Global Sensitivity Analysis Techniques Research Articles

Sensitivity analysis with various parameters in undermoded reverberation chambers

PurposeThe purpose of this paper is to investigate the influence of measurement uncertainties and the environment characteristics themselves on the desired field uniformity (FU) in reverberation chambers (RCs) by means of state-of-the-art global sensitivity analysis techniques. There are many quantities to describe the FU. The authors attempted to inspect many of the most important ones in two different orientations of the stirrer (horizontal, vertical).Design/methodology/approachSurrogate modelling techniques are involved to compute the Sobol’ indices efficiently with a modest number of required electromagnetic (EM) simulations. This can be only achieved if the behaviour of an appropriately chosen output quantity is predictable in such a way, which enables to extract useful information. Therefore, this choice should be made with extra care of the stochastic fluctuations, which have to be as low as possible. To this end, in this paper, various figures of merit are investigated.FindingsThis method can provide useful knowledge in the lower frequency range, where the ideal properties of the EM field in RCs cannot be established, and the importance of the setup parameters can vary from configuration to configuration.Originality/valueConsidering the current research tendencies related to RCs, the application of the method of Sobol’ indices to RCs is unique, which has only been done by the authors of this work so far. The main contribution presented in the paper is the thorough investigation of the effect of configuration parameters on the statistical properties of RCs through many output quantities describing the FU.

Active Learning of Ensemble Polynomial Chaos Expansion Method for Global Sensitivity Analysis

Global sensitivity analysis (GSA) techniques, especially Sobol indices, have gained prominence in assessing the impact of uncertainty across all input variables on the variation of model response. However, GSA can incur intensive computational costs, particularly when dealing with time-consuming models. To address this issue, an ensemble polynomial chaos expansion (EPCE) surrogate model based on an active learning hybrid (ALH) criterion is proposed. The proposed method integrates a weighted combination of multiple sparse PCE surrogate models to formulate the EPCE method. To enhance the performance, the ALH criterion, which balances local exploitation and global exploration, is developed to sequentially select samples for updating the EPCE model. In terms of local exploitation, the model correlation and sensitivity pursuit criteria are derived to identify the local region displaying both the largest discrepancy among multiple sparse PCE methods and the most substantial contribution to the total variance. The ALH criterion also incorporates a minimum distance-based measure for global exploration. The performance of the proposed method is evaluated by four benchmark functions and an engineering application. The numerical studies demonstrate that the proposed method exhibits favorable performance for conducting GSA.

Complex Dynamics and Fractional-Order Optimal Control of an Epidemic Model with Saturated Treatment and Incidence

In this study, we have developed a novel SIR epidemic model by incorporating fractional-order differential equations and utilizing saturated-type functions to describe both disease incidence and treatment. The intricate dynamical characteristics of the proposed model, encompassing the determination of the conditions for the existence of all possible feasible equilibria with their local and global stability criteria, are investigated thoroughly. The model undergoes backward bifurcation with respect to the parameter representing the side effects due to treatment. This phenomenon emphasizes the critical role of treatment control parameters in shaping epidemic outcomes. In addition, to understand the optimal role of the treatment in mitigating the disease prevalence and minimizing the associated cost, we investigated a fractional-order optimal control problem. To further visualize the analytical results, we have conducted simulation works considering feasible parameter values for the model. Finally, we have employed local and global sensitivity analysis techniques to identify the factors that have the greatest potential to reduce the impact of the disease.

Global sensitivity analysis for seismic performance of shear wall with high-strength steel bars and recycled aggregate concrete

In terms of bearing lateral loads, a reinforced concrete shear wall (SW) is one of the most crucial structural elements in structures. Despite their significance, recent experimental research and post-earthquake surveys have exposed the inadequate safety margins of the SWs. Significant SW components cannot be accurately identified due to the absence of empirical and mechanistic models. This study introduces a novel paradigm for assessing the SW's crucial elements by using two consecutive modeling strategies. Initially, a finite element model is calibrated to mimic one of the laboratory-experimented SW structures. Then, deep residual neural networks (DRNNs) for non-parametric techniques are used to enhance the Abaqus software prediction skills and comprehensively understand the input parameters' influence on the selected SW structure's displacement value. The suggested DRNNs' design uses residual shortcuts (i.e., connections) that skip several levels in the deep network structure in order to address the issue of training with high accuracy. A thorough global sensitivity analysis (GSA) is done using the Latin Hypercube Simulation. Three distinct GSA techniques are used to emphasize the influence of each input variable on the amount of displacement in real-world applications while limiting the risk of result misinterpretation owing to interactions between input variables. In each GSA approach, an effort would be made to rank, filter, or map the input variables. The performance metrics of the DRNNs prediction models lend confidence to the GSA's results. The diameter of steel stirrups is reported to be the most significant component in the SW structure, while SW's displacement is more sensitive to higher and lower values of the lateral load domain.

