Probabilistic Analysis Approach Research Articles

Efficient Random Field Generation With Rotational Anisotropy for Probabilistic SPH Analysis of Slope Failure

ABSTRACTDue to geological processes such as sedimentation, tectonic movement, and backfilling, natural soil often exhibits characteristics of rotated anisotropy. Recent studies have shown the significant impact of rotated anisotropy on slope stability. However, little research has explored how this rotated anisotropy affects the large deformations occurring after slope failure. Therefore, this study integrates rotated random field theory with smoothed particle hydrodynamics (SPH) to investigate its influence on post‐failure slope behavior. Focusing on a typical slope scenario, this research utilizes graphics processing unit (GPU)–accelerated covariance matrix decomposition (CMD) method to create rotated anisotropy random fields and applies the SPH framework for analysis. It examines the influence of rotated anisotropy angles and the cross‐correlation between cohesion and internal friction angle on landslides. The results indicate that the rotational anisotropy of the slope significantly influences post‐failure behavior. When the rotation angle is close to the slope surface, it tends to amplify both the magnitude and variability of slope failure. Furthermore, the study evaluates the efficiency of generating these random fields and emphasizes the substantial computational speed improvements achieved with GPU acceleration. These findings offer a robust approach for probabilistic analysis of slope large deformations considering rotated anisotropy. They provide a theoretical foundation for accurately assessing the risk of slope collapse, holding significant practical implications for geotechnical engineering.

Parameter estimation of grouting pressure and surface subsidence on the reliability of shield tunnel excavation under incomplete probability information

Most of the results obtained from traditional tunnel reliability models are based on conclusions of deterministic parameters, and ignoring the correlation between parameters tends to generate unreliable conclusions for the analysis. This study investigated the influence of grouting pressure and surface subsidence on the reliability of shield tunnel excavation considering the dependency structures between parameters. A probabilistic analysis approach based on copula method is applied to evaluate the bivariate dependency structure. Firstly, 88 sets of measured data are selected from various tunnel projects at home and abroad, and their statistical parameters and marginal distribution functions are determined. Secondly, a bivariate joint probability distribution model of shield grouting excavation is established, and Monte Carlo Simulation is applied to explore the influence of the selection of the copula function on the failure probability of the shield grouting excavation. The results indicate that under incomplete probabilistic information, disregarding the negative correlation between the parameters will underestimate the reliability of shield grouting construction and yield an overly conservative reliability design. Subsequently, varying the magnitude of the parameter limit values to explore the effect on the failure probability will be advantageous for reliability analysis in dynamic construction. Finally, by varying the sample size of the simulation and original measured data, it is found that excessively small simulated and original sample sizes can lead to inaccurate reliability assessment.

A baseline approach for probabilistic blast risk analysis of building cladding under external explosions

The state of the practice in blast-resistant applications against explosions is to design the structural components for a prescribed combination of explosive mass and location, namely the design basis threat. In this context, the blast source is represented by specific scenarios, mostly associated with expert judgement, rating systems or code provisions. While offering a useful basis for practical applications, the level of detail can be significantly enhanced within a probabilistic framework for risk assessment. In research practice, plenty simplified probabilistic approaches have been proposed on external explosions in order to perform risk assessment. A rigorous methodology for such an assessment is presented herein, using tools and techniques derived from seismic risk-assessment applications. Specifically, the mean annual frequency of different explosive mass hazards is represented via a recurrence law, while the potential locations are modelled as a 2D spatial distribution, accounting for the various layers of defense that exist around the structure, i.e., perimeter protection, landscape, public or private spaces, etc. The methodology is finally substantiated with the case study of a typical building subjected to potential blast loadings from external aggressors.

