Unknown Input Parameters Research Articles

종이 헬리콥터 낙하해석모델의 통계적 교정 및 검증

Mathematical models are actively used to reduce the experimental expenses required to understand physical phenomena. However, they are different from real phenomena because of assumptions or uncertain parameters. In this study, we present a calibration and validation method using a paper helicopter and statistical methods to quantify the uncertainty. The data from the experiment using three nominally identical paper helicopters consist of different groups, and are used to calibrate the drag coefficient, which is an unknown input parameter in both analytical models. We predict the predicted fall time data using probability distributions. We validate the analysis models by comparing the predicted distribution and the experimental data distribution. Moreover, we quantify the uncertainty using the Markov Chain Monte Carlo method. In addition, we compare the manufacturing error and experimental error obtained from the fall-Time data using Analysis of Variance. As a result, all of the paper helicopters are treated as one identical model.

A ground temperature map of the North Atlantic permafrost region based on remote sensing and reanalysis data

Abstract. Permafrost is a key element of the terrestrial cryosphere which makes mapping and monitoring of its state variables an imperative task. We present a modeling scheme based on remotely sensed land surface temperatures and reanalysis products from which mean annual ground temperatures (MAGT) can be derived at a spatial resolution of 1 km at continental scales. The approach explicitly accounts for the uncertainty due to unknown input parameters and their spatial variability at subgrid scale by delivering a range of MAGTs for each grid cell. This is achieved by a simple equilibrium model with only few input parameters which for each grid cell allows scanning the range of possible results by running many realizations with different parameters. The approach is applied to the unglacierized land areas in the North Atlantic region, an area of more than 5 million km2 ranging from the Ural Mountains in the east to the Canadian Archipelago in the west. A comparison to in situ temperature measurements in 143 boreholes suggests a model accuracy better than 2.5 °C, with 139 considered boreholes within this margin. The statistical approach with a large number of realizations facilitates estimating the probability of permafrost occurrence within a grid cell so that each grid cell can be classified as continuous, discontinuous and sporadic permafrost. At its southern margin in Scandinavia and Russia, the transition zone between permafrost and permafrost-free areas extends over several hundred km width with gradually decreasing permafrost probabilities. The study exemplifies the unexploited potential of remotely sensed data sets in permafrost mapping if they are employed in multi-sensor multi-source data fusion approaches.

A new hybrid artificial intelligence approach to predicting global thermal comfort of stretch knitted fabrics

Today numerous consumers consider thermal comfort to be one of the most significant attributes when purchasing textile and apparel products, so there is a need to develop a model able to simulate objectively the consumers’ perception. The global thermal comfort of stretch knitted fabrics is a multi-criteria phenomenon that requires the satisfaction of several properties at the same time. In this paper, we used the desirability functions to evaluate the satisfaction degree of global thermal comfort. Statistical method was used to investigate the interrelationship among knit thermo-physical properties, and group them into factors. Two models of artificial neural network (general and special) have been set up to predict the global thermal comfort from structural parameters (inputs) of knitted fabrics made from pure yarn cotton (cellulose) and viscose (regenerated cellulose) fibers and plated knitted with elasthane (Lycra) fibers. A virtual leave one out approach dealing with over fitting phenomenon and allowing the selection of the optimal neural network architecture was used. By combining the strengths of statistics and fuzzy logic (data reduction and information summation) also a neural network (self-learning ability), hybrid model was developed to simulate the consumer thermal comfort perception. After that, ANN model is inverted. With a required output value and some input parameters it is possible to calculate the unknown optimum input parameter. Finally, this forecasting can help industrials to anticipate the consumer’s taste. Thus, they can adjust the knitting production parameter to reach the desired global thermal comfort to satisfy this consumer.

