Variation Of Uncertain Parameters Research Articles

Experimental evaluation of the backstepping‐based input resistance controller in step‐up DC–DC converter for maximum power point tracking of the thermoelectric generators

AbstractIn this paper, a novel non‐linear model‐based approach is presented for maximum power point (MPP) tracking of thermoelectric generators (TEGs) using the backstepping controller. Considering the output voltage range of the thermoelectric devices, a step‐up DC–DC converter is employed as an interface between the load and input power source. According to the maximum power transfer theorem, if the equivalent input resistance of the converter (Rin) is equal to the internal resistance of the input source (RTEG), the TEG operation at the MPP will be achieved. Hence, defining the RTEG as a reference value and Rin as a feedback variable for a closed‐loop controller, the backstepping non‐linear controller is developed for input resistance control of the boost DC–DC converter. Owing to the non‐linear nature of the error variable in the input resistance control of the converters, conventional linear controllers cannot guarantee the system's closed‐loop stability within an extensive operational range. However, despite changes in generator's open‐circuit voltage (VOC) and RTEG, the designed closed‐loop controller can successfully stabilize the thermoelectric converter in different operational conditions. Considering the Lyapunov theorem and the Barbalat lemma, the asymptotic stability of the backstepping controller is proved. During the steady‐state operation, the actual values of the VOC and RTEG are updated periodically by the measurement of the converter input voltage/current values. To verify the functionality of the designed control method, PC‐based simulations are carried out in MATLAB/Simulink software. Moreover, by using TMS320F28335 digital signal processor from Texas Instruments and a simple thermoelectric simulator, the experimental response of the proposed controller is evaluated in dynamic and steady‐state conditions. The developed closed‐loop system can track the MPP of a TEG with zero steady‐state error, regardless of uncertain parameter variations.

Assessing the social cost of municipal solid waste management in Beijing: A systematic life cycle analysis

The increased municipal solid waste generation poses ponderous pressure on the economy, environment, and public health. The current waste treatment process has multiple limitations. To inform policymakers on the best practices and feasibility, we develop a more comprehensive social costing model to assess the impacts of municipal solid waste management throughout its life cycle. The prominent findings show that the life cycle social cost of municipal solid waste in Beijing in 2021 is 12.4 billion yuan. Incineration has the highest social cost, totaling 10.172 billion yuan. The social cost per unit of waste incineration is 2,045 yuan/t, which is higher than that of landfill (1,288 yuan/t), composting (1,132 yuan/t), anaerobic digestion (1,057 yuan/t), and recyclables resource utilization (-344 yuan/t). The life cycle assessment results show that economic costs, including collection, transportation, and treatment costs, account for about 61%, and health loss costs account for about 37%. The scenario analysis suggests a significant potential for social cost savings from food waste and recyclables utilization. Ideally, a social cost reduction of almost 38% could be achieved. Error analysis examines the influence of variation in uncertain parameters on the evaluation results. This paper provides scientific strategies for optimal investment and decision-making on the comprehensive municipal solid waste management. These findings could provide an essential reference for policymakers and stakeholders in municipal solid waste management, replicated in different cities and other emerging economies.

A natural logarithm sliding mode controller for stochastic time-delay systems

This paper presents a new method for sliding mode control to create a compromise between duration of reaching phase and response rate of the stochastic time-delay systems. A natural logarithm sliding surface is first constructed and then, the asymptotic stability with probability one for the closed-loop system has been analyzed by Lyapunov method. Some practical considerations are uncertain parameter variations, environmental matched disturbances, actuator degradation, stochastic environmental mismatched disturbances, and unmodeled dynamics. Finally, the simulation results show how to adjust the response rate and the sensitivity of the closed-loop system to the variations by regulating a special parameter.

A logarithmic sliding mode controller for stochastic active suspension systems

In this paper, a new approach for stochastic logarithmic variable structure control has been proposed to create a compromise between reaching phase duration and response rate of the stochastic suspension system. The asymptotic stability with probability one for the closed-loop suspension system has been analyzed by Lyapunov method. Some practical considerations in proving theorems are uncertain parameter variations, environmental matched disturbances, actuator degradation, stochastic environmental mismatched disturbances, which is a representative of the change in road profile with time, and unmodeled dynamics. Finally, by regulating a specific parameter, the simulation results corroborate the advantage of the proposed controller in managing and reducing the sensitivity of the closed-loop system. Also, compared with other sliding surfaces of past researches, the designed sliding variable minimizes a certain performance function and therefore provides better performance for the closed-loop system, which is also verified in the simulation results.

