Beta Probability Density Function Research Articles

Satin bowerbird algorithm with an adaptive constriction factor for enhanced photovoltaic integration in distribution feeders

—This paper introduces an enhanced Satin bowerbird optimizer (SBO), specifically tailored for the integration of photovoltaic distributed generation (DG) units into radial distribution systems. The upgraded SBO version involves two pivotal adjustments. Firstly, the positional updating mechanism of the newly generated bower is modified to enable exploration around the iteration's elite bower. Secondly, an adaptive constriction factor is introduced, progressively decreasing during iterations to concentrate the search in promising areas. These modifications significantly amplify the exploration capacity of each new bower in the SBO algorithm. The proposed upgraded SBO aims at minimizing costs related to CO2 emissions from the grid and those linked with photovoltaic units, in addition to energy losses. The variability of photovoltaic DG units is represented using the Beta Probability Density Function (PDF) to portray distinct solar irradiation conditions experienced daily. The enhanced SBO version undergoes testing on a practical Nigerian distribution system, the Ajinde 62-bus network, and a standard IEEE 69 nodes system. Simulation results underscore the effectiveness of the upgraded SBO version, revealing substantial reductions in energy losses and emissions. Specifically, for the Ajinde 62-bus network, the proposed SBO version achieves a noteworthy 31 % reduction in the combined yearly costs of energy losses and emissions compared to the initial case. Additionally, for the IEEE 69-bus system, it attains a considerable reduction of 35 %. Furthermore, the simulation results illustrate the competitive performance of the suggested SBO version when compared to Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms, as well as the standard SBO.

An imprecise probability approach-based determination of over-represented southern African plant genera and families used in ethnopharmacology

Ethnopharmacological relevanceThe analyses of patterns of over-representation of southern African traditional medicinal plants at the genus and family level provide information about the differences in plant use among southern African countries and disease categories. ‘Over-representation’ refers to the phenomenon whereby the proportion of plants belonging to a taxonomic group is higher in ethnobotanical pharmacopoeia than in the total flora. Aim of the studyThis study aimed to use the Imprecise Dirichlet Model (IDM) to analyse data from ten southern African countries to establish how over-represented medicinal plant families compare with over-represented genera, how over-represented medicinal taxa differ among countries in this region of Africa, and how over-represented taxa differ among six major disease categories. Materials and methodsFloral data for the total species composition of each country were obtained from online databases. Medicinal plant species lists were generated from published surveys, inventories, and books. IDM calculations were executed using the inverse of the cumulative beta probability density function in Microsoft Excel™. Python programming language source code was used to calculate Pearson correlation (r) values and Jaccard coefficients (J). ResultsNine of forty-two over-represented medicinal plant families in southern Africa (group 1) do not have over-represented genera. Seven of the forty genera with the highest margins of over-representation belong to under-represented families. Nineteen of the forty-two over-represented families have margins of over-representation smaller than the cumulative margins of their over-represented genera. Groups of countries with similar overall flora (J ≥ 0.333) are Botswana and Namibia (group 2), Malawi, Mozambique, Zambia and Zimbabwe (group 3). The families and genera with the highest margins of over-representation are Loganiaceae and Albizia in group 1, Combretaceae and Vachellia in group 2, Dioscoreaceae and Senna in group 3, and Sapotaceae and Solanum in group 4 (South Africa). The families and genera with the highest margins of over-representation across disease categories are Ebenaceae and Albizia, Canellaceae and Dicoma, Combretaceae and Pterocelastrus, Ebenaceae and Bersama, Francoaceae and Erythrina, and Aristolochiaceae and Strychnos for plants used in the treatment of STIs, febrile and mosquito-vector diseases, microbial infections, pain, skin conditions, and female sexual/reproductive problems, respectively. ConclusionsGenus-level calculations are more efficient in generating taxonomic lists that can be used for ethnopharmacological investigations due to the exclusion of under-represented genera. Limiting the size of geographical areas from which medicinal plant lists are sampled and targeting plants used to treat specific types of disease prevents the underestimation of niche over-represented taxa.

