Calibration Framework Research Articles

Resolving double-sided inverse heat conduction problem using calibration integral equation method

In this paper, a novel calibration integral equation is derived for resolving double-sided, two-probe inverse heat conduction problem of surface heat flux estimation. In contrast to the conventional inverse heat conduction techniques, this calibration approach does not require explicit input of the probe locations, thermophysical properties of the host material and temperature sensor parameters related to thermal contact resistance, sensor capacitance and conductive lead losses. All those parameters and properties are inherently contained in the calibration framework in terms of Volterra integral equation of the first kind. The Laplace transform technique is applied and the frequency domain manipulations of the heat equation are performed for deriving the calibration integral equation. Due to the ill-posed nature, regularization is required for the inverse heat conduction problem, a future-time method or singular value decomposition (SVD) can be used for stabilizing the ill-posed Volterra integral equation of the first kind.

A game theory-based approach for modelling mandatory lane-changing behaviour in a connected environment

The connected environment provides real-time information about surrounding traffic; such information can be helpful in complex driving manoeuvres, such as lane-changing, that require information about surrounding vehicles. Lane-changing modelling in the connected environment has so far received little attention. This is due to the novelty of connected environment, and the consequent scarcity of data. A behaviourally sound lane-changing model is not even available for the traditional environment; that is, an environment without driving aids. To address this need, this study develops a game theory-based mandatory lane-changing model (AZHW model) for the traditional environment and extends it for the connected environment. The CARRS-Q advanced driving simulator is used to collect high-quality vehicle trajectory data for the connected environment. The developed models (for traditional environment and connected environment) are calibrated using NGSIM and simulator data in a bi-level calibration framework. The performance of the models has been rigorously evaluated using various performance indicators. These include the true positive, false positive, detection rate, false alarm rate, time prediction error, and location prediction error. Results consistently show that the developed game theory-based models can effectively capture mandatory lane-changing decisions with a high degree of accuracy. Furthermore, the performance of the developed AZHW models is compared with representative game theory-based lane-changing models in the literature. The comparative analysis reveals that the AZHW models developed in this study outperform existing models.

Quantitative integration of sedimentological core descriptions and petrophysical data using high-resolution XRF core scans

Abstract In light of the huge investments needed to acquire sediment cores and the growing need of energy-providing companies to predict reservoir quality, it is remarkable that the standard workflow in core analysis has not been optimized to extract as much information from cores as possible. The Integrated Core Analysis (ICA) protocol presented in this study provides a statistical framework for multivariate calibration and prediction of a wide range of properties measured in core, based on integration of high-resolution X-ray fluorescence core-scanning (XRF-CS) proxy records with records of sparsely sampled petrophysical data and sedimentological core descriptions. The downscaling of numerical data involves the application of invertible transformations to remove range constraints on data, followed by calibration with Partial Least Squares regression through cross validation. Categorical data (i.e. lithofacies) are downscaled by associating each class with a statistical model based on the XRF-CS data. All data points are reassigned to their most likely class by applying Quadratic Discriminant Analysis. The result of the ICA is a multivariate data set in which all properties are specified at the same high resolution along the core with their prediction uncertainties. Downscaling of all variables to 1-cm vertical resolution permits investigation of the variability among petrophysical properties, geochemical proxies, and lithofacies memberships. Petrographic analysis is fundamental for interpretation of the XRF-CS records (element-mineral affinity) and for understanding the sedimentological controls on predicted petrophysical properties. Application of the ICA protocol to a 32 m thick, heterogeneous, Upper Carboniferous fluvial sandstone interval resulted in a near 30-fold increase of the petrophysical data base, which allowed identification of the main depositional and diagenetic controls on the spatial distribution of reservoir quality. Successful implementation of the novel ICA protocol will greatly increase the economic value of legacy core data in studies that aim to re-use depleted hydrocarbon reservoirs.

