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.

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.

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.

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.

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)).

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.

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.

Rapid accessibility evaluation for ballistic lunar capture via manifolds: A Gaussian process regression application

In this study,a supervised machine learning approach called Gaussian process regression(GPR)was applied to approximate optimal bi-impulse rendezvous maneuvers in the cis-lunar space.We demonstrate the use of the GPR approximation of the optimal bi-impulse transfer to patch points associated with various invariant manifolds in the cis-lunar space.The proposed method advances preliminary mission design operations by avoiding the computational costs associated with repeated solutions of the optimal bi-impulsive Lambert transfer because the learned map is computationally efficient.This approach promises to be useful for aiding in preliminary mission design.The use of invariant manifolds as part of the transfer trajectory design offers unique features for reducing propellant consumption while facilitating the solution of trajectory optimization problems.Long ballistic capture coasts are also very attractive for mission guidance,navigation,and control robustness.A multi-input single-output GPR model is presented to represent the fuel costs(in terms of theΔV magnitude)associated with the class of orbital transfers of interest efficiently.The developed model is also proven to provide efficient approximations.The multi-resolution use of local GPRs over smaller sub-domains and their use for constructing a global GPR model are also demonstrated.One of the unique features of GPRs is that they provide an estimate of the quality of approximations in the form of covariance,which is proven to provide statistical consistency with the optimal trajectories generated through the approximation process.The numerical results demonstrate our basis for optimism for the utility of the proposed method.

A Gaussian process regression accelerated multiscale model for conduction-radiation heat transfer in periodic composite materials with temperature-dependent thermal properties

Prediction of the coupled conduction-radiation heat transfer in composite materials with periodic structure is important in high-temperature applications of the materials. The temperature dependence of thermal properties complicates the problem. In this work, a multiscale model is proposed for the conduction-radiation heat transfer in periodic composite materials with temperature-dependent thermal properties. Homogenization analysis of the coupled conduction and radiative transfer equations is conducted, in which the temperature dependence of thermal properties is considered. Both the macroscopic homogenized equations and the local unit cell problems are derived. It is proved that the macroscopic average temperature can be used in the unit cell problems for the first-order corrections of the temperature and radiative intensity, and the calculations of effective thermal properties. The temperature dependence of thermal properties only influences the higher-order corrections. A multiscale numerical method is proposed based on the analysis. The Gaussian process (GP) regression is coupled into the multiscale algorithm to build a correlation between thermal properties and temperature for the macroscale iterations and prevent the repetitive solving of unit cell problems. The GP model is updated by additional solutions of unit cell problems during the iteration according to a variance threshold. Numerical simulations of conduction-radiation heat transfer in composite with isotropic and anisotropic periodic structures are used to validate the proposed multiscale model. It is found that the accuracy and efficiency of the multiscale method can be guaranteed by using a proper variance threshold for the GP model. The multiscale model can provide both the average temperature and radiative intensity fields and their detailed fluctuations due to the local structures.

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.

Multi-fidelity Gaussian process based empirical potential development for Si:H nanowires

In material modeling,the calculation speed using the empirical potentials is fast compared to the first principle calculations,but the results are not as accurate as of the first principle calculations.First principle calculations are accurate but slow and very expensive to calculate.In this work,first,the H-H binding energy and H2-H2 interaction energy are calculated using the first principle calculations which can be applied to the Tersoff empirical potential.Second,the H-H parameters are estimated.After fitting H-H parameters,the mechanical properties are obtained.Finally,to integrate both the low-fidelity empirical potential data and the data from the high-fidelity firstprinciple calculations,the multi-fidelity Gaussian process regression is employed to predict the HH binding energy and the H2-H2 interaction energy.Numerical results demonstrate the accuracy of the developed empirical potentials.

Peri-Net-Pro: the neural processes with quantified uncertainty for crack patterns

This paper develops a deep learning tool based on neural processes(NPs)called the Peri-Net-Pro,to predict the crack patterns in a moving disk and classifies them according to the classification modes with quantified uncertainties.In particular,image classification and regression studies are conducted by means of convolutional neural networks(CNNs)and NPs.First,the amount and quality of the data are enhanced by using peridynamics to theoretically compensate for the problems of the finite element method(FEM)in generating crack pattern images.Second,case studies are conducted with the prototype microelastic brittle(PMB),linear peridynamic solid(LPS),and viscoelastic solid(VES)models obtained by using the peridynamic theory.The case studies are performed to classify the images by using CNNs and determine the suitability of the PMB,LBS,and VES models.Finally,a regression analysis is performed on the crack pattern images with NPs to predict the crack patterns.The regression analysis results confirm that the variance decreases when the number of epochs increases by using the NPs.The training results gradually improve,and the variance ranges decrease to less than 0.035.The main finding of this study is that the NPs enable accurate predictions,even with missing or insufficient training data.The results demonstrate that if the context points are set to the 10th,100th,300th,and 784th,the training information is deliberately omitted for the context points of the 10th,100th,and 300th,and the predictions are different when the context points are significantly lower.However,the comparison of the results of the 100th and 784th context points shows that the predicted results are similar because of the Gaussian processes in the NPs.Therefore,if the NPs are employed for training,the missing information of the training data can be supplemented to predict the results.