# Similarity Analysis for Time Series-Based 2D Temperature Measurement of Engine Exhaust Gas in TDLAT
## 3 Experiment and Tomography Analysis  
A schematic diagram of a TDLAS system measuring engine exhaust temperature is shown in Figure 2. The OHC (over head camshaft) gasoline engine (EX17, Subaru Robin, Doylestown, PA, USA) is driven in idle mode to produce emissions. The exhaust pipe installed 5 mm below the measurement cell was 20 mm in diameter and 150 mm in length. The distributed feedback (DFB) laser (NLK1E5 GAAA, NTT Electronics, Japan) for H\({}_{2}\)O gas target is tuned to the near-infrared spectral region at 1388 nm by a laser diode controller (LDC-3900, ILX Lightwave, Bozeman, MT, USA). The modulated laser beam is split into 16 channels by a 1 \(\times\) 16 fiber optic coupler (SMF-28e, OPNETI, NY, USA). Among them, the 10 beams are irradiated into 10 collimators (50-1310-APC, THORLABS, Newton, NJ, USA) and the transmitted optical signals are detected by 10 photodetectors (G12180-010A, Hamamatsu Photonics, Japan). The received laser signals are amplified and filtered by low pass filters to remove signal noise. The amplified signals are transmitted into a data recorder (8861 Memory High Coda HD Analog16, HIOKI, Japan) in real time at a sampling rate of 500 kHz. Simultaneously, the real temperature for verification is measured by a B-type TC at the sampling rate of 1 kHz at the center of the target area. After absorption, signals collect by the data acquisition card are sent to the computer for reconstruction calculation. Multiple parallel laser beams pass through the region of interest. The intersected spectral information is used to reconstruct 2D temperature by CT analysis. Figure 3 shows the laser paths and grids in the measurement region. The laser path consists of 10 real beams in a 5 \(\times\) 5 layout and eight interpolated virtual beams The interpolated virtual beams imply the virtual signal data interpolated from the signal of the actual beam, and in the signal application field a widely introduced cubic spline interpolation is used in this study [22]. The cell length through which the laser passes in the measurement area is 60 mm and reconstruction area is 40 mm, and the spatial region for CT analysis consist of 81 (9 \(\times\) 9) square grids with a grid size of 2.0 mm \(\times\) 2.0 mm. Figure 1: Theoretical H\({}_{2}\)O absorption spectrum. Unexpected error signals due to harsh conditions were removed to reduce reconstruction calculation time for converging. The formula is as follows:  
\[\delta_{t}=\sum_{n=1}^{N}\frac{\left|\overline{I}_{v0,i}-\overline{I}_{v,i} \right|_{t}}{\left|\overline{I}_{v0,i}-\overline{I}_{v,i}\right|_{t-1}}, \tag{5}\]  
where, the subscript \(t\) denotes a cycle at \(t\) time and \(n\) denotes the data number in a cycle. \(\delta\) denotes the error rate, which is a ratio of absolute error sum in \(\overline{I}_{v}\) and \(\overline{I}_{v0}\) of the cycle to that of the previous cycle. Here, the signal cycle was eliminated when \(\delta_{t}\) is greater than 1.5. This method effectively reduced the error when converting the signal into the spectra. The noises generated by beam steering, window foul, and thermoelectric noises were approximated by Gaussian noise modeling, and the stabilized absorption spectra was obtained by the polynomial reduction method (PRM) averaging a number of absorption signal cycles [10; 23; 24] Although averaging a significant number of absorption cycles provides more stable signal, it has the drawback of degrading time-resolution and distorting raw signals. Hence, it is necessary to investigate appropriate number of cycles with good reconstruction performance and fast time-resolution simultaneously. Figure 4 shows the result of mean transmitted signals (\(\overline{I}_{v}\)) and mean absorption spectra using a total of 201 cycles (1 reference cycle, 100 cycles in front and 100 cycle in back) measured by the TDLAS system. Here, one cycle of measured signal consists of 500 samples with a recording time of 1 ms. A total of 5 million signals were received during 10 s of engine operation.