A multicriteria integral framework for agent-based model calibration using evolutionary multiobjective optimization and network-based visualization

Automated calibration methods are a common approach to agent-based model calibration as they can estimate those parameters which cannot be set because of the lack of information. The modeler requires to validate the model by checking the parameter values before the model can be used and this task is very challenging when the model considers two or more conflicting outputs. We propose a multicriteria integral framework to assist the modeler in the calibration and validation of agent-based models that combines evolutionary multiobjective optimization with network-based visualization, which we believe is the first integral approach to model calibration. On the one hand, evolutionary multiobjective optimization provides several sets of calibration solutions (i.e., parameter values) with different trade-offs for the considered objectives in a single run. On the other hand, network-based visualization is used to better understand the decision space and the set of solutions from the obtained Pareto set approximation. To illustrate our proposal, we face the calibration of three agent-based model examples for marketing which consider two conflicting criteria: the awareness of the brand and its word-of-mouth volume. The final analysis of the calibrated solutions shows how our proposed framework eases the analysis of Pareto sets with high cardinality and helps with the identification of flexible solutions (i.e., those having close values in the design space).

A macroscopic approach for calibration and validation of a modified social force model for bidirectional pedestrian streams

The original social force model of pedestrians and its variants have been extensively studied in the past. However, little attention has been given to their parameter estimation and validation specifically for the environments with high density and complex phenomena such as self-organization and lane formation. This paper presents a macroscopic framework for calibration and validation of a modified social force model for bidirectional pedestrian streams based on the concept of pedestrian area-wide fundamental diagram, also known as pedestrian Macroscopic Fundamental Diagram (p-MFD). Results demonstrate that the proposed calibration process and the modified social force model can reproduce the empirically observed p-MFD with features such as hysteresis while consistently generating microscopic emergent self-organization and lane formation phenomena. Overall, validation and application results suggest that the calibrated model successfully replicates pedestrian traffic patterns and support the future applications of the model for various operations and planning purposes.

Multiobjective Calibration Framework for Pedestrian Simulation Models: A study on the Effect of Movement Base Cases, Metrics, and Density Levels

Ideally, a multitude of steps has to be taken before a commercial implementation of a pedestrian model is used in practice. Calibration, the main goal of which is to increase the accuracy of the predictions by determining the set of values for the model parameters that allows for the best replication of reality, has an important role in this process. Yet, up to recently, calibration has received relatively little attention within the field of pedestrian modelling. Most studies focus only on one specific movement base case and/or use a single metric. It is questionable how generally applicable a pedestrian simulation model is that has been calibrated using a limited set of movement base cases and one metric. The objective of this research is twofold, namely, to (1) determine the effect of the choice of movement base cases, metrics, and density levels on the calibration results and (2) to develop a multiple-objective calibration approach to determine the aforementioned effects. In this paper a multiple-objective calibration scheme is presented for pedestrian simulation models, in which multiple normalized metrics (i.e., flow, spatial distribution, effort, and travel time) are combined by means of weighted sum method that accounts for the stochastic nature of the model. Based on the analysis of the calibration results, it can be concluded that (1) it is necessary to use multiple movement base cases when calibrating a model to capture all relevant behaviours, (2) the level of density influences the calibration results, and (3) the choice of metric or combinations of metrics influence the results severely.

The Road is Enough! Extrinsic Calibration of Non-overlapping Stereo Camera and LiDAR using Road Information

This paper presents a framework for the targetless extrinsic calibration of stereo cameras and Light Detection and Ranging (LiDAR) sensors with a non-overlapping Field of View (FOV). In order to solve the extrinsic calibrations problem under such challenging configuration, the proposed solution exploits road markings as static and robust features among the various dynamic objects that are present in urban environment. First, this study utilizes road markings that are commonly captured by the two sensor modalities to select informative images for estimating the extrinsic parameters. In order to accomplish stable optimization, multiple cost functions are defined, including Normalized Information Distance (NID), edge alignment and, plane fitting cost. Therefore a smooth cost curve is formed for global optimization to prevent convergence to the local optimal point. We further evaluate each cost function by examining parameter sensitivity near the optimal point. Another key characteristic of extrinsic calibration, repeatability, is analyzed by conducting the proposed method multiple times with varying randomly perturbed initial points.