Epistemic uncertainty in URANS based CFD analysis of buoyancy driven flows—Comparison of URANS and LES

The containment is the last barrier to prevent the release of radioactive materials into the environment in case of a severe reactor accident. Thus, it is important to understand the flow and transport processes of combustible gases and to develop strategies to maintain the integrity of the containment. A holistic OpenFOAM-based CFD software package, containmentFOAM, is developed for containment analysis. During the validation of the code with regard to free convection flows and mixing processes, it became apparent that the simulation results are fairly sensitive to the definition of initial and boundary conditions, which are often not precisely known from the experiment. Therefore, establishing the validity of the models is impossible without a quantification of uncertainties.Generally, the uncertainty is categorized in two types, namely aleatoric and epistemic uncertainties. The first exhibits stochastic variations around the exact value. The latter has two possible effects on the uncertainty quantification: first a different sensitivity of the model to the input variation and second a bias to the exact value. Both effects can affect the significance of an aleatoric uncertainty quantification. The epistemic uncertainty originating from URANS turbulence modelling is investigated in this study by means of a direct comparison with the results obtained by LES, assuming that LES turbulence closures have smaller epistemic uncertainty. For a buoyancy driven natural circulation flow as well as a superimposed mixing process, both epistemic effects of the URANS approach are identified in terms of different sensitivities with respect to a variation of uncertain input parameters and the deviations of the URANS output variation ranges to those of LES. Nevertheless, the analysis of uncertainty bands derived on the basis of the most relevant parameter revealed that these epistemic effects ultimately result in a negligible effect on the aleatoric uncertainty quantification conducted with URANS.

A surrogate model-assisted robustness-oriented tolerance design method based on ‘reverse model’

The uncertainties of parameters are inevitable in practical engineering problems, which may cause unexpected variations of objectives and constraints. Tolerance design methods can specify the allowable variation of uncertain parameters, thereby maintaining product quality while achieving lower manufacturing cost. In this paper, a novel tolerance design method is proposed, in which the ‘reverse model’ is used to directly analyse the robustness of the preexisting alternatives and the Kriging model is introduced to reduce computational cost. Firstly, the sensitivity region is generated by the ‘reverse model’ that maps the given acceptable objective and feasibility variations into the parameter space to analyse the robustness. Secondly, interval uncertainty is introduced to describe tolerance within the sensitive region. Thirdly, a nested double-loop structure is adopted to implement the search process. Two numerical examples and one engineering case are used to illustrate the effectiveness of the proposed method. Verification of robustness for the obtained interval is performed by Monte Carlo Method, and the worst-case analysis is applied to verify whether the tolerance is the maximum interval. The obtained maximum tolerance that meets the performance requirements reflects the trade-off between quality and manufacturing cost.

A Robust Bi-objective Optimization Model for Resource Levelling Project Scheduling Problem with Discounted Cash Flows

Due to limited financial resources and high costs of infrastructure projects, project stakeholders seek to gain maximum profits with optimal resource utilization as well as cost and time minimization. Therefore, this study presents a multi-mode resource-constrained project scheduling model considering the uncertain parameters of cost and time together with the goals of maximizing the net present value and minimizing resource usage fluctuation. Also, the assumptions related to the real-world projects regarding multi-mode activities, limitation of renewable resources, and the deadline of project are incorporated into the proposed model. Moreover, a robust scheduling method is presented to better deal with the inherent uncertainties of projects regarding cost and time. The model is solved with the exact method named lexicographic goal programming (LGP). Due to the NP-hardness of the problem, two metaheuristic algorithms named Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO) are applied to solve various medium and large size problems. The obtained results indicate the high efficiency of the two metaheuristic algorithms in solving the problem and the better performance of the MOPSO algorithm compared with NSGA-II in terms of five indices. Furthermore, the model is implemented in an offshore equipment installation phase of a wellhead platform project. Finally, the sensitivity analysis of the proposed robust model is performed considering different conservation levels, and the results are evaluated by Monte Carlo simulation with three normal, uniform and triangular distributions. The findings demonstrate that the robustness of the model against the variations of uncertain parameters.

