Uncertainty quantification of MEMS using a data-dependent adaptive stochastic collocation method

This paper presents a unified framework for uncertainty quantification (UQ) in microelectromechanical systems (MEMS). The goal is to model uncertainties in the input parameters of micromechanical devices and to quantify their effect on the final performance of the device. We consider different electromechanical actuators that operate using a combination of electrostatic and electrothermal modes of actuation, for which high-fidelity numerical models have been developed. We use a data-driven framework to generate stochastic models based on experimentally observed uncertainties in geometric and material parameters. Since we are primarily interested in quantifying the statistics of the output parameters of interest, we develop an adaptive refinement strategy to efficiently propagate the uncertainty through the device model, in order to obtain quantities like the mean and the variance of the stochastic solution with minimal computational effort. We demonstrate the efficacy of this framework by performing UQ in some examples of electrostatic and electrothermomechanical microactuators. We also validate the method by comparing our results with experimentally determined uncertainties in an electrostatic microswitch. We show how our framework results in the accurate computation of uncertainties in micromechanical systems with lower computational effort.     

Multi-objective genetic programming approach for robust modeling of complex manufacturing processes having probabilistic uncertainty in experimental data

In this paper, a multi-objective uniform-diversity genetic programming (MUGP) algorithm deployed for robust Pareto modeling and prediction of complex nonlinear processes using some input-output data table. The uncertainties included in measured data are considered to obtain more robust models. The considered benchmarks are an explosive cutting and forming processes, in which the nonlinear behavior between the input and output of processes are detected using MUGP. For both case studies, a multi-objective modeling and prediction procedure firstly performed using deterministic data. Secondly, the same identification procedure carried out using probabilistic uncertainty in the experimental input-output data. The objective functions considered are namely, training error, prediction error and number of tree nodes (complexity of models) in the deterministic approach. Accordingly, the mean and standard deviation of training error and prediction error are considered in robust Pareto modeling and prediction of such processes. In this way, Pareto front of such modeling and prediction is first obtained for both explosive cutting and forming processes with deterministic data. Such Pareto front is then obtained using experimental input-output-data having probabilistic uncertainty in input parameters through a Monte Carlo simulation (MCS) approach. In addition, it has been shown that for both cases, the trade-off models obtained from deterministic data have significant biases when tested on data with probabilistic uncertainty. Finally, the obtained results of such multi-objective robust model identification show promising results in terms of compensating uncertainty in the experimental input-output-data.     

A GUI platform for uncertainty quantification of complex dynamical models

Uncertainty quantification (UQ) refers to quantitative characterization and reduction of uncertainties present in computer model simulations. It is widely used in engineering and geophysics fields to assess and predict the likelihood of various outcomes. This paper describes a UQ platform called UQ-PyL (Uncertainty Quantification Python Laboratory), a flexible software platform designed to quantify uncertainty of complex dynamical models. UQ-PyL integrates different kinds of UQ methods, including experimental design, statistical analysis, sensitivity analysis, surrogate modeling and parameter optimization. It is written in Python language and runs on all common operating systems. UQ-PyL has a graphical user interface that allows users to enter commands via pull-down menus. It is equipped with a model driver generator that allows any computer model to be linked with the software. We illustrate the different functions of UQ-PyL by applying it to the uncertainty analysis of the Sacramento Soil Moisture Accounting Model. We will also demonstrate that UQ-PyL can be applied to a wide range of applications.     

Stochastic model predictive control for central HVAC plants

We present a stochastic model predictive control (MPC) framework for central heating, ventilation, and air conditioning (HVAC) plants. The framework uses real data to forecast and quantify uncertainty of disturbances affecting the system over multiple timescales (electrical loads, heating/cooling loads, and energy prices). We conduct detailed closed-loop simulations and systematic benchmarks for the central HVAC plant of a typical university campus. Results demonstrate that deterministic MPC fails to properly capture disturbances and that this translates into economic penalties associated with peak demand charges and constraint violations in thermal storage capacity (overflow and/or depletion). Our results also demonstrate that stochastic MPC provides a more systematic approach to mitigate uncertainties and that this ultimately leads to cost savings of up to 7.5% and the mitigation of storage constraint violations. Benchmark results also indicate that these savings are close to ideal savings (9.6%) obtained under MPC with perfect information.     

