# Continuous Dynamic Analysis Method and Case Verification of Cable Structure Based on Digital Twin

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## Abstract

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## 1. Introduction

#### 1.1. Research Background

#### 1.2. Literature Review

#### 1.3. Research Significance

## 2. Continuous Dynamic Analysis Method of Cable Structure Based on DT

#### 2.1. Continuous Dynamic Analysis Mechanism

#### 2.2. Multi-Dimensional DT Model Establishment Method

#### 2.2.1. DT Framework for Dynamic Construction Process of Cable Structures

#### 2.2.2. Construction of Multi-Dimensional DT Model

#### 2.3. Optimization of Finite Element Calculation Method for Cable Structure

#### 2.3.1. Correction of the Intrinsic Constitution Equation and Equilibrium Equation

**λ**is introduced into the equilibrium equation. The specific Equation (7) is as follows:

#### 2.3.2. Adjustment of Equations during Construction Simulation

#### 2.3.3. Calculation Method of Connection of Cable Unit and Rigid Unit

## 3. Case Study

#### 3.1. Multidimensional DT Modeling of Cable Structures

#### 3.1.1. Information Capture in Physical Space

#### 3.1.2. Virtual Construction Model Construction

#### 3.2. Development of Intelligent Simulation System Based on DT

#### 3.2.1. System Functional Requirements Analysis

#### 3.2.2. System Solution Design

- I.
- Simulation Calculation Function: This feature is responsible for executing the continuous dynamic analysis of the cable structure. It achieves this by optimizing the finite element calculation method used for cable structures. The optimization is designed to enhance the accuracy and efficiency of the simulation process. By employing this function, users can obtain reliable and comprehensive insights into the structural behavior of the cable system during various construction phases.
- II.
- Simulation Result Function: This component is focused on displaying and filtering the outcomes generated from the continuous dynamic analysis. Users can access the simulation results, which may include information about structural displacement, cable forces, deformations, and other relevant mechanical responses. The simulation results can be presented in a structured and visually informative manner, allowing users to better comprehend the dynamic behavior of the cable structure. Additionally, this function may provide filtering options to refine and customize the displayed results. Users can select specific parameters, time frames, or construction stages for analysis, enabling them to extract meaningful insights from the simulation data. The simulation model’s dynamic visualization is a notable aspect of this function. Users can explore the simulation models interactively, switch between different views, and manipulate the visual representation to gain a clearer understanding of the structural behavior. Moreover, the ability to switch between simulation models from various projects through new creations and imports enhances flexibility and adaptability in the analysis process.

- I.
- Early Warning Setting Function: This component is dedicated to configuring parameters that govern the early warning system. Users can establish a comparison between real-time monitoring values of key structural components’ mechanical responses and the corresponding simulation values. For each component, users can define threshold values that act as triggers for early warnings. When the real-time monitoring value surpasses the predefined threshold, the system will initiate an early warning to indicate a potential issue.
- II.
- Early Warning Display Function: The primary role of this feature is to provide an interface for users to access and visualize early warnings. When the system detects that a monitored component’s mechanical response exceeds the set threshold value, it generates an early warning. This information is then compiled into a warning list, which users can access through this function. The warning list presents all pertinent details about the components that have triggered early warnings. Additionally, to enhance user understanding and rapid response, this function employs a 3D model visualization approach. By overlaying early warning markers on the 3D model of the cable structure, users can swiftly identify the specific location of the components causing concern. This visual representation is highly effective in conveying the urgency and location of potential issues.

