Extra Uncertainties Research Articles

Adaptive sliding mode control for vibration reduction on UAV carrying a payload

Unmanned aerial vehicles (UAVs) have been used to transport a variety of payloads, including medical materials, foods, and different electronic devices. This type of innovation generates important concerns regarding payload integrity, mainly when involving medical goods that can be affected by vibration. This paper presents the flight dynamics of suspended payload carried by an UAV, considering a flexible attachment between a quadrotor and its payload. Adaptive sliding mode control (ASMC) is proposed to enhance the trajectory tracking and consequently minimize the payload vibration. Adaptive coefficients are introduced to compensate the payload dynamics and uncertainties, which are computed for each proposed trajectory and cargo mass. The proposed adaptive control can efficiently compensate the extra dynamics and uncertainties caused by the attached payload, regardless of the chosen trajectory and weight of the cargo. A root mean square–based index is used to quantitatively evaluate the oscillations. The results show a significant attenuation of the undesired oscillations up to 27%, when the adaptive control is used. Therefore, the use of the proposed ASMC aims to guarantee an improved trajectory tracking and the attenuation of residual oscillations on the main state variables, allowing to be safely employed for transporting several types of medicines, including those sensitive to vibration and those that are dropped during a flight.

An Improved System to Measure Leaf Gas Exchange on Adaxial and Abaxial Surfaces.

Measurement of leaf carbon gain and water loss (gas exchange) in planta is a standard procedure in plant science research for attempting to understand physiological traits related to water use and photosynthesis. Leaves carry out gas exchange through the upper (adaxial) and lower (abaxial) surfaces at different magnitudes, depending on the stomatal density, stomatal aperture, cuticular permeability, etc., of each surface, which we account for in gas exchange parameters such as stomatal conductance. Most commercial devices measure leaf gas exchange by combining the adaxial and abaxial fluxes and calculating bulk gas exchange parameters, missing details of the plant's physiological response on each side. Additionally, the widely used equations to estimate gas exchange parameters neglect the contribution of small fluxes such as cuticular conductance, adding extra uncertainties to measurements performed in water-stress or low-light conditions. Accounting for the gas exchange fluxes from each side of the leaf allows us to better describe plants' physiological traits under different environmental conditions and account for genetic variability. Here, apparatus and materials are presented for adapting two LI-6800 Portable Photosynthesis Systems to work as one gas exchange system to measure adaxial and abaxial gas exchange simultaneously. The modification includes a template script with the equations to account for small fluxes. Instructions are provided for incorporating the add-on script into the device's computational sequence, display, variables, and spreadsheet results. We explain the method to obtain an equation to estimate boundary layer conductance to water for the new setup and how to embed this equation in the devices' calculations using the provided add-on script. The apparatus, methods, and protocols presented here provide a simple adaptation combining two LI-6800s to obtain an improved system to measure leaf gas exchange on adaxial and abaxial surfaces. Graphical overview Figure 1.Diagram of the connection of two LI-6800s.Figure adapted from Márquez et al. (2021).

A Direct Method for the Estimation of Top-of-Atmosphere Outgoing Longwave Radiation from Himawari-8/AHI Data

Top-of-atmosphere (TOA) outgoing longwave radiation (OLR), a key component of the Earth’s energy budget, serves as a diagnostic of the Earth’s climate system response to incoming solar radiation. However, existing products are typically estimated using the traditional two-step method, which may bring extra uncertainties. This paper presents a direct machine learning method to estimate TOA OLR by directly linking Himawari-8/Advanced Himawari Imager (AHI) TOA radiances with TOA OLR determined by Clouds and the Earth’s Radiant Energy System (CERES) and other information, such as the viewing geometry. Models are built separately under clear- and cloudy-sky conditions using a gradient-boosting regression tree. Independent test results show that the root mean square errors (RMSEs) of the clear-sky and cloudy-sky models for estimating instantaneous values are 7.46 W/m2 (3.0%) and 11.61 W/m2 (5.8%), respectively. Daily results are obtained by averaging all the instantaneous results in one day. Intercomparisons of the daily results with CERES TOA OLR data show that the RMSE of the estimated AHI OLR is ~6 W/m2 (3%). The developed high-resolution AHI TOA OLR dataset will be beneficial in analyzing the regional energy budget.

