Deterministic Parameters Research Articles

Modelling of wind and solar power output uncertainty in power systems based on historical data: A characterisation through deterministic parameters

Modelling of wind and solar power output uncertainty in power systems based on historical data: A characterisation through deterministic parameters

Characterizing the as-built surface topography of Inconel 718 specimens as a function of laser powder bed fusion process parameters

Purpose The ability to use laser powder bed fusion (LPBF) to print parts with tailored surface topography could reduce the need for costly post-processing. However, characterizing the as-built surface topography as a function of process parameters is crucial to establishing linkages between process parameters and surface topography and is currently not well understood. The purpose of this study is to measure the effect of different LPBF process parameters on the as-built surface topography of Inconel 718 parts. Design/methodology/approach Inconel 718 truncheon specimens with different process parameters, including single- and double contour laser pass, laser power, laser scan speed, build orientation and characterize their as-built surface topography using deterministic and areal surface topography parameters are printed. The effect of both individual process parameters, as well as their interactions, on the as-built surface topography are evaluated and linked to the underlying physics, informed by surface topography data. Findings Deterministic surface topography parameters are more suitable than areal surface topography parameters to characterize the distinct features of the as-built surfaces that result from LPBF. The as-built surface topography is strongly dependent on the built orientation and is dominated by the staircase effect for shallow orientations and partially fused metal powder particles for steep orientations. Laser power and laser scan speed have a combined effect on the as-built surface topography, even when maintaining constant laser energy density. Originality/value This work addresses two knowledge gaps. (i) It introduces deterministic instead of areal surface topography parameters to unambiguously characterize the as-built LPBF surfaces. (ii) It provides a methodical study of the as-built surface topography as a function of individual LPBF process parameters and their interaction effects.

Dynamic Analysis of Geared Rotor System with Hybrid Uncertainties

Current research on the dynamics and vibrations of geared rotor systems primarily focuses on deterministic models. However, uncertainties inevitably exist in the gear system, which cause uncertainties in system parameters and subsequently influence the accurate evaluation of system dynamic behavior. In this study, a dynamic model of a geared rotor system with mixed parameters and model uncertainties is proposed. Initially, the dynamic model of the geared rotor-bearing system with deterministic parameters is established using a finite element method. Subsequently, a nonparametric method is introduced to model the hybrid uncertainties in the dynamic model. Deviation coefficients and dispersion parameters are used to reflect the levels of parameter and model uncertainty. For example, the study evaluates the effects of uncertain bearing and mesh stiffness on the vibration responses of a geared rotor system. The results demonstrate that the influence of uncertainty varies among different model types. Model uncertainties have a more significant than parametric uncertainties, whereas hybrid uncertainties increase the nonlinearities and complexities of the system’s dynamic responses. These findings provide valuable insights into understanding the dynamic behavior of geared system with hybrid uncertainties.

Uncertainty quantification analysis of bifurcations of the Allen–Cahn equation with random coefficients

In this work we consider the Allen–Cahn equation, a prototypical model problem in nonlinear dynamics that exhibits bifurcations corresponding to variations of a deterministic bifurcation parameter. Going beyond the state-of-the-art, we introduce a random coefficient in the linear reaction part of the equation, thereby accounting for random, spatially-heterogeneous effects. Importantly, we assume a spatially constant, deterministic mean value of the random coefficient. We show that this mean value is in fact a bifurcation parameter in the Allen–Cahn equation with random coefficients. Moreover, we show that the bifurcation points and bifurcation curves become random objects. We consider two distinct modelling situations: (i) for a spatially homogeneous coefficient we derive analytical expressions for the distribution of the bifurcation points and show that the bifurcation curves are random shifts of a fixed reference curve; (ii) for a spatially heterogeneous coefficient we employ a generalized polynomial chaos expansion to approximate the statistical properties of the random bifurcation points and bifurcation curves. We present numerical examples in 1D physical space, where we combine the popular software package Continuation Core and Toolboxes (COCO) for numerical continuation and the Sparse Grids Matlab Kit for the polynomial chaos expansion. Our exposition addresses both, dynamical systems and uncertainty quantification, highlighting how analytical and numerical tools from both areas can be combined efficiently for the challenging uncertainty quantification analysis of bifurcations in random differential equations.