Quantification of model-form and predictive uncertainty for multi-physics simulation

Traditional uncertainty quantification in multi-physics design problems involves the propagation of parametric uncertainties in input variables such as structural or aerodynamic properties through a single, or series of models constructed to represent the given physical scenario. These models are inherently imprecise, and thus introduce additional sources of error to the design problem. In addition, there often exists multiple models to represent the given situation, and complete confidence in selecting the most accurate model among the model set considered is beyond the capability of the user. Thus, quantification of the errors introduced by this modeling process is a necessary step in the complete quantification of the uncertainties in multi-physics design problems. In this work, a modeling uncertainty quantification framework was developed to quantify to quantify both the model-form and predictive uncertainty in a design problem through the use of existing methods as well as newly developed modifications to existing methods in the literature. The applicability of this framework to a problem involving full-scale simulation was then demonstrated using the AGARD 445.6 Weakened Wing and three different aeroelastic simulation packages to quantify the flutter conditions of the wing.     

A top-down approach to calibration, validation, uncertainty quantification and predictive accuracy assessment

This paper describes a “top-down” uncertainty quantification (UQ) approach for calibration, validation and predictive accuracy assessment of the SNL Validation Workshop Structural Dynamics Challenge Problem. The top-down UQ approach differs from the more conventional (“bottom-up”) approach in that correlated statistical analysis is performed directly with the modal characteristics (frequencies, mode shapes and damping ratios) rather than using the modal characteristics to derive the statistics of physical model parameters (springs, masses and viscous damping elements in the present application). In this application, a stochastic subsystem model is coupled with a deterministic subsystem model to analyze stochastic system response to stochastic forcing functions. The weak nonlinearity of the stochastic subsystem was characterized by testing it at three different input levels, low, medium and high. The calibrated subsystem models were validated with additional test data using published NASA and Air Force validation criteria. The validated subsystem models were first installed in the accreditation test bed where system response simulations involving stochastic shock-type force inputs were conducted. The validated stochastic subsystem model was then installed in the target application and simulations involving limited duration segments of stationary random vibration excitation were conducted.     

Uncertainty analysis in air dispersion modeling

The Taylor series approach for uncertainty analyses is advanced as an efficient method of producing a probabilistic output from air dispersion models. A probabilistic estimate helps in making better-informed decisions when compared to results of deterministic models. In this work, the Industrial Source Complex Short Term (ISCST) model is used as an analytical model to predict pollutant transport from a point source. First- and second-order Taylor series approximations are used to calculate the uncertainty in ground level concentrations of ISCST calculations. The results of the combined ISCST and uncertainty calculations are then validated with traditional Monte Carlo (MC) simulations. The Taylor series uncertainty estimates are a function of the variance in input parameters (wind speed and temperature) and the model sensitivities to input parameters. While the input variance is spatially invariant, sensitivity is spatially variable; hence the uncertainty in modeled output varies spatially. A comparison with the MC approach shows that uncertainty estimated by first-order Taylor series is found to be appropriate for ambient temperature, while second-order Taylor series is observed to be more accurate for wind speed. Since the Taylor series approach is simple and time-efficient compared to the MC method, it provides an attractive alternative.     