A framework for material calibration and deformation predictions applied to additive manufacturing of metals

Additive manufacturing of metals offers the possibility of net-shape production of topologies that are infeasible by conventional subtractive methods, e.g. milling. However, additive manufacturing of metals posses a high defect density, which necessitates accounting for the larger statistical material variation than in conventional metals. To prevent time-consuming experimental component testing, computational methods are required that account for the topology and metal as well as that precisely predict component failure even for metals with statistically varying properties. Predictions require an automatic and modular evaluation of the possibly large set of material properties and their scatter by employing calibration experiments. In addition, a module for failure and deformation prediction as well as a module for the aggregation of experimental data are required. In this contribution, such a modular framework is presented and the encapsulated and non-structured storage of statistically varying material properties is highlighted. In addition, the framework includes multiple FEM solvers and a multitude of optimizers, which are compared and the objective function is addressed. The approach is employed for the third Sandia Fracture Challenge for which two configurations (homogeneous and heterogeneous material properties) are studied and discussed. The blind-predictions of the verification geometry are used to identify the benefits and drawbacks of the framework.

Physically-based urban stormwater quality modelling: An efficient approach for calibration and sensitivity analysis

Physically-based urban stormwater quality modelling is helpful for increasing the understanding of spatial-temporal dynamics of urban pollution, and for designing innovative management technologies. However, because of the high computational cost, calibration and validation of physically-based models is still challenging. In this context, this study aims to develop a new meta-model based framework for efficient calibration and sensitivity analysis of complex and computationally intensive physically-based models. The proposed approach is applied to the FullSWOF-HR model. According to the average rainfall intensity, 21 rainfall events are categorized into three groups, such as 9 light rains, 6 moderate rains and 6 heavy rains. After upscaling the original high-resolution model, 77 parameter nodes are selected by using the adaptive stochastic collocation method with sparse grids algorithm on the lower-resolution surrogate. 77 simulation runs are then performed with the original model for three representative rainfall events, respectively. The interpolating polynomials of the original models are hence generated. Once the meta-model is constructed, we performed the sensitivity analysis with the variance-based Sobol's method, the results of which are consistent with our previous studies. Calibration process of the meta-model is based on the Markov chain Monte Carlo method. The optimized parameters are verified with the original model and then validated for different rainfall events. These promising results show that the proposed meta-model based approach can efficiently perform sensitivity analysis and parameter optimization for complex physical stormwater quality models, and hence will be very helpful for spreading the detailed water quantity and quality modelling for urban water management issues.

Multivariate calibration of large scale hydrologic models: The necessity and value of a Pareto optimal approach

Multivariate calibration using measurements of multiple water balance components has emerged as a potential solution for improving the performance and realism of large scale hydrologic models. In this study we develop a novel multivariate calibration framework to rigorously test whether incorporation of multiple water balance components into calibration can result in sufficiently accurate (behavioral) solutions for all model responses. Unlike previous studies, we use Bayesian calibration to formally define limits of acceptability or error thresholds in order to distinguish behavioral solutions for each of the incorporated fluxes. We apply the framework in the Mississippi river basin for the calibration of a large scale distributed hydrologic model (Noah-MP) with different combinations of model responses - evapotranspiration (ET), soil moisture (SM), and streamflow (SF). The results of the study show that incorporation of additional fluxes and soil moisture (a storage variable) is not always valuable due to significant trade-offs in accuracy among the model responses. In our experiments, only ET and SF could be simulated simultaneously to a reasonable degree of accuracy. In addition, we quantify the trade-offs in accuracy between the model responses using the concept of Pareto optimality. We find that combining ET with other fluxes entails higher trade-offs in accuracy compared to either SM or SF. Unlike deterministic calibration, with the developed framework we are able to identify deficiencies in model parameterization that lead to significant trade-offs in accuracy, especially between ET and SM. We find that the parameters which are insensitive to individual model responses can influence the trade-off relationship between them.

