# Risk Analysis and Optimization of Water Surface Deviation from Shafts in the Filling–Emptying System of a Mega-Scale Hydro-Floating Ship Lift

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials

#### 2.1. Study Area

_{1}) and second (L

_{2}) diversions are arranged on a horizontal flat surface, and the third (L

_{3}) and fourth (L

_{4}) diversions are carried out on a vertical facade. After these four divergences, water flow from the upstream is distributed to each individual shaft along the pipeline. The geometric structure of the filling–emptying system with equal inertia is designed in a symmetrical way, and so the branch pipeline is completely symmetrical. According to theoretical calculation analysis, water flow from the upstream could be distributed to each individual shaft evenly and equally. The water level in each shaft rises and falls synchronously. It is helpful for the safe operation of hydro-floating ship lifts to ensure the synchronous rising and falling of the water level among the shafts.

_{i}) from the shafts causes torque (T) to be generated by the roller among drums (Figure 3). The larger the water surface deviation from the shafts, the larger the D-value of tension (F

_{i}≠ F

_{i}′) among wire ropes, which leads to the corresponding increase of the torque (T) to be generated by the roller among drums and threatens the safe operation of the ship lift. Thus, reasonable measures must be taken to reduce the water surface deviation from the shafts.

#### 2.2. Optimization of Layout

## 3. Methodology

#### 3.1. Numerical Simulation

^{3}/s, respectively.

#### 3.2. Risk Analysis

#### 3.2.1. Cloud Model Definition

- Ex refers to the expectation of the cloud droplets, which is the central value in the universe of the qualitative concept. In this paper, the expected value (Ex) reflects the average variation degree of water surface deviation from the shafts in the filling–emptying system.
- En is the uncertainty measurement of the qualitative concept, which is codetermined by the randomness and fuzziness of the concept. In this paper, entropy (En) can reflect the uncertainty degree of the water surface deviation from the shafts.
- He is the uncertainty measurement of En; i.e., the entropy of En. It reflects the discrete degree of the cloud droplets. A larger He value represents a higher cloud dispersion. In this paper, if the value of hyper entropy (He) is larger, the uncertainty of water surface deviation from the shafts is more discrete.

#### 3.2.2. Cloud Generator

^{2}), and λ obeys the Gaussian distribution λ~n (En, He

^{2}), the certainty degree of x to A, μ(x), satisfies

Algorithm 1. Algorithm of forward cloud generator (FCG). |

Input: Parameters Ex, En and He and the number of cloud droplets to be generated, n. Output: Quantitative values of n cloud droplets x _{i} and their corresponding certainty degrees μ(x_{i}) (i = 1,2,…,n).Algorithm steps: Step 1: Generate a normally distributed random number λ with expectation En and variance He: λ~n (En, He ^{2});Step 2: Generate a normally distributed random number x _{i} with expectation Ex and variance λ: x_{i}~n (Ex, λ^{2});Step 3: Calculate the certainty degree of x _{i}, $\mu \left({x}_{i}\right)=\mathrm{exp}\{-\frac{{\left({x}_{i}-Ex\right)}^{2}}{2{\lambda}^{2}}\}$;Step 4: Generate a cloud drop (x _{i}, μ(x_{i})), and repeat steps 1 to 3 until n cloud drops are generated. |

Algorithm 2. Algorithm of backward cloud generator (BCG). |

Input: Sample point data value x_{i} (i = 1,2,…,n).Output: Parameters Ex, En, and He. Algorithm steps: Step 1: Calculate the sample mean of these data x _{i} (i = 1,2,…,n), $\overline{X}=\frac{1}{n}{{\displaystyle \sum}}_{i=1}^{n}{x}_{i}$, and sample variance, ${S}^{2}=\frac{1}{n-1}{{\displaystyle \sum}}_{i=1}^{n}{\left({x}_{i}-\overline{X}\right)}^{2}$;Step 2: Calculate the expected value $\overline{X}$, $Ex=\overline{X}$; Step 3: Calculate the entropy value, $En=\sqrt{\frac{\pi}{2}}\times \frac{1}{n}{{\displaystyle \sum}}_{i=1}^{n}\left|{x}_{i}-Ex\right|$; Step 4: Calculate the hyper-entropy value, $He=\sqrt{{S}^{2}-E{n}^{2}}$. |