An Enhanced Strategy for Adaptive Output-Feedback Control of Uncertain Nonlinear Systems

We are concerned with global practical tracking for uncertain nonlinear systems with intrinsic dependence on unmeasured states. Typically, we aim to remove the polynomial restrictions on system growth rates in relevant works, admitting the rates to be of arbitrary function-of-output type. Note that such highly nonlinear rates could alter so drastically in magnitude that no polynomial can upper bound them on any unbounded region, and would undermine the design rationale and the analysis route that are followed in polynomial rate scenarios. This entails refining/integrating state-of-the-art techniques and developing new ones, from design to analysis. Concretely, to circumvent the need for knowledge on polynomials, dual dynamic high gains are devised ingeniously which particularly incorporate certain highly nonlinear components to counteract the arbitrary function-of-output rates and other inherent nonlinearities and uncertainties. But unfavorable impacts of the components would also arise putting the effectiveness of the high gains at risk, which necessitates noticeable changes in the choice of vital variables/functions. In addition, to provide tractable observer error dynamics for control design and analysis, a nonlinear high-gain observer is pursued, which is filter based and of reduced order, following the design methodologies in relevant works. In terms of performance analysis, practical tracking suffers extra time variants and additive uncertainties which together with the highly nonlinear rates would carry over to stability analysis inevitably and in turn ruin the existing analysis routes. Hence, a new analysis route is paved to verify the anticipated performance. Notably, by unfolding an important implication, the performance verification boils down largely to the boundedness of the high gains. This makes plain and intelligible the verification, although sophisticated integration of multiple composite Lyapunov functions is still required. An exception, i.e., asymptotic stabilization, is presented to demonstrate its close connection with practical tracking.

Air pollutant emissions induced by rural-to-urban migration during China's urbanization (2005–2015)

As the world's most populous country, China has witnessed rapid urbanization in recent decades, with population migration from rural to urban (RU) regions as the major driving force. Due to the large gap between rural and urban consumption and investment level, large-scale RU migration impacts air pollutant emissions and creates extra uncertainties for air quality improvement. Here, we integrated population migration assessment, an environmentally extended input–output model and structural decomposition analysis to evaluate the NOx, SO2 and primary PM2.5 emissions induced by RU migration during China's urbanization from 2005 to 2015. The results show that RU migration increased air pollutant emissions, while the increases in NOx and SO2 emissions peaked in approximately 2010 at 2.4 Mt and 2.2 Mt, accounting for 9.2% and 8.7% of the national emissions, respectively. The primary PM2.5 emissions induced by RU migration also peaked in approximately 2012 at 0.3 Mt, accounting for 2.8% of the national emissions. The indirect emissions embodied in consumption and investment increased, while household direct emissions decreased. The widening gap between urban and rural investment and consumption exerted a major increasing effect on migration-induced emissions; in contrast, the falling emission intensity contributed the most to the decreasing effect benefitting from end-of-pipe control technology applications as well as improving energy efficiency. The peak of air pollutant emissions induced by RU migration indicates that although urbanization currently creates extra environmental pressure in China, it is possible to reconcile urbanization and air quality improvement in the future with updating urbanization and air pollution control policies.

The stochastic decision making framework for long-term multi-objective energy-water supply-ecology operation in parallel reservoirs system under uncertainties

The long-term multi-objective reservoir operation (LTMORO) involving multiple competitive goals such as energy, water supply and ecology protection is usually implemented under uncertain and changeable environment. Conventional methods usually obtain trade-off solutions and select most preferred one by multi-criteria decision making (MCDM) under deterministic environment. However, these methods are difficult to handle real-world reservoir system where multiple uncertainties exist in criteria performance values (PVs) and weights (CWs). In this paper, framework for solving reservoir operation and MCDM problem under various uncertainties is developed. A novel multi-objective method based on shuffled frog leaping algorithm (SFLA) is proposed to obtain high-quality trade-off solutions. Besides, hybrid utility forms based on TOPSIS, grey correlation analysis (GCA) or other models are impacted by subjectivity of combination coefficient, resulting in extra uncertainties for MCDM. To this end, the stochastic multi-criteria acceptability analysis (SMAA) model is developed by constructing new utility function based on SMAA-2 and modified GCA. The modified GCA helps to offset the uneven distribution problem in conventional version and enhance differentiation of utility function in SMAA-2. Moreover, deterministic CWs are obtained based on minimum deviation principle and two types of stochastic CWs following probability distributions are used to estimate CWs uncertainty. The risk caused by uncertain information propagating from PVs and CWs to decision results is also quantified. Finally, efficiency of established framework is tested by conducting three numerical experiments compared with deterministic GCA and SMAA-2. Results indicate that, compared with deterministic models, the novel framework provides decision maker with more reliable decision support and quantified risk information. The novel SMAA-GCA model produces relatively high probabilities for solutions to obtain their respective ranks compared with that of SMAA-2. It is effective to reduce impact of complex uncertainties on MCDM for LTMORO under stochastic environment.

