# Research on the Crane Safety Assessment Method Based on the Cloud Model and ICWGT

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. The Crane Safety Assessment System, Based on the Cloud Model and ICWGT

#### 2.1.1. Fuzzy Integrated Assessment Method, Based on the Cloud Model

#### 2.1.2. Commentary Set Cloud Model

#### 2.1.3. Determination of the Fuzzy Relationship Matrix

#### 2.2. Determination of Optimization Weights for the Crane Assessment System

#### 2.2.1. Determination of Subjective Weight Cloud

#### 2.2.2. Determination of the Objective Weight Cloud

#### 2.2.3. Determination of the Weight Cloud for ICWGT-Based Portfolio Optimization

#### 2.3. Improved Fuzzy Synthesis Algorithm

## 3. Results

#### 3.1. Fuzzy Integrated Assessment

#### 3.1.1. Determination of the Membership Cloud Model Matrix

#### 3.1.2. Determination of the Weight Cloud for the ICWGT-Based Portfolio Optimization

- (1)
- Determination of the subjective and objective weight cloud model matrix

- (2)
- Determination of the weight cloud model matrix for combinatorial optimization

#### 3.1.3. Determination of the Assessment Results

## 4. Discussion and Conclusions

#### 4.1. Discussion

#### 4.2. Conclusions

- (1)
- The cloud model theory can convert the qualitative concept of safety levels into a quantitative representation with mathematics. The randomness and fuzziness of the crane safety assessment indexes are handled by this theory. Based on the cloud model to improve the fuzzy comprehensive assessment method, the numerical characteristics of the cloud model are used to represent the fuzzy relationship matrix, the weight coefficient matrix, and the final assessment results. Then, the cloud map is generated by a forward cloud generator to make the presentation of assessment results more intuitive.
- (2)
- In this study, a new crane safety assessment method is obtained by combining ICWGT with cloud model theory. In calculating the combination optimized weight cloud of the crane metal structure, based on the sample values, the game theory idea is applied to optimize the combination coefficients, which makes the allocation of subjective and objective weight clouds more reasonable. In the synthesis calculations, the synthesis algorithm is improved by using a fine-tuned synthesis operator. The method not only takes expert experience and currently available sample information into account but also overcomes the influence of human subjective factors and the fluctuation of data information in weight assignment.
- (3)
- The crane safety assessment method based on the cloud model and ICWGT has been applied to a comprehensive assessment of the operation condition and safety level of the shipyard portal crane. The assessment results match the engineering reality. This validation result proves the accuracy of the method and has a theoretical reference value for a comprehensive assessment study of crane safety levels.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**The cloud images of the assessment results: (

**a**) the boom system; (

**b**) the herringbone system; (

**c**) the gantry system; (

**d**) the turntable column system; (

**e**) other structures; (

**f**) the complete machine system.

Definition | Scaled Cloud Model | |
---|---|---|

${B}_{i}$$\mathrm{is}\mathrm{more}\mathrm{important}\mathrm{than}{B}_{j}$ | Absolute | ${A}_{9}\left(9,0.167,0.05\right)$ |

Between adjacent levels | ${A}_{8}\left(8,0.167,0.05\right)$ | |

Strong | ${A}_{7}\left(7,0.167,0.05\right)$ | |

Between adjacent levels | ${A}_{6}\left(6,0.167,0.05\right)$ | |

Obvious | ${A}_{5}\left(5,0.167,0.05\right)$ | |

Between adjacent levels | ${A}_{4}\left(4,0.167,0.05\right)$ | |

Slight | ${A}_{3}\left(3,0.167,0.05\right)$ | |

Between adjacent levels | ${A}_{2}\left(2,0.167,0.05\right)$ | |

${B}_{i}$$\mathrm{is}\mathrm{as}\mathrm{important}\mathrm{as}{B}_{j}$ | ${A}_{1}$ (1,0,0) | |

