Effects Of Uncertain Parameters Research Articles

An attention-based deep learning method for safety of uncertain vehicle-bridge system with random near fault earthquakes

In this paper, a novel approach, based on the principle of the deep learning method, is proposed to study the stochastic responses of vehicle-bridge system (VBS) subjected to near fault earthquakes (NFEs), which also considers the effects of uncertain parameters. To generate the training data as the input of the proposed deep learning model, the dynamic formulas of the VBS are deduced by Newmark-β method. The proposed analysis model comprises three modules: the CNN module for seismic data feature extraction, the Attention Mechanism module for enhancing the selection for information between time series to improve the accuracy and efficiency of the final prediction, and the Bidirectional Gated Recurrent Unit (BiGRU) for predicting VBS responses. The mapping connection between earthquake action and the system response is established. The BiGRU model is capable of conveying both the excitation's randomness and the system's uncertain parameters. An actual railway cable-stayed bridge subjected to the running railway vehicle and NFEs is utilized to verify the proposed model. The uncertain train weight, bridge damping ratio and the randomness of NFEs are incorporated into the dynamic responses analysis of VBS. As a result, the time-varying responses obtained by the proposed model show significant agreement with results from a validated dynamic VBS framework. The mean value and standard deviation (STD) of the responses obtained by the proposed method are also compared with those by the Monte Carlo method and probability density evolution method. Therefore, both the individual sample of the dynamic response and the statistical data from diverse stochastic responses are chosen to validate the model's accuracy and efficiency in the VBS analysis under NFEs. In addition, the effects of the stochastic characteristics on the system's random vibrations are also explored through the time-histories of statistical data and the probability density function of the absolute maximum of responses.

Optimal design of pressure swing adsorption units for hydrogen recovery under uncertainty

Abstract The paper proposes an approach to the optimal design of pressure swing adsorption (PSA) units for hydrogen recovery under uncertainty, which provides a reasonable margin of the potential resource of the PSA hydrogen unit and compensates for the negative impact of a random change in uncertain parameters within specified limits. A heuristic iterative algorithm is proposed to solve the design problem with a profit criterion, which is guaranteed to provide the technological requirements for the PSA unit, regardless of the values that take uncertain parameters from the specified intervals of their possible change. An experimental verification of the approach with the root-mean-square error of 19.43 % has been carried out. Optimization problems of searching for a combination of mode and design parameters under uncertainty for a range of 4-bed 4-step VPSA units with a capacity of 100–2000 L/min STP have been solved taking into account the requirements for hydrogen purity of 99.99+ %, gas inlet velocity of 0.2 m/s, and bed pressure drop (no more than 1 atm). It has been established that taking into account uncertainties leads to an increase in energy costs by 8–10 %, a decrease in profit by 10–15 %, and a decrease in hydrogen recovery by 4–5 %, which is a payment for the uninterrupted operation of the PSA unit. The effect of uncertain parameters (percentage composition of the gas mixture; gas temperature; the diameter of adsorbent particles) on the key indicators of the PSA process (recovery, profit, hydrogen purity, unit capacity) has been established and trends in adsorption duration, adsorption and desorption pressure, P/F ratio, valve capacity, bed length, adsorber diameter for design of hydrogen PSA unit, which are necessary for subsequent design and scaling of units.

Hydraulic and Water Quality Reliability of Water Distribution System under Uncertain Conditions

Reliability assessment plays a significant role in the planning, design, and operation of water distribution systems (WDS). Herein, pressure, flow, chlorine concentration, and water age are simulated by continuity, energy, and transport equations; and hydraulic, water quality, and system reliability assessments are proposed based on a comparison between simulated hydraulic and water quality conditions and the desired service level. Because the independent parameters in hydraulic and water quality simulations cannot be estimated accurately, a hydraulic and water quality reliability assessment based on Monte Carlo simulation was applied to a network under three uncertain levels under steady- and unsteady-states. The effects of uncertain parameters on hydraulic and water quality reliability under steady- and unsteady-states were evaluated and compared to obtain the most significant parameters. The results indicated that the mean hydraulic reliability decreases with an increase in the uncertainty level for various nodes under steady- and unsteady-states, while the regulation is not suitable for water quality reliability. Pipe diameters have the most significant effects on hydraulic reliability under steady-state conditions, and mean hydraulic reliability under unsteady-state conditions. Nodal demand, bulk decay coefficient, and wall decay coefficient have effects on water quality reliability under steady-state conditions, while the roughness coefficient and pipe diameter also have effects on mean water quality reliability under unsteady-state condition. The results obtained can give managers more information about network reliability under uncertain conditions.