Supply Chain Management in Food Chains: Improving Performance by Reducing Uncertainty

This paper investigates the impact of Supply Chain Management on logistical performance indicators in food supply chains. From a review of quantitative and more qualitative managerial literature, we believe that Supply Chain Management should be concerned with the reduction or even elimination of uncertainties to improve the performance of the chain. The following clusters of sources of uncertainty are identified: order forecast horizon, input data, administrative and decision processes and inherent uncertainties. For each source of uncertainty, several improvement principles are identified. A case study was conducted in a food chain in which a simulation model helped quantify the effects of alternative configurations and operational management concepts. By comparing this simulation study with a pilot study, the model is validated against real data, and organisational consequences are identified. The results of the case study suggest that reduction of uncertainties can improve service levels significantly, although current supply chain configurations restrict possible benefits. The availability of real-time information systems is found to be a requirement for obtaining efficient and effective Supply Chain Management concepts.     

An overview of methods to evaluate uncertainty of deterministic models in decision support

There is an increasing need for environmental management advice that is wide-scoped, covering various interlinked policies, and realistic about the uncertainties related to the possible management actions. To achieve this, efficient decision support integrates the results of pre-existing models. Many environmental models are deterministic, but the uncertainty of their outcomes needs to be estimated when they are utilized for decision support. We review various methods that have been or could be applied to evaluate the uncertainty related to deterministic models' outputs. We cover expert judgement, model emulation, sensitivity analysis, temporal and spatial variability in the model outputs, the use of multiple models, and statistical approaches, and evaluate when these methods are appropriate and what must be taken into account when utilizing them. The best way to evaluate the uncertainty depends on the definitions of the source models and the amount and quality of information available to the modeller.     

Nonlinear Robust Adaptive Deterministic Control for Flexible Hypersonic Vehicles in the Presence of Input Constraint

A nonlinear deterministic robust control scheme is developed for a flexible hypersonic vehicle with input saturation. Firstly, the model analysis is conducted for the hypersonic vehicle model via the input‐output linearized technique. Secondly, the sliding mode manifold is designed based on homogeneity theory. Then an adaptive high order sliding mode control scheme is proposed to achieve tracking for the step change in altitude and velocity for hypersonic vehicles where the uncertainty boundary is unknown. Furthermore, the control input constraint is investigated and another new adaptive law is proposed to estimate the uncertainties and to guarantee the stability of the system with input saturation. Finally, the simulation results are provided to demonstrate the effectiveness of the proposed method.     

Assessment and weighting of meteorological ensemble forecast members based on supervised machine learning with application to runoff simulations and flood warning

Numerical weather forecasts, such as meteorological forecasts of precipitation, are inherently uncertain. These uncertainties depend on model physics as well as initial and boundary conditions. Since precipitation forecasts form the input into hydrological models, the uncertainties of the precipitation forecasts result in uncertainties of flood forecasts. In order to consider these uncertainties, ensemble prediction systems are applied. These systems consist of several members simulated by different models or using a single model under varying initial and boundary conditions. However, a too wide uncertainty range obtained as a result of taking into account members with poor prediction skills may lead to underestimation or exaggeration of the risk of hazardous events. Therefore, the uncertainty range of model-based flood forecasts derived from the meteorological ensembles has to be restricted.In this paper, a methodology towards improving flood forecasts by weighting ensemble members according to their skills is presented. The skill of each ensemble member is evaluated by comparing the results of forecasts corresponding to this member with observed values in the past. Since numerous forecasts are required in order to reliably evaluate the skill, the evaluation procedure is time-consuming and tedious. Moreover, the evaluation is highly subjective, because an expert who performs it makes his decision based on his implicit knowledge.Therefore, approaches for the automated evaluation of such forecasts are required. Here, we present a semi-automated approach for the assessment of precipitation forecast ensemble members. The approach is based on supervised machine learning and was tested on ensemble precipitation forecasts for the area of the Mulde river basin in Germany. Based on the evaluation results of the specific ensemble members, weights corresponding to their forecast skill were calculated. These weights were then successfully used to reduce the uncertainties within rainfall-runoff simulations and flood risk predictions.     