A probabilistic performance-based analysis approach for a vibrator-ground interaction system

There is an increasing interest in investigating the effects of input uncertainties on dynamic systems. The probabilistic analyses for a vibrator-ground (VG) interaction system are rare and the effects of system uncertainties need to be revealed. This study aims to present an approach for the probabilistic performance-based analysis of the VG system under multi-source uncertainties. The probabilistic model of the VG system is constructed on the basis of the Monte Carlo (MC) simulation combined with the Latin Hypercube Sampling (LHS) method, while the artificial neural networks optimized by the genetic algorithms are employed to reduce the large computational expenses in the MC simulation. Then, a multi-criteria sensitivity analysis is presented by using a technique for order preference by similarity to ideal solution (TOPSIS) to evaluate the effects of input uncertainties on the dynamic performance of the vibrator. Finally, a probabilistic simulation analysis of the VG system is conducted by implementing the presented approach. The results demonstrate the effectiveness of the presented probabilistic performance-based analysis approach for the VG system and evaluate the effects of input uncertainties on the dynamic performance of the system.

Probabilistic learning approach for the liquid holdup analysis of high-viscosity intermittent flows

A Gaussian mixture model (GMM) was implemented to investigate the relationship between the liquid holdup (in various parts of the flow) and the pressure for different experimental realizations of high-viscosity gas–liquid flows. We considered a Newtonian fluid with a constant viscosity of 6 Pa s (600 cP) under a laboratory-controlled temperature. Because the pressure and the holdup do not exhibit a clear-cut relationship in the time domain, a supervised classification algorithm and a “deep” neural network (DNN) were first applied to classify the data points and predict average holdup values. Then, the GMM was applied to determine the holdup in various liquid aggregation structures of the flow as a function of the pressure. The growth rates of the cumulative lengths of the liquid structures (i.e., slug body, mixing front, and liquid film) and the gas bubbles were obtained. The GMM predicted holdup values were in close agreement with the experimental data.

A Novel Approach to Determine Multi-Tiered Nearly Zero-Energy Performance Benchmarks Using Probabilistic Reference Buildings and Risk Analysis Approaches

The Energy Performance of Buildings Directive (EPBD) mandates European Union Member States (MS) to conduct cost-optimal studies using the national calculation methodology (NCM), typically through non-calibrated asset-rating software. Nearly zero-energy building (NZEB) levels must be derived for each chosen Reference Building (RB), which are generally defined using deterministic parameters. Previous research proposed an innovative cost-optimal method that replaces ‘non-calibrated deterministic RBs’ with ‘probabilistically Bayesian calibrated reference building (RB)’ to better handle building stock uncertainties and diversities when deriving benchmarks. This paper aims to develop a framework to address two research gaps necessary for the successful application of the innovative cost optimal method: (1) providing objective criteria for defining NZEB benchmarks and (2) propagating uncertainties and financial risk for each defined benchmark. A robust approach for defining NZEB benchmarks according to four different ambition levels (low, medium, high, and highest) was developed by objectively considering distinct points from multiple cost-optimal plots employing different financial perspectives. Risk analysis is then performed for each defined benchmark by propagating risk from the posterior calibration parameter distributions to visualize and statistically quantify the financial risk, including robust risk, that the private investor could face for reaching each derived benchmark ambition level. The innovative cost-optimal methodology that incorporates the developed framework was applied to a hotel RB case study. The results showed that the developed framework is capable of deriving distinct benchmarks and quantitatively uncovering the full financial risk levels for the four different renovation ambition levels. The current cost-optimal method was also performed for the hotel case study with the RB defined determinitically and using the non-calibrated NCM software, SBEM-mt v4.2c. It was found that the financial feasibility and energy-saving results per benchmark are significantly more realistic and transparent for the proposed innovative cost-optimal method including a better match between the simulated and metered energy consumption with a difference of less than 1% in annual performance. Thus, the performance gap between calculated and actual energy performance that is synonymous with the EPBD methodology, as reported in the literature, is bridged. The case study also showed the importance of the risk analysis. Performing the cost-optimal analysis for a Bayesian calibrated RB using the mean value of the posterior calibrated parameter distributions without propagating uncertainty produced highly optimistic results that obscured the real financial risk for achieving the higher ambition levels of the NZEB benchmarks. Consequently, the developed framework demonstrated a time-bound tightening approach to achieve higher energy performance ambitions, improve risk transparency to private investors, and facilitate more targeted policies towards a net zero-carbon status. Thus, the proposed method considering parameter uncertainty and calibrated RBs is instrumental for devising robust policy measures for the EPBD, to achieve a realistic and long-lasting sustainable energy goal for European buildings.