Equilibrium optimiser for the economic load dispatch problem with multiple fuel option and renewable sources

The integration of thermal units with renewable sources leads to a highly nonlinear and difficult Economic Load Dispatch (ELD) problem. However, dependency of wind speed and solar irradiance, renewable sources like wind-solar plants cannot guarantee their output. It has been possible to anticipate the wind speed and solar irradiation by Weibull and beta probability density functions. Wind and solar energy output powers have been estimated using the 2-m point estimation method. The renewable-based ELD problem has a solution thanks to the equilibrium optimizer (EO) technique. Finding the answer in a relatively short amount of computing time is made possible by the method's exploration and exploitation stages. The suggested technique has been validated in three, five, six, fifteen, and huge 160 thermal units linked to renewable energy sources by meeting restrictions such generator operating restrictions, valve point loading impact, and numerous fuel possibilities.

A Strategy for Multi-Objective Energy Optimization in Smart Grid Considering Renewable Energy and Batteries Energy Storage System

Multi-objective energy optimization is pivotal for reliable and secure power system operation. However, multi-objective energy optimization is challenging due to interdependent and conflicting objectives. Thus, a multi-objective optimization model is needed to cater to conflicting objectives. On this note, a multi-objective optimization model is developed, where a non-dominated genetic sorting algorithm is employed to optimize objectives pollution emission, operation cost, and loss of load expectation (LOLE) considering renewable energy sources (RES). RES, like wind and solar, are intermittent and uncertain, which are modelled using a beta probability density function (PDF). The developed method’s effectiveness and applicability are analyzed by implementing it on the 30-bus system, and the results are compared for two cases. Findings reveal that the developed multi-objective optimization model minimizes operation cost, pollution emission, and LOLE by 59%, 7%, and 2.67%, respectively, compared to existing models.

A Multi-Hop QoS-Aware and Predicting Link Quality Estimation (PLQE) Routing Protocol for Reliable WBSN

Technological advancements and miniaturization of sensor have made it possible to use tiny size sensors nodes to monitor patients’ physiological data in real-time at very low cost. The network of such small size sensor nodes is often called wireless body sensor networks (WBSNs). The patient’s data is highly sensitive which required to reach reliably and timely at the destination node. However, short range wireless nodes and postural body movements cause frequent topological changes and recurrent network partitioning. The network partitioning leads to delayed and significant loss of critical patient’s data such as Electrocardiogram (ECG), Electroencephalogram (EEG) and Electromyogram (EMG). Therefore, QoS requirement of WBSNs in terms of reliability, end-to-end delay and throughput are highly compromise. We in this paper propose a Predicting routing protocol PLQE to address reliable data transmission and network partitioning due to node mobility. The PLQE dynamically determines the efficient links by using beta probability density function, link quality and link delay estimation (LDE). The PLQE is composed of link reliability factor (LRF) and expected probability Indicator (EPI) to obtain most often updated status of the links to figure out stable and reliable end to end route to the destination node. The simulation results confirm the higher performance of the proposed scheme against state of the art routing protocols in terms of packet delivery ratio, end to end delay, throughput and normalized routing load.

Quantifying the influence of modeling uncertainties on performance evaluation of mega column-core tube-outrigger structure under near-field and far-field ground motions

Different types of ground motions have the potential to aggravate the failure state of mega column-core tube-outrigger structure(MCCTOS) considering uncertainty. It is of great engineering significance to comprehensively analyze the seismic fragility of the structure under different types of ground motions. The purpose of this work is to analyze and predict the impact of modeling uncertainties on the performance evaluation of MCCTOS under different types of ground motions and determine the sensitivity of independent input parameters. On the premise of considering both seismic uncertainty and structural uncertainty, the Latin hypercube sampling and first-order second-moment, which are respectively combined with incremental dynamic analysis, are adopted to perform seismic fragility analyses of MCCTOS. By comparing the fragility curves of MCCTOS under non-pulse near-field ground motions, pulse-type near-field ground motions, and far-field ground motions, the influence of the randomness of earthquakes and structural parameters on the fragility of MCCTOS under different types of ground motions is analyzed. In addition, the seismic damage index is introduced into the fragility assessment of MCCTOS. By combining the seismic damage index with the beta distribution function, the matrix and probability density function of the seismic damage index of MCCTOS are established. Furthermore, the influence of structural parameter uncertainty on the seismic damage index of MCCTOS under different types of ground motions is investigated. The sensitivity analysis of uncertain parameters in the MCCTOS is carried out by using tornado analysis technology and Sobol' method to investigate the influence of the considered parameters on the seismic response of MCCTOS. The results show that pulse-type near-field ground motions are easier to cause structural damage than non-pulse near-field ground motions and far-field ground motions. However, for the MCCTOS under the non-pulse near-field ground motions, the modeling uncertainties have the greatest impact on the seismic capacity and lead to the maximum reduction of the average seismic damage index. The structural responses are found to be most sensitive to the density of concrete, compressive strength of concrete, and structural damping ratio.