On the selection of Morris trajectories for parametric sensitivity analysis in spectroscopic ellipsometry modeling

Spectroscopic ellipsometry and some other optical metrology techniques, such as reflectometry and scatterometry, are model-based optical measurements and, therefore, require appropriate modeling to determine the geometric and material properties of substrates, thin films, and multilayer structures. Parametric sensitivity analysis (SA) provides essential assistance in the model-building process to quantify the relative importance of model parameters for model output and to identify those with high/little influence. SA can be performed in a variety of ways, and this article discusses an application of the Morris or elementary effect (EE) method, a screening type SA procedure, to spectroscopic ellipsometry modeling. The method is a global SA technique and uses a stepping of m parameters along certain so-called “trajectories” or sequences of points in parameter space, randomly constructed in order to maximally fill the volume of the m-dimensional parameter space. However, it was thought that the EE method relies greatly on a sampling strategy or a way of selecting “optimized trajectories” in the parameter space, i.e., a necessary number of trajectories chosen to be well spread over the space to properly cover the entire realistic ranges of all input factors. Here, we use two sampling methods for selecting trajectories with possibly different distributions and investigate their effects on the estimation of various sensitivity measures in spectroscopic ellipsometry data modeling. The SA results indicate that the performance of the sampling strategy should not be judged only by maximizing the trajectory spread but also include some additional convergence criteria for the sensitivity measures.

Exploring global uncertainty quantification and sensitivity analysis methodologies: CO2 capture absorber model with MEA solvent as a test case

A set of global metamodeling uncertainty quantification (UQ) techniques belonging to non-intrusive and forward propagation categories; Polynomial Chaos Expansion (PCE), Kriging, Canonical Low Rank Approximation (LRA), and Polynomial Chaos Kriging (PC-Kriging) and global sensitivity analysis (SA) techniques, Sobol’ indices, Borgonovo, and Morris were compared to a benchmark methodology of direct Monte Carlo Simulation (MCS). The comparative analysis was demonstrated on a CO2 capture absorber model with MEA solvent. Our analysis concluded as follows; (1) although significant variation in the CO2 capture ratio in the prediction profile is shown, there is no apparent advantage of using a larger sample size via direct MCS except achieving a higher clarity in the output distribution, (2) while a very little effect on the convergence was observed which confirms the number of sample size, the fraction of computational time is enhanced by using Sobol sampling method, (3) the benefit of using metamodeling techniques compared to direct MCS was proven as they provide equal predictions in the output statistical measures with fewer evaluations of the original model and are therefore computationally cheaper, and (4) the global SA results showed Sobol indices is computationally more efficient while sharing similar ranking for the most influential parameter with Borgonovo and Morris.

A two-stages global sensitivity analysis by using the δ sensitivity index in presence of correlated inputs: application on a tumor growth inhibition model based on the dynamic energy budget theory

Global sensitivity analysis (GSA) evaluates the impact of variability and/or uncertainty of the model parameters on given model outputs. GSA is useful for assessing the quality of Pharmacometric model inference. Indeed, model parameters can be affected by high (estimation) uncertainty due to the sparsity of data. Independence between model parameters is a common assumption of GSA methods. However, ignoring (known) correlations between parameters may alter model predictions and, then, GSA results. To address this issue, a novel two-stages GSA technique based on the δ index, which is well-defined also in presence of correlated parameters, is here proposed. In the first step, statistical dependencies are neglected to identify parameters exerting causal effects. Correlations are introduced in the second step to consider the real distribution of the model output and investigate also the ‘indirect’ effects due to the correlation structure. The proposed two-stages GSA strategy was applied, as case study, to a preclinical tumor-in-host-growth inhibition model based on the Dynamic Energy Budget theory. The aim is to evaluate the impact of the model parameter estimate uncertainty (including correlations) on key model-derived metrics: the drug threshold concentration for tumor eradication, the tumor volume doubling time and a new index evaluating the drug efficacy-toxicity trade-off. This approach allowed to rank parameters according to their impact on the output, discerning whether a parameter mainly exerts a causal or ‘indirect’ effect. Thus, it was possible to identify uncertainties that should be necessarily reduced to obtain robust predictions for the outputs of interest.