Time-Dependent Probabilistic Seismic Hazard Analysis for Seismic Sequences Based on Hybrid Renewal Process Models

ABSTRACT Probabilistic seismic hazard analysis (PSHA) is a methodology with a long history and has been widely implemented. However, in the conventional PSHA and sequence-based probabilistic seismic hazard analysis (SPSHA) approaches, the occurrence of mainshocks is modeled as the homogeneous Poisson process, which is unsuitable for large earthquakes. To account for the stationary occurrence of small-to-moderate (STM) mainshocks and the nonstationary behavior of large mainshocks, we propose a time-dependent sequence-based probabilistic seismic hazard analysis (TD-SPSHA) approach by combining the time-dependent mainshock probabilistic seismic hazard analysis (TD-PSHA) and aftershock probabilistic seismic hazard analysis, consisting of four components: (1) STM mainshocks, (2) aftershocks associated with STM mainshocks, (3) large mainshocks, and (4) aftershocks associated with large mainshocks. The approach incorporates an exponential-magnitude, exponential-time model for STM mainshocks, and a renewal-time, characteristic-magnitude model for large mainshocks to assess the time-dependent hazard for mainshocks. Then nonhomogeneous Poisson process is used to model the occurrence of associated aftershocks, in which the aftershock sequences can be modeled using the Reasenberg and Jones (RJ) model or the epidemic-type aftershock sequence (ETAS) model. To demonstrate the proposed TD-SPSHA approach, a representative site of the San Andreas fault is selected as a benchmark case, for which five time-dependent recurrence models, including normal, lognormal, gamma, Weibull, and Brownian passage time (BPT) distributions, are chosen to determine the occurrence of large mainshocks. Then sensitivity tests are presented to show the effects on TD-SPSHA, including (1) time-dependent recurrence models, (2) mainshock magnitude, (3) rupture distance, (4) aftershock duration, (5) escaped time since the last event, and (6) future time interval. Furthermore, the bimodal hybrid renewal model is utilized by TD-SPSHA for another case site. The comparison results illustrate that the sequence hazard analysis approach ignoring time-varying properties of large earthquakes for long periods and the effects of associated aftershocks will result in a significantly underestimated hazard. The TD-SPSHA-based hazard curves using the ETAS model are larger than those of the RJ model. The proposed TD-SPSHA approach may be of significant interest to the field of earthquake engineering, particularly in the context of structural design or seismic risk analysis for the long term.

A Hybrid Probabilistic Risk Analytical Approach to Ship Pilotage Risk Resonance with FRAM

Collision risk in ship pilotage process has complex characteristics that are dynamic, uncertain, and emergent. To reveal collision risk resonance during ship pilotage process, a hybrid probabilistic risk analysis approach is proposed, which integrates the Functional Resonance Analysis Method (FRAM), Dempster–Shafer (D–S) evidence theory, and Monte Carlo (MC) simulation. First, FRAM is used to qualitatively describe the coupling relationship and operation mechanism among the functions of the pilotage operation system. Then, the D–S evidence theory is used to determine the probability distribution of the function output in the specified pilotage scenario after quantitatively expressing the function variability, coupling effect, and the influence of operation conditions through rating scales. Finally, MC simulation is used to calculate the aggregated coupling variability between functions, and the critical couplings and risk resonance paths under different scenarios are identified by setting the threshold and confidence level. The results show that ship collision risk transmission is caused by function resonance in the pilotage system, and the function resonance paths vary with pilotage scenarios. The critical coupling ‘F2-F7(I)’ emerges as a consistent factor in both scenarios, emphasizing the significance of maintaining a proper lookout. The hybrid probabilistic risk analytical approach to ship pilotage risk resonance with FRAM can be a useful method for analysing the causative mechanism of ship operational risk.

