Optimization of Artificial Viscosity in Production Codes Based on Gaussian Regression Surrogate Models

To accurately model flows with shock waves using staggered-grid Lagrangian hydrodynamics, the artificial viscosity has to be introduced to convert kinetic energy into internal energy, thereby increasing the entropy across shocks. Determining the appropriate strength of the artificial viscosity is an art and strongly depends on the particular problem and experience of the researcher. The objective of this study is to pose the problem of finding the appropriate strength of the artificial viscosity as an optimization problem and solve this problem using machine learning (ML) tools, specifically using surrogate models based on Gaussian Process regression (GPR) and Bayesian analysis. We describe the optimization method and discuss various practical details of its implementation. The shock-containing problems for which we apply this method all have been implemented in the LANL code FLAG (Burton in Connectivity structures and differencing techniques for staggered-grid free-Lagrange hydrodynamics, Tech. Rep. UCRL-JC-110555, Lawrence Livermore National Laboratory, Livermore, CA, 1992, 1992, in Consistent finite-volume discretization of hydrodynamic conservation laws for unstructured grids, Tech. Rep. CRL-JC-118788, Lawrence Livermore National Laboratory, Livermore, CA, 1992, 1994, Multidimensional discretization of conservation laws for unstructured polyhedral grids, Tech. Rep. UCRL-JC-118306, Lawrence Livermore National Laboratory, Livermore, CA, 1992, 1994, in FLAG, a multi-dimensional, multiple mesh, adaptive free-Lagrange, hydrodynamics code. In: NECDC, 1992). First, we apply ML to find optimal values to isolated shock problems of different strengths. Second, we apply ML to optimize the viscosity for a one-dimensional (1D) propagating detonation problem based on Zel’dovich-von Neumann-Doring (ZND) (Fickett and Davis in Detonation: theory and experiment. Dover books on physics. Dover Publications, Mineola, 2000) detonation theory using a reactive burn model. We compare results for default (currently used values in FLAG) and optimized values of the artificial viscosity for these problems demonstrating the potential for significant improvement in the accuracy of computations.

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.

Application of a Novel Method for Machine Performance Degradation Assessment Based on Gaussian Mixture Model and Logistic Regression

The currently prevalent machine performance degradation assessment techniques involve estimating a machine＇s current condition based upon the recognition of indications of failure features,which entail complete data collected in different conditions.However,failure data are always hard to acquire,thus making those techniques hard to be applied.In this paper,a novel method which does not need failure history data is introduced.Wavelet packet decomposition（WPD） is used to extract features from raw signals,principal component analysis（PCA） is utilized to reduce feature dimensions,and Gaussian mixture model（GMM） is then applied to approximate the feature space distributions.Single-channel confidence value（SCV） is calculated by the overlap between GMM of the monitoring condition and that of the normal condition,which can indicate the performance of single-channel.Furthermore,multi-channel confidence value（MCV）,which can be deemed as the overall performance index of multi-channel,is calculated via logistic regression（LR） and that the task of decision-level sensor fusion is also completed.Both SCV and MCV can serve as the basis on which proactive maintenance measures can be taken,thus preventing machine breakdown.The method has been adopted to assess the performance of the turbine of a centrifugal compressor in a factory of Petro-China,and the result shows that it can effectively complete this task.The proposed method has engineering significance for machine performance degradation assessment.

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 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.

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.

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.

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. /

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.

Penalized Flexible Bayesian Quantile Regression

The selection of predictors plays a crucial role in building a multiple regression model. Indeed, the choice of a suitable subset of predictors can help to improve prediction accuracy and interpretation. In this paper, we propose a flexible Bayesian Lasso and adaptive Lasso quantile regression by introducing a hierarchical model framework approach to enable exact inference and shrinkage of an unimportant coefficient to zero. The error distribution is assumed to be an infinite mixture of Gaussian densities. We have theoretically investigated and numerically compared our proposed methods with Flexible Bayesian quantile regression (FBQR), Lasso quantile regression (LQR) and quantile regression (QR) methods. Simulations and real data studies are conducted under different settings to assess the performance of the proposed methods. The proposed methods perform well in comparison to the other methods in terms of median mean squared error, mean and variance of the absolute correlation criterions. We believe that the proposed methods are useful practically.

Gaussian process hydrodynamics

We present a Gaussian process(GP)approach,called Gaussian process hydrodynamics(GPH)for approximating the solution to the Euler and Navier-Stokes(NS)equations.Similar to smoothed particle hydrodynamics(SPH),GPH is a Lagrangian particle-based approach that involves the tracking of a finite number of particles transported by a flow.However,these particles do not represent mollified particles of matter but carry discrete/partial information about the continuous flow.Closure is achieved by placing a divergence-free GP priorξon the velocity field and conditioning it on the vorticity at the particle locations.Known physics(e.g.,the Richardson cascade and velocityincrement power laws)is incorporated into the GP prior by using physics-informed additive kernels.This is equivalent to expressingξas a sum of independent GPsξl,which we call modes,acting at different scales(each modeξlself-activates to represent the formation of eddies at the corresponding scales).This approach enables a quantitative analysis of the Richardson cascade through the analysis of the activation of these modes,and enables us to analyze coarse-grain turbulence statistically rather than deterministically.Because GPH is formulated by using the vorticity equations,it does not require solving a pressure equation.By enforcing incompressibility and fluid-structure boundary conditions through the selection of a kernel,GPH requires significantly fewer particles than SPH.Because GPH has a natural probabilistic interpretation,the numerical results come with uncertainty estimates,enabling their incorporation into an uncertainty quantification(UQ)pipeline and adding/removing particles(quanta of information)in an adapted manner.The proposed approach is suitable for analysis because it inherits the complexity of state-of-the-art solvers for dense kernel matrices and results in a natural definition of turbulence as information loss.Numerical experiments support the importance of selecting physics-informed kernels and illustrate the major impact of such kernels on the accuracy and stability.Because the proposed approach uses a Bayesian interpretation,it naturally enables data assimilation and predictions and estimations by mixing simulation data and experimental data.

考虑策略型消费者的高斯过程回归动态定价算法

现有需求不确定下的动态定价算法鲜有考虑消费者策略行为的。将零售商的价格决策过程描述为一个多摇臂(Multi-Armed Bandit,MAB)问题,提出一种非参数贝叶斯算法。将高斯过程回归与汤普森抽样算法相结合,并加入策略型消费者购买决策过程,帮助零售商进行价格决策。仿真结果表明,该算法能有效提高零售商收益,收敛速度更快。此外,策略型消费者的存在可以改善需求学习算法的性能,降低由于需求不确定性导致的零售商收益损失。