#### 3.2.3. System Reliability Check

- (1)
- In the single cable self-weight problem, the displacement results obtained from the modified cable unit, Orcaflex, Midas, and the analytical solution exhibit strong agreement. Additionally, the maximum displacement error between Ansys and the analytical solution is approximately 4.58%. In the case of the single cable subjected to a point load, the results obtained from the modified cable unit, Orcaflex, and Midas closely correspond, whereas the Ansys results are not directly comparable due to loading considerations. For various other single cable scenarios, the maximum error between the modified cable unit and Midas is 5.71%, with an error of about 2.1% when considering only self-weight.
- (2)
- In the self-weight problem of the cable network, the shapes of the modified cable unit, Orcaflex, Midas, and Ansys exhibit remarkable similarity. Regarding cable force, the difference between the modified cable unit and Orcaflex is minimal, with a maximum discrepancy of only 0.14%. Midas is compared with a single 100-unit and a 10-unit planar model due to the relatively lower number of units per cable in the network. It is observed that the difference between the 100-unit and 10-unit modified cable units is negligible. The average discrepancy between the modified cable units and Midas is approximately 5%, with specific values of 5.46% for 100 units and 4.95% for 10 units. There are four groups showing errors exceeding 10% in the 100-unit comparison and three groups in the 10-unit comparison, all of which occur at internal nodes of the cable network, with deviations remaining within 10% or less.
- (3)
- From the comparison of the beam cable forces, it can be observed that the discrepancies in cable forces among the diagonal cable, vertical cable, ring cable, left and right diagonal cable platform, and Midas are all within 0.6%, indicating a close alignment. Although there is a difference of more than 20% in the vertical cable force, a specific analysis reveals that the vertical cable force exhibiting larger divergence differs in magnitude from the normal cable force by an order of magnitude. As a result, this difference has minimal influence on the analysis outcomes. The discrepancies in the transverse cable force are predominantly constrained to within ±1.7%, falling within an acceptable range.

#### 3.3. Continuous Dynamic Simulation Analysis

## 4. Conclusions

- I.
- The DT model of the construction process of the cable structure integrates the construction mechanical response values with the finite element analysis values, realizing the continuous comparison in time.
- II.
- The finite element optimization method of the cable structure adopts the same analytical model to calculate all stages from lifting to tension forming. The results showed that the optimization method has good convergence and the average calculation accuracy is higher than 97%.
- III.
- The Intelligent Simulation System developed based on the continuous dynamic simulation method realizes continuous analysis of each stage of cable structure construction in the actual project, which ensures the safety and quality of the construction process.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 7.**Soldier–strain relationship diagram [38].

**Figure 9.**Layout of measurement points: (

**a**) description of total station measurement point layout; (

**b**) description of GPS bit-type monitoring arrangement diagram.

**Figure 13.**Comparison of the results of the single-cord deadweight bit pattern test. (

**a**) Single cable ends at the same level; (

**b**) the difference between the two ends of the single cable is 8 m [38].

**Figure 14.**Comparison of calculation results under the self-weight of the cable network. (

**a**) Intelligent simulation system for calculating deflection (unit: m); (

**b**) Ansys calculation of deflection (unit: m); (

**c**) Midas calculates deflection (unit: m); (

**d**) Orcaflex calculates deflection (unit: m); (

**e**) computational deflection in the literature (unit: m); (

**f**) deviation of calculation results by above software.

**Figure 15.**Comparison of the results of the two software bitmap calculations (unit: m). (

**a**) Midas calculates deflection (unit: m); (

**b**) intelligent simulation system for calculating deflection (unit: m); (

**c**) deviation of calculation results by Midas.

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## Share and Cite

**MDPI and ACS Style**

Wang, Z.; Li, M.; Liu, Z.; Dezhkam, M.; Zhao, Y.; Hu, Y.
Continuous Dynamic Analysis Method and Case Verification of Cable Structure Based on Digital Twin. *Sustainability* **2023**, *15*, 16125.
https://doi.org/10.3390/su152216125

**AMA Style**

Wang Z, Li M, Liu Z, Dezhkam M, Zhao Y, Hu Y.
Continuous Dynamic Analysis Method and Case Verification of Cable Structure Based on Digital Twin. *Sustainability*. 2023; 15(22):16125.
https://doi.org/10.3390/su152216125

**Chicago/Turabian Style**

Wang, Zeqiang, Mingming Li, Zhansheng Liu, Majid Dezhkam, Yifeng Zhao, and Yang Hu.
2023. "Continuous Dynamic Analysis Method and Case Verification of Cable Structure Based on Digital Twin" *Sustainability* 15, no. 22: 16125.
https://doi.org/10.3390/su152216125