diff --git a/docs/funcs/BreakDetection.md b/docs/funcs/BreakDetection.md deleted file mode 100644 index 936bb1bb6045da3203e1b14cd4ad5a7f94abb2c8..0000000000000000000000000000000000000000 --- a/docs/funcs/BreakDetection.md +++ /dev/null @@ -1,67 +0,0 @@ -# Break Detection - -## Index -[breaks_flagSpektrumBased](#breaks_flagspektrumbased) - -## breaks_flagSpektrumBased - -``` -breaks_flagSpektrumBased(thresh_rel=0.1, thresh_abs=0.01, - first_der_factor=10, first_der_window="12h", - scnd_der_ratio_range=0.05, scnd_der_ratio_thresh=10, - smooth=True, smooth_window=None, smooth_poly_deg=2) -``` - -| parameter | data type | default value | description | -|-----------------------|---------------------------------------------------------------|---------------|------------------------------------------------------------------------------------------------------------------------------------------------------------| -| thresh_rel | float | `0.1` | Minimum relative difference between two values to consider the latter as a break candidate. See condition (1) | -| thresh_abs | float | `0.01` | Minimum absolute difference between two values to consider the latter as a break candidate. See condition (2) | -| first_der_factor | float | `10` | Multiplication factor for arithmetic mean of the first derivatives surrounding a break candidate. See condition (3). | -| first_der_window | [offset string](docs/ParameterDescriptions.md#offset-strings) | `"12h"` | Window around a break candidate for which the arithmetic mean is calculated. See condition (3) | -| scnd_der_ratio_range | float | `0.05` | Maximum deviation from one of the ratio of the second derivatives of a break candidate and its preceding value. See condition (5) | -| scnd_der_ratio_thresh | float | `10.0` | Threshold for the ratio of the second derivatives of a break candidate and its succeeding value. See condition (5) | -| smooth | bool | `True` | Smooth the time series before differentiation using the Savitsky-Golay filter | -| smooth_window | [offset string](docs/ParameterDescriptions.md#offset-strings) | `None` | Size of the smoothing window of the Savitsky-Golay filter. The default value `None` results in a window of two times the sampling rate (i.e. three values) | -| smooth_poly_deg | integer | `2` | Degree of the polynomial used for smoothing with the Savitsky-Golay filter | - -The function flags breaks (jumps/drops) by evaluating the derivatives of a time series. - -A value $`x_k`$ of a time series $`x_t`$ with timestamps $`t_i`$, is considered to be a break, if: - -1. $`x_k`$ represents a sufficiently large relative jump: - - $`|\frac{x_k - x_{k-1}}{x_k}| >`$ `thresh_rel` - -2. $`x_k`$ represents a sufficient absolute jump: - - $`|x_k - x_{k-1}| >`$ `thresh_abs` - -3. The dataset $`X = x_i, ..., x_{k-1}, x_{k+1}, ..., x_j`$, with $`|t_{k-1} - t_i| = |t_j - t_{k+1}| =`$ `first_der_window` - fulfills the following condition: - - $`|x'_k| >`$ `first_der_factor` $` \cdot \bar{X} `$ - - where $`\bar{X}`$ denotes the arithmetic mean of $`X`$. - -4. The ratio (last/this) of the second derivatives is close to 1: - - $` 1 -`$ `scnd_der_ratio_range` $`< |\frac{x''_{k-1}}{x_{k''}}| < 1 + `$`scnd_der_ratio_range` - -5. The ratio (this/next) of the second derivatives is sufficiently height: - - $`|\frac{x''_{k}}{x''_{k+1}}| > `$`scnd_der_ratio_thresh` - -NOTE: -- Only works for time series -- The time series is expected to be harmonized to an - [equidistant frequency grid](docs/funcs/TimeSeriesHarmonization.md) - - -This Function is a generalization of the spectrum based spike flagging -mechanism as presented in [1]. - -### References -[1] Dorigo,W. et al.: Global Automated Quality Control of In Situ Soil Moisture - Data from the international Soil Moisture Network. 2013. Vadoze Zone J. - doi:10.2136/vzj2012.0097. -