Stochastic Method Research Articles

Stochastic assessment of voltage sags and techno-economic optimization

Power quality has become an essential concern for industries and domestic energy consumption with the development of sophisticated equipment like micro-electronic devices. When a power quality event happens, such as voltage sag, financial losses for industries increase tremendously. Therefore, voltage sag evaluation becomes crucial for predicting the number of events and severity of voltage sag events of the electrical network. Industries can determine the mitigation investment needed for optimal operation using the knowledge obtained through voltage sag analysis method. Thus, the first part of the study addressed the development of a stochastic assessment method for voltage sag at an interested bus in the power system network, which was an initial objective of the study. The second part of the research investigates dynamic voltage restorer (DVR) control techniques, as well as the necessary capacitance and energy storage dimensions. The studies also recommend a technique for economic evaluation that emphasizes the expense of voltage sag events as well as the cost of investment in DVR with and without voltage sag events. The size of DVR and economic assessment model established in these studies enables industries to rate the cost of voltage sag and the total investment in mitigation devices.

Optimal planning for hybrid renewable energy systems under limited information based on uncertainty quantification

Developing hybrid renewable energy systems (HRES) is crucial for ensuring affordable, sustainable, and reliable energy access in remote rural and island regions. Rich and detailed data play a pivotal role in the optimal design of HRES. However, remote areas often face data limitations due to inadequate metering infrastructure, which further increases uncertainties in HRES design. This paper proposes a planning optimization method that quantifies multiple uncertainties, requiring only limited information for the optimal HRES design. First, uncertainties in HRES planning are classified into different types based on intrinsic randomness, data availability, and impact level. Then, by integrating uncertainty quantification with credibility theory, knowledge-based scenario generation models are developed to leverage limited available information to generate extreme and typical operating conditions for a tailored HRES design. Finally, a fuzzy credibility-constrained stochastic-robust optimization model is proposed to optimize the design of HRES. A practical case facing significant data scarcity and gaps is used to validate the effectiveness of the proposed method. The proposed approach reduces the loss of load probability for HRES to 0.02% and lowers the levelized cost of energy to $0.16/kWh—33% lower than that of the deterministic method and 79% lower than that of the traditional stochastic method.

Electrical resistivity tomography inversion combining deep variational autoencoder and stochastic adaptive sampling

Geophysical methods, such as electrical resistivity tomography (ERT), can be used to imaging the near-surface electrical resistivity as field measurements depend on the subsurface porosity, water saturation and fluid salinity. ERT has been widely applied to investigate mineral and groundwater resources, and in archaeological, environmental, and engineering studies. The prediction of subsurface electrical conductivity from ERT data requires solving a geophysical inverse problem. For near-surface characterization studies, this is often accomplished with deterministic inverse methods. These methods linearize the problem around an initial solution, and their smoothness depends on an imposed a priori spatial regularization term. Depending on this parameterization, these methodologies might struggle to capture the natural variability of the subsurface. Moreover, deterministic solutions have limited capabilities for uncertainty assessment. On the contrary, stochastic inverse methods can assess uncertainties by predicting multiple model realizations that fit similarly the recorded ERT data. However, they are often more computationally expensive than deterministic solutions. Deep learning algorithms based on deep generative models have been used to re-parametrize model and data spaces into low-dimensional domains and efficiently solve geophysical inverse problems. However, within this context, uncertainty assessment is challenging. We propose a deep convolutional variational autoencoder (VAE) coupled with stochastic adaptive optimization to perform stochastic ERT inversion. Geostatistical simulations of electrical resistivity are used as training data set of the VAE. After training, the VAE generates electrical resistivity models that reproduce the statistics and spatial continuity patterns of the training data set. Then, the VAE latent space is iteratively perturbed and updated with adaptive stochastic sampling based on the misfit between observed and predicted ERT data. The proposed methodology is illustrated in two-dimensional synthetic and real data sets to illustrate the ability of the proposed method to predict reliable electrical resistivity models while generating multiple possible scenarios for uncertainty assessment.

