Operational optimization of copper flotation process based on the weighted Gaussian process regression and index-oriented adaptive differential evolution algorithm

Concentrate copper grade(CCG)is one of the important production indicators of copper flotation processes,and keeping the CCG at the set value is of great significance to the economic benefit of copper flotation industrial processes.This paper addresses the fluctuation problem of CCG through an operational optimization method.Firstly,a density-based affinity propagationalgorithm is proposed so that more ideal working condition categories can be obtained for the complex raw ore properties.Next,a Bayesian network(BN)is applied to explore the relationship between the operational variables and the CCG.Based on the analysis results of BN,a weighted Gaussian process regression model is constructed to predict the CCG that a higher prediction accuracy can be obtained.To ensure the predicted CCG is close to the set value with a smaller magnitude of the operation adjustments and a smaller uncertainty of the prediction results,an index-oriented adaptive differential evolution(IOADE)algorithm is proposed,and the convergence performance of IOADE is superior to the traditional differential evolution and adaptive differential evolution methods.Finally,the effectiveness and feasibility of the proposed methods are verified by the experiments on a copper flotation industrial process.

Optimization of Generator Based on Gaussian Process Regression Model with Conditional Likelihood Lower Bound Search

The noise that comes from finite element simulation often causes the model to fall into the local optimal solution and over fitting during optimization of generator.Thus,this paper proposes a Gaussian Process Regression(GPR)model based on Conditional Likelihood Lower Bound Search(CLLBS)to optimize the design of the generator,which can filter the noise in the data and search for global optimization by combining the Conditional Likelihood Lower Bound Search method.Taking the efficiency optimization of 15 kW Permanent Magnet Synchronous Motor as an example.Firstly,this method uses the elementary effect analysis to choose the sensitive variables,combining the evolutionary algorithm to design the super Latin cube sampling plan;Then the generator-converter system is simulated by establishing a co-simulation platform to obtain data.A Gaussian process regression model combing the method of the conditional likelihood lower bound search is established,which combined the chi-square test to optimize the accuracy of the model globally.Secondly,after the model reaches the accuracy,the Pareto frontier is obtained through the NSGA-II algorithm by considering the maximum output torque as a constraint.Last,the constrained optimization is transformed into an unconstrained optimizing problem by introducing maximum constrained improvement expectation(CEI)optimization method based on the re-interpolation model,which cross-validated the optimization results of the Gaussian process regression model.The above method increase the efficiency of generator by 0.76%and 0.5%respectively;And this method can be used for rapid modeling and multi-objective optimization of generator systems.

Fast Remaining Capacity Estimation for Lithium-ion Batteries Based on Short-time Pulse Test and Gaussian Process Regression

It remains challenging to effectively estimate the remaining capacity of the secondary lithium-ion batteries that have been widely adopted for consumer electronics,energy storage,and electric vehicles.Herein,by integrating regular real-time current short pulse tests with data-driven Gaussian process regression algorithm,an efficient battery estimation has been successfully developed and validated for batteries with capacity ranging from 100%of the state of health(SOH)to below 50%,reaching an average accuracy as high as 95%.Interestingly,the proposed pulse test strategy for battery capacity measurement could reduce test time by more than 80%compared with regular long charge/discharge tests.The short-term features of the current pulse test were selected for an optimal training process.Data at different voltage stages and state of charge(SOC)are collected and explored to find the most suitable estimation model.In particular,we explore the validity of five different machine-learning methods for estimating capacity driven by pulse features,whereas Gaussian process regression with Matern kernel performs the best,providing guidance for future exploration.The new strategy of combining short pulse tests with machine-learning algorithms could further open window for efficiently forecasting lithium-ion battery remaining capacity.

Multi-output Gaussian Process Regression Model with Combined Kernel Function for Polyester Esterification Processes

In polyester fiber industrial processes,the prediction of key performance indicators is vital for product quality.The esterification process is an indispensable step in the polyester polymerization process.It has the characteristics of strong coupling,nonlinearity and complex mechanism.To solve these problems,we put forward a multi-output Gaussian process regression(MGPR)model based on the combined kernel function for the polyester esterification process.Since the seasonal and trend decomposition using loess(STL)can extract the periodic and trend characteristics of time series,a combined kernel function based on the STL and the kernel function analysis is constructed for the MGPR.The effectiveness of the proposed model is verified by the actual polyester esterification process data collected from fiber production.