A calibration method for whole-building airflow simulation in high-rise residential buildings

The simulation results for airflow in high-rise buildings may not match actual behavior due to various airflow paths and impact factors, such as temperature, wind direction, wind velocity, and building characteristics (airtightness, layout, and others). When conducting whole-building airflow simulation for high-rise buildings, it is important to reasonably define uncertain input parameters in order to minimize the difference between measurement and simulation results. This study proposes a calibration method for airflow simulation modeling of high-rise buildings using the data-driven method and estimating uncertain input data through output data.The output data for comparing measured values with simulated values were focused on pressure distributions in buildings, because this value indicates the driving force of the airflows between building partitions and in the entire building. Based on the measured pressure distribution of the analyzed building, the unknown input parameters were deduced primarily using the Thermal Draft Coefficient (TDC). The uncertain input parameters (leakage area, flow coefficient, and exponent) were then optimized using Genetic Algorithm (GA). Through the processes suggested in this study, the uncertain input parameters for whole-building airflow simulation can be optimized, and the discrepancy between simulation results and measured values can be minimized. The advantage of this method is that the input parameters can be optimized for reasonable simulation modeling using limited measurement results in high-rise buildings.

INVESTIGATING THE SLOPE STABILITY BASED ON UNCERTAINTY BY USING FUZZY POSSIBILITY THEORY

Abstract The main purpose of this paper is to investigate the slope stability condition by using fuzzy estimation method based on fuzzy possibility theory. Due to use of this theory, the inaccuracy, ambiguity and uncertainty in input parameters are considered and therefore, the calculated factor of safety (FOS) is highly reliable. In this research, first, the input parameters of slope stability analysis, based on statistical characteristics and grade of membership concept, as a fuzzy numbers are defined. Then the performance function of slope behavior is defined and by using the fuzzy parameters, the FOS is calculated. In next step, by using the several α - cut, the calculated FOS is defined as a fuzzy form and subsequently, the slope stability condition based on fuzzy presentation of FOS is evaluated. The results show that, although based on deterministic analysis the studied slope is stable but based on fuzzy interpretation of FOS, the slope stability condition is scare. The fuzzy analysis of slope stability condition, by applying the uncertainty in calculating the FOS and defining the grade of membership for each unknown input parameters in model, a more realistic interpretation of slope stability condition is provided. In addition, the fuzzy presentation of the FOS, allowing more accurate judgments about slope stability condition.

슬라이딩 모드 제어기법을 이용한 도립진자 시스템 제어

슬라이딩모드 제어의 문제는 제어입력에 포함된 알려지지 않은 외란 등 비선형 입력으로 인한 채터링의 발생이다. 본 연구는 채터링 발생의 문제를 해결하기 위한 제어 알고리듬에 대하여 고찰하고 채터링을 억제하는 슬라이딩모드 제어기를 설계하고자 한다. 슬라이딩모드 제어 시 발생하는 채터링을 억제하기 위해 알려지지 않은 외란을 포함한 비선형 입력에 대하여 평활함수를 적용한다. 이 방법에 의하여 도립진자 시스템의 동적 방정식에 포함된 비선형 요소와 외란에 의한 문제가 해결될 수 있음을 보인다. 또 슬라이딩모드 제어를 위한 제어 입력을 시스템에 적용하였고, 제안한 제어기의 제어성능을 검증하기 위하여 도립진자를 대상으로 컴퓨터 모의실험을 수행하였다. 모의실험 결과 제어입력에 포함된 큰 폭의 채터링이 제거되었음을 확인할 수 있다. A problem of sliding mode control is chattering because of controle input signal included unknown disturbance and nonlinear input parameters. This paper presents a sliding mode controller design to inverted pendulum system. In this paper, a sliding mode control algorithm to reduce a chattering is proposed. The reduction of chattering is accomplished by smoothing function for nonlinear control input. In this method, the dynamic equations of the inverted pendulum is decoupled by considering nonlinear parameters and external disturbances. Therefore, this study is applied to obtain switching control inputs for sliding mode controller. The proposed technique is tested to the control of inverted pendulum through computer simulations. The result shown reduced chattering in control input.

