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In order to monitor and forecast the deformation of the brick-concrete building, by taking a brick-concrete building as research object, fiber grating sensors were used to collect the monitoring data and double logarithmic curve of limit value characteristic and monitoring data were obtained based on the fractal theory. Constant dimension fractal method cannot be used to analyze the data directly. With the method of variable dimension fractal, we accumulate data, and the double logarithmic curve is smooth. Piecewise fractal dimensions are close. The outer interpolation method is used to calculate the fractal dimension of the next point and then back calculate the vertical displacement. The relative errors are calculated by comparing the forecast values and monitoring values, and the maximum relative error is 5.76%. The result shows that the fractal theory is suitable to use in the forecast of the deformation and the accuracy is good.

In China, the structure is generally divided into brick-concrete building, post and panel structure, and reinforced concrete structure, and these buildings during service are bound to produce cumulative damage affected by corrosion, fatigue, aging and other factors, so it is particularly important to monitor the buildings which are on active service.

Health monitoring is an important means to understand the situation of the buildings in use and to layout reasonable monitoring position; analyzing and processing monitoring data will be a key step to master the state of buildings in use; reasonable data processing and effective monitoring models can help staffs to discover abnormities and they can take appropriate measures to ensure the security of the persons and property within the building [

Fractal geometry developed by the Mandelbrot [

Fractal theory means the parts in some way are similar to the whole, under normal circumstances it can be regarded as the state of gathering of fragments. It generally has the following characteristics: 1) fractal sets have a ratio of the details of any small scales, or have a fine structure; 2) fractal sets have some self-similar forms, they may be approximate self-similarity or statistical self-similarity; 3) the fractal dimension of fractal sets is strictly greater than its corresponding topological dimension.

The remote monitoring and warning system used in the experiment includes: fiber sensing systems, signal acquisition and transmission systems, data processing and monitoring and warning system. Fiber grating sensor system includes: types of fiber grating sensors, modulation system and installation of fiber grating sensors. The system of signal transmission and collection includes a correction of fiber grating sensors, application of module, storage structure and methods of vast amounts of real-time data. Data processing, monitoring and warning system is a key part of this experiment, including visualization system of data analyzing and structure running status, and the function of disaster early warning. This study is based on the fractal theory, using the methods of constant dimension fractal and variable dimension fractal to deal with the data collected by fiber grating sensors, and we can predict the vertical displacement of the next point in time, and then to achieve the goal of monitoring and early warning.

At present, the application of constant dimension fractal is described by Equation (1)

Here: r is the characteristic linearity; N is the function associated with r; C is undetermined constant; D is the dimension. Because D is a constant, Equation (1) in log-log line is a straight line, so any two data points

If there is a negative number in the logarithm operation, all the values of this sequence plus a constant to eliminate the impact of negative number. However, in the curve of log-log line, if there is a nonlinear function, this constant dimension fractal cannot be dealt with. Variable dimension fractal can be introduced to solve the problem, specifically as follows:

Because the fractal dimension D is a function of the characteristic linearity r:

Then a Function relationship

available variable dimension fractal form,

That is a form of variable dimension fractal.

We can know from the Equation (5), any functions the same as

Then use the basic sequence to construct other cumulative sequence. If you construct a first order accumulation sequence

and

The test takes the telecommunication building of Hebei University as research object. The telecommunication building belongs to brick-concrete building, 6 layers, 5 layers of main building, built in 1973.12-1976.12, parts of beams, columns exists aging, corrosion and other phenomena. Damage of the aging, corrosion place can easily occur in the future, the main building appears minute vibrations, deformation under the environmental loads, then the vibrations and deformation may lead to crack development, even worse, the whole building may collapse. To make sure the safety of the whole building, teachers and students, we analyze the status of the telecommunication building, then make sure the physical types and the appropriate sensor type and the sensor location.