Validation and updating in a large automotive vibro-acoustic model using a P-box in the frequency domain

In this paper, a model validation framework is proposed and applied to a large vibro-acoustic finite element (FE) model of a passenger car. The framework introduces a p-box approach with an efficient quantification scheme of uncertainty sources and a new area metric which is relevant to the responses in the frequency domain. To prioritize the input uncertainties out of the enormous FE model, the experts’ knowledge is utilized to select candidate input parameters which have large potential influences on the response of interests (ROI) among several thousands of input parameters. Next, a variance-based sensitivity analysis with an orthogonal array is introduced in effort to quantify the influence of the selected input parameters on the ROIs. The employment of the eigenvector dimension reduction method and orthogonal combinations of interval-valued input parameters provides the p-box of the ROI even if the size of the FE model is very large. A color map and the u-pooling of the p-boxes over the frequency band as well as the p-box at different frequencies are introduced to assess the model error and quantitative contributions of the aleatory and the epistemic input uncertainties to the overall variability of the ROIs in the frequency domain. After assessing the model error, the FE model is updated. It was found that the sensitivity results and the experts’ knowledge about the associated components effectively determine the modifications of the component models and the input parameter values during the updating process.     

Seasonal hydrological and nutrient loading forecasts for watersheds over the Southeastern United States

We show useful seasonal deterministic and probabilistic prediction skill of streamflow and nutrient loading over watersheds in the Southeastern United States (SEUS) for the winter and spring seasons. The study accounts for forecast uncertainties stemming from the meteorological forcing and hydrological model uncertainty. Multi-model estimation from three hydrological models, each forced with an ensemble of forcing derived by matching observed analogues of forecasted quartile rainfall anomalies from a seasonal climate forecast is used. The attained useful hydrological prediction skill is despite the climate model overestimating rainfall by over 23% over these SEUS watersheds in December–May period. The prediction skill in the month of April and May is deteriorated as compared to the period from December–March (zero lead forecast). A nutrient streamflow rating curve is developed using a log linear tool for this purpose. The skill in the prediction of seasonal nutrient loading is identical to the skill of seasonal streamflow forecast.     

Albero: A Visual Analytics Approach for Probabilistic Weather Forecasting

Probabilistic weather forecasts are amongst the most popular ways to quantify numerical forecast uncertainties. The analog regression method can quantify uncertainties and express them as probabilities. The method comprises the analysis of errors from a large database of past forecasts generated with a specific numerical model and observational data. Current visualization tools based on this method are essentially automated and provide limited analysis capabilities. In this paper, we propose a novel approach that breaks down the automatic process using the experience and knowledge of the users and creates a new interactive visual workflow. Our approach allows forecasters to study probabilistic forecasts, their inner analogs and observations, their associated spatial errors, and additional statistical information by means of coordinated and linked views. We designed the presented solution following a participatory methodology together with domain experts. Several meteorologists with different backgrounds validated the approach. Two case studies illustrate the capabilities of our solution. It successfully facilitates the analysis of uncertainty and systematic model biases for improved decision‐making and process‐quality measurements.     

A Stochastic Programming Strategy in Microgrid Cyber Physical Energy System for Energy Optimal Operation

This paper focuses on the energy optimal operation problem of microgrids (MGs) under stochastic environment. The deterministic method of MGs operation is often uneconomical because it fails to consider the high randomness of unconventional energy resources. Therefore, it is necessary to develop a novel operation approach combining the uncertainty in the physical world with modeling strategy in the cyber system. This paper proposes an energy scheduling optimization strategy based on stochastic programming model by considering the uncertainty in MGs. The goal is to minimize the expected operation cost of MGs. The uncertainties are modeled based on autoregressive moving average (ARMA) model to expose the effects of physical world on cyber world. Through the comparison of the simulation results with deterministic method, it is shown that the effectiveness and robustness of proposed stochastic energy scheduling optimization strategy for MGs are valid.      