Improving the Predictivity of a Steam Generator Clogging Numerical Model by Global Sensitivity Analysis and Bayesian Calibration Techniques

In pressurized nuclear reactors, steam generators are massive tubular heat exchangers transferring heat from the primary to the secondary fluid to produce the steam needed by the turbines. After several years of operation, because of deposit, their tube support plates (TSPs) can undergo clogging that may cause important economic and safety issues in case of nonpreventive actions. To understand and predict this phenomenon, several nondestructive examinations can generally be gathered at various times during the heat exchanger operation. A numerical mechanistic model has been recently developed and implemented in a dedicated computer code. The objective of this work is to improve the modeling of the clogging phenomenon to increase the predictive capability of the computer code. A global sensitivity analysis, based on Sobol’ indices, is first performed by the use of a metamodel that is learned on several runs of the computer code. Such an analysis, cast under a physical perspective, helps the identification of the most influential physical parameters and paves the way to a better understanding of TSP clogging. A Bayesian calibration of an epistemic calibration model parameter is then applied to fit the simulation results to experimental data. The additional information coming from the experimental data is then transferred to the calibration parameter with a mathematical model (artificial neural network). The resulting hybrid model thus compensates some lacks of the initial physical model on the considered data set.

Modeling of land use change under the recent climate projections of CMIP6: a case study of Indian river basin.

The aim of the study was to investigate the land use change dynamics under CMIP6 projections using Land Change Modeler(LCM). The Global Sensitivity Analysis (GSA) techniques was applied to quantify the sensitivity of single parameter and combinationof parameters. Land use and land cover (LULC) transitions of the baseline period (2006-2016) was assessed with a model performance accuracy of 80%. Receiver operating characteristic (ROC) analysis shows that the model has performed well for all the LULC classes except builtup land. Prediction under the SSP245 scenario depicts that areal extent of agricultural, forest, and snow, and glacier will decrease by the mid-century (2045). However, the grassland and barren land areawill increase from the baseline period. A similar change pattern with a higher magnitude has also been predicted under SSP585 scenario. The CMIP6 forcing index considers socio-economic effects and LCMpredicted an expansion in barren land which may be attributed to changes in cryosphere in the studied area.

Neighbourhood-level pedestrian navigation using the construal level theory

Pedestrian navigation decisions take place simultaneously at multiple spatial scales. Yet most models of pedestrian behaviour focus either on local physical interactions or optimisation of routes across a road network. We present a novel hierarchical pedestrian route choice framework that integrates dynamic, perceptual decisions at the street level with abstract, network-based decisions at the neighbourhood level. The framework is based on construal level theory which states that decision makers construe decisions based on their psychological distance from the object of the decision. We implement this route choice framework in a spatial agent-based model in which pedestrian and vehicle agents complete trips in an urban environment. Using global sensitivity analysis techniques, we demonstrate the interaction between route choice components representing decision making at different spatial and temporal scales. Additionally, through comparison to a least cost network model, we demonstrate the increased route heterogeneity produced by this approach. This work could form the basis of an alternative method for producing pedestrian route alternatives. The granularity and scale of the modelled pedestrian trajectories could also help improve appraisals of street infrastructure.

Optimization of an Integrated Reservoir-Production System Using Polynomial Chaos Expansion and Sobol Sensitivity Analysis

Summary Integrated reservoir-production modeling is a collaborative multidisciplinary tool that can facilitate optimization of oil and gas production operations during the field development planning stage of exploiting subsurface resources. The critical issue with this technique is the excessive computational burden of the large integrated model with many input variables, which has not been effectively addressed to date. This study aims to reduce the computational costs and runtimes associated with the production integration and optimization process from oil fields. To do so, the reservoir and the surface network models of an Iranian oil field were coupled to create an integrated model for the optimization of field parameters to achieve the highest oil production rate. In the first step of simplification, polynomial chaos expansion (PCE) was used to establish a surrogate model from the integrated system. Next, Sobol sensitivity analysis, which is a variance-based, global, and model-free sensitivity analysis technique, was performed to reduce the number of input variables by identifying the most influential variables. Finally, the optimization was implemented using genetic algorithm (GA) on the PCE surrogate model of the integrated system with the most important variables. The results from the case study showed that the integrated model can be replaced with the PCE surrogate model while the accuracy is maintained. Moreover, performing sensitivity analysis considerably decreased the number of input variables for optimization by revealing their significance. The proposed methodology in this study can substantially improve the computational efficiency of the optimization for the integrated reservoir-production system.

