Gaussian Process-based Model Research Articles

Optimized structure design for binary particle mixing in rotating drums using a combined DEM and gaussian process-based model

Particle mixing is a crucial operation in various industrial production processes. However, phenomena like segregation or local accumulation can arise, especially when particles differ in properties like radius and density. Numerical simulation of particles using Discrete Element Method (DEM) allows for the manipulation of control variables in batches, generating a large amount of data and facilitating quantitative research. In this study, the mixing behaviors of binary particles in rotating drums are systematically investigated. The DEM model is first validated with experimental data and then rotating drums with varying obstacles, rotation speeds, particle radii, and densities are simulated. Moreover, a Gaussian process-based optimization is conducted by correlating Lacey mixing index (MI) and parameterized shape of obstacle to find the optimized mixing condition. Experimental validations are further performed on the optimized condition to verify the design. It is shown that this integrated approach holds significant potential for enhancing the efficiency, effectiveness of industrial mixing processes and the consideration of energy consumption when balancing the mixing efficiency and optimal rotating speed.

Pointwise profile monitoring considering covariates based on Gaussian process

In the intelligent manufacturing process, sensors are increasingly becoming an important means of measurement and data acquisition. Profile data from sensors are generally huge, irregular, and correlated. Meanwhile, profiles are usually affected by many external factors, which are referred to as covariates in this paper. Existing statistical process control methods are mainly based on statistical models, which have many limitations in dealing with such complex profile data. Motivated by the real life problem of industrial busbar temperature monitoring, this paper proposes a nonparametric pointwise profile monitoring scheme for unbalanced data considering time varying covariates. The developed Gaussian process-based model provides flexibility for predicting autocorrelated profiles. To incorporate time varying covariates, the Gaussian process model kernel is modified by an automatic relevance determination structure. The control chart is then constructed based on the difference between the observed and predicted profiles. Instantaneous anomalies within a profile can be detected by pointwise monitoring without waiting for the entire profile data collection. The effectiveness and applicability of the proposed monitoring scheme are validated by both simulations and a real case of busbar temperature monitoring in the workshop of an automotive manufacturer.

Disturbance rejection design for Gaussian process-based model predictive control using extended state observer

Gaussian process (GP) regression has gained significant popularity in machine learning because it has the intrinsic capability to capture uncertainty in function prediction and requires a limited number of hyperparameters to be optimized. In this study, a Gaussian process model predictive control (GPMPC) algorithm is proposed to model the unknown dynamics of the process using Gaussian process regression. The GPMPC incorporates the expected variance of the GP model to account for the model's uncertainty and to achieve prudent control. Meanwhile, the extended state observer (ESO) is introduced for the GPMPC, which can estimate the unmodeled dynamics and unknown disturbance. With the designed feedforward gain, the proposed extended state observer-based GPMPC (GPMPC-ESO) method can achieve offset-free performance. Theoretical analysis is conducted to evaluate the stability and disturbance rejection performance of the control system. Finally, the algorithms are validated by simulation in continuous stirred tank reactor (CSTR) process control.

Bayesian hidden mark interaction model for detecting spatially variable genes in imaging-based spatially resolved transcriptomics data.

Recent technology breakthroughs in spatially resolved transcriptomics (SRT) have enabled the comprehensive molecular characterization of cells whilst preserving their spatial and gene expression contexts. One of the fundamental questions in analyzing SRT data is the identification of spatially variable genes whose expressions display spatially correlated patterns. Existing approaches are built upon either the Gaussian process-based model, which relies on ad hoc kernels, or the energy-based Ising model, which requires gene expression to be measured on a lattice grid. To overcome these potential limitations, we developed a generalized energy-based framework to model gene expression measured from imaging-based SRT platforms, accommodating the irregular spatial distribution of measured cells. Our Bayesian model applies a zero-inflated negative binomial mixture model to dichotomize the raw count data, reducing noise. Additionally, we incorporate a geostatistical mark interaction model with a generalized energy function, where the interaction parameter is used to identify the spatial pattern. Auxiliary variable MCMC algorithms were employed to sample from the posterior distribution with an intractable normalizing constant. We demonstrated the strength of our method on both simulated and real data. Our simulation study showed that our method captured various spatial patterns with high accuracy; moreover, analysis of a seqFISH dataset and a STARmap dataset established that our proposed method is able to identify genes with novel and strong spatial patterns.