Utilizing Satellite Surface Soil Moisture Data in Calibrating a Distributed Hydrological Model Applied in Humid Regions Through a Multi-Objective Bayesian Hierarchical Framework

The traditional calibration objective of hydrological models is to optimize streamflow simulations. To identify the value of satellite soil moisture data in calibrating hydrological models, a new objective of optimizing soil moisture simulations has been added to bring in satellite data. However, it leads to problems: (i) how to consider the trade-off between various objectives; (ii) how to consider the uncertainty these satellite data bring in. Among existing methods, the multi-objective Bayesian calibration framework has the potential to solve both problems but is more suitable for lumped models since it can only deal with constant variances (in time and space) of model residuals. In this study, to investigate the utilization of a soil moisture product from the Soil Moisture Active Passive (SMAP) satellite in calibrating a distributed hydrological model, the DEM (Digital Elevation Model) -based Distributed Rainfall-Runoff Model (DDRM), a multi-objective Bayesian hierarchical framework is employed in two humid catchments of southwestern China. This hierarchical framework is superior to the non-hierarchical framework when applied to distributed models since it considers the spatial and temporal residual heteroscedasticity of distributed model simulations. Taking the streamflow-based single objective calibration as the benchmark, results of adding satellite soil moisture data in calibration show that (i) there is less uncertainty in streamflow simulations and better performance of soil moisture simulations either in time and space; (ii) streamflow simulations are largely affected, while soil moisture simulations are slightly affected by weights of objectives. Overall, the introduction of satellite soil moisture data in addition to observed streamflow in calibration and putting more weights on the streamflow calibration objective lead to better hydrological performance. The multi-objective Bayesian hierarchical framework implemented here successfully provides insights into the value of satellite soil moisture data in distributed model calibration.

Toward Precise Gaze Estimation for Mobile Head-Mounted Gaze Tracking Systems

The gaze estimation in the mobile scenario often suffers from the extrapolation and parallax errors. In this paper, we propose a novel calibration framework to achieve the precise gaze estimation for head-mounted gaze trackers. Our proposed framework consists of two steps to learn a point-to-point and a point-to-line relations, respectively. The aim of step I is to infer the relation between pupil centers and spatially constrained points of regard. By adopting the “CalibMe” gaze data acquisition method, a sparse Gaussian Process using pseudo-inputs is used to capture the smooth residual field unmodeled by the polynomial function. Meanwhile, a distraction detection criterion is introduced to identify the moment when user's attention is taken away from the calibration point thereby removing outliers. By combining with the point-to-point relation inferred in step I, the observed parallax errors are leveraged in step II to obtain a point-to-line relation, i.e., each pupil center will correspond to an epipolar line. Thus, the real image gaze point projected from different depths is predicted as the intersection of two epipolar lines inferred from binocular data. The simulation and experimental results show the effectiveness of our proposed calibration framework for head-mounted gaze trackers.

Continuous-time Bayesian calibration of energy models using BIM and energy data

The present study proposes a framework for the continuous Bayesian calibration of whole building energy simulation (BES) models utilizing data from building information models (BIM) and building energy management systems (BEMS). The ability to import data from BIM and BEMS provides the potential to significantly reduce the time and effort needed for the continuous calibration of BES models. First, five gbXML geometric test cases were used to check the BIM to BES model translation. Translation of the test cases indicates good geometric agreement between the native BIM and the gbXML-based BES model. An actual building calibration case study (with BIM and three years of monthly electrical energy consumption data) was then used to evaluate the proposed continuous calibration method. The results suggest that compared to a non-continuous approach, the continuous Bayesian calibration method showed reduced prediction uncertainty and improved prediction accuracy on a test dataset. The paper also presents information and comparison of the coefficient of variance of the root mean square error (CVRMSE) and the normalized mean biased error (NMBE), recommending looking at their distributions when working with probabilistic BES predictions.