Solving Neutrosophic Multi-Dimensional Fixed Charge Transportation Problem

In the decision making problems, transportation problem (TP) is one of the most significant applications that aim to optimize the objective function of products shipped from different sources to different destinations. When an additional charge such as toll tax, parking fee, permit fee and so on are included in the transportation cost then the problem becomes a fixed charge TP. If the shipped products are damageable, they are affected by the type of vehicle and the distance of route. So it is quite evident that the vehicle type and the distance of route play a significant role in TP. In reality, along with sources and destinations, the decision maker (DM) desires to consider the parameters such as the mode of transport and routes of transportation that are used for shipment of the products from sources to destinations in order to minimize the loss of damageable products and to maximize the profit. As a result, mode of transport and routes of transportation are added to TP, then the TP becomes a four-dimensional TP. Sometimes, the data/parameters of the problems may not be always precise due to incomplete information, inadequate data or shortage of evidence. To deal with these obstacles, the parameters of the problem can be represented as the single-valued trapezoidal neutrosophic numbers (SVTrNNs). The neutrosophic data facilitate a reasonable and practicable way for DMs to tackle decisionmaking problems by managing indeterminacy and providing an effective framework for analysis and synthesis of complex decision scenarios. In view of this, in this paper we have considered the single objective four-dimensional fixed charge transportation problem (4DFCTP) with parameters, supply, demand, conveyance, transportation cost, fixed charge as single-valued trapezoidal neutrosophic numbers and the distance of routes as real numbers. First, the score function is utilized to transform the neutrosophic parameter into its deterministic parameter in order to avoid the negative values for the decision variable. Then the deterministic problem comprises deterministic parameters such as supply, demand, conveyance, transportation cost with fixed charges and distance of routes. Secondly, a novel approach namely, min zeromin cost approach is introduced for finding the optimal solution to the equivalent deterministic problem in polynomial time. The main objective of this paper is to optimize the breakable products and routing plan of vehicles in a way to minimize the total transportation cost with fixed cost of the business organizations using the proposed min zero-min cost approach. To demonstrate the problem’s validity and relevance, two numerical examples are solved using our proposed approach. To highlight the proposed approach, comparison of the solution with the LINGO software is performed. The obtained optimal solution from the proposed approach is the same as the LINGO software. At last, conclusions as well as future work related to the study are presented.

On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields

Deep Learning is having a remarkable impact on the design of Reduced Order Models (ROMs) for Partial Differential Equations (PDEs), where it is exploited as a powerful tool for tackling complex problems for which classical methods might fail. In this respect, deep autoencoders play a fundamental role, as they provide an extremely flexible tool for reducing the dimensionality of a given problem by leveraging on the nonlinear capabilities of neural networks. Indeed, starting from this paradigm, several successful approaches have already been developed, which are here referred to as Deep Learning-based ROMs (DL-ROMs). Nevertheless, when it comes to stochastic problems parameterized by random fields, the current understanding of DL-ROMs is mostly based on empirical evidence: in fact, their theoretical analysis is currently limited to the case of PDEs depending on a finite number of (deterministic) parameters. The purpose of this work is to extend the existing literature by providing some theoretical insights about the use of DL-ROMs in the presence of stochasticity generated by random fields. In particular, we derive explicit error bounds that can guide domain practitioners when choosing the latent dimension of deep autoencoders. We evaluate the practical usefulness of our theory by means of numerical experiments, showing how our analysis can significantly impact the performance of DL-ROMs.

