Stochastic Parameters Research Articles

On the multi‐parameters identification of concrete dams: A novel stochastic inverse approach

AbstractThis paper introduces a novel stochastic inverse method that utilizes perturbation theory and advanced intelligence techniques to solve the multi‐parameter identification problem of concrete dams using displacement field monitoring data. The proposed method considers the uncertainties associated with the dam displacement monitoring data, which are comprised of two distinct sources: the first is related to stochastic mechanical properties of the dam, and the second is due to observation errors. The displacements at different measuring points generated by dam mechanical properties exhibit spatial correlation, while the observation errors at different points can be considered statistically random. In this context, the inversion formulas are derived for unknown stochastic parameters of the dam by combining perturbation equations and Taylor expansion methods. An improved meta‐heuristic optimization method is employed to identify the mean of stochastic parameters, while mathematical and statistical methods are used to determine the variance of stochastic parameters. The feasibility of the proposed method is verified through numerical examples of a typical dam section under different conditions. Additionally, the paper discusses and demonstrates the applicability of this method in a practical dam project. Results indicate that this method can effectively capture the uncertainty of dam's mechanical properties and separates them from observation errors.

Exploring chaos and ergodic behavior of an inductorless circuit driven by stochastic parameters

There exist extensive studies on periodic and random perturbations of various smooth maps investigating their dynamics. Unlike smooth maps, non-smooth maps are yet to be studied extensively under a stochastic regime. This paper presents a stochastic piecewise-smooth map derived from a simple inductorless switching circuit. The stochasticity is introduced in parameter values. The distribution of the parameter values is bounded and randomly selected from uniform and triangular distributions and ranges between high and low bifurcation parameter values of the deterministic map. Due to this inherent stochasticity in parameter values, the time evolution of the state variable cannot be predicted at a specific time instant. We observe that the state variable exhibits completely ergodic behavior when the minimum value of the parameter is the same as the minimum bifurcation parameter of the deterministic system. However, the ensemble average of the state variable converges to a fixed value. The system demonstrates nonchaotic behavior for a particular range of parameter values but the deterministic map in that bifurcation range shows interplay between chaos and periodic orbits. The values of Lyapunov exponents decrease monotonically with increased asymmetry of the distribution from which the bifurcation parameter values are chosen. We determine the probability density function of the stochastic map and verify its invariance under initial conditions. The most noteworthy result is the disappearance of chaotic behavior when the lower range of the distribution is varied while maintaining a fixed upper threshold for a particular distribution, even though the deterministic map exhibits an array of periodic and chaotic behaviors within the range. As the period-incrementing cascade with chaotic inclusion only occurs in nonsmooth maps, this paper numerically shows the stochasticity of a piecewise-smooth map obtained from a practical system for the first time where randomness is introduced in the parameter space.

A Reliability-Based Design Approach for the Flexural Resistance of Compression Yielded Fibre-Reinforced Polymer (FRP)-Reinforced Concrete Beams

Fibre-reinforced polymer (FRP) reinforcement has been employed as an alternative to conventional steel reinforcement in concrete structures, which is attributed to its excellent strength and corrosion resistance. However, one drawback is that FRP reinforcements are brittle and affect the ductility of concrete structures. One of the recent effective techniques proposed to overcome ductility issues is the compression yielding (CY) concept. The CY mechanism allows the structure to fail differently than the conventional FRP-reinforced concrete structure. Thus, the existing design recommendations as per the current codes for FRP-reinforced concrete structures are not appropriate. Hence, reliability studies are crucial for the development of a functional CY beam design in order to emphasise the structure’s lifetime performance and to guarantee safety requirements. In this study, a reliability-based design approach is developed for a compression-yielded FRP-reinforced concrete beam (CY beam) using load and resistance factor design (LRFD). Firstly, the flexural failure modes of CY beams are discussed. The uncertainties involved in the development of the probabilistic model for the CY beam are defined. A case study is consequently conducted for a CY beam with random variables that are associated with the statistical characteristics of material properties and load. The reliability analysis method employed in this research is the Hasofer–Lind method. The results suggest the importance of choosing appropriate design variables and stochastic parameters for CY blocks that contribute to a higher level of reliability. The reliability index and resistance factors of a CY beam are then evaluated using the Monte Carlo Simulation computational method. The reliability index value of 3.336 is obtained from the simulation, which indicates that the CY beam demonstrates ductile behaviour. The results not only demonstrate ductile behaviour but also contribute to a possible reduction in material costs and a substantial safety margin. When compared to conventional FRP-reinforced concrete beams, for different load ratios, CY beams showed higher resistance and better reliability levels.

