# Quantitative Analysis of Influencing Factors on Changzhou Ship Lock Capacity
## 3 Methods  
### Estimate Confidence Intervals Based on Lognormal Distribution  
Factors such as lock water filling and emptying time in the upstream and downstream ship locks, ship lock scheduling strategies, ship lock chamber scheduling rules, and ship maneuvering are significantly influenced by human factors. For an individual ship passage, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Data Name** & **Data Content** & **Data Description** \\ \hline \multirow{8}{*}{Ship Passing Data} & Ship Name & / \\  & Ship Lock Lane & first lane, second lane, third lane, fourth lane \\  & Ship Lock Sill & minimum water depth above the lock sill \\  & Operation Direction & up or down \\  & Ship Dimension & ship length, ship width \\  & Ship Draft & reported draft depth, unit: meters \\  & Ship Load & load capacity, approved load, actual load, unit: ton \\  & Goods Type & coal, containers, corn, empty, etc. \\  & Passing Time & report time and departure time \\  & Travel Place & Start Place and Arrival Place \\ \hline \multirow{8}{*}{Hydrological Monitoring Data} & Data Time & data release time \\  & Upstream Water Level & water level value collected by monitoring stations, \\ \cline{1-1}  & Downstream Water Level & unit: meters \\ \cline{1-1}  & Inflow Volume & calculated volume value, unit:m\({}^{3}\)/s \\ \cline{1-1}  & Outflow Volume & calculated volume value, unit:m\({}^{3}\)/s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Detailed data content. Figure 2: Changes in cargo volume of Changzhou ship lock over the years. The data is from the navigation statistics of the Pearl River Administration of Navigational Affairs. MOT. these factors have a certain degree of randomness and dominance, which directly affects the analysis results of ship lock capacity. In terms of analyzing the constraints under saturated operation, abnormal navigation records caused by human factors are considered noise data. Removing the noise data and ensuring that the input data truly reflects the ship passing situation under saturated operation is a prerequisite for analyzing the constraints on ship lock capacity. To visually identify the distribution pattern of ship passing time, a histogram was created for ship passing time. The horizontal axis represents the passing time, in 10-min intervals, while the vertical axis indicates the probability of blockage durations occurring within each interval. The statistic results are shown in Figure 3. It can be observed that the passing time exhibits a distinct lognormal distribution, with values relatively concentrated and a shape similar to the normal distribution, but with a tail extending noticeably to the right. The passing time has a possibility of greater upward fluctuation and a smaller downward fluctuation, which can well explain the right-skewed nature of the lognormal distribution. Assuming the ship passing time x follows a lognormal distribution, its density distribution function p(x) is given by Equation (1), and the mathematical expectation E(X) and variance D(X) are given by Equations (2) and (3), respectively. The cumulative distribution function F(x) is given by Equation (4). \[p(x)=\frac{1}{x\sigma\sqrt{2\pi}}\exp(-\frac{(\ln x-\mu)^{2}}{2\sigma^{2}}) \tag{1}\]  
\[E(X)=\exp(\mu+\sigma^{2}/2) \tag{2}\]  
\[\text{D}(X)=\left(\exp(\sigma^{2})-1\right)\exp(2\mu+\sigma^{2}) \tag{3}\]  
\[\text{F}(x)=\frac{1}{2}\bigg{\{}1+erf\left[\frac{\ln x-\mu}{\sqrt{2}\sigma} \right]\bigg{\}} \tag{4}\]  
Parameters \(\mu\) and \(\sigma\) are crucial for accurately fitting the lognormal distribution. SciPy is an open-source Python algorithm library and mathematical toolkit, with the sub-module \"stats\" containing various statistical analysis functions for describing and analyzing the  
Figure 3: Probability density distribution of ship passing time. statistical properties of data. The \"lognorm\" function can perform maximum likelihood estimations on observed values to fit the parameters of lognormal distribution, yielding parameter estimates of \(\mu\) = 0.83 and \(\sigma\) = 0.44.