Renewable Energy Micro-Grid Interfacing: Economic and Environmental Issues

This paper presents a study on the technical, economic, and environmental aspects of renewable energy resources-based distributed generation units (DGs). These units are connected to the medium-voltage network to create a new structure called a microgrid (MG). Renewable energies, especially wind and solar, are the most important generation units among DGs. The stochastic behavior of renewable resources increases the need to find the optimum operation of the MG. The optimal operation of a typical MG aims to simultaneously minimize the operational costs and the accompanied emission pollutants over a daily scheduling horizon. Several renewable DGs are investigated in the MG, consisting of biomass generators (BGs), wind turbines (WTs), and photovoltaics (PV). For the proposed operating strategy of the MG, a recent equilibrium optimization (EO) technique is developed and is inspired by the mass balance models for a control volume that are used to estimate their dynamic and equilibrium states. The uncertainties of wind speed and solar irradiation are considered via the Weibull and Beta-probability density functions (PDF) with different states of mean and standard deviation for each hour, respectively. Based on the developed EO, the hourly output powers of the PV, WT, and BGs are optimized, as are the associated power factors of the BGs. The proposed MG operating strategy based on the developed EO is tested on the IEEE 33-bus system and the practical large-scale 141-bus system of AES-Venezuela in the metropolitan area of Caracas. The simulation results demonstrate the significant benefits of the optimal operation of a typical MG using the developed EO by minimizing the operational costs and emissions while preserving the penetration level of the DGs by 60%. Additionally, the voltage profile of the MG operation for each hour is highly enhanced where the minimum voltage at each hour is corrected within the permissible limit of [0.95–1.05] Pu. Moreover, the active power losses per hour are greatly reduced.

A stochastic analytic-probabilistic approach to distributed generation hosting capacity evaluation of active feeders

The unregulated penetration of distributed generation (DG) on distribution networks can cause wide-ranging technical issues, such as voltage variation, thermal loading, and unbalance. To regulate penetration, a planner needs to determine the maximum penetration or hosting capacity (HC) of a network, which requires extensive studies assessing the technical impacts of DG on the most sensitive quality of supply variables. Several uncertainties complicate the HC computation, such as the stochasticity of customer loads, variable DG outputs, and unknown location and capacity of future DG installations. This uncertainty demands approaches with the capability of stochastic simulation of DG allocation and probabilistic assessment of the corresponding range of feeder performance. Existing uncertainty-based HC computation methods have inadequate probabilistic representation, high computational burden, and restricted scope of technical variables, reducing any confidence in the assessed HC. We use a stochastic analytic-probabilistic approach that embeds an analytic probabilistic load flow (PLF) transform in a Monte-Carlo simulation (MCS) of DG allocation, and applies a polynomial smoothing technique to further enhance computational efficiency. The acceptable variation of radial distribution feeder performance is identified by voltage limits, thermal capacity, and unbalance. The PLF has significant benefits in reducing the overall computational burden. The HC is quantified statistically using the beta probability density function, reflecting the composite risk from the multiple uncertainties. Compared with other formulations, this stochastic-analytic approach to HC improves feeder performance evaluation under a wide range of DG penetration scenarios and is appropriate for design and operational analysis.

Generalization Capability of Convolutional Neural Networks for Progress Variable Variance and Reaction Rate Subgrid-Scale Modeling

Deep learning has recently emerged as a successful approach to produce accurate subgrid-scale (SGS) models for Large Eddy Simulations (LES) in combustion. However, the ability of these models to generalize to configurations far from their training distribution is still mainly unexplored, thus impeding their application to practical configurations. In this work, a convolutional neural network (CNN) model for the progress-variable SGS variance field is trained on a canonical premixed turbulent flame and evaluated a priori on a significantly more complex slot burner jet flame. Despite the extensive differences between the two configurations, the CNN generalizes well and outperforms existing algebraic models. Conditions for this successful generalization are discussed, including the effect of the filter size and flame–turbulence interaction parameters. The CNN is then integrated into an analytical reaction rate closure relying on a single-step chemical source term formulation and a presumed beta PDF (probability density function) approach. The proposed closure is able to accurately recover filtered reaction rate values on both training and generalization flames.