A Two-stage Inexact Programming with Value-at-risk under Uncertainty

Abstract Measuring risks for two-stage programming model has certain theoretical and actual significance. Therefore, a model of two-stage inexact programming with value-at-risk (TIPV) has been developed. The highlights of TIPV are (1) it can reflect the effects of uncertain parameters including random variables and intervals of fuzzy boundary; and (2) the potential risks of recourse can be revealed. A solution algorithm is developed through considering uncertainties, two-stage and VaR comprehensively.

Dynamic Optimisation of Beer Fermentation under Parametric Uncertainty

Fermentation is one of the most important stages in the entire brewing process. In fermentation, the sugars are converted by the brewing yeast into alcohol, carbon dioxide, and a variety of by-products which affect the flavour of the beer. Fermentation temperature profile plays an essential role in the progression of fermentation and heavily influences the flavour. In this paper, the fermentation temperature profile is optimised. As every process model contains experimentally determined parameters, uncertainty on these parameters is unavoidable. This paper presents approaches to consider the effect of uncertain parameters in optimisation. Three methods for uncertainty propagation (linearisation, sigma points, and polynomial chaos expansion) are used to determine the influence of parametric uncertainty on the process model. Using these methods, an optimisation formulation considering parametric uncertainty is presented. It is shown that for the non-linear beer fermentation model, the linearisation approach performed worst amongst the three methods, while second-order polynomial chaos worked the best. Using the techniques described below, a fermentation process can be optimised for ensuring high alcohol content or low fermentation time while ensuring the quality constraints. As we explicitly consider uncertainty in the process, the solution, even though conservative, will be more robust to parametric uncertainties in the model.

Seismic time-history response and system reliability analysis of slopes considering uncertainty of multi-parameters and earthquake excitations

In practical geotechnical engineering of slopes, it is well-known that the uncertainty of soil properties and ground motions need to be considered for the safety of the project. The effect of uncertain parameters and stochastic ground motions on seismic responses as well as dynamic failure probabilities of slopes are analyzed and discussed in this study. A recently proposed generalized probability density evolution method (GPDEM) is formulated to investigate the system reliability of complex slopes with consideration to uncertainty in multiple slope parameters and in ground motions. Firstly, the fundamental theory of dynamic stability, GPDEM, dynamic system reliability, generation of random samples and stochastic ground motion model are described. Then, the efficiency and accuracy of proposed GPDEM are verified and a novel evaluating index is presented. Four complex slopes, each with multi-parameter uncertainties, are examined in separate study cases. Each study case uses GPDEM to study the random dynamic responses as well as probability responses of slopes while considering deterministic ground motion. The efficiency and accuracy of GPDEM used in complex slopes are validated by comparing with the Monte Carlo method (MCM). In addition, a novel evaluating index called the average large failure probability Pff, is proposed to describe the failure probability of the slopes, and can take the probability time histories intoaccount. Finally, the seismic system reliability of complex slopes is evaluated using the time-history method, and randomness in earthquakes, parameters and their coupling are investigated. The stochastic dynamic responses and probability responses of deterministic parameters subjected to stochastic earthquake excitations, and random parameters subjected to stochastic earthquake excitations are also discussed and are compared based on study case 3. The results demonstrate the high accuracy and validity of the GPDEM. Furthermore, the probability of failure and the degree of safety for the slopes can be directly estimated through probability analysis. In addition, the results also indicate that randomness in ground motions have a much larger influence than randomness in slope parameters, but randomness in slope parameters cannot be completely neglected.

Probability analysis of bistable composite laminates using the subset simulation method

Bistable composite laminates are advanced composite structures which are potential candidates for morphing structure applications. The geometrical dimensions, material properties, ambient temperature and moisture have significant effects on the bistable behaviour, and the effect of uncertain parameters should be quantified. Reliability analysis is well established for the quantitative assessment of the probability of an event due to parameter uncertainty. Thus, subset simulation is applied to the reliability and sensitivity analysis of bistable composite plates with multiple random parameters. The bistability probability is estimated using the principle of minimum energy; the Rayleigh-Ritz method is used to develop the equations of motion and the limit state function. The results indicate that the stacking sequence has a large effect on bistability probability, and cross-ply composite laminates are most likely to be bistable. Moreover, moisture absorption by the laminate can dramatically reduce this probability. The sensitivity reliability analysis demonstrates that for bistable laminates subject to humidity, the coefficient of thermal and moisture expansions have the greatest influence on the bistability probability. However, for bistable laminates without moisture the thickness is the most important factor. The accuracy and efficiency of the subset simulation method is validated by Monte Carlo simulation.