Probabilistic machine learning approach for structural reliability analysis

In recent years, the surrogate modeling technique has been increasingly employed for the failure probability estimation of civil structures. The surrogate modeling technique acts as a black box that predicts the performance of expensive-to-evaluate problems. However, the uncertainty of failure probability estimation due to the discrepancy between the surrogate model and physical model has not been well studied. This study introduces a new surrogate modeling technique for failure probability estimation of civil structures that utilizes a Bayesian neural network. Specifically, a fully connected neural network is constructed to approximate the limit state function. The hyperparameters in the neural network are obtained within the Bayesian paradigm, and the probability distributions are estimated through Laplace approximation. When the Bayesian neural network method is used for reliability analysis, the failure curve and the corresponding uncertainty can be estimated. Numerical studies on 2d truss, a simple support beam under moving load, and dynamic analysis of subway station considering the soil–structure interaction are conducted to validate the efficiency of the approach. Results with Monte Carlo simulation and subset simulation are also presented. The results demonstrate the proposed method’s potential for improving prediction accuracy by factoring in the uncertainty embedded in the surrogate model. Additionally, it exhibits higher levels of efficiency than traditional methods.

EFFECT OF EPISTEMIC UNCERTAINTY ON SEISMIC FRAGILITY OF BASE-ISOLATED RC-BUILDING FRAME USING INCREMENTAL DYNAMIC ANALYSIS

The quantification and impact of epistemic uncertainty in the RC frame building can analyze due to recent advancements in processing power and the availability of reliable seismic vulnerability assessment techniques. In the present study, a base-isolated 10-story RC building frame is designed and analyzed per the latest Indian standards, with lead rubber bearing as the base isolation system. The selected base-isolated RC frame building was analyzed using probabilistic and deterministic approaches. As the fundamental epistemic uncertainty parameter, the mechanical strength of concrete and steel is considered. The Monte-Carlo method is determined the unpredictability of the RC frames' structures. The incremental dynamic analysis is conducted per the FEMA P695 guidelines to evaluate the wide range of 32 far-field ground motions on the base-isolated RC frame structure. Maximum roof drift ratio responses are utilized to generate the seismic fragility curve by adopting the several threshold values of damage index, such as, slight, moderate, severe, and complete. The traditional linear regression method is implemented to derive the seismic fragility curves of various damage thresholds. The study results reveal that the deterministic strategy is more likely to predict damage by 10 to 25 percent less than the probabilistic approach. The probabilistic analysis approach shows that epistemic uncertainty significantly affects the prediction of the seismic damage probability

Stochastic seepage analysis in embankment dams using different types of random fields

Random field theory has become a very popular approach for probabilistic analysis of earth dams. This study performs a stochastic analysis of seepage through an embankment dam to account for the spatial variability of hydraulic parameters. The originality of this study consists in using and comparing three types of Random Fields RFs for the seepage analysis: classical stationary RFs, conditional RFs (to consider the position of available measurements), and non-stationary RFs (to consider the mean variation with depth). The same sample of hydraulic conductivity values is considered to generate the three types of random fields. The hydraulic conductivity RFs are integrated into a Finite Element seepage analysis model to evaluate the flow velocity, hydraulic gradient, pore water pressure, and flow rate. The process is repeated by Monte Carlo simulations to characterize the spatial variability of the seepage results in terms of mean and standard deviation at each point of the studied dam and its foundation. The results show a higher dispersion for the stationary RF case and a lower dispersion for the conditional RF case. For the case study, the results also show that the use of different RFs for modelling the spatial variability of hydraulic conductivity induces differences that can be considered significant for flow velocity, moderate for hydraulic gradient and minor for pore pressure.