In the outer wall surface of each floor of typical aging parts, we put FBG surface crack meters to monitor the development of main cracks. In the southeast, northeast, southwest and northwest corners of the main building roof, we install a FBG fiber level to monitor the vertical deformation of main building under outside interference. This is because the top of the building is the most sensitive to external factors, and it seems inconspicuous to artificial disturbance. In the typical beams, columns of the building, we arrange FBG strain gauge to monitor the strain of the beams and columns under outside interference, monitoring point arrangement is as shown in

Equipment name | Model | Standard Range | Accuracy /%FS | Sensitivity /%FS | Temperature compensation | frequency /Hz |
---|---|---|---|---|---|---|

FBG meter Crack | BSIL-GS600 | 200 mm | 0.3 | 0.1 | Internal | 100 |

FBG Level | BGK-FBG-4675T | 100 mm | ≤0.1 | 0.1 | Internal | 100 |

FBG strain gauge | BSIL-GS220T | ±1500 με | 0.3 | 0.1 | Internal | 100 |

ing devices are as shown in

Due to the huge amount of test data, the test is in order to deal with the level monitoring data, we cut out 30 s data of vertical displacement from the northeast corner of the telecommunication building roof, we cut out a data point every second, a total of 30 data points, we take these points as the research object, then we numbers them in chronological order, we use the former 20 points to build prediction model, then use the latter

10 points to check the correctness of the prediction model.

The data after processing can obtain piecewise fractal dimension of monitoring data according to Equation (2),

We build log-log coordinate according to the data in

So we deal with the original monitoring data by first-order accumulation, depending on Equation (7), then we obtain the piecewise fractal dimension (

Sequence (r) | Monitoring values (N) mm | Sequence (r) | Monitoring values (N) mm |
---|---|---|---|

1 | −0.064 | 11 | 0.120 |

2 | −0.032 | 12 | 0.096 |

3 | 0.008 | 13 | −0.048 |

4 | −0.120 | 14 | −0.056 |

5 | −0.088 | 15 | 0.008 |

6 | 0.096 | 16 | −0.144 |

7 | 0.040 | 17 | −0.008 |

8 | 0.024 | 18 | 0.040 |

9 | −0.032 | 19 | 0.016 |

10 | −0.040 | 20 | −0.032 |

Sequence (r) | Monitoring values (N) mm | Sequence (r) | Monitoring values (N) mm |
---|---|---|---|

1 | 0.136 | 11 | 0.320 |

2 | 0.168 | 12 | 0.296 |

3 | 0.208 | 13 | 0.152 |

4 | 0.080 | 14 | 0.144 |

5 | 0.112 | 15 | 0.208 |

6 | 0.296 | 16 | 0.056 |

7 | 0.240 | 17 | 0.192 |

8 | 0.224 | 18 | 0.240 |

9 | 0.168 | 19 | 0.216 |

10 | 0.160 | 20 | 0.168 |

By comparing

1.

2.