Gaussian Process-Based Model Predictive Control for Autonomous Underwater Vehicles

Traditional MPC algorithms, assuming constant values, suffer from performance degradation caused by model mismatch. This paper addresses the enhancement of predictability in Autonomous Underwater Vehicles (AUVs) under uncertain disturbances and unknown system dynamics through the design of Model Predictive Controllers (MPCs). We propose a hybrid model that integrates a first-principles nominal model with a learning-based model utilizing Gaussian Processes (GPs). The algorithm addresses the problem of model mismatch in AUV motion control by constructing a precise GP model, which captures the dynamic characteristics of the process through the collection and learning of deviations between the reference model and the controlled system. Additionally, the GP model transforms stochastic constraints into deterministic convex constraints, enhancing safety guarantees in complex and challenging environments. The effectiveness of the proposed algorithm is demonstrated through two simulation examples.

Zero-order optimization for Gaussian process-based model predictive control

By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based control community. Yet, solving the resulting optimal control problem in real-time generally remains a major challenge, due to (i) the increased number of augmented states in the optimization problem, as well as (ii) computationally expensive evaluations of the posterior mean and covariance and their respective derivatives. To tackle these challenges, we employ (i) a tailored Jacobian approximation in a sequential quadratic programming (SQP) approach and combine it with (ii) a parallelizable GP inference and automatic differentiation framework. Reducing the numerical complexity with respect to the state dimension nx for each SQP iteration from O(nx6) to O(nx3), and accelerating GP evaluations on a graphical processing unit, the proposed algorithm computes suboptimal, yet feasible, solutions at drastically reduced computation times and exhibits favorable local convergence properties. Numerical experiments verify the scaling properties and investigate the runtime distribution across different parts of the algorithm.

Drone-based Volume Estimation in Indoor Environments

Volume estimation in large indoor spaces is an important challenge in robotic inspection of industrial warehouses. We propose an approach for volume estimation for autonomous systems using visual features for indoor localization and surface reconstruction from 2D-LiDAR measurements. A Gaussian Process-based model incorporates information collected from measurements given statistical prior information about the terrain, from which the volume estimate is computed. Our algorithm finds feasible trajectories which minimize the uncertainty of the volume estimate. We show results in simulation for the surface reconstruction and volume estimate of topographic data.

Stochastic and a posteriori optimization to mitigate coil manufacturing errors in stellarator design

It was recently shown in Wechsung et al (2022 Proc. Natl Acad. Sci. USA 119 e2202084119) that there exist electromagnetic coils that generate magnetic fields, which are excellent approximations to quasi-symmetric fields and have very good particle confinement properties. Using a Gaussian process-based model for coil perturbations, we investigate the impact of manufacturing errors on the performance of these coils. We show that even fairly small errors result in noticeable performance degradation. While stochastic optimization yields minor improvements, it is not possible to mitigate these errors significantly. As an alternative to stochastic optimization, we then formulate a new optimization problem for computing optimal adjustments of the coil positions and currents without changing the shapes of the coil. These a-posteriori adjustments are able to reduce the impact of coil errors by an order of magnitude, providing a new perspective for dealing with manufacturing tolerances in stellarator design.