A Semi-implicit Stochastic Multiscale Method for Radiative Heat Transfer Problem in Composite Materials

A Semi-implicit Stochastic Multiscale Method for Radiative Heat Transfer Problem in Composite Materials

Predicting Mortality Rates and Longevity Using Cains -Blake-Dowd Model

Pension schemes and annuity providers frequently guarantee their retirement payouts until the retirees' deaths. As a result of longer life expectancies and declining rates of death in old age, trends in mortality and longevity have become evident. Academicians and actuaries have been forced to concentrate their research on mortality and longevity concerns in particular as a result of this. Instead of a provident fund, the new National Social Security Fund Act Number 45 of 2013 established a pension fund that is a requirement for every employee. Annuity service providers are exposed to the longevity risk when the scheme's participants retire. For pricing and reserving, appropriate modeling tools or projected life tables are required. In comparison to deterministic models, which were based on projected present values, stochastic models allow a variety of risk causes and components as well as pertinent effect on portfolio performance. The long term mean level of Longevity has become more uncertain exposing the annuity service providers such as assurance companies and states to the risk of uncertainty after retirement. Most industrialized countries' national security systems, pension plans, and annuity providers have revised their mortality tables to account for longevity risks due to decline mortality rates and rising life expectancy. Kenya is one of the developing nations that has seen a drop-in death rates and a rise in life expectancy recently. Since developing nations choose to take the longevity risk into account when pricing and reserving annuities because such long term mean level in mortality rates declines and increases life expectancy, particularly at retirement age, pose risks to annuity service providers and pension plans that has been pricing annuities based on mortality tables that do not take these trends into account. The stochastic aspect of mortality was ignored by earlier actuarial models used to estimate trends. The actuary will therefore likely be interested in knowing how the future mortality trend utilizing stochastic models affects annuity pricing and reserve. Demographers and actuaries have since employed a variety of stochastic methods to forecast mortality while examining a variety of stochastic model ranges. The CBD stochastic model, which was the first to take longer life expectancies into account, is now extensively used, and a number of expansions and adjustments have been suggested to stop the major characteristics of mortality intensity. The CBD model, developed by Andrew Cairn, David Blake, and Kevin Dowd, is being used in this study to fit mortality rates, forecast mortality trends, using least square method and then calculate projections for life expectancy. Regarding the longevity risk, we take into account the possibilities of computing annuity benefits by connecting the benefits to actual mortality and calculating the present value on annuities. The results of the study showed that, the CBD model can be used to forecast mortality rates where parameters estimating the CBD model are performed using the bivariate random walk (drift).

Applying and benchmarking a stochastic programming-based bidding strategy for day-ahead hydropower scheduling

AbstractAneo is one of the first Nordic power companies to apply stochastic programming for day-ahead bidding of hydropower. This paper describes our experiences in implementing, testing, and operating a stochastic programming-based bidding method aimed at setting up an automated process for day-ahead bidding. The implementation process has faced challenges such as generating price scenarios for the optimization model, post-processing optimization results to create feasible and understandable bids, and technically integrating these into operational systems. Additionally, comparing the bids from the new stochastic-based method to the existing operator-determined bids has been challenging, which is crucial for building trust in new procedures. Our solution is a rolling horizon comparison, benchmarking the performance of the bidding methods over consecutive two-week periods. Our benchmarking results show that the stochastic method can replicate the current operator-determined bidding strategy. However, additional work is needed before we can fully automate the stochastic bidding setup, particularly in addressing inflow uncertainty and managing special constraints on our watercourses.

Radiation dose estimation for indoor radon, thoron and their progenies using a stochastic method-a small-scale survey in Wuhan, China.

