First-order Index Research Articles

Model parameter influence on probabilistic flood risk analysis

Flood risk models are critical for effective evidence-based flood management interventions. Risk models typically analyse flood hazards, elements (e.g., buildings) exposed, and their susceptibility to monetary losses. These model parameters are inherently uncertain and their interactions within a risk model create an uncertain loss outcome. This study constructed an object-level probabilistic flood risk model for Westport (New Zealand) to analyse parameter uncertainty and sensitivities for residential building monetary loss prediction. Several model parameter combinations were assessed: 1) water depth spatial sampling method, 2) replacement valuation method, and 3) univariable and multivariable vulnerability model. Monetary loss uncertainty was analysed using test models that varied parameter combinations. Sensitivity to parameter uncertainty distributions were assessed using a global sensitivity analysis based on Sobol's method. Monetary loss estimates ranged between ± NZD 1 million to ± NZD 6 million (90 % confidence interval) for test models by varying parameter combinations. Loss estimates ranged from 2 % to 100 % across the analysed test models. Replacement valuation and vulnerability models were the primary drivers of loss uncertainty. Sobol first-order indices confirmed vulnerability models had the largest parameter influence on uncertainty while total-order indices showed replacement value has a larger overall contribution. The study outcomes emphasise flood risk modellers' need to investigate model uncertainties to inform accuracy improvement solutions.

Co-Occurrence, Extension, and Social Salience: The Emergence of Indexicality in an Artificial Language.

We investigated the emergence of sociolinguistic indexicality using an artificial-language-learning paradigm. Sociolinguistic indexicality involves the association of linguistic variants with nonlinguistic social or contextual features. Any linguistic variant can acquire "constellations" of such indexical meanings, though they also exhibit an ordering, with first-order indices associated with particular speaker groups and higher-order indices targeting stereotypical attributes of those speakers. Much natural-language research has been conducted on this phenomenon, but little experimental work has focused on how indexicality emerges. Here, we present three miniature artificial-language experiments designed to break ground on this question. Results show ready formation of first-order indexicality based on co-occurrence alone, with higher-order indexicality emerging as a result of extension to new speaker groups, modulated by the perceived practical importance of the indexed socialfeature.

Uncertainty and sensitivity analysis of building-stock energy models: sampling procedure, stock size and Sobol’ convergence

Despite broad recognition of the need for applying Uncertainty (UA) and Sensitivity Analysis (SA) to Building-Stock Energy Models (BSEMs), limited research has been done. This article proposes a scalable methodology to apply UA and SA to BSEMs, with an emphasis on important methodological aspects: input parameter sampling procedure, minimum required building stock size and number of samples needed for convergence. Applying UA and SA to BSEMs requires a two-step input parameter sampling that samples ‘across stocks’ and ‘within stocks’. To make efficient use of computational resources, practitioners should distinguish between three types of convergence: screening, ranking and indices. Nested sampling approaches facilitate comprehensive UA and SA quality checks faster and simpler than non-nested approaches. Robust UA-SA's can be accomplished with relatively limited stock sizes. The article highlights that UA-SA practitioners should only limit the UA-SA scope after very careful consideration as thoughtless curtailments can rapidly affect UA-SA quality and inferences. Abbreviations, definitions and indices BEM: Building Energy Model; BSEM: Building-Stock Energy Model; UA: Uncertainty Analysis focuses on how uncertainty in the input parameters propagates through the model and affects the model output parameter(s); SA: Sensitivity Analysis is the study of how uncertainty in the output of a model (numerical or otherwise) can be apportioned to different sources of uncertainty in the model input factors; GSA: Global Sensitivity Analysis (e.g. Sobol’ SA);LSA: Local Sensitivity Analysis (e.g. OAT); OAT: One-At-a-Time; LOD: Level of Development; : The model output; : The -th model input parameter and denotes the matrix of all model input parameters but ; : The first-order sensitivity index, which represents the expected amount of variance reduction that would be achieved for , if was specified exactly. The first-order index is a normalized index (i.e. always between 0 and 1); : The total-order sensitivity index, which represents the expected amount of variance that remains for , if all parameters were specified exactly, but . It takes into account the first and higher-order effects (interactions) of parameters and can therefore be seen as the residual uncertainty; : The higher-order effects index is calculated as the difference between and and is a measure of how much is involved in interactions with any other input factor; : The second order sensitivity index, which represents the fraction of variance in the model outcome caused by the interaction of parameter pair (,); M: Mean (µ); SD: Standard deviation (σ); Mo: Mode; n: number of buildings in the modelled stock;N: number of samples (i.e. matrices of or stock model runs; batches of or are required to calculate Sobol’ indices); K: number of uncertain parameters; ME: number of model evaluations (i.e. stocks to be calculated); *: Table 1: Aleatory uncertainty: Uncertainty due to inherent or natural variation of the system under investigation;Epistemic uncertainty: Uncertainty resulting from imperfect knowledge or modeller error; can be quantified and reduced.

