Uncertainties In Individual Parameters Research Articles

Characterization and uncertainty analysis of volumetric error variation with temperature

An artefact-based fast and automated volumetric error mapping solution for medium size 3-axis machine tools that enables the calibration of a 1m3 workspace in less than 1 h is proposed for characterizing how temperature variations affect the volumetric accuracy of the machine without a priori knowledge of the temperature variations. A continuous measurement during seven days is performed on a machine affected by different heat sources and a volumetric error variation model is identified. Residual errors remaining from the identification process are used to estimate the uncertainties of individual parameters and motion errors, and Monte Carlo simulations are used to propagate them to the TCP. This model is used to understand how the volumetric positioning error of the machine changes over time and how it is generated within the kinematic chain of the machine.

Uncertainty quantification of borehole heat exchanger design length based on a global sensitivity analysis

Ground heat exchangers are essential components of ground-source heat pump systems. One of the most-used ground heat exchanger types is a borehole heat exchanger (BHE). Many parameters, such as the building thermal loads, ground thermal properties, and BHE components, influence the required BHE length. Therefore, understanding how individual parameter uncertainties are propagated to the output is counterintuitive. In this study, a global sensitivity analysis (GSA) was performed using the framework of the American Society of Heating, Refrigerating, and Air Conditioning Engineers (ASHRAE) BHE design method. The GSA was conducted to identify the subparameters behind the input parameters of ASHRAE design method, which indirectly determine the BHE lengths by impacting the direct input parameters in the ASHRAE formula. The results reveal that the zone infiltration, heat pump efficiency, ground temperature, effective borehole thermal resistance, and electric equipment heat gain are the most influential parameters on the BHE design length.

Thermodynamic Characterization and Equation of State for Solid and Liquid Lead

A high-temperature equation of state (EoS) for the fcc phase of solid lead and liquid lead was developed herein using experimental data on thermodynamic properties, volumetric thermal expansion, compressibility, temperature-dependent bulk modulus, and sound velocity from ultrasonic measurements and melting curve. The whole totality of experimental data was optimized using the temperature-dependent Murnaghan EoS over a pressure range of 0–130 kbar. The temperature dependences of thermodynamic and thermophysical parameters were described herein using an expanded Einstein model. The resultant EoS describes well the whole set of available experimental data within measurement uncertainties of individual parameters.

Assessing the role of selected constraints in Bayesian dynamic source inversion: application to the 2017Mw 6.3 Lesvos earthquake

SUMMARYA dynamic finite-fault source inversion for stress and frictional parameters of the Mw 6.3 2017 Lesvos earthquake is carried out. The main shock occurred on June 12, offshore the southeastern coast of the Greek island of Lesvos in the north Aegean Sea. It caused 1 fatality, 15 injuries, and extensive damage to the southern part of the island. Dynamic rupture evolution is modelled on an elliptic patch, using the linear slip-weakening friction law. The inversion is posed as a Bayesian problem and the Parallel Tempering Markov Chain Monte Carlo algorithm is used to obtain posterior probability distributions by updating the prior distribution with progressively more constraints. To calculate the first posterior distribution, only the constraint that the model should expand beyond the nucleation patch is used. Then, we add the constraint that the model should reach a moment magnitude similar to that obtained from our centroid moment tensor inversion. For the final posterior distribution, 15 acceleration records from Greek and Turkish strong motion networks at near regional distances (≈ 30–150 km) in the frequency range of 0.05–0.15 Hz are used. The three posterior distributions are compared to understand how much each constraint contributes to resolving different quantities. The most probable values and uncertainties of individual parameters are also calculated, along with their mutual trade-offs. The features best determined by seismograms in the final posterior distribution include the position of the nucleation region, the mean direction of rupture (towards WNW), the mean rupture speed (with 68 per cent of the distribution lying between 1.4 and 2.6 km s–1), radiated energy (12–65 TJ), radiation efficiency (0.09–0.38) and the mean stress drop (2.2–6.5 MPa).

Cosmological constraints using the newest VLT-KMOS H ii galaxies and the full Planck CMB spectrum

ABSTRACT We present novel cosmological constraints based on a joint analysis of our H ii galaxies (HIIG) Hubble relation with the full Planck cosmic microwave background (CMB) anisotropy spectrum and the baryon acoustic oscillations (BAO) probes. The HIIG span a large redshift range (0.088 ≤ z ≤ 2.5), reaching significantly higher redshifts than available Type Ia supernovae (SNeIa) and hence they probe the cosmic expansion at earlier times. Our independent constraints compare well with those based on the ‘Pantheon’ compilation of SNeIa data, which we also analyse. We find our results to be in agreement with the conformal Λ cold dark matter (ΛCDM) model within 1σ. We also use our HIIG data to examine the behaviour of the dark energy equation-of-state parameter under the Chevallier–Polarski–Linder (CPL) parametrization, w = w0 + waz/(1 + z), and find consistent results with those based on SNeIa, although the degeneracy in the parameter space and the individual parameter uncertainties, when marginalizing one over the other, are quite large.

The Application and Implications of Novel Deterministic Sensitivity Analysis Methods.