Stochastic Generation of Future Hydroclimate Using Temperature as a Climate Change Covariate

AbstractIt is now standard practice for water supply agencies to use stochastic models to generate synthetic hydroclimate sequences that preserve the key statistics contained in the observed/instrumental hydroclimate data (usually rainfall, potential evapotranspiration, and streamflow) for use as inputs when determining water security. However, this approach is only adequate for determining current and future water supply risks if nonstationarity in past and future climate is accounted for. In this study, we develop an approach for stochastically generating future seasonal (monthly to annual) hydroclimatic conditions at multiple sites for water supply security assessment that capitalizes on an Australia‐wide relationship between annual average daily maximum temperature and annual rain (and flow). This approach is practical as it (i) avoids the extra time and additional uncertainties introduced by downscaling and bias correction of climate model produced rainfall information and (ii) takes advantage of the fact that climate model projections for temperature change are more realistic than climate model projections for rainfall. The approach is applied to a case study for catchments supplying Sydney, Australia's largest city. Two future scenarios were evaluated, 1 and 2°C warming over the next 50 years. Large reductions in streamflow were simulated, particularly for the 2°C scenario, resulting in major impacts on water security in the absence of any intervention. This is consistent with recent warming since 1990 being associated with more than a 40% decrease in average annual streamflow when compared with the average annual streamflow over the ∼110 years historical record.

Parton-shower effects in Higgs production via vector-boson fusion

We present a systematic investigation of parton-shower and matching uncertainties of perturbative origin for Higgs-boson production via vector-boson fusion. To this end we employ different generators at next-to-leading order QCD accuracy matched with shower Monte Carlo programs, PYTHIA8, and HERWIG7, and a next-to-next-to-leading order QCD calculation. We thoroughly analyse the intrinsic sources of uncertainty within each generator, and then compare predictions among the different tools using the respective recommended setups. Within typical vector-boson fusion cuts, the resulting uncertainties on observables that are accurate to next-to-leading order are at the 10% level for rates and even smaller for shapes. For observables sensitive to extra radiation effects uncertainties of about 20% are found. We furthermore show how a specific recoil scheme is needed when PYTHIA8 is employed, in order not to encounter unphysical enhancements for these observables. We conclude that for vector-boson fusion processes an assessment of the uncertainties associated with simulation at next-to-leading order matched to parton showers based only on the variation of renormalisation, factorisation and shower scales systematically underestimates their true size.

Towards the analysis of JWST exoplanet spectra: the effective temperature in the context of direct imaging

ABSTRACT The current sparse wavelength range coverage of exoplanet direct imaging observations, and the fact that models are defined using a finite wavelength range, lead both to uncertainties on effective temperature determination. We study these effects using blackbodies and atmospheric models and we detail how to infer this parameter. Through highlighting the key wavelength coverage that allows for a more accurate representation of the effective temperature, our analysis can be used to mitigate or manage extra uncertainties being added in the analysis from the models. We find that the wavelength range coverage will soon no longer be a problem. An effective temperature computed by integrating the spectroscopic observations of the James Webb Space Telescope will give uncertainties similar to, or better than, the current state–of–the–art, which is to fit models to data. Accurately calculating the effective temperature will help to improve current modelling approaches. Obtaining an independent and precise estimation of this crucial parameter will help the benchmarking process to identify the best practice to model exoplanet atmospheres.