${B}_{i}$$\mathrm{is}\mathrm{more}\mathrm{important}\mathrm{than}{B}_{j}$ | Between adjacent levels | ${A}_{1/2}\left(1/2,0.167/4,0.05/4\right)$ |

Slight | ${A}_{1/3}\left(1/3,0.167/9,0.05/9\right)$ | |

Between adjacent levels | ${A}_{1/4}\left(1/4,0.167/16,0.05/16\right)$ | |

Obvious | ${A}_{1/5}\left(1/5,0.167/25,0.05/25\right)$ | |

Between adjacent levels | ${A}_{1/6}\left(1/6,0.167/36,0.05/36\right)$ | |

Strong | ${A}_{1/7}\left(1/7,0.167/49,0.05/49\right)$ | |

Between adjacent levels | ${A}_{1/8}\left(1/8,0.167/64,0.05/64\right)$ | |

Absolute | ${A}_{1/9}\left(1/9,0.167/81,0.05/81\right)$ |

**Table 2.**Test data and assessment values of sample indicators of the shipyard portal crane [32].

Structure | Strength | Rigidity | Stability | Crack | Deformation | Corrosion | Maintenance Situation | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Status Value /MPa | Rating Value | Status Value /MPa | Rating Value | Status Value /MPa | Rating Value | Status Value /d | Rating Value | Status Value /% | Rating Value | Status Value /% | Rating Value | Status Value /d | Rating Value | |

Boom | 125 | 0.47 | 50 | 0.66 | 125 | 0.79 | 1000 | 0.99 | 0.5 | 0.95 | 1 | 0.9 | 1000 | 0.99 |

Herringbone | 148 | 0.37 | 20 | 0.83 | 148 | 0.92 | 250 | 0.96 | 0.7 | 0.93 | 3 | 0.7 | 143 | 0.93 |

Gantry | 119 | 0.49 | 15 | 0.78 | 119 | 0.81 | 1000 | 0.99 | 1 | 0.9 | 4 | 0.6 | 200 | 0.95 |

Turntable column | 185 | 0.21 | 5 | 0.89 | 185 | 0.89 | 91 | 0.89 | 0.1 | 0.99 | 2 | 0.8 | 250 | 0.96 |

Other structures | 154 | 0.34 | 10 | 0.82 | 154 | 0.95 | 56 | 0.82 | 1.2 | 0.88 | 2.1 | 0.79 | 111 | 0.91 |

Security Level | Strength | Rigidity | Stability | Crack | Deformation | Corrosion | Maintenance Situation |
---|---|---|---|---|---|---|---|

$\mathrm{Very}\mathrm{good}{\mathrm{C}}_{1}$ | (0.6, 1.0] | (0.8, 1.0] | (0.8, 1.0] | (0.9, 1.0] | (0.8, 1.0] | (0.8, 1.0] | (0.8, 1.0] |

$\mathrm{Good}{\mathrm{C}}_{2}$ | (0.4, 0.6] | (0.6, 0.8] | (0.6, 0.8] | (0.8, 0.9] | (0.6, 0.8] | (0.6, 0.8] | (0.6, 0.8] |

$\mathrm{Fair}{\mathrm{C}}_{3}$ | (0.25, 0.4] | (0.4, 0.6] | (0.4, 0.6] | (0.7, 0.8] | (0.4, 0.6] | (0.4, 0.6] | (0.4, 0.6] |

$\mathrm{Poor}{\mathrm{C}}_{4}$ | (0.15, 0.25] | (0.2, 0.4] | (0.2, 0.4] | (0.5, 0.7] | (0.2, 0.4] | (0.2, 0.4] | (0.2, 0.4] |

$\mathrm{Very}\mathrm{poor}{\mathrm{C}}_{5}$ | (0, 0.15] | (0, 0.2] | (0, 0.2] | (0, 0.5] | (0, 0.2] | (0, 0.2] | (0, 0.2] |

