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Using high-precision sensors to monitor and predict the deformation trend of supertall buildings is a hot research topic for a long time. And in terms of deformation trend prediction, the main way to realized deformation trend prediction is the deep learning algorithm, but the accuracy of prediction result needs to be improved. To solve the problem described above, firstly, based on the conditional deep belief network (CDBN) model, the levenberg-marquardt (LM) was used to optimize the CDBN model; the LM-CDBN model has been constructed. Then taking CITIC tower, the tallest building in Beijing as the research object, the real-time monitoring data of the shape acceleration array (SAA) as an example, we used LM-CDBN model to analyse and predict the building deformation. Finally, to verify the accuracy and robustness of LM-CDBN model, the prediction results of the LM-CDBN model are compared with the prediction results of the CDBN model, the extreme learning machine (ELM) model, and the unscented Kalman filter-support vector regression (UKF-SVR) model, and we evaluated the result from three aspects: training error, fitness, and stability of prediction results. The results show that the LM-CDBN model has higher precision and fitting degree in the prediction of deformation trend of supertall buildings. And the MRE, MAE, and RMSE of the LM-CDBN model prediction results are only 0.0060, 0.0023mm, and 0.0031mm, and the prediction result was more in line with the actual deformation trend.

Affected by its own structural characteristics and external changes, supertall buildings will continue to produce complex deformations such as differential settlement, compression, inclination, deflection, and vibration during the construction process. It is necessary to implement high-precision deformation monitoring and prediction to ensure its construction safety. With the continuous advancement of sensor technology, a lot of progress has been made in obtaining deformation data by installing high-precision sensors on supertall buildings; for example, Su, J.Z. et al. designed a supertall building precision structural performance monitoring system consisting of more than 400 sensors, applied to the structural health monitoring of Shanghai Tower [

Using deformation data to predict the deformation of supertall buildings is one of the current research hotspots. Deformation of supertall buildings has strong temporal and spatial linkage and obvious time-varying characteristics. On the concept of time, the monitoring data has a strong dependence on the concept of time slip; and during the different deformation periods, the structural integrity deformation are both random and time-variation, as well as having continuity and periodicity in time; it requires the model to have higher time-varying information extraction capabilities. In the spatial range, the deformation of supertall buildings has a close spatial correlation with the complexity of the environmental factors, spatial characteristics, and change trends. The different changes of environmental factors in different time periods and different fields have different effects on the deformation of supertall buildings. How to deeply mine and extract the feature attributes of environmental factors has always been one of the research difficulties.

Recently, many advances have been made in the prediction of deformation of buildings using neural network technology. In aspect of shallow neural networks [

The deep learning algorithm [

CDBN model is a variant of the traditional DBN model. It inherits many excellent features of the DBN model and resamples the distortion data of the supertall building through normal distribution. The deformation data of supertall building has a high degree of four-dimensional spatial characteristics, of which the temporal and spatial characteristics are particularly prominent. In the process of extracting deformation information from a supertall building, the CDBN model uses an automatic regression mechanism to dynamically mine, extract, and feedback the temporal and spatial characteristics of the deformation data. The model can be used to excavate the dynamic change characteristics of deformation trend from historical data. These features complement and guide the in-depth digging of the current deformation trend. In addition, the automatic regression (AR) adjustment capability also provides convenient conditions for analysis of supertall deformation trend, deformation extrapolation, and trend fitting.

As shown in Figure

Structure diagram of single layer of CDBN model, consisting of historical data, target data, and hidden nods.

The energy function of CDBN is obtained by (

The CDBN network model uses the gradient descent algorithm to search for optimal solution. The gradient descent algorithm is the most commonly used optimization algorithm for neural network model training. For the function

Finally, training and learning is performed by comparing the divergence sampling method [

Deformation of supertall buildings is more complex, and the characteristics of spatiotemporal linkage are more obvious. Therefore, the deformation prediction of it needs higher prediction accuracy and prediction stability. The CDBN model has a high ability to extract deformation tendency. But due to the use of a gradient descent algorithm to find the optimal solution during the process of weight determination, the predicted output and the actual deformation output are significantly different, and the predicted oscillation is more obvious. In order to solve this problem, we used the L-M algorithm to model the weight, and the Gauss-Newton algorithm was used to update the weight and threshold of the model to speed up the convergence of the algorithm. The combination of powerful deformation information extraction capability and stable nonlinear optimization ability can help improve the prediction accuracy and stability of supertall buildings.