Physics-constrained polynomial chaos expansion for scientific machine learning and uncertainty quantification

We present a novel physics-constrained polynomial chaos expansion as a surrogate modeling method capable of performing both scientific machine learning (SciML) and uncertainty quantification (UQ) tasks. The proposed method possesses a unique capability: it seamlessly integrates SciML into UQ and vice versa, which allows it to quantify the uncertainties in SciML tasks effectively and leverage SciML for improved uncertainty assessment during UQ-related tasks. The proposed surrogate model can effectively incorporate a variety of physical constraints, such as governing partial differential equations (PDEs) with associated initial and boundary conditions constraints, inequality-type constraints (e.g., monotonicity, convexity, non-negativity, among others), and additional a priori information in the training process to supplement limited data. This ensures physically realistic predictions and significantly reduces the need for expensive computational model evaluations to train the surrogate model. Furthermore, the proposed method has a built-in uncertainty quantification (UQ) feature to efficiently estimate output uncertainties. To demonstrate the effectiveness of the proposed method, we apply it to a diverse set of problems, including linear/non-linear PDEs with deterministic and stochastic parameters, data-driven surrogate modeling of a complex physical system, and UQ of a stochastic system with parameters modeled as random fields.

Resetting as a swift equilibration protocol in an anharmonic potential

We present and characterize a method to accelerate the relaxation of a Brownian object between two distinct equilibrium states. Instead of relying on a deterministic time-dependent control parameter, we use stochastic resetting to guide and accelerate the transient evolution. The protocol is investigated theoretically, and its thermodynamic cost is evaluated with the tools of stochastic thermodynamics. Remarkably, we show that stochastic resetting significantly accelerates the relaxation to the final state. This stochastic protocol exhibits energetic and temporal characteristics that align with the scales observed in previously investigated deterministic protocols. Moreover, it expands the spectrum of stationary states that can be manipulated, incorporating new potential profiles achievable through experimentally viable protocols. Published by the American Physical Society 2024

Bayesian calibration and uncertainty quantification of a rate-dependent cohesive zone model for polymer interfaces

This study presents a rate-dependent cohesive zone model for the fracture of polymeric interfaces and performs a Bayesian calibration, an uncertainty quantification, and a sensitivity analysis for the model. The proposed cohesive zone model accounts for both reversible elastic and irreversible rate-dependent separation sliding deformation at the interface. The viscous dissipation due to the irreversible opening at the interface is modeled using elastic-viscoplastic kinematics that incorporates the effects of strain rate. Inverse calibration of parameters for such complex models through trial and error is challenging due to the large number of parameters of the model. Moreover, the calibrated parameter values are often non-unique and uncertain when the available experimental data is limited. To tackle this challenge, we employ a Bayesian calibration approach to identify parameters from experimental data, the resulting parameters significantly enhance the accuracy of the model. To quantify the uncertainty associated with the inverse parameter estimation, a modular Bayesian approach is employed to calibrate the unknown model parameters, accounting for the parameter uncertainty of the cohesive zone model. The advantages of the Bayesian calibration over a deterministic parameter fit are demonstrated. Further, to quantify the model uncertainties, such as incorrect assumptions or missing physics, a discrepancy function is introduced, which significantly improves the model’s prediction. Finally, the total uncertainty of the model is quantified in a predictive setting. A sensitivity analysis is performed to assess how changes in the input variables of the model affect the peak load, facilitating the identification of a concise set of highly influential parameters. The present approach can be used for calibration and uncertainty quantification for other complex computational mechanics models. It should also facilitate the designing of interface materials under uncertainty.