The electroweak contributions to(g−2)μafter the Higgs-boson mass measurement

The Higgs boson mass used to be the only unknown input parameter of the electroweak contributions to (g-2)_\mu\ in the Standard Model. It enters at the two-loop level in diagrams with e.g. top loops, W- or Z-exchange. We re-evaluate these contributions, providing analytic expressions and exact numerical results for the Higgs boson mass recently measured at the LHC. Our final result for the full Standard Model electroweak contributions is (153.6\pm1.0)*10^{-11}, where the remaining theory error comes from unknown three-loop contributions and hadronic uncertainties.

Breast lesion co-localisation between X-ray and MR images using finite element modelling

This paper presents a novel X-ray and MR image registration technique based on individual-specific biomechanical finite element (FE) models of the breasts. Information from 3D magnetic resonance (MR) images was registered to X-ray mammographic images using non-linear FE models subject to contact mechanics constraints to simulate the large compressive deformations between the two imaging modalities. A physics-based perspective ray-casting algorithm was used to generate 2D pseudo-X-ray projections of the FE-warped 3D MR images. Unknown input parameters to the FE models, such as the location and orientation of the compression plates, were optimised to provide the best match between the pseudo and clinical X-ray images. The methods were validated using images taken before and during compression of a breast-shaped phantom, for which 12 inclusions were tracked between imaging modalities. These methods were then applied to X-ray and MR images from six breast cancer patients. Error measures (such as centroid and surface distances) of segmented tumours in simulated and actual X-ray mammograms were used to assess the accuracy of the methods. Sensitivity analysis of the lesion co-localisation accuracy to rotation about the anterior-posterior axis was then performed. For 10 of the 12 X-ray mammograms, lesion localisation accuracies of 14 mm and less were achieved. This analysis on the rotation about the anterior-posterior axis indicated that, in cases where the lesion lies in the plane parallel to the mammographic compression plates, that cuts through the nipple, such rotations have relatively minor effects.This has important implications for clinical applicability of this multi-modality lesion registration technique, which will aid in the diagnosis and treatment of breast cancer.

Sparse, adaptive Smolyak quadratures for Bayesian inverse problems

Based on the parametric deterministic formulation of Bayesian inverse problems with unknown input parameter from infinite-dimensional, separable Banach spaces proposed in Schwab and Stuart (2012 Inverse Problems 28 045003), we develop a practical computational algorithm whose convergence rates are provably higher than those of Monte Carlo (MC) and Markov chain Monte Carlo methods, in terms of the number of solutions of the forward problem. In the formulation of Schwab and Stuart, the forward problems are parametric, deterministic elliptic partial differential equations, and the inverse problem is to determine the unknown diffusion coefficients from noisy observations comprising linear functionals of the system’s response. The sparsity of the generalized polynomial chaos representation of the posterior density being implied by sparsity assumptions on the class of the prior (Schwab and Stuart 2012), we design, analyze and implement a class of adaptive, deterministic sparse tensor Smolyak quadrature schemes for the efficient approximate numerical evaluation of expectations under the posterior, given data. The proposed, deterministic quadrature algorithm is based on a greedy, iterative identification of finite sets of most significant, ‘active’ chaos polynomials in the posterior density analogous to recently proposed algorithms for adaptive interpolation (Chkifa et al 2012 Report 2012-NN, 2013 Math. Modelling Numer. Anal. 47 253–80). Convergence rates for the quadrature approximation are shown, both theoretically and computationally, to depend only on the sparsity class of the unknown, but are bounded independently of the number of random variables activated by the adaptive algorithm. Numerical results for a model problem of coefficient identification with point measurements in a diffusion problem confirm the theoretical results.

