# Robust Algorithm for Calculating the Alignment of Guide Rolls in Slab Continuous Casting Machines
## 4 Results and Discussion
### Performance Under Error Influence
This is important because in the presence of a random distribution of errors, the compensation method is not able to completely remove the constant component of angle measurement errors. The geometric algorithms will accumulate the residual error while the third term of the optimization-based algorithm will suppress most of it. This effect seems to be the main reason for the superior results of the optimization-based algorithm. In Experiment 4, all error types except random angle measurement errors are set to zero. The zero-mean compensation is activated, even though it would not show a strong effect in this experiment, since the mean of the randomly sampled angle measurement errors is near zero by definition of the normal distribution. The result is shown in Figure 16.  
Both geometric algorithms show similar performance because the overall calculation error is much bigger than the systematic errors of the simplified algorithm. Their calculation errors mostly stay below 0.4 mm. The performance of the optimization-based algorithm is significantly better, with calculation errors mostly staying below 0.15 mm. No error accumulation is visible, since the error type is purely random. None of the algorithms can keep all calculation errors below the targeted 0.1 mm. This is the worst result of the four experiments (with activated zero-mean compensation), indicating that this error type is the primary cause of calculation errors. Experiment 5 combines all errors from the previous four experiments. This represents the most realistic case, since the error types never occur isolated in the real world. The first four experiments were useful to explore and understand the algorithm's behavior under different conditions. Experiment 5 will show which algorithm works best in a real world scenario. Figure 17 shows the result. Figure 16: Result of Experiment 4 with zero-mean compensation. The differences between the geometric algorithms differences are insignificant compared to the influence of the random angle measurement errors. In this experiment, the strengths of the optimization-based algorithm show clearly. The results of Experiment 5 are similar, but slightly worse than Experiment 4, indicating again that the influence of random angle measurement errors is dominant. Looking at the previous experiments, the reason why the other error types have minor influence becomes apparent: The radial components of the roll position errors do not have a strong influence because the algorithms are designed to calculate those. The tangential components of the roll position errors only have a small influence on the measured angles and thus on the algorithms. Lastly, the constant angle measurement errors are effectively removed by the zero-mean compensation. This leaves only the random angle measurement errors to have a strong impact on the performance of the algorithms. The results of all five experiments are summarized in Figure 18.  
Figure 17: Results of Experiment 5 with zero-mean compensation. The result is similar to Experiment 4, suggesting that random angle measurement errors are the dominant cause of computational errors. Figure 11:0 Results comparison for all experiments. Three metrics were extracted: the biggest computation error that occured in 100 runs, the threshold under which 90% of the computation errors occured and the mean computation error. The first four diagrams illustrate the sensitivity of each algorithm regarding the four error types. In the first and third experiment, the zero-mean compensation was turned off to better illustrate the algorithms properties. The rightmost diagram contains the result of Experiment 5, where all error types were combined to simulate a realistic scenario.