Spatial heterogeneity effects on land surface modeling of water and energy partitioning

Abstract. Understanding the influence of land surface heterogeneity on surface water and energy fluxes is crucial for modeling earth system variability and change. This study investigates the effects of four dominant heterogeneity sources on land surface modeling, including atmospheric forcing (ATM), soil properties (SOIL), land use and land cover (LULC), and topography (TOPO). Our analysis focused on their impacts on the partitioning of precipitation (P) into evapotranspiration (ET) and runoff (R), partitioning of net radiation into sensible heat and latent heat, and corresponding water and energy fluxes. An initial set of 16 experiments were performed over the continental US (CONUS) using the E3SM land model (ELMv1) with different combinations of heterogeneous and homogeneous datasets. The Sobol' total and first-order sensitivity indices were utilized to quantify the relative importance of the four heterogeneity sources. Sobol' total sensitivity index measures the total heterogeneity effects induced by a given heterogeneity source, consisting of the contribution from its own heterogeneity (i.e., the first-order index) and its interactions with other heterogeneity sources. ATM and LULC are the most dominant heterogeneity sources in determining spatial variability of water and energy partitioning, mainly contributed by their own heterogeneity and slightly contributed by their interactions with other heterogeneity sources. Their heterogeneity effects are complementary, both spatially and temporally. The overall impacts of SOIL and TOPO are negligible, except TOPO dominates the spatial variability of R/P across the transitional climate zone between the arid western and humid eastern CONUS. Accounting for more heterogeneity sources improves the simulated spatial variability of water and energy fluxes when compared with ERA5-Land reanalysis dataset. An additional set of 13 experiments identified the most critical components within each heterogeneity source, which are precipitation, temperature, and longwave radiation for ATM, soil texture, and soil color for SOIL and maximum fractional saturated area parameter for TOPO.

Health Evaluation Model of higher Education based on optimized BP Neural Network Model

This paper mainly studies the comprehensive evaluation of the development level of higher education system, and establishes the health evaluation model and sustainable evaluation model. First of all, this paper divides the indicators of higher education into three aspects, collects the data of 7 countries with different development levels, and establishes 11 indicators for evaluating the development quality of higher education. Principal component analysis is used to reduce 11 secondary indicators to 3 first-level indicators. Secondly, the BP neural network is used to construct three first-order indexes as input vectors, and genetic algorithm is used to improve the accuracy and convergence of the model.

Integrating hydrogeological and second-order geo-electric indices in groundwater vulnerability mapping: A case study of alluvial environments

AVI (Aquifer vulnerability index), GOD (groundwater occurrence, overlying lithology and depth to the aquifer), GLSI (geo-electric layer susceptibility indexing) and S (longitudinal unit conductance) models were used to assess economically exploitable groundwater resource in the coastal environment of Akwa Ibom State, southern Nigeria. The models were employed in order to delineate groundwater into its category of vulnerability to contamination sources using the first- and second-order geo-electric indices as well as hydrogeological inputs. Vertical electrical sounding technique employing Schlumberger electrode configuration was carried out in 16 locations, close to logged boreholes with known aquifer core samples. Primary or first-order geo-electric indices (resistivity, thickness and depth) measured were used to determine S. The estimated aquifer hydraulic conductivity, K, calculated from grain size diameter and water resistivity values were used to calculate hydraulic resistance (C) used to estimate AVI. With the indices assigned to geo-electric parameters on the basis of their influences, GOD and FSLI were calculated using appropriate equations. The geologic sequence in the study area consists of geo-electric layers ranging from motley topsoil, argillites (clayey to fine sands) and arenites (medium to gravelly sands). Geo-electric parametric indices of aquifer overlying layers across the survey area were utilized to weigh the vulnerability of the underlying water-bearing resource to the contaminations from surface and near-surface, using vulnerability maps created. Geo-electrically derived model maps reflecting AVI, BOD, FLSI and S were compared to assess their conformity to the degree of predictability of groundwater vulnerability. The AVI model map shows range of values of log C ( −3.46—0.07) generally less than unity and hence indicating high vulnerability. GOD model tomographic map displays a range of 0.1–0.3, indicating that the aquifer with depth range of 20.5 to 113.1 m or mean depth of 72. 3 m is lowly susceptible to surface and near-surface impurities. Again, the FLSI map displays a range of FLSI index of 1.25 to 2.75, alluding that the aquifer underlying the protective layer has a low to moderate vulnerability. The S model has values ranging from 0.013 to 0.991S. As the map indicates, a fractional portion of the aquifer at the western (Ikot Abasi) part of the study area has moderate to good protection (moderate vulnerability) while weak to poor aquifer protection (high vulnerability) has poor protection. The S model in this analysis seems to overstate the degree of susceptibility to contamination than the AVI, GOD and GLSI models. From the models, the categorization of severity of aquifer vulnerability to contaminations is relatively location-dependent and can be assessed through the model tomographic maps generated.

