# Model Output Analysis

Once the model was developed, the Team analyzed the data for accuracy.  The Team graphed the data calculated by the mathematical model vs. the recorded data and performed t-tests to determine if the mathematical model results were statistically equivalent to the recorded data.  Analysis of Variance (ANOVA) was used to test the average fuel consumption amongst all vessels.

During the process of assigning sea state factors, the Team analyzed the ratio of the predicted to recorded fuel consumption data for assessing how well the model imitated real-life data.  For this measurement, a ratio of .7 to 1.3 indicated that the predicted data could be “equivalent to” the recorded data.  This ratio takes into consideration that models do not precisely represent real-world and because only two factors that affect sea state were taken into consideration.  Once the predicted-to-recorded fuel consumption ratios were within .7 to 1.3, the Team continued the mathematical model analysis.

The graphs below demonstrate the mathematical model results compared to the recorded data for each vessel.

Figure 20.  Bowditch - Predicted and Recorded Propulsion Consumption

Figure 21. Heezen - Predicted and Recorded Propulsion Consumption

Figure 22.  Henson - Predicted and Recorded Propulsion Consumption

Figure 23.  Mary Sears - Predicted and Recorded Propulsion Consumption

Figure 24.  Pathfinder - Predicted and Recorded Propulsion Consumption

Figure 25.  Sumner - Predicted and Recorded Propulsion Consumption

Overall, the graphics indicate that the mathematical model produced results that closely mimic the recorded real-life data.  The goal of the model was to predict ship fuel consumption based on power consumption.  Speed and sea state were determined to be the major additive parameters for fuel consumption.  The underlying hypothesis of the model was as follows:  Predicted fuel consumption will not be affected by the skeg modifications since it is computed from speed, but actual fuel consumption will be affected by the skeg modifications.  Because of this hypothesis, predicted fuel consumption was expected to deviate from actual fuel consumption when the skeg modifications occurred.  During the analysis, the Team determined that the mathematical model overestimated the fuel consumption prior to modifications and was nearly identical to the real-life fuel consumption data post modifications.

The Team then performed t-tests to determine if the predicted fuel consumption was statistically equivalent to the recorded fuel consumption.  The table below contains the results of the t-test analysis.

Table 1.  Predicted vs. Recorded Statistical Analysis

 Recorded vs. Predicted Fuel Consumption Paired T-test P-Value < 0.05? 95% CL USNS Bowditch No Reject H0 USNS Heezen Yes Fail to reject H0 USNS Henson No Reject H0 USNS Mary Sears Yes Fail to reject H0 USNS Pathfinder No Reject H0 USNS Sumner No Reject H0

The team used the paired t-test procedure to compare the mean difference between the recorded and predicted fuel consumption for each vessel.  The null hypothesis was a mean difference between the predicted and recorded fuel consumption did not exist, µpredicted = µrecorded.  The alternative hypothesis was a mean difference between the predicted and recorded fuel consumption existed, µpredicted ? µrecorded.

For the following four vessels, Bowditch, Henson, Pathfinder and Sumner, the team failed to reject the null hypothesis, there was no difference in the means between the predicted and recorded fuel consumption since the p-values for each of these vessels were greater than 0.05 at the ? = 0.05 level of significance.  Thus there was a lack of sufficient evidence to state that there was a difference between the predicted and recorded fuel consumption at the 95% level of confidence for Bowditch, Henson, Pathfinder and Sumner.

For the following two vessels, Heezen and Mary Sears, the team rejected the null hypothesis that there was no difference in the means between the predicted and recorded fuel consumption since the p-values for each of these vessels were less than 0.05 at the ? = 0.05 level of significance.  Thus the team rejected the null hypothesis in favor of the alternative hypothesis.  There was strong evidence that a difference between the predicted and recorded fuel consumption for Heezen and Mary Sears existed.  This analysis indicated that the mathematical model developed was sufficient for predicting fuel consumption in the real world.

Finally, ANOVA was used to test if the predicted average fuel consumption amongst all vessels were equal.  The average fuel consumption for before all modifications, post-skeg modification, and post- all modifications were analyzed for each vessel with applicable data.[1]  The null hypothesis was:

H0:  µfuel consump vessel 1 = µfuel consump vessel 2 = ... = µfuel consump vessel 6

The alternative analysis was that not all of the average fuel consumption amongst vessels was the same.  The analysis indicated that the null hypothesis was to be rejected for each case; the calculated p-value was less than 0.05, the ? level of significance.

[1] As previously discussed, Bowditch, Sumner has the same skeg and other modifications date; Henson and Mary Sears do not have available data post-other modifications; and Pathfinder has identical data points for post-skeg and post-other modifications.