Security Level | Score Range | Operating Conditions | Description of Security Level |
---|---|---|---|

I | (0.85, 1] | Normal operation | The crane safety is in excellent condition, routine maintenance recommended. |

II | (0.75, 0.85] | Normal operation | The crane safety condition is in good condition, it is recommended to strengthen maintenance. |

III | (0.5, 0.75] | Operation with faults | The crane is faulty, safety in general, specific inspection and minor repairs are recommended. |

IV | (0.25, 0.5] | Shutdown | Crane has a large fault and poor safety. Repair is recommended (intermediate repair). |

V | (0, 0.25] | Immediate shutdown | Crane has serious faults and poor safety. Overhaul or scrapping is recommended. |

System | Membership Cloud Model Matrix |
---|---|

Boom | ${R}_{{P}_{1}}=\left[\begin{array}{c}\left(0.470,0.048,0.010\right)\\ \left(0.660,0.053,0.010\right)\\ \left(0.790,0.037,0.010\right)\\ \left(0.990,0,0.010\right)\\ \left(0.950,0,0.010\right)\\ \begin{array}{c}\left(0.900,0,0.010\right)\\ \left(0.990,0,0.010\right)\end{array}\end{array}\right]$ |

Herringbone | ${R}_{{P}_{2}}=\left[\begin{array}{c}\left(0.370,0.043,0.010\right)\\ \left(0.830,0.023,0.010\right)\\ \left(0.920,0,0.010\right)\\ \left(0.960,0,0.010\right)\\ \left(0.930,0,0.010\right)\\ \begin{array}{c}\left(0.700,0.067,0.010\right)\\ \left(0.930,0,0.010\right)\end{array}\end{array}\right]$ |

Gantry | ${R}_{{P}_{3}}=\left[\begin{array}{c}\left(0.490,0.055,0.010\right)\\ \left(0.780,0.040,0.010\right)\\ \left(0.810,0.030,0.010\right)\\ \left(0.990,0,0.010\right)\\ \left(0.900,0,0.010\right)\\ \begin{array}{c}\left(0.600,0.033,0.010\right)\\ \left(0.950,0,0.010\right)\end{array}\end{array}\right]$ |

Turntable column | ${R}_{{P}_{4}}=\left[\begin{array}{c}\left(0.340,0.047,0.010\right)\\ \left(0.820,0.027,0.010\right)\\ \left(0.950,0,0.010\right)\\ \left(0.820,0.023,0.010\right)\\ \left(0.880,0.007,0.010\right)\\ \begin{array}{c}\left(0.790,0.037,0.010\right)\\ \left(0.910,0,0.010\right)\end{array}\end{array}\right]$ |

Other structures | ${R}_{{P}_{5}}=\left[\begin{array}{c}\left(0.210,0.038,0.010\right)\\ \left(0.890,0.003,0.010\right)\\ \left(0.890,0.003,0.010\right)\\ \left(0.890,0.020,0.010\right)\\ \left(0.990,0,0.010\right)\\ \begin{array}{c}\left(0.800,0.033,0.010\right)\\ \left(0.960,0,0.010\right)\end{array}\end{array}\right]$ |

Complete machine | ${R}_{P}=\left[\begin{array}{c}\begin{array}{c}{V}_{{P}_{1}}\\ {V}_{{P}_{2}}\end{array}\\ {V}_{{P}_{3}}\\ \begin{array}{c}{V}_{{P}_{4}}\\ {V}_{{P}_{5}}\end{array}\end{array}\right]=\left[\begin{array}{c}\begin{array}{c}\left(0.814,0.095,0.093\right)\\ \left(0.763,0.082,0.081\right)\end{array}\\ \left(0.813,0.092,0.087\right)\\ \begin{array}{c}\left(0.884,0.094,0.094\right)\\ \left(0.794,0.088,0.089\right)\end{array}\end{array}\right]$ |

System | Subjective Weight Cloud Model Matrix | Objective Weight Cloud Model Matrix |
---|---|---|