Vehicle yaw stability control with a two-layered learning MPC

This paper proposes a novel framework to address the model-vehicle mismatch (MVM) challenge of yaw stability control, which introduces the Gaussian Process-based Model Predictive Control into the classical two-layer structure. In the upper layer, the supervisor controller calculates the compensation torque required for vehicle turning. Gaussian Process regression is employed to compensate model mismatch and unmodelled dynamics. The chance constraints on sideslip angle are converted into double half-space constraints by the normal distribution quantile function. In the lower layer, the subordinate controller utilises the nonlinear slip rate model to distribute torque to the wheels in the form of braking torque. A new assignment rule of braking torque weight is proposed according to the yaw torque analysis. The stability of the two-layered learning MPC is ensured through proof and simulation. In the Simulink and Carsim co-simulation environment, the superiority of the proposed method is verified in the task of rapid double-lane change. Compared with the traditional MPC-based yaw stability controller, the proposed method has increased the stability tracking index and energy consumption index by around 13% and 8%.

Application of the Gaussian process for fatigue life prediction under multiaxial loading

Fatigue life prediction with failure probability estimation for materials subjected to multiaxial loading is an important task in engineering design because it reduces the financial cost by eliminating expensive experimental tests. Owing to the complex deterioration mechanisms of fatigue failure, existing fatigue life prediction models are of the empirical or semi-empirical type, and their applicability is limited to validating the loading condition and material. Improper selection of the fatigue model could result in non-conservative life prediction with high financial and catastrophic consequences. To solve this problem, an innovative approach based on the Gaussian process for fatigue life prediction under multiaxial loading is presented. The inherent features of the Gaussian process predispose its application to fatigue life prediction under multiaxial loading as an efficient and practical approach to avoid the problem in selecting adequate semi-empirical parametric fatigue models. The model was validated on two sets of experimental data obtained by fatigue testing of S355N steel and 2124 T851 aluminum alloy under uniaxial and multiaxial loadings. In the model training process, only data obtained under uniaxial and pure torsion cyclic loadings were applied. Owing to the implemented physics-based input data, which are related to the stress components acting on the critical plane of crack initiation, the model accurately predicted the fatigue lives of the two tested materials by implementing the squared exponential covariance function. In addition, the fatigue lives were also computed using four parametric fatigue strength criteria (Crossland, Matake, Carpinteri et al., and Papuga–Růžička models). The best results obtained by the parametric models exhibited a lower fatigue prediction performance than the results using the Gaussian process-based model.

A screening-based gradient-enhanced Gaussian process regression model for multi-fidelity data fusion

The prediction accuracy of multi-fidelity models can be enhanced by incorporating gradient formation. However, the computational complexity would increase dramatically as the number of design variables increase. In this work, a gradient-enhanced multi-fidelity Gaussian process model using a portion of gradients (PGEMFGP) is proposed. To be specific, a Bayesian Gaussian process regression model for multi-fidelity (MF) data fusion is developed, which incorporates high-fidelity (HF) and low-fidelity (LF) responses, as well as the corresponding gradients. A screening technique based on distance correlation is applied to select a portion of gradients of the low-fidelity model so that the modeling complexity can be greatly reduced. The merit of the proposed method is tested with six numerical examples ranging from 10-D to 30-D, as well as an aerodynamic airfoil case with 18 design variables. The proposed method is compared to two other existing gradient-enhanced Gaussian process-based models. It is shown that the modeling efficiency of the proposed model is dramatically improved compared to the original gradient-enhanced multi-fidelity Gaussian process model, while the loss of the prediction accuracy can be almost negligible. In consequence, it can be a promising approach for gradient-enhanced models dealing with multi-fidelity data.

Gaussian Process Based Model Predictive Control for Overtaking in Autonomous Driving.

This paper proposes a novel framework for addressing the challenge of autonomous overtaking and obstacle avoidance, which incorporates the overtaking path planning into Gaussian Process-based model predictive control (GPMPC). Compared with conventional control strategies, this approach has two main advantages. Firstly, combining Gaussian Process (GP) regression with a nominal model allows for learning from model mismatch and unmodeled dynamics, which enhances a simple model and delivers significantly better results. Due to the approximation for propagating uncertainties, we can furthermore satisfy the constraints and thereby the safety of the vehicle is ensured. Secondly, we convert the geometric relationship between the ego vehicle and other obstacle vehicles into the constraints. Without relying on a higher-level path planner, this approach substantially reduces the computational burden. In addition, we transform the state constraints under the model predictive control (MPC) framework into a soft constraint and incorporate it as relaxed barrier function into the cost function, which makes the optimizer more efficient. Simulation results indicate that the proposed method can not only fulfill the overtaking tasks but also maintain safety at all times.

