Surrogate Neural Network Model for Prediction of Load-Bearing Capacity of CFSS Members Considering Loading Eccentricity
Abstract
:1. Introduction
2. Materials and Methods
2.1. Database
2.2. Methods Used
2.2.1. Artificial Neural Network
- Hyperbolic tangent sigmoid function, denoted by tansig;
- Log-sigmoid function, denoted by logsig;
- Linear function, denoted by purelin;
- Positive linear function, denoted by rectilin;
- Saturating linear function, denoted by satlin;
- Symmetric saturating linear function, denoted by satlins.
- Levenberg-Marquardt [74], denoted by LM;
- Scaled conjugate gradient [75], denoted by SCG;
- BFGS quasi-Newton [76], denoted by BFG;
- Resilient [77], denoted by RP;
- Conjugate gradient with Powell-Beale restarts [78], denoted by CGB;
- Conjugate gradient with Fletcher-Reeves updates [79], denoted by CGF;
- Conjugate gradient with Polak-Ribiére updates [79], denoted by CGP;
- One-step secant [80], denoted by OSS.
2.2.2. Monte Carlo Random Sampling Technique
2.2.3. Quality Assessment Criteria
3. Results and Discussion
3.1. Convergence of Random Samples
3.2. Results of Parametric Study
3.2.1. Results in Terms of Training Function
3.2.2. Results in Terms of Activation Function
3.2.3. Results in Terms of Number of Neurons
3.2.4. Optimal Parameters
- 15 neurons in the hidden layer;
- A rectilin activation function;
- A LM training algorithm;
- Mean square error as a cost function.
3.3. Analysis of Performance of the Final ANN Model
3.3.1. Regression Analysis
3.3.2. Uncertainty Analysis
3.3.3. Sensitivity Analysis
3.4. Discussion on Effect of Eccentric Loading
4. Conclusions and Outlook
- For the considered problem, the optimal ANN model includes 15 neurons, rectilin activation function, mean squared error cost function and LM training algorithm;
- The proposed ANN model offers reliable prediction in terms of various performance indicators: R2 = 0.975, Slope = 0.975, RMSE = 294.424 kN and MAE = 191.878 kN, respectively;
- By performing sensitivity analysis based on the ICE technique, the geometric parameters of the cross section (B and δ), together with the compressive strength of the concrete (f‘c), have been found to be the most influential variables on the LBC;
- The effect of eccentric loading on the LBC of CFSS members is explored, within the ranges of the input variables adopted in this study;
- The proposed ANN model is able to assist the initial phase of research and design of CFSS members before any experiments are carried out.
Author Contributions
Funding
Conflicts of Interest
Data Availability
References
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Variable | Min | Mean | Max | StD | CV (%) | Symbol | Unit | Type |
---|---|---|---|---|---|---|---|---|
Yield strength of steel tube | 194.18 | 472.79 | 835.00 | 192.91 | 40.80 | fy | MPa | Input |
Compressive strength of concrete | 7.90 | 59.84 | 183.00 | 36.50 | 61.00 | f’c | MPa | Input |
Width of cross section | 60.00 | 147.18 | 324.00 | 56.86 | 38.63 | B | mm | Input |
Length of column | 195.00 | 1426.55 | 4500.00 | 1110.43 | 77.84 | L | mm | Input |
Thickness of steel tube | 0.70 | 4.88 | 12.50 | 2.17 | 44.40 | δ | mm | Input |
Loading eccentricity at the top | 0.00 | 14.58 | 300.00 | 37.10 | 254.37 | et | mm | Input |
Loading eccentricity at the bottom | −25.00 | 13.51 | 300.00 | 37.02 | 274.01 | eb | mm | Input |
Load-bearing capacity | 105.40 | 2205.44 | 8990.00 | 2036.74 | 92.35 | Fn | kN | Target |
Data Used | RMSE (kN) | MAE (kN) | Error Mean (kN) | Error StD (kN) | R2 | Slope | Slope Angle (°) |
---|---|---|---|---|---|---|---|
Training | 217.717 | 139.685 | −1.712 | 218.062 | 0.989 | 0.980 | 44.429 |
Testing | 294.424 | 191.878 | −7.358 | 295.445 | 0.975 | 0.975 | 44.263 |
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Le, T.-T. Surrogate Neural Network Model for Prediction of Load-Bearing Capacity of CFSS Members Considering Loading Eccentricity. Appl. Sci. 2020, 10, 3452. https://doi.org/10.3390/app10103452
Le T-T. Surrogate Neural Network Model for Prediction of Load-Bearing Capacity of CFSS Members Considering Loading Eccentricity. Applied Sciences. 2020; 10(10):3452. https://doi.org/10.3390/app10103452
Chicago/Turabian StyleLe, Tien-Thinh. 2020. "Surrogate Neural Network Model for Prediction of Load-Bearing Capacity of CFSS Members Considering Loading Eccentricity" Applied Sciences 10, no. 10: 3452. https://doi.org/10.3390/app10103452