Global sensitivity analysis for a prediction model of soil solute transfer into surface runoff

The solute transfer from soil to surface runoff has been recognized as a major source of non-point source pollution, and it is of great significance to predict the solute transfer process using a modeling approach. Tong et al. (2010) developed a two-layer soil mixing model with a soil mixing layer and a layer of ponding-runoff water on soil surface. The model has three critical parameters, i.e., depth dmix of the soil mixing layer and incomplete mixing parameters α and γ that determine solute concentration in the ponding-runoff layer and the soil layer beneath the soil mixing layer, respectively. Using the variance-based Sobol’s methods, a global sensitivity analysis (GSA) was performed for this model to determine importance or influence of the three parameters to the model prediction of solute transfer from soil to surface runoff αCw(t). The GSA evaluated the time-varying first order index (FOI), second order index (SOI), third order index (DOI), total order index (TOI), and TOI-FOI for cases 1, 2 and 3, i.e., initially unsaturated soil with controlled sub-surface drainage, initially saturated soil with controlled sub-surface drainage, and initially saturated soil with restricted sub-surface drainage. The FOIs of α and dmix varied oppositely, and the interactions between α and dmix became stronger with time for three cases. For cases 1 and 2, γ was important for the predicted αCw(t), which was the most important at later time, and it had strong interactions with α and dmix. γ was found to be the most sensitive and important parameter for the predicted αCw(t) all the time for case 1. However, in case 3, γ was not sensitive to the predicted αCw(t), with almost no interactions of γ with α or dmix, where γ can be set as a constant.

Adaptive use of replicated Latin Hypercube Designs for computing Sobol’ sensitivity indices

As recently pointed out in the field of Global Sensitivity Analysis (GSA) of computer simulations, the use of replicated Latin Hypercube Designs (rLHDs) is a cost-saving alternative to regular Monte Carlo sampling to estimate first-order Sobol’ indices. Indeed, two rLHDs are sufficient to compute the whole set of those indices regardless of the number of input variables. This relies on a permutation trick which, however, only works within the class of estimators called Oracle 2. In the present paper, we show that rLHDs are still beneficial to another class of estimators, called Oracle 1, which often outperforms Oracle 2 for estimating small and moderate indices. Even though unlike Oracle 2 the computation cost of Oracle 1 depends on the input dimension, the permutation trick can be applied to construct an averaged (triple) Oracle 1 estimator whose great accuracy is presented on a numerical example.Thus, we promote an adaptive rLHDs-based Sobol’ sensitivity analysis where the first stage is to compute the whole set of first-order indices by Oracle 2. If needed, the accuracy of small and moderate indices can then be reevaluated by the averaged Oracle 1 estimators. This strategy, cost-saving and guaranteeing the accuracy of estimates, is applied to a computer model from the nuclear field.

Iterative estimation of Sobol’ indices based on replicated designs

In the field of sensitivity analysis, Sobol’ indices are widely used to assess the importance of the inputs of a model to its output. Among the methods that estimate these indices, the replication procedure is noteworthy for its efficient cost. A practical problem is how many model evaluations must be performed to guarantee a sufficient precision on the Sobol’ estimates. The present paper tackles this issue by rendering the replication procedure iterative. The idea is to enable the addition of new model evaluations to progressively increase the accuracy of the estimates. These evaluations are done at points located in under-explored regions of the experimental designs, but preserving their characteristics. The key feature of this approach is the construction of nested space-filling designs. For the estimation of first-order indices, a nested Latin hypercube design is used. For the estimation of closed second-order indices, two constructions of a nested orthogonal array design are proposed. Regularity and uniformity properties of the nested designs are studied.

