Probability Distribution Model Research Articles

Concurrent 2. Presentation for: Techno-economic evaluation of blue hydrogen production with carbon capture and storage for onshore Eastern Australia

Presented on Tuesday 17 May: Session 2 This techno-economic assessment models the feasibility of a greenfield blue hydrogen development with production capacity of 400 tons of hydrogen per day (TH2/day). At an assumed 85% CO2 recovery rate, the 400 TH2/day production scale equates to a need for approximately 1.241 million tons of CO2 per year (MtCO2/year) of subsurface CO2 storage capacity over an assumed project life of 25 years (approximately 31 Mt of total CO2 sequestered). The blue hydrogen production technology applied to the assessment is a Steam Methane Reformer (SMR) with two points of CO2 recovery (pre-combustion process stream amine scrubbing and post-combustion flue gas capture). The remaining key scope components are the CO2 compression and dehydration system, 65 km of CO2 distribution pipeline and a CO2 injection and storage hub comprised of three injection wells, three deep observation wells and three groundwater monitoring wells. The study includes the screening process applied to identify five high-grade depleted gas reservoirs in the Cooper Basin that are the CO2 storage candidates, and which ultimately define the project location. The economic evaluation of the project includes the definition of cost and operations estimates to determine a mean project case and then applies a Palisade @Risk probabilistic distribution model to key project inputs as to risk the project under various scenarios. The analysis concludes that the economic viability of large-scale, greenfield blue hydrogen projects in Australia is highly dependent on hydrogen sale price, Australian Carbon Credit Unit (ACCU) value, wholesale natural gas prices and capital cost efficiency. To access the presentation click the link on the right. To read the full paper click here

A Mathematical Framework for Learning Probability Distributions

The modeling of probability distributions, specifically generative modeling and density estimation, has become an immensely popular subject in recent years by virtue of its outstanding performance on sophisticated data such as images and texts. Nevertheless, a theoretical understanding of its success is still incomplete. One mystery is the paradox between memorization and generalization: In theory, the model is trained to be exactly the same as the empirical distribution of the finite samples, whereas in practice, the trained model can generate new samples or estimate the likelihood of unseen samples. Likewise, the overwhelming diversity of distribution learning models calls for a unified perspective on this subject. This paper provides a mathematical framework such that all the well-known models can be derived based on simple principles. To demonstrate its efficacy, we present a survey of our results on the approximation error, training error and generalization error of these models, which can all be established based on this framework. In particular, the aforementioned paradox is resolved by proving that these models enjoy implicit regularization during training, so that the generalization error at early-stopping avoids the curse of dimensionality. Furthermore, we provide some new results on landscape analysis and the mode collapse phenomenon.

A survey of security and smart home automation based on internet of things technology

The <span>internet of things (IoT) refers to the physical tools that are embedded with Internet, software, electronics, sensors and network connectivity. This involves many different systems, for example, healthcare, smart home and so on. The security problem of the Internet of Things and the Smart Home infrastructure is considered, which has become an urgent issue due to the high popularity, low systemic research and the growth of threats to "us" (people seeking comfort) from "them" (surrounding things, which becoming increasingly intelligent, automated). The research is based both on a systemic, infrastructure understanding, and on an architectural, problem-oriented level. Key security risks for the infrastructure of various types-software and technical, technological, socio-psychological and others-were analyzed. The evolutionary problems of the internet of things and factors influencing the vulnerability of infrastructures have been investigated. In addition to traditional network security tasks, specific tasks (direct and reverse, for identification) are highlighted in IoT interactions and environments. This paper provides an overview of the related work in IoT, together with the open challenges and future research directions using Arduino platform (such as "thick server-thin client") to simulation modeling of time delay probability distribution based on identified simple model.</span>

X-ray constrained wavefunctions based on Hirshfeld atoms. I. Method and review.

The X-ray constrained wavefunction (XCW) procedure for obtaining an experimentally reconstructed wavefunction from X-ray diffraction data is reviewed. The two-center probability distribution model used to perform nuclear-position averaging in the original paper [Grimwood & Jayatilaka (2001). Acta Cryst. A57, 87-100] is carefully distinguished from the newer one-center probability distribution model. In the one-center model, Hirshfeld atoms are used, and the Hirshfeld atom based X-ray constrained wavefunction (HA-XCW) procedure is described for the first time, as well as its efficient implementation. In this context, the definition of the related X-ray wavefunction refinement (XWR) method is refined. The key halting problem for the XCW method - the procedure by which one determines when overfitting has occurred - is named and work on it reviewed.

