*3.2. WT—Wavelet Transformation*

A wavelet transform (WT) orthogonally decomposes a time series into wavelet and scaling coefficients. The main difference to the Fourier transform, which splits a signal into cosine and sine, is the use of (real and Fourier space) functions by the WT. The deletion of irrelevant data points increase the compression ratio and reduce the mean percentage error (MPE) and mean absolute error (MAE). That is why, it is important to find the best thresholds, levels of decomposition (LoD), and Daubechies' wavelets (DW). For further explanation, see [19–21].

## *3.3. TFA—Triangular Function Algorithm*

The Triangular Function Algorithm (TFA) encloses the steps (I)-(VI) and is an enhanced version of the approach developed in [17]. (I) Read the dataset and choose your preferred percentiles (e.g., *Q*5–*Q*95). (II) Generate percentiles of the original dataset and save the data points *y*i Q, *xi Q*. Perform a moving average FIR filter to smooth the (remainder of the) dataset. (III) Read *a*0 data points, which is the step width. (IV) Choose number of polynomials of least square fit. Perform Λ in (6), to obtain the slope *b*1 and intercept *b*0 (6). Determine the mean square error and unbiased standard deviation ( *σ*).

$$\Lambda\_{\perp} = \sum\_{i=1}^{d} \left[ y\_i - (b\_1 \mathbf{x}\_i + b\_0) \right]^2 \tag{6}$$

In our case, quadratic or higher polynomial functions should be avoided because of the lower compression-error-ratio depending on the higher number of compressed and saved datapoints (e.g., *b*2, *b*1, *b*0). (V) Read and check the following data point (*yi*, *xi*). If its value is within ( ± m *σ*, with factor *m*) the predicted values, jump to (III). Otherwise start a new line segmen<sup>t</sup> and go to step (IV). (VI) After compressing the whole dataset, insert percentiles (*y*iQ, *xiQ*) to finish the algorithm. For further explanation, please see [17].

#### **4. Proposed Approach and Key Metrics**