The Social Meaning Potential of the Global English Based on Data from Different Communities

This paper describes the social value of the global English language as identified in the investigations of various communities worldwide and shows how the social meanings of English relate to each other in a broader ideological field universal for today’s locally global world. The notions of indexical field (Eckert 2008) and bivalent indexicality (Cotter, Valentinsson 2018) are applied in the analysis. The aim of the study is to synthesize results obtained by different researchers from different ideological and communicative contexts and to explore the indexical potential of English, including its local varieties and mixed speech styles. The study is based on a qualitative analysis of a corpus of secondary sources, consisting of a total of 74 scholarly publications from the Expanding Circle communities, which were published in English in 1990–2020 (most of them during the second decade of the 21st century).In total, more than 50 social meanings of the global English language have been identified. It is likely that the abundance of social associations with English is due to the strong first-order indexes. Hence, the social meanings were grouped into the following nine indexical categories based on the presumed first-order sociocultural indexicalities: British and American culture; International sphere; Technologies, science and education; Economic and social status; Personal capital; Youth; Popular culture and media; Urban sphere; and Male. Positive social meanings dominate the indexicalities, but for some of them, bivalent indexicality (presence of contradictory positive and negative values) has been recorded. Although there is much overlap between these relative categories, the constellation as a whole is interpreted as a complex of several separate and multivalent indexical fields. It is to be hoped that this study not only illustrates that the notion of indexical field is applicable for analysis of the imagined global community of users of English, but also provides a broader ideological context for further research of the social meaning-making potential of the global English language.

Uncertainty and sensitivity analyses of co-combustion/pyrolysis of textile dyeing sludge and incense sticks: Regression and machine-learning models

Bioenergy generation from biomass waste through co-combustion/pyrolysis fulfills simultaneously multiple objectives of reductions in fossil fuel use, greenhouse gas emission, and solid waste stream. This experimental study aimed to quantify the multiple co-combustion/pyrolysis responses of textile dyeing sludge (TDS) and incense sticks (IS) as a function of blend ratio (BR), heating rate (HR), atmosphere type (Atm), and temperature (Temp). Joint optimizations, and predictor importance, sensitivity, uncertainty and interaction analyses were conducted using data-driven models for the responses of remaining mass (RM), derivative thermogravimetry (DTG), and differential scanning calorimetry (DSC). The data-driven models compared in this study were Box Behnken design (BBD)-based regression models, general linear models (GLM), and the six full models with all the predictors included of multivariate adaptive regression splines, multiple linear regressions, random forests (RF), regression decision tree (RDT), RDT with ensemble and bagger, and gradient boosting machine. BBD, GLM, and Sobol’s total and first-order indices indicated HR as the most important and sensitive predictor in the joint optimizations. GLM pointed to a three-way interaction among HR, BR, and Atm, while BBD, and Sobol’s second-order index showed a two-way interaction between HR and BR as the most important ones. RF outperformed the other full models for all the responses in terms of validation metrics. RF showed the two most important predictors as Temp and BR for RM; HR and Temp for DSC; and Temp and HR for DTG, respectively, which also constituted the most important two-way interactions.

Multi-Resolution Sensitivity Analysis of Model of Immune Response to Helicobacter pylori Infection via Spatio-Temporal Metamodeling

Computational immunology studies the interactions between the components of the immune system that includes the interplay between regulatory and inflammatory elements. It provides a solid framework that aids the conversion of pre-clinical and clinical data into mathematical equations to enable modeling and in silico experimentation. The modeling-driven insights shed lights on some of the most pressing immunological questions and aid the design of fruitful validation experiments. A typical system of equations, mapping the interaction among various immunological entities and a pathogen, consists of a high-dimensional input parameter space that could drive the stochastic system outputs in unpredictable directions. In this paper, we perform spatio-temporal metamodel-based sensitivity analysis of immune response to Helicobacter pylori infection using the computational model developed by the ENteric Immune SImulator. We propose a two-stage procedure to obtain the estimates of the Sobol’ total and first-order indices for each input parameter, for quantifying their time-varying impacts on each output of interest. In particular, we fully reuse and exploit information from an existing simulated dataset, develop a novel sampling design for constructing the two-stage metamodels, and perform metamodel-based sensitivity analysis. The proposed procedure is scalable, easily interpretable, and adaptable to any multi-input multi-output complex systems of equations with a high-dimensional input parameter space.