Uncertainty propagation of turbulence parameters for typhoon and Non-typhoon winds in buffeting analysis of Long-span bridges

Wind turbulence-induced buffeting vibration affects the serviceability of long-span bridges and lead to fatigue problems. The randomness of turbulence parameters in the power spectrum density function is always disregarded, failing to well reproduce the dispersion of structural buffeting responses and achieve the extreme vibration amplitude. This study proposes a probabilistic buffeting analysis approach based on multi-point estimation, dimension reduction techniques, and the principle of maximum entropy accounting for the uncertainty of turbulence parameters. The uncertainties in turbulence power spectral density functions are quantified based on the long-term real observational wind data captured by the sensors installed at Xihoumen Bridge. These uncertainties are propagated into the buffeting response of the bridge using the proposed method. The results are compared with those of Monte Carlo simulation, suggesting a good agreement with substantially lower computational costs can be attained by the proposed method. Then, the probability density evolution of buffeting response versus wind speed is calculated. Results reveal that typhoon-induced buffeting response is greater than non-typhoon’s under low mean wind speeds (e.g., 25 m/s), whereas it is the opposite at high wind speeds (e.g., 30 m/s). The predicted probability density evolution of buffeting response exhibits a great consistency with real observations. By introducing the mean wind speed hazard curves for both typhoon and non-typhoon winds, the exceeding probability of vibration within a given period can be easily attained. It allows the estimation of return periods of structural responses and development of the uniform-risk approach for structure design rather than the conventional uniform-hazard design method.

A Practical Approach of Probabilistic Seismic Hazard Analysis for Vector IMs Regarding Mainshock with Potentially Largest Aftershock

ABSTRACT Seismic hazard and risk may be underestimated if aftershocks are ignored within the traditional probabilistic seismic hazard analysis (PSHA). In this study, a practical approach is proposed to calculate the mean annual rate of the joint exceedance of different ground motion vector intensity measures (IMs) for mainshocks and their potentially largest aftershock. The proposed approach is built based on an indirect vector-valued PSHA framework, which was originally used to compute the joint hazard of multiple IMs for mainshocks. Within the proposed approach, the overall hazard caused by mainshock-aftershock scenarios is calculated by including two key components, namely: 1) the occurrence rate of a given hazard level of mainshock as calculated by the standard PSHA; and 2) the occurrence probability of a given hazard level of aftershock conditioned on the mainshock, which is calculated by establishing the joint distribution of the IMs for both mainshocks and aftershocks using the Copula theory. Based on 662 groups of mainshock-aftershock ground motions from 13 earthquake events in the NGA-West2 database, the empirical joint probability distribution model between the peak ground accelerations of mainshocks and aftershocks (i.e. PGA MS and PGA AS) is developed. The Clayton Copula function is calibrated as the optimal choice and the marginal distributions of PGA MS or PGA AS could be properly modelled using the generalized extreme value distributions. The proposed approach is implemented to construct the joint hazard surface regarding both PGA MS and PGA AS for a hypothetical site. The results indicate that using different types of copula functions and marginal distributions of PGA MS and PGA AS has a noticeable impact on the final joint hazard level. Moreover, a coarse assumption that PGA MS and PGA AS follow a joint Gaussian distribution in the logarithm scale would lead to considerable bias in the mainshock-aftershock joint hazard especially at low mean annual rates of exceedance.

Reliability analysis of floating wind turbine dynamic cables under realistic environmental loads

The need for more robust design of dynamic cables used for power export in floating wind turbine (FWT) systems is accentuated by the frequent occurrence of power cable failures. Such failures contribute considerably to the cost of global offshore wind farm losses. Fatigue is often times a critical consideration in the structural safety of these cables. This is understandably so, given that they experience numerous loading cycles–mainly induced by the combined action of wind and waves throughout their service life. It is therefore pertinent that the reliability level attainable by these cables is quantified and elaborated upon. In this paper, a probabilistic reliability analysis approach is developed to quantify the reliability levels of dynamic power cables. Uncertainties emanating from the randomness of realistic environmental scatter, geometric and material variables are all taken into account in this study. To facilitate the computation of the structural demands on the dynamic power cable, an efficient analytical model was developed. Key aspects such as cable–soil interaction and boundary-layer phenomenon are captured by the analytical model. Kriging metamodel is then employed to propagate relevant uncertainties into the reliability problem, making it possible to quantify the reliability levels of these cables.