Freeway travel time estimation based on the general motors model: a genetic algorithm calibration framework

Travel time estimation plays an important role in freeway performance assessment and reliability management. Conventional estimation methods based on speed information do not consider the level of congestion during modelling, leading to unreliable estimations under congested conditions. This study presents a freeway travel time estimation method based on the general motors (GM) model, where the concept ‘virtual vehicle’ was proposed to apply macroscopic traffic flow data to the microscopic GM model. First, a GM-based travel time estimation (GMTTE) model was developed to estimate link travel time. Three sets of parameters l , m and α were separately used under free-flowing, congestion and transition conditions. Next, two corridor estimation models, namely GMTTE time-slice-based (GMTTE-TSB) model and GMTTE continuous-speed (GMTTE-CS) model, were proposed. To calibrate the three parameters, a genetic algorithm framework was developed. The proposed method was calibrated and evaluated using traffic data collected from seven freeway segments in the greater St. Louis, Missouri region. Results show that (i) the GMTTE-CS model outperformed the GMTTE-TSB model; (ii) the optimal parameters of the GMTTE-CS model under free-flowing and congested conditions are l = 1.1 , m = 2.0 , α = 8.0 and l = 1 , m = 0.1 , α = 8.0 , respectively; (iii) the GMTTE-CS model outperformed the instantaneous and time-slice models under congested conditions, while showing similar accuracies with the two models under free-flowing and status-transition conditions; and (iv) the optimal time interval was found to be 9–10 min for free-flowing conditions and 6–7 min for congested conditions.

Geometric Calibration of Continuum Robots: Joint Space and Equilibrium Shape Deviations

Currently, surgical continuum robots (CRs) are predominantly used as telemanipulators where modeling errors are overcome by the user. Such errors preclude their use for autonomous tasks. In this paper, we investigate the calibration of CRs with specific focus on capturing joint space errors due to homing offsets, assembly errors causing twist about the robot's backbone, and uncertainty in the equilibrium bending shapes of segments of these robots. A kinematic framework focusing on multibackbone CR is presented with emphasis on deriving calibration identification Jacobians. This framework captures the coupling between twist and the equilibrium shapes of a continuum segment as a function of its bending angle. To capture equilibrium shape variations as a function of bending, a homotopy of curves is defined and represented by respective modal coefficients. The estimation of the calibration parameters is cast as a nonlinear least-squares problem. The framework is validated by simulations and experimentally using a single-port access surgery robot. We believe this calibration framework will facilitate semiautomation of surgical tasks carried out by CRs.

Accurate Intrinsic and Extrinsic Calibration of RGB-D Cameras With GP-Based Depth Correction

In recent years, more and more robots have been equipped with low-cost RGB-D sensors, such as Microsoft Kinect and Intel Realsense, for safe navigation and active interaction with objects and people. In order to obtain more accurate and reliable fused color and depth information (coloured point clouds), not only the intrinsic and extrinsic parameters of color and depth sensor should be precisely calibrated but also the external corrections of depth measurements are required. In this paper, using motion capture system, we propose a reliable calibration framework that enables the precise estimation of the intrinsic and extrinsic parameters of RGB-D sensors and provide a model-free depth calibration method based on heteroscedastic Gaussian processes. Compared with the existing depth correction techniques, our method can simultaneously estimate the mean and variance of the depth error at different measurement distances, i.e., the probability distribution of the depth error relative to the measured distance, which is essential in the state estimation problems. To verify the effectiveness of our approach, we conduct a thorough qualitative and quantitative analysis of the major steps of our calibration method, and compare our experimental results with other related work. Furthermore, we demonstrate an experiment about the overall improvement of visual SLAM with a Kinect device calibrated by our calibration technique.

Primary beam effects of radio astronomy antennas – I. Modelling the Karl G. Jansky Very Large Array (VLA) L-band beam using holography

Modern interferometric imaging relies on advanced calibration that incorporates direction-dependent effects. Their increasing number of antennas (e.g. in LOFAR, VLA, MeerKAT/SKA) and sensitivity are often tempered with the accuracy of their calibration. Beam accuracy drives particularly the capability for high dynamic range imaging (HDR - contrast > 1:$10^6$). The Radio Interferometric Measurement Equation (RIME) proposes a refined calibration framework for wide field of views (i.e. beyond the primary lobe and first null) using beam models. We have used holography data taken on 12 antennas of the Very Large Array (VLA) with two different approaches: a `data-driven' representation derived from Principal Component Analysis (PCA) and a projection on the Zernike polynomials. We determined sparse representations of the beam to encode its spatial and spectral variations. For each approach, we compressed the spatial and spectral distribution of coefficients using low-rank approximations. The spectral behaviour was encoded with a Discrete Cosine Transform (DCT). We compared our modelling to that of the Cassbeam software which provides a parametric model of the antenna and its radiated field. We present comparisons of the beam reconstruction fidelity vs. `compressibility'. We found that the PCA method provides the most accurate model. In the case of VLA antennas, we discuss the frequency ripple over L-band which is associated with a standing wave between antenna reflectors. The results are a series of coefficients that can easily be used `on-the-fly' in calibration pipelines to generate accurate beams at low computing costs.