Probabilistic fatigue life prediction model of natural rubber components based on the expanded sample data

A novel method for determine the probabilistic distribution model of natural rubber (NR) fatigue life is proposed. Uniaxial tension fatigue tests are carried out on dumbbell-shaped cylindrical specimens. According to the fatigue test data, a support vector machine (SVM) model is established, in which the empirical reliability and the rubber fatigue life are considered as input and output variables, respectively. The SVM model is used to expand the NR fatigue life data. The analysis of the expanded data demonstrates that the NR fatigue life follows a lognormal distribution. Accordingly, the fatigue reliability evaluation of NR components is carried out.

A STUDY OF LONG-TERM SUNSPOTS AND K-INDEX GEOMETRIC CYCLES USING PROBABILISTIC MODELING

The research work done in this paper comprises the application of different well-known probability distribution models. This includes the understanding of the behavior and dynamics of 24 sunspot cycles with total data. The time-series data sets were selected from 1749 to 2014. To observe the solar activity effects on K-index activity the double cycles from 1932 to 2014 were also incorporated in the study. The comparative study is useful to observe the long-term solar-terrestrial connection. The magnetic field of the sun reverses its polarity after every 11 years of the cycle. So after every 22 years, the north pole becomes again north pole. By using the two well-known tests Kolmogorov-Smirnov (KST) and Anderson-Darling test (ADT) the probability distribution models were obtained for each sunspot cycles and compare. The significant probability models for all the sunspot cycles have been obtained. The fitted probability distribution models on selected data sets may be useful to understand the trend of solar and geomagnetic activity.

Prediction of long dry spells for appropriate cropping system in Gusau Northwestern Nigeria

The objective of this study was to predict the probabilities of occurrences of long dry spells and their lengths during the planting period in rainfed farming season for future planning in Gusau and its environs North-Western Nigeria. Markov chain and probability distribution models were used to help predict in advance the longtime dry spells occurrences in the study area. Daily rainfall amount for each year was used to determine the probabilities of wet and dry days at different orders of Markov Chain. Gamma distribution was used with the help of INSTAT plus statistical package to estimate the length of dry spells in May, June and July. The early season dry spells were determined to occur usually between the first and the last decades of May. The Longest dry spells for the month of May were determined to be 26, 25 and 21 days in 2020, 2022 and 2030 respectively. Low frequencies of dry spells are to be anticipated in June with only 10 days in 2026 and July with only 12 days in 2024. The month of May from 2011 to 2020 with mean dry days of measured and predicted data were found to be 14 and 15 days respectively while coefficient of variation (CV) of 0.3, shows a stable dry spell in the coming years in May. The R between the observed and the predicted values were averagely good, mean error (ME) -1.25,-1.00 and 1.63 between the longest monthly observed and predicted dry spell were less than all the observed data. The root mean square error (RMSE) indicated that the month of June has the highest measure of precision 3.18, followed by the month of July4.46 and May 5.50. Since, early season rainfall is uncertain and erratic than the mid-season, early planting of moisture sensitive crop like maize in Gusau without supplementary irrigation would be highly risky.

Techno-economic evaluation of blue hydrogen production with carbon capture and storage for onshore Eastern Australia

This techno-economic assessment models the feasibility of a greenfield blue hydrogen development with production capacity of 400 tons of hydrogen per day (TH2/day). At an assumed 85% CO2 recovery rate, the 400 TH2/day production scale equates to a need for approximately 1.241 million tons of CO2 per year (MtCO2/year) of subsurface CO2 storage capacity over an assumed project life of 25 years (approximately 31 Mt of total CO2 sequestered). The blue hydrogen production technology applied to the assessment is a Steam Methane Reformer (SMR) with two points of CO2 recovery (pre-combustion process stream amine scrubbing and post-combustion flue gas capture). The remaining key scope components are the CO2 compression and dehydration system, 65 km of CO2 distribution pipeline and a CO2 injection and storage hub comprised of three injection wells, three deep observation wells and three groundwater monitoring wells. The study includes the screening process applied to identify five high-grade depleted gas reservoirs in the Cooper Basin that are the CO2 storage candidates, and which ultimately define the project location. The economic evaluation of the project includes the definition of cost and operations estimates to determine a mean project case and then applies a Palisade @Risk probabilistic distribution model to key project inputs as to risk the project under various scenarios. The analysis concludes that the economic viability of large-scale, greenfield blue hydrogen projects in Australia is highly dependent on hydrogen sale price, Australian Carbon Credit Unit (ACCU) value, wholesale natural gas prices and capital cost efficiency.