The renormalization group for large-scale structure: primordial non-Gaussianities

The renormalization group for large-scale structure (RG-LSS) describes the evolution of galaxy bias and stochastic parameters as a function of the cutoff Λ. In this work, we introduce interaction vertices that describe primordial non-Gaussianity into the Wilson-Polchinski framework, thereby extending the free theory to the interacting case.The presence of these interactions forces us to include new operators and bias coefficients to the bias expansion to ensure closure under renormalization.We recover the previously-derived “scale-dependent bias” contributions, as well as a new (subdominant) stochastic contribution.We derive the renormalization group equations governing the RG-LSS for a large class of interactions which account for vertices at linear order in f NL that parametrize interacting scalar and massive spinning fields during inflation.Solving the RG equations, we show the evolution of the non-Gaussian contributions to galaxy clustering as a function of scale.

Optimized Real-Time Stochastic Model of Power Electronic Converters based on FPGA

Stochastic models can effectively describe the operating characteristics of power electronic converters with stochastic parameters. However, it is difficult to implement the models in FPGA-based real-time simulation (RTS) because their high order leads to a large calculation. This paper proposes an optimized real-time stochastic modeling method for power electronic converters based on generalized polynomial chaos (gPC). Firstly, an orthogonal polynomials construction method is used based on Schmidt orthogonalization to describe stochastic variables with atypical probability distributions and provide conditions for simplifying the system model. Secondly, the method of probability space transformation is adopted to divide the system model into multiple sub-models to suppress the exponential growth of the model order while maintaining the statistical properties. This method has performed over the traditional stochastic modeling method. The proposed model is built on FPGA-based hardware-in-the-loop (HIL) experiment platform with 1us simulation step. The optimized model uses approximately 37% fewer resources than the traditional stochastic model while maintaining the same level of accuracy.

Analyze the Stochastic Solid Fuzzy Transportation Problem with Mixed Constraints through Weibull Distribution

This paper proposed a general formulation of the stochastic solid transportation problem (SSTP) with mixed constraints such as supply, demand and conveyance capacity taken as uncertain under stochastic environment, following the Weibull distribution (WD). The aim of this study is to minimize the transportation cost includes probabilistic constraints have inequalities of stochastic solid transportation problem (SSTP). SSTP with probabilistic constraints is represented as a chance constrained programming problem. Obtain alpha cut representation from cost coefficient of the fuzzy objective function. We have developed four models for stochastic solid transportation problem. The suggested models are demonstrated by taken as numerical example. A sensitivity analysis is performed to understand parameter’s sensitivity in the proposed model. Introduction: In system of transportation, goods are moved from various sources to destinations using different vehicles and organizational systems, involving both technology and human efforts. Efficient resource allocation in transportation system is crucial for industries and imprecision from factors like fluctuating demand, unreliable supply chains and unpredictable traffic. To address these complexities, advanced mathematical models are needed to manage stochasticity, fuzziness and mixed constraints. The study explores the stochastic solid fuzzy transportation problem with mixed constraint by utilizing the Weibull distribution to model uncertainties inherent in transportation systems. This research addresses the complexity introduced by stochastic variables and fuzzy parameters, particularly in situations where demand, supply and cost of transportation are not deterministic. Objectives: The aim of this study is to minimize the cost of transportation includes probabilistic constraints have inequalities of stochastic solid transportation problem (SSTP). Methods: Obtain alpha cut representation form the cost coefficient of the fuzzy objective function and four models are developed for stochastic solid transportation problem. These models are demonstrating by using a numerical example and a sensitivity analysis is conducted to understand the sensitivity of the parameters in the propose model. Results: Obtained optimal solutions for developed four models of SFSTPMC and sensitivity analysis shows that cost of transportation and flow of unit are sensitive to change in probabilities of demand. Improve transportation system by understanding sensitivity patterns that help decision maker choose appropriate supply availability probabilities. Conclusions: This study presented an approach for solving the SFSTPMC using the Weibull distribution for probabilistic constraints and fuzzy objective functions for transportation cost. Developed and optimized four models, focusing on stochastic parameters. Sensitivity analysis demonstrated the impact of these parameters on transportation cost and unit flow. The results validate the model’s effectiveness in practical resource allocation and decision making under uncertainty.

