## 3 Materials and Methods
### Outliers  
Outliers are defined as data points that lie far away from the main clusters of data and are caused by experimental errors, measurement variation, changes in system behavior, human error, or natural deviations in populations. In research, numerous approaches exist for the detection of outliers, which are also referred to as anomaly detection or novelty detection. Essentially, they can be categorized into the three areas of statistics, neural networks, and machine learning [41]. A further distinction is made between methods for univariate and for multivariate analyses. The first approaches for outlier detection were developed using statistical methods [42,43]. Statistical methods are based on proximity-based, parametric, non-parametric, and semi-parametric methods. Often, fixed threshold values or dynamic values (e.g., interquartile range, standard deviation) are used for univariate outlier detection. Methods used in the field of neural networks and machine learning offer a wide range of applications for multivariate analysis. [PERSON] and [PERSON] (2004) provide a comprehensive overview of different methods and areas of application for outlier detection [41]. The selection of the appropriate method essentially depends on the type of dataset with regard to the underlying distribution model, scalability, speed, and modeling accuracy. The presented approach addresses a univariate data analysis problem, whose outlier detection should be kept simple and low-computational due to the subsequent continuous update of model input parameters. Therefore, no algorithms from machine learning or the field of neural networks are considered. The application of an exemplary statistical filter using 1.5 times the interquartile range for outlier detection is shown in Figure 4a. As can be seen, values near zero are not detected using this method, although they are physically impossible. Values above 70 are identified as outliers, although they belong very likely to the natural population of the ringbuild duration dataset. The difficulty in outlier detection is excluding measurement errors while taking extreme values, which are of high importance for reliable forecasts, into account. In tunneling, this is especially quite complex, since data fluctuate a lot, particularly due to the uncertainty of the ground conditions. The challenge of distinguishing extreme values from outliers cannot be tackled by any statistical filters. Plausibility checks can be performed in parallel, however, to support the detection of sensor failures (e.g., comparison of accumulated cycle times to total time). The rule-based detection of outliers offers the possibility to include domain-specific knowledge in outlier detection. Permissible range limits are defined for each parameter by a project-specific expert evaluation, and physically impossible values are deleted by rule-based cleaning (e.g., durations below zero). Figure 4b illustrates such rule-based cleaning. In this particular instance, experts defined that the ringbuild could not be performed faster than 17.5 min per ring (2.5 min per segments). Consequently, any values below this threshold are considered invalid. For the upper threshold, a value of 180 min has been set to include extreme values while excluding instances of highly disturbed ringbuild durations. Data points above this value can be attributed to downtimes or are discarded if plausibility checks fail. The definition of the upper value can be supported using statistical values; however, it should always be checked by experts. Noise in Time Series  
Data from construction sites are influenced by multiple components and are rarely free of noise. Dealing with noise is one of the challenges in data processing and data mining that makes it difficult to identify an underlying distribution or a trend in the data. It is usually caused either by implicit errors, by measurement instruments, or by random errors. Data polishing and filtering methods are generally employed to reduce noise.