Stochastic Framework Research Articles

Assessing rainfall radar errors with an inverse stochastic modelling framework

Abstract. Weather radar is a crucial tool for rainfall observation and forecasting, providing high-resolution estimates in both space and time. Despite this, radar rainfall estimates are subject to many error sources – including attenuation, ground clutter, beam blockage and drop-size distribution – with the true rainfall field unknown. A flexible stochastic model for simulating errors relating to the radar rainfall estimation process is implemented, inverting standard weather radar processing methods and imposing path-integrated attenuation effects, a stochastic drop-size-distribution field, and sampling and random errors. This can provide realistic weather radar images, of which we know the true rainfall field and the corrected “best-guess” rainfall field which would be obtained if they were observed in a real-world case. The structure of these errors is then investigated, with a focus on the frequency and behaviour of “rainfall shadows”. Half of the simulated weather radar images have at least 3 % of their significant rainfall rates shadowed, and 25 % have at least 45 km2 containing rainfall shadows, resulting in underestimation of the potential impacts of flooding. A model framework for investigating the behaviour of errors relating to the radar rainfall estimation process is demonstrated, with the flexible and efficient tool performing well in generating realistic weather radar images visually for a large range of event types.

Enhanced stochastic coding framework for discriminating faults and cyber incidents in hybrid systems

AbstractThis article presents an innovative approach for distinguishing replay attacks from faults in hybrid systems. To develop the idea at first, a novel technique for replay attack detection, which differentiates it from typical system faults, is introduced. This is achieved through a tactical combination of stochastic coding and a window‐based comparison mechanism, setting a new standard in hybrid system security. In the realm of fault detection, robust L2‐L∞ adaptive observers are employed for precise mode detection, allowing for an accurate assessment of the system's operational state. Additionally, robust H∞ Sliding Mode Observers are utilized to identify abnormal behaviours in the system's output, further solidifying the fault detection capabilities. A significant enhancement in the proposed approach is the integration of a Luenberger observer with the Butterworth low‐pass filter. This novel addition not only refines the filtering process but also contributes to the overall reliability and accuracy of the system. The efficiency and versatility of these methods are demonstrated through their application to a four‐tank hybrid system. This practical simulation showcases the adaptability of the approach to real‐world scenarios, highlighting its potential in diverse applications within the field of hybrid systems.

Stochastic optimal power flow framework with incorporation of wind turbines and solar PVs using improved liver cancer algorithm

AbstractThe present study introduces a nature inspired improved liver cancer algorithm (ILCA) for solving the non‐convex engineering optimization issues. The traditional LCA (t‐LCA) inspires from the conduct of liver tumours and integrates biological ethics during the optimization procedure. However, t‐LCA facing stagnation issues and may trap into local optima. To avoid such issues and provide the optimal solution, there are some modifications are implemented into the internal structure of t‐LCA based on Weibull flight operator, mutation‐based approach, quasi‐opposite‐based learning and gorilla troops exploitation‐based mechanisms to enhance the overall strength of the algorithm to obtain the global solution. For validation of ILCA, the non‐parametric and the statistical analysis are performed using benchmark standard functions. Moreover, ILCA is applied to resolve the stochastic renewable‐based (wind turbines + PVs) optimal power flow problem using a modified RER‐based IEEE 57‐bus. The objective of this work is to obtain the minimum predicted power losses and enhance the predicted voltage stability. By incorporation of renewable resources into the modified IEEE57‐bus network can help the system to reduce the power losses from 5.6622 to 3.8142 MW, while the voltage stability is enhanced from 0.1700 to 0.1164 p.u.

A Stochastic Dynamic Operator framework that improves the precision of analysis and prediction relative to the classical spike-triggered average method, extending the toolkit.

