time span is within the time span covered by the NVM space allocation then this approach should be valid.
By keeping the oldest estimate, and discarding every other estimate in the NVM, the time span of the prediction routine is doubled. Once every other entry has been deleted, new estimates can be added to the free NVM spaces. This doubling of time span can be repeated until the desired time span is achieved.
By predicting failures days in advance, maintenance can be scheduled to replace or repair servos before they fail.
Fault prediction of several months will allow replacement spare parts to be ordered only when they are needed. This will allow a reduction in spare parts inventories.
Fault prediction years in advance will allow procurement of new more reliable equipment to replace the servos that are most apt to fail in service.
On line fault prediction will be useful for flight safety. If a fault is predicted minutes or hours in advance, a pilot can take action to prevent catastrophe.
On-line fault prediction will require a separate storage space in the computer memory for the time series of estimates because the time series in the NVM will have too wide of a time span to cover in-flight faults. In flight faults would appear sudden to the time series in the NVM.
Since prediction of linear drift has been proven successful, application should be attempted on a real servo system. Once the system is developed, experimentation should be done to determine the optimal prediction model for the system. Ideally, a graph should be developed to show a family of curves representing the model type, the computer resource usage, and the prediction accuracy averaged from several fault simulations.
Test results or field data for wear out failures experienced on existing servo systems would be useful to determine the nature of the time series most likely to be encountered.
More research is needed to determine the relationship between the rate or "suddenness" of a parameter's failure trend, and the success of failure prediction for that parameter. The result should be a direct relationship between the skip factor and the suddenness showing greater success for slower trends.References - Bibliography
Abstract - Fault Prediction With Regression Models