Boom | ${W}_{{P}_{1}}^{S}={\left[\begin{array}{c}\left(0.308,0.298,0.321\right)\\ \left(0.226,0.231,0.244\right)\\ \left(0.130,0.102,0.100\right)\\ \left(0.131,0.149,0.153\right)\\ \left(0.047,0.076,0.035\right)\\ \begin{array}{c}\left(0.103,0.112,0.111\right)\\ \left(0.047,0.031,0.035\right)\end{array}\end{array}\right]}^{T}$ | ${W}_{{P}_{1}}^{O}={\left[\begin{array}{c}\left(0.118,0.020,0.010\right)\\ \left(0.124,0.020,0.010\right)\\ \left(0.147,0.020,0.010\right)\\ \left(0.139,0.020,0.010\right)\\ \left(0.164,0.020,0.010\right)\\ \begin{array}{c}\left(0.145,0.020,0.010\right)\\ \left(0.164,0.020,0.010\right)\end{array}\end{array}\right]}^{T}$ |

Herringbone | ${W}_{{P}_{2}}^{S}={\left[\begin{array}{c}\left(0.258,0.248,0.269\right)\\ \left(0.168,0.153,0.158\right)\\ \left(0.109,0.106,0.107\right)\\ \left(0.113,0.112,0.114\right)\\ \left(0.211,0.201,0.203\right)\\ \begin{array}{c}\left(0.102,0.112,0.101\right)\\ \left(0.039,0.029,0.035\right)\end{array}\end{array}\right]}^{T}$ | ${W}_{{P}_{2}}^{O}={\left[\begin{array}{c}\left(0.119,0.020,0.010\right)\\ \left(0.139,0.020,0.010\right)\\ \left(0.143,0.020,0.010\right)\\ \left(0.148,0.020,0.010\right)\\ \left(0.124,0.020,0.010\right)\\ \begin{array}{c}\left(0.145,0.020,0.010\right)\\ \left(0.165,0.020,0.010\right)\end{array}\end{array}\right]}^{T}$ |

Gantry | ${W}_{{P}_{3}}^{S}={\left[\begin{array}{c}\left(0.323,0.313,0.309\right)\\ \left(0.159,0.151,0.155\right)\\ \left(0.111,0.107,0.113\right)\\ \left(0.108,0.106,0.112\right)\\ \left(0.058,0.068,0.047\right)\\ \begin{array}{c}\left(0.178,0.168,0.169\right)\\ \left(0.059,0.061,0.055\right)\end{array}\end{array}\right]}^{T}$ | ${W}_{{P}_{3}}^{O}={\left[\begin{array}{c}\left(0.117,0.020,0.010\right)\\ \left(0.138,0.020,0.010\right)\\ \left(0.148,0.020,0.010\right)\\ \left(0.149,0.020,0.010\right)\\ \left(0.162,0.020,0.010\right)\\ \begin{array}{c}\left(0.136,0.020,0.010\right)\\ \left(0.162,0.020,0.010\right)\end{array}\end{array}\right]}^{T}$ |

Turntable column | ${W}_{{P}_{4}}^{S}={\left[\begin{array}{c}\left(0.309,0.297,0.321\right)\\ \left(0.101,0.112,0.111\right)\\ \left(0.049,0.031,0.035\right)\\ \left(0.179,0.169,0.178\right)\\ \left(0.098,0.112,0.111\right)\\ \begin{array}{c}\left(0.157,0.147,0.153\right)\\ \left(0.107,0.105,0.113\right)\end{array}\end{array}\right]}^{T}$ | ${W}_{{P}_{4}}^{O}={\left[\begin{array}{c}\left(0.118,0.020,0.010\right)\\ \left(0.145,0.020,0.010\right)\\ \left(0.161,0.020,0.010\right)\\ \left(0.136,0.020,0.010\right)\\ \left(0.149,0.020,0.010\right)\\ \begin{array}{c}\left(0.138,0.020,0.010\right)\\ \left(0.148,0.020,0.010\right)\end{array}\end{array}\right]}^{T}$ |

