Machine learning Vasicek model calibration with Gaussian processes

In this article, we calibrate the Vasicek interest rate model under the risk neutral measure by learning the model parameters using Gaussian processes for machine learning regression. The calibration is done by maximizing the likelihood of zero coupon bond log prices, using mean and covariance functions computed analytically, as well as likelihood derivatives with respect to the parameters. The maximization method used is the conjugate gradients. The only prices needed for calibration are zero coupon bond prices and the parameters are directly obtained in the arbitrage free risk neutral measure.

Actuarial applications of multivariate phase-type distributions : model calibration and credibility

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Control and optimization of an SBR for nitrogen removal: from model calibration to plant operation

En aquesta tesis s'ha desenvolupat un sistema de control capaç d'optimitzar el funcionament dels Reactors Discontinus Seqüencials dins el camp de l'eliminació de matèria orgànica i nitrogen de les aigües residuals. El sistema de control permet ajustar en línia la durada de les etapes de reacció a partir de mesures directes o indirectes de sondes. En una primera etapa de la tesis s'ha estudiat la calibració de models matemàtics que permeten realitzar fàcilment provatures de diferents estratègies de control. A partir de l'anàlisis de dades històriques s'han plantejat diferents opcions per controlar l'SBR i les més convenients s'han provat mitjançant simulació. Després d'assegurar l'èxit de l'estratègia de control mitjançant simulacions s'ha implementat en una planta semi-industrial. Finalment es planteja l'estructura d'uns sistema supervisor encarregat de controlar el funcionament de l'SBR no només a nivell de fases sinó també a nivell cicle.

Solute transport in crystalline rocks at Äspö — I: Geological basis and model calibration

Water-conducting faults and fractures were studied in the granite-hosted A¨ spo¨ Hard Rock Laboratory (SE Sweden). On a scale of decametres and larger, steeply dipping faults dominate and contain a variety of different fault rocks (mylonites, cataclasites, fault gouges). On a smaller scale, somewhat less regular fracture patterns were found. Conceptual models of the fault and fracture geometries and of the properties of rock types adjacent to fractures were derived and used as input for the modelling of in situ dipole tracer tests that were conducted in the framework of the Tracer Retention Understanding Experiment (TRUE-1) on a scale of metres. After the identification of all relevant transport and retardation processes, blind predictions of the breakthroughs of conservative to moderately sorbing tracers were calculated and then compared with the experimental data. This paper provides the geological basis and model calibration, while the predictive and inverse modelling work is the topic of the companion paper [J. Contam. Hydrol. 61 (2003) 175]. The TRUE-1 experimental volume is highly fractured and contains the same types of fault rocks and alterations as on the decametric scale. The experimental flow field was modelled on the basis of a 2D-streamtube formalism with an underlying homogeneous and isotropic transmissivity field. Tracer transport was modelled using the dual porosity medium approach, which is linked to the flow model by the flow porosity. Given the substantial pumping rates in the extraction borehole, the transport domain has a maximum width of a few centimetres only. It is concluded that both the uncertainty with regard to the length of individual fractures and the detailed geometry of the network along the flowpath between injection and extraction boreholes are not critical because flow is largely one-dimensional, whether through a single fracture or a network. Process identification and model calibration were based on a single uranine breakthrough (test PDT3), which clearly showed that matrix diffusion had to be included in the model even over the short experimental time scales, evidenced by a characteristic shape of the trailing edge of the breakthrough curve. Using the geological information and therefore considering limited matrix diffusion into a thin fault gouge horizon resulted in a good fit to the experiment. On the other hand, fresh granite was found not to interact noticeably with the tracers over the time scales of the experiments. While fracture-filling gouge materials are very efficient in retarding tracers over short periods of time (hours–days), their volume is very small and, with time progressing, retardation will be dominated by altered wall rock and, finally, by fresh granite. In such rocks, both porosity (and therefore the effective diffusion coefficient) and sorption Kds are more than one order of magnitude smaller compared to fault gouge, thus indicating that long-term retardation is expected to occur but to be less pronounced.

Concrete constitutive model, calibration and applications

A methodology has been developed for characterising the mechanical behaviour of concrete, based on the damaged plasticity model, enriched with a user subroutine (V)USDFLD in order to capture better the ductility of the material under moderate confining pressures. The model has been applied in the context of the international benchmark IRIS_2012, organised by the OECD/NEA/CSNI Nuclear Energy Agency, dealing with impacts of rigid and deformable missiles against reinforced concrete targets. A slightly modified version of the concrete damaged plasticity model was used to represent the concrete. The simulation results matched very well the observations made during the actual tests. Particularly successful predictions involved the energy spent by the rigid missile in perforating the target, the crushed length of the deformable missile, the crushed and cracked areas of the concrete target, and the values of the strains recorded at a number of locations in the concrete slab.