Spatial zoning to conserve fish species with complex life cycles in estuaries

Fish conservation in estuaries is complex because there are diverse social values and interests associated with estuarine ecosystems and multiple ecological processes (e.g., nursery, connectivity, and population dynamics). Furthermore, ontogenetic shift has an important role in determining fish habitat use (e.g. pelagic vs benthic environments), and consequently, critical implications for conservation. Here, we develop a prioritisation approach to create conservation zones in an estuarine system that considers fishery costs while also integrating pelagic and benthic habitats for different life history stages (from eggs to adults), and multiple conservation objectives. We applied our approach to the whitemouth croaker Micropogonias furnieri in the Patos Lagoon estuary (Brazil) and tested four scenarios based on different objectives, zone types and targets. In this study, we used Marxan and Marxan with Zones and accounted for 41 conservation features (including habitat type, vegetation and seasonal distribution of whitemouth croaker within the estuary). Overall, we found two important results. First, spatial priorities for the no-take and partially protected zones did not change substantially and were very robust to variation in uncertain parameters. Second, an integrated conservation plan with multiple zones requires less area to be designated as no-take zone than a traditional conservation plan with a single zone. A well-designed conservation plan based on multiple life stages may help to ensure the recruitment, persistence and management of important estuarine resources.

LMI-Based State Feedback Control Structure for Resolving Grid Connectivity Issues in DFIG-Based WT Systems

Pertaining to the connectivity issues in wind power plants with grids, this study introduces an efficient mechanism based on a state feedback control structure to establish a fast and stable grid connection for a wind-driven doubly-fed induction generator (DFIG). Owing to a direct link through stator windings, a DFIG is significantly vulnerable to grid disturbances and experiences sizable inrush currents when connected to the power grid. The proposed control structure is designed based on a linear matrix inequality stabilization criterion, which is framed using a suitable Lyapunov candidate function. The control objective is to ensure that the stator voltage can exponentially converge to the grid voltage, accounting for balanced and unbalanced grid conditions. This is achieved by generating appropriate rotor voltage references for rotor-side converter control. This study also explores the capability of the proposed control structure to enhance the system’s robustness to external disturbances and uncertain parametric variations. Simulations confirmed the effectiveness and suitability of the developed structure in mitigating the adverse effects of the rapid onset of the grid voltage at the stator terminals of the DFIG under various grid conditions; the proposed structure could thus establish a reliable connection with negligible effects on the DFIG and the grid.

Double stage controller optimization for load frequency stabilization in hybrid wind-ocean wave energy based maritime microgrid system

The momentum towards reduction of greenhouse gas emissions by reduced use of conventional source in marine power networks as well as significant development of renewable energy resources (RRs) have been the motivating factors for inclusion RRs in hybrid maritime microgrid system (HMμGS) and investigation of consequent frequent control mechanism. This article presents an approach of load frequency control in an independent HMμGS consisting of wind driven generation (WDG), Archimedes wave power generation (AWPG), marine biodiesel generator (MBG), solid-oxide fuel cell (SOFC) energy units, heat pump (HP) and freezer (FZR). The stability of the HMμGS model have been evaluated through the rigorous tests considering non-availability of renewable resources, concurrent random generation of AWPG, load demand, real recorded data of WDG. Comparative performance of several controllers such as PID, PID with filter (PIDN) and PI-(1 + PD) controller are presented with their parameters optimized using genetic algorithmic technique (GA), particle swarm technique (PSO), firefly algorithmic technique (FA), cultural algorithmic technique (CA) and the recent metaheuristic grasshopper algorithmic technique (GOA). The proposed frequency control strategy of HMμGS model is benchmarked by comparative statistical assessment and decision indicators. Finally, sensitivity assessment of GOA tuned PI-(1 + PD) controller under uncertain parametric variations such as; variation of WDG gain, droop factor (R), inertia constant (M) and loading without reoptimizing the optimal base condition values is conducted as an evidence of the sturdiness of the proposed frequency control strategy. The analysis of the results shows that the proposed GOA optimized PI-(1 + PD) control strategy perform much better than other control schemes.

