In combination of the actual project in Dalian Baiyun Mountain Tunnel, this paper introduces the principle of fiber optic sensor monitoring system based on optical time domain reflectometer. Then, based on the orthogonal design and even design scheme, this paper carries out a numerical experiment on the tunnel surrounding rock and establishes a regression model of the mapping relation between surrounding rock parameters of operation tunnel and the monitored displacement in order to set the difference between the monitored displacement and the calculated displacement as the fitness function. In the end, this paper carries out parameter identification based on the differential evolution algorithm. Achievements of the study proved that realtime safety warning could be realized inside the tunnel by monitoring the deformation parameters of tunnel vault at real time relying on the opticalfiber sensing system of the optical time domain reflectometer (OTDR). Parameters identification was carried out on the structure with differential evolution according to measured data and selected parameters, and great coincidence was obtained between the measured displacement and the identified parameters displacement, which proved the strong adaptability of the method.
The distributed fiber optic sensing technology is a new type of sensing technology which is developed on the basis of optical time domain reflectometry (OTDR) in opticalfiber engineering [
As the quantum leaps in computer technology, the site safety monitoring of tunnel and method which adopts various inverse analysis calculations have been hotly focused and researched on by the engineering community. Consequently, carrying out quantitative identification analysis from the level of mechanical model is of great engineering significance and academic value [
As a photoelectric integrated instrument for testing optical fiber, optical Time Domain Reflectometer (OTDR) can measure the length of optical fiber, transmission loss of optical fiber, splice attenuation, and fault location. Specifically, OTDR is a photoelectric integrated instrument which uses the backward scattering of Rayleigh scattering and Fresnel reflection of light to test the optical fiber when it is transmitted through optical fiber. This backward Rayleigh scattering technology mainly measures the time it takes for the pulse light wave to transmit in the optical fiber for locating the place with scattering loss [
OTDR test is realized by emitting optical pulses into the optical fiber and later receiving returned information at the OTDR port. The optical pulses will scatter and reflect when transmitting in the optical fiber, due to the properties, connectors, junction points, bending, or other similar events, of the optical fiber, and some scattering and reflection will return to OTDR. The returned useful information is measured by the detector of OTDR and will be used as the time or curve slices at different points inside the optical fiber. This process repeats again and again and the final results will be averaged and shown as a track. This track indicates the strength (strong or weak) of signals in the whole opticalfiber section [
Based on all the above merits, this paper developed a realtime monitoring system for tunnel vault based on the OTDR distributed sensor [
Layout of distributed opticalfiber sensors in the tunnel.
The OTDR in the tunnel vault strain monitoring system emitted pulsed light into the optical fiber. Later, the pulsed light enters into the tunnel through the optical fiber and undergoes brillouin backscattering due to disturbance from the tested structure. Some scattered light and reflected light moved backward to the OTDR. The OTDR received the reflected light returned from the optical fiber and then identified loss signals in the reflected light and finally showed on the display after event study. Based on the loss conditions obtained from OTDR analysis for the full line of optical fiber, the operator could tell whether there were concrete cracks on the tunnel vault, the dislocation of cracks, and fiber cuts and locate such dislocation and fiber cuts. By arranging multiple optical fibers on the vault horizontally along the tunnel axial direction and studying the mechanism of action and location distribution, of deformations, damage, and leakages at weak points of the vault in axial direction, during the operation period of the tunnel, actual parameters can be provided to the study model and realtime safety warning can be realized inside the tunnel, so that the personal and property loss from accidents can be cut down.
Optimization of objective function is finally formed through basic principle transformation in tunnel surrounding rock structure parameter identification. The problem can be described as follows generally:
Constraint is
In the formula,
This paper plans to carry out numerical calculation through orthogonal design and even design. In addition, range analysis and polynomial fitting are adopted to analyze the data sample generated by numerical experiment. The specific method of differential evolution algorithm realized in this paper is as follows:
Threedimensional numerical simulation model is established according to field monitoring data. Besides, L1_{6}(4^{5}) orthogonal sheet is selected to construct parameter combination scheme for numerical test. In this model, the single point restart function in ANSYS is adopted to carry out secondary loading. The strain value after secondary loading is used as the following analysis data.
Sensitivity analysis is carried out on the orthogonal results. The mechanical parameters with stronger sensitivity are selected as the tobeinversed variant while the insensitive parameters are selected as constants according to engineering experience. In addition, sample from orthogonal experiment calculation is adopted to fit in with the curve as the regression function model, thus obtaining the coefficients of the polynomial. Later, even design scheme is used to test the regression model in order to make the regression precision meet the requirements.
Mean square deviation of field monitoring strain data and strain data calculated from regression model is adopted as the fitness function and substituted into the differential optimization algorithm with the tobeinversed parameter as the optimization variant in order to achieve the surround rock parameter search.
Figure
Implementation of displacement back analysis ideas.
DE algorithm [
As for the problem,
In above formulas,
The generation of initial group generally adopts random method. The initial group randomly generated should be evenly distributed in the solution space:
In above formula,
In above formula,
In above formulas,
DE algorithm parameter search flow is shown in Figure
Differences in evolutionary algorithm flow chart of the search parameters.
Dalian Baiyun Tunnel was built in 1984 and completed and put into use in 1986, and it belongs to a doublehole twoway fourlane tunnel, the west hole is 374 meters long, and the east hole is 400 meters long. The tunnel belongs to a straight wall lining structure. The tunnel is designed according to the principle of mining method, and a composite structure is adopted. Existing Baiyun Tunnel has been operated for 30 years at present. Lining concrete suffers from serious aging and cracking phenomena. A new tunnel is excavated and constructed between two existing tunnels according to the requirements of engineering construction. Existing Baiyun Tunnel is reinforced through injection of lightweight concrete and grouting; the healthy and safe state monitoring still should be reinforced. Therefore, an opticalfiber health monitoring system is introduced this time. A lot of monitoring data are provided for evaluating structure status during operation period and predicating operation status and engineering service life through monitoring the tunnel structure status and other working status in order to achieve online monitoring for the safe state of existing Baiyun Tunnel arch and lining structure in real time, thereby guaranteeing safe operation of the tunnel.
Since Baiyun Tunnel is constructed on rock foundation, the excavation depth is deeper and topsoil inhomogeneity is not considered. Meanwhile, since the tunnel is in the linear state during most operating period (nonlinear state is on the brink of destruction), SOILD45 unit of the linear elastic constitutive relation is adopted for simulating the mountain. The model contains a total of 14688 nodes and 12870 units. Ideal elasticplastic constitutive model and DP yield criterion are adopted for simulating surrounding rock. Crustal stress is not considered temporarily. Rock mass gravity stress is considered only (as shown in Figure
Arrangement plan of measuring points within model grid.
Firstly, we adopt prior information to select five representative mechanical parameters of surrounding rock: elastic modulus, Poisson’s ratio, cohesive force, internal friction angle, and tensile strength; then we carry out orthogonal experiment and numerical simulation according to the orthogonal sheet L_{16}(4^{5}). In the process, we adopt single restart function in ANSYS for numerical simulation and use the load of upper covering soil and rock as the initial load. Later, we apply Hooke’s law to calculate the change of strain force by monitoring strain and assumed elastic modulus and then carry out secondary loading analysis on the tunnel based on the above. Next, we carry out a sensitivity analysis on the results of orthogonal experiment and then select parameters
In the above formula,
The parameters of the surrounding rock have influence on the structure. The above sensitivity analysis shows that the elastic modulus and cohesive force are parameters with higher influence on surrounding rock. The two parameters are selected as inversion objects in order to simplify the numerical test. The mathematical model is shown as follows:
In above formula, we suppose that
Contrast on regression model forecast with FEM calculation.