Probabilistic evaluation of above-zone pressure and geochemical monitoring for leakage detection at geological carbon sequestration site

Above-zone monitoring has been proposed as a promising technique for monitoring geological carbon sequestration (GCS) projects for storage integrity. This study presents a probabilistic framework to assess and compare effectiveness of above-zone monitoring of pressure and geochemical parameters for the pilot GCS project at the Cranfield site. Pressure responses in the above-zone monitoring interval (AZMI) to leaks were modeled with a single-phase flow equation and solved analytically and geochemical responses were modeled with a solute transport equation coupled with geochemical reactions, such as mineral dissolution, aqueous complexation, cation exchange, caused by intrusion of the leaked fluids having lower pH and solved semi-analytically. A total of one million realizations were generated using the Monte-Carlo method in terms of 11 parameters required to calculate pressure and geochemical responses to leaks in the AZMI. For each individual realization, time to detect leaks in the AZMI was estimated with pressure with threshold values 200 MPa, 2000 MPa, and 10000 MPa or geochemical parameter (dissolved CO2 in groundwater) with threshold values of 2.33 mmol/kg H2O, 2.82 mmol/kg H2O, 6.94 mmol/kg H2O as indicator and further analyzed statistically over the one million realizations. Our results show that pressure monitoring can detect more than 90% of the leaks whereas geochemical monitoring can detect only up to 50% of the leaks. Detection time ranges from several hours to 200 days for pressure monitoring and from 1 year to 30 years for geochemical monitoring, suggesting that pressure monitoring can provide much early leakage detection. The local relative and global sensitivity analyses were conducted to rank relative importance of the model parameters. Our results show that detection time is sensitive to distance of monitoring well, leakage rate, thickness of the AZMI, and permeability. The global sensitivity analysis shows that the total indices are much higher than the first-order indices, indicating that interactions among the model parameters are crucial to detection time. The probabilistic framework presented in this study can be easily applied to the site configurations of other commercial-scale GCS projects.

Probability models for data-Driven global sensitivity analysis

This paper presents a probability model-based global sensitivity analysis (PM-GSA) framework, to compute various Sobol’ indices when only input-output data are available. The PM-GSA framework consists of two main elements, namely data extraction and probability model training. The data extraction step extracts data of the variables of interest (VoI) and quantity of interest (QoI) from an input-output data matrix. Following that, a probability model is built to approximate the joint probability density function between the VoI and QoI. The learned probability model is then used to compute various Sobol’ indices. The implementation of the PM-GSA framework is investigated through three probability models including Gaussian copula model, Gaussian mixture model, and a new Gaussian mixture copula model. The number of dimensions of the probability model in the PM-GSA framework, is independent of the number of input variables and is always N+1 (e.g. 2 for the first-order index), where N is the order of the Sobol’ index. In addition, the PM-GSA framework is applicable to global sensitivity analysis with not only independent input variables, but also with dependent input variables and for sets of variables. Four numerical examples are used to demonstrate the effectiveness of the proposed method and analyze the advantages and disadvantages of the different probability models.

An efficient modularized sample-based method to estimate the first-order Sobol׳ index

Sobol׳ index is a prominent methodology in global sensitivity analysis. This paper aims to directly estimate the Sobol׳ index based only on available input–output samples, even if the underlying model is unavailable. For this purpose, a new method to calculate the first-order Sobol׳ index is proposed. The innovation is that the conditional variance and mean in the formula of the first-order index are calculated at an unknown but existing location of model inputs, instead of an explicit user-defined location. The proposed method is modularized in two aspects: 1) index calculations for different model inputs are separate and use the same set of samples; and 2) model input sampling, model evaluation, and index calculation are separate. Due to this modularization, the proposed method is capable to compute the first-order index if only input–output samples are available but the underlying model is unavailable, and its computational cost is not proportional to the dimension of the model inputs. In addition, the proposed method can also estimate the first-order index with correlated model inputs. Considering that the first-order index is a desired metric to rank model inputs but current methods can only handle independent model inputs, the proposed method contributes to fill this gap.