Data-consistent inversion for stochastic input-to-output maps**The views expressed in the article do not necessarily represent the views of the U.S. Department of Energy or the United States Government. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of

Data-consistent inversion is a recently developed measure-theoretic framework for solving a stochastic inverse problem involving models of physical systems. The goal is to construct a probability measure on model inputs (i.e., parameters of interest) whose associated push-forward measure matches (i.e., is consistent with) a probability measure on the observable outputs of the model (i.e., quantities of interest). Previous implementations required the map from parameters of interest to quantities of interest to be deterministic. This work generalizes this framework for maps that are stochastic, i.e., contain uncertainties and variation not explainable by variations in uncertain parameters of interest. Generalizations of previous theorems of existence, uniqueness, and stability of the data-consistent solution are provided while new theoretical results address the stability of marginals on parameters of interest. A notable aspect of the algorithmic generalization is the ability to query the solution to generate independent identically distributed samples of the parameters of interest without requiring knowledge of the so-called stochastic parameters. This work therefore extends the applicability of the data-consistent inversion framework to a much wider class of problems. This includes those based on purely experimental and field data where only a subset of conditions are either controllable or can be documented between experiments while the underlying physics, measurement errors, and any additional covariates are either uncertain or not accounted for by the researcher. Numerical examples demonstrate application of this approach to systems with stochastic sources of uncertainties embedded within the modeling of a system and a numerical diagnostic is summarized that is useful for determining if a key assumption is verified among competing choices of stochastic maps.

Multiobjective robust shape and topology optimization of plane frames using order statistics

This paper presents a worst-case approach to robust optimization of plane frame structures under variation in uncertain parameters. The optimization procedure is first implemented without considering uncertainty, resulting in an optimal structure that may be unstable without bending stiffness. Based on such optimal solution, we then take variation in uncertain parameters into consideration and estimate the quantile response or trimmed mean of order statistics, where the quantile response is used as a relaxation of worst value of structural response. In order to obtain robust optimal solutions at various robustness levels, a multiobjective optimization problem is formulated and solved to simultaneously minimize the several order statistics or trimmed means with different orders. It is demonstrated in the numerical examples that the optimal distribution of cross-sectional areas of elements vary with the change of robustness level, and the convergence by using trimmed mean as estimation of quantile response is better than that of the simple order statistics.

Predicting stochastic characteristics of generalized eigenvalues via a novel sensitivity-based probability density evolution method

This paper proposes a novel numerical method for predicting the probability density function of generalized eigenvalues in the mechanical vibration system with consideration of uncertainties in structural parameters. The eigenproblem of structural vibration is presented by first and the sensitivity of generalized eigenvalues with respect to structural parameters can be derived. The probability density evolution method is then developed to capture the probability density function of generalized eigenvalues considering uncertain material properties. Within the proposed method, the probability density evolution equation for the generalized eigenvalue problem is established accounting for the sensitivity of generalized eigenvalues with respect to structural parameters. A new variable which connects generalized eigenvalues to structural parameters is then introduced to simplify the original probability density evolution equation. Next, the simplified probability density evolution equation is solved by using the finite difference method with total variation diminishing schemes. Finally, the probability density function as well as the second-order statistical quantities of generalized eigenvalues can be predicted. Numerical examples demonstrate that the proposed method yields results consistent with Monte-Carlo simulation method within significantly less computation time and the coefficients of variation of uncertain parameters as well as the total number of them have remarkable effects on stochastic characteristics of generalized eigenvalues.