Sliding mode synchronization between uncertain Watts-Strogatz small-world spatiotemporal networks

Based on the topological characteristics of small-world networks, a nonlinear sliding mode controller is designed to minimize the effects of internal parameter uncertainties. To qualify the effects of uncertain parameters in the response networks, some effective recognition rates are designed so as to achieve a steady value in the extremely fast simulation time period. Meanwhile, the Fisher-Kolmogorov and Burgers spatiotemporal chaotic systems are selected as the network nodes for constructing a drive and a response network, respectively. The simulation results confirm that the developed sliding mode could realize the effective synchronization problem between the spatiotemporal networks, and the outer synchronization is still achieved timely even when the connection probability of the small-world networks changes.

Effects of random interval parameters on spur gear vibration

Gear driving devices are commonly used in mechanical transmission systems. Due to the inevitable random errors in manufacturing, installation, and operation, the dynamics of a gear transmission system will fluctuate randomly. To reveal the dynamic characteristics, an interval parameters dynamic model of a single-stage spur gear pair is established, in which the uncertainties of displacement excitation, load excitation, and stiffness excitation are included, and their formulations are derived in detail by using interval mathematics. The established interval parameters dynamic model is solved by combining the Chebyshev inclusion function method and the Runge–Kutta method. Finally, the influence of the random interval parameters of meshing stiffness, input torque, and transmission error as well as backlash on the vibration velocity interval and transmission reliability of the gear transmission system are studied. The analysis results show that the three types of excitations have different effects on the dynamic characteristics. To be specific, the effects of uncertain parameters on the dynamic characteristics can be ordered as meshing stiffness, input torque, backlash, and transmission error in sequence from the strongest to the weakest. The present study may serve as a sound theoretical basis and can provide references for the design and vibration control of spur gear transmission systems.

Comprehensive sensitivity analysis of rotational stability of a super-deep underground spherical structure considering uncertainty

Jiangmen Underground Neutrino Observatory central detector is located 700 m below the ground and also submerged into an ultrapure water pool. The main structure of the Jiangmen Underground Neutrino Observatory central detector is a hybrid spherical shell that is vulnerable to rotation under the buoyancy effect. The influences of the model parameters on the rotational stability of this complex and unique structure are investigated. Since the model parameters are inevitably subjected to many sources of uncertainties (e.g. manufacturing tolerances and geometrical imperfections), the parameter uncertainty is taken into account. In addition, linear and nonlinear rotational stabilities of this super-deep underground spherical structure are also under consideration. Specifically, the critical loading multiplier is used as the evaluation indicator of linear rotational stability and the load proportionality factor- θ curve is considered as the evaluation indicator of nonlinear rotational stability. The sensitivity of linear and nonlinear rotational stabilities to uncertain parameters is systematically studied in terms of univariate and multivariate global sensitivity analyses. The univariate global sensitivity analysis is able to evaluate the effects of uncertain parameters on each evaluation indicator, whereas multivariate global sensitivity analysis enables to assess the global influence of uncertain parameters on all evaluation indicators. A polynomial chaos expansion surrogate model is utilized to replace the time-consuming simulation model for analytical implementation of the univariate and multivariate global sensitivity analyses. The present polynomial chaos expansion-based univariate and multivariate global sensitivity analyses effectively and efficiently reveal the sensitivity of the rotational stability of this super-deep underground spherical structure to uncertain parameters, and provide a practical method for comprehensive sensitivity analysis of similar structures.

Interval Analysis of the Eigenvalues of Closed-Loop Control Systems with Uncertain Parameters

Uncertainty caused by a parameter measurement error or a model error causes difficulties for the implementation of the control method. Experts can divide the uncertain system into a definite part and an uncertain part and solve each part using various methods. Two uncertainty problems of the control system arise: problem A for the definite part—how does one find out the optimal number and position of actuators when the actuating force of an actuator is smaller than the control force? Problem B for the uncertain part—how does one evaluate the effect of uncertainty on the eigenvalues of a closed-loop control system? This paper utilizes an interval to express the uncertain parameters and converts the control system into a definite part and an uncertain part using interval theory. The interval state matrix is constructed by physical parameters of the system for the definite part of the control system. For Problem A, the paper finds out the singular value element sensitivity of the modal control matrix and reorders the optimal location of the actuators. Then, the paper calculates the state feedback gain matrix for a single actuator using the receptance method of pole assignment and optimizes the number and position of the actuators using the recursive design method. For Problem B, which concerns the robustness of closed-loop systems, the paper obtains the effects of uncertain parameters on the real and imaginary parts of the eigenvalues of a closed-loop system using the matrix perturbation theory and interval expansion theory. Finally, a numerical example illustrates the recursive design method to optimize the number and location of actuators and it also shows that the change rate of eigenvalues increases with the increase in uncertainty.

