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基于稳定性可行域的渠道PI控制参数两阶段贝叶斯优化方法

Two-stage Bayesian optimization method for canal PI control parameters based on a stability feasible region

  • 摘要: 针对渠道比例-积分(Proportional Integral, PI)控制器参数整定中仿真评估成本高、多目标处理依赖经验等问题,该文提出一种两阶段贝叶斯优化方法。第一阶段以系统稳定时间为目标,基于高斯过程代理模型构建稳定性判别函数,通过贝叶斯优化引导采样,筛选满足稳定性要求的参数可行域;第二阶段在可行域内以归一化的积分绝对误差(Integral Absolute Error, IIAE与控制量总变差(Total Variation, TTV)加权组合为综合性能指标,采用动态采集策略开展贝叶斯优化,实现控制精度与调节平稳性的协同优化。以美国土木工程师学会(American Society of Civil Engineers, ASCE)提出的缓坡测试渠道第一长渠池为试验算例,将所提方法与粒子群优化算法(Particle Swarm Optimization, PSO)和标准贝叶斯优化方法进行对比。结果显示:所提方法仅需50次仿真即可获得准确的稳定性边界;优化结果与PSO相比,系统稳定时间缩短34.5%,IIAETTV分别降低15.8%和9.9%,仿真评估总次数减少86.7%,参数整定效率与可靠性显著提升;与标准贝叶斯优化相比,TTV显著降低32.6%,有效抑制了控制过程振荡;多目标处理中,权重系数λ在0.3~0.7之间时可兼顾控制精度与调节平稳性,实际应用中建议在该推荐范围基础上进行微调。该方法在保证系统稳定性的前提下,大幅降低仿真评估成本,有效提升了PI控制参数整定效率与渠道综合控制性能,可为渠道自动化控制提供理论依据与技术支撑。

     

    Abstract: Parameter tuning of Proportional Integral (PI) controllers was a key step in the automatic control of canals, directly affecting system stability, control accuracy, and regulation smoothness. However, traditional PI tuning methods suffered from high computational costs, heavy reliance on engineering experience, and difficulty in balancing multiple performance criteria, severely restricting practical applications. Therefore, this study proposed an efficient and reliable PI parameter tuning method to solve the above problems and improve the overall control performance of canal systems. A two-stage Bayesian optimization method was designed for this purpose. In the first stage, the system settling time was taken as the core evaluation index. A stability discriminant function was established based on a Gaussian process surrogate model with an anisotropic composite kernel, combining the radial basis function and the Matérn kernel to capture the nonlinear behavior of settling time across the parameter space. This function characterized the stability of the PI control system under different parameter combinations. A Bayesian optimization algorithm guided adaptive parameter sampling to screen out the feasible region that ensured stable canal system. The discrimination threshold was determined by the optimal settling time obtained from the first-stage optimization multiplied by a safety factor, with prediction uncertainty explicitly incorporated to avoid misclassification of marginally stable points. In the second stage, a comprehensive performance index was constructed within the feasible region by the weighted combination of the normalized Integral Absolute Error(IIAE) and the normalized Total Variation(TTV) of the control action. A dynamic acquisition strategy, combining Expected Improvement and the Lower Confidence Bound criteria with a linearly decreasing exploration weight, was adopted to guide the Bayesian optimization process, achieving coordinated improvement of control accuracy and regulation smoothness. The proposed method was validated using the first long reach of the gentle slope test canal recommended by the American Society of Civil Engineers (ASCE). Particle Swarm Optimization (PSO) and standard Bayesian optimization were used as benchmark methods. All simulations were performed using a one-dimensional unsteady flow model based on the Saint-Venant equations. Results showed that the proposed method quickly and accurately determined the stability boundary of PI control parameters, requiring only about 50 simulation evaluations to obtain the stable feasible region. Within the feasible region, 100% of the sampled parameter combinations satisfied the stability requirement, while outside the region only 2% did so, demonstrating the high precision of the identified boundary. Compared with PSO, the proposed method reduced settling time by 34.5%, decreased IIAE by 15.8% and TTV by 9.9%, and cut total evaluations by 86.7%, significantly improving tuning efficiency. Compared with standard Bayesian optimization, the proposed method reduced TTV by 32.6%, effectively suppressing control oscillations during canal operation and improving system smoothness, although it led to a slight increase (about 12%) in the Integral Absolute Error, indicating a successful trade-off between control accuracy and smoothness. In the multi-objective optimization process, when the weight coefficient of the comprehensive performance index was in the range of 0.3 to 0.7, the method could effectively balance control accuracy and regulation smoothness, meeting practical needs of canals. By ensuring stable canal operation, the proposed two-stage Bayesian optimization method effectively overcame the high computational cost and experience-dependent tuning of traditional approaches. It significantly improved tuning efficiency and overall system control performance, providing a reliable theoretical basis and technical support for canal automation.

     

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