Passive radon monitors with CR-39s are widely used in major epidemiological surveys. However, the conventional CR-39 track density determining strategy makes it difficult to accurately estimate the concentration because of the heterogeneity of tracks on CR-39s. This study introduced a stochastic method, Latin hypercube sampling, to improve the track density determining strategy and provide the probability distribution of 222Rn concentration and equilibrium equivalent thoron concentration. The first 222Rn and 220Rn discriminated survey was conducted in Wuhan, China, in 2018 using RADUET® and deposition-based passive 220Rn progeny monitors and applying the stochastic method to the measurement. The results indicate that the stochastic method could decrease the effects of the track heterogeneity on the CR-39s and provide reliable results. The 220Rn progeny contributed more than 40% of the total inhalation dose in the survey, which cannot be ignored in urban family dwellings.

Comparative study of deterministic and stochastic optimization algorithms applied to the absorption of CO2 by alkanolamine solution

Abstract A model based on simulated annealing approach is used with e-UNIQUAC model as well as two other algorithms to study the absorption of carbon dioxide by monoethanolamine solutions. In this work, we propose to compare the performance (through the knowledge of RMSD values) of two stochastic methods, namely the GA (genetic algorithm) and SA (simulated annealing) methods and a deterministic method that is the simplex method. These methods were applied to the absorption of carbon dioxide by an alkanolamine solution using a chemical equilibrium model and a thermodynamic equilibrium model. The latter is based on the use of the modified-UNIQUAC (UNIQUAC-electrolyte) model instead of e-NRTL model for the liquid phase and a fugacity model for the vapor phase. The chemical equilibrium in this work represents the absorption of CO2 by monoethanolamine solution at different temperatures. Solving the coupled system of material and charge balances gives us the carbon dioxide pressure while taking into account the non-ideality of the system. The three-optimization methods show good agreement with the experimental data with a better performance of the simulated annealing method..

SmoQyDEAC.jl: A differential evolution package for the analytic continuation of imaginary time correlation functions

We introduce the SmoQyDEAC.jl package, a Julia implementation of the Differential Evolution Analytic Continuation (DEAC) algorithm [N. S. Nichols et al., Phys. Rev. E 106, 025312 (2022)] for analytically continuing noisy imaginary time correlation functions to the real frequency axis. Our implementation supports fermionic and bosonic correlation functions on either the imaginary time or Matsubara frequency axes, and treatment of the covariance error in the input data. This paper presents an overview of the DEAC algorithm and the features implemented in the SmoQyDEAC.jl package. It also provides detailed benchmarks of the package’s output against the popular maximum entropy and stochastic analytic continuation methods. The code for this package can be downloaded from our GitHub repository at https://github.com/SmoQySuite/SmoQyDEAC.jl or installed using the Julia package manager. The online documentation, including examples, can be accessed at https://smoqysuite.github.io/SmoQyDEAC.jl/stable/.

Codebase release r1.1 for SmoQyDEAC.jl

We introduce the SmoQyDEAC.jl package, a Julia implementation of the Differential Evolution Analytic Continuation (DEAC) algorithm [N. S. Nichols et al., Phys. Rev. E 106, 025312 (2022)] for analytically continuing noisy imaginary time correlation functions to the real frequency axis. Our implementation supports fermionic and bosonic correlation functions on either the imaginary time or Matsubara frequency axes, and treatment of the covariance error in the input data. This paper presents an overview of the DEAC algorithm and the features implemented in the SmoQyDEAC.jl package. It also provides detailed benchmarks of the package’s output against the popular maximum entropy and stochastic analytic continuation methods. The code for this package can be downloaded from our GitHub repository at https://github.com/SmoQySuite/SmoQyDEAC.jl or installed using the Julia package manager. The online documentation, including examples, can be accessed at https://smoqysuite.github.io/SmoQyDEAC.jl/stable/.

Multicellular adaptation to electrophysiological perturbations analyzed by deterministic and stochastic bioelectrical models.

