## 2 Experimental Approach and Optimization
### Experiments  
The measurement is influenced by various disturbances under laboratory conditions. Precise and useful measurements are desired under the following conditions:  
* **Constant velocity:** A measurement at constant velocity and without further disturbances is modelled. All measurements, with the exception of the acceleration and deceleration measurements, are performed at constant speed.
* **Acceleration & Deceleration:** The situation of accelerating and braking is emulated. This should according to [PERSON] [21] not affect the chord method. For this purpose, the slider is stopped several times along the rail and then set in motion again.
* **Heat:** Additional heat flux affects the optical properties of the air between the rail and the sensor. For this purpose, a 300 \({}^{\circ}\)C heat stream from a heat gun was directed towards the region between the sensor and the rail.
* **Water:** Wet track conditions occur in operation, for example during rainfall. Water or moisture on the rail will be rolled over, and will have no influence on the acoustic emission from the wheel-rail contact. Nevertheless, water can affect the optical measurement method, and must be considered in this study. Water is sprayed onto the surface of the rails. A uniform distribution is targeted, which is shown in Figure 2.
* **Dust:** Sand is applied to the rail near railway stations to achieve better adhesion. The sand would be overrun by following vehicles, and is therefore relevant for acoustic emissions resulting from the wheel-rail contact. In order to test the effect of the presence of particles on the rail surface, dust is applied to the rail. The particle distribution is kept identical for all tests with dust on the rail.
* **Displacement & Tilting:** Displacements of the entire measurement setup perpendicular to the rail surface occur because of the bogie suspension. A tilting of the measuring system can result, for example, from an inclined mounting position on the train. Both scenarios are artificially realized in the experimental setup by suspending the sensors from the pneumatic actuators. The degree of freedom to tilt in lateral direction is prevented by guides. The two pneumatic actuators are actuated at a frequency \(f_{P}\) using rectangular pulses, either synchronously (displacement) or asynchronously (tilting). The amplitude \(d\) represents the displacement at the location of each pneumatic actuator. Three different amplitudes are tested for displacement and tilting, respectively: \(\bigcirc\) Level 1: \(f_{P}=1\) Hz, \(d=0.5\) mm \(\bigcirc\) Level 2: \(f_{P}=1\) Hz, \(d=1.1\) mm \(\bigcirc\) Level 3: \(f_{P}=1\) Hz, \(d=2.0\) mm
* **Vibration:** Vibrations can originate from the train and its movement. [PERSON] et al. [27] applied a simulation for a car body structure to determine modal frequencies up to 29.598 Hz. Therefore, three different and realistic frequencies are tested experimentally from 20 Hz to 40 Hz, by inducing small displacements with the pneumatic actuators, using identical pneumatic pressures for all frequencies. \(\bigcirc\) Level 1: \(f_{P}=20\) Hz, \(d<0.1\) mm \(\bigcirc\) Level 2: \(f_{P}=30\) Hz, \(d<0.1\) mm \(\bigcirc\) Level 3: \(f_{P}=40\) Hz, \(d<0.1\) mm