CMB Tensions with Low-Redshift H0 and S8 Measurements: Impact of a Redshift-Dependent Type-Ia Supernovae Intrinsic Luminosity

With the recent increase in precision of our cosmological datasets, measurements of Λ CDM model parameter provided by high- and low-redshift observations started to be in tension, i.e., the obtained values of such parameters were shown to be significantly different in a statistical sense. In this work we tackle the tension on the value of the Hubble parameter, H 0 , and the weighted amplitude of matter fluctuations, S 8 , obtained from local or low-redshift measurements and from cosmic microwave background (CMB) observations. We combine the main approaches previously used in the literature by extending the cosmological model and accounting for extra systematic uncertainties. With such analysis we aim at exploring non standard cosmological models, implying deviation from a cosmological constant driven acceleration of the Universe expansion, in the presence of additional uncertainties in measurements. In more detail, we reconstruct the Dark Energy equation of state as a function of redshift, while we study the impact of type-Ia supernovae (SNIa) redshift-dependent astrophysical systematic effects on these tensions. We consider a SNIa intrinsic luminosity dependence on redshift due to the star formation rate in its environment, or the metallicity of the progenitor. We find that the H 0 and S 8 tensions can be significantly alleviated, or even removed, if we account for varying Dark Energy for SNIa and CMB data. However, the tensions remain when we add baryon acoustic oscillations (BAO) data into the analysis, even after the addition of extra SNIa systematic uncertainties. This points towards the need of either new physics beyond late-time Dark Energy, or other unaccounted systematic effects (particulary in BAO measurements), to fully solve the present tensions.

Implication of heterogeneities on core porosity measurements

Heterogeneities within core samples affect the accuracy of the laboratory measured core plug interconnected porosity. The laboratory measures the volume averaged porosity of the interconnected pores, <ϕm>. For homogeneous cores this is the correct porosity ± any experimental error. However for heterogeneous cores when any embedded material (unknown or ignored) has a differing porosity, ϕi, to that of the containing outer shell, ϕo, there will be increased uncertainty. We show that the difference between the measured volume averaged porosity, <ϕm>, and the porosity of the outer shell of the core, ϕo can be quantified by our Heterogeneity Factor, H. H is defined as (<ϕm>- ϕo)/ϕo and given by H = F(R-1), where F is the ratio of the bulk volume of the embedded material to the total core bulk volume (measured), VBi/VBm, and R is the ratio of the embedded and the host outer porosity, ϕi/ϕo. The core plug homogeneous model can create increased error bounds in porosity for heterogeneous plugs.When H is zero there is no error in the porosity measurement due to heterogeneity, but when H≠ 0 then the differences can be significant and increases the experimental error bound. We present graphs for relevant industry scenarios to demonstrate the effect of any inclusions in the measured porosity. We find that when F is ∼0.1 i.e., inner included porosity is 10% of bulk volume, the relative error between <ϕm> and ϕo can reach ∼30% and even larger differences when F > 0.1. We then give a real example from a faulted vuggy outcrop carbonate which demonstrates extra porosity uncertainties, even for a very small vug. Finally we discuss the possible effect of embedded clay intrusions emitting adsorbed gas on grain/pore volume determinations of porosity using gas expansion, a common laboratory method of porosity determination.Appreciation of core heterogeneity on the precision of the laboratory porosity measurements is essential to improve the confidence in the error bounds for the quality control of laboratory core porosity measurements, and of the porosity distribution frequency for inputs to statistical methods such as Monte Carlo analysis for oil-in-place estimations, STOIIP.

Systematic analysis of double-scale evolution

Often the factorization of differential cross sections results in the definition of fundamental hadronic functions/distributions which have a double-scale evolution, as provided by a pair of coupled equations. Typically, the two scales are the renormalization and rapidity scales. The two-dimensional structure of their evolution is the object of the present study. In order to be more specific, we consider the case of the transverse momentum dependent distributions (TMD). Nonetheless, most of our findings can be used with other double-scale parton distributions. On the basis of the two-dimensional structure of TMD evolution, we formulate the general statement of the ζ-prescription introduced in [1], and we define an optimal TMD distribution, which is a scaleless model-independent universal non-perturbative function. Within this formulation the non-perturbative definition of the distribution is disentangled from the evolution, which clarifies the separation of perturbative and non-perturbative effects in the phenomenology. A significant part of this work is devoted to the study of the effects of truncation of perturbation theory on the double-scale evolution. We show that within truncated perturbation theory the solution of evolution equations is ambiguous and this fact generates extra uncertainties within the resummed cross-section. The alternatives to bypass this issue are discussed. Finally, we discuss the sources and distribution of the scale variation uncertainties.