Other structures | ${W}_{{P}_{5}}^{S}={\left[\begin{array}{c}\left(0.351,0.334,0.355\right)\\ \left(0.098,0.089,0.090\right)\\ \left(0.039,0.035,0.045\right)\\ \left(0.168,0.148,0.150\right)\\ \left(0.079,0.071,0.076\right)\\ \begin{array}{c}\left(0.169,0.171,0.163\right)\\ \left(0.092,0.089,0.095\right)\end{array}\end{array}\right]}^{T}$ | ${W}_{{P}_{5}}^{O}={\left[\begin{array}{c}\left(0.116,0.020,0.010\right)\\ \left(0.149,0.020,0.010\right)\\ \left(0.165,0.020,0.010\right)\\ \left(0.139,0.020,0.010\right)\\ \left(0.159,0.020,0.010\right)\\ \begin{array}{c}\left(0.138,0.020,0.010\right)\\ \left(0.142,0.020,0.010\right)\end{array}\end{array}\right]}^{T}$ |

Complete machine | ${W}_{P}^{S}={\left[\begin{array}{c}\begin{array}{c}\left(0.339,0.287,0.284\right)\\ \left(0.324,0.342,0.341\right)\end{array}\\ \left(0.107,0.110,0.111\right)\\ \begin{array}{c}\left(0.185,0.231,0.232\right)\\ \left(0.045,0.031,0.032\right)\end{array}\end{array}\right]}^{T}$ | ${W}_{P}^{O}={\left[\begin{array}{c}\begin{array}{c}\left(0.153,0.040,0.010\right)\\ \left(0.140,0.040,0.010\right)\end{array}\\ \left(0.233,0.040,0.010\right)\\ \begin{array}{c}\left(0.178,0.040,0.010\right)\\ \left(0.296,0.040,0.010\right)\end{array}\end{array}\right]}^{T}$ |

System | Weight Cloud Model Matrix for Combinatorial Optimization |
---|---|

Boom | ${W}_{{P}_{1}}^{I}={\left[\begin{array}{c}\left(0.221,0.161,0.174\right)\\ \left(0.179,0.125,0.132\right)\\ \left(0.138,0.056,0.054\right)\\ \left(0.134,0.081,0.083\right)\\ \left(0.101,0.042,0.020\right)\\ \begin{array}{c}\left(0.122,0.061,0.060\right)\\ \left(0.101,0.019,0.020\right)\end{array}\end{array}\right]}^{T}$ |

Herringbone | ${W}_{{P}_{2}}^{I}={\left[\begin{array}{c}\left(0.191,0.129,0.140\right)\\ \left(0.154,0.080,0.082\right)\\ \left(0.125,0.056,0.056\right)\\ \left(0.130,0.059,0.060\right)\\ \left(0.169,0.105,0.106\right)\\ \begin{array}{c}\left(0.123,0.059,0.053\right)\\ \left(0.099,0.018,0.019\right)\end{array}\end{array}\right]}^{T}$ |

Gantry | ${W}_{{P}_{3}}^{I}={\left[\begin{array}{c}\left(0.228,0.169,0.167\right)\\ \left(0.149,0.082,0.084\right)\\ \left(0.128,0.058,0.061\right)\\ \left(0.127,0.058,0.061\right)\\ \left(0.106,0.038,0.026\right)\\ \begin{array}{c}\left(0.159,0.091,0.091\right)\\ \left(0.106,0.034,0.030\right)\end{array}\end{array}\right]}^{T}$ |

Turntable column | ${W}_{{P}_{4}}^{I}={\left[\begin{array}{c}\left(0.219,0.158,0.170\right)\\ \left(0.122,0.060,0.059\right)\\ \left(0.102,0.019,0.019\right)\\ \left(0.159,0.090,0.094\right)\\ \left(0.122,0.060,0.059\right)\\ \begin{array}{c}\left(0.148,0.078,0.081\right)\\ \left(0.126,0.056,0.060\right)\end{array}\end{array}\right]}^{T}$ |