Cells can compensate a disruptive change in one ion channel by compensatory changes in other channels. We have simulated the adaptation of a multicellular aggregate of non-excitable cells to the electrophysiological perturbation produced by the external blocking of a cation channel. In the biophysical model employed, we consider that this blocking provokes a cell depolarization that opens a voltage-gated calcium channel, thus allowing toxic Ca2+ levels. The cell adaptation to this externally-induced perturbation is ascribed to the multiplicity of channels available to keep the cell membrane potential within a physiological window. We propose that the cell depolarization provokes the upregulated expression of a compensatory channel protein that resets the cell potential to the correct polarized value, which prevents the calcium entry. To this end, we use two different simulation algorithms based on deterministic and stochastic methods. The simulations suggest that because of the local correlations coupling the cell potential to transcription, short-term bioelectrical perturbations can trigger long-term biochemical adaptations to novel stressors in multicellular aggregates. Previous experimental data on planarian flatworms' adaptation to a barium-containing environment is also discussed.

Advancing Parameter Estimation in Differential Equations: A Hybrid Approach Integrating Levenberg–Marquardt and Luus–Jaakola Algorithms

This study presents an integrated approach that combines the Levenberg–Marquardt (LM) and Luus–Jaakola (LJ) algorithms to enhance parameter estimation for various applications. The LM algorithm, known for its precision in solving non-linear least squares problems, is effectively paired with the LJ algorithm, a robust stochastic optimization method, to improve accuracy and computational efficiency. This hybrid LM-LJ methodology is demonstrated through several case studies, including the optimization of MESH equations in distillation processes, modeling controlled diffusion in biopolymer films, and analyzing heat and mass transfer during the drying of cylindrical quince slices. By overcoming the convergence issues typical of gradient-based methods and performing global searches without initial parameter bounds, this approach effectively handles complex models and closely aligns simulation results with experimental data. These capabilities highlight the versatility of this approach in engineering and environmental modeling, significantly enhancing parameter estimation in systems governed by differential equations.

Analysis of a stochastic SEIS epidemic model motivated by Black–Karasinski process: Probability density function

This paper examines a stochastic SEIS epidemic model motivated by Black–Karasinski process. First, it is shown that Black–Karasinski process is a both biologically and mathematically reasonable assumption compared with existing stochastic modeling methods. By analyzing the diffusion structure of the model and solving the relevant Kolmogorov–Fokker–Planck equation, a complete characterization for explicitly approximating the stationary density function near some quasi-positive equilibria is provided. Then for the deterministic model, the basic reproduction number and related asymptotic stability are studied. Finally, several numerical examples are given to substantiate our theoretical findings.

Conceptual advances in petrophysical inversion techniques: The synergy of machine learning and traditional inversion models

Petrophysical inversion techniques are essential for estimating reservoir properties such as porosity, permeability, and fluid saturation, which are critical for optimizing hydrocarbon recovery and reservoir management. Traditionally, deterministic and stochastic inversion methods have relied on well log data, core samples, and seismic information to generate models of subsurface properties. However, these techniques face limitations in handling large datasets, nonlinear relationships, and uncertainties in complex reservoir environments. Recent advances in machine learning (ML) offer an opportunity to enhance these traditional methods by providing a data-driven approach capable of learning patterns and refining inversion models. This review explores the potential synergy between traditional petrophysical inversion techniques and machine learning algorithms to create a new paradigm for reservoir parameter estimation and analysis. Machine learning’s ability to process large volumes of diverse data and capture nonlinear relationships complements the physics-based constraints of traditional inversion methods. By combining these two approaches, hybrid models can provide improved accuracy in predicting reservoir properties and handling data gaps or uncertainties. The review discusses specific case studies where machine learning-assisted inversion models have been successfully applied, such as the estimation of porosity and permeability, seismic inversion for lithology identification, and fluid saturation modeling. These hybrid models demonstrate enhanced predictive accuracy, faster computational efficiency, and real-time adaptability, transforming reservoir characterization and management. The integration of machine learning with traditional inversion techniques represents a major advancement in petrophysical analysis. This synergy holds the potential to revolutionize reservoir parameter estimation, making it more accurate, robust, and responsive to real-time data, ultimately improving decision-making in reservoir engineering and maximizing hydrocarbon recovery. Keywords: Petrophysical Inversion, Machine Learning, Traditional Inversion, Models.