Here we test the Stochastic Dynamic Operator (SDO) as a new framework for describing physiological signal dynamics relative to spiking or stimulus events. The SDO is a natural extension of existing spike-triggered average (STA) or stimulus-triggered average techniques currently used in neural analysis. It extends the classic STA to cover state-dependent and probabilistic responses where STA may fail. In simulated data, SDO methods were more sensitive and specific than the STA for identifying state-dependent relationships. We have tested SDO analysis for interactions between electrophysiological recordings of spinal interneurons, single motor units, and aggregate muscle electromyograms (EMG) of major muscles in the spinal frog hindlimb. When predicting target signal behavior relative to spiking events, the SDO framework outperformed or matched classical spike-triggered averaging methods. SDO analysis permits more complicated spike-signal relationships to be captured, analyzed, and interpreted visually and intuitively. SDO methods can be applied at different scales of interest where spike-triggered averaging methods are currently employed, and beyond, from single neurons to gross motor behaviors. SDOs may be readily generated and analyzed using the provided SDO Analysis Toolkit We anticipate this method will be broadly useful for describing dynamical signal behavior and uncovering state-dependent relationships of stochastic signals relative to discrete event times.Significance Statement Here the authors introduce new tools and demonstrate data analysis using a new probabilistic and state-dependent technique, which is an expansion and extension of the classical spike-triggered average, the Stochastic Dynamic Operator. Stochastic Dynamic Operator methods extend application into domains where classical spike-triggered averages fail, capture more information on spike correlations, and match or outperform the spike-triggered average when generating predictions of signal amplitude based on spiking events. A data and code package toolkit for utilizing and interpreting Stochastic Dynamic Operator methods is provided together with example simulated and physiological data analyses. Both the method and the associated toolkit are expected to be broadly useful in research domains where the spike triggered average is currently used for analysis, and beyond.

Robust and stochastic sparse subspace clustering

Sparse subspace clustering (SSC) has been widely employed in machine learning and pattern recognition, but it still faces scalability challenges when dealing with large-scale datasets. Recently, stochastic SSC (SSSC) has emerged as an effective solution by leveraging the dropout technique. However, SSSC cannot robustly handle noise, especially non-Gaussian noise, leading to unsatisfactory clustering performance. To address the above issues, we propose a novel robust and stochastic method called stochastic sparse subspace clustering with the Huber function (S3CH). The key idea is to introduce the Huber surrogate to measure the loss of the stochastic self-expression framework, thus S3CH inherits the advantage of the stochastic framework for large-scale problems while mitigating sensitivity to non-Gaussian noise. In algorithms, an efficient proximal alternating minimization (PAM)-based optimization scheme is developed. In theory, the convergence of the generated sequence is rigorously proved. Extensive numerical experiments on synthetic and six real datasets validate the advantages of the proposed method in clustering accuracy, noise robustness, parameter sensitivity, post-hoc analysis, and model stability.

Stochastic hazard assessment framework of landslide blocking river by depth-integrated continuum method and random field theory

AbstractLandslide-induced barrier dams pose a threat to the safety of humans, livestock and nearby infrastructures. The efficient assessment of landslide blocking river is crucial for disaster prevention and mitigation solutions. This study proposes a novel stochastic assessment framework to evaluate the landslide blocking river through the prediction of their deposition depths and considering the heterogeneity of shear strength parameters on the potential sliding surface. The depth-integrated continuum method (DICM) is used to simulate the landslide runout process. Using an enhanced Karhunen-Loève expansion (KLE) method, the spatial variations in soil's shear strength parameters are modeled by random fields to incorporate the effects of soil's spatial heterogeneity on the landslide deposition pattern. Subsequently, the multi-response surrogate model is constructed to relate the random field variables to the deposition depths based on extreme gradient boosting (XGBoost). To improve the performance of the surrogate model, principal component analysis (PCA) and sliced inverse regression (SIR) methods are employed for the dimension reduction of output and input variables, respectively. Furthermore, the algorithm for river blockage identification is developed to search for the deposition ridges. To demonstrate the capability of the stochastic assessment framework, an example of the first Baige landslide in Tibet, China is simulated, and the affected region and deposition depths of the landslide are predicted to calculate the probability of river damming. The presented methodology provides a practical means for improving the landslide blocking river prediction and new insights for early warning and risk mitigation.