Assume

The mean squared error (MSE) of the model training is defined as the minimum reference standard.

In the initial stage of model training, the value of

The network training and learning process of the LM-CDBN model is constructed as follows and the flow of algorithm was shown in Figure

Flow chart of LM-CDBN algorithm.

The original data is preprocessed (denoised, filtered, normalized, and batched) and the topology of the network is determined.

Enter the first batch of data and prepare for network training.

Use (

Use (

According to the visible layer node state value

Dynamically update the offsets of the visible and implicit nodes thresholds.

Use the state

Establish a matrix vector of the network weights and thresholds. Use (

Enter the second batch of data and go to Step

Use the function softmax to output the predicted value, denormalize data, and evaluate the network prediction results.

To objectively evaluate the prediction results, the prediction model needs to be evaluated based on full consideration of the prediction error and the accuracy of the prediction value fitting degree. The evaluation mechanism is mainly composed of three aspects: model training error evaluation, fitting degree evaluation, and prediction accuracy.

Taking the three aspects of root mean square error (RMSE), mean absolute error (MAE), mean relative error (MRE) as evaluation indices, as shown in (

R represents the degree of fit between the actual observed value and the predicted output value. If the value of R is very large, it means that the predicted value and the actual observed value are compliant; else it means that the correlation between the two is poor. The equation for R is shown in

Put the prediction results of LM-CDBN model to compare with CDBN model, extreme learning machine (ELM), and UKF-SVR model to evaluate the training error and predictive performance of the LM-CDBN model.

The supertall building CITIC tower is in the core area of CBD, Chaoyang District, Beijing, China. The external shape is the overall shape of the “bottle” of Chinese ancient wine containers (Figure

Concept and structure figure of CITIC tower. (a) CITIC tower concept design. (b)CITIC tower schematic.

With the continuous development of global navigation satellite system (GNSS) [

GNSS receiver placement. (a) Location figure of reference stations and observation stations. (b) Receiver antenna figure.

GNSS deformation monitoring system diagram consists of GNSS receiver, DTU, control center, and reference station.

The shape acceleration array (SAA) system [

Shape acceleration array system, consisting of standard test section, flexible joint, and special section.

Assuming

According to the CITIC tower’s architectural characteristics, two SAAs are placed in PVC sleeves and embedded along the vertical axis of the outside of the core tube. The ends are fixed on the floor of the structure and the front end is connected to a wireless serial modem (WSM) to achieve long-distance communication.

As shown in Table

Monitoring data of CITIC office building.

Serial number | Time | Z [mm] | Temperature [°C] | Wind speed [m·s^{−1}] | Light intensity [Lx] |
---|---|---|---|---|---|

1 | 2017-10-11 0:00 | 28.281 | 14.1 | 5.8 | 2.732 |

2 | 2017-10-11 1:00 | 27.556 | 14.3 | 5.4 | 2.452 |

3 | 2017-10-11 2:00 | 28.428 | 14.2 | 5.5 | 2.543 |

4 | 2017-10-11 3:00 | 29.779 | 14.9 | 5.4 | 2.654 |

5 | 2017-10-11 4:00 | 30.250 | 14.8 | 4.9 | 2.687 |

6 | 2017-10-11 5:00 | 27.895 | 14.1 | 5.2 | 2.754 |

-- | -- | -- | -- | -- | -- |

69 | 2017-10-13 21:00 | 49.753 | 11.9 | 6.7 | 2.543 |

70 | 2017-10-13 22:00 | 49.341 | 11.6 | 7.5 | 2.654 |

During the construction phase, the core barrel is subject to environmental cross-wind loads, temperature differences between the inside and outside of the shell structure, and changes in light intensity, which are easily subject to dynamic deformation. The training data set consists of core barrel displacement data, temperature, wind speed, light intensity, and time series. During the training of the model, the influence factors such as temperature, wind speed, and light intensity are taken as the characteristic values of the network input layer, and the displacement data of the core cylinder is used as the output feature vector.

