Stochastic Parameters Research Articles

Jointly Distributed Filtering Based on Generalized Maximum Correntropy Criterion: Memory-Based Event-Triggered Cases

This article addresses jointly distributed entropy filtering issues based on the generalized maximum correntropy criterion (GMCC) for discrete-time stochastic parameter systems with fault and non-Gaussian noise effects. By taking current and historical triggered information, a memory-based event-triggered scheme with a time-varying threshold is put forward to govern the network communication. According to the constructed jointly distributed entropy filter with a two-step form, the upper bounds of the filtering error covariance matrices are derived and an ideal filter gain is obtained to maximize GMCC. Furthermore, an accessible gain is received via fixed-point iterative rules and the corresponding convergence is disclosed in theory. Finally, an application of the proposed distributed filter in ballistic object tracking is provided to show its effectiveness under non-Gaussian environments.

Response Analysis of the Three-Degree-of-Freedom Vibroimpact System with an Uncertain Parameter.

The inherent non-smoothness of the vibroimpact system leads to complex behaviors and a strong sensitivity to parameter changes. Unfortunately, uncertainties and errors in system parameters are inevitable in mechanical engineering. Therefore, investigations of dynamical behaviors for vibroimpact systems with stochastic parameters are highly essential. The present study aims to analyze the dynamical characteristics of the three-degree-of-freedom vibroimpact system with an uncertain parameter by means of the Chebyshev polynomial approximation method. Specifically, the vibroimpact system model considered is one with unilateral constraint. Firstly, the three-degree-of-freedom vibroimpact system with an uncertain parameter is transformed into an equivalent deterministic form using the Chebyshev orthogonal approximation. Then, the ensemble means responses of the stochastic vibroimpact system are derived. Numerical simulations are performed to verify the effectiveness of the approximation method. Furthermore, the periodic and chaos motions under different system parameters are investigated, and the bifurcations of the vibroimpact system are analyzed with the Poincaré map. The results demonstrate that both the restitution coefficient and the random factor can induce the appearance of the periodic bifurcation. It is worth noting that the bifurcations fundamentally differ between the stochastic and deterministic systems. The former has a bifurcation interval, while the latter occurs at a critical point.

Characterization of the iPhone LiDAR-Based Sensing System for Vibration Measurement and Modal Analysis.

Portable depth sensing using time-of-flight LiDAR principles is available on iPhone 13 Pro and similar Apple mobile devices. This study sought to characterize the LiDAR sensing system for measuring full-field vibrations to support modal analysis. A vibrating target was employed to identify the limits and quality of the sensor in terms of noise, frequency, and range, and the results were compared to a laser displacement transducer. In addition, properties such as phone-to-target distance and lighting conditions were investigated. It was determined that the optimal phone-to-target distance range is between 0.30 m and 2.00 m. Despite an indicated sampling frequency equal to the 60 Hz framerate of the RGB camera, the LiDAR depth map sampling rate is actually 15 Hz, limiting the utility of this sensor for vibration measurement and presenting challenges if the depth map time series is not downsampled to 15 Hz before further processing. Depth maps were processed with Stochastic Subspace Identification in a Monte Carlo manner for stochastic modal parameter identification of a flexible steel cantilever. Despite significant noise and distortion, the natural frequencies were identified with an average difference of 1.9% in comparison to the laser displacement transducer data, and high-resolution mode shapes including uncertainty ranges were obtained and compared to an analytical solution counterpart. Our findings indicate that mobile LiDAR measurements can be a powerful tool in modal identification if used in combination with prior knowledge of the structural system. The technology has significant potential for applications in structural health monitoring and diagnostics, particularly where non-contact vibration sensing is useful, such as in flexible scaled laboratory models or field scenarios where access to place physical sensors is challenging.

A posteriori multiobjective approach for techno-economic allocation of PV and BES units in a distribution system hosting PHEVs

This paper proposes a posteriori multiobjective approach to effectively integrate photovoltaic (PV) units into the distribution network. PV units are inherently non-dispatchable sources due to the intermittent nature of solar irradiance. To address this limitation, battery energy storage (BES) units are employed to support the PV units, thereby transforming them into dispatchable sources. The objective of this study is to optimally allocate dispatchable PV-BES units within a distribution network that accommodates plug-in hybrid electric vehicles (PHEVs). The PHEVs are modelled considering stochastic parameters at three different demand response levels. A multiobjective optimization problem is formulated to address the conflicting technical and economic objectives associated with the allocation of PV-BES units. The multiobjective manta ray foraging optimizer algorithm is utilized for solving the multiobjective optimization problem. Additionally, the technique for order of preference by similarity to ideal solution is used to identify the best trade-off solution, and multiple solutions are presented based on the decision-makers preferences regarding the conflicting objectives under consideration. The proposed approach is validated on 33-bus and 69-bus distribution networks, and extensive case studies are conducted to showcase the advantages of the proposed methodology.