Reliability optimization through soft digital twins

This paper presents a framework for developing a “soft digital twin” (SDT) for reliability optimization through modeling and simulation. The focus is on demonstrating the effectiveness of the SDT in modeling maintenance task processes within mission-critical facilities, which is particularly essential for reliable operations in critical infrastructure such as nuclear facilities. The need for efficient completion of maintenance tasks (MTs) to ensure high reliability and minimal downtime underscores the challenge faced by managers, who desire a predictive tool akin to a “crystal ball” for optimal resource configuration in the face of uncertainties from equipment failures, staffing issues, and supply chain disruptions. The proposed SDT functions as this predictive tool, leveraging the simulation’s versatility to provide insights into resource configurations and staff planning. This work extends the prior research by incorporating additional model validation, sensitivity testing, and analysis of the impact of various resource changes on the system. It employs a combination of data-driven frameworks and stochastic modeling methods to construct an adaptive SDT capable of accommodating changes in system behavior. The work provides a framework for the construction of SDT, testing and validation of its results, and its application to a case study of a mission-critical facility focused on replication and then optimizing of two key performance indicators based on human resource mixtures. Initial findings suggest that the SDT yields reliable results comparable to retrospective test datasets, offering the potential to minimize MTs’ time in the system while maximizing throughput within specified time frames through scenario experimentation and optimization.

Investigation of the Effect of Integrated Offset, GPS, and InSAR Data in the Stochastic Source Modeling of the 2002 Denali Earthquake

This study investigates the effect of geological field measurement (offset), global positioning system (GPS), and interferometric synthetic aperture radar (InSAR) data on the estimation of the co-seismic earthquake displacements of the 2002 Denali earthquake. The analysis is conducted using stochastic source modeling. Uncertainties associated with each dataset limit their effectiveness in source model selection and raise questions about the adequate number of datasets and their type for reliable source estimation. To address these questions, stochastic source models with heterogeneous earthquake slip distributions are synthesized using the von Kármán wavenumber spectrum and statistical scaling relationships. The surface displacements of the generated stochastic sources are obtained using the Okada method. The surface displacements are compared with the available datasets (i.e., offset, GPS, and InSAR) individually and in an integrated form. The results indicate that the performance of stochastic source generation can be significantly improved in the case of using GPS data and in the integrated case. Overall, based on the case study of the 2002 Denali earthquake, the combined use of all available datasets increases the robustness of the stochastic source modeling method in characterizing surface displacement. However, GPS data contribute more than InSAR and offset data in producing reliable source models.

Dynamic Testing and Finite Element Model Adjustment of the Ancient Wooden Structure Under Traffic Excitation

In situ dynamic testing is conducted to study the dynamic characteristics of the wooden structure of the North House main hall. The velocity response signals on the measurement points are obtained and analyzed using the self-interaction spectral method and stochastic subspace method, yielding natural frequencies, mode shapes, and damping ratios. This study reveals that the natural frequencies and damping ratios are highly consistent between the two methods. Therefore, to eliminate errors, the average of the results from both modal identification methods is taken as the final measured modal parameters of the structure. The natural frequencies of the first and second order in the X direction were 2.097 Hz and 3.845 Hz and in the Y direction were 3.955 Hz and 5.701 Hz. The modal frequency in the Y direction of the structure exceeds that in the X direction. Concurrently, a three-dimensional finite element model was established using ANSYS 2021R1, considering the semi-rigid properties of mortise–tenon connections, and validated based on in situ dynamic testing. The sensitivity analysis indicates adjustments to parameters such as beam–column elastic modulus, tenon–mortise joint stiffness, and roof mass for finite element model refinement. Modal parameter calculations from the corrected finite element model closely approximate the measured modal results, with maximum errors of 9.41% for the first two frequencies, both within 10% of the measured resonant frequencies. The adjusted finite element model closely matches the experimental results, serving as a benchmark model for the wooden structure of North House main hall. The validation confirms the rationality of the benchmark finite element model, providing valuable insights into ancient timber structures along transportation routes.

