Improved Gaussian Process Research Articles

Probabilistic prediction model for critical chloride concentration of reinforcement corrosion based on improved Gaussian process regression

Probabilistic prediction model for critical chloride concentration of reinforcement corrosion based on improved Gaussian process regression

An improved Gaussian process for filling the missing data in GNSS position time series considering the influence of adjacent stations

Due to various unavoidable reasons or gross error elimination, missing data inevitably exist in global navigation satellite system (GNSS) position time series, which may result in many analysis methods not being applicable. Typically, interpolating the missing data is a crucial preprocessing step before analyzing the time series. The conventional methods for filling missing data do not consider the influence of adjacent stations. In this work, an improved Gaussian process (GP) approach is developed to fill the missing data of GNSS time series, in which the time series of adjacent stations are applied to construct impact factors, together with a comparison of the conventional GP and the commonly used cubic spline methods. For the simulation experiments, the root mean square error (RMSE), mean absolute error (MAE) and correlation coefficient (R) are adopted to evaluate the performance of the improved GP. The results show that the filled missing data of the improved GP are closer to the true values than those of the conventional GP and cubic spline methods, regardless of the missing percentages ranging from 5 to 30%, with an interval of 5%. Specifically, the mean relative RMSE and MAE improvements for the improved GP with respect to the conventional GP are 21.2%, 21.3% and 8.3% and 12.7%, 16.2% and 11.01% for the North (N), East (E) and Up (U) components, respectively. In the real experiment, eight GNSS stations are analyzed using improved GP, together with conventional GP and a cubic spline. The results indicate that the first three principal components (PCs) of the improved GP can perverse 98.3%, 99.8% and 77.0% of the total variance for the N, E and U components, respectively. This value is obviously higher than those of the conventional GP and cubic spline. Therefore, we can conclude that the improved GP can better fill in the missing data in GNSS position time series than the conventional GP and cubic spline because of the impacts of adjacent stations.

Enhanced Fault Localization in Multi-Terminal HVDC Systems Using Improved Gaussian Process Regression

Enhanced Fault Localization in Multi-Terminal HVDC Systems Using Improved Gaussian Process Regression

Fast flow field prediction of three-dimensional hypersonic vehicles using an improved Gaussian process regression algorithm

Conducting large-scale numerical computations to obtain flow field during the hypersonic vehicle engineering design phase can be excessively costly. Although deep learning algorithms enable rapid flow field prediction with high-precision, they require a significant investment in training samples, contradicting the motivation of reducing the cost of acquiring flow field. The combination of feature extraction algorithms and regression algorithms can also achieve high-precision prediction of flow fields, which is more suitable to tackle three-dimensional flow prediction with a small dataset. In this study, we propose a reduced-order model (ROM) for the three-dimensional hypersonic vehicle flow prediction utilizing proper orthogonal decomposition to extract representative features and Gaussian process regression with improved automatic kernel construction (AKC-GPR) to perform a nonlinear mapping of physical features for prediction. The selection of variables is based on sensitivity analysis and modal assurance criterion. The underlying relationship is unveiled between flow field variables and inflow conditions. The ROM exhibits high predictive accuracy, with mean absolute percentage error (MAPE) of total field less than 3.5%, when varying altitudes and Mach numbers. During angle of attack variations, the ROM only effectively reconstructs flow distribution by interpolation with a MAPE of 7.02%. The excellent small-sample fitting capability of our improved AKC-GPR algorithm is demonstrated by comparing with original AKC-GPRs with a maximum reduction in a MAPE of 35.28%. These promising findings suggest that the proposed ROM can serve as an effective approach for rapid and accurate vehicle flow predicting, enabling its application in engineering design analysis.