A new paradigm for the efficient inclusion of stochasticity in engineering simulations: Time-separated stochastic mechanics

AbstractAs a physical fact, randomness is an inherent and ineliminable aspect in all physical measurements and engineering production. As a consequence, material parameters, serving as input data, are only known in a stochastic sense and thus, also output parameters, e.g., stresses, fluctuate. For the estimation of those fluctuations it is imperative to incoporate randomness into engineering simulations. Unfortunately, incorporating uncertain parameters into the modeling and simulation of inelastic materials is often computationally expensive, as many individual simulations may have to be performed. The promise of the proposed method is simple: using extended material models to include stochasticity reduces the number of needed simulations to one. This single computation is cheap, i.e., it has a comparable numerical effort as a single standard simulation. The extended material models are easily derived from standard deterministic material models and account for the effect of uncertainty by an extended set of deterministic material parameters. The time-dependent and stochastic aspects of the material behavior are separated, such that only the deterministic time-dependent behavior of the extended material model needs to be simulated. The effect of stochasticity is then included during post-processing. The feasibility of this approach is demonstrated for three different and highly non-linear material models: viscous damage, viscous phase transformations and elasto-viscoplasticity. A comparison to the Monte Carlo method showcases that the method is indeed able to provide reliable estimates of the expectation and variance of internal variables and stress at a minimal fraction of the computation cost.

Modal–based uncertainty quantification for deterministically estimated structural parameters in low-fidelity model updating of complex connections

Modeling complex joints in structures entails significant time and effort, necessitating simplifications. Epistemic uncertainties arising from low-fidelity modeling can be quantified through probabilistic model updating. However, finding a surrogate physical model to represent simplified joint configurations poses challenges. Additionally, establishing a Bayesian formulation capable of incorporating structural parameters of connections is necessary. This study employs a validated simplifying parameterization approach for surrogate modeling of complex semi-rigid connections in a benchmark laboratory steel grid. It proposes a modal probabilistic Bayesian methodology to quantify uncertainties in the structure's joints. Three modal-based objective functions are utilized for finite element model updating. The modal properties of the structure are extracted by experimental modal analysis during an impact test, which will be utilized in the model updating process. Deterministic and probabilistic structural parameter estimations are integrated to enhance the robustness of the Bayesian technique. Furthermore, a guideline for selecting optimal hyperparameters is provided. Results demonstrate that utilizing deterministically estimated parameters as prior knowledge can facilitate and improve modal probabilistic model updating for structures with complex joints. Also, it is found that despite significant simplifications of joints, structural parameter tolerance around the maximum a posteriori estimate in surrogate models remains low.

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

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

Deterministic Parameters of Growth and Yield of Wheat (Triticum aestivum L.) as Influenced by Fractional Application of Nitrogen and Potassium

Deterministic Parameters of Growth and Yield of Wheat (Triticum aestivum L.) as Influenced by Fractional Application of Nitrogen and Potassium

Cyclic behavior of laminated bio-based connections with slotted-in steel plates: Genetic algorithm, deterministic neural network-based model parameter identification, and uncertainty quantification

To support more sustainable construction, this paper experimentally investigates the cyclic behavior of laminated timber (Laminated Veneer Lumber (LVL)) and glubam (Glue Laminated Bamboo) connections with slotted-in steel plates in terms of experimental test, numerical simulations and parameter identification. Experimental tests included eight different configurations: two materials (LVL and glubam), two bolt diameters (8 and 10 mm), and one or two bolts. Two different cyclic-loading protocols were applied for each type of connection: only tension and tension/compression. The observed behavior is then compared to a finite element model developed in OpenSeesPy, which takes into account factors such as sliding, contact, pinching, cyclic stiffness, and strength degradation. To identify the best set of parameters for the model, three different approaches are considered: genetic algorithm, fast deterministic neural network, and probabilistic Bayesian method. First, the model identification is carried out by means of a genetic algorithm-based optimization. The parameter-identification results are evaluated in terms of elastic stiffness, yielding point, and ductility. Next, a sensitivity analysis is performed to determine the significance of the parameters, and an innovative approach combining neural network and sensitivity analysis is proposed for fast and preliminary parameter identification. Then, probabilistic Bayesian identification is employed to calculate the posterior distribution of the model parameters identified and the confidence bounds of the estimated response. Finally, different model identification parameters are compared and suggestions for algorithm selection are provided.