Deterministic sensitivity analyses (DSA) remain important to interpret the effect of uncertainties in individual parameters on results of cost-effectiveness analyses. Classic DSA methodologies may lead to wrong conclusions due to a lack of or misleading information regarding marginal effects, non-linearity, likelihood and correlations. In addition, tornado diagrams are misleading in some situations. Recent advances in DSA methods have the potential to provide decision makers with more reliable information regarding the effects of uncertainties in individual parameters. This practical application discusses advances to classic DSA methods and their implications. Three methods are discussed: stepwise DSA, distributional DSA and probabilistic DSA. For each method, the technical specifications, options for presenting results, and its implications for decision making are discussed. Options for visualizing DSA results in incremental cost-effectiveness ratios and in incremental net benefits are presented. The use of stepwise DSA increases interpretability of marginal effects and non-linearities in the model, which is especially relevant when arbitrary ranges are implemented. Using the probability distribution of each parameter in distributional DSA provides insight on the likelihood of model outcomes while probabilistic DSA also includes the effects of correlations between parameters.Probabilistic DSA, preferably expressed in incremental net benefit, is the most appropriate method for providing insight on the effect of uncertainty in individual parameters on the estimate of cost effectiveness. However, the opportunities provided by probabilistic DSA may not always be needed for decision making. Other DSA methods, in particular distributional DSA, can sometimes be sufficient depending on model features. Decision makers must determine to which extent they will accept and implement these new and improved DSA methodologies and adjust guidelines accordingly.

Evaluating the Propagation of Uncertainties in Biologically Based Treatment Planning Parameters.

Biologically based treatment planning is a broad term used to cover any instance in radiotherapy treatment planning where some form of biological input has been used. This is wide ranging, and the simpler forms (e.g., fractionation modification/optimization) have been in use for many years. However, there is a reluctance to use more sophisticated methods that incorporate biological models either for plan evaluation purposes or for driving plan optimizations. This is due to limited data available regarding the uncertainties in these model parameters and what impact these have clinically. This work aims to address some of these issues and to explore the role that uncertainties in individual model parameters have on the overall tumor control probability (TCP)/normal tissue complication probability (NTCP) calculated, those parameters that have the largest influence and situations where extra care must be taken. In order to achieve this, a software tool was developed, which can import individual clinical DVH's for analysis using a range of different TCP/NTCP models. On inputting individual model parameters, an uncertainty can be applied. Using a normally distributed random number generator, distributions of parameters can be generated, from which TCP/NTCP values can be calculated for each parameter set for the DVH in question. These represent the spread in TCP/NTCP parameters that would be observed for a simulated population of patients all being treated with that particular dose distribution. A selection of clinical DVHs was assessed using published parameters and their associated uncertainties. A range of studies was carried out to determine the impact of individual parameter uncertainties including reduction of uncertainties and assessment of what impact fractionation and dose have on these probabilities.

Optimal and Robust Power Allocation for Visible Light Positioning Systems Under Illumination Constraints

The problem of optimal power allocation among light emitting diode (LED) transmitters in a visible light positioning system is considered for the purpose of improving localization performance of visible light communication (VLC) receivers. Specifically, the aim is to minimize the Cramer-Rao lower bound (CRLB) on the localization error of a VLC receiver by optimizing LED transmission powers in the presence of practical constraints, such as individual and total power limitations and illuminance constraints. The formulated optimization problem is shown to be convex and thus can efficiently be solved via standard tools. We also investigate the case of imperfect knowledge of localization parameters and develop robust power allocation algorithms by taking into account both overall system uncertainty and individual parameter uncertainties related to the location and orientation of the VLC receiver. In addition, we address the total power minimization problem under predefined accuracy requirements to obtain the most energy-efficient power allocation vector for a given CRLB level. Numerical results illustrate the improvements in localization performance achieved by employing the proposed optimal and robust power allocation strategies over the conventional uniform and non-robust approaches.

Cost-effectiveness analysis of a multivariate index assay compared to modified American College of Obstetricians and Gynecologists criteria and CA-125 in the triage of women with adnexal masses

Objective:To evaluate the cost-effectiveness of the multivariate index assay (MIA) for use in triaging women with an adnexal mass relative to modified American College of Obstetricians and Gynecologists (mACOG) referral guidelines and CA-125 testing alone.Methods:The MIA triage algorithm was based on qualitative serum testing of five biomarkers: transthyretin, apolipoprotein, A-1, 2-microglobulin, transferrin, and CA-125. An economic analysis was developed to evaluate the clinical and cost implications of adopting MIA in clinical practice versus the mACOG referral guidelines and CA-125 alone, over a lifetime horizon, from the perspective of the public payer. Clinical parameters used to characterize patients’ disease status, quality of life, and treatment decisions were estimated using the results of published studies; costs were approximated using reimbursement rates from CMS fee schedules. Model endpoints included overall survival (OS), costs, quality-adjusted life years (QALYs), and incremental cost-effectiveness ratio (ICER). The cost-effectiveness threshold was set to $50,000 per QALY. One-way sensitivity analysis was performed to assess uncertainty of individual parameters included in the analysis. All costs were reported in 2014 US dollars.Results:Use of MIA was cost-effective, resulting in fewer re-operations and pre-treatment CT scans. Overall MIA resulted in an ICER of $35,094/QALY gained. MIA was also cost-saving and QALY-increasing compared to use of CA-125 alone with an ICER of $12,189/QALY gained. One-way sensitivity analysis showed the ICER was most affected by the following parameters: (1) sensitivity of MIA; (2) sensitivity of mACOG; and (3) percentage of patients, not referred to a gynecologic oncologist, who were correctly diagnosed with advanced epithelial ovarian cancer (EOC).Conclusion:Use of MIA is a more cost-effective triage strategy than mACOG or CA-125. It is expected to increase the percentage of women with ovarian cancer that are referred to gynecologic oncologists, which is shown to improve clinical outcomes. Limitations include the use of assumptions when published data was unavailable, and the use of multiple sources for survival data.

