Variable weight synthesis method is a safety assessment method which is using the varied weight principle, based on analytic hierarchy process and combining the theory of grey relevancy, it reduce influence that secondary cause is not obvious in assessment process, and make the result more correct and dependable. In the paper, variable weight principle and the assessment method were expounded in detail.
Variable weight synthesis method ; Bridge structure ; Safety assessment
In the literature (Bai, 2007 and Liu et al., 2004 ), variable weight synthesis method is the definition of:

( 1) 
be called m –d vector of parts variable weight。
In the variable weights method, when synthesis assessment the assessed value of hundredmark system, it will result data with denominator larger, and produce larger roundoff error. For convenience of calculations and considering the required precision, to transform hundredmark system into percentage of system, and then, by adjusting coefficients in the formulas, getting the synthesis assessed value of hundredmark system. in addition, for some sequences of inspection data, it is impossible to collect all the data, but it is needed to compare the curve of sequences of inspection data, so in this paper, considering base on the grey theory related principle to offset the malconformation and incomprehensive of data (Lan and Shi, 2001 ). The paper makes the improvement.

( 2) 
In formula: V is the assessed value; is initial weight value of the j th indicators, and ; is weight value after variable weight; x_{j} is the percentage of assessment value of the j th indicators, and

( 3) 
In formula, B (x_{1} , …, x_{n} ) is balanced function, according to experience of engineering practice, the balanced function is:

( 4) 
simultaneous Eqs. (3) and (4) , it can get:

( 5) 
so

( 6) 
α : balance coefficient, according to experience of engineering practice, α = 0.2, it can meet most of engineering situation.
The inspection data of bridge can be divided into three categories: the first kind is nonnumeric data with describing the state of bridge components only or dividing grade simply; the second is a single numerical; and the third is a data series. It is needed that applies dimensionless method to the third kind data, compare and analyse the two curves of data series. Introduce grey correlativity analysis and calculate nonuniform variation coefficient to get the assessment result, the formula as follows:

( 7) 
And r (x_{0} , x_{i} ) calculate according to the formula as below (5) and (8) :

( 8) 
Compared with constant weight synthesis method, variable weight synthesis method can make the influence of components with damage badly more prominent. In structure, maybe individual component damage can be lead to the bridge operational be limited, even impact to the safety of the bridge (Gao and Wang, 2000 , Lan and Shi, 2001 , Wu and Xiang, 1995 , Xiang and Wu, 2005 and Zhang and Feng, 2001 ). Comparison with the result of constant weight synthesis method and variable weight synthesis method is given.
Using the data in Table 2.1 and Table 2.2 , assessment of the health of bridge with variable weight synthesis method and constant weight synthesis method is shown.

The conclusion is “qualified”;

score V_{2} :

The conclusion is “disqualified”.
Indicator  Weight  Technical status  Explain 

Pier and abutment  0.31  80  Better 
Girder  0.13  80  Better 
Pylon  0.14  75  Normal 
Stay cable  0.37  80  Better 
Subsidiary facilities  0.04  5  Failure badly 
Equal coefficient  α = 0  α = 0.2  α = 0.5  α = 0.8  α = 1.0 

Score of girder  49.52  58.64  68.59  74.19  75.51 
Explain: The value of α reflects tolerance of local damage, with the increase of α , tolerance increase.
By the above examples, it can be got that when the subsidiary facilities damage badly, the result of constant weight synthesis method is “qualified” while variable weight synthesis method is “disqualified”. It is show that variable weight synthesis method can well reflect the local defect and considering the malconformation into assessment. It is more tallies with the actual situation.
The inspection data of line shape control about abridge is in Table 3.1 .
Coordinate (m )  Designed elevation (X_{0} )  Measured elevation (X_{i} )  Error (m )  Assessed value (D_{i} ) 

0  86.550  86.538  0.012  90 
20  86.844  86.830  0.014  90 
40  87.079  87.056  0.023  80 
60  87.247  87.235  0.012  90 
80  87.432  87.419  0.013  90 
100  87.534  87.520  0.014  90 
120  87.541  87.517  0.024  80 
140  87.531  87.508  0.023  80 
160  87.371  87.357  0.014  90 
180  87.168  87.153  0.015  90 
200  86.993  86.977  0.016  90 
220  86.774  86.752  0.022  80 
240  86.537  86.526  0.011  90 
According to formula (5) , calculate variation of weight shown in Fig. 3.1 .

Figure 3.1. Variational weight in observation point of girder line.

According to formula (7) and (8) calculate as:

x_{k} = D_{i} /100, D_{i} : assessed value. (n = 13) initial weight value, see Table 3.1 .

Assessment score of girder alignment is 84.14, contrast Table 3.2 , the bridge can be classified grade 1.
Score  Grade  Explain 

80 < V ≤ 100  Grade 1  Well, only daily maintenance 
60 < V ≤ 80  Grade 2  Normal, daily maintenance and minor repair 
40 < V ≤ 60  Grade 3  Weak, repair and load test 
20 < V ≤ 40  Grade 4  Bad, Stop running and strengthen 
0 < V ≤ 20  Grade 5  Danger, considering dismantle and rebuild 
Note : The evaluation standard is made according to “Evaluation procedure for bearing capacity of highway bridge”.
In the safety process of assessment, the method, by using the variable weight principle to assess actual state of the assessment indexes, extrude the influence of the parts of damaged badly, especially the effect of secondary cause. And on this basis, apply method of grey relational to calculate the correlation degree of sequence data, it make up malconformation and incomplete collection of the test data.
The article explains the variable weight synthesis method, and applies the method into the process of bridge assessment. Though it has the rationality of the method, but it still exist some problem. First, although the assessment applies new method, but most of the index still reference codes and specifications and previous research results, it needs to do a more indepth discussion. Second, the initial weight value used in the paper, it is still the average weight which has certain blindness, it needs to do a more indepth discussion, too.
The author declares that there is no conflict of interest.
Published on 05/10/16
Licence: Other
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