Ground water model calibration using pilot points and regularization

Use of nonlinear parameter estimation techniques is now commonplace in ground water model calibration. However, there is still ample room for further development of these techniques in order to enable them to extract more information from calibration datasets, to more thoroughly explore the uncertainty associated with model predictions, and to make them easier to implement in various modeling contexts. This paper describes the use of pilot points as a methodology for spatial hydraulic property characterization. When used in conjunction with nonlinear parameter estimation software that incorporates advanced regularization functionality (such as PEST), use of pilot points can add a great deal of flexibility to the calibration process at the same time as it makes this process easier to implement. Pilot points can be used either as a substitute for zones of piecewise parameter uniformity, or in conjunction with such zones. In either case, they allow the disposition of areas of high and low hydraulic property value to be inferred through the calibration process, without the need for the modeler to guess the geometry of such areas prior to estimating the parameters that pertain to them. Pilot points and regularization can also be used as an adjunct to geostatistically based stochastic parameterization methods. Using the techniques described herein, a series of hydraulic property fields can be generated, all of which recognize the stochastic characterization of an area at the same time that they satisfy the constraints imposed on hydraulic property values by the need to ensure that model outputs match field measurements. Model predictions can then be made using all of these fields as a mechanism for exploring predictive uncertainty.

An advanced regularization methodology for use in watershed model calibration

A calibration methodology based on an efficient and stable mathematical regularization scheme is described. This scheme is a variant of so-called Tikhonov regularization in which the parameter estimation process is formulated as a constrained minimization problem. Use of the methodology eliminates the need for a modeler to formulate a parsimonious inverse problem in which a handful of parameters are designated for estimation prior to initiating the calibration process. Instead, the level of parameter parsimony required to achieve a stable solution to the inverse problem is determined by the inversion algorithm itself. Where parameters, or combinations of parameters, cannot be uniquely estimated, they are provided with values, or assigned relationships with other parameters, that are decreed to be realistic by the modeler. Conversely, where the information content of a calibration dataset is sufficient to allow estimates to be made of the values of many parameters, the making of such estimates is not precluded by preemptive parsimonizing ahead of the calibration process. White Tikhonov schemes are very attractive and hence widely used, problems with numerical stability can sometimes arise because the strength with which regularization constraints are applied throughout the regularized inversion process cannot be guaranteed to exactly complement inadequacies in the information content of a given calibration dataset. A new technique overcomes this problem by allowing relative regularization weights to be estimated as parameters through the calibration process itself. The technique is applied to the simultaneous calibration of five subwatershed models, and it is demonstrated that the new scheme results in a more efficient inversion, and better enforcement of regularization constraints than traditional Tikhonov regularization methodologies. Moreover, it is argued that a joint calibration exercise of this type results in a more meaningful set of parameters than can be achieved by individual subwatershed model calibration. (c) 2005 Elsevier B.V. All rights reserved.

Efficient accommodation of local minima in watershed model calibration

The Gauss-Marquardt-Levenberg (GML) method of computer-based parameter estimation, in common with other gradient-based approaches, suffers from the drawback that it may become trapped in local objective function minima, and thus report optimized parameter values that are not, in fact, optimized at all. This can seriously degrade its utility in the calibration of watershed models where local optima abound. Nevertheless, the method also has advantages, chief among these being its model-run efficiency, and its ability to report useful information on parameter sensitivities and covariances as a by-product of its use. It is also easily adapted to maintain this efficiency in the face of potential numerical problems (that adversely affect all parameter estimation methodologies) caused by parameter insensitivity and/or parameter correlation. The present paper presents two algorithmic enhancements to the GML method that retain its strengths, but which overcome its weaknesses in the face of local optima. Using the first of these methods an intelligent search for better parameter sets is conducted in parameter subspaces of decreasing dimensionality when progress of the parameter estimation process is slowed either by numerical instability incurred through problem ill-posedness, or when a local objective function minimum is encountered. The second methodology minimizes the chance of successive GML parameter estimation runs finding the same objective function minimum by starting successive runs at points that are maximally removed from previous parameter trajectories. As well as enhancing the ability of a GML-based method to find the global objective function minimum, the latter technique can also be used to find the locations of many non-global optima (should they exist) in parameter space. This can provide a useful means of inquiring into the well-posedness of a parameter estimation problem, and for detecting the presence of bimodal parameter and predictive probability distributions. The new methodologies are demonstrated by calibrating a Hydrological Simulation Program-FORTRAN (HSPF) model against a time series of daily flows. Comparison with the SCE-UA method in this calibration context demonstrates a high level of comparative model run efficiency for the new method. (c) 2006 Elsevier B.V. All rights reserved.