Sequence(r) | Measurements (N) mm | D | ||
---|---|---|---|---|

1 | 0.136 | 0.000000 | −1.995100 | ---- |

2 | 0.168 | 0.693147 | −1.783791 | −0.304855 |

3 | 0.208 | 1.098612 | −1.570217 | −0.526738 |

4 | 0.080 | 1.386294 | −2.525729 | 3.321417 |

5 | 0.112 | 1.609438 | −2.189256 | −1.507874 |

6 | 0.296 | 1.791759 | −1.217396 | −5.330489 |

7 | 0.240 | 1.945910 | −1.427116 | 1.360484 |

8 | 0.224 | 2.079442 | −1.496109 | 0.516678 |

9 | 0.168 | 2.197225 | −1.783791 | 2.442475 |

10 | 0.160 | 2.302585 | −1.832582 | 0.463089 |

11 | 0.320 | 2.397895 | −1.139434 | −7.272563 |

12 | 0.296 | 2.484907 | −1.217396 | 0.895302 |

13 | 0.152 | 2.564949 | −1.883875 | 8.326616 |

14 | 0.144 | 2.639057 | −1.937942 | 0.729570 |

15 | 0.208 | 2.708050 | −1.570217 | −5.329889 |

16 | 0.056 | 2.772589 | −2.882404 | 20.331690 |

17 | 0.192 | 2.833213 | −1.650260 | −20.324360 |

18 | 0.240 | 2.890372 | −1.427116 | −3.903917 |

19 | 0.216 | 2.944439 | −1.532477 | 1.948712 |

20 | 0.168 | 2.995732 | −1.783791 | 4.899577 |

sequence (r) | Measurements (N) mm | |||
---|---|---|---|---|

1 | 0.136 | 0.000000 | −1.995100 | ---- |

2 | 0.168 | 0.693147 | −1.190728 | −1.160464 |

3 | 0.208 | 1.098612 | −0.669431 | −1.285677 |

4 | 0.080 | 1.386294 | −0.524249 | −0.504661 |

5 | 0.112 | 1.609438 | −0.350977 | −0.776503 |

6 | 0.296 | 1.791759 | 0.000000 | −1.925050 |

7 | 0.240 | 1.945910 | 0.215111 | −1.395456 |

8 | 0.224 | 2.079442 | 0.381172 | −1.243605 |

9 | 0.168 | 2.197225 | 0.489806 | −0.922323 |

10 | 0.160 | 2.302585 | 0.583332 | −0.887680 |

11 | 0.320 | 2.397895 | 0.747635 | −1.723880 |

12 | 0.296 | 2.484907 | 0.878797 | −1.507401 |

13 | 0.152 | 2.564949 | 0.940007 | −0.764724 |

14 | 0.144 | 2.639057 | 0.994732 | −0.738449 |

15 | 0.208 | 2.708050 | 1.068840 | −1.074138 |

16 | 0.056 | 2.772589 | 1.087888 | −0.295144 |

17 | 0.192 | 2.833213 | 1.150572 | −1.033975 |

18 | 0.240 | 2.890372 | 1.223775 | −1.280691 |

19 | 0.216 | 2.944439 | 1.285368 | −1.139198 |

20 | 0.168 | 2.995732 | 1.330782 | −0.885384 |

3. depending on the equation we can obtain:

We can predict the displacement of the sequence (21 ~ 30), substituting D of Equation (8) into Equation (9). According to the result, we can discover that the relative error is between −5.74% and +5.76% (

The result of the test shows that FBG sensing technology can achieve the goal of the remote real-time dynamic prediction to the deformation and displacement of the brick- concrete buildings. Through processing the displacement-time graph, we can visually monitor the state of buildings. Health monitoring data usually presents self-similarity and satisfies the conditions of application of fractal theory. Fractal theory can make a reasonable assessment quickly for the health status of the buildings which are in use after analyzing the dimension changes of displacement curve. When the range of the measurements and time changes, there is no need to change the prediction model, and the similarity of systematic measurements of the brick-concrete structures can be reflected. Displacement data which FBG sensors collect meet the fractal characteristics, but D, piecewise fractal dimension, has a big fluctuation, then variable dimension fractal can be a predictive model to monitor brick-concrete buildings, and the relative error between predictive value and true value ranges from −5.74% to +5.76%, so accuracy of the prediction is better than others. By setting the alarm value of the building, fractal theory provides a new type of monitoring, early warning methods for the practical engineering. Related conclusions have yet to be studied further.

Sequence (r) | Measurements (N) mm | First-order cumulative fractal dimension | Predictive value ( | Relative error % |
---|---|---|---|---|

21 | 0.176 | −0.870906 | 0.175 | −0.57 |

22 | 0.188 | −0.856428 | 0.183 | −2.66 |

23 | 0.185 | −0.841950 | 0.195 | +5.41 |

24 | 0.196 | −0.827472 | 0.192 | −2.04 |

25 | 0.191 | −0.812994 | 0.202 | +5.76 |

26 | 0.203 | −0.798516 | 0.197 | −2.96 |

27 | 0.195 | −0.784038 | 0.206 | +5.64 |

28 | 0.190 | −0.769560 | 0.199 | +4.73 |

29 | 0.209 | −0.755082 | 0.197 | −5.74 |

30 | 0.221 | −0.740604 | 0.213 | −3.62 |

Yang, C.M. Zhao, X., Yao, Y.F. and Zhang, Z.Q. (2016) Application of Fractal Theory in Brick-Concrete Structural Health Monitoring. Engineering, 8, 646-656. http://dx.doi.org/10.4236/eng.2016.89058