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提出了采用基因表达式编程(Gene Expression Programming,GEP)和混合粒子群相结合计算边坡可靠度的新方法。该方法采用均匀设计法确定样本点,通过数值计算求解安全系数,应用GEP方法拟合边坡的功能函数;借鉴遗传算法中的杂交概念,将其引入标准粒子群方法(Particle Swarm Optimization,PSO),形成混合粒子群方法(MPSO),改善了PSO方法的全局搜索能力,提高了方法的收敛速度和计算精度,可用于计算可靠度指标及相应的验算点。以2个典型的边坡为例,通过算例1与其他方法对比,验证了MPSO方法较标准PSO方法计算精度高、收敛速度快;分析了算法中各控制参数对可靠度指标的影响;算例2为隐式功能函数问题,将MPSO方法与GEP方法相结合求解可靠度指标。结果表明:MPSO-GEP方法对求解隐式功能函数的边坡可靠性问题具有很好的适应性,该方法科学可行且具有很好的应用前景。
A new method for calculating slope reliability by using gene expression programming (GEP) and mixed particle swarm optimization (PSO) was proposed. This method uses the uniform design method to determine the sample points, calculates the safety factor by numerical calculation, and applies the GEP method to fit the slope’s function. Using the concept of hybridization in genetic algorithm, this method is introduced into Particle Swarm Optimization (PSO) , A hybrid particle swarm optimization (MPSO) method is proposed to improve the global search ability of PSO method and improve the convergence speed and accuracy of the method. It can be used to calculate the reliability index and the corresponding checking points. Taking two typical slopes as an example, compared with other methods by the example 1, it is verified that the MPSO method has higher computational accuracy and faster convergence rate than the standard PSO method. The influence of each control parameter on the reliability index is analyzed. Example 2 is an implicit functional problem. The MPSO method is combined with the GEP method to solve the reliability index. The results show that the MPSO-GEP method has good adaptability to the slope reliability problem of implicit function. The method is feasible and has good application prospects.