# Event Detection and Spatio-temporal Analysis of Low-Altitude Unstable Approach
## 2 Methodology
### Methods and Models
#### 2.2.2 Quantitative Risk Evaluation Model  
In this study, an empirical data set was produced via questionnaire survey with experienced pilots. To quantitatively evaluate the risk of UA events, we adopted the multiple linear regression technique to explore the relationships between the risk scores of UA events and relative flight parameters. In the first place, step-wise regression was adopted to specify a proper regression model [23]. Its workflow was designed as follows:  
STEP 1: Select one of the available variables that produces the smallest Akaike information criterion (AIC) value to form a one-way regression equation; \begin{table}
\begin{tabular}{l l} \hline \hline
**Flight Indicator** & **Interpretation** \\ \hline ROLL & Gradient angle of flight \\ PITCH & Pitch angle of flight \\ HEADNG & Heading angle of flight \\ IVV & Instantaneous vertical velocity \\ VRTG & Vertical acceleration \\ VREF & Reference speed \\ IAS & Indicated airspeed \\ FLAP & Angle of left and right flap \\ LGD & Left and right main gear AIR/GND \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Interpretations of flight parameters in the quick access recorder (QAR) data. \begin{table}
\begin{tabular}{l|l} \hline \hline
**Flight Parameter** & **UA Triggering Logic** \\ \hline Gradient & \(|\)ROLL\(|\)\(>\) 20 \\ Pitch angle & PITCH \(>\) 10 or \(<\) –5 \\ Alignment of track and runway direction & \(|\)HEAD\(\mathrm{\SIUnitSymbolMicro}\)\(\  
STEP 2: Select one of the remaining independent variables, along with the regression equation in STEP 1, to form a binary regression equation. The binary regression equation should have a smaller AIC value;  
STEP 3: Repeat while selecting one variable each iteration until all the variables are introduced. If the first variable is no longer important due to the introduction of some variable, then remove the first variable;  
STEP 4: The model is optimized when no variables need to be introduced or eliminated. Repeat STEP 1 to STEP 4 until an overrun model for all 5 parameters is obtained. Note that this procedure was tried several times with scores amended and outliers excluded so that the models could be developed optimally. The stepwise regression equation of pitch overrun modeling is as follows,  
\[ \begin{split} SCORE=-0.4946+0.1213\times\text{PITCH}\\ +0.01042\times\text{ROLL}-0.0001017\times\text{IVV}\end{split}  \tag{1}\]  
where \(SCORE\) is the risk score marked optimally for each UA event. The results of the stepwise regression demonstrate that the track deviation and airspeed were deleted in the process of stepwise regression, which indicates that airspeed is not a statistically significant factor in the modeling of pitch overrun. The stepwise regression equation of track deviation modeling is as follows,  
\[ \begin{split} SCORE=-0.2982+0.00007\times Flight\_speed+\\ 0.003271\times\\ 0.003429\times\text{ROLL}-0.00001623\times\text{IVV}+\\ 0.08546\times Alignment\_TRD\end{split}  \tag{2}\]  
where \(Flight\_speed\) means the flight speed by (Reference speed \(-\) Indicated airspeed, (VREF \(-\) IAS)), and \(Alignment\_TRD\) means the alignment of track and runway direction. The stepwise regression equation of excessive airspeed modeling is as follows:  
\[ \begin{split} SCORE=-0.2410498-0.0019022\times\\ Alignment\_TRD\ +0.0501647\times Flight\_speed\end{split}  \tag{3}\]  
The results of the stepwise regression demonstrate that the excessive airspeed limit is only related to airspeed and track deviation. The stepwise regression equation of slope overrun modeling is as follows:  
\[ \begin{split} SCORE=-0.4631086+0.0584883\times\text{ROLL}\end{split}  \tag{4}\]  
The stepwise regression equation of the rate reduction overrun modeling is as follows:  
\[ \begin{split} SCORE=-1.018-0.00975\times\text{IVV}\end{split}  \tag{5}\]  
With the above models, the UA events happening at each airport could be chosen carefully and evaluated quantitatively. These models could play important roles in evaluating risk scores of detected suspicious UA events.