Bayesian calibration of underwater propagation models under uncertainty

Propagation models are notorious for the uncertainty of important parameters such as source strength, speed of sound profiles, and reflecting surface profiles. In many cases, one calibrates a model to measured data (e.g., sound levels or transmission loss) for the purposes of estimating these model parameters, i.e., for inverse modeling. Bayesian calibration methods have been developed that are extremely useful for calibration of models where parameters have high levels of uncertainty and problems may be under or over determined. The Kennedy and O’Hagen framework which uses a Gaussian process surrogate model to replace the model under calibration is especially useful when the underlying model is computationally expensive, and so, it may be difficult to apply many optimization based calibration methods. In this talk, we describe the application of the Kennedy and O’Hagen Bayesian Calibration framework to the calibration of an underwater ray tracing propagation model. The source strength and parameters for the sound speed profile are considered as highly uncertain. The Bayesian calibration technique is shown to improve model prediction and reduce the uncertainty of the unknown propagation parameters.

Heterogeneous materials design in additive manufacturing: Model calibration and uncertainty-guided model selection

Multi-material additive manufacturing enables high-performance heterogeneous design at the mesoscale, through which bulk parts can be engineered to adapt to complex loading conditions. The optimization of multi-material parts relies on accurate forward prediction, which is challenging to achieve owing to the complex processing conditions in additive manufacturing and the resultant uncertainties in material properties. To address these limitations, here we present a new model calibration and model selection framework based on the high dimensional, local-scale deformation data. By matching the pixel-level deformation data from digital image correlation experiments and constitutive modeling, the presented framework enables more accurate prediction and significant reduction of the prediction uncertainties, as compared to the single material calibration approach that is widely used in additive manufacturing. In turn, this enables quantitative comparison of the candidate models, so the most accurate and computationally efficient constitutive model can be selected for forward prediction in heterogeneous material design. The advantages of the framework are demonstrated using a multi-polymer system manufactured by dual-extrusion additive manufacturing, which consists of two constituent materials with dramatically different deformation behaviors.

National-scale Traffic Model Calibration in Real Time with Multi-source Incomplete Data

Real-time traffic modeling at national scale is essential to many applications, but its calibration is extremely challenging due to its large spatial and fine temporal coverage. The existing work is focused on urban-scale calibration with complete field data from single data sources (e.g., loop sensors or taxis), which cannot be generalized to national scale because complete single-source field data at national scale are almost impossible to obtain. To address this challenge, in this article, we design MultiCalib, a model calibration framework to optimize traffic models based on multiple incomplete data sources at national scale in real time. Instead of simply combining multi-source data, we theoretically formulate a multi-source model calibration problem based on real-world contexts and multi-view learning. In particular, we design (i) convex multi-view learning to integrate multi-source data by quantifying biases of data sources, and (ii) context-aware tensor decomposition to infer incomplete multi-source data by extracting real-world contexts. More importantly, we implement and evaluate MultiCalib with two heterogeneous nationwide vehicle networks with 340,000 vehicles to infer traffic conditions on 36 expressways and 119 highways, along with four cities across China. The results show that MultiCalib outperforms baseline calibration by 25% on average with the same input data. Based on the proposed national-scale traffic model calibration, we design a novel dispatching framework integrated with our speed calibration model where we guide a vehicular fleet among national-scale highways with a routing strategy to reduce general traveling time. The results show that a routing strategy based on MultiCalib outperforms a routing strategy based on a state-of-the-art traffic model by 45% on average.