Information-Based Probabilistic Verification Scores for Two-Dimensional Ensemble Forecast Data: A Madden–Julian Oscillation Index Example

Abstract Probabilistic forecasting is a common activity in many fields of the Earth sciences. Assessing the quality of probabilistic forecasts—probabilistic forecast verification—is therefore an essential task in these activities. Numerous methods and metrics have been proposed for this purpose; however, the probabilistic verification of vector variables of ensemble forecasts has received less attention than others. Here we introduce a new approach that is applicable for verifying ensemble forecasts of continuous, scalar, and two-dimensional vector data. The proposed method uses a fixed-radius near-neighbors search to compute two information-based scores, the ignorance score (the logarithmic score) and the information gain, which quantifies the skill gain from the reference forecast. Basic characteristics of the proposed scores were examined using idealized Monte Carlo simulations. The results indicated that both the continuous ranked probability score (CRPS) and the proposed score with a relatively small ensemble size (<25) are not proper in terms of the forecast dispersion. The proposed verification method was successfully used to verify the Madden–Julian oscillation index, which is a two-dimensional quantity. The proposed method is expected to advance probabilistic ensemble forecasts in various fields. Significance Statement In the Earth sciences, stochastic future states are estimated by solving a large number of forecasts (called ensemble forecasts) based on physical equations with slightly different initial conditions and stochastic parameters. The verification of probabilistic forecasts is an essential part of forecasting and modeling activity in the Earth sciences. However, there is no information-based probabilistic verification score applicable for vector variables of ensemble forecasts. The purpose of this study is to introduce a novel method for verifying scalar and two-dimensional vector variables of ensemble forecasts. The proposed method offers a new approach to probabilistic verification and is expected to advance probabilistic ensemble forecasts in various fields.

Experimental and numerical investigations on the stress waves propagation in strain-hardening fiber-reinforced cementitious composites: Stochastic analysis using polynomial chaos expansions

The propagation of stress waves can result in spalling fractures in materials, which poses a threat to the safety of engineering structures. Hence, in-depth studies are necessary to mitigate such risks. Ultra-high toughness cementitious composites (UHTCC) with significant tensile strain-hardening properties are advanced engineering materials with great potential for impact engineering. The study used a combination of experimental and numerical methods to analyse the propagation and attenuation behaviour of stress waves in the UHTCC. The numerical model was developed using the Smooth Particle Galerkin (SPG) method and the Karagozian & Case concrete/cementitious (KCC) material constitutive model. Additionally, a quantitative global sensitivity analysis (GSA) using a polynomial chaos expansion (PCE) surrogate model and Sobol's method was conducted to analyse the stochastic input parameters of the numerical model. Results show that compressive stress waves undergo significant attenuation during propagation in UHTCC, and the developed numerical model accurately simulated the stress wave propagation process Furthermore, the PCE-Sobol GSA revealed that the selected stress wave propagation responses are most sensitive to the tensile strength of UHTCC. This study is expected to deepen the understanding of the propagation behaviour of stress waves in UHTCC and pave the way for promising applications of UHTCC in impact engineering.

Decoding the Autoencoder

Cross-sectional training of auto-encoder neural networks suggests that yield-curve dynamics are well described by two to three factors and are dynamically arbitrage-free. In this article, we discuss the evidence and identify stochastic model parameters that support the auto-encoders.

Estimation of Solar PV Plant output using Polynomial Regression and ANN Algorithm

The paper proposes the use of Artificial Neural Networks (ANN) and Polynomial Regression (PR) algorithms for estimating the output of a Solar Photovoltaic (PV) Plant. The study compares the performance of these two methods, using a dataset of weather parameters and PV Plant output. The results show that both the methods can effectively estimate the PV Plant output, with the ANN model having a slightly higher accuracy than the polynomial regression model as ANNs can learn the nonlinear relationship between input stochastic parameters and output in a better manner. The study highlights the potential of machine learning techniques for optimizing the performance of solar PV plants and improving their efficiency.

