HS model had the lowest mean RMSE. In Section 5.1, HS model showed lower
accuracy than type 1 and type 5 Prophet and Arima, but the effect of
hierarchical information pooling of HS model was significant when
applying new data that was not learned. HS model showed lower RMSE than
Arima in all types. Prophet showed lower RMSE in type 4 than HS model,
but did not show much difference.
5.2.2. New engine type
Robust estimation is possible even when forecasting the failure rate of
ship with unforseen engine type; information on engine archetype is
stored in hyperparameters of layer1 with which forecast can be made. In
other words, the resulting \(\overset{\overline{}}{\alpha_{0}}\ \) and\(\overset{\overline{}}{w_{0}}\ \) value of a prefit, B-spline fit on
averaged failure rate, are used for\(\overset{\overline{}}{\alpha_{s}}\ \)and\(\overset{\overline{}}{w_{s}}\ \)from equation 1.
Fig. 6, 7, and 8 show the prediction results of HS and comparative
models. Commonly, the black dots are the location of the test set data.
Small red dots are the location of the train data. The green lines of HS
model are the prediction line of each ship engine, the red lines are the
prediction line of each engine type, and the blue line is the engine
archetype prediction line. The blue line of Prophet and ARIMA is the
prediction line of the whole life cycle and corresponds to the archetype
prediction line of the HS model. In the figures, y-axis is expressed as
scaled values due to data privacy. The test for new engine type data has
the following meaning. As technology evolves, the new engine type will
replace the previous engine types. Or, depending on the purpose, you may
need to introduce a new engine type that has not been used before. In
this case, you can refer to similar types of engine type or engine
archetype trend for prediction. In this section, we confirmed that HS
performed well when only the information on engine archetype could be
referenced. The prediction situation in this section is notable because
it is the most difficult but necessary real situation. The accuracy was
compared with Prophet and Arima. The result is shown in Table 4.
In all new types, the HS model had a lower RMSE than the comparative
model. In the case of type 6, it is located in the section of 10 to 20
years with the smallest number of train data. The HS model predicts
relatively accurately by pooling information between layers even when
the number of data is small.
Table 4. Test set data RMSE (New ship engine which engine type was not
trained)