General probability distribution model for wireless body sensors in the medical monitoring system

States are making every effort and huge investment to keep human health at the highest level with a growing population. For this purpose, networks of multifunctional sensors have been developed. The main reason affecting the wireless sensors on the body is the noise level. The noise is due to the environment, and the receiver distance that characterizes the channel. The noise is random and most of the time requires pre-knowledge of the source for successful representation. Normally, details about the source help in determining the type of random distribution. This research article first introduces and proves the validity of a new probability distribution function to accurately represent the random noise without pre-knowledge of the source, location, and distance related to the wireless sensors. Next, the performance of the model was tested with a real experimental application. The proposed model has better representation than the most applicable distributions such as Weibull, lognormal, Gaussian, Rayleigh, and Nakagami. The results obtained are promising to apply the introduced model for a realistic random noise representation at very low signal levels. The accurate representation of the noise level is directly related to the channel characteristic and provides a more precise representation of the signal level at the receiver which is of great importance in the designs of the receiver units.

Quantifying impact and response in markets using information filtering networks

We present a novel methodology to quantify the ‘impact’ of and ‘response’ to market shocks. We apply shocks to a group of stocks in a part of the market, and we quantify the effects in terms of average losses on another part of the market using a sparse probabilistic elliptical model for the multivariate return distribution of the whole market. Sparsity is introduced with an L 0-norm regularization, which forces to zero some elements of the inverse covariance according to a dependency structure inferred from an information filtering network. Our study concerns the FTSE 100 and 250 markets and analyzes impact and response to shocks both applied to and received from individual stocks and group of stocks. We observe that the shock pattern is related to the structure of the network associated with the sparse structure of the inverse covariance of stock log-returns. Central sectors appear more likely to be affected by shocks, and stocks with a large level of underlying diversification have a larger impact on the rest of the market when experiencing shocks. By analyzing the system during times of crisis and comparative market calmness, we observe changes in the shock patterns with a convergent behavior in times of crisis.

Rough maximal cliques enumeration in incomplete graphs based on partially-known concept learning

The emerging massive noisy and incomplete data is transforming the conventional graph to the uncertain graph. In this paper, we study rough maximal cliques enumeration (RMCE) in incomplete graphs, which we define as the novel problem of enumerating all maximal cliques where some of edges are unknown to users. The hardness of RMCE is proved to NP-complete. To tackle this problem, an efficient framework for obtaining the rough maximal cliques based on Partially-Known Concept Learning (PKCL). With this framework, a given incomplete graph is initially represented as an incomplete formal context. Then, the partially-known SE-ISI concept lattice is generated through the constructed incomplete formal context. Based on the constructed SE-ISI concept lattice, an equivalence theorem between SE-ISI equiconcepts and rough maximal cliques is presented. The detailed topological structural analysis from the point of views of roughness and SE-ISI concept stability of rough maximal cliques are separately discussed. The evaluation results demonstrate that our proposed PKCL algorithm can better identify the rough maximal cliques under different probability distribution models of links compared to the existing baseline algorithms.

Typhoon-Induced Fragility Analysis of Transmission Tower in Ningbo Area Considering the Effect of Long-Term Corrosion

The purpose of this paper was to investigate the influence of long-term corrosion on the deterioration of wind resistance of a steel transmission tower during its service life. An analytical model for predicting the long-term corrosion depth of carbon steel was established, and the corrosion depth of carbon steel in the Ningbo area was predicted based on the local atmospheric environment data. With the help of typhoon full-track simulation and wind field simulation technology, a joint probability distribution model of multidirectional extreme wind speeds was constructed using the t-Copula function to determine the typhoon climate of the transmission tower site. Finite element models of the ZM4 cathead transmission tower under 30/60/90 corrosion years were then established, respectively, according to the predicted corrosion depth of carbon steel in Ningbo. Three damage modes, i.e., minor damage, moderate damage and severe damage, corresponding to the transmission tower under wind loads, were defined, and pushover analyses were used to determine the limit values of each damage mode so as to obtain the typhoon-induced fragility curves of the transmission tower within 30/60/90 corrosion years. The results show that the increase in corrosion age leads to a deterioration in the nominal mechanical properties of the transmission tower components, making the damage probability to the transmission tower increase. Under the typhoon wind loads of a 50-year return period in the most unfavorable wind direction in Ningbo, the probability of moderate damage of the tower is within 10% and the probability of minor damage is controlled between 10% and 40%.