An Improved Gaussian Process Regression Based Aging Prediction Method for Lithium-Ion Battery

A reliable aging-prediction method is significant for lithium-ion batteries (LIBs) to prolong the service life and increase the efficiency of operation. In this paper, an improved Gaussian-process regression (GPR) is proposed to predict the degradation rate of LIBs under coupled aging stress to simulate working conditions. The complicated degradation processes at different ranges of the state of charge (SOC) under different discharge rates were analyzed. A composed kernel function was conducted to optimize the hyperparameter. The inputs for the kernel function of GPR were improved by coupling the constant and variant characteristics. Moreover, previous aging information was employed as a characteristic to improve the reliability of the prediction. Experiments were conducted on a lithium–cobalt battery at three different SOC ranges under three discharge rates to verify the performance of the proposed method. Some tips to slow the aging process based on the coupled stress were discovered. Results show that the proposed method accurately estimated the degradation rate with a maximum estimation root-mean-square error of 0.14% and regression coefficient of 0.9851. Because of the proposed method’s superiority to the exponential equation and GPR by fitting all cells under a different operating mode, it is better for reflecting the true degradation in actual EV.

Active design of dynamic GP models for model predictive control using expected improvement

AbstractModelling is a basic and key requirement for model‐based controlling, monitoring, or other process strategies. In non‐linear model predictive control (NMPC), although data‐driven models can be more easily established than first‐principle ones, representative data may not be adequately included in advance to train a complete model, which is an attractive research topic. An actively improved Gaussian process (GP) model building strategy is developed, especially for incomplete models based on the idea of Bayesian optimization. The GP model can be used online as the internal model of model predictive control (MPC) directly. The model‐building objective is based on the expected improvement strategy, which can exploit information gained from the currently gathered data as well as explore uncharted regions. The proposed method is a real‐time design of experiments based on variance information of GP for efficient model building with insufficient initial training data for NMPC. Multi‐step ahead prediction model is considered to give full play to predicting features of NPMC. Besides, a novel disturbance rejection strategy is also proposed based on GP outputs. Two simulation results, including comparisons with some traditional algorithms, are presented to demonstrate the effectiveness of the proposed method.

A Method for Abnormal Battery Charging Capacity Diagnosis Based on Electric Vehicles Operation Data

Overcharging due to an abnormal charging capacity is one of the most common causes of thermal runaway (TR). This study proposes a method for diagnosing abnormal battery charging capacity based on electric vehicle (EV) data. The proposed method can obtain the fault frequency and output the corresponding state of charge (SOC) when a fault occurs. First, a machine-learning-based data cleaning framework is developed to overcome the limitations of the interpolation method. Then, offline training is implemented, based on big vehicle operation data and an improved Gaussian process regression (GPR). Thereafter, online monitoring of the discrete capacity increment (DCI) is used to identify the abnormal charging capacity. The abnormal charging capacity fault is identified by the absolute error between the GPR outputs and the true DCI, and the thresholds are determined using a Box–Cox transformation with a value of 3σ. The diagnostic results indicate that the abnormal charging capacity of the TR vehicle is identified two months in advance, and the fault frequency of the abnormal and normal vehicles is 0.5221 and 0.0311, respectively. EV operation data and various methods are used to validate the robustness and applicability of the proposed method.

Remaining Useful Life Prediction of Lithium-Ion Batteries: A Hybrid Approach of Grey–Markov Chain Model and Improved Gaussian Process

Accurate prediction of the lithium-ion battery’s future capacity and remaining useful life (RUL) is of great significance to battery health management. To the best of our knowledge, most of the existing methods only focus on capturing the degradation trend of the battery, which results in an inaccurate prediction because of the occasional capacity regeneration phenomena in practice. To improve the prediction precision, a hybrid approach of the Grey–Markov chain model (GMCM) and the improved Gaussian process is proposed in this article. Firstly, the historical capacity data is decomposed into two components, namely, the degradation trend and regeneration phenomena, by ensemble empirical mode decomposition. Then, the GMCM method and the multioutput mixture of Gaussian processes are developed for degradation and regeneration prediction, respectively. Lastly, an online calibration strategy is proposed for further prediction accuracy improvement. Extensive experiments are established to validate the proposed GPGM approach, with the results demonstrating that the proposed GPGM consistently outperforms other counterpart methods in terms of one-step and multistep prediction.