Comparative magnetotail flapping: an overview of selected events at Earth, Jupiter and Saturn

Abstract. A comparison of magnetotail flapping (the up-and-down wavy motion) between the Earth and the two giant planets Jupiter and Saturn has been performed through investigation of the current sheet normal of the magnetotail. Magnetotail flapping is commonly observed in the Earth's magnetotail. Due to single spacecraft missions at the giant planets, the normal is determined through minimum variance analysis of magnetometer data during multiple intervals when the spacecraft crossed through the current sheet. It is shown that indeed a case can be made that magnetotail flapping also occurs at Jupiter and Saturn. Calculations of the wave period using generic magnetotail models show that the observed periods are much shorter than their theoretical estimates, and that this discrepancy can be caused by unknown input parameters for the tail models (e.g., current sheet thickness) and by possible Doppler shifting of the waves in the spacecraft frame through the fast rotation of the giant planets.

Multi-output separable Gaussian process: Towards an efficient, fully Bayesian paradigm for uncertainty quantification

Computer codes simulating physical systems usually have responses that consist of a set of distinct outputs (e.g., velocity and pressure) that evolve also in space and time and depend on many unknown input parameters (e.g., physical constants, initial/boundary conditions, etc.). Furthermore, essential engineering procedures such as uncertainty quantification, inverse problems or design are notoriously difficult to carry out mostly due to the limited simulations available. The aim of this work is to introduce a fully Bayesian approach for treating these problems which accounts for the uncertainty induced by the finite number of observations. Our model is built on a multi-dimensional Gaussian process that explicitly treats correlations between distinct output variables as well as space and/or time. The proper use of a separable covariance function enables us to describe the huge covariance matrix as a Kronecker product of smaller matrices leading to efficient algorithms for carrying out inference and predictions. The novelty of this work, is the recognition that the Gaussian process model defines a posterior probability measure on the function space of possible surrogates for the computer code and the derivation of an algorithmic procedure that allows us to sample it efficiently. We demonstrate how the scheme can be used in uncertainty quantification tasks in order to obtain error bars for the statistics of interest that account for the finite number of observations.

Numerical modelling of heat transfer and fluid flow in laser microwelding

As an intense heat source laser has been successfully employed in microwelding of materials for manufacturing various miniature components. A sophisticated mathematical model of laser microwelding is ever demanding since experimental investigation of the same is costly, expensive, and time consuming. Very little work has been reported in literature on material flow behaviour in microwelding process. Hence, present work is focused on three-dimensional finite element modelling of heat transfer and fluid flow in laser microwelding process. The fluid flow behaviour is validated using order-of-magnitude analysis of liquid velocity under various driving forces. Estimation of several dimensionless numbers describes the nature of material flow within small weld pool. Temperature dependent material properties, latent heat of melting and solidification are incorporated in the model. A harmony search-based meta-heuristic algorithm is incorporated to identify most suitable unknown model input parameters. Simulated results have been validated against experimental data adapted from independent literature.

Optimal COP prediction of a solar intermittent refrigeration system for ice production by means of direct and inverse artificial neural networks

A direct and inverse artificial neural network (ANN and ANNi) approach were developed to predict the required coefficient of performance (COP) of a solar intermittent refrigeration system for ice production under various experimental conditions. Ammonia/lithium nitrate was used as a working fluid considering different solution concentrations. The configuration 6-6-1 (6 inputs, 6 hidden and 1 output neurons) presented an excellent agreement (R>0.986) between experimental and simulated values. The used inputs parameters were: the solution concentration, the cooling water temperature, the generation temperature, the ambient temperature, the generation pressure and the solar radiation. The sensitivity analysis showed that all studied input variables have effect on the COP prediction but the generation pressure is the most influential parameter on the COP, while the rest of input parameters were less significant. COP performance was also determined by inverting ANN to calculate the unknown input parameter from a required COP. Because of the high accuracy and short computing time makes this methodology useful to simulate and to optimize the solar refrigerator system.