Pair-Copula-based trivariate joint probability model of wind speed, wind direction and angle of attack

The temporal and spatial distribution of wind fields in the deep-cut gorge bridge site is complex, and the impact of different incoming flows on the structure is also essentially different. Therefore, it is essential to comprehensively consider the correlation between wind direction, wind speed, and angle of attack. The joint probability models between average wind parameters are first established using the Pair-Copula decomposition based on the field-measured data. Then, the concept of the probability-segmentation-based first order inverse reliability method (PSB-IFORM) is proposed for calculating the environmental surface of the multi-peak joint distribution model. The results show that the mixed von Mises distribution is ideal to fit the wind direction with multi-peak characteristics. The trivariate joint probability model constructed in this paper ultimately represents the correlation of average wind parameters, and the most unfavorable combination of design wind parameters can be found on the environmental surface. Furthermore, the proposed PSB-IFORM can effectively avoid the defects of the inverse first-order reliability method (IFORM) and the conservative highest probability contour (HDC) method in solving the multi-peak joint probability distribution model. This study is of particular interest to researchers and engineers engaged in wind resistance of mountain structures.

Analysis of Information Search around the Time of Childbirth: Estimating Probability Distributions of Search Dates via Mathematical Optimization

Many mothers have considerable anxiety about pregnancy, childbirth, and childcare. For such mothers, searching for information on the Internet is an effective means of dissolving their anxieties. We consider the problem of estimating, for each search word, a distribution of search dates with respect to children’s birth dates. Most of the empirical distributions have unimodal or bimodal shapes, and some of them are asymmetric about extremal points and rise or fall sharply. We propose nonparametric estimation methods based on mathematical optimization models for such probability distributions. Our unimodal and bimodal optimization models automatically estimate the optimal extremal points and can be extended to multimodal distributions. These models are formulated as mixed-integer convex quadratic optimization problems, which can be solved exactly using optimization software. Experimental results using real-world and synthetic datasets demonstrate that our methods are effective by comparison to conventional moving average and kernel estimation methods.

The application of the distributed-order time fractional Bloch model to magnetic resonance imaging

It is now well known that the magnetic resonance imaging (MRI) signal decay deviates from the classical mono-exponential relaxation. This deviation is referred to in the literature as anomalous relaxation. The modelling of this anomalous relaxation can provide a better understanding of MRI magnetization. The purpose of this work is to investigate the utility of the distributed-order time fractional Bloch equations to describe anomalous relaxation processes in human brain MRI data. Two choices of continuous distribution weight functions, which are parameterised by their mean μ and standard deviation σ, are studied to investigate their impact on the model solution behaviour. An implicit numerical method implemented on a graded mesh is proposed to solve the model and the stability and convergence analysis are presented. We also derive semi-analytical solutions of the fully coupled Bloch equations using the Laplace transform technique to assess the accuracy of the numerical scheme. Furthermore, three different voxel models of continuous distribution weight functions, namely a single continuous probability distribution (model 1), two distinct continuous probability distributions (model 2) and a mixture of two continuous probability distributions (model 3), are applied to the in vivo human brain MRI data, and a feasible and reliable parameter estimation method based on a modified hybrid Nelder-Mead simplex search and particle swarm optimization is presented to perform the voxel-level temporal fitting of the MRI data. The application of these distributed-order time fractional Bloch models highlights the validity of the proposed models, and based on the mean square error we conclude that models 2 and 3 might be more suitable than model 1 to characterize anomalous relaxation processes in human brain MRI data.

COMPARISON OF L-MOMENT AND METHOD OF MOMENTS AS PARAMETER ESTIMATORS FOR IDENTIFICATION AND CHOICE OF THE MOST APPROPRIATE RAINFALL DISTRIBUTION MODELS FOR DESIGN OF HYDRAULIC STRUCTURES

In rainfall frequency analysis, the choice of a suitable probability distribution and parameter estimation method is critical in forecasting design rainfall values for varying return periods at every location. Previously, some researchers in Nigeria used the method of moments (MoM) while others used the L-moment method (LMM) as parameter estimators. However, a more accurate result is obtainable if both estimators are used and their results are compared and ranked to obtain the most appropriate distribution models for each location This study compared the performance of two forms of parameter estimation, namely the method of moments (MoM) and the L-moment method (LMM). This was aimed at identifying and selecting the best fit probability distribution models among three distribution models for the design of hydraulic structures. These models are Generalized Pareto (GPA), Generalized Extreme Value (GEV), and Gumbel Extreme Value (EVI). Annual rainfall series of ten gauging stations with data from 33-50 years from ten southern States of Nigeria obtained from NIMET were used for Rainfall Frequency Analysis (RFA). At five locations, the best fit probability model was the GPA probability distribution model with L-Moment. EVI and GEV probability distribution models with the method of moments were the most appropriate probability models at two locations each. EVI probability distribution model with the L-moment was the most appropriate probability model at one place. The findings confirmed that no single distribution outperformed all others at all stations. Since no single model is regarded preferable for all practical purposes, the best-fit probability model with parameter estimator at any location is site-specific. Consequently, available models and parameter estimators are filtered based on the situation at hand and the type of data available. The identified best fit models with the most appropriate parameter estimator would be a tool to help decision-makers in sizing hydraulic structures in the area.