The cost of uniqueness in groundwater model calibration

Calibration of a groundwater model requires that hydraulic properties be estimated throughout a model domain. This generally constitutes an underdetermined inverse problem, for which a Solution can only be found when some kind of regularization device is included in the inversion process. Inclusion of regularization in the calibration process can be implicit, for example through the use of zones of constant parameter value, or explicit, for example through solution of a constrained minimization problem in which parameters are made to respect preferred values, or preferred relationships, to the degree necessary for a unique solution to be obtained. The cost of uniqueness is this: no matter which regularization methodology is employed, the inevitable consequence of its use is a loss of detail in the calibrated field. This, ill turn, can lead to erroneous predictions made by a model that is ostensibly well calibrated. Information made available as a by-product of the regularized inversion process allows the reasons for this loss of detail to be better understood. In particular, it is easily demonstrated that the estimated value for an hydraulic property at any point within a model domain is, in fact, a weighted average of the true hydraulic property over a much larger area. This averaging process causes loss of resolution in the estimated field. Where hydraulic conductivity is the hydraulic property being estimated, high averaging weights exist in areas that are strategically disposed with respect to measurement wells, while other areas may contribute very little to the estimated hydraulic conductivity at any point within the model domain, this possibly making the detection of hydraulic conductivity anomalies in these latter areas almost impossible. A study of the post-calibration parameter field covariance matrix allows further insights into the loss of system detail incurred through the calibration process to be gained. A comparison of pre- and post-calibration parameter covariance matrices shows that the latter often possess a much smaller spectral bandwidth than the former. It is also demonstrated that, as all inevitable consequence of the fact that a calibrated model cannot replicate every detail of the true system, model-to-measurement residuals can show a high degree of spatial correlation, a fact which must be taken into account when assessing these residuals either qualitatively, or quantitatively in the exploration of model predictive uncertainty. These principles are demonstrated using a synthetic case in which spatial parameter definition is based oil pilot points, and calibration is Implemented using both zones of piecewise constancy and constrained minimization regularization. (C) 2005 Elsevier Ltd. All rights reserved.

The inclusion of differentially assessed lands in urban growth model calibration: a comparison of two approaches using SLEUTH

This research sought to understand the role that differentially assessed lands (lands in the United States given tax breaks in return for their guarantee to remain in agriculture) play in influencing urban growth. Our method was to calibrate the SLEUTH urban growth model under two different conditions. The first used an excluded layer that ignored such lands, effectively rendering them available for development. The second treated those lands as totally excluded from development. Our hypothesis was that excluding those lands would yield better metrics of fit with past data. Our results validate our hypothesis since two different metrics that evaluate goodness of fit both yielded higher values when differentially assessed lands are treated as excluded. This suggests that, at least in our study area, differential assessment, which protects farm and ranch lands for tenuous periods of time, has indeed allowed farmland to resist urban development. Including differentially assessed lands also yielded very different calibrated coefficients of growth as the model tried to account for the same growth patterns over two very different excluded areas. Excluded layer design can greatly affect model behavior. Since differentially assessed lands are quite common through the United States and are often ignored in urban growth modeling, the findings of this research can assist other urban growth modelers in designing excluded layers that result in more accurate model calibration and thus forecasting.

Finite element model calibration of an instrumented RC building based on seismic excitation including non-structural components and soil-structure- interaction

Peer reviewed

Prediction model of the buildup of volatile organic compounds on urban roads

A model to predict the buildup of mainly traffic-generated volatile organic compounds or VOCs (toluene, ethylbenzene, ortho-xylene, meta-xylene, and para-xylene) on urban road surfaces is presented. The model required three traffic parameters, namely average daily traffic (ADT), volume to capacity ratio (V/C), and surface texture depth (STD), and two chemical parameters, namely total suspended solid (TSS) and total organic carbon (TOC), as predictor variables. Principal component analysis and two phase factor analysis were performed to characterize the model calibration parameters. Traffic congestion was found to be the underlying cause of traffic-related VOC buildup on urban roads. The model calibration was optimized using orthogonal experimental design. Partial least squares regression was used for model prediction. It was found that a better optimized orthogonal design could be achieved by including the latent factors of the data matrix into the design. The model performed fairly accurately for three different land uses as well as five different particle size fractions. The relative prediction errors were 10–40% for the different size fractions and 28–40% for the different land uses while the coefficients of variation of the predicted intersite VOC concentrations were in the range of 25–45% for the different size fractions. Considering the sizes of the data matrices, these coefficients of variation were within the acceptable interlaboratory range for analytes at ppb concentration levels.