Inverse neural network for optimal performance in polygeneration systems

In this paper, inverse neural network (ANNi) is applied to optimization of operating conditions or parameters in energy processes. The proposed method ANNi is a new tool which inverts the artificial neural network (ANN), and it uses a Nelder-Mead optimization method to find the optimum parameter value (or unknown parameter) for a given required condition in the process. In order to accomplish the target, first, it is necessary to build the artificial neural network (ANN) that simulates the output parameters for a polygeneration process. In general, this class of ANN model is constituted of a feedforward network with one hidden layer to simulate output layer, considering well-known input parameters of the process. Normally, a Levenberg–Marquardt learning algorithm, hyperbolic tangent sigmoid transfer-function, linear transfer-function and several neurons in the hidden layer (due to the complexity of the process) are considered in the constructed model. After that, ANN model is inverted. With a required output value and some input parameters it is possible to calculate the unknown input parameter using the Nelder-Mead algorithm. ANNi results on three different applications in energy processes showed that ANNi is in good agreement with target and calculated input data. Consequently, ANNi is applied to determine the optimal parameters, and it already has applications in different processes with a very short elapsed time (seconds). Therefore, this methodology can be useful for the controlling of engineering processes.

Using a variance-based sensitivity analysis for analyzing the relation between measurements and unknown parameters of a physical model

Abstract. An implementation of uncertainty analysis (UA) and quantitative global sensitivity analysis (SA) is applied to the non-linear inversion of gravity changes and three-dimensional displacement data which were measured in and active volcanic area. A didactic example is included to illustrate the computational procedure. The main emphasis is placed on the problem of extended Fourier amplitude sensitivity test (E-FAST). This method produces the total sensitivity indices (TSIs), so that all interactions between the unknown input parameters are taken into account. The possible correlations between the output an the input parameters can be evaluated by uncertainty analysis. Uncertainty analysis results indicate the general fit between the physical model and the measurements. Results of the sensitivity analysis show quite different sensitivities for the measured changes as they relate to the unknown parameters of a physical model for an elastic-gravitational source. Assuming a fixed number of executions, thirty different seeds are observed to determine the stability of this method.

User Influence on Indoor Aerosol Model Calibration

Calibration, or in other words ”validation”, of complex indoor aerosol models that simulate the dynamic behavior of particle number size distributions are often assumed to solely depend on the characteristics of the model and its setup. The user influence is rarely mentioned in that regard. This paper shows, with a simple exercise, the user influence on the calibration of an indoor aerosol model. It is also shown that a reasonable model simulation was achieved with a different understanding of the system modeled and several input parameter values. We utilized a single compartment and size-resolved indoor aerosol model approach to be calibrated against a model room. This kind of simple indoor aerosol models is very common in the literature and widely used in the analysis of indoor-to-outdoor relationship of aerosol particles. The input parameters for such indoor aerosol models are: outdoor particle number size distributions, indoor domain geometries, ventilation rate, penetration factor, and friction velocity (or deposition rate onto indoor surfaces). For simplicity, we considered the penetration factor and friction velocity are the only unknown input parameters to be chosen freely by the user so that the model is calibrated. We made it clear by this study that a user can influence the input parameter values significantly. Even though this suggests different sets of input parameter values can be valid for a model calibration, the model simulation differences between different calibration results remained within 1%. This implies that it is more challenging to calibrate a complex indoor aerosol model that requires many input parameters.

Stability of algorithms for a two domain natural convection problem and observed model uncertainty

Two numerical algorithms are presented that couple a Boussinesq model of natural heat convection in two domains, motivated by the dynamic core of climate models. The first uses a monolithic coupling across the fluid–fluid interface. The second is a parallel implementation decoupled via a partitioned time stepping scheme with two-way communication. These new approaches are both proven to be unconditionally stable, a property not shared by traditional climate codes that use one-way coupling. Another critical property for a robust climate code is the reliability of the computation with respect to noise in unknown input parameters. This effect is measured by adding stochastic noise to two nonlinear coupling terms, involving momentum and heat transfer. Using an uncertainty quantification method known as stochastic collocation, we empirically measure the resulting variance in average surface temperature for each numerical model, including a third variant that employs one-way coupling for comparison. Throughout the duration of the simulation, we observe the smallest increase in variance using the monolithic algorithm and the largest increase using the one-way coupled algorithm.

