The fault rate in equipment increases significantly along with the service life of the equipment, especially for multiple fault. Typically, the Bayesian theory is used to construct the model of faults, and intelligent algorithm is used to solve the model. Lagrangian relaxation algorithm can be adopted to solve multiple fault diagnosis models. But the mathematical derivation process may be complex, while the updating method for Lagrangian multiplier is limited and it may fall into a local optimal solution. The particle swarm optimization (PSO) algorithm is a global search algorithm. In this paper, an improved Lagrange-particle swarm optimization algorithm is proposed. The updating of the Lagrangian multipliers is with the PSO algorithm for global searching. The difference between the upper and lower bounds is proposed to construct the fitness function of PSO. The multiple fault diagnosis model can be solved by the improved Lagrange-particle swarm optimization algorithm. Experiment on a case study of sensor data-based multiple fault diagnosis verifies the effectiveness and robustness of the proposed method.

中文翻译：

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改进的Lagrange粒子群优化算法及其在多故障诊断中的应用

设备的故障率随着设备的使用寿命而显着增加，尤其是对于多重故障。通常，使用贝叶斯理论构造故障模型，并使用智能算法求解模型。可以采用拉格朗日松弛算法来解决多个故障诊断模型。但是，数学推导过程可能很复杂，而拉格朗日乘数的更新方法受到限制，并且可能会陷入局部最优解。粒子群优化（PSO）算法是一种全局搜索算法。提出了一种改进的拉格朗日粒子群优化算法。拉格朗日乘数的更新是使用PSO算法进行全局搜索的。提出了上下限之间的差异来构造PSO的适应度函数。改进的拉格朗日粒子群算法可以解决多故障诊断模型。通过基于传感器数据的多故障诊断案例研究，验证了该方法的有效性和鲁棒性。