Abstract
Utilizing the improved one-dimensional optimization algorithm conveniently solved the nonprobabilistic reliability index, however, only searching the part of probable failure points. Utilizing the global optimal solution method produced heavy computation, although it was capable of searching all probable failure points. This paper, based on these two methods, proposed an improved nonprobabilistic global optimal solution method. The presented method possessed the advantages of searching all probable failure points and generating less computation, by means of which the values of interval variables were determined based on the monotonicity of performance function to the corresponding variables. Without losing any probable failure points, this method was contributive to reducing root value point equations, lowering the computational complexity, and improving the computational efficiency. The effectiveness and feasibility of the presented method were verified by two examples. The proposed method was also introduced to build the nonprobabilistic reliability evaluation process of existing bridges. Taking the Longganhu bridge for example, the nonprobabilistic reliability index of it was calculated using the presented nonprobabilistic reliability evaluation process. The computed nonprobabilistic reliability index η = 0.737 < 1 indicated that the Longganhu bridge was unreliable and needed to be reinforced. Reinforcement measures were carried out for a hollow slab and bridge deck of the Longganhu bridge, respectively. The reinforced bridge was reevaluated as η = 2.159 > 1. The results showed that the bridge was reliable after reinforcement. The study illustrated the application and feasibility of the improved nonprobabilistic global optimal solution method and nonprobabilistic reliability evaluation process in reliability assessment and reinforcement of existing bridges.
Highlights
Substantial uncertainties appear unavoidably in practical engineering, such as structural engineering, geotechnical engineering, and environmental engineering
The reliability method for fatigue crack growth prediction with limited uncertainty information proposed by Wang et al [3, 4] was consistent with the nonprobabilistic reliability concept presented by BenHaim [5], which effectively dealt with the reliability problems when only few or less statistical data were available [6]
As stated by Chen et al [6], Chen and Fan [14], and Fan and Chen [18], there were many advantages for improved one-dimensional optimization algorithm and global optimization method in solving the nonprobabilistic reliability index. Disadvantages of these two methods were reclarified here. e improved one-dimensional optimization algorithm only searched part of the probable failure points and faced with risk of losing the probable failure points. e global optimization method required a large amount of calculation, because there were (1 + n!(n − 1)!/2) extreme point equations and 2n−1 root value point equations to be solved for obtaining the nonprobabilistic reliability index in n-dimensional cases
Summary
Substantial uncertainties appear unavoidably in practical engineering, such as structural engineering, geotechnical engineering, and environmental engineering. An evidence theory-based reliability analysis method was presented by Jiang et al [16], introducing design optimization to obtain the nonprobability index and design point and to reduce the number of limit state functions for computation with the help of interval analysis method. E global optimization method required a large amount of calculation, because there were (1 + n!(n − 1)!/2) extreme point equations and 2n−1 root value point equations to be solved for obtaining the nonprobabilistic reliability index in n-dimensional cases. 2. Nonprobabilistic Reliability Index Based on Interval Model e limit state function (failure surface) representing structure failure is given as follows:. Determine the nonprobabilistic reliability index. e minimum of the absolute values of all solutions according to minimum points and root value points is the final nonprobabilistic reliability index
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