Nested High Order Sliding Mode Controller with Back-EMF Sliding Mode Observer for a Brushless Direct Current Motor

This work presents a nested super-twisting second-order sliding mode speed controller for a brushless direct current motor with a high order sliding mode observer used for back electromotive force (back-EMF) estimation. Due to the trapezoidal nature of the back-EMF, a modified Park transformation is used in order to achieve proper field orientation. Such transformation requires information from the back-EMF that is not accessible. A second-order sliding mode observer is used to estimate the back electromotive forces needed in the modified transformation. Sliding mode control is known to be robust to matched uncertain disturbances and parametric variations but it is prone to unmatched perturbations that affect the performance of the system. A nested scheme is used to improve the response of the controller in presence of unmatched disturbances. Simulations performed under similar conditions to real-time experimentation show a good regulation of the rotor speed in terms of transient and steady-state responses along with a reduced torque ripple.

Robust Geotechnical Design for Soil Slopes considering Uncertain Parameters

Designing the geometry of soil slope is an effective treatment for preventing slope failure. How to deal with the uncertainties involved in soil parameters in geotechnical design is a main concern of geotechnical engineers. In this study, a robust geotechnical design for soil slopes (RGDS) approach was proposed, in which the Uncertainty Theory was introduced to describe explicitly the uncertainties involved in soil parameters. The uncertain reliability is often used to describe the risk of slope failure. The design robustness describing the insensitivity between the variation in the system response and the variation of input uncertain soil parameters was evaluated by the signal-to-noise ratio. The objectives of this design are to maximize the design robustness, minimize the excavation cost, and guarantee the safety (maximize the uncertain reliability). Therefore, the RGDS was formulated as a multiobjective optimization, and the optimal design can be determined based on the concepts of Pareto front and knee point. The proposed RGDS approach was illustrated through a numerical case of a two-layer slope design. The numerical results indicate that the RGDS approach is not only more intuitive and easier to follow but also more computationally efficient.

Combined multi-objective optimization and robustness analysis framework for building integrated energy system under uncertainty

The optimal design of building integrated energy system is sensitive to the variation of uncertain parameters. For addressing the tradeoff of uncertainty and optimality-robustness, this study proposes a combined multi-objective optimization and robustness analysis framework for optimal design of building integrated energy system. The proposed framework includes two parts. In the optimization part, on the basis of scenario generation for capturing the uncertainties of renewable energy sources and energy demands, two-stage multi-objective stochastic mixed-integer nonlinear programming is conducted to optimize the system‘s economic and environmental objectives. Two decision-making methods are introduced to identify the final optimum solution from the obtained Pareto frontier. In the robustness-analysis part, a combined Monte Carlo simulation and optimization method is implemented to verify the robustness of the optimal solutions. The two parts of the framework are integrated to investigate the case of a hotel in Beijing, China. The results indicate that compared with the stochastic model, the deterministic model underestimates the annual total cost. Achieving economic and environmental optimum is conflicting and needs a trade-off through decision making. Moreover, in the robustness analysis, an acceptable robustness value is identified, considering both the selected objectives and the operation constraints’ probability of failure. The Shannon-entropy-based final optimum solution exhibits the best comprehensive performance, with an annual total cost of $695 × 103/year, an annual carbon emissions of 2100 tons/year, and an 8.81% probability of failure.

A Cost-Utility Analysis of Switching from Reference to Biosimilar Infliximab Compared to Maintaining Reference Infliximab in Adult Patients with Crohn's Disease.

Background and AimsLower-cost biosimilar infliximab may address affordability concerns in the treatment of adults with Crohn’s disease (CD), however, evidence regarding the cost-effectiveness of switching from reference to biosimilar is warranted. The aim of this research was to assess the incremental cost of switching from treatment with reference infliximab to biosimilar compared with maintaining reference infliximab in adults with CD per quality-adjusted life year (QALY) gained.MethodsA probabilistic cohort Markov model with 8-week cycle lengths was constructed to estimate the incremental costs and effects of switching over a 5-year time horizon from a public payer perspective. Base-case clinical inputs were obtained from NOR-SWITCH subgroup analyses and other published trials. Costs were obtained from Canadian sources. A total of 10,000 simulations were run. Sensitivity analysis was used to test the robustness of the results to variations in uncertain parameters.ResultsSwitching to biosimilar infliximab was less costly but also less effective with incremental savings of $46,194 (95% confidence interval [CI]: $42,420, $50,455) and a loss in QALYs of −0.13 (95% CI: −0.16, −0.07). Eighty-three per cent of the simulations demonstrated incremental cost savings and an incremental loss of effectiveness. The model was sensitive to differences in rates of disease worsening between reference and biosimilar infliximab.ConclusionsWhile biosimilar infliximab is associated with incremental savings for patients on maintenance therapy who are switched from reference infliximab, funding decision makers must decide whether a small loss of effectiveness is justified. Further evidence will help to inform reimbursement policy.