Gaussian Process-Based Model to Optimize Additively Manufactured Powder Microstructures From Phase Field Modeling

Abstract A persistent problem in the selective laser sintering process is to maintain the quality of additively manufactured parts, which can be attributed to the various sources of uncertainty. In this work, a two-particle phase-field microstructure model has been analyzed using a Gaussian process-based model. The sources of uncertainty as the two input parameters were surface diffusivity and interparticle distance. The response quantity of interest (QOI) was selected as the size of the neck region that develops between the two particles. Two different cases with equal and unequal-sized particles were studied. It was observed that the neck size increased with increasing surface diffusivity and decreased with increasing interparticle distance irrespective of particle size. Sensitivity analysis found that the interparticle distance has more influence on variation in neck size than that of surface diffusivity. The machine learning algorithm Gaussian process regression was used to create the surrogate model of the QOI. Bayesian optimization method was used to find optimal values of the input parameters. For equal-sized particles, optimization using Probability of Improvement provided optimal values of surface diffusivity and interparticle distance as 23.8268 and 40.0001, respectively. The Expected Improvement as an acquisition function gave optimal values of 23.9874 and 40.7428, respectively. For unequal-sized particles, optimal design values from Probability of Improvement were 23.9700 and 33.3005, respectively, while those from Expected Improvement were 23.9893 and 33.9627, respectively. The optimization results from the two different acquisition functions seemed to be in good agreement.

Three-Dimensional Extended Object Tracking and Shape Learning Using Gaussian Processes

In this study, we investigate the problem of tracking objects with unknown shapes using three-dimensional (3D) point cloud data. We propose a Gaussian process-based model to jointly estimate object kinematics, including position, orientation and velocities, together with the shape of the object for online and offline applications. We describe the unknown shape by a radial function in 3D, and induce a correlation structure via a Gaussian process. Furthermore, we propose an efficient algorithm to reduce the computational complexity of working with 3D data. This is accomplished by casting the tracking problem into projection planes which are attached to the object's local frame. The resulting algorithms can process 3D point cloud data and accomplish tracking of a dynamic object. Furthermore, they provide analytical expressions for the representation of the object shape in 3D, together with confidence intervals. The confidence intervals, which quantify the uncertainty in the shape estimate, can later be used for solving the gating and association problems inherent in object tracking. The performance of the methods is demonstrated both on simulated and real data. The results are compared with an existing random matrix model, which is commonly used for extended object tracking in the literature.

Streaming Synthetic Time Series for Simulated Condition Monitoring

The transformation of the common production plant to a cyber-physical system is one of the most recent developments in manufacturing industry. The analysis of data streams produced by such sensor-equipped plants promises potential for process optimization. However, for competitive reasons and due to the novelty of the development, the access to publicly available real-world data is quite limited. Hence, businesses and researchers new to this area are often confronted with the cumbersome and complex task of synthesizing time series in order to gain first experiences. This work presents a novel concept and a corresponding software implementation for the stream-wise generation and publication of sensor data, to simulate condition monitoring of industrial production plants. The resulting configuration file-driven tool is capable of acting like a sensor-equipped plant by generating data points from various Gaussian Process-based models and mathematical expressions, or by replaying data sets. Moreover, it can be seamlessly connected with existing surrounding systems by using the MQTT protocol. In this context, the software aims at laying the foundation for real-world applications and improving them by providing a simulation tool to prototype and test with.