Gaussian process regression-based quaternion unscented Kalman robust filter for integrated SINS/GNSS

High-precision filtering estimation is one of the key techniques for strapdown inertial navigation system/global navigation satellite system(SINS/GNSS)integrated navigation system,and its estimation plays an important role in the performance evaluation of the navigation system.Traditional filter estimation methods usually assume that the measurement noise conforms to the Gaussian distribution,without considering the influence of the pollution introduced by the GNSS signal,which is susceptible to external interference.To address this problem,a high-precision filter estimation method using Gaussian process regression(GPR)is proposed to enhance the prediction and estimation capability of the unscented quaternion estimator(USQUE)to improve the navigation accuracy.Based on the advantage of the GPR machine learning function,the estimation performance of the sliding window for model training is measured.This method estimates the output of the observation information source through the measurement window and realizes the robust measurement update of the filter.The combination of GPR and the USQUE algorithm establishes a robust mechanism framework,which enhances the robustness and stability of traditional methods.The results of the trajectory simulation experiment and SINS/GNSS car-mounted tests indicate that the strategy has strong robustness and high estimation accuracy,which demonstrates the effectiveness of the proposed method.

Dynamic soft sensor development based on Gaussian mixture regression for fermentation processes

The dynamic soft sensor based on a single Gaussian process regression(GPR) model has been developed in fermentation processes.However,limitations of single regression models,for multiphase/multimode fermentation processes,may result in large prediction errors and complexity of the soft sensor.Therefore,a dynamic soft sensor based on Gaussian mixture regression(GMR) was proposed to overcome the problems.Two structure parameters,the number of Gaussian components and the order of the model,are crucial to the soft sensor model.To achieve a simple and effective soft sensor,an iterative strategy was proposed to optimize the two structure parameters synchronously.For the aim of comparisons,the proposed dynamic GMR soft sensor and the existing dynamic GPR soft sensor were both investigated to estimate biomass concentration in a Penicillin simulation process and an industrial Erythromycin fermentation process.Results show that the proposed dynamic GMR soft sensor has higher prediction accuracy and is more suitable for dynamic multiphase/multimode fermentation processes.

A Gaussian process regression-based sea surface temperature interpolation algorithm

The resolution of ocean reanalysis datasets is generally low because of the limited resolution of their associated numerical models.Low-resolution ocean reanalysis datasets are therefore usually interpolated to provide an initial or boundary field for higher-resolution regional ocean models.However,traditional interpolation methods(nearest neighbor interpolation,bilinear interpolation,and bicubic interpolation)lack physical constraints and can generate significant errors at land-sea boundaries and around islands.In this paper,a machine learning method is used to design an interpolation algorithm based on Gaussian process regression.The method uses a multiscale kernel function to process two-dimensional space meteorological ocean processes and introduces multiscale physical feature information(sea surface wind stress,sea surface heat flux,and ocean current velocity).This greatly improves the spatial resolution of ocean features and the interpolation accuracy.The eff ectiveness of the algorithm was validated through interpolation experiments relating to sea surface temperature(SST).The root mean square error(RMSE)of the interpolation algorithm was 38.9%,43.7%,and 62.4%lower than that of bilinear interpolation,bicubic interpolation,and nearest neighbor interpolation,respectively.The interpolation accuracy was also significantly better in off shore area and around islands.The algorithm has an acceptable runtime cost and good temporal and spatial generalizability.

Nonnegativity-enforced Gaussian process regression

Gaussian process(GP)regression is a flexible non-parametric approach to approximate complex models.In many cases,these models correspond to processes with bounded physical properties.Standard GP regression typically results in a proxy model which is unbounded for all temporal or spacial points,and thus leaves the possibility of taking on infeasible values.We propose an approach to enforce the physical constraints in a probabilistic way under the GP regression framework.In addition,this new approach reduces the variance in the resulting GP model.