Langmuir Forcing and Collapsing Subsonic Density Cavitons via Random Modulations

Electrostatic nonlinear random Langmuir structures have been propagated in stochastic magnetospheres, clouds and solar wind. A theoretical description of Langmuir waves can be modeled by Schrödinger and Zakharov models with stochastic terms. It was explained that the stochastic parameter affects the forcing, collapsing in strongly density turbulence and density crystalline structures. The unified method has been implemented to provide new stochastic solutions for a Zakharov system in subsonic limit with noises via the Itô sense. This unified approach provides a variety of advantages, such as avoiding difficult calculations and explicitly providing pivotal solutions. It is easy to use, efficient, and precise. The induced generated energy during the collapsing of solar Langmuir wave bursts and clouds is determined by the solitonic formations. In addition, the collapsing strong turbulence or forcing density crystalline structures depend mainly on stochastic processes. Furthermore, electrostatic waves in clouds that may collapse are represented sometimes as dissipative shapes. So, the results of this investigation could be applicable to observations of energy seeding and collapsing in clouds. This energy is based on the electrostatic field and its related densities’ perturbation in subsonic limits. Finally, it has been explored how noise parameters in the Itô sense affect the solar wind Langmuir waves’ properties. So, the findings of this discussion may be applicable to real observations of energy collapsing and seeding in clouds.

Probability of rail break caused by out-of-round wheel loads

A simulation procedure to predict the probability of rail break due to a measured wheel load spectrum is presented. The load distribution includes a representative proportion of high-magnitude dynamic loads generated by out-of-round wheels. Linear elastic fracture mechanics is applied to determine the stress intensities of pre-existing rail head cracks in a continuously welded rail subjected to combined bending and temperature loading. Rail bending moments are evaluated using a validated time-domain model of dynamic vehicle–track interaction. The considered multi-dimensional stochastic parameter space includes field test data of dynamic loads from a wheel impact load detector and crack depths from eddy current data. Meta-models based on poly-harmonic splines are applied to reduce the computational cost of the analysis. Supported by the extensive field test data, the simulation procedure is demonstrated by investigating the influences of freight traffic type, track support stiffness and rail temperature on the probability of a rail break initiated at a pre-existing rail head crack.

A tunnelling crack density evolution model for FRP laminates subjected to cyclic multi-axial strain-controlled loading

A multi-scale stochastic crack density evolution model for tunnelling cracks under multi-directional cyclic loading is presented. The damage model proposed utilizes a multi-scale stress-based criterion for crack initiation and a triple unit cell approach with inputs from the GLOB-LOC model for crack-front growth rate. Biaxial cruciform specimens subjected to strain-controlled cyclic loading are used to calibrate the crack initiation SN curve and the Paris-Erdogan type of law required for crack growth. Additionally, uniaxial force-controlled cyclic tests are used to calibrate the stochastic parameters associated with crack initiation and crack growth. The performance of the damage model in predicting the crack-front growth compared well with experimental data and 3D finite element analyses. The damage model includes a crack element discretisation scheme which allows for multiple collinear cracks to initiate and coalesce. The model also accounts for the growth of damage outside the window of a primary representative volume element. The crack density predictions of the model are compared with measurements from cruciform specimens. It is shown that the damage model captures the trend of the crack density evolution well and provides a conservative prediction of the crack saturation level.

On the stationarity and existence of moments of the periodic EGARCH process

Abstract In this paper, we will consider periodic EGARCH ⁡ ( p , p ) {\operatorname{EGARCH}(p,p)} (exponential generalized autoregressive conditional heteroscedastic) processes denoted by PEGARCH ⁡ ( p , p ) {\operatorname{PEGARCH}(p,p)} . These processes are similar to the standard EGARCH processes, but include seasonally varying coefficients. We examine the probabilistic structure of an EGARCH-type stochastic difference equation with periodically-varying parameters. We propose necessary and sufficient conditions ensuring the existence of stationary solutions (in a periodic sense) based on a Markovian representation. The closed forms of higher moments are, under these conditions, established. Furthermore, the expressions for the Kurtosis coefficient and the autocorrelations of squared observations are derived. The general theory is illustrated by considering special cases such as the symmetric and the asymmetric cases of the second order PEGARCH model.

