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.

State of health prediction for lithium-ion batteries based on ensemble Gaussian process regression

The performance of lithium-ion batteries(LIBs)gradually declines over time,making it critical to predict the battery’s state of health(SOH)in real-time.This paper presents a model that incorporates health indicators and ensemble Gaussian process regression(EGPR)to predict the SOH of LIBs.Firstly,the degradation process of an LIB is analyzed through indirect health indicators(HIs)derived from voltage and temperature during discharge.Next,the parameters in the EGPR model are optimized using the gannet optimization algorithm(GOA),and the EGPR is employed to estimate the SOH of LIBs.Finally,the proposed model is tested under various experimental scenarios and compared with other machine learning models.The effectiveness of EGPR model is demonstrated using the National Aeronautics and Space Administration(NASA)LIB.The root mean square error(RMSE)is maintained within 0.20%,and the mean absolute error(MAE)is below 0.16%,illustrating the proposed approach’s excellent predictive accuracy and wide applicability.

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.

Quality prediction of batch process using the global-local discriminant analysis based Gaussian process regression model

The conventional single model strategy may be ill- suited due to the multiplicity of operation phases and system uncertainty. A novel global-local discriminant analysis （GLDA） based Gaussian process regression （GPR） approach is developed for the quality prediction of nonlinear and multiphase batch processes. After the collected data is preprocessed through batchwise unfolding, the hidden Markov model （HMM） is applied to identify different operation phases. A GLDA algorithm is also presented to extract the appropriate process variables highly correlated with the quality variables, decreasing the complexity of modeling. Besides, the multiple local GPR models are built in the reduced- dimensional space for all the identified operation phases. Furthermore, the HMM-based state estimation is used to classify each measurement sample of a test batch into a corresponding phase with the maximal likelihood estimation. Therefore, the local GPR model with respect to specific phase is selected for online prediction. The effectiveness of the proposed prediction approach is demonstrated through the multiphase penicillin fermentation process. The comparison results show that the proposed GLDA-GPR approach is superior to the regular GPR model and the GPR based on HMM （HMM-GPR） model.

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.

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.

Determination of reservoir induced earthquake using support vector machine and gaussian process regression

The prediction of magnitude （M） of reservoir induced earthquake is an important task in earthquake engineering. In this article, we employ a Support Vector Machine （SVM） and Gaussian Process Regression （GPR） for prediction of reservoir induced earthquake M based on reservoir parameters. Comprehensive parameter （E） and maximum reservoir depth] （H） are considered as inputs to the SVM and GPR. We give an equation for determination oil reservoir induced earthquake M. The developed SVM and GPR have been compared with] the Artificial Neural Network （ANN） method. The results show that the developed SVM and] GPR are efficient tools for prediction of reservoir induced earthquake M. /

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.

Two-phase early prediction method for remaining useful life of lithium-ion batteries based on a neural network and Gaussian process regression

Lithium-ion batteries(LIBs)are widely used in transportation,energy storage,and other fields.The prediction of the remaining useful life(RUL)of lithium batteries not only provides a reference for health management but also serves as a basis for assessing the residual value of the battery.In order to improve the prediction accuracy of the RUL of LIBs,a two-phase RUL early prediction method combining neural network and Gaussian process regression(GPR)is proposed.In the initial phase,the features related to the capacity degradation of LIBs are utilized to train the neural network model,which is used to predict the initial cycle lifetime of 124 LIBs.The Pearson coefficient’s two most significant characteristic factors and the predicted normalized lifetime form a 3D space.The Euclidean distance between the test dataset and each cell in the training dataset and validation dataset is calculated,and the shortest distance is considered to have a similar degradation pattern,which is used to determine the initial Dual Exponential Model(DEM).In the second phase,GPR uses the DEM as the initial parameter to predict each test set’s early RUL(ERUL).By testing four batteries under different working conditions,the RMSE of all capacity estimation is less than 1.2%,and the accuracy percentage(AP)of remaining life prediction is more than 98%.Experiments show that the method does not need human intervention and has high prediction accuracy.

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.

Gaussian process regressions on hot deformation behaviors of FGH98 nickel-based powder superalloy

The hot deformation behaviors of FGH98 nickel-based powder superalloy were experimentally investigated and theoretically analyzed by Arrhenius models and machine learning(ML).Hot compression tests were conducted with a Gleeble-3800 thermo-mechanical simulation machine on the FGH98 superalloy at strain rates of 0.001–1 s–1 and temperatures of 1025–1175℃.The peak stresses under different deformation conditions were analyzed via the Sellars model and an ML-inspired Gaussian process regression(GPR)model.The prediction of the GPR model outperformed that from the Sellars model.In addition,the stress-strain responses were predicted by the GPR model and tested by experimentally measured stress-strain curves.The results indicate that the developed GPR model has great power with wide generalization capability in the prediction of hot deformation behaviors of FGH98 superalloy,as evidenced by the R2 value higher than 0.99 on the test dataset.