A genetic Gaussian process regression model based on memetic algorithm

Gaussian process(GP)has fewer parameters,simple model and output of probabilistic sense,when compared with the methods such as support vector machines.Selection of the hyper-parameters is critical to the performance of Gaussian process model.However,the common-used algorithm has the disadvantages of difficult determination of iteration steps,over-dependence of optimization effect on initial values,and easily falling into local optimum.To solve this problem,a method combining the Gaussian process with memetic algorithm was proposed.Based on this method,memetic algorithm was used to search the optimal hyper parameters of Gaussian process regression(GPR)model in the training process and form MA-GPR algorithms,and then the model was used to predict and test the results.When used in the marine long-range precision strike system(LPSS)battle effectiveness evaluation,the proposed MA-GPR model significantly improved the prediction accuracy,compared with the conjugate gradient method and the genetic algorithm optimization process.

Rolling Gaussian Process Regression with Application to Regime Shifts

Gaussian Process Regression (GPR) can be applied to the problem of estimating a spatially-varying field on a regular grid, based on noisy observations made at irregular positions. In cases where the field has a weak time dependence, one may desire to estimate the present-time value of the field using a time window of data that rolls forward as new data become available, leading to a sequence of solution updates. We introduce “rolling GPR” (or moving window GPR) and present a procedure for implementing that is more computationally efficient than solving the full GPR problem at each update. Furthermore, regime shifts (sudden large changes in the field) can be detected by monitoring the change in posterior covariance of the predicted data during the updates, and their detrimental effect is mitigated by shortening the time window as the variance rises, and then decreasing it as it falls (but within prior bounds). A set of numerical experiments is provided that demonstrates the viability of the procedure.

利用SE-GPR模型对甲醇/柴油混合燃料柴油机性能的预测

为了对柴油机的经济性和排放参数进行高效、准确的预测,根据4190型船用柴油机实验数据与边界参数,建立AVL-BOOST甲醇/柴油混合燃料柴油机仿真模型;利用模型进行仿真实验,并建立甲醇掺混比、废气再循环(exhaust gas recirculation,EGR)率、喷油提前角和进气压力4个控制参数对有效油耗率和NO x排放预测数据集;利用该数据集对5种不同核函数的高斯过程回归(Gaussian process regression,GPR)模型进行训练;最后将最优的平方指数高斯过程回归(squared exponential-Gaussian process regression,SE-GPR)模型、AVL-BOOST仿真数据和柴油机实验数据进行对比。结果表明:在数据量为180组时,SE-GPR模型对有效油耗率和NO x排放均取得拟合关联度99%以上,均方根误差(root mean square error,RMSE)分别为1.859,0.3445,平均绝对误差(mean absolute error,MAE)分别为0.954,0.2489;并且,相较于AVL-BOOST仿真实验,SE-GPR模型对实验数据具有更好的拟合性。

基于GPR模型的用户量预测优化方法

高斯过程回归(Gaussian process regression,GPR)是一种基于高斯过程的非参数化贝叶斯回归方法,其可以灵活适应不同类型数据,用于建模和预测数据之间的复杂关系,具有拟合能力强、泛化能力好等特点。针对海量用户场景下用户量实时预测问题,提出一种基于GPR的用户量预测优化方法。在滑动窗口方法处理数据的基础上,选择合适的核函数,基于k折交叉验证得到最佳超参数组合以实现GPR模型训练,完成在线用户量的实时预测并进行性能评估。实验结果表明,相比于采用训练集中输出数据方差的50%作为信号噪声估计量的传统方案,所提方法具有较高的预测准确度,并且在测试集均方根误差(root mean square,RMS)、平均绝对误差(mean absolute error,MAE)、平均偏差(mean bias error,MBE)和决定系数R 2这4个评估指标方面均有提升,其中MBE至少提升了43.3%。