#### 3.2.3. Cloud Model for the Filling–Emptying System

- (1)
- “Security”: The data regarding the hydrodynamic risk factor for the filling–emptying system fall in the cloud droplet group of the [0, Ex + En] interval. The [0, Ex + En] interval accounts for 84.13% of the total area. If the measured data of the hydrodynamic factors fall in this range, this indicates the running safety of the filling–emptying system.
- (2)
- “Weak security”: The data regarding the hydrodynamic risk factor for the filling–emptying system fall in the cloud droplet group of the [Ex + En, Ex + 2En] interval. The [Ex + En, Ex + 2En] interval accounts for 13.59% of the total area. If the measured data of the hydrodynamic factors fall in this range, this indicates the weak running safety of the filling–emptying system. The operator should pay attention to changes in the measured data.
- (3)
- “Weak risk”: The data regarding the hydrodynamic risk factor for the filling–emptying system fall in the cloud droplet group of the [Ex + 2En, Ex + 3En] interval. The [Ex + 2En, Ex + 3En] interval accounts for 2.15% of the total area. If the measured data of the hydrodynamic factors are concentrated in this interval, this indicates that the filling–emptying system of the hydro-floating ship lift is in a state of “weak risk”. The operator should report the “weak risk” of the filling–emptying system and look up possible problems.
- (4)
- “Risk”: The data regarding the hydrodynamic risk factor for the filling–emptying system fall in the cloud droplet group of the [Ex + 3En, +∞] interval. The [Ex + 3En, +∞] interval accounts for 0.13% of the total area. If the measured data for the hydrodynamic factors fall in this range, the filling–emptying system exhibits a risk state. The operator should report the “risk” state of the filling–emptying system and stop the running of the hydro-floating ship lift according to the corresponding operation process and deal with the risk-causing fault.

## 4. Results and Discussion

#### 4.1. Water Surface Deviation from the Shafts of an Equal Inertial Pipeline

#### 4.1.1. Jinghong Hydro-Floating Ship lift

#### 4.1.2. Numerical Simulation of 100 m Lifting Height

#### 4.2. Risk Analysis of Water Surface Deviation from the shafts in the Longitudinal Culvert

- (1)
- Flow of branch outlet

_{i}within the first 200 s at the lifting height of 150 m is shown in Figure 15. In the filling–emptying system, the flow rate deviation of each branch outlet became larger with the gradual increase of the flow rate of branch outlet.

_{q}between the flow rate of each branch outlet and the average flow rate was calculated as shown in Figure 16. In the running of the equal inertial pipeline filling–emptying system, the maximum D

_{q}of each branch outlet flow rate exceeded 1.0 m

^{3}/s. However, the maximum D

_{q}of each branch outlet flow rate was less than 0.4 m

^{3}/s in the longitudinal culvert filling–emptying system. Therefore, the longitudinal culvert filling–emptying system performed better than the equal inertial pipeline from the perspective of the branch outflow.

- (2)
- Water surface deviation from the shafts

#### 4.3. Optimization of Water Surface Deviation from the Shafts

## 5. Conclusions

- (1)
- A layout optimization method for the longitudinal culvert filling–emptying system was put forward to be applied in a hydro-floating ship lift. Two kinds of filling–emptying system were compared and analyzed by using a numerical simulation method and cloud model theory.
- (2)
- Taking the engineering project of the Jinghong hydro-floating ship lift as an example, the uniformity of the diverging flow and synchronicity of the water level among the shafts showed a chaotic trend in the equal inertial pipeline filling–emptying system under the condition of a 100 m scale lifting height. The lifting height forces the water surface deviation from the shafts to increase, and the hydrodynamic risk will therefore be greatly increased.
- (3)
- To analyze the hydrodynamic risk of water surface deviation from the shafts, two kinds of filling–emptying systems (equal inertial pipeline and longitudinal culvert) were compared with each other under the condition of a 150 m lifting height. The longitudinal culvert filling–emptying system was better than the equal inertial pipeline in the branch outflow and better able to solve the risk problem of water surface deviation from the shafts.
- (4)
- A longitudinal culvert was applied for the optimization of running safety in the filling–emptying system. Three parameters (Ex, En, He) showed that the layout of the longitudinal culvert significantly reduced the uncertainty of water surface deviation from the shafts.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Schematic diagram of equal inertial pipeline filling–emptying system: (

**a**) three-dimensional and (

**b**) plane mode.

**Figure 3.**Water surface deviation from the shafts causes torque to be generated by the roller among drums.

**Figure 6.**Numerical simulation of the equal inertial pipeline filling–emptying system: (

**a**) modeling and (

**b**) meshing.

**Figure 7.**Numerical simulation of the longitudinal culvert filling–emptying system: (

**a**) modeling and (

**b**) meshing.

**Figure 8.**The change process of the filling water flow in the filling–emptying system under the condition of 80 m, 100 m, 120 m and 150 m lifting heights.