Bayesian optimization for congestion pricing problems: A general framework and its instability

In this study, we proposed a generic Bayesian optimization (BO) framework to solve congestion pricing problems. In the BO framework, the Gaussian process (GP) serves as a surrogate model to approximate the highly nonlinear and expensive-to-evaluate objective functions. This study reveals that GP exhibits an instability phenomenon, which inherently limits the accuracy of BO. We investigate the sources and influences of instability from the perspective of error analysis, and then propose an improved GP (IGP) model to address the instability issue. The associated improvements are twofold: matrix inversion and matrix multiplication. A tailored preconditioner is developed to reduce the matrix inversion errors. To address multiplication errors, a tailored dot product algorithm in conjunction with a GP reformulation scheme is proposed. To validate the proposed models and methods, a link-based second-best congestion pricing problem is considered as an example. The results indicate that, in comparison to benchmark approaches (the sensitivity analysis method and genetic algorithm), the proposed BO framework shows higher computational efficiency and solution accuracy. With modifications on GP, the instability phenomenon is substantially mitigated in several instances, hence enhancing the accuracy of the BO framework.

Constrained Multi-Objective Optimization for Double-Sided Tubular Machine With Hybrid Segmented PM

Double-sided tubular machines (DSTM) have greatly improved space utilization and power density, and are widely used in tidal power generation and high-power electric drives, while the thrust force ripple is also significant. To get the minimum cogging force with the maximum thrust force, hybrid segmented PM array topology is introduced to the DSTM and used as research object for multi-objective optimization. Due to the constraints among the parameters to be optimized, this paper proposes a new constrained multi-parameter multi-objective optimization method. In this method, a new optimal Latin hypercube(OLH) is put forward to solve the constrained parameter sampling problem. RReliefF is used to distinguish the importance of multi-parameter and divide them into three layers: strong, medium and weak, and surrogate models are established hierarchically to simplify the optimization complexity. In addition, an improved Gaussian process regression(GPR) algorithm is proposed to improve the optimization accuracy of strong significance parameters. The optimization results show that the average thrust force is increased by 4.7%, the cogging force is reduced by 28%, and total harmonic distortion rate of the voltage is reduced by 30.5% without loss of efficiency, which significantly improves the performance of the machine, and verifies the effectiveness of the proposed method, which is suitable for constrained multi-parameter multi-objective optimization.

An Integrated Framework Based on an Improved Gaussian Process Regression and Decomposition Technique for Hourly Solar Radiation Forecasting

The precise forecast of solar radiation is exceptionally imperative for the steady operation and logical administration of a photovoltaic control plant. This study proposes a hybrid framework (CBP) based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), an enhanced Gaussian process regression with a newly designed physical-based combined kernel function (PGPR), and the backtracking search optimization algorithm (BSA) for solar radiation forecasting. In the CEEMDAN-BSA-PGPR (CBP) model, (1) the CEEMDAN is executed to divide the raw solar radiation into a few sub-modes; (2) PACF (partial autocorrelation coefficient function) is carried out to pick the appropriate input variables; (3) PGPR is constructed to predict each subcomponent, respectively, with hyperparameters optimized by BSA; (4) the final forecasting result is produced by combining the forecasted sub-modes. Four hourly solar radiation datasets of Australia are introduced for comprehensive analysis and several models available in the literature are established for multi-step ahead prediction to demonstrate the superiority of the CBP model. Comprehensive comparisons with the other nine models reveal the efficacy of the CBP model and the superb impact of CEEMDAN blended with the BSA, respectively. The CBP model can produce more precise results compared with the involved models for all cases using different datasets and prediction horizons. Moreover, the CBP model is less complicated to set up and affords extra decision-making information regarding forecasting uncertainty.