A seismic-risk-based bi-objective stochastic optimization framework for the pre-disaster allocation of earthquake search and rescue units

Accurately predicting earthquakes' time, location and size is nearly impossible with today’s technology. Severe earthquakes require prompt and effective mobilization of available resources, as the speed of intervention has a direct impact on the number of people rescued alive. This, in turn, calls for a strategic pre-disaster allocation of search and rescue (SAR) units, both teams and equipment, to make the deployment of resources as quick and equitable as possible. In this paper, a seismic risk-based framework is introduced that takes into account distance-based contingencies between cities. This framework is then integrated into a mixed-integer non-linear programming (MINLP) problem for the allocation of SAR units under uncertainty. The two minimization objectives considered are the expected maximum deployment time of different SAR units and the expected mean absolute deviation of the fulfillment rates. We recover the best vulnerability-adjusted routes for each size-location scenario as input to the optimization model using the dynamic programming (DP) approach as part of the broader area of reinforcement learning (RL). The results of the hypothetical example indicate that the comprehensive model is feasible in various risk scenarios and can be used to make allocation-deployment decisions under uncertainty. The results of the sensitivity analysis verify that the model behaves reasonably against changes in selected parameters, namely the number of allowed facilities and weights of individual objectives. Under the assumption that the two objectives are equally important, the model achieves a total deviation of %3.5 from the objectives with an expected maximum dispatch time of 1.1327 hours and an expected mean absolute deviation of 0.01.

A decision-making model for joint energy and reserve scheduling of wind power producers with local intraday demand response exchange market

In this paper, a three-stage stochastic bi-level optimization framework is presented for optimal participation of wind power producers (WPPs) in day-ahead (DA), intraday, and balancing markets. In this framework, to leverage demand response (DR) services, a peer-to-peer (P2P) energy trading platform is implemented that allows local load aggregators (LAs) to contribute to the intraday markets improving both LAs’ and WPP’s benefits. Participating in the intraday DR exchange (IDRX) market enables WPP to purchase DR services from LAs, to reduce the penalty cost on the deviation between the day-head bidding and the real-time dispatch. A Stackelberg game for the bi-level decision-making model captures the conflict of interests between the WPP and LAs, in which, the upper level seeks to maximize WPP profit, while the lower level aims to maximize LAs’ economic surplus. The bi-level model is converted into its equivalent single-level mixed-integer quadratic problem (MIQP) employing the Karush-Kuhn-Tucker (KKT) conditions and strong duality theorem. Simulation results show that participation of the WPP in the IDRX market and employing spinning reserve and DR services for compensating the uncertainties are greatly dependent on its risk preferences and increase its expected profit in all conditions, significantly.

Optimal energy management and scheduling of a microgrid considering hydrogen storage and PEMFC with uncertainties

Renewable energy sources have been widely installed and operated in power systems, particularly in microgrids in the form of distributed generation units. This issue requires efficient energy management tools which take into account the inherent uncertainties of such energy resources. Thus, this paper presents a stochastic framework aimed at scheduling the renewable energy-based and thermal units in a coordinated way. The generation units comprise fuel cell units with proton exchange membrane known as PEMFC-CHP producing heat and power, concurrently. Moreover, the uncertainties arising from wind and solar power as well as market prices are characterized by deploying scenario-based optimization. The mentioned framework considers storing hydrogen and the model is presented within a stochastic mixed-integer nonlinear programming (MINLP) framework. The resulting problem is simulated on a modified 33-bus distribution network and tackled using the modified marine predators algorithm (MMPA)algorithm. The obtained results indicate that the revenue increases by more than 5% compared to other optimization algorithms. Furthermore, taking into account CHP will increase the total profit of the system by more than 15%.

Species interactions drive continuous assembly of freshwater communities in stochastic environments

Understanding the factors driving the maintenance of long-term biodiversity in changing environments is essential for improving restoration and sustainability strategies in the face of global environmental change. Biodiversity is shaped by both niche and stochastic processes, however the strength of deterministic processes in unpredictable environmental regimes is highly debated. Since communities continuously change over time and space—species persist, disappear or (re)appear—understanding the drivers of species gains and losses from communities should inform us about whether niche or stochastic processes dominate community dynamics. Applying a nonparametric causal discovery approach to a 30-year time series containing annual abundances of benthic invertebrates across 66 locations in New Zealand rivers, we found a strong negative causal relationship between species gains and losses directly driven by predation indicating that niche processes dominate community dynamics. Despite the unpredictable nature of these system, environmental noise was only indirectly related to species gains and losses through altering life history trait distribution. Using a stochastic birth-death framework, we demonstrate that the negative relationship between species gains and losses can not emerge without strong niche processes. Our results showed that even in systems that are dominated by unpredictable environmental variability, species interactions drive continuous community assembly.