Gaussian process regression for prediction and confidence analysis of fruit traits by near-infrared spectroscopy

Detection of fruit traits by using near-infrared(NIR)spectroscopy may encounter out-of-distribution samples that exceed the generalization ability of a constructed calibration model.Therefore,confidence analysis for a given prediction is required,but this cannot be done using common calibration models of NIR spectroscopy.To address this issue,this paper studied the Gaussian process regression(GPR)for fruit traits detection using NIR spectroscopy.The mean and variance of the GPR were used as the predicted value and confidence,respectively.To show this,a real NIR data set related to dry matter content measurements in mango was used.Compared to partial least squares regression(PLSR),GPR showed approximately 14%lower root mean squared error(RMSE)for the in-distribution test set.Compared with no confidence analysis,using the variance of GPR to remove abnormal samples made GPR and PLSR showed approximately 58%and 10%lower RMSE on the mixed distribution test set,respectively(when the type 1 error rate was set to 0.1).Compared with traditional one-class classification methods,the variance of the GPR can be used to effectively eliminate poorly predicted samples.

Gaussian process regression model incorporated with tool wear mechanism

Cutting tool condition directly affects machining quality and efficiency.In order to avoid severely worn tools used during machining process and fully release the remaining useful life in the meanwhile,a reliable evaluation method of remaining useful life of cutting tools is quite necessary.Due to the variation of cutting conditions,it is a challenge to predict remaining useful life of cutting tools by a unified model.In order to address this issue,this paper proposes a method for predicting the remaining useful life of cutting tools in variable cutting conditions based on Gaussian process regression model incorporated with tool wear mechanism,where the predicted value at adjacent moments is constrained to a linear relationship by the covariance matrix of Gaussian model based on the assumption of progressive tool wear process,so the wear process under continuous changing conditions can be modelled.In addition to that,the input feature space and the output of the model are also enhanced by considering the tool wear mechanism for improving prediction accuracy.Machining experiments are performed to verify the proposed method,and the results show that the proposed could improve the prediction of tool remaining useful life significantly.

Determination of effective stress parameter of unsaturated soils:A Gaussian process regression approach

This article examines the capability of Gaussian process regression(GPR)for prediction of effective stress parameter(χ)of unsaturated soil.GPR method proceeds by parameterising a covariance function,and then infers the parameters given the data set.Input variables of GPR are net confining pressure(σ_(3)),saturated volumetric water content(θ_(s)),residual water content(θ_(r)),bubbling pressure(h_(b)),suction(s)and fitting parameter(l).A comparative study has been carried out between the developed GPR and Artificial Neural Network(ANN)models.A sensitivity analysis has been done to determine the effect of each input parameter onχ.The developed GPR gives the variance of predictedχ.The results show that the developed GPR is reliable model for prediction ofχof unsaturated soil.

Wavelet-Gaussian process regression model for forecasting daily solar radiation in the Saharan climate

Forecasting solar radiation is fundamental to several domains related to renewable energy where several methods have been used to predict daily solar radiation,such as artificial intelligence and hybrid models.Recently,the Gaussian process regression(GPR)algorithm has been used successfully in remote sensing and Earth sciences.In this paper,a wavelet-coupled Gaussian process regression(W-GPR)model was proposed to predict the daily solar radiation received on a horizontal surface in Ghardaia(Algeria).For this purpose,3 years of data(2013-15)have been used in model training while the data of 2016 were used to validate the model.In this work,different types of mother wavelets and different combinations of input data were evaluated based on the minimum air temperature,relative humidity and extraterrestrial solar radiation on a horizontal surface.The results demonstrated the effectiveness of the new hybrid W-GPR model compared with the classical GPR model in terms of root mean square error(RMSE),relative root mean square error(rRMSE),mean absolute error(MAE)and determination coefficient(R^(2)).

A Gaussian process regression‐based surrogate model of the varying workpiece dynamics for chatter prediction in milling of thin‐walled structures

Since the dynamics of thin‐walled structures instantaneously varies during the milling process,accurate and efficient prediction of the in‐process workpiece(IPW)dynamics is critical for the prediction of chatter stability of milling of thin‐walled structures.This article presents a surrogate model of the IPW dynamics of thin‐walled structures by combining Gaussian process regression(GPR)with proper orthogonal decomposition(POD)when IPW dynamics at a large number of cutting positions has to be predicted.The GPR method is used to learn the mapping between a set of the known IPW dynamics and the corresponding cutting positions.POD is used to reduce the order of the matrix assembled by the mode shape vectors at different cutting positions,before the GPR model of the IPW mode shape is established.The computation time of the proposed model is mainly composed of the time taken for predicting a known set of IPW dynamics and the time taken for training GPR models.Simulation shows that the proposed model requires less computation time.Moreover,the accuracy of the proposed model is comparable to that of the existing methods.Comparison between the predicted stability lobe diagram and the experimental results shows that IPW dynamics predicted by the proposed model is accurate enough for predicting the stability of milling of thin‐walled structures.

Cross Trajectory Gaussian Process Regression Model for Battery Health Prediction

Accurate battery capacity prediction is important to ensure reliable battery operation and reduce the cost.However,the complex nature of battery degradation and the presence of capacity regeneration phenomenon render the prediction task very challenging.To address this problem,this paper proposes a novel and efficient algorithm to predict the battery capacity trajectory in a multi-cell setting.The proposed method is a new variant of Gaussian process regression(GPR)model,and it utilizes similar trajectories in the historical data to enhance the prediction of desired capacity trajectory.More importantly,the proposed method adds no extra computation cost to the standard GPR.To demonstrate the effectiveness of the proposed method,validation tests on two different battery datasets are implemented in the case studies.The prediction results and the computation cost are carefully benchmarked with cuttingedge GPR approaches for battery capacity prediction.