Confidence-based reliability assessment considering limited numbers of both input and output test data

Simulation-based methods can be used for accurate uncertainty quantification and prediction of the reliability of a physical system under the following assumptions: (1) accurate input distribution models and (2) accurate simulation models (including accurate surrogate models if utilized). However, in practical engineering applications, often only limited numbers of input test data are available for modeling input distribution models. Thus, estimated input distribution models are uncertain. In addition, the simulation model could be biased due to assumptions and idealizations used in the modeling process. Furthermore, only a limited number of physical output test data is available in the practical engineering applications. As a result, target output distributions, against which the simulation model can be validated, are uncertain and the corresponding reliabilities become uncertain as well. To assess the conservative reliability of the product properly under the uncertainties due to limited numbers of both input and output test data and a biased simulation model, a confidence-based reliability assessment method is developed in this paper. In the developed method, a hierarchical Bayesian model is formulated to obtain the uncertainty distribution of reliability. Then, we can specify a target confidence level. The reliability value at the target confidence level using the uncertainty distribution of reliability is the confidence-based reliability, which is the confidence-based estimation of the true reliability. It has been numerically demonstrated that the proposed method can predict the reliability of a physical system that satisfies the user-specified target confidence level, using limited numbers of input and output test data.     

Lazy Learning based surrogate models for air quality planning

Air pollution in atmosphere derives from complex non-linear relationships, involving anthropogenic and biogenic precursor emissions. Due to this complexity, Decision Support Systems (DSSs) are important tools to help Environmental Authorities to control/improve air quality, reducing human and ecosystems pollution impacts. DSSs implementing cost-effective or multi-objective methodologies require fast air quality models, able to properly describe the relations between emissions and air quality indexes. These, namely surrogate models (SM), are identified processing deterministic model simulation data. In this work, the Lazy Learning technique has been applied to reproduce the relations linking precursor emissions and pollutant concentrations. Since computational time has to be minimized without losing precision and accuracy, tests aimed at reducing the amount of input data have been performed on a case study over Lombardia Region in Northern Italy.     

A General Probabilistic Framework for uncertainty and global sensitivity analysis of deterministic models: A hydrological case study

The present study proposes a General Probabilistic Framework (GPF) for uncertainty and global sensitivity analysis of deterministic models in which, in addition to scalar inputs, non-scalar and correlated inputs can be considered as well. The analysis is conducted with the variance-based approach of Sobol/Saltelli where first and total sensitivity indices are estimated. The results of the framework can be used in a loop for model improvement, parameter estimation or model simplification. The framework is applied to SWAP, a 1D hydrological model for the transport of water, solutes and heat in unsaturated and saturated soils. The sources of uncertainty are grouped in five main classes: model structure (soil discretization), input (weather data), time-varying (crop) parameters, scalar parameters (soil properties) and observations (measured soil moisture). For each source of uncertainty, different realizations are created based on direct monitoring activities. Uncertainty of evapotranspiration, soil moisture in the root zone and bottom fluxes below the root zone are considered in the analysis. The results show that the sources of uncertainty are different for each output considered and it is necessary to consider multiple output variables for a proper assessment of the model. Improvements on the performance of the model can be achieved reducing the uncertainty in the observations, in the soil parameters and in the weather data. Overall, the study shows the capability of the GPF to quantify the relative contribution of the different sources of uncertainty and to identify the priorities required to improve the performance of the model. The proposed framework can be extended to a wide variety of modelling applications, also when direct measurements of model output are not available.     

复杂系统仿真模型的分层确认

介绍一种解决复杂系统仿真可信性问题的模型确认方法.该方法首先将复杂系统划分成相对简单的子系统、基准系统、单元,得到一分层模型树;接下来对模型树中的模型进行排序并安排确认试验;然后利用信息差方法对拥有试验数据的子层模型进行单层确认;最后通过灵敏度分析将子层模型的确认结果传播到父层模型,最后得到全系统模型的确认结果.文中提出的方法适用于试验数据少、可分层的复杂系统.