Uncertain stochastic vibration characteristic analysis of composite laminated rectangular plate based on improved kriging model

The stochastic vibration analysis of composite laminated structures has been conducted extensively in the field of structural dynamics. Existing studies in this field are primarily conducted based on deterministic structural parameters, whereas the effects of parametric uncertainties on the stochastic vibration characteristics of composite laminated structures are disregarded. This study investigates a composite laminated rectangular plate by considering the effect of interval uncertainty in the intrinsic parameters and load on its stochastic vibration characteristics. A rapid analysis model for the structural stochastic vibration characteristics is established based on an improved kriging model. Additionally, an innovative approach that combines the improved kriging model with intelligent optimization is proposed to solve problems pertaining to uncertainty-propagation analysis of structures. Based on this method, an uncertainty-propagation analysis of structural stochastic vibration responses is efficiently implemented. The effectiveness of the proposed method is demonstrated by comparing the results with those obtained from Monte Carlo simulation. The numerical results indicate that different uncertain factors exert varying degrees of effect on the stochastic vibration characteristics of the plate. Finally, the effects of density, elastic modulus ratio, fiber orientation and load on the interval fluctuation patterns of uncertain responses are discussed.

Data‐driven out‐of‐order model for synchronized planning, scheduling, and execution in modular construction fit‐out management

AbstractFit‐out operations in modular construction exhibit unique features, such as limited room space and diversely distributed operations in the building. These features pose significant challenges to planning, scheduling, and execution (PSE) of fit‐out activities due to operational parallelism, distributional diversity, and narrower constrained time window in modular construction. Hence, logistics‐operation and multi‐operations synchronizations in a real‐time manner are crucial for PSE of modular construction fit‐out management. With the support of cutting‐edge information technologies, the real‐time data inside the generated digital twins can simplify online optimization models and convert stochastic factors into deterministic parameters. This paper formulates a novel real‐time data‐driven Out‐of‐Order (OoO) model for synchronized PSE in modular construction fit‐out management. Drawing inspiration from OoO mechanism in Central Processing Unit (CPU), a real‐time data‐driven and rolling‐horizon‐based OoO model is proposed for PSE of modular construction fit‐out, employing a forward heuristic algorithm for solution. Time–space–state data from digital twins are updated to facilitate dynamic decision‐making of managers. Through stochastic computational experiments, we demonstrate the effectiveness of OoO model in optimizing project metrics and the improved resilience in uncertain environments.

Temperature fluctuations in mesoscopic systems.

Temperature is a fundamental concept in thermodynamics. In macroscopic thermodynamics, systems possess their own intrinsic temperature which equals the reservoir temperature when they equilibrate. In stochastic thermodynamics for simple systems at the microscopic level, thermodynamic quantities other than temperature (a deterministic parameter of the reservoir) are stochastic. To bridge the disparity in the perspectives about temperature between the micro- and macroregimes, we assign a generic mesoscopic N-body system an intrinsic fluctuating temperature T in this work. We simplify the complicated dynamics of numerous particles to one stochastic differential equationwith respect to T, where the noise term accounts for finite-size effects arising from random energy transfer between the system and the reservoir. Our analysis reveals that these fluctuations make the extensive quantities (in the thermodynamic limit) deviate from being extensive. Moreover, we derive finite-size corrections, characterized by heat capacity of the system, to the Jarzynski equality. A possible violation of the principle of maximum work that scales with N^{-1} is also discussed. Additionally, we examine the impact of temperature fluctuations in a finite-size Carnot engine. We show that irreversible entropy production resulting from the temperature fluctuations of the working substance diminishes the average efficiency of the cycle as η_{C}-〈η〉∼N^{-1}, highlighting the unattainability of the Carnot efficiency η_{C} for mesoscopic heat engines even under the quasistatic limit. Our general framework paves the way for further exploration of nonequilibrium thermodynamics and the corresponding finite-size effects in a mesoscopic regime.