Other structures | ${W}_{{P}_{5}}^{I}={\left[\begin{array}{c}\left(0.244,0.183,0.194\right)\\ \left(0.121,0.049,0.049\right)\\ \left(0.096,0.021,0.025\right)\\ \left(0.155,0.081,0.082\right)\\ \left(0.115,0.040,0.042\right)\\ \begin{array}{c}\left(0.155,0.094,0.089\right)\\ \left(0.115,0.049,0.052\right)\end{array}\end{array}\right]}^{T}$ |

Complete machine | ${W}_{P}^{I}={\left[\begin{array}{c}\begin{array}{c}\left(0.250,0.151,0.148\right)\\ \left(0.236,0.180,0.178\right)\end{array}\\ \left(0.167,0.060,0.058\right)\\ \begin{array}{c}\left(0.182,0.122,0.121\right)\\ \left(0.165,0.025,0.017\right)\end{array}\end{array}\right]}^{T}$ |

System | Assessment Result |
---|---|

Boom | ${V}_{{P}_{1}}\left(0.814,0.095,0.093\right)$ |

Herringbone | ${V}_{{P}_{2}}\left(0.763,0.082,0.081\right)$ |

Gantry | ${V}_{{P}_{3}}\left(0.813,0.092,0.087\right)$ |

Turntable column | ${V}_{{P}_{4}}\left(0.794,0.088,0.089\right)$ |

Other structures | ${V}_{{P}_{5}}\left(0.884,0.094,0.094\right)$ |

Complete machine | ${V}_{P}\left(0.811,0.153,0.150\right)$ |

System | FAHP [26] | The Approximating the Ideal Solution Ordering Method [28] | The ICWGT Combined with the Gray Correlation Analysis [32] | Fuzzy Integrated Assessment Model Based on the Cloud Model and ICWGT | ||||
---|---|---|---|---|---|---|---|---|

Security Level | Security Level | Trends in Security Level Changes | Security Level | $\mathit{E}\mathit{x}$ | $\mathit{E}\mathit{n}$ | $\mathit{H}\mathit{e}$ | Security Level | |

Boom | II | II | The initial stage of II | II | 0.814 | 0.095 | 0.093 | II |

Herringbone | II | II | The initial stage of II | II | 0.763 | 0.082 | 0.081 | II |

Gantry | II | II | The end-stage of I | I | 0.813 | 0.092 | 0.087 | II |

Turntable column | II | II | The end-stage of I | I | 0.794 | 0.088 | 0.089 | II |

Other structures | II | I | The end-stage of I | I | 0.884 | 0.094 | 0.094 | I |

Complete machine | II | II | The initial stage of II | II | 0.805 | 0.153 | 0.150 | II |

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## Share and Cite

**MDPI and ACS Style**

Zhu, Z.; Luo, Y.; Xiao, H.; Xiong, C.; Chen, C.
Research on the Crane Safety Assessment Method Based on the Cloud Model and ICWGT. *Appl. Sci.* **2022**, *12*, 4399.
https://doi.org/10.3390/app12094399

**AMA Style**

Zhu Z, Luo Y, Xiao H, Xiong C, Chen C.
Research on the Crane Safety Assessment Method Based on the Cloud Model and ICWGT. *Applied Sciences*. 2022; 12(9):4399.
https://doi.org/10.3390/app12094399

**Chicago/Turabian Style**

Zhu, Ze, Yangyi Luo, Hanbin Xiao, Chuchen Xiong, and Chentong Chen.
2022. "Research on the Crane Safety Assessment Method Based on the Cloud Model and ICWGT" *Applied Sciences* 12, no. 9: 4399.
https://doi.org/10.3390/app12094399