Optimal siting of solar based distributed generation (DG) in distribution system for constant power load model

Abstract In this paper optimal location and sizing of Non-dispatchable Distributed Generation (NDG) based distributed generation (DG) is investigated by considering uncertainty of NDG. In present study a solar photovoltaic (SPV) is considered as NDG because SPV based DG has uncertain nature of generated power because it is powered by solar irradiance which has uncertain characteristics. To investigate the uncertainty of intermittent nature of solar irradiance Beta Probability Density Function (BPDF) based PDF is considered for addressing the uncertainty of solar insolation. For determining the optimal size of DG unit an analytical based methodology is developed. In this study optimal capacity of NDG is estimated by deriving the expressions of DG unit at each bus. Further, a multi-objective index factor (MIF) is designed in order to find out the candidate bus for DG placement. The proposed technique is applied on IEEE 33-bus distribution network. The obtained results reveal that proposed technique provide almost similar result to that of other method which is available in literature.

Optimal Network Reconfiguration with Distributed Generation and Electric Vehicle Charging Stations

This paper proposes an optimal network reconfiguration (ONR) by integrating the renewable energy (RE) based distributed generation (DG) resources, i.e., wind and solar photovoltaic (PV) modules, and electric vehicle charging stations (EVCS). The uncertainties related to renewable energy sources (RESs) are handled by using probability analysis. In this work, wind uncertainty is handled by using Weibull probability density function (PDF), and solar PV uncertainty is modeled by using Beta PDF. This paper also models the load of EVCSs. The ONR is a tool to operate distribution systems (DSs) at optimum cost/loss. In the literature, most of the ONR problems are solved as single objective type. This neccessiate the development of multi-objective based ONR problem and solved using the multi-objective algorithms by considering multiple objectives. Therefore in this paper, total cost of operation and power losses are considered as two objectives functions. The single objective-based ONR is solved using crow search algorithm (CSA) and multi-objective-based ONR is solved using multi-objective-based CSA. As the DS is unbalanced, the power flow for the unbalanced system will include the three-phase transformer. The ONR problem has been solved by considering 17 bus unbalanced and balanced DSs.

The Impact of Voltage Stability Constraint L-Index on Power System Optimization Base on Interior Point Algorithm by Considering the Integration of Renewable Energy

Renewable energy (RE) generation including wind and solar farms has experienced significant growth due to the challenge of climate and energy crisis. High penetration of RE affects system stability and generation cost optimization. In this paper, voltage stability L-index is proposed as the constraint of the primal-dual interior point method for optimal power flow by considering the integration of wind and photovoltaic cell power on system. L-index is used in this study to indicate the voltage security while renewable energy is prefixed into power system to build a new (REL-OPF) formulation that can consider the voltage stability margin and generation cost of the power grid. Weibull and Beta probability density functions are applied to determine the outputs of wind and photovoltaic power generation respectively. This model has the advantage that there is no need to calculate the critical point and could obtain the demanded voltage security level by adjusting the upper limits of indicator L constraints. The optimal solution can concurrently satisfy both the voltage security and the economical demand for power systems. The overall problem is simulated under coding written in MATLAB environment. The results obtained from regulating the upper limit of voltage stability constraint on IEEE30-bus has shown that the attention of RE generations into the system leads the fuel cost objective to decrease randomly as well as enlarge the distance of stability to a critical point with faster convergence.

Application of the Beta Probability Density Function for Representing Infiltration of Water-Repellent Soil

Laboratory experiments were conducted to investigate the infiltration of water-repellent soil. The most suitable mathematical model to represent infiltration of water-repellent soil was investigated and water infiltration into this column was measured for both hydrophilic and water-repellent soils of the Guishui River Basin. The results showed a monotonous increase and decrease in cumulative infiltration and infiltration rate over time within the hydrophilic soil, respectively. In contrast, the results for water-repellent soil showed: (1) The existence of a turning point in cumulative infiltration above which the infiltration rate increased sharply, with higher initial soil moisture content resulting in an earlier and larger increase in the infiltration rate; (2) A larger stable infiltration rate after the peak compared to that before the peak, with the overall infiltration rate presenting a single peak curve if the beginning of rapid infiltration is ignored. The applicability of the Kostiakov, segmented Kostiakov, Gaussian, segmented Gaussian, Beta and segmented Beta function infiltration models were analysed for the two soil types. The numerical analysis indicated that: (3) The Kostiakov and Beta function models showed better applicability for both hydrophilic and water-repellent soils; (4) For water-repellent soil, the Gaussian function infiltration model not only represented the monotonous decrease in infiltration rate, but also demonstrated a steady infiltration rate during the initial stage and a gradual increase and decrease in infiltration rate pre- and post-peak, respectively. Similarly, the Beta function model was able to represent the monotonous decrease in infiltration rate, and the segmented Beta function represented the U-shaped change in rapid infiltration before the threshold as well as the gradual increase and right-skewed distribution curve of infiltration pre- and post-turning point in water-repellent soil. The Beta function model achieved the highest simulation accuracy and showed the widest applicability.