In the process of sample priming, gross errors and noise elimination are first performed. Select the first 55 periods of data as a priori samples for network pretraining, and the last 15 samples for deformation analysis and prediction.

Due to the large range of deformation fluctuations and the large magnitude difference between the input factors of each group, the logarithmic interpolation algorithm (as shown in (

In the network topology determination process, the precise determination of network depth, the number of hidden layer nodes, and various training parameters are the key to accurate prediction.

In the process of model building, the network depth means the number of network layers of the model. In the process of layer-by-layer network training, reconstruction error (RE) is generated, which is an important indicator to measure network stability. In the case of a certain input layer data pattern, the network reconstruction error is calculated to effectively determine the network depth. As shown in Figure

Reconstruction error of hidden layer. (a) Number of hidden layer is 1. (b) Number of hidden layer is 2. (c) Number of hidden layer is 3. (d) Number of hidden layer is 4.

As shown in Figure

According to (

In this prediction of deformation for supertall buildings, take the number of input layer nodes m=4, the number of output layer nodes n=1, and the range of hidden layer nodes is

Statistical table of the number of hidden layer’s nodes.

layers | RMSE/mm | MAE/mm | MRE | R/% |
---|---|---|---|---|

2 | 0.0369 | 0.0167 | 0.0237 | 93.52 |

3 | 0.0400 | 0.0213 | 0.0316 | 92.98 |

4 | 0.0665 | 0.0342 | 0.0500 | 88.31 |

5 | 0.0395 | 0.0214 | 0.0317 | 93.07 |

6 | 0.0285 | 0.0117 | 0.0162 | 95.00 |

7 | 0.0113 | 0.0052 | 0.0075 | 98.01 |

8 | 0.0450 | 0.0236 | 0.0348 | 92.10 |

9 | 0.0225 | 0.0091 | 0.0125 | 96.05 |

10 | 0.0330 | 0.0135 | 0.0187 | 94.20 |

11 | 0.0162 | 0.0066 | 0.0091 | 97.16 |

12 | 0.0325 | 0.0159 | 0.0231 | 94.29 |

Statistical diagram of the number of hidden layer’s nodes. (a) Red line with respect to the RMSE, blue line with respect to the MAE, and yellow line with respect to the MRE. (b) Blue line with respect to the R.

When the hidden layer node is 7, the RMSE, MAE, and MRE have the minimum value and the fitting R also has the largest value. Currently, the model has the best deformation prediction ability and nonlinear generalization ability.

As shown in Table

Comparison table of prediction.

DATE | Z [mm] | CDBN [mm] | RE [%] | LM-CDBN [mm] | RE [%] | ELM [mm] | RE [%] | UKF-SVR [mm] | RE [%] |
---|---|---|---|---|---|---|---|---|---|

10-13 08:00 | 36.3700 | 35.6869 | 1.88 | 36.2744 | 0.26 | 34.0753 | 6.31 | 36.9076 | 1.48 |

10-13 09:00 | 35.9685 | 34.7454 | 3.40 | 35.8914 | 0.21 | 38.9832 | 8.38 | 36.8897 | 2.56 |

10-13 10:00 | 34.1020 | 33.0588 | 3.06 | 34.0540 | 0.14 | 38.0791 | 11.66 | 33.5363 | 1.66 |

10-13 11:00 | 34.2450 | 32.6750 | 4.58 | 34.1812 | 0.19 | 34.6637 | 1.22 | 30.5105 | 10.91 |

10-13 12:00 | 39.0745 | 38.2927 | 2.00 | 38.8679 | 0.53 | 35.8950 | 8.14 | 39.1214 | 0.12 |

10-13 13:00 | 37.1475 | 35.9385 | 3.25 | 37.0167 | 0.35 | 39.5860 | 6.56 | 38.7017 | 4.18 |

10-13 14:00 | 37.7950 | 36.8189 | 2.58 | 37.6317 | 0.43 | 36.9923 | 2.12 | 34.8703 | 7.74 |