Sources of uncertainty in annual global horizontal irradiance data

The major sources of uncertainty in short-term assessment of global horizontal radiation (G) are the pyranometer type and their operation conditions for measurements, whereas the modeling approach and the geographic location are critical for estimations. The influence of all these factors in the uncertainty of the data has rarely been compared. Conversely, solar radiation data users are increasingly demanding more accurate uncertainty estimations. Here we compare the annual bias and uncertainty of all the mentioned factors using 732 weather stations located in Spain, two satellite-based products and three reanalyses.The largest uncertainties were associated to operational errors such as shading (bias = −8.0%) or soiling (bias = −9.4%), which occurred frequently in low-quality monitoring networks but are rarely detected because they pass conventional QC tests. Uncertainty in estimations greatly changed from reanalysis to satellite-based products, ranging from the gross accuracy of ERA-Interim (+6.1-6.7+18.8%) to the high quality and spatial homogeneity of SARAH-1 (+1.4-5.3+5.6%). Finally, photodiodes from the Spanish agricultural network SIAR showed an uncertainty of -5.4+6.9%, which is far greater than that of secondary standards (±1.5%) and similar to SARAH-1. This is probably caused by the presence of undetectable operational errors and the use of uncorrected photodiodes. Photodiode measurements from low-quality monitoring networks such as SIAR should be used with caution, because the chances of adding extra uncertainties due to poor maintenance or inadequate calibration considerably increase.

Quantification of marine aerosol subgrid variability and its correlation with clouds based on high‐resolution regional modeling

AbstractOne limitation of most global climate models (GCMs) is that with the horizontal resolutions they typically employ, they cannot resolve the subgrid variability (SGV) of clouds and aerosols, adding extra uncertainties to the aerosol radiative forcing estimation. To inform the development of an aerosol subgrid variability parameterization, here we analyze the aerosol SGV over the southern Pacific Ocean simulated by the high‐resolution Weather Research and Forecasting model coupled to Chemistry. We find that within a typical GCM grid, the aerosol mass subgrid standard deviation is 15% of the grid‐box mean mass near the surface on a 1 month mean basis. The fraction can increase to 50% in the free troposphere. The relationships between the sea‐salt mass concentration, meteorological variables, and sea‐salt emission rate are investigated in both the clear and cloudy portion. Under clear‐sky conditions, marine aerosol subgrid standard deviation is highly correlated with the standard deviations of vertical velocity, cloud water mixing ratio, and sea‐salt emission rates near the surface. It is also strongly connected to the grid box mean aerosol in the free troposphere (between 2 km and 4 km). In the cloudy area, interstitial sea‐salt aerosol mass concentrations are smaller, but higher correlation is found between the subgrid standard deviations of aerosol mass and vertical velocity. Additionally, we find that decreasing the model grid resolution can reduce the marine aerosol SGV but strengthen the correlations between the aerosol SGV and the total water mixing ratio (sum of water vapor, cloud liquid, and cloud ice mixing ratios).

An Ensemble 4D-Seismic History-Matching Framework With Sparse Representation Based On Wavelet Multiresolution Analysis

SummaryIn this work, we propose an ensemble 4D-seismic history-matching framework for reservoir characterization. Compared with similar existing frameworks in the reservoir-engineering community, the proposed one consists of some relatively new ingredients, in terms of the type of seismic data in choice, wavelet multiresolution analysis for the chosen seismic-data and related-data noise estimation, and the use of recently developed iterative ensemble history-matching algorithms.Typical seismic data used for history matching, such as acoustic impedance, are inverted quantities, whereas extra uncertainties may arise during the inversion processes. In the proposed framework, we avoid such intermediate inversion processes. In addition, we also adopt wavelet-based sparse representation to reduce data size. Concretely, we use intercept and gradient attributes derived from amplitude vs. angle (AVA) data, apply multilevel discrete wavelet transforms (DWTs) to attribute data, and estimate noise level of resulting wavelet coefficients. We then select the wavelet coefficients above a certain threshold value, and history match these leading wavelet coefficients with an iterative ensemble smoother (iES).As a proof-of-concept study, we apply the proposed framework to a 2D synthetic case originated from a 3D Norne field model. The reservoir-model variables to be estimated are permeability (PERMX) and porosity (PORO) at each active gridblock. A rock-physics model is used to calculate seismic parameters (velocity and density) from reservoir properties (porosity, fluid saturation, and pressure); then, reflection coefficients are generated with a linearized AVA equation that involves velocity and density. AVA data are obtained by computing the convolution between reflection coefficients and a Ricker wavelet function. The multiresolution analysis applied to the AVA attributes helps to obtain a good estimation of noise level and substantially reduce the data size. We compare history-matching performance in three scenarios: (S1) with production data only, (S2) with seismic data only, and (S3) with both production and seismic data. In either Scenario S2 or Scenario S3, we also inspect two sets of experiments, one with the original seismic data (full-data experiment) and the other adopting sparse representation (sparse-data experiment). Our numerical results suggest that, in this particular case study, the use of production data largely improves the estimation of permeability, but has little effect on the estimation of porosity. Using seismic data only improves the estimation of porosity, but not that of permeability. In contrast, using both production and 4D-seismic data improves the estimation accuracies of both porosity and permeability. Moreover, in either Scenario S2 or Scenario S3, provided that a certain stopping criterion is equipped in the iES, adopting sparse representation results in better history-matching performance than using the original data set.