Hybrid energy system optimization integrated with battery storage in radial distribution networks considering reliability and a robust framework

This research presents a robust optimization of a hybrid photovoltaic-wind-battery (PV/WT/Batt) system in distribution networks to reduce active losses and voltage deviation while also enhancing network customer reliability considering production and network load uncertainties. The best installation position and capacity of the hybrid system (HS) are found via an improved crow search algorithm with an inertia weight technique. The robust optimization issue, taking into account the risk of uncertainty, is described using the gap information decision theory method. The proposed approach is used with 33- and 69-bus networks. The results reveal that the HS optimization in the network reduces active losses and voltage variations, while improving network customer reliability. The robust optimization results show that in the 33-bus network, the system remains resilient to prediction errors under the worst-case uncertainty scenario, with a 44.53% reduction in production and a 22.18% increase in network demand for a 30% uncertainty budget. Similarly, in the 69-bus network, the system withstands a 36.22% reduction in production and a 16.97% increase in load for a 25% uncertainty budget. When comparing stochastic and robust methods, it was found that the stochastic Monte Carlo method could not consistently provide a reliable solution for all objectives under uncertainty, whereas the robust approach successfully managed the maximum uncertainty related to renewable generation and network demand across different uncertainty budgets.

Low-dose radiographic inspection of welding by a novel aperiodic reverse stochastic resonance method

Abstract Low-dose radiographic inspection is a growing trend in industry to minimize radiation risks to humans and the environment. However, reduction in radiation dose often introduces significant noise, which affects image quality and hinders accurate identification of subtle defects. This study addresses this issue by introducing a novel phenomenon called aperiodic reverse stochastic resonance (ARSR), observed in nonlinear systems excited by aperiodic binary signals. ARSR enables simultaneous amplitude amplification and reversal of signals under specific noise conditions. Leveraging ARSR, we propose an image denoising framework for low-dose radiographic inspections. First, a set of projection data is obtained by using Radon transform to reduce the dimensionality of x-ray images from different angles. Then, the projection data is modulated based on the ARSR system. Finally, the image is reconstructed based on the inverse Radon transform. Simulations and experimental comparison results in welding applications validate the effectiveness of the framework, demonstrating significant improvements in image quality for low-dose radiographic defect detection. Unlike advanced methods such as Gaussian filtering, BM3D, and DnCNN, which operate at the pixel level, ARSR performs denoising at the projection data stage, reducing noise impact, preserving original information, and focusing on physical data processing during imaging. This approach enhances the detection of subtle defects, highlighting the potential of stochastic resonance in image processing.

Two‐stage stochastic energy and reserve market clearing model considering real‐time offering strategy of renewable energy

AbstractWith the introduction of decarbonization policies worldwide, renewable energy, especially wind and solar power, is gradually taking a significant share in the power system. The two‐stage stochastic optimization methods are generally adopted to address the uncertainty issues and the two‐stage stochastic market clearing models are established with the participation of renewable energy. However, most existing two‐stage stochastic market clearing models usually intuitively presume the offering quantities of renewable energy are equal to their forecast values, neglecting the potential impacts of the strategic offerings on the market results and thus affecting the secure operation of power systems. To fill the gaps, this paper incorporates the strategic offering models of renewable energy into the two‐stage stochastic energy and reserve market clearing model. Within the two‐stage framework, the first day‐ahead stage serves for energy and reserve market clearing, while the second real‐time stage considers the adjustments on offering quantities of renewable energy according to the fluctuations of renewable generations. The two‐stage stochastic market clearing model is formulated as a mixed‐integer non‐linear programming problem, and an iterative algorithm is devised to obtain market clearing results after proper linearizations. The effectiveness of the proposed method is validated using the extended IEEE‐118 test system.