Particle Swarm Optimization-Based Variable Scale Asymmetric Stochastic Resonance Bearing Diagnostic Method

Abstract A diagnostic method for bearing faults, centered around the extraction and identification of diagnostic signals, is introduced. This method utilizes a Particle Swarm Optimization (PSO) algorithm to optimize a variable-scale asymmetric stochastic resonance (SR) framework. The PSO algorithm dynamically fine-tunes the parameters of the asymmetric stochastic resonance system to align more effectively with the demands of bearing fault diagnosis. An asymmetric factor-controlled potential function for the stochastic resonance system is established, using the Signal-to-Noise Ratio Improvement (A-SNRI) of the fault signal as the objective function for the optimization algorithm. The PSO algorithm is employed for global optimization to adjust the structural parameters a 0, b 0 and the asymmetric factor of the asymmetric α bistable stochastic resonance system. Simulations and experimental validations are conducted using the optimized stochastic resonance system parameters, demonstrating the robustness and effectiveness of the algorithm through the extraction of fault characteristic frequencies. Experimental results indicate the proposed bearing fault diagnostic method can stably extract fault characteristic frequencies, effectively filter out noise, and the extracted fault frequencies align with theoretical values.

Stochastic bulk density in the fire spread model

AbstractIn this study, we investigate the impact of inherent randomness on fire spread rates, with a particular focus on the stochastic parameter ε, representing the ratio of effective to actual fuel bulk density. By employing various probability distributions, such as the beta random distribution model ε, we explore the complex interplay between wind and slope factors in determining fire behavior. Our 3D visualizations and density plots illuminate the multidimensional nature of fire spread, emphasizing the significant role of stochastic variability in enhancing the accuracy of fire behavior models. This approach not only deepens our theoretical understanding but also provides valuable insights for improving fire management strategies.

Прогнозирование углеводородоперспективных структур кольцевого вида в Баренцевоморском регионе по результатам применения стохастического метода при использовании совокупности геопараметров

The article presents the results of the application of the stochastic method used to predict hydrocarbon-prospective geostructures of a concentric type within the Barents Sea region. According to thecalculated values ofstochastic parameters for the 21 geostructures of aconcentric view in the waters of the Barents region, based on four different geoparameters a summary table of stochastic parameters was compiled and an encouraging forecast was made for 13 concentric geostructures promising for the search for new oil deposits within the Barents Sea region.

A novel in-situ micro-mechanical testing of paper fracture and its stochastic network model

Understanding and simulating the evolution of fracture in cellulose-based paper materials is vital for many eco-sustainable applications of packaging solutions. In this work, we conduct an integrated experimental-statistical mechanics analysis to elucidate how the microstructural mechanisms govern the fracture behavior of paper. We employ in-situ tensile tests combined with confocal microscopy to observe and analyze key microstructural phenomena, such as fibers’ activation and recruitment, and progressive tensile failure of unnotched paper samples under uniaxal loading. The developed stochastic mechanics critical cross-section model to treat the cellulose fiber network is able to decouple the stochastic morphological parameters from the constitutive model of the fibers. Notably, it robustly predicts the anisotropic properties of paper materials in the machine direction (MD) and cross-machine direction (CD) as a direct consequence of the different statistical distribution of fibers’ orientation, for the same fiber constitutive model. The proposed approach is finally employed to get an insight into the role of the main morphological parameters, local/non-local fibers’ strain redistribution, and finite elasticity of fibers on the whole mechanical behavior of paper.