On the dispatch of minigrids with large penetration levels of variable renewable energy

The continuous use of fossil fuels for decades in electricity generation has led to dire environmental consequences. This has fostered the incorporation of variable renewable energy resources (RES) to improve the environmental outlook and minimize emissions. This paper presents an approach for the dispatch of a minigrid considering variable solar photovoltaic (PV) generation. Due to the variability of the solar irradiance received from the sun during daytime only, solar irradiance is modeled as a stochastic random variable that is fitted into a Beta probability density function (PDF). The minigrid dispatch problem, modeled using stochastic optimization, is then approximated into a linear equivalent to become a mixed integer linear programming (MILP) problem that can be solved efficiently. The proposed approach is implemented on the modified IEEE 14-bus test system to verify its capability in solving the minigrid dispatch under various test case scenarios. <em> </em>

Chaotic darwinian particle swarm optimization for real-time hierarchical congestion management of power system integrated with renewable energy sources

The increasing penetration of renewable energy sources that have intermittent outputs challenge the Independent System Operator while managing transmission congestion. A new Real-Time Hierarchical Congestion Management (RHCM) technique is proposed that reschedules generators in two stages based on Available Congestion Clearing Time (ACCT) of the transmission lines in presence of renewable energy sources. Chaotic Darwinian Particle Swarm Optimization (CDPSO) is used for determining the optimal schedules of demand response loads and reschedules of conventional generators to mitigate congestion. The solar and wind energy sources are modelled using Rayleigh and Beta probability density functions; Latin Hyper cube sampling is adopted for sampling. IEEE 39 bus system is simulated for cases of overloads and contingencies and RHCM using CDPSO is tested to ensure the security of the system. The benefit of RHCM incorporating demand response is presented in terms of reduced congestion relieving costs and decreased power loss.

Mesh-Sequenced Realizations for Evaluation of Subgrid-Scale Models for Turbulent Combustion

This paper develops a new approach for analysis of subgrid closures for turbulent combustion as modeled using direct quadrature (finite-rate chemistry) techniques. The approach, termed multiresolution analysis through mesh-sequenced realizations (MRA-MSR), conducts simultaneous, constrained large-eddy simulations on a set of hierarchically coarsened meshes. The availability of underlying fine-mesh (subgrid) data corresponding to coarse-mesh locations allows a clearer assessment of the effects of unresolved fluctuations on apparent reactivity. A key to MRA-MSR is the correlation of eddy structures at coarser mesh levels, which is facilitated by the transfer of filtered fine-mesh velocity information. A seven-mesh MRA-MSR hierarchy using three resolution levels is applied to one of the Sydney bluff-body stabilized methane–hydrogen flames. Analysis of the simultaneously evolved data at different resolution levels reveals several interesting trends. First, at high Damköhler numbers, there is clear evidence of attenuation of apparent reactivity due to the effects of unresolved fluctuations. Secondly, single-point, single-time filtered density functions of a normalized subgrid Damköhler number show a characteristic beta probability density function (PDF) form and display evidence of scale similarity. Interrogation of the MRA-MSR database also shows that the recently-proposed least-squares minimization (LSM) turbulence–chemistry interaction model can account for the observed diminishment in reactivity at high Damköhler numbers but cannot reduce scatter significantly. A new form of the LSM model, which makes use of the normalized subgrid Damköhler number beta PDF distribution, performs slightly better than the original model, illustrating the potential of MRA-MSR both in assessing existing closure concepts and in developing new ones.

A non-central beta model to forecast and evaluate pandemics time series.