How to ensure greenhouse gas emission reductions by increasing the use of biofuels? – Suitability of the European Union sustainability criteria

Abstract Biofuels are promoted in many parts of the world. However, concern of environmental and social problems have grown due to increased production of biofuels. Therefore, many initiatives for sustainability criteria have been announced. As a part of the European Union (EU) renewable energy promotion directive (RED), the EU has introduced greenhouse gas (GHG) emission-saving requirements for biofuels along with the first-ever mandate methodology to calculate the GHG emission reduction. As explored in this paper, the RED methodology, based on life-cycle assessment (LCA) approach, excludes many critical issues. These include indirect impacts due to competition for land, biomass and other auxiliary inputs. Also, timing issues, allocation problems, and uncertainty of individual parameters are not yet considered adequately. Moreover, the default values provided in the RED for the GHG balances of biofuels may significantly underestimate their actual impacts. We conclude that the RED methodology cannot ensure the intended GHG emission reductions of biofuels. Instead, a more comprehensive approach is required along with additional data and indicators. Even if it may be very difficult to verify the GHG emission reductions of biofuels in practice, it is necessary to consider the uncertainties more closely, in order to mitigate climate change effectively.

Analytical uncertainty propagation in life cycle inventory and impact assessment: application to an automobile front panel

Background, aim, and scope Uncertainty information is essential for the proper use of life cycle assessment (LCA) and environmental assessments in decision making. So far, parameter uncertainty propagation has mainly been studied using Monte Carlo techniques that are relatively computationally heavy to conduct, especially for the comparison of multiple scenarios, often limiting its use to research or to inventory only. Furthermore, Monte Carlo simulations do not automatically assess the sensitivity and contribution to overall uncertainty of individual parameters. The present paper aims to develop and apply to both inventory and impact assessment an explicit and transparent analytical approach to uncertainty. This approach applies Taylor series expansions to the uncertainty propagation of lognormally distributed parameters.

Uncertainties in the Rain Profiling Algorithm for the TRMM Precipitation Radar

This paper describes the basic structure and flow of the rain profiling algorithm for the TRMM Precipitation Radar, and discusses the major assumptions and sources of error in the algorithm. In particular, it describes how the uncertainties in individual parameters affect the attenuation correction and rain estimates. Major parameters involved are the drop size distribution, the phase state of precipitating particles, their density and shape, inhomogeneity of precipitation distribution within the footprint, attenuation due to cloud liquid water and water vapor, freezing height, uncertainty of the surface scattering cross section, and fluctuation of the radar echo signal. Among these parameters that affect the rain estimates, the effect of inhomogeneity of rain distribution is summarized in detail. The paper also describes how these parameters are taken into account in different versions of the standard algorithm 2A25.

An investigation of noise factor effects in parameter design

Parameter design aims to determine nominal values of a set of design parameters so as to minimize variability in one or more key performance measures, in the presence of uncertainties in the design parameters, whilst maintaining the required nominal (design point) performance and the overall design concept. A theoretical analysis of some aspects of parameter design and of some related approximate methods is carried out and the results studied with the aim of determining the effect of changes in the magnitudes of the uncertainties in the design parameters on the resulting values of nominal parameter values in the optimum design. It is shown that there is reason to expect that, allowing for the effects of constraints, a given parameter design would be robust against overall changes, by a constant factor, in the parameter uncertainties but not in the presence of changes in individual parameter uncertainties, or by numerous such changes when the change factor varies between individual parameters. Some numerical results are obtained for problems in beam design and are shown to support the above assertions. The results imply that nominal values in a previously determined robust design may continue to be valid when parameter tolerances change, provided such changes are by the same factor for all free design parameters, i.e. those not fixed on a constraint boundary. Copyright © 2002 John Wiley & Sons, Ltd.

Variability and quality in ASR data represented by the Sandia model

1. 1 The Sandia Model has been extended to yield individual parameter uncertainties and a measure of data quality. 2. 2 Parameter uncertainties are small (1–3%) where there are a large number of degrees of freedom and the model is appropriate (Q < 1.0). 3. 3 Data analysis suggests that the Sandia method, as published, calculates only the ‘residual stress’ in the sample but that the data might be used to determine in situ stress if core retrieval time is allowed for.