Optimization of CD200 checkpoint immunotherapy for treating glioblastoma.

Glioblastoma Multiforme (GBM) is a lethal brain cancer with a median survival between 10-14 months. The standard of care for GBM is a combination of resection, followed by chemotherapy, and radiotherapy. Recent advances in cancer immunotherapy have significantly improved the survival of patients in selected solid tumors. However, in the case of GBM, current immunotherapy has failed, potentially, due to obstacles including immunosuppressive molecules in the tumor microenvironment. CD200 is an immunosuppressive protein that is overexpressed on tumors suppressing the immune system. The University of Minnesota developed a novel CD200 checkpoint immunotherapy, currently in Phase I clinical trial (NCT04642937), targeting the activation receptors on immune cells with a peptide ligand to overcome its immunosuppressive effect on recurrent GBM. While the treatment shows promising results in patient outcomes, the CD200 mechanism in the dendritic cells is still unclear. In this study, we postulate a detailed pathway and develop an Ordinary Differential Equation model, based on the law of mass action, to describe its behavior. Using Global Sensitivity analysis techniques, we explore the parameter space and identify potential targets on the pathway to optimize the CD200 checkpoint therapy and improve its clinical impact.

Uncertainty quantification and global sensitivity analysis of seismic metabarriers

Seismic metabarriers consist of an array of locally resonant elements (i.e., mechanical resonators) installed over the soil surface, whose design is rationally engineered to reduce ground-induced vibrations and shield vulnerable structures against seismic surface waves. Successful design and implementation of seismic metabarriers require a comprehensive knowledge and characterization of the role played by the model parameters (and their associated uncertainty) governing soil-barrier dynamic interaction. In this context, sensitivity analysis techniques allow assessing the response of a given model through the quantification of the influence and action of model inputs (and model input uncertainties) concerning a target model output. This study relies on global sensitivity analysis techniques to investigate the influence that the uncertainty associated with three key mechanical parameters of a metabarrier (i.e., soil density, soil shear modulus, and mass of mechanical resonators) has on its seismic isolation performance. The latter is measured in terms of transmission coefficient (TC). We do so by employing a two-dimensional wave finite element model developed under the plane-strain conditions to evaluate the dispersion relation and transmission coefficient of a metabarrier interacting with Rayleigh waves in the low-frequency regime (i.e., frequencies between 2 Hz and 7 Hz). Our results suggest that the shear modulus is the uncertain parameter with the most significant influence on the transmission coefficient of the metabarrier across the entire frequency range of interest. Otherwise, the resonator mass plays a substantial role in the frequency range close to the metabarrier resonant frequency.

The impact of a power law-induced memory effect on the SARS-CoV-2 transmission

It is well established that COVID-19 incidence data follows some power law growth pattern. Therefore, it is natural to believe that the COVID-19 transmission process follows some power law. However, we found no existing model on COVID-19 with a power law effect only in the disease transmission process. Inevitably, it is not clear how this power law effect in disease transmission can influence multiple COVID-19 waves in a location. In this context, we developed a completely new COVID-19 model where a force of infection function in disease transmission follows some power law. Furthermore, different realistic epidemiological scenarios like imperfect social distancing among home-quarantined individuals, disease awareness, vaccination, treatment, and possible reinfection of the recovered population are also considered in the model. Applying some recent techniques, we showed that the proposed system converted to a COVID-19 model with fractional order disease transmission, where order of the fractional derivative (α) in the force of infection function represents the memory effect in disease transmission. We studied some mathematical properties of this newly formulated model and determined the basic reproduction number (R0). Furthermore, we estimated several epidemiological parameters of the newly developed fractional order model (including memory index α) by fitting the model to the daily reported COVID-19 cases from Russia, South Africa, UK, and USA, respectively, for the time period March 01, 2020, till December 01, 2021. Variance-based Sobol’s global sensitivity analysis technique is used to measure the effect of different important model parameters (including α) on the number of COVID-19 waves in a location (WC). Our findings suggest that α along with the average transmission rate of the undetected (symptomatic and asymptomatic) cases in the community (β1) are mainly influencing multiple COVID-19 waves in those four locations. Numerically, we identified the regions in the parameter space of α and β1 for which multiple COVID-19 waves are occurring in those four locations. Furthermore, our findings suggested that increasing memory effect in disease transmission (α→ 0) may decrease the possibility of multiple COVID-19 waves and as well as reduce the severity of disease transmission in those four locations. Based on all the results, we try to identify a few non-pharmaceutical control strategies that may reduce the risk of further SARS-CoV-2 waves in Russia, South Africa, UK, and USA, respectively.