A volume‐averaging and stochastic turbulence modeling framework for homogeneous roughness‐induced drag in turbulent flows

AbstractThe goal of this work is the formulation of a model for the parameterization of homogeneous roughness‐induced drag in turbulent flow simulations. We characterize rough surfaces using their surface‐area moments of roughness‐peaks. Additionally, we consider a probabilistic self‐similar power law distribution for the roughness heights, in such a way that an assumed set of discrete roughness elements can behave as a probabilistic fractal set. Upon these assumptions, the surface characterization is complete and yields wall‐normal profiles of porosity, average roughness element diameter, and equivalent pore diameter of the roughness affected porous flow. The profiles are supplied to a (pore‐based) Reynolds number and porosity‐based drag parameterization for staggered cylinder arrays available in the literature, as well as a one‐dimensional map‐based turbulence model, the one‐dimensional turbulence (ODT) model. The purpose of the latter is a way to provide the missing effects of the equivalent dispersion tensor in the porous flow close to the rough surface, as well as that of the nonlinear turbulent transport away from the wall. Simulations are then carried out in order to evaluate the effects of two different rough surfaces on a turbulent channel flow, comparing results with existing direct numerical simulation (DNS) data. Overall, reasonable agreement is obtained, which suggests that, by using the proposed model, it is possible to model the effects of rough surfaces on wall‐bounded turbulent flows, without the explicit need of the full topological representation of the surface on the numerical domain. To that extent, one clear flow control application for the suggested approach would be that of drag‐based surface optimization.

Hybrid life insurance valuation based on a new standard deviation premium principle in a stochastic interest rate framework

Hybrid life insurance valuation based on a new standard deviation premium principle in a stochastic interest rate framework

Performance analysis of joint transmission in TDD-based mm-wave networks with BS heights

Dynamic-time division duplexing (D-TDD) is used in millimeter-wave (mm-wave) networks to allocate time-frequency resources for both downlink (DL) and uplink (UL) transmissions. This scheduling mechanism adapts to varying data traffic to meet the different quality of service (QoS) requirements of heterogeneous services. However, blockage is the major bottleneck to millimeter wave (mm-Wave) networks since it causes signal outages. Moreover, the dense deployment of base stations (BSs) to reduce the signal outage problem may lead to severe interference due to solid line-of-sight (LoS) BSs. To solve the problem of less coverage, this paper utilizes a joint transmission mechanism in the DL of D-TDD-based mm-Wave networks. Further, examining the network performance also entails considering the elevation disparity between the Base Station (BS) and User Equipment (UE). The primary focus of this work is to study the effects of joint transmission in D-TDD-based DL mm-Wave networks with different BS heights and directional beamforming using the stochastic geometry framework. For D-TDD with Joint Transmission, numerical evaluations indicate that the SINR coverage probability reaches approximately 0.7 when the coverage radius (rc) is 100 m. Conversely, at a coverage radius of 200 m, the SINR coverage probability drops to around 0.25. The simulation results demonstrate using MATLAB 2019b tool, that D-TDD-based mm-Wave networks achieve superior coverage using the joint transmission scheme compared to single BS association. Besides, results show that optimal UL and DL split and load balancing are required to achieve better DL coverage.