10-13 15:00 | 41.6840 | 39.6342 | 4.92 | 41.2798 | 0.97 | 40.3191 | 3.27 | 43.4704 | 4.29 |

10-13 16:00 | 39.1225 | 38.3562 | 1.96 | 38.8977 | 0.57 | 43.4842 | 11.15 | 41.1197 | 5.10 |

10-13 17:00 | 40.6580 | 39.2225 | 3.53 | 40.2930 | 0.90 | 44.4703 | 9.38 | 37.4763 | 7.83 |

10-13 18:00 | 47.0815 | 44.5459 | 5.39 | 45.8757 | 2.56 | 40.8088 | 13.32 | 48.4904 | 2.99 |

10-13 19:00 | 46.3970 | 44.8205 | 3.40 | 45.3267 | 2.31 | 44.6929 | 3.67 | 47.7502 | 2.92 |

10-13 20:00 | 47.3470 | 45.7168 | 3.44 | 46.0723 | 2.69 | 48.1102 | 1.61 | 47.8773 | 1.12 |

10-13 21:00 | 51.0815 | 47.3883 | 7.23 | 48.8165 | 4.43 | 45.8864 | 10.17 | 52.2852 | 2.36 |

10-13 22:00 | 49.5470 | 47.0194 | 5.10 | 47.7546 | 3.62 | 47.7797 | 3.57 | 49.2904 | 0.52 |

Mean Relative Error (MRE)[%] | 3.72 | -- | 1.34 | -- | 6.70 | -- | 3.72 |

Compared with CDBN model, ELM, and improved SVR, LM-CDBN model has higher prediction accuracy and stability, and the model's extrapolation ability is better than other forecast models. The average relative error of the 15 forecast results is 3.12%. At the same time, the relative error of the LM-CDBN model prediction is even and stable. The prediction results of LM-CDBN model are less volatile than UKF-SVR. In addition, compared with the CDBN model, the L-M algorithm is used for optimization and improvement, the generalization ability of the CDBN model is enhanced, and the stability and prediction accuracy of the prediction are improved.

Similarly, as shown in Table

Comparison of the result of prediction evaluation.

Evaluation Standard | CDBN | LM-CDBN | ELM | UKF-SVR |
---|---|---|---|---|

MRE | 0.0296 | 0.0060 | 0.0487 | 0.0283 |

MAE [mm] | 0.0141 | 0.0023 | 0.0262 | 0.0155 |

RMSE [mm] | 0.0212 | 0.0031 | 0.0385 | 0.0223 |

R [%] | 94.9 | 98.9 | 91.3 | 95.1 |

As shown in Figure

Results of fitting and prediction. (a) Fitting result comparison. (b) Forecast result comparison.

A new deformation prediction approach for supertall building was proposed in the paper. The LM algorithm was used to optimize the weighting method of CDBN model in this approach. Then use this model to predict the deformation of the supertall building CITIC tower and value the perdition results using several different methods. In terms of error, the MAE value of the LM-CDBN model is 0.0023 mm, while the MAE of the CDBN model, the ELM model, and the UKF-SVR model was 0.0141 mm, 010262 mm, and 0.0155 mm. The RMSE of LM-CDBN model was 0.0031 mm, while the RMSE of CDBN model, ELM model, and UKF-SVR model was 0.0212 mm, 0.0385 mm, and 0.0223 mm. In terms of fitness, the fitting performance of the LM-CDBN model increased by 64%, 80%, and 64%, compared with the CDBN model, the ELM model, and the UKF-SVR model. By comparing experiments and data analysis, we can find that the LM-CDBN model has higher prediction accuracy than three other models, and the variation law of the prediction data is more consistent with the actual variation law. Hence, we can conclude that the LM-CDBN model is suitable for the variable prediction of supertall buildings and also has better robustness and deformation prediction ability.

The data used to support the findings of this study are available from the corresponding author upon request.

There is no conflict of interest regarding the publication of this paper.

This research was supported mainly by the National Key Research and Development Program of China [no. 2017YFB0503700], the Fundamental Research Funds for Beijing University of Civil Engineering and Architecture [no. FZ02], and Beijing University of Civil Engineering and Architecture Postgraduate Innovation Project [no. PG2018054, no. PG2018062].