Reliability Modelling of Pipeline Failure under the Impact of Submarine Slides-Copula Method

The instability of seabed slope sediments is the main factor influencing the safety of marine resource development. Therefore, to ensure the safe operation of submarine pipelines under complex and uncertain seabed rock and soil conditions, a reliability model was developed to elucidate the trend of impact-related pipeline damage due to submarine slides. Then, a risk assessment of the damage process of submarine slides impacting pipelines was conducted, which is of great significance for the in-depth safety assessment of pipelines impacted by submarine slides. Based on the copula function, a joint probability distribution model considering the correlation among risk variables was established for rational correlation characterization. A probability analysis method of impact-related pipeline damage attributed to submarine slides based on the copula function was proposed. The Monte Carlo simulation (MCS) method was employed to simulate the random uncertainty in limited observation values and accurately determine the reliability of safe pipeline operation under the action of submarine slides. The conclusions were as follows: (1) Based on the copula function, a joint probability distribution model of risk variables with any marginal distribution function and related structure could be developed. (2) The copula function could reasonably characterize relevant nonnormal distribution characteristics of risk variables and could simulate samples conforming to the distribution pattern of the risk variables. (3) The failure probability calculated with the traditional independent normal distribution model was very low, which could result in a notable overestimation of the reliability of submarine pipelines.

Uncertainty modeling method of weather elements based on deep learning for robust solar energy generation of building

During the actual use stage, the uncertainty of weather leads to errors between the performance of building energy and the simulated values. Usually, uncertainty of weather cannot be eliminated, and difficult to quantify accurately due to complex occurrence rules. Based on the influence of weather uncertainty on solar power generation, this research propose a highly reliable and high-efficiency uncertainty modeling method based on two neural networks: (i) dual-stage attention-based recurrent neural network(DARNN): due to the use of two-stage attention mechanism, as the method to achieve importance interpretability in this study. (ii) Bayesian recurrent neural network(Bayesian RNN): regard the weight and bias value as an unknown distribution, as the method of uncertainty modeling in this study. DARNN analyzes the weight value of each weather element at each time point as the importance through a single learning, and the results show that the importance of solar radiation and relative humidity to solar power generation ranks in the top two. Based on the above results, Bayesian RNN establishes the probability distribution models of solar radiation and relative humidity at each time point of a year by learning the potential correlation between weather elements and taking the historical data of low importance weather elements as input.

A probability distribution model based on the maximum entropy principle for wind power fluctuation estimation

Volatility is an inherent characteristic of wind power. The normal, Weibull, and other distributions are commonly used to describe the characteristics of wind power. However, many of these single distribution models are not suitable to characterize wind power, particularly those converging from multiple wind farm groups. In this study, the maximum entropy distribution model is utilized as probability density function to fit wind power fluctuations. To evaluate the effectiveness and performance of the model, we compared the probability density function curve and cumulative distribution function curve fitting with the mixed Gaussian, the mixed logistic, and the mixed Weibull distribution models using simulation experiments. We developed four scenarios with different numbers of wind farm groups and calculated the fitting error, determination coefficient, and K–S test value for the four models. The simulation results show that the maximum entropy distribution model has the best fitting effect in all four scenarios. Compared with the other three distribution models, the maximum entropy distribution model has clear advantages and is more suitable to describe the fluctuation characteristics of wind power. The parameter estimation of the maximum entropy distribution model can be transformed into a linear optimization problem to significantly reduce calculation complexity.

Transmuted shifted exponential distribution and applications

In this paper, we used the quadratic transmutation map approach to propose a new distribution model called the transmuted shifted exponential distribution (TSED). We derived some of its useful statistical properties such as the moment, Characteristic function, Quantile function, Shannon Entropy, relative entropy, Renyi entropy, moment generating function, mean inactivity function, hazard rate function, survival rate function, and the order statistics. The simulation results showed that as the sample size increases, the biases, variances, and root mean square errors become smaller for the censored sample. We used two life data sets to evaluate the numerical applications of the proposed TSED. The results obtained are compared with some existing probability distribution models. It is observed that the TSED gave a better fit to all the data sets under consideration than other models.