Error value (%)  Calculation result of finite element  Calculation result of regression model 

A  
3.5  0.35 



4.2  0.50 



4.8  0.60 



5.3  0.3 



6.0  0.45 



6.5  0.55 





B  
3.5  0.35 



4.2  0.50 



4.8  0.60 



5.3  0.3 



6.0  0.45 



6.5  0.55 





C  
3.5  0.35 



4.2  0.50 



4.8  0.60 



5.3  0.3 



6.0  0.45 



6.5  0.55 





D  
3.5  0.35 



4.2  0.50 



4.8  0.60 



5.3  0.3 



6.0  0.45 



6.5  0.55 





E  
3.5  0.35 



4.2  0.50 



4.8  0.60 



5.3  0.3 



6.0  0.45 



6.5  0.55 





F  
3.5  0.35 



4.2  0.50 



4.8  0.60 



5.3  0.3 



6.0  0.45 



6.5  0.55 





G  
3.5  0.35 



4.2  0.50 



4.8  0.60 



5.3  0.3 



6.0  0.45 



6.5  0.55 





H  
3.5  0.35 



4.2  0.50 



4.8  0.60 



5.3  0.3 



6.0  0.45 



6.5  0.55 





I  
3.5  0.35 



4.2  0.50 



4.8  0.60 



5.3  0.3 



6.0  0.45 



6.5  0.55 



We substitute the polynomial model obtained from the fitting process and the monitored displacement in Table
Relations between the iteration steps and the convergence value under different CR values when
Relations between the iteration steps and the convergence value under different
In this paper, we select
Comparison between tiny displacements computed via identification parameters and measured.
Measuring point  A  B  C  D  E  F  G  H  I 

Monitored displacement (mm) 









Forecasted displacement (mm) 









Relative error (%) 









Following conclusions can be drawn based on reverse analysis on the operational tunnel structure through the distributed opticalfiber sensing system in the paper:
Realtime safety warning can be realized inside the tunnel by monitoring at real time the deformation parameters of tunnel vault with the OTDR opticalfiber sensing system.
Study on the selection of parameters
Parameters identification was done on the structure with differential evolution according to measured data and selected parameters, and great coincidence between the measured displacement and the identified parameters displacement was obtained, which proved the strong adaptability of this method.
The authors declare that they have no conflicts of interest.