Asymptotic Tracking for Aircraft via Robust and Adaptive Dynamic Inversion Methods

Two asymptotic tracking controllers are designed in this paper, which combine model reference adaptive control and dynamic inversion methodologies in conjunction with the robust integral of the signum of the error (RISE) technique for output tracking of an aircraft system in the presence of parametric uncertainty and unknown, nonlinear disturbances, which are not linearly parameterizable (non-LP). The control designs are complicated by the fact that the control input is multiplied by an uncertain, non-square matrix. A robust control design is presented first, in which partial knowledge of the aircraft model along with constant feedforward estimates of the unknown input parameters are used with a robust control term to stabilize the system. Motivated by the desire to reduce the need for high-gain feedback, an adaptive extension is then presented, in which feedforward adaptive estimates of the input uncertainty are used. These results show how asymptotic tracking control can be achieved for a nonlinear system in the presence of a non-square input matrix containing parametric uncertainty and nonlinear, non-LP disturbances. Asymptotic output tracking is proven via Lyapunov stability analysis, and high-fidelity simulation results are provided to verify the efficacy of the proposed controllers.

Bayesian Approach for Parameter Estimation in the Structural Analysis and Prognosis

In this study, a Bayesian framework is outlined for the parameter estimation that arises during the uncertainty quantification in the numerical simulation as well as in the prognosis of the structural performance. In the framework, the parameters are estimated in the form of posterior distribution conditional on the provided data. Several case studies that implement the estimation are presented to illustrate the concept. First one is an inverse estimation, in which the unknown input parameters are inversely estimated based on a finite number of measured response data. Next one is a metamodel uncertainty problem that arises when the original response function is approximated by a metamodel using a finite set of response values. Third and fourth one are a prognostics problem, in which the unknown parameters of the degradation model are estimated based on the monitored data. During the numerical implementation, Markov Chain Monte Carlo (MCMC) method is employed, which is a modern computational technique for the efficient and straightforward estimation of parameters. Once the samples are obtained, one can proceed to the posterior predictive inference on the response at the unobserved points or at the future time in the form of confidence interval.

Application of the Bayesian calibration methodology for the parameter estimation in CoupModel

Abstract. This study provides results for the optimization strategy of highly parameterized models, especially with a high number of unknown input parameters and joint problems in terms of sufficient parameter space. Consequently, the uncertainty in model parameterization and measurements must be considered when highly variable nitrogen losses, e.g. N leaching, are to be predicted. The Bayesian calibration methodology was used to investigate the parameter uncertainty of the process-based CoupModel. Bayesian methods link prior probability distributions of input parameters to likelihood estimates of the simulation results by comparison with measured values. The uncertainty in the updated posterior parameters can be used to conduct an uncertainty analysis of the model output. A number of 24 model variables were optimized during 20 000 simulations to find the "optimum" value for each parameter. The likelihood was computed by comparing simulation results with observed values of 23 output variables including soil water contents, soil temperatures, groundwater level, soil mineral nitrogen, nitrate concentrations below the root zone, denitrification and harvested carbon from grassland plots in Northern Germany for the period 1997–2002. The posterior parameter space was sampled with the Markov Chain Monte Carlo approach to obtain plot-specific posterior parameter distributions for each system. Posterior distributions of the parameters narrowed down in the accepted runs, thus uncertainty decreased. Results from the single-plot optimization showed a plausible reproduction of soil temperatures, soil water contents and water tensions in different soil depths for both systems. The model performed better for these abiotic system properties compared to the results for harvested carbon and soil mineral nitrogen dynamics. The high variability in modeled nitrogen leaching showed that the soil nitrogen conditions are highly uncertain associated with low modeling efficiencies. Simulated nitrate leaching was compared to more general, site-specific estimations, indicating a higher leaching during the seepage periods for both simulated grassland systems.