Assessing by Simulation the Effect of Process Variability in the SALB-1 Problem

The simple assembly line balancing (SALB) problem is a significant challenge faced by industries across various sectors aiming to optimise production line efficiency and resource allocation. One important issue when the decision-maker balances a line is how to keep the cycle time under a given time across all cells, even though there is variability in some parameters. When there are stochastic elements, some approaches use constraint relaxation, intervals for the stochastic parameters, and fuzzy numbers. In this paper, a three-part algorithm is proposed that first solves the balancing problem without considering stochastic parameters; then, using simulation, it measures the effect of some parameters (in this case, the inter-arrival time, processing times, speed of the material handling system which is manually performed by the workers in the cell, and the number of workers who perform the tasks on the machines); finally, the add-on OptQuest in SIMIO solves an optimisation problem to constrain the cycle time using the stochastic parameters as decision variables. A Gearbox instance from literature is solved with 15 tasks and 14 precedence rules to test the proposed approach. The deterministic balancing problem is solved optimally using the open solver GLPK and the Pyomo programming language, and, with simulation, the proposed algorithm keeps the cycle time less than or equal to 70 s in the presence of variability and deterministic inter-arrival time. Meanwhile, with stochastic inter-arrival time, the maximum cell cycle is 72.04 s. The reader can download the source code and the simulation models from the GitHub page of the authors.

An integrated chance-constrained stochastic model for a preemptive multi-skilled multi-mode resource-constrained project scheduling problem: A case study of building a sports center

A multi-mode resource-constrained project scheduling problem (MRCPSP) with multiple skills is investigated in this paper. Unlike the traditional form of this problem, and considering the real-world project circumstances, project activities can be preempted. In this paper, a new multi-objective mixed-integer linear programming (MILP) model with three objective functions is extended. These objectives are: (1) minimizing the project makespan, (2) minimizing the total resource costs, and (3) minimizing the total project risk. Based on real-life projects, non-renewable resources are represented as an uncertain stochastic parameter. To cope with the uncertain environment, chance-constrained programming with a confidence level is considered. A real-world construction project of a sports center in Tehran is utilized to demonstrate the applicability of the presented formulation. A well-known lexicographic optimization method, namely AUGMECON2, is applied to solve the proposed formulation with three objectives. Ultimately, for the case study and two datasets J30 and MM50, the proposed lexicographic optimization algorithm is compared with an efficient multi-objective mathematical programming technique known as the AUGMECON method. The comparison is based on performance metrics (i.e., IGD and HV) commonly used in multi-objective optimization. The results show the relative dominance of the proposed lexicographic optimization algorithm over the AUGMECON method in all sizes of the problem instances.

Sensitivity-enhanced generalized polynomial chaos for efficient uncertainty quantification

We consider the Least Squares (LSQ) regression method for Uncertainty Quantification (UQ) using generalised polynomial chaos (gPC) and augment the linear system with the gradient of the Quantity of Interest (QoI) with respect to the stochastic variables. The gradient is computed very efficiently for all variables from the adjoint system of equations. To minimise the condition number of the augmented LSQ system, an effective sampling strategy of the stochastic space is required. We compare two strategies. In the first, we apply pivoted QR decomposition to the standard LSQ matrix and evaluate both the QoI and its gradient at the sample points identified. In the second strategy, we apply QR decomposition directly to the augmented matrix. We find that the first strategy is more efficient in terms of accuracy vs number of evaluations. We call the new approach sensitivity-enhanced generalised polynomial chaos, or se-gPC, and apply it to several test cases including an aerodynamic case with 40 stochastic parameters. The method can produce accurate estimations of the statistical moments using a small number of sampling points. The computational cost scales as ∼mp−1, instead of ∼mp of the standard LSQ formulation, where m is the number of stochastic variables and p the chaos order. The solution of the adjoint system of equations is implemented in many computational mechanics packages, thus the infrastructure exists for the application of the method to a wide variety of engineering problems.

Machine learning enabled quantification of stochastic active metadamping in acoustic metamaterials

System uncertainties often lead to deviation from the anticipated behaviour of acoustic metamaterials (AMs) and thus, make their intended design ineffective. Therefore, in this study, the effect of stochastic parameters on a recently developed phenomenon in AMs, known as active metadamping is quantified using machine learning (ML). The enhancement of damping in an active feedback-controlled metamaterial over an equivalent uncontrolled counterpart is defined as active metadamping. Metadamping enables a metamaterial to dissipate energy faster in addition to its inherent bandgap characteristics. The ML technique, Gaussian process is used as the surrogate model to capture the stochastic dynamics of the active AM. A trade-off in the spatial attenuation and temporal energy dissipation characteristics is observed while velocity-feedback control is applied within the resonating units of the metamaterial. The overall dissipation and the decay ratio increase around five times in the controlled case; whereas, the attenuation bandwidth reduces or even vanishes. Most importantly, the results elucidate that metadamping is robust to the uncertainty of the system parameters, unlike the energy and the decay amplitude for the controlled case. Additionally, Gaussian process is able to capture the behaviour of active AMs by using only 1% computational cost as compared to that of the Monte Carlo simulations.