基于Tri-training GPR的半监督软测量建模方法

集成学习因通过构建并结合多个学习器,常获得比单一学习器显著优越的泛化能力。但是在标记数据比例较少时,建立高性能的集成学习软测量模型依然是个挑战。针对这一个问题,提出一种基于半监督集成学习的软测量建模方法——Tri-training GPR模型。该建模策略充分发挥了半监督学习的优势,减轻建模过程对标记样本数据的需求,在低数据标签率下,仍能通过对无标记数据进行筛选从而扩充可用于建模的有标记样本数据集,并进一步结合半监督学习和集成学习的优势,提出一种新的选择高置信度样本的思路。将所提方法应用于青霉素发酵和脱丁烷塔过程,建立青霉素和丁烷浓度预测软测量模型,与传统的建模方法相比获得了更优的预测结果,验证了模型的有效性。

面向光纤光栅传感线性拟合度的PSO-GPR算法

【目的】为了提高光纤布拉格光栅(FBG)传感系统中反射光谱中心波长与外部环境变量之间的线性拟合度,文章提出了使用粒子群优化的高斯过程回归模型应用于FBG应力传感领域。【方法】针对FBG的反射光谱特性,文章研究了对于FBG传感系统在光谱拟合中线性拟合度的影响,通过粒子群算法去寻找高斯过程回归模型中的最优超参数以提升对反射光谱中心波长的预测性能。文章搭建了FBG应力传感实验平台,将FBG铺设在强度梁上,在等强度梁一端施加不同重量的砝码对FBG产生轴向应变,通过光谱仪采集反射光谱数据并使用文章所提模型进行线性拟合分析处理,将未优化的高斯过程回归模型、最大值法、高斯拟合法和质心法得到的结果作为对照组。【结果】结果表明,在掺铒光纤放大器输出功率为10 dBm、传输光纤距离为50 m、光谱仪采样点个数为501的条件下,反射光谱中心波长与砝码重量之间的线性拟合度均优于对照组,文章所提模型的线性拟合度最高能达到0.9519,相较于对照组均有所提升。在501、251、167和126点的光谱采样点条件下,文章所提模型能将系统的线性拟合度提升到0.9900,相较于最大值法最大提升了0.2587。【结论】分析结果表明,使用粒子群优化的高斯过程回归模型能够有效提高FBG应力传感系统的线性拟合度。

基于一阶ECM-IGPR的锂离子电池SOC及SOH联合估计框架

为解决锂电池荷电状态与健康状态互相耦合问题,提出一种基于等效电路模型-改进高斯过程回归的锂离子电池荷电状态(SOC)-健康状态(SOH)的联合估计框架。该框架通过提取容量增量曲线中的健康特征,进行主成分分析,然后建立电池老化的改进高斯过程回归模型进行SOH预测。在此基础上,建立锂电池一阶状态空间模型,并结合改进粒子滤波算法对后一周期的SOC更新,实现SOC及SOH的联合长期估计。牛津数据集中的8个电池被用来验证该框架的准确性和适应性,取得了较好的估计结果。

基于SSA-GPR模型的风电机组运行状态监测

为提高风电机组发电效率,增加经济收益,实现风电机组运行状态的在线监测,提出一种基于麻雀搜索算法优化高斯过程回归(SSA-GPR)模型的风电机组状态监测新方法。首先对数据采集与监视控制(SCADA)系统采集到的数据进行预处理分析,利用相关性分析完成模型的输入量选择;然后利用机组正常运行状态下的参数建立常态回归模型,实时计算重构误差,通过实时监测功率残差值是否超过动态故障阈值来判断机组状态。实例结果表明,所提方法的预测误差更小,并可以提前120 min实现机组异常运行状态预警。

LiDAR-based estimation of bounding box coordinates using Gaussian process regression and particle swarm optimization