Trajectory-based global sensitivity analysis in multiscale models

This research introduces a novel global sensitivity analysis (GSA) framework for agent-based models (ABMs) that explicitly handles their distinctive features, such as multi-level structure and temporal dynamics. The framework uses Grassmannian diffusion maps to reduce output data dimensionality and sparse polynomial chaos expansion (PCE) to compute sensitivity indices for stochastic input parameters. To demonstrate the versatility of the proposed GSA method, we applied it to a non-linear system dynamics model and epidemiological and economic ABMs, depicting different dynamics. Unlike traditional GSA approaches, the proposed method enables a more general estimation of parametric sensitivities spanning from the micro level (individual agents) to the macro level (entire population). The new framework encourages the use of manifold-based techniques in uncertainty quantification, enhances understanding of complex spatio-temporal processes, and equips ABM practitioners with robust tools for detailed model analysis. This empowers them to make more informed decisions when developing, fine-tuning, and verifying models, thereby advancing the field and improving routine practice for GSA in ABMs.

Particle filter‐based prognostics for composite curing process

AbstractProcess‐induced deformation (PID) arises in thermoset parts due to internal residual stress developed from their anisotropic properties, resulting in distortions. While passive numerical manufacturing control exists, active manufacturing control is crucial for enhancing the manufacturing process. The work focuses on diagnosing the polymerization reaction, known as the curing process, to consider the influence of uncertainties in thermal loading conditions on the behavior of cure kinetics. This is achieved using a Particle Filter approach, wherein a posterior distribution of cure evolution is recursively approximated based on observed measurements from characterization tests. The algorithm is designed to simultaneously perform the diagnosis and prognosis of the Degree of Cure and PID. This approach adopts the augmented cure formulation to address various scenarios with uncertainties in thermal loading conditions. It offers the advantage of providing comparable PID predictions with minimal computational costs. C‐shaped thermoset parts made of epoxy/carbon fibers with varying thicknesses are cured using the Manufacturing Recommended Curing Cycle, and the predictions with the developed algorithm are validated against experimental measures. Upon validation, the converged prognosis capability of the Particle Filter model is employed to assess the impact of thermal loading uncertainty on cure profiles, which, in turn, affects the final PIDs outcome.Highlights A Bayesian sampling approach enables the estimation of cure kinetics parameters. The estimated stochastic parameters forecast the process‐induced deformations. The augmented Degree of Cure accounts for uncertainties linked to thermal loadings. Analysis on AS4/8552 C‐shaped parts shows the cure kinetics impact. The framework reduces the computational costs required for active control.

Buffeting reliability of high-rise bridge tower in mountain area based on CNN-BiLSTM

In recent years, the wind-induced vibration of structures has received a great deal of scholarly attention due to the increasing scale of large structures. In this study, an algorithm that combines a stochastic pseudo excitation method (SPEM), a convolutional neural network (CNN) and a bidirectional long short-term memory network (BiLSTM), named as SPEM-CNN-BiLSTM (SCBL), is proposed. The SCBL is a surrogate model consisting of three different computational modules, in which the SPEM can provide training samples for CNN-BiLSTM (CBL) network architecture, a convolutional layer extracts features of stochastic parameters and a BiLSTM handles time histories of bridge response. The accuracy of the SCBL prediction results is ensured by the set error threshold. The model also accounts for structural uncertainty in the inputs and is adapted during the training step to be more suitable for reliability analysis. According to the output qualified prediction data, the dynamic reliability based on the 99 % threshold is calculated by obtaining its probability density function, and the wind-induced vibration responses of uncertain bridge towers are studied. Firstly, the wind environment of the bridge tower was analyzed, and the average wind speed of 20 m/s among the bridge area was obtained by field measurements, and Computational Fluid Dynamics (CFD). Secondly, the proposed artificial neural network algorithm is applied to bridge jitter reliability analysis and compared with the traditionally recognized methods: the Monte Carlo method (MCM) and the stochastic pseudo excitation method (SPEM). The results of SCBL calculations are closer to the results of MCM than those of other methods. Additionally, the computational efficiency of the method is improved by 40 times over MCM and 2 times over SPEM. Finally, the data generated by the SCBL method will be used for reliability analysis. Uncertainties in structure, wind speed, and yaw angle all contribute to the uncertainty and dispersion of the stochastic response prediction. Among them, the uncertainty in wind speed has the greatest impact on the reliability.