Impact of Stochastic Ocean Density Corrections on Air‐Sea Flux Variability

AbstractAir‐sea flux variability has contributions from both ocean and atmosphere at different spatio‐temporal scales. Atmospheric synoptic scales and the air‐sea turbulent heat flux that they drive are well represented in climate models, but ocean mesoscales and their associated variability are often not well resolved due to non‐eddy‐resolving spatial resolutions of current climate models. We deploy a physics‐based stochastic subgrid‐scale parameterization for ocean density, that reinforces the lateral density variations due to oceanic eddies, and examine its effect on air‐sea heat flux variability in a comprehensive coupled climate model. The stochastic parameterization substantially modifies sea surface temperature (SST) and latent heat flux (LHF) variability and their co‐variability, primarily at scales near the resolution of the ocean model grid. Enhancement in the SST‐LHF anomaly covariance, and correlations, indicate that the ocean‐intrinsic component of the air‐sea heat flux variability is more consistent with high‐resolution satellite observations, especially in Gulf Stream region.

Analytical formulation for explaining the variations in traffic states: A fundamental diagram modeling perspective with stochastic parameters

Despite the simplicity and practicality of (deterministic) fundamental diagram models in highway traffic flow theory, the wide scattering effect observed in empirical data remains highly controversial, particularly for explaining traffic state variations. Owing to the analytical properties of the fundamental diagram modeling approach, in this study, we proposed an analytical and quantitative method for analyzing traffic state variations. We investigated the scattering effect in the fundamental diagram and proposed two stochastic fundamental diagram (SFD) models with lognormal and skew-normal distributions to explain the variations in traffic states. The first SFD model assumes that the scattering effect results from stochasticity in both the free-flow speed and the speed at critical density. Both random variables were assumed to follow the lognormal distribution. In the second SFD model, an integrated error term that was assumed to follow the skew-normal distribution over different density ranges was appended to the deterministic fundamental diagram. The properties of these two SFD models were analyzed and compared, and the parameters in these SFD models were calibrated using real-world loop detector data. The observed scatters from the empirical data were reproduced well by the simulated fundamental diagram model, indicating the validity of the proposed SFD models for explaining traffic state variations. Using these two analytical SFD models, we can analyze the stochastic capacity of freeways with closed forms. More importantly, the sources of stochasticity in freeway capacity can be traced in terms of randomly distributed parameters in fundamental diagram models.

A New Switching System Protocol for Synchronization in Probability of RDNNs With Stochastic Sampling

The synchronization in probability of reaction-diffusion neural networks (RDNNs) with stochastic sampling is studied in this article. By introducing a stochastic switching parameter, a new switching system protocol is proposed for stochastic sampling control systems. The switching system protocol effectively improves the existing methods. By the protocol, the stochastic switching sampled-data controller is designed, and the considered system is transformed into a switching system. Different from the existing sampled-data controllers with determined control gains, the stochastic switching sampled-data controller is with switching gains, which is more elastic. Then, by constructing a new stochastic switching Lyapunov–Krasovskii functional (LKF), using the law of large numbers and the Lagrange mean value theorem, new synchronization in probability criteria are established for RDNNs. In the mean time, the wanted stochastic switching sampled-data controller gains are obtained. Moreover, the synchronization in probability issue is also studied for NNs with stochastic sampling. Finally, the effectiveness of the proposed results are verified by two numerical examples.

A stochastic stability equation for unsteady turbulence in the stable boundary layer

AbstractThe atmospheric boundary layer is particularly challenging to model in conditions of stable stratification, which can be associated with intermittent or unsteady turbulence. We develop a modelling approach to represent unsteady mixing possibly associated with turbulence intermittency and with unresolved fluid motions, called sub‐mesoscale motions. This approach introduces a stochastic parametrisation by randomising the stability correction used in the classical Monin–Obhukov similarity theory. This randomisation alters the turbulent momentum diffusion and accounts for sporadic events that cause unsteady mixing. A data‐driven stability correction equation is developed, parametrised, and validated with the goal to be modular and easily combined with existing Reynolds‐averaged Navier–Stokes models. Field measurements are processed using a statistical model‐based clustering technique, which simultaneously models and classifies the non‐stationary stable boundary layer. The stochastic stability correction obtained includes the effect of the static stability of the flow on the resolved flow variables, and additionally includes random perturbations that account for localised intermittent bursts of turbulence. The approach is general and effectively accounts for the stochastic mixing effects of unresolved processes of possibly unknown origin.