SINDy-SA framework: enhancing nonlinear system identification with sensitivity analysis.

Machine learning methods have revolutionized studies in several areas of knowledge, helping to understand and extract information from experimental data. Recently, these data-driven methods have also been used to discover structures of mathematical models. The sparse identification of nonlinear dynamics (SINDy) method has been proposed with the aim of identifying nonlinear dynamical systems, assuming that the equations have only a few important terms that govern the dynamics. By defining a library of possible terms, the SINDy approach solves a sparse regression problem by eliminating terms whose coefficients are smaller than a threshold. However, the choice of this threshold is decisive for the correct identification of the model structure. In this work, we build on the SINDy method by integrating it with a global sensitivity analysis (SA) technique that allows to hierarchize terms according to their importance in relation to the desired quantity of interest, thus circumventing the need to define the SINDy threshold. The proposed SINDy-SA framework also includes the formulation of different experimental settings, recalibration of each identified model, and the use of model selection techniques to select the best and most parsimonious model. We investigate the use of the proposed SINDy-SA framework in a variety of applications. We also compare the results against the original SINDy method. The results demonstrate that the SINDy-SA framework is a promising methodology to accurately identify interpretable data-driven models.Supplementary InformationThe online version contains supplementary material available at 10.1007/s11071-022-07755-2.

Improving deep neural network using hyper-parameters tuning in predicting the bearing capacity of shallow foundations

ABSTRACT Ultimate bearing capacity is one of the most important parameters in designing shallow foundations. This study focused on developing a hybrid model using Random Search (RS) technique and Deep Neural Network (DNN) to predict the maximum bearing capacity of shallow foundations in sandy soil. The data included 97 load tests on the steps that were used to train and test the model. This data is divided into two parts of the training data set (7%) and the testing set (30%) to build and validate the corresponding models. The performance of the final DNN model is comprehensively assessed with a random hyper-parameters DNN model developed independently using the same data. The values of performance evaluation measures such as R-squared (R2), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and the Variance Accounted For (VAF) are used to determine to get the performance of the DNN model in predicting the ultimate bearing capacity of shallow foundations. In addition, a parallel coordinate plot is utilized to show and evaluate the effect of hyperparameters combination on the performance of DNN model. Besides, a global sensitivity analysis technique was deployed to detect the most important input variables in predicting the ultimate bearing capacity of shallow foundations. This study can provide an effective tool to identify the ultimate bearing capacity of shallow foundations.

A framework for uncertainty and sensitivity analysis of district energy systems considering different parameter types

A variety of renewable energy sources, demand side loads, and other factors bring a lot of uncertainties to the operation of district energy systems. However, there is no strict standard for the selection of uncertainty factors. Too much uncertainty, or not enough of it, is not appropriate for the system optimization. In this paper, a method of uncertainty and sensitivity analysis for district energy system is proposed to identify the important uncertainties in the system optimization process. Firstly, the mathematical model of the system is established and the uncertain parameters are screened from technological, economic, environmental and demand-side perspectives. In addition, the selected parameters are divided into two categories according to whether they are time-related, and two methods are adopted to collect samples. Further, a global sensitivity analysis technique is introduced to calculate the sensitivity index of each parameter simultaneously. Case study is performed for a classic district energy system in a typical day of transition season. The sensitivity indexes under different objective functions are also discussed on this basis. The results show that the proposed framework can effectively analyze the uncertain parameters of the system, which can further contribute to the optimal operation decision.