Global Sensitivity Analysis for Impedance Spectrum Identification of Lithium-Ion Batteries Using Time-Domain Response

Accurate modeling is of great importance for describing battery dynamics under different working conditions. To achieve high accuracy and obtain insights into battery operations, it is critical to bridge the time-domain equivalent circuit model and frequency-domain electrochemical impedance spectroscopy. However, the practical battery running data are recorded at a very low sampling frequency, it is thus challenging to identify the frequency-domain impedance spectrum using time-domain response data. To solve this problem, this article proposes a systematic battery time-domain modeling approach considering impedance spectrum identification. First, a probabilistic approach for global sensitivity analysis is proposed to evaluate the impact of different parameters on model performance. The parameter sensitivity of both integer-order and fractional-order models are evaluated using the Sobol indices obtained by Monte Carlo simulations. Then, a Bayesian optimization algorithm is proposed to identify model parameters to reduce the evaluation times of the battery model. Finally, the experimental data conducted on LiFePO <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{4}$</tex-math></inline-formula> cells are employed to verify the proposed method. The results indicate that the total Sobol indices show a miscellaneous sensitivity of parameters on impedance spectra, which consolidates the understanding of impedance characteristics, and the higher order integer-order models with well-initialized low sensitive parameters are more suitable for predicting frequency-domain characteristics.

Probabilistic Seismic Hazard Analysis on Pavement Failure Restoration; Case Study of Sorong–Makbon Road

The Sorong–MakbonSorong–Makbon Corridor is one of the key routes connecting Sorong to other sections of the West Papua region in Indonesia. Throughout the Sorong–Makbon Corridor, roads and slopes often sustain damage. When landslides reach the road shoulder and destroy the pavement, they often prevent access to the road. In addition to the influence of surface water runoff, there are indications that earthquakes contribute to the ineffectiveness of the previous design. This seems to be accurate since the author has seen the typical movement of avalanches. Using the Probabilistic Seismic Hazard Analysis (PSHA) approach, the earthquake’s effects on this corridor were mapped out. With the use of the Indonesian earthquake data library, the Matlab-Zmap Program, and the Spectrum Response, the history of earthquakes in the Sorong–Makbon corridor was analysed to determine their velocity. This analysis reveals that the earthquake’s influence on the Sorong–Makbon corridor has an acceleration value between 1.2 and 1.5 G. The prior design did not account for a quake of this magnitude. With this study, the correctly identified seismic impact could be sent back into the simulation to more adequately repair and restore the damage.

Physics-based probabilistic assessment of creep-fatigue failure for pressurized components

To achieve a high-reliability design of high-temperature structures with a feasible balance between accuracy and efficiency, the physics-based probabilistic assessment for creep-fatigue failure is proposed under the probabilistic Linear Matching Method (pLMM) framework. At the physical level, the structural failure mechanism is reflected in the prepared training database, which is generated by the direct method procedures. And to efficiently express the relationship between design parameters and structural responses implicitly, the direct method-driven artificial neural network is built with the superior fitting quality of damage and lifetime. With the benchmarks provided, the applicability of the proposed probabilistic analysis approach for risk management of critical infrastructures is demonstrated, where the reliability-based creep-fatigue evaluation diagram is established according to different requirements. Furthermore, a novel data classification scheme is proposed to deal with the randomness in creep damage-dominated probabilistic assessment.