Government, researchers, and health professionals have been challenged to model, forecast, and evaluate pandemics time series (e.g. new coronavirus SARS-CoV-2, COVID-19). The main difficulty is the level of novelty imposed by these phenomena. Information from previous epidemics is only partially relevant. Further, the spread is local-dependent, reflecting a number of social, political, economic, and environmental dynamic factors. The present paper aims to provide a relatively simple way to model, forecast, and evaluate the time incidence of a pandemic. The proposed framework makes use of the non-central beta (NCB) probability density function. Specifically, a probabilistic optimisation algorithm searches for the best NCB model of the pandemic, according to the mean square error metric. The resulting model allows one to infer, among others, the general peak date, the ending date, and the total number of cases as well as to compare the level of difficult imposed by the pandemic among territories. Case studies involving COVID-19 incidence time series from countries around the world suggest the usefulness of the proposed framework in comparison with some of the main epidemic models from the literature (e.g. SIR, SIS, SEIR) and established time series formalisms (e.g. exponential smoothing - ETS, autoregressive integrated moving average - ARIMA).

Seismic vulnerability comparison between rural Weinan and other rural areas in Western China

Generally, the anti-seismic capacity of rural buildings in China is poor due to their irregular design and construction. On the basis of historical destructive earthquake records, corresponding earthquake loss evaluation compilations (1993–2016), field investigations, and remote sensing interpretation, building structures in rural Weinan are classified into two types and analyzed to acquire the seismic vulnerability matrices by employing the fitting method of beta probability density function (BPDF). Results show that BPDF can well reveal the probability density distribution of seismic damage index, and also the damage ratio obtained agrees well with the description of damage degrees in Chinese macroseismic intensity scale.The vulnerability indexes in rural areas of Yunnan, Sichuan, Qinghai provinces and in Weinan City (Shaanxi province) were calculated and a comparison of aseismic ability was made. Results show that, among the rural areas in Western China, the aseismic abilities of traditional buildings in rural Weinan are the lowest while those of masonry buildings are highest. Moreover, potential losses in rural Weinan are estimated on the assumption that a scenario earthquake with a magnitude Ms 6¾ hit Weinan City, proposed by the UK-China Collaboration programme ‘‘Increasing Resilience to Natural Hazards in Earthquake-Prone regions in China”. It was found that the damage ratios obtained captured the distribution of the aseismic abilities of the rural buildings and therefore improved the accuracy of the loss assessment, which provides scientific basis for the scenario narratives. What we discovered in this paper is also helpful in future earthquake damage prediction and enhancement of public awareness on earthquake resistance.

Mycophilic degree among the Wixaritari and mestizos in Villa Guerrero, Jalisco, Mexico

The appreciation and taste towards mushrooms are influenced by sociocultural factors and ecological variables. This study evaluated the mycophilic degree among the Wixaritari and mestizo communities in a municipality in the north of Jalisco, settled in different types of vegetation, to determine if ecological and sociocultural factors influence the attitude towards the mushrooms. The Mycophilia-Mycophobia Index was evaluated in 10 communities in which semi-structured interviews were conducted with a representative number of people. Responses to 18 indicators were analyzed by χ2 test and multivariate techniques. To determine which factors best explain the observed attitudes, six models were constructed using a Beta probability-density function with maximum likelihood adjustment; finally, a comparison using the Akaike Information Criterion was made. In general, the population resulted mycophilic; the χ2 test showed that there were significant differences between the Wixaritari and mestizo attitudes in 10 of the 18 indicators. In the ordination and classification analyses, the communities did not cluster by cultural group or vegetation, and one mestizo community was isolated from the others. The model that best explains the mycophilic attitudes was community-cultural group in which the vegetation was involved. One Wixarika community in pine forest was extremely mycophilic, in contrast to a mestizo community in oak forest that was indifferent to the mushrooms; these attitudes were the result of historical events that have modified the lifestyle of people. The differences in the evaluated indicators were due to the cosmovision of each cultural group.

PoCET: a Polynomial Chaos Expansion Toolbox for Matlab

We introduce PoCET: a free and open-scource Polynomial Chaos Expansion Toolbox for Matlab, featuring the automatic generation of polynomial chaos expansion (PCE) for linear and nonlinear dynamic systems with time-invariant stochastic parameters or initial conditions, as well as several simulation tools. It offers a built-in handling of Gaussian, uniform, and beta probability density functions, projection and collocation-based calculation of PCE coefficients, and the calculation of stochastic moments from a PCE. Efficient algorithms for the calculation of the involved integrals have been designed in order to increase its applicability. PoCET comes with a variety of introductory and instructive examples. Throughout the paper we show how to perform a polynomial chaos expansion on a simple ordinary differential equation using PoCET, as well as how it can be used to solve the more complex task of optimal experimental design.