The Bubble Box: Towards an Automated Visual Sensor for 3D Analysis and Characterization of Marine Gas Release Sites.

Several acoustic and optical techniques have been used for characterizing natural and anthropogenic gas leaks (carbon dioxide, methane) from the ocean floor. Here, single-camera based methods for bubble stream observation have become an important tool, as they help estimating flux and bubble sizes under certain assumptions. However, they record only a projection of a bubble into the camera and therefore cannot capture the full 3D shape, which is particularly important for larger, non-spherical bubbles. The unknown distance of the bubble to the camera (making it appear larger or smaller than expected) as well as refraction at the camera interface introduce extra uncertainties. In this article, we introduce our wide baseline stereo-camera deep-sea sensor bubble box that overcomes these limitations, as it observes bubbles from two orthogonal directions using calibrated cameras. Besides the setup and the hardware of the system, we discuss appropriate calibration and the different automated processing steps deblurring, detection, tracking, and 3D fitting that are crucial to arrive at a 3D ellipsoidal shape and rise speed of each bubble. The obtained values for single bubbles can be aggregated into statistical bubble size distributions or fluxes for extrapolation based on diffusion and dissolution models and large scale acoustic surveys. We demonstrate and evaluate the wide baseline stereo measurement model using a controlled test setup with ground truth information.

Fractional order fuzzy terminal sliding mode control of aerodynamics load simulator

Fractional order adaptive fuzzy continuous non-singular terminal sliding mode control is proposed for electrical aerodynamics load simulator system which is subjected to extra torque disturbance and parametric uncertainties. A fractional order sliding surface is constructed and a continuous non-singular terminal sliding mode control law is derived to ensure faster convergence and precise control without singularity problem. Fractional order adaptive fuzzy logic system is used to estimate the unknown extra torque disturbance. Moreover, nonlinear friction is compensated using LuGre model. Practically, electrical aerodynamics load simulator system is affected by additional un-modeled dynamics due to uncertainty in system parameters and friction model combined with fuzzy approximation error. The un-modeled dynamics are compensated using fractional order adaptive law which is derived using Lyapunov function. The validity and effectiveness of proposed control scheme are verified using numerical simulations.

Bayesian calibration of power plant models for accurate performance prediction

Abstract Gas turbine combined cycles are expected to play an increasingly important role in the balancing of supply and demand in future energy markets. Thermodynamic modeling of these energy systems is frequently applied to assist in decision making processes related to the management of plant operation and maintenance. In most cases, model inputs, parameters and outputs are treated as deterministic quantities and plant operators make decisions with limited or no regard of uncertainties. As the steady integration of wind and solar energy into the energy market induces extra uncertainties, part load operation and reliability are becoming increasingly important. In the current study, methods are proposed to not only quantify various types of uncertainties in measurements and plant model parameters using measured data, but to also assess their effect on various aspects of performance prediction. The authors aim to account for model parameter and measurement uncertainty, and for systematic discrepancy of models with respect to reality. For this purpose, the Bayesian calibration framework of Kennedy and O’Hagan is used, which is especially suitable for high-dimensional industrial problems. The article derives a calibrated model of the plant efficiency as a function of ambient conditions and operational parameters, which is also accurate in part load. The article shows that complete statistical modeling of power plants not only enhances process models, but can also increases confidence in operational decisions.