Avian diversification patterns across the K-Pg boundary: Influence of calibrations, datasets, and model misspecification

Birds represent the most diverse extant tetrapod clade, with ca. 10,000 extant species, and the timing of the crown avian radiation remains hotly debated. The fossil record supports a primarily Cenozoic radiation of crown birds, whereas molecular divergence dating analyses generally imply that this radiation was well underway during the Cretaceous. Furthermore, substantial differences have been noted between published divergence estimates. These have been variously attributed to clock model, calibration regime, and gene type. One underappreciated phenomenon is that disparity between fossil ages and molecular dates tends to be proportionally greater for shallower nodes in the avian Tree of Life. Here, we explore potential drivers of disparity in avian divergence dates through a set of analyses applying various calibration strategies and coding methods to a mitochondrial genome dataset and an 18-gene nuclear dataset, both sampled across 72 taxa. Our analyses support the occurrence of two deep divergences (i.e., the Palaeognathae/Neognathae split and the Galloanserae/Neoaves split) well within the Cretaceous, followed by a rapid radiation of Neoaves near the K-Pg boundary. However, 95% highest posterior density intervals for most basal divergences in Neoaves cross the boundary, and we emphasize that, barring unreasonably strict prior distributions, distinguishing between a rapid Early Paleocene radiation and a Late Cretaceous radiation may be beyond the resolving power of currently favored divergence dating methods. In contrast to recent observations for placental mammals, constraining all divergences within Neoaves to occur in the Cenozoic does not result in unreasonably high inferred substitution rates. Comparisons of nuclear DNA (nDNA) versus mitochondrial DNA (mtDNA) datasets and NT- versus RY-coded mitochondrial data reveal patterns of disparity that are consistent with substitution model misspecifications that result in tree compression/tree extension artifacts, which may explain some discordance between previous divergence estimates based on different sequence types. Comparisons of fully calibrated and nominally calibrated trees support a correlation between body mass and apparent dating error. Overall, our results are consistent with (but do not require) a Paleogene radiation for most major clades of crown birds.

Combining data sets of satellite-retrieved products for basin-scale water balance study: 2. Evaluation on the Mississippi Basin and closure correction model

In this study, we applied the integration methodology developed in the companion paper by Aires (2014) by using real satellite observations over the Mississippi Basin. The methodology provides basin-scale estimates of the four water budget components (precipitation P, evapotranspiration E, water storage change Delta S, and runoff R) in a two-step process: the Simple Weighting (SW) integration and a Postprocessing Filtering (PF) that imposes the water budget closure. A comparison with in situ observations of P and E demonstrated that PF improved the estimation of both components. A Closure Correction Model (CCM) has been derived from the integrated product (SW+PF) that allows to correct each observation data set independently, unlike the SW+PF method which requires simultaneous estimates of the four components. The CCM allows to standardize the various data sets for each component and highly decrease the budget residual (P - E - Delta S - R). As a direct application, the CCM was combined with the water budget equation to reconstruct missing values in any component. Results of a Monte Carlo experiment with synthetic gaps demonstrated the good performances of the method, except for the runoff data that has a variability of the same order of magnitude as the budget residual. Similarly, we proposed a reconstruction of Delta S between 1990 and 2002 where no Gravity Recovery and Climate Experiment data are available. Unlike most of the studies dealing with the water budget closure at the basin scale, only satellite observations and in situ runoff measurements are used. Consequently, the integrated data sets are model independent and can be used for model calibration or validation.

Formal calibration methodology for CFD models of naturally ventilated indoor environments

Well planned natural ventilation strategies and systems in the built environments may provide healthy and comfortable indoor conditions, while contributing to a significant reduction in the energy consumed by buildings. Computational Fluid Dynamics (CFD) is particularly suited for modelling indoor conditions in naturally ventilated spaces, which are difficult to predict using other types of building simulation tools. Hence, accurate and reliable CFD models of naturally ventilated indoor spaces are necessary to support the effective design and operation of indoor environments in buildings. This paper presents a formal calibration methodology for the development of CFD models of naturally ventilated indoor environments. The methodology explains how to qualitatively and quantitatively verify and validate CFD models, including parametric analysis utilising the response surface technique to support a robust calibration process. The proposed methodology is demonstrated on a naturally ventilated study zone in the library building at the National University of Ireland in Galway. The calibration process is supported by the on-site measurements performed in a normally operating building. The measurement of outdoor weather data provided boundary conditions for the CFD model, while a network of wireless sensors supplied air speeds and air temperatures inside the room for the model calibration. The concepts and techniques developed here will enhance the process of achieving reliable CFD models that represent indoor spaces and provide new and valuable information for estimating the effect of the boundary conditions on the CFD model results in indoor environments. © 2012 Elsevier Ltd.