State of Health Estimation for Li-ion Batteries using Improved Gaussian Process Regression and Multiple Health Indicators

State of Health Estimation for Li-ion Batteries using Improved Gaussian Process Regression and Multiple Health Indicators

Self‐Discharge Voltage Drop Estimation Method Based on Improved Gaussian Process Regression

The self‐discharge rate is an important index for determining the quality of a lithium‐ion battery. Currently, the self‐discharge of a battery is mainly determined through experimental tests, which are time‐consuming and laborious. To provide a fast and reliable self‐discharge rate estimation, an improved Gaussian process regression (GPR) model based on the charge–discharge curve is proposed to estimate the self‐discharge voltage drop. In this method, the voltage features extracted from the charge–discharge curve are used as the input of the GPR model. These features reflect the self‐discharge performance of batteries from different angles. The gray correlation analysis method is used to analyze the degree of correlation between the selected features and self‐discharge voltage drop. Furthermore, a kernel function suitable for voltage drop estimation is selected. Simultaneously, the GPR model is adjusted, and the particle swarm optimization algorithm is used to optimize the superparameters of the GPR model to improve the estimation accuracy of the self‐discharge voltage drop of the model. The self‐discharge voltage drop data from the experiment are used to demonstrate the estimation effect of the proposed method. The results reveal that this method is reliable and has a high estimation accuracy for the self‐discharge voltage drop.

A novel method for identifying geomechanical parameters of rock masses based on a PSO and improved GPR hybrid algorithm

In view of the shortcomings of existing artificial neural network (ANN) and support vector regression (SVR) in the application of three-dimensional displacement back analysis, Gaussian process regression (GPR) algorithm is introduced to make up for the shortcomings of existing intelligent inversion methods. In order to improve the generality of the standard GPR algorithm with single kernel function, an improved Gaussian process regression (IGPR) algorithm with combined kernel function is proposed by adding two single kernel functions. In addition, in the training process of IGPR model, the particle swarm optimization (PSO) is combined with the IGPR model (PSO-IGPR) to optimize the parameters of the IGPR model. After the IGPR model can accurately map the relationship between geomechanical parameters and rock mass deformation, the PSO algorithm is directly used to search the best geomechanical parameters to match the deformation calculated by igpr model with the measured deformation of rock mass. The application case of Beikou tunnel shows that the combined kernel function GPR has higher identification accuracy than the single kernel function GPR and SVR model, the IGPR model with automatic correlation determination (ARD) kernel function can obtain higher identification accuracy than the IGPR model with isotropic (ISO) kernel function, and the PSO-IGPR hybrid model based on ARD kernel function has the highest identification accuracy. Therefore, this paper proposes a displacement back analysis method of the PSO-IGPR hybrid algorithm based on ARD kernel function, which can be used to identify the geomechanical parameters of rock mass and solve other engineering problems.

An Empirical-Data Hybrid Driven Approach for Remaining Useful Life prediction of lithium-ion batteries considering capacity diving

Considering the variabilities among each cell especially during the battery accelerated decay period, the parameterized empirical model is doubtful for predicting the Lithium-ion (Li-ion) battery Remaining Useful Life (RUL). Thus, an Empirical-Data Hybrid Driven Approach (EDHDA) is proposed to utilize both the prior knowledge and the historical dataset for the lifetime prediction of the Li-ion battery under capacity diving conditions. A polynomial-based model is firstly proposed to provide the basic accuracy for the EDHDA. Meanwhile, an improved Gaussian Process Regression (GPR) with a partial charging voltage profile is designed to make full use of the operational dataset. The EDHDA is then established with a dual Particle Filter (PF) framework combining the advantages of the above two methods. In this way, accurate estimations of the current capacity can be obtained by fusing the two models, even under capacity diving conditions. The parameters of the empirical model can also be updated according to the fused capacity to obtain accurate RUL predictions with uncertainty levels. Experimental results show that the proposed EDHDA has a high RUL prediction accuracy under capacity diving even with limited data.