Peculiar velocity decomposition, redshift space distortion, and velocity reconstruction in redshift surveys: The methodology

Massive spectroscopic surveys will measure the redshift space distortion (RSD) induced by galaxy peculiar velocity to unprecedented accuracy and open a new era of precision RSD cosmology. We develop a new method to improve the RSD modeling and to carry out robust reconstruction of the 3D large scale peculiar velocity through galaxy redshift surveys, in light of RSD. (1) We propose a mathematically unique and physically motivated decomposition of peculiar velocity into three eigencomponents: an irrotational component completely correlated with the underlying density field (${\mathbf{v}}_{\ensuremath{\delta}}$), an irrotational component uncorrelated with the density field (${\mathbf{v}}_{S}$), and a rotational (curl) component (${\mathbf{v}}_{B}$). The three components have different origins, different scale dependences, and different impacts on RSD. (2) This decomposition has the potential to simplify and improve the RSD modeling. (i) ${\mathbf{v}}_{B}$ damps the redshift space clustering. (ii) ${\mathbf{v}}_{S}$ causes both damping and enhancement to the redshift space power spectrum ${P}^{s}(k,u)$. Nevertheless, the leading order contribution to the enhancement has a ${u}^{4}$ directional dependence, distinctively different from the Kaiser formula. Here, $u\ensuremath{\equiv}{k}_{z}/k$, $k$ is the amplitude of the wave vector, and ${k}_{z}$ is the component along the line of sight. (iii) ${\mathbf{v}}_{\ensuremath{\delta}}$ is of the greatest importance for the RSD cosmology. We find that the induced redshift clustering shows a number of important deviations from the usual Kaiser formula. Even in the limit of ${\mathbf{v}}_{S}\ensuremath{\rightarrow}0$ and ${\mathbf{v}}_{B}\ensuremath{\rightarrow}0$, the leading order contribution $\ensuremath{\propto}(1+f\stackrel{\texttildelow{}}{W}(k){u}^{2}{)}^{2}$. It differs from the Kaiser formula by a window function $\stackrel{\texttildelow{}}{W}(k)$. Nonlinear evolution generically drives $\stackrel{\texttildelow{}}{W}(k)\ensuremath{\le}1$. We hence identify a significant systematical error causing underestimation of the structure growth parameter $f$ by as much as $O(10%)$ even at a relatively large scale $k=0.1h/\mathrm{Mpc}$. (iv) The velocity decomposition reveals the three origins of the ``finger-of-God'' (FOG) effect and suggests how to simplify and improve the modeling of FOG by treating the three components separately. (v) We derive a new formula for the redshift space power spectrum. Under the velocity decomposition scheme, all high order Gaussian corrections and non-Gaussian corrections of order ${\ensuremath{\delta}}^{3}$ can be taken into account without introducing extra model uncertainties. Here $\ensuremath{\delta}$ is the nonlinear overdensity. (3) The velocity decomposition clarifies issues in peculiar velocity reconstruction through 3D galaxy distribution. We discuss two possible ways to carry out the 3D ${\mathbf{v}}_{\ensuremath{\delta}}$ reconstruction. Both use the otherwise troublesome RSD in velocity reconstruction as a valuable source of information. Both have the advantage of rendering the reconstruction of a stochastic 3D field into the reconstruction of a deterministic window function ${W}^{s}(k,u)$ of limited degrees of freedom. Both can automatically and significantly alleviate the galaxy bias problem and, in the limit of a deterministic galaxy bias, completely overcome it. Part 1 of this series of works lays out the methodology. Companion papers Y. Zheng et al. (in preparation). will extensively evaluate its performance against N-body simulations.

On redundant types and Bayesian formulation of incomplete information

A type structure is non-redundant if no two types of a player represent the same hierarchy of beliefs over the given set of basic uncertainties, and it is redundant otherwise. Under a mild necessary and sufficient condition termed separativity, we show that any redundant structure can be identified with a non-redundant structure with an extended space of basic uncertainties. The belief hierarchies induced by the latter structure, when “marginalized,” coincide with those induced by the former. We argue that redundant structures can provide different Bayesian equilibrium predictions only because they reflect a richer set of uncertainties entertained by players but unspecified by the analyst. The analyst shall make use of a non-redundant structure, unless he believes that he misspecified the players' space of basic uncertainties. We also consider bounding the extra uncertainties by the action space for Bayesian equilibrium predictions.