MATHEMATICAL ANALYSIS AND NUMERICAL SIMULATION OF A NONLINEAR DYNAMICAL MODEL FOR THE COEXISTENCE OF AGRICULTURE AND MINING IN RURAL AREAS

Agriculture and mining get interlinked with each other when they take place concurrently in rural parts of the world. In order to explore it in mathematical terms, a nonlinear dynamical model system is proposed in this study with agricultural yield, human population and mining as system variables. The agricultural yield is assumed to have logistic growth and also, supplements rural human population growth. Mining is assumed to be not only advancing with constant rate, but also getting induced through rural human population. The model is qualitatively analyzed for the identification of different equilibrium states and their stability behaviors. The model analysis reveals the conditions under which agriculture and mining together with rural population can achieve a stable system. These qualitative findings are substantiated with quantitative results, under which sensitiveness of different parameters of the model towards the model outcomes are investigated through global sensitivity analysis technique. Also, bifurcation parameters and their critical values are determined to predict the states of qualitative behavioral change. The results suggest that a balanced system can be obtained by taking measures to control unconducive mining and augment agricultural outputs.

Application of Ensemble Learning Using Weight Voting Protocol in the Prediction of Pile Bearing Capacity

Accurate prediction of pile bearing capacity is an important part of foundation engineering. Notably, the determination of pile bearing capacity through an in situ load test is costly and time-consuming. Therefore, this study focused on developing a machine learning algorithm, namely, Ensemble Learning (EL), using weight voting protocol of three base machine learning algorithms, gradient boosting (GB), random forest (RF), and classic linear regression (LR), to predict the bearing capacity of the pile. Data includes 108 pile load tests under different conditions used for model training and testing. Performance evaluation indicators such as R-square (R2), root mean square error (RMSE), and MAE (mean absolute error) were used to evaluate the performance of models showing the efficiency of predicting pile bearing capacity with outstanding performance compared to other models. The results also showed that the EL model with a weight combination of w 1 = 0.482, w 2 = 0.338, and w 3 = 0.18 corresponding to the models GB, RF, and LR gave the best performance and achieved the best balance on all data sets. In addition, the global sensitivity analysis technique was used to detect the most important input features in determining the bearing capacity of the pile. This study provides an effective tool to predict pile load capacity with expert performance.

Use of sensitivity analysis for a determination of dominant design parameters affecting energy efficiency of timber buildings in different climates

A large part of the energy for heating and cooling is consumed due to human needs for thermal comfort in the living environment. It is important to use a suitable method to design an energy-efficient building to satisfy the thermal comfort of residents throughout the year. This paper focuses on the implementation of the sensitivity analysis in the area of energy analysis of a prefabricated timber building on box models. The sensitivity analysis plays an important role in early planning, partially also presenting the energy analysis. A combination of the building energy simulation and the sensitivity analysis technique identifies key variables by order, which can either have a strong or insignificant impact on the further design of the energy efficiency of a building. Moreover, this paper presents a sensitivity analysis method performed on the case study of six different timber building models where design parameters, such as geometry, insulation features, glazing ratio and distribution, shading control and interior set-point temperatures, are varied in environments with different climatic conditions: moderate (Ljubljana), warm (Athens), and cold (Helsinki). The sensitivity analysis for a range of variable input parameters is conducted by using the global sensitivity analysis technique, i.e. the Morris method, which is based on the elementary effect. The main objective of the article is to provide guidance for researchers, professionals and building planners about the parameters they should focus on in the early planning of an energy-efficient timber building to reduce the energy required for heating and cooling, thereby ensuring constant thermal comfort in the living environment. The results of the sensitivity analysis, which serve as guidelines, show that the overall U-factor of a window, the solar heat gain coefficient, and a set-point temperature for heating are design variables that most affect the heating energy demand for the considered one- and two-storey box models in the three locations. The dominant parameters have on average 30% more influence on heating energy demand in cold climates than parameters in moderate climates and 88% more than in warm climates. While shading control and solar heat gain coefficient are the most influential parameters for cooling energy demand, with the dominant parameters in warm climates having on average 39% more influence than parameters in moderate climates and 49% more influence than parameters in cold climates. In the total energy demand for the operation of all box models under all climatic conditions, special attention should be paid to shading control. In addition, in moderate and cold climates, the overall U-value of the window and the internal set- point temperature in winter must be considered, and in hot climates, the solar heat gain coefficient is important. In the case of the two-storey box model, designers need to be careful about the glazing-to-wall ratio which depends on the orientation of the glazing (south-north or east-west). In this case, the dominant parameters have on average 47% more influence in warm climates than in cold climates and 56% more than in temperate climates.