SOH and RUL prediction of Li-ion batteries based on improved Gaussian process regression

SOH and RUL prediction of Li-ion batteries based on improved Gaussian process regression

A health indicator extraction and optimization for capacity estimation of Li-ion battery using incremental capacity curves

Accurate lithium battery online capacity and remaining useful life (RUL) estimation are critical to increasing penetration of electric vehicles. Motivated by this, health indicators (HIs) extraction and optimization using incremental capacity curves are proposed. This paper reports a straightforward approach to smooth the noise on IC curves, thereby capturing accurate and reliable HIs. To prevent overfitting in machine learning, a combined weighting method is emphasized to reduce the dimensionality of HIs. It is then used in the modeling of battery capacity estimation as the improved Gaussian process regression is applied. In this framework, results show that the correlation between the battery capacity and dimension-reducing HIs is desirable. Analysis results reveal the above measures' trustworthiness, with the average error of the six batteries is 2.3% under the cross-validation test. What's more, a set of different types of batteries are used to verify the robustness of this method.

The State of Health Estimation Framework for Lithium-Ion Batteries Based on Health Feature Extraction and Construction of Mixed Model

Accurate estimation of the state of health (SOH) is one of the most dominant contents for prognostics and health management of a lithium battery system. However, it has not been well solved owing to its internal electrochemical reactions and complex nonlinear system. Here, an SOH estimation framework for lithium-ion batteries depending on health features (HF) extraction and the construction of the mixed model is proposed. The overall trend and local dynamic changes of capacity degradation was simultaneously considered in the mixed model. First, the double exponential empirical model describing the overall degradation trend of capacity was established from historical data and the error between its output and the SOH reference value was calculated. Then, with the constructed HF as the input and error as the output, the improved gaussian process regression (IGPR) model describing the local dynamic changes of capacity degradation was established. Finally, the output of the mixed model was obtained by feeding back the output of the IGPR model to the result of the empirical model. The proposed framework has been verified on two different data sets. With the result of 5% relative percentage error, the proposed framework shows high accuracy and robustness in a lithium battery system.

Concrete performance time-varying effect of CFST arch bridges

Concrete-filled arch ribs of concrete-filled steel tubular (CFST) arch bridges experience temperature effects and shrinkage/creep effects, as well as effects based on their interaction, that reduce the calculated stiffness of the arch ribs of the CFST arch bridges, resulting in a reduced bearing capacity. To address this problem, this paper proposes a Gaussian process response surface method based on the concept of dichotomy. When the training sample parameter interval is uncertain, it achieves the fastest retrieval of training samples that meet the requirements, it makes up for the shortcomings of the traditional small sample Gaussian process method. It can accurately predict the equivalent stiffness of the concrete-filled arch ribs of the CFST arch bridge, considering the effects of temperature and time, and grasp the time-varying degradation law of the mechanical performance of the CFST arch bridge arch rib. To verify the correctness and reliability of the proposed method, a refined analysis model of a CFST arch bridge is established using the general finite element software ANSYS, and the optimal creep equation and temperature effect function are selected. Using the improved Gaussian process model, the equivalent calculated stiffness of the arch rib filled with concrete after ten years under the combined action of shrinkage, creep and temperature effects of the concrete-filled steel tube arch bridge is predicted, and the deflection value and stability coefficient are proposed as the evaluation index of the prediction accuracy. The research results show that the proposed method provides a more simplified and high-precision method for the performance degradation analysis of concrete filled steel tube arch bridge arch ribs under the coupling action of complex factors such as shrinkage, creep, and temperature effects.

Improved Gaussian Process Acquisition for Targeted Bayesian Optimization

A black-box optimization problem is considered, in which the function to be optimized can only be expressed in terms of a complicated stochastic algorithm that takes a long time to evaluate. The value returned is required to be sufficiently near to a target value, and uses data that has a significant noise component. Bayesian Optimization with an underlying Gaussian Process is used as an optimization solution, and its effectiveness is measured in terms of the number of function evaluations required to attain the target. To improve results, a simple modification of the Gaussian Process ‘Lower Confidence Bound’ (LCB) acquisition function is proposed. The expression used for the confidence bound is squared in order to better comply with the target requirement. With this modification, much improved results compared to random selection methods and to other commonly used acquisition functions are obtained.