Replication procedure for grouped Sobol' indices estimation in dependent uncertainty spaces

This paper deals with the estimation of grouped Sobol' indices in the case where the dependence inside each group is given by sets of linear ordered constraints. In the framework of independent inputs, the replication method allows to estimate first-order indices with only two designs. Through the use of orthogonal arrays of strength two the replication method can be applied to estimate closed second-order indices. We extend this methodology to estimate first-order and closed second-order grouped Sobol' indices under sets of linear constraints. The construction of the two designs required by the replication method is now based on the simplex geometric structure to handle the constraints within each set. We propose a space filling strategy to construct these designs.

Second-order properties of tail probabilities of sums and randomly weighted sums

Let X1, … , Xn be independent nonnegative random variables with respective survival functions \(\overline {F}_{1}, \ldots , \overline {F}_{n}\), and let Θ1, … , Θn be (not necessarily independent) nonnegative random variables, independent of X1, … , Xn, satisfying certain moment conditions. This paper consists of two parts. In the first part, we investigate second-order expansions of 𝗣 \( \left ({\sum }^{n}_{i=1} X_{i}>t\right )\) as \(t\to {\infty }\) under the assumption that the \(\overline {F}_{i}\) are of second-order regular variation (2RV) with the same first-order index but with different second-order indexes. In the second part, under the assumption that the \(\overline {F}_{1}=\cdots =\overline {F}_{n}\) have 2RV tails, second-order expansions of tail probabilities of the randomly weighted sum \({\sum }^{n}_{i=1} {\Theta }_{i} X_{i}\) are studied. The closure property of 2RV under randomly weighted sum is also discussed. The main results in this paper generalize and strengthen several known results in the literature.

Parameter identification and global sensitivity analysis of Xin'anjiang model using meta-modeling approach

Parameter identification, model calibration, and uncertainty quantification are important steps in the model-building process, and are necessary for obtaining credible results and valuable information. Sensitivity analysis of hydrological model is a key step in model uncertainty quantification, which can identify the dominant parameters, reduce the model calibration uncertainty, and enhance the model optimization efficiency. There are, however, some shortcomings in classical approaches, including the long duration of time and high computation cost required to quantitatively assess the sensitivity of a multiple-parameter hydrological model. For this reason, a two-step statistical evaluation framework using global techniques is presented. It is based on (1) a screening method (Morris) for qualitative ranking of parameters, and (2) a variance-based method integrated with a meta-model for quantitative sensitivity analysis, i.e., the Sobol method integrated with the response surface model (RSMSobol). First, the Morris screening method was used to qualitatively identify the parameters' sensitivity, and then ten parameters were selected to quantify the sensitivity indices. Subsequently, the RSMSobol method was used to quantify the sensitivity, i.e., the first-order and total sensitivity indices based on the response surface model (RSM) were calculated. The RSMSobol method can not only quantify the sensitivity, but also reduce the computational cost, with good accuracy compared to the classical approaches. This approach will be effective and reliable in the global sensitivity analysis of a complex large-scale distributed hydrological model.

Sensitivity analysis of complex models: Coping with dynamic and static inputs

In this paper, we address the issue of conducting a sensitivity analysis of complex models with both static and dynamic uncertain inputs. While several approaches have been proposed to compute the sensitivity indices of the static inputs (i.e. parameters), the one of the dynamic inputs (i.e. stochastic fields) have been rarely addressed. For this purpose, we first treat each dynamic as a Gaussian process. Then, the truncated Karhunen–Loève expansion of each dynamic input is performed. Such an expansion allows to generate independent Gaussian processes from a finite number of independent random variables. Given that a dynamic input is represented by a finite number of random variables, its variance-based sensitivity index is defined by the sensitivity index of this group of variables. Besides, an efficient sampling-based strategy is described to estimate the first-order indices of all the input factors by only using two input samples. The approach is applied to a building energy model, in order to assess the impact of the uncertainties of the material properties (static inputs) and the weather data (dynamic inputs) on the energy performance of a real low energy consumption house.

Distributed feedback 3.27 µm diode lasers with continuous‐wave output power above 15 mW at room temperature

GaSb-based type-I quantum well laterally coupled distributed feedback diode lasers emitting in the methane absorption band near 3.27 µm were designed and fabricated. The first-order index grating with a period of 480 nm was defined by e-beam lithography and etched on both sides of 6 µm-wide shallow ridge waveguide. Coated 2 mm-long devices demonstrated stable continuous-wave single-frequency operation in a wide temperature range with an output power of 15 mW at +17°C and 40 mW at −20°C. The Bragg wavelength temperature tuning rate was ∼0.27 nm/K.