Uncertainty quantification and probabilistic performance-based assessment of nonlinear behavior of moment resisting frames under design and extreme wind loads

Recent advancements in performance-based assessment and design of buildings subjected to wind loads call for the incorporation of uncertainties in the simulation of both loading and structural response. Additionally, they require a better understanding of nonlinear wind-induced response of buildings. Probabilistic analysis approaches are commonly used for the incorporation of uncertainties in performance-based assessment of building response. These approaches, however, focus more on the wind loading side as opposed to incorporating detailed nonlinear models for the structures. This study leverages SimCenter's newly developed tool WE-UQ to integrate a detailed nonlinear structural model of a 20-story 2D building frame into larger probabilistic simulations. The detailed structural model is created in finite element software OpenSEES and can simulate complex behavior such as stiffness and strength degradation and provide reasonably accurate predictions of yield and collapse. Simulation results are then utilized for probabilistic performance-based assessment of the building frame using the new guidelines proposed by the ASCE pre-standard for performance-based wind design. Additionally, performance of the frame under higher wind speeds that would lead to yielding or collapse of the building is also assessed. The results obtained from the probabilistic simulations are compared with pure deterministic simulation outcomes to investigate the effects and necessity of adding uncertainties into the response prediction of buildings subjected to wind loads.

Probabilistic deconvolution of PET images using informed priors.

We present a probabilistic approach to medical image analysis that requires, and makes use of, explicit prior information provided by a medical expert. Depending on the choice of prior model the method can be used for image enhancement, analysis, and segmentation. The methodology is based on a probabilistic approach to medical image analysis, that allows integration of 1) arbitrarily complex prior information (for which realizations can be generated), 2) information about a convolution operator of the imaging system, and 3) information about the noise in the reconstructed image into a posterior probability density. The method was demonstrated on positron emission tomography (PET) images obtained from a phantom and a patient with lung cancer. The likelihood model (multivariate log-normal) and the convolution operator were derived from phantom data. Two examples of prior information were used to show the potential of the method. The extended Metropolis-Hastings algorithm, a Markov chain Monte Carlo method, was used to generate realizations of the posterior distribution of the tracer activity concentration. A set of realizations from the posterior was used as the base of a quantitative PET image analysis. The mean and variance of activity concentrations were computed, as well as the probability of high tracer uptake and statistics on the size and activity concentration of high uptake regions. For both phantom and in vivo images, the estimated images of mean activity concentrations appeared to have reduced noise levels, and a sharper outline of high activity regions, as compared to the original PET. The estimated variance of activity concentrations was high at the edges of high activity regions. The methodology provides a probabilistic approach for medical image analysis that explicitly takes into account medical expert knowledge as prior information. The presented first results indicate the potential of the method to improve the detection of small lesions. The methodology allows for a probabilistic measure of the size and activity level of high uptake regions, with possible long-term perspectives for early detection of cancer, as well as treatment, planning, and follow-up.

A Copula-Hammersley approach for probabilistic analysis of integrated power and heat networks

As the interaction between the electrical and district heating networks have been increased due to the wide utilization of combined heat and power units, the interest in providing an appropriate tool to analyze these integrated systems dramatically grows. Besides, the installation of renewable energy power plants, such as wind turbines, is increased because of their clean power generation. However, the amount of their generated power is uncertain since wind speed is not exactly determined. In this regard, deterministic approaches cannot be employed to solve the power flow problem, and it is necessary to use a probabilistic viewpoint. This paper presents a probabilistic power flow framework for the integrated power and heat networks based on a novel Copula-Hammersley technique. The proposed method is able to consider various system uncertainties along with the existed interaction between the heat and power networks to successfully solve the power flow problem. Simulations on a case study of Barry Island networks demonstrate the applicability and effectiveness of the proposed methodology. The superiority of this technique is verified by studying various indices and characteristics of the obtained results in comparison with some other conventional approaches. It is verified that the proposed technique reduces the average mean and standard deviation errors by approximately 45% and 72% compared to traditional methods, respectively. Furthermore, the efficiency ratio of the proposed approach is 15% higher than that of the conventional methods which shows that it is faster and more accurate than those techniques.