On the practical stability with respect to [formula omitted]-manifolds of hybrid Kolmogorov systems with variable impulsive perturbations

The present paper is devoted to the problems of practical stability with respect to h-manifolds for impulsive Kolmogorov systems. Variable impulsive perturbations are considered. We will investigate these problems in the light of the vector Lyapunov’s method of piecewise continuous functions. As an example, the case of Lotka–Volterra systems is elaborated. The effect of uncertain parameters on the stability behavior of the model is also examined. The obtained results extend and complement the existing stability results for Kolmogorov and related systems.

A fuzzy-budgeted robust optimization model for joint network design-pricing problem in a forward−reverse supply chain: the viewpoint of third-party logistics

The increasing opportunities for cost savings and customer satisfaction have propelled third-party logistics providers (3PLs) to get involved in the forward and reverse logistics operations. The forward−reverse supply chain network design (FRSCND) for 3PLs have been somehow studied under various conditions, so far. However, some very common business configurations and real-world concerns such as pricing and uncertainty are less investigated in the literature. Accordingly, this paper proposes a novel robust model for the design of a 3PL’s logistics network and pricing decisions. Since the value of uncertainty budget parameter in the robust model is an epistemic uncertain one, the fuzzy-robust model regarding the uncertainty budget parameter as a fuzzy number is also developed. The results of numerical examples show that the proposed models outperform the deterministic model regarding solution robustness and computational time. Considering the robust sensitivity analysis, the effects of uncertain parameters on total cost, based on their conservatism levels are analyzed. In addition, the conducted sensitivity analysis over penalty values for constraints violation reveal that for the medium- and large-size problems, the proposed models are more cost-effective for high penalty values, while the models’ performance is related to the problem size, for their low amounts.

Adaptive Sliding Mode Control of Vehicular Platoons With Prescribed Tracking Performance

This paper investigates a vehicular platoon control problem with prescribed tracking performance in the presence of actuator saturation, uncertain parameters, and unknown disturbances. Two adaptive sliding mode control schemes based on leader–predecessor and leader–bidirectional information flows are presented to ensure string stability and strong string stability, respectively, with a prescribed tracking performance. The actuator saturation nonlinearity is addressed by approximating it with a smooth hyperbolic tangent function. The effects of uncertain parameters and exogenous disturbances are dealt with by introducing a set of adaptation laws. The effectiveness of the proposed control schemes is demonstrated via numerical simulation results.

Surrogate modelling to enable structural assessment of collision between vertical concrete dry casks

Vertical concrete dry casks, used for interim storage of spent nuclear fuel, are susceptible to large horizontal displacements caused by lateral loads. This study explores the collision between adjacent casks in the case of such large motions. To estimate an upper bound for the probability of failure, a common collision scenario that causes severe structural damage is determined through a comparative deterministic analysis. Then the effects of uncertain parameters on the cask’s performance in the specific collision scenario are studied with a probabilistic approach. Numerical simulations are conducted for 200 realisations of the collision problem to evaluate the canister maximum strain and the overpack accelerations. Then surrogate models, such as polynomial response surface models, multivariate adaptive regression splines, regression trees, and support vector machines, are trained on the response data to derive efficient approximating functions for these responses. Utilising the best developed surrogate models, fragility and the failure probability given collision are estimated. The findings show that the structural integrity of the dry cask is generally maintained in case of the collision. That is, the canister might yield due to the impact loads, but the probability of the canister fracture is negligible for the cask and parameter space considered here.

Stochastic Vibration Analyses of Laminated Composite Plates via a Statistical Moments-Based Methodology

In the present study, stochastic vibration analyses of a symmetrically laminated composite plate having uncertain input parameters are performed via a probabilistic methodology. Here, uncertain input parameters are selected as plate thickness, specific volume (inverse of density) and structural damping. These parameters are modeled statistically as a normal distribution. The methodology carries out the closed form solution of stochastic partial differential equation governing a structural vibration by discrete singular convolution (DSC) method in terms of its first two statistical moments: mean and standard deviation. The effects of uncertain parameters (combined in six different cases) on modal and vibration displacement response due to a harmonic excitation force are investigated. In this manner, firstly, mean and standard deviation of natural frequencies of the composite plate are obtained by solving its partial differential equation using discrete singular convolution method. After that, statistics of vibration frequency response are obtained by predicted natural frequencies’ statistics. Monte Carlo simulations are also performed to test the proposed methodology. It is shown that the methodology is more reliable in higher frequencies where the uncertainty is much more considerable. Besides, the computation time is very efficient when comparing with Monte Carlo simulations.