Camera-based object tracking systems in a given closed environment lack privacy and confidentiality.In this study,light detection and ranging(LiDAR)was applied to track objects similar to the camera tracking in a closed environment,guaranteeing privacy and confidentiality.The primary objective was to demonstrate the efficacy of the proposed technique through carefully designed experiments conducted using two scenarios.In Scenario I,the study illustrates the capability of the proposed technique to detect the locations of multiple objects positioned on a flat surface,achieved by analyzing LiDAR data collected from several locations within the closed environment.Scenario II demonstrates the effectiveness of the proposed technique in detecting multiple objects using LiDAR data obtained from a single,fixed location.Real-time experiments are conducted with human subjects navigating predefined paths.Three individuals move within an environment,while LiDAR,fixed at the center,dynamically tracks and identifies their locations at multiple instances.Results demonstrate that a single,strategically positioned LiDAR can adeptly detect objects in motion around it.Furthermore,this study provides a comparison of various regression techniques for predicting bounding box coordinates.Gaussian process regression(GPR),combined with particle swarm optimization(PSO)for prediction,achieves the lowest prediction mean square error of all the regression techniques examined at 0.01.Hyperparameter tuning of GPR using PSO significantly minimizes the regression error.Results of the experiment pave the way for its extension to various real-time applications such as crowd management in malls,surveillance systems,and various Internet of Things scenarios.

基于ECM和SGPR的高鲁棒性锂离子电池健康状态估计方法

锂离子电池健康状态(SOH)的准确估计对于保障电池系统安全运行具有重要意义.针对传统SOH估计方法在可变工况下失效的问题,提出了一种基于等效电路模型和稀疏高斯过程回归的锂离子电池SOH在线估计方法.通过两个在线滤波器,在恒流充电过程中动态地辨识了锂离子电池等效电路模型的各项参数,构建了工况不敏感的健康因子,结合稀疏高斯过程回归实现SOH的间接估计.该方法在多种工况下使用统一的信号处理方法和特征映射模型,兼具鲁棒性强和冗余度低的优点.实验结果表明,该方法在多种工况下的平均绝对误差不超过0.94%,均方根误差不超过1.12%,与现有方法相比,该方法在综合性能上具有显著优势.

基于数据预处理和VMD-LSTM-GPR的锂离子电池剩余寿命预测

锂离子电池的剩余使用寿命(RUL)是健康管理中重要参数,其准确评估对于保证电池设备的安全稳定运行非常重要。该文提出一种数据预处理联合变分模态分解(VMD)、长短期记忆网络(LSTM)和高斯回归过程(GPR)的预测框架。首先选取充放电循环过程中的信息作为间接健康因子(HI),并通过核主元分析方法(KPCA)实现间接HI的特征提取,完成数据预处理;其次通过VMD-LSTM方法实现健康因子的分解、预测和重构,并将重构得到的数据应用于RUL预测的GPR模型,完成预测模型搭建;最后以NASA锂电池数据集作为算法测试数据,结果表明,所提取的健康因子能够准确跟踪锂电池的退化过程;所提预测方法能够准确地估计电池的剩余寿命,同时具有较高的可靠性和稳定性。

基于GPR代理模型和GA-APSO混合优化算法的软基水闸底板脱空反演

软基水闸底板脱空是水闸在长期服役期间受水流侵蚀等环境因素影响所产生的一种危害极大且难以察觉的病害。由于其病害部位于水下,传统方法难以检测,该研究提出一种基于高斯过程回归(Gaussian process regression,GPR)代理模型和遗传-自适应惯性权重粒子群(genetic algorithm-adaptive particle swarm optimization,GA-APSO)混合优化算法的水闸底板脱空动力学反演方法,用于检测软基水闸底板脱空。首先,构建表征软基水闸底板脱空参数和水闸结构模态参数之间非线性关系的GPR代理模型;其次,基于GPR代理模型与水闸实测模态参数建立脱空反演的最优化数学模型,将反演问题转化为目标函数最优化求解问题;最后,为提高算法寻优计算的精度,提出一种GA-APSO混合优化算法对目标函数进行脱空反演计算,并提出一种更合理判断反演脱空区域面积和实际脱空区域面积相对误差的指标—面积不重合度。为验证所提方法性能,以一室内软基水闸物理模型为例,对两种不同脱空工况开展研究分析,结果表明,反演脱空区域面积和模型实际设置脱空区域面积的相对误差分别为8.47%和10.77%,相对误差值较小,证明所提方法能有效反演出水闸底板脱空情况,可成为软基水闸底板脱空反演检测的一种新方法。