Variance-Reduced Accelerated First-Order Methods: Central Limit Theorems and Confidence Statements

In this paper, we consider a strongly convex stochastic optimization problem and propose three classes of variable sample-size stochastic first-order methods: (i) the standard stochastic gradient descent method, (ii) its accelerated variant, and (iii) the stochastic heavy-ball method. In each scheme, the exact gradients are approximated by averaging across an increasing batch size of sampled gradients. We prove that when the sample size increases at a geometric rate, the generated estimates converge in mean to the optimal solution at an analogous geometric rate for schemes (i)–(iii). Based on this result, we provide central limit statements, whereby it is shown that the rescaled estimation errors converge in distribution to a normal distribution with the associated covariance matrix dependent on the Hessian matrix, the covariance of the gradient noise, and the step length. If the sample size increases at a polynomial rate, we show that the estimation errors decay at a corresponding polynomial rate and establish the associated central limit theorems (CLTs). Under certain conditions, we discuss how both the algorithms and the associated limit theorems may be extended to constrained and nonsmooth regimes. Finally, we provide an avenue to construct confidence regions for the optimal solution based on the established CLTs and test the theoretical findings on a stochastic parameter estimation problem. Funding: This work was supported by the Office of Naval Research [Grant N00014-22-1-2589] and Basic Energy Sciences [Grant DE-SC0023303]. The work of J. Lei was partially supported by the National Natural Science Foundation of China [Grants 72271187 and 62088101]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/moor.2021.0068 .

Generative Convective Parametrization of a Dry Atmospheric Boundary Layer

AbstractTurbulence parametrizations will remain a necessary building block in kilometer‐scale Earth system models. In convective boundary layers, where the mean vertical gradients of conserved properties such as potential temperature and moisture are approximately zero, the standard ansatz which relates turbulent fluxes to mean vertical gradients via an eddy diffusivity has to be extended by mass‐flux parametrizations for the typically asymmetric up‐ and downdrafts in the atmospheric boundary layer. We present a parametrization for a dry and transiently growing convective boundary layer based on a generative adversarial network. The training and test data are obtained from three‐dimensional high‐resolution direct numerical simulations. The model incorporates the physics of self‐similar layer growth following from the classical mixed layer theory of Deardorff by a renormalization. This enhances the training data base of the generative machine learning algorithm and thus significantly improves the predicted statistics of the synthetically generated turbulence fields at different heights inside the boundary layer, above the surface layer. Differently to stochastic parametrizations, our model is able to predict the highly non‐Gaussian and transient statistics of buoyancy fluctuations, vertical velocity, and buoyancy flux at different heights thus also capturing the fastest thermals penetrating into the stabilized top region. The results of our generative algorithm agree with standard two‐equation mass‐flux schemes. The present parametrization provides additionally the granule‐type horizontal organization of the turbulent convection which cannot be obtained in any of the other model closures. Our proof of concept‐study also paves the way to efficient data‐driven convective parametrizations in other natural flows.

An aerodynamic digital twin of real-world leading edge erosion: Acquisition, Generation and 3D CFD

Wind turbine blades face extremely challenging environmental conditions over their operating life-time, that can easily exceed 2 decades. Airborne particles (insects, sand, rain, hail, ice, sea spray etc.) strike the blade leading edge (LE) first and erode or attach to it, roughening its surface. Leading edge roughness (LER) can critically alter the aerodynamic performance of blades, as its aerodynamic impact is strongly coupled to its height with respect to the local boundary layer thickness, which is thinnest around the LE. The actual, detailed topographic manifestation of LER on in-service blades—needed to accurately assess its aerodynamic impact—is highly probabilistic, as it depends on the interaction of multiple stochastic parameters, like the environmental conditions, material composition and production process. Yet little high-resolution topographic LER data of this kind is currently available. This paper details how such data is collected from blades of different turbine manufacturers and processed consistently to build digital twins of the measured LER, that can be analysed aerodynamically using 3D CFD or wind tunnels. Here a special focus lies on how to reconstruct the LER topography and build the computational mesh such that the correct aerodynamic response is observed. For this purpose multiresolution signal decomposition is used to process the topographies and a special meshing procedure established.