Interval Nonprobabilistic Reliability Analysis for Ancient Landslide considering Strain‐Softening Behavior: A Case Study

Uncertainties in geotechnical parameters significantly affect the stability evaluation of an ancient landslide, especially when considering the strain‐softening behavior. Due to the great difficulty in obtaining the probability density distribution of geoparameters, an interval nonprobability reliability analysis framework combined with numerical strain‐softening constitutive relations was established in this paper. Interval variables were defined as the uncertain parameters in the strain‐softening model. The interval nonprobabilistic reliability was defined as the minimum distance from the origin point to the failure surface in the standard normal space, which is the key index for describing the ability of a system to tolerate the variation of uncertain parameters. The proposed method was used to evaluate the reliability of Baishi ancient landslide. The parameter sensitivity analysis was also conducted. Through the proposed method, it is considered that Baishi ancient landslide is safe and stable, and the strain threshold kr is the dominant parameter. The results calculated by the proposed method agree well with the actual situation. This indicates the proposed method is more applicable than the traditional probability method when the data are scare.

New Discretization Methodology for Three-Dimensional Mechanical Parameters Considering Spatial Variations

In this paper, the uncertain mechanical parameters are modeled as spatial random fields (RFs). A new tetrahedral discretization methodology of three-dimensional (3D) RF is proposed based on the local average (LA) theory. An analytical formula and a numerical formula of the covariance for any two tetrahedral RF elements are developed. Its main advantage, compared to similar studies employing hexahedral discretization method, is that tetrahedral LA method can perfectly combine with tetrahedral finite element (FE) method. Also, the corresponding relation between RF mesh and FE mesh is clearer and the computer codes are simpler. The accuracy of proposed LA method in this study was verified by comparing with other discretization techniques of RF. Finally, an illustrative example is presented to demonstrate the analysis process. The validity and the advantage of the proposed LA method are proven. Taking the spatial variations of uncertain mechanical parameters into account, the stochastic effects of scale of fluctuation on the RF are estimated. The proposed method can be widely applied to 3D stochastic FE analysis, and the sample results will improve our understanding of the stochastic influence of scale of fluctuation on the RF.

In search of flexible and robust wind farm layouts considering wind state uncertainty

Variations in wind states are generally ignored while designing the wind farm layouts. As a result, given the highly uncertain nature of wind the ability of the wind farms to produce power on a sustained basis gets severely affected in the long run. In this study, a robust optimization methodology has been proposed and successfully adopted to design wind farm layouts (optimum number and location of wind turbines) that are immune to varying wind state conditions. Assuming different realizations of wind state uncertainty distributions of wind speeds and directions, the proposed methodology provides uncertainty resilient robust solutions for the conservative worst case and the optimistic best case situations by adopting maximum and minimum extent of variations in uncertain parameters, respectively. Additionally, the flexibility introduced in the formulation enables a designer to create solution anywhere between these two extremes. This set of robust solutions provide with a realistic envelope for the farm performance parameters under uncertainty helping meeting the guaranteed service levels. It has been observed that the turbine layout corresponds to the worst case can produce an average of ∼49% more power than the guaranteed value and provide with 100% success rate on meeting the service levels under changing wind conditions. Representing the wind farm by uniform set of coarse grids initially, need based grids of variable resolution along with novel repair operator are adopted to generate Pareto solutions for the multi-objective cost-power trade-off problem. The proposed grid based technique is validated against other techniques of no-grid and grid with fixed resolution and improvements of ∼9.0% in power production and ∼1.7% in the ratio of cost and power can be seen. Furthermore, improvements of 75.7% in produced power as compared to rigorously explored benchmark case study and 1–10% in cost to power ratio compared to other techniques presented in literature, show the merits of the proposed technique.