Sliding Window Filtering for Ground Moving Targets with Cross-Correlated Sensor Noises

This paper reports a sliding window filtering approach for ground moving targets with cross-correlated sensor noise and uncertainty. In addition, the effect of uncertain parameters during a tracking error on the model performance is considered. A distributed fusion sliding window filter is also proposed. The distributed fusion filtering algorithm represents the optimal linear combination of local filters under the minimum mean-square error criterion. The derivation of the error cross-covariances between the local sliding window filters is the key to the proposed method. Simulation results of the motion of the ground moving target a demonstrate high accuracy and computational efficiency of the distributed fusion sliding window filter.

Evaluating the Use of Global Sensitivity Analysis in Dynamic MFA

SummaryDynamic material flow analysis (MFA) provides information about material usage over time and consequent changes in material stocks and flows. In order to understand the effect of limited data quality and model assumptions on MFA results, the use of sensitivity analysis methods in dynamic MFA studies has been on the increase. So far, sensitivity analysis in dynamic MFA has been conducted by means of a one‐at‐a‐time method, which tests parameter perturbations individually and observes the outcomes on output. In contrast to that, variance‐based global sensitivity analysis decomposes the variance of the model output into fractions caused by the uncertainty or variability of input parameters. The present study investigates interaction and time‐delay effects of uncertain parameters on the output of an archetypal input‐driven dynamic material flow model using variance‐based global sensitivity analysis. The results show that determining the main (first‐order) effects of parameter variations is often sufficient in dynamic MFA because substantial effects attributed to the simultaneous variation of several parameters (higher‐order effects) do not appear for classical setups of dynamic material flow models. For models with time‐varying parameters, time‐delay effects of parameter variation on model outputs need to be considered, potentially boosting the computational cost of global sensitivity analysis. Finally, the implications of exploring the sensitivities of model outputs with respect to parameter variations in the archetypical model are used to derive model‐ and goal‐specific recommendations on choosing appropriate sensitivity analysis methods in dynamic MFA.

Factorial-Based Inexact Stochastic Fuzzy Chance Constraint Programming Framework for Municipal Solid Waste Management with GHG Emission Trading: Analysis of Multilevel Parametric Interactions

This study proposes a factorial inexact stochastic fuzzy chance constraint programming framework for dealing with uncertainties in municipal solid waste management under consideration of greenhouse gas (GHG) emission trading. It can reflect uncertainties expressed as fuzzy, interval, and random variables and generate desired management strategies for minimizing the integrated cost for solid waste disposal and purchasing GHG emission credit. Moreover, multilevel factorial analysis is conducted to reveal the main and interactive effects of uncertain parameters. The results show that effective waste allocation schemes can be obtained to meet the waste disposal demands and GHG emission requirements under different α-cut levels. The changes in the fuzzy confidence level have impacts on the waste allocation schemes, especially for the waste flow to the incinerator. The disposal cost differs across the three levels of 0.3, 0.5, and 0.7 for incinerator capacity constraint when the fuzzy confidence level of composting capacity constraint is equal to 0.5, implying the existence of the interaction between uncertainties in the incinerator and composting facility. Comparison between the waste management practices with and without considering GHG emission requirements indicates that the purchase of GHG emission credits would contribute about 10 % to the total cost, which would not be influenced significantly by the α-cut level.

Unraveling Optimal Biomass Processing Routes from Bioconversion Product and Process Networks under Uncertainty: An Adaptive Robust Optimization Approach

A bioconversion product and process network converts different types of biomass to various fuels and chemicals via a plethora of technologies. Reliable bioconversion processing pathways should be designed considering the effect of uncertain parameters, such as biomass feedstock price and biofuel product demand. Given a large-scale bioconversion product and process network of 194 technologies and 139 materials/compounds, we propose a two-stage adaptive robust mixed-integer nonlinear programming problem. The model allows for decisions at the design and operational stages to be made sequentially and considers budgets of uncertainty to control the level of robustness. Nonlinearity in this model appears in the first-stage objective function, and the second-stage problem is a linear program. We efficiently solve the proposed problem with a tailored algorithm. The robust optimal solutions corresponding to various uncertainty budgets show that the minimum total annualized cost is more sensitive to biofuel demand ...