ENTROPY-RANDOMIZED ESTIMATION OF NONLINEAR DYNAMICAL MODEL PARAMETERS ON OBSERVATION OF DEPENDENT PROCESS

The work is devoted to the development of the method of randomized machine learning in the direction of estimating dynamic models of related processes using real data, one of which is considered as the main one, and the other as a dependent one. The model of the main process in this concept is implemented by a dynamic model based on differential equations with parameters, which in turn are implemented by a static model in a different time scale. Randomized machine learning is a new theory at the intersection of data science, machine learning and data mining, based on the concept of entropy to estimate the probabilistic characteristics of model parameters. Such characteristics are the probability distributions of the corresponding objects, the estimates of which are the distributions implemented by the probability density functions or discrete distributions. Achieving this goal becomes possible thanks to the idea of moving from models with deterministic parameters to models with random parameters and, additionally, measured at the output with random noise, which achieves the consideration of the stochastic nature, which is obviously present in any natural phenomenon. As a demonstration of the proposed method, we consider the problem of predicting the total number of infected people based on the SIR dynamic epidemiological model, in which one of the parameters is considered as the state of the associated process implemented by the static model. Its evaluation is carried out according to the observations of the main process, and forecasting is carried out using the model of the associated one. Conducted experiment using real data on COVID-19 cases in Germany shows the efficiency of the proposed approach. The forecast obtained by the classical least squares method leads to an underestimation of the model output compared to the real observed data, while the proposed approach demonstrates more flexibility and potentially allows you to obtain forecasts that are more adequate to the real data, which confirms its effectiveness and adequacy under conditions a small amount of data with a high level of uncertainty.

Characterizing the variability of bauxite mine tailings from CPTU test results

In geotechnical engineering, there is a high degree of uncertainty associated with soil parameters, since soil materials are variable due to mineralogy, stress history, and deposition processes in the same layer of soil profile. Given the high degree of variability, there are limitations when calculating and simulating models based on deterministic parameters extracted from the field. Mine tailings are part of this scenario, to which must be added the difficulty of extracting samples and characterizing them in the laboratory, making field investigation crucial for basing geomechanical models. This study aims to quantify statistical properties such as mean, standard deviation, probability density function, and scale of fluctuation obtained from the analysis of direct measurements of piezocone tests, such as tip resistance, lateral friction, and pore pressure. A set of data from a bauxite tailing deposit will be used in the analysis, which which was done by implementing an algorithm in Python to calculate the statistical parameters. Q-Q plots and histograms were presented for the most variable CPTu data to evaluate the probability density function that best fits. The results found indicate a material with high variability with statistical parameters that are close to those pointed out by the literature for other mine tailings. By elucidating the statistical properties of the soil parameters, this study contributes to a better understanding of the geomechanical behavior of mine tailings deposits, aiding in the development of more accurate predictive models. Furthermore, the methodology employed underscores the importance of robust field investigations and advanced statistical analysis techniques in geotechnical engineering research.

Natural frequency analysis of gear system with interval shaft misalignment in multidimensions

Due to the existing tolerances, the shaft misalignment of gear system is inevitably uncertain and shows interval property, which will cause the natural frequency to fluctuate in an interval range, therefore the traditional dynamics analysis that takes it as a deterministic parameter cannot reflect the interval characteristics of natural frequency. To overcome this conundrum, an improved interval eigenvalue algorithm based on matrix non-negative factorization and the Chebyshev inclusion function was proposed to find the natural frequency range of gear system under such uncertainty. First, the average meshing stiffness range of the gears with interval shaft misalignment is obtained by the Chebyshev interval approach. Then combined with the consideration of the remaining excitation parameter deviation coefficients, the global interval stiffness matrix and mass matrix of a single-stage gear system are obtained. Afterwards, the non-negative factorizations of these two interval matrices are carried out and parameter vertex theory is finally employed to obtain the upper and lower bounds of the eigenvalues. The feasibility of the applied algorithm is verified through comparison with the scanning method. Numerical results show that the uncertainty of shaft misalignment will enormously widen the system's resonance bandwidth and intensify oscillation, these will provide a new and valuable perspective for the tolerance allocation in gearbox design.