**Figure 11.**Water surface deviation from the shafts in Jinghong ship lift: (

**a**) the diagram of water surface deviation from the shafts and (

**b**) the cloud model expression.

**Figure 12.**Water surface deviation from the shafts in the filling–emptying system with an equal inertial pipeline under 100 m lifting height: (

**a**) the diagram of water surface deviation from the shafts and (

**b**) the cloud model expression.

**Figure 13.**Hydrodynamic characteristics of the equal inertial pipeline filling–emptying system under the condition of a 150 m lifting height: (

**a**) the diagram of the vertical shaft water level and (

**b**) longitudinal profile velocity.

**Figure 14.**Hydrodynamic characteristics of the longitudinal culvert filling–emptying system under the condition of a 150 m lifting height: (

**a**) the diagram of the vertical shaft water level and (

**b**) longitudinal profile velocity.

**Figure 15.**The change process of each branch outlet flow in the filling–emptying system under the condition of a 150 m lifting height: (

**a**) the diagram of an equal inertial pipeline and (

**b**) the longitudinal culvert.

**Figure 16.**The D

_{q}process of each branch outlet flow in the filling–emptying system under the condition of a 150 m lifting height: (

**a**) the diagram of the equal inertial pipeline and (

**b**) the longitudinal culvert.

**Figure 17.**The change process of water surface deviation from the shafts in the filling–emptying system under the condition of a 150 m lifting height: (

**a**) the diagram of the equal inertial pipeline and (

**b**) the longitudinal culvert.

Item | Design Value | Item | Design Value |
---|---|---|---|

Maximum lifting height (m) | 66.86 | Highest navigable water levels upstream (m) | 602.00 |

Maximum passing ship tonnage (tons) | 500 | Lowest navigable water levels upstream (m) | 591.00 |

Ship chamber size (m) | 69.1 × 12.0 × 2.5 (length × width × depth) | Highest navigable water levels downstream (m) | 544.90 |

Ship chamber single running time (min) | 17 | Lowest navigable water levels downstream (m) | 534.80 |

Total weight of the ship chamber (tons) | 3140 | Freight traffic in main years (ten thousand tons) | 135 |

Item | Equal Inertial Pipeline | Longitudinal Culvert |
---|---|---|

Main pipe diameter (m) | 2.5 | 2.5 |

Shaft sectional area (m^{2}) | 531 | 554 |

Flow coefficient | 0.297 | 0.318 |

Resistance coefficient | 0.321 | 0.334 |

**Table 3.**Early warning threshold of water surface deviation from the shafts under different lifting heights in the filling–emptying system with an equal inertial pipeline.

Lifting Height (m) | Threshold of Water Surface Deviation from Shafts (m) | |||
---|---|---|---|---|

Security | Weak Security | Weak Risk | Risk | |

80 | (0, 0.24) | (0.24, 0.29) | (0.29, 0.35) | (0.35, +∞) |

100 | (0, 0.28) | (0.28, 0.33) | (0.33, 0.39) | (0.39, +∞) |

120 | (0, 0.31) | (0.31, 0.35) | (0.35, 0.41) | (0.41, +∞) |

**Table 4.**Three parameters of water surface deviation from the shafts in the filling–emptying system under the condition of a 150 m lifting height.

Parameters of Cloud Model | Equal Inertial Pipeline | Longitudinal Culvert | ||||
---|---|---|---|---|---|---|

Jinghong (66.86 m) | 80 m Lifting | 100 m Lifting | 120 m Lifting | 150 m Lifting | 150 m Lifting | |

Ex | 0.1199 | 0.1959 | 0.2223 | 0.2394 | 0.5334 | 0.1545 |

En | 0.0149 | 0.0463 | 0.0547 | 0.0568 | 0.1131 | 0.0531 |

He | 0.0015 | 0.0089 | 0.0107 | 0.0121 | 0.0494 | 0.0198 |

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**MDPI and ACS Style**

Liu, J.; Hu, Y.; Li, Z.; Xue, S. Risk Analysis and Optimization of Water Surface Deviation from Shafts in the Filling–Emptying System of a Mega-Scale Hydro-Floating Ship Lift. *Water* **2021**, *13*, 1377.
https://doi.org/10.3390/w13101377

**AMA Style**

Liu J, Hu Y, Li Z, Xue S. Risk Analysis and Optimization of Water Surface Deviation from Shafts in the Filling–Emptying System of a Mega-Scale Hydro-Floating Ship Lift. *Water*. 2021; 13(10):1377.
https://doi.org/10.3390/w13101377

**Chicago/Turabian Style**

Liu, Jingkai, Yaan Hu, Zhonghua Li, and Shu Xue. 2021. "Risk Analysis and Optimization of Water Surface Deviation from Shafts in the Filling–Emptying System of a Mega-Scale Hydro-Floating Ship Lift" *Water* 13, no. 10: 1377.
https://doi.org/10.3390/w13101377