Modeling energy management of an energy hub with hybrid energy storage systems for a smart island considering water–electricity nexus

Energy hubs (EHs) represent a pivotal paradigm in achieving optimal resource utilization across various energy domains. This paper presents an advanced framework for the optimal management of a smart island, leveraging the synergies within the water-electricity nexus. By integrating diverse resources, including electricity, water, heat, and hydrogen, the proposed EH model aims to meet the multifaceted demands of consumers on the island. To enhance operational efficiency, this study delves into the nuanced impacts of key EH components, elucidating their roles in meeting demand profiles and minimizing operational costs. Formulated as a mixed integer linear programming (MILP) model, the EH optimization problem is addressed using the GAMS optimization tool. The overarching objective is to fulfill consumer demand while concurrently optimizing resource utilization, considering factors such as storage degradation costs and emissions from fossil-fuel-based units. In addition to strategic optimization, this study pioneers a novel approach to stochastic parameter forecasting, integrating convolutional neural networks (CNNs) and long-short-term memory networks (LSTMs). By harnessing the capabilities of these advanced forecasting techniques, the EH model can anticipate dynamic changes in demand patterns with heightened accuracy and precision. The empirical results underscore the transformative potential of the proposed EH framework, showcasing significant reductions—up to 30%—in emission costs. Moreover, the study underscores the pivotal role of EHs as enablers for scaling up renewable energy penetration, offering a robust foundation for sustainable energy transitions in island communities and beyond. Additionally, implementing a load-shifting demand response program can lower total costs by approximately $257 per day, offering significant savings for EHs over extended periods.

Dynamic event-triggered synchronization for semi-Markovian switching inertial neural networks with generally uncertain transition rates in finite-time interval

This paper investigates the finite-time synchronization for inertial neural networks with stochastic switching parameters based on dynamic event-triggered protocol. Due to the complexity of network environment, semi-Markovian process is introduced into the modeling of inertial neural networks, in which the transition rates vary with the operating time. The dynamic event-triggered protocol is developed to determine whether the signal is transmitted, in which Zeno phenomenon is eliminated under limited bandwidth resources. The objective is to construct an appropriate dynamic event-triggered control law such that the drive-response system maintains finite-time synchronization under generally uncertain transition rates. Based on the Lyapunov functional theory, finite-time synchronization criterion is proposed for the related inertial neural networks. Furthermore, a dynamic event-triggered controller is constructed in a finite-time interval. A numerical example and an image encryption process are given to show the efficiency of the proposed method.

Blockchain design for optimal joint production and maintenance over multiple periods for oil-filling production lines

Joint maintenance and production planning result in enhanced system efficiency and a significant reduction in expensive costs. Therefore, this research proposed an integrated blockchain design of two optimization models for the joint scheduling and sequencing of production orders and maintenance jobs over multiple periods with probabilistic and stochastic parameters for the oil-filling process. In the scheduling model, the objective function was to minimize total production and maintenance costs. Further, the sequencing model aimed to minimize the total overtime cost and the sum start times of jobs and orders. The proposed models were implemented on five production lines of five-liter lube oil bottles. Results showed that the developed optimization models effectively achieved concurrent production and maintenance planning at minimal total cost. In practice, this results in effective resource utilization, and saving costly production and maintenance costs. In conclusion, the developed blockchain design is valuable in developing, managing, and controlling optimal joint production and maintenance planning of oil-filling production lines.

Probabilistic Forecasts of Atmospheric River events using the HRRR Ensemble

The nine-member High-Resolution Rapid Refresh Ensemble (HRRRE) is evaluated for its ability to forecast five Atmospheric River (AR) events that impacted California in February–March 2019. Two sets of retrospective HRRRE simulations are conducted, a control with the standard set of perturbations (initial and boundary conditions, stochastic parameters, and physics tendency), and an experiment with initial and boundary perturbations only. Reliability plots suggest the HRRRE control represents the observed Stage IV precipitation frequency well at 6-h to 24-h lead times, and rank histograms suggest the ensemble is slightly underdispersive. The HRRRE overpredicts precipitation frequency at the higher (25 mm) threshold. These results suggest the HRRRE is a useful tool to quantify probabilistic forecasts of AR events in this region. Removing stochastic physics perturbations did not substantially impact probabilistic forecasts, suggesting most of the ensemble spread is from initial and boundary condition perturbations. Spatially, ensemble precipitation coefficient of variance is lower (less forecast uncertainty) over the Sierra Nevada range than other regions, suggesting that these ensemble perturbations have a smaller impact on precipitation processes occurring over the Sierra Nevada range. More work should be conducted to understand the impacts of other model perturbations, such as microphysics, on ensemble performance, and to improve Stage IV accuracy with frozen precipitation in mountainous regions.