A comparison of centring parameterisations of Gaussian process-based models for Bayesian computation using MCMC

Markov chain Monte Carlo (MCMC) algorithms for Bayesian computation for Gaussian process-based models under default parameterisations are slow to converge due to the presence of spatial- and other-induced dependence structures. The main focus of this paper is to study the effect of the assumed spatial correlation structure on the convergence properties of the Gibbs sampler under the default non-centred parameterisation and a rival centred parameterisation (CP), for the mean structure of a general multi-process Gaussian spatial model. Our investigation finds answers to many pertinent, but as yet unanswered, questions on the choice between the two. Assuming the covariance parameters to be known, we compare the exact rates of convergence of the two by varying the strength of the spatial correlation, the level of covariance tapering, the scale of the spatially varying covariates, the number of data points, the number and the structure of block updating of the spatial effects and the amount of smoothness assumed in a Matérn covariance function. We also study the effects of introducing differing levels of geometric anisotropy in the spatial model. The case of unknown variance parameters is investigated using well-known MCMC convergence diagnostics. A simulation study and a real-data example on modelling air pollution levels in London are used for illustrations. A generic pattern emerges that the CP is preferable in the presence of more spatial correlation or more information obtained through, for example, additional data points or by increased covariate variability.

Efficient Gaussian Process-Based Modelling and Prediction of Image Time Series.

In this work we propose a novel Gaussian process-based spatio-temporal model of time series of images. By assuming separability of spatial and temporal processes we provide a very efficient and robust formulation for the marginal likelihood computation and the posterior prediction. The model adaptively accounts for local spatial correlations of the data, and the covariance structure is effectively parameterised by the Kronecker product of covariance matrices of very small size, each encoding only a single direction in space. We provide a simple and flexible framework for within- and between-subject modelling and prediction. In particular, we introduce the Hoffman-Ribak method for efficient inference on posterior processes and its uncertainty. The proposed framework is applied in the context of longitudinal modelling in Alzheimer's disease. We firstly demonstrate the advantage of our non-parametric method for modelling of within-subject structural changes. The results show that non-parametric methods demonstrably outperform conventional parametric methods. Then the framework is extended to optimize complex parametrized covariate kernels. Using Bayesian model comparison via marginal likelihood the framework enables to compare different hypotheses about individual change processes of images.

Inverse Gaussian process-based corrosion growth modeling and its application in the reliability analysis for energy pipelines

This paper describes an inverse Gaussian process-based model to characterize the growth of metal-loss corrosion defects on energy pipelines. The model parameters are evaluated using the Bayesian methodology by combining the inspection data obtained from multiple inspections with the prior distributions. The Markov Chain Monte Carlo (MCMC) simulation techniques are employed to numerically evaluate the posterior marginal distribution of each individual parameter. The measurement errors associated with the ILI tools are considered in the Bayesian inference. The application of the growth model is illustrated using an example involving real inspection data collected from an in-service pipeline in Alberta, Canada. The results indicate that the model in general can predict the growth of corrosion defects reasonably well. Parametric analyses associated with the growth model as well as reliability assessment of the pipeline based on the growth model are also included in the example. The proposed model can be used to facilitate the development and application of reliability-based pipeline corrosion management.

Inverse Gaussian process-based corrosion growth model for energy pipelines considering the sizing error in inspection data

This paper describes an inverse Gaussian process-based model to characterize the growth of the depth of corrosion defects on underground energy pipelines based on inspection data. The model is formulated in a hierarchical Bayesian framework, which allows consideration of uncertainties from different sources. The Markov Chain Monte Carlo (MCMC) simulation techniques are used to evaluate the probabilistic characteristics of the model parameters by incorporating the defect depths reported by multiple in-line inspections (ILIs) as well as the prior knowledge about these parameters. The bias and random scattering error associated with the ILI tool as well as the correlation between the random scattering errors associated with different ILI tools are considered in the analysis. An example involving real ILI data collected from an in-service pipeline is employed to illustrate the application of the growth model. The results indicate that the model in general can predict the growth of corrosion defects reasonably well. The proposed model can be used to facilitate the development and application of reliability-based pipeline corrosion management.