Valuation of guaranteed lifelong withdrawal benefit with the long-term care option

In this paper, under the stochastic interest rate framework, we consider the valuation of a Guaranteed Lifelong Withdrawal Benefit (GLWB) annuity product by explicitly incorporating the health state of the policyholder through the long-term care (LTC) option. The product provides policyholders with protection against longevity risk and market downturns, as well as financial support when facing LTC needs. Within the context of dynamic withdrawals, the valuation of the GLWB annuity with the LTC option is characterized as a stochastic optimal control problem. We introduce a novel bang-bang analysis approach without the usual convexity assumption in literature and prove that the optimal withdrawal strategies for the policyholder are constrained to a finite set. Furthermore, we perform a sensitivity analysis on the price determinants of GLWB annuities with and without the LTC option, and provide economic interpretations. Lastly, we investigate the impact of gender on the optimal withdrawal strategy and the fair fee of the annuity with the LTC option.

A new multi-objective-stochastic framework for reconfiguration and wind energy resource allocation in distribution network incorporating improved dandelion optimizer and uncertainty

Improving the reliability and power quality of unbalanced distribution networks is crucial for ensuring consistent and reliable electricity supply. In this research, multi-objective optimization of unbalanced distribution networks reconfiguration integrated with wind turbine allocation (MORWTA) is implemented considering uncertainties of networks load, and also wind power incorporating a stochastic framework. The multi-objective function is defined by the minimization of power loss, voltage sag (VS), total harmonic distortion (THD), voltage unbalance (VU), energy not-supplied (ENS), system average interruption frequency index (SAIFI), system average interruption duration index (SAIDI), and momentary average interruption frequency (MAIFI). A new improved dandelion optimizer (IDO) with adaptive inertia weight is recommended to counteract premature convergence to identify decision variables, including the optimal network configuration through opened switches and the best location and size of wind turbines in the networks. The stochastic problem is modeled using the 2m + 1 point estimate method (PEM) combined with K-means clustering, taking into account the mentioned uncertainties. The proposed stochastic methodology is implemented on three modified 33-bus, and unbalanced 25-, and 37-bus distribution networks. The results demonstrated that the MORWTA enhanced all study objectives in comparison to the base networks. The results also demonstrated that the IDO had superior capability to solve the deterministic- and stochastic-MORWTA in comparison to the conventional DO, grey wolf optimizer (GWO), particle swarm optimization (PSO), and arithmetic optimization algorithm (AOA) in terms of achieving greater objective value. Moreover, the results demonstrated that when the stochastic-MORWTA model is considered, the power loss, VS, THD, VU, ENS, SAIFI, SAIDI, and MAIFI are increased by 18.35%, 9.07%, 10.43%, 12.46%, 11.90%, 9.28%, 12.16% and 14.36%, respectively for 25-bus network, and also these objectives are increased by 12.21%, 10.64%, 12.37%, 9.82%, 14.30%, 12.65%, 12.63% and 13.89%, respectively for 37-bus network compared to the deterministic-MORWTA model, which is related to the defined uncertainty patterns.

A hierarchical framework for integration of smart buildings in fully-renewable multi-microgrids and distribution systems: Towards more sustainable societies

Using smart buildings would be a crucial step towards sustainability. Although in the literature, some research effort has focused on integration of smart buildings into power systems; the integration of fully-renewable smart buildings into fully-renewable microgrids and distribution systems has not been addressed before. In this paper, a tri-level hierarchical stochastic framework is developed for the integration of fully renewable smart buildings in fully renewable multi-microgrids (MGs) and distribution systems. The studied smart buildings have electric water heater, air conditioner, PV and battery. In the first level, the model of each smart building is separately solved to find optimal schedule of its resources and the desired electricity exchange with its corresponding MG. In the second level, each MG solves its operational planning model, considering its transactions with the connected smart buildings and finally, in the third level, distribution system operator solves its operational planning model, accepting the electricity exchange requests taken from all MGs. The proposed methodology is applied to a 69-bus 100 % renewable distribution system with 4 100 % renewable microgrids, integrated with 100 % renewable smart buildings. The results confirm the efficacy of the proposed methodology for the integration of 100 % renewable smart buildings in 100 % renewable multi-MGs. The results testify that that building-to-grid (B2G) capability decreases the operation cost of all smart buildings; the average decrease in operation cost of buildings, caused by B2G, is 38 %. The results on the studied case indicate that that the impact of batteries on operation cost of smart buildings is marginal. The results also show that the higher threshold of comfort index in smart buildings, results in their higher operation cost. The results of this research may be helpful for both smart building operators and power system operators. This research is in line with the global energy transition and decarbonisation targets as the considered smart buildings, microgrids and distribution system are fully renewable.

Operation of coupled power-gas networks with hydrogen refueling stations, responsive demands and storage systems: A novel stochastic framework

Because of factors such as low natural gas prices, low greenhouse gas emission and high efficiency has increased the penetration of natural gas-fired generators in electric power systems. Large gas consumption of gas-fired generators has caused intense interdependence of electricity and gas systems. Most often, the operational planning of power and gas systems is conducted through a co-optimisation model in which the total cost of electricity and gas systems is minimised and the constraints of both systems are considered. On the other hand, due to environmental concerns, the usage of fuel cell vehicles (FCVs) is increasing. Hydrogen refueling stations (HRSs) are needed for refueling FCVs. This paper puts forward a stochastic model for co-optimisation of wind-integrated power and gas systems, hosting HRSs, electric storage systems (ESS's) and responsive electricity and gas demands. The effect of ESS's, responsive demands, contingencies, wind uncertainties and demand response on operation of power-gas nexus is scrutinized. An incentive-based demand response program has been used for both electricity and gas demands. The case study is the Belgian gas network connected to the a 24-bus power system. The findings indicate that responsive electric demands reduce electric system cost by 9.4 %, while responsive gas demands reduce the gas network cost and total operation cost by 1 %. The contingency analysis on the power-gas nexus shows that single line outage contingencies in power system does not result in any demand shed and does not increase the operation cost of either electricity network or gas network.

A two-stage stochastic programming framework for blood product inventory management with ABO substitution and lateral transshipment

This work proposes a two-stage stochastic optimization model for managing the inventory of a two-echelon blood supply chain comprised of a blood center and a network of hospitals and transfusion points. The proposed model identifies optimal distribution quantities across the supply chain, considering demand stochasticity and product perishability. Furthermore, the model utilizes redistribution policies, such as lateral transshipment and product substitution based on ABO compatibility, as corrective actions to minimize outdates (i.e., expired product) and shortages across the network. Using a computational experiment that includes a network with one regional blood center and twenty hospitals, we show that inventory management policies that include both ABO substitution and transshipment can significantly decrease the expected total network costs. Similarly, we see corresponding reductions in the expected number of outdated units and emergency requests to external networks for additional supply to satisfy unmet demand.

Competitive exclusion and coexistence in a general two-species stochastic chemostat model with Markov switching

In this paper, a stochastic framework with a general nonmonotonic response function is formulated to investigate the competition dynamics between two species in a chemostat environment. The model incorporates both white noise and telegraph noise, the latter being described by Markov process. The existence of a unique global positive solution for the stochastic chemostat model is established. Subsequently, by using the ergodic theory of Markov process and utilizing techniques of stochastic analysis, the critical value differentiating between persistence in mean and extinction for the microorganism species is explored. Moreover, the existence of a unique stationary distribution is proved by using stochastic Lyapunov analysis. Finally, numerical simulations are introduced to support the obtained results.

Logistics Model for Indonesia’s National Freight Model System: From a Deterministic to a Stochastic Framework

One of the components of a new model, called INTRAMOD, for Indonesia’s domestic freight transport is the logistics model. The logistics model describes shipment size choice and the choice between five different transport chain alternatives involving four main modes: truck, train, vessel, and plane. This paper presents the work to forecast the disaggregate transport chain and shipment size choices for Indonesia’s domestic shipments by applying a deterministic and a stochastic approach. Using a standard economic order quantity model with a consolidation assumption, a deterministic approach is used to determine the transport chain and shipment size, minimizing total logistics cost. As an alternative for this, a stochastic model aims to improve the logistics choice modeling by employing data on the manufacturer’s revealed preferences and stated preferences about only the transport chain choice. The chosen specification for the stochastic approach is utilizing the multinomial logit model. Using the demand elasticities for all alternatives with respect to changes in its transport cost, a comparison will be made between the two approaches. In addition, it is concluded that the deterministic model is susceptible to sticky and flip-flop behaviors. In contrast, this characteristic is absent from the stochastic approach.