Mixed Uncertainties Research Articles

Design and Evaluation of an Automatic Extraventricular Drainage Control System

Until this day, the drainage of cerebrospinal fluid, as necessary in case of an acute increased intracranial pressure, is conducted manually by adjusting the hydrostatic height of an external drainage bag. The associated problems with the manual open-loop control strategy are an increasing pressure error over time periods involving no correction and the inherent risk of an overdrainage, which may occur, for example, after changes of the patient’s upper body inclination angle. In this paper, an automatic control strategy is suggested to alleviate these problems thereby increasing the patient’s safety and the overall quality of the therapy. The automatic controller presented in this paper is designed for our newly developed intelligent external ventricular drainage system. The proposed controller has to guarantee robustness and performance in face of uncertain patient intracranial dynamics and nonlinearities associated with the actuator. The controller is thus designed to guarantee robust performance using a mixed uncertainty modeling approach and extended by a self-scheduling approach to compensate for input nonlinearities. Controller performance is validated in nonlinear simulations, an experimental test setup, and animal experiments, involving pigs with an artificially induced hydrocephalus.

Mixed Uncertainty Analysis of Pole Placement and H∞ Controllers for Directional Drilling Attitude Tracking

This paper describes the design of attitude-hold controllers and their subsequent stability and performance analysis for directional drilling tools as typically used in the oil industry. Based on an input transformation developed in earlier work that partially linearizes and decouples the plant dynamics of the drilling tool, the resulting plant model is used as the basis for both pole placement and optimal H∞ controller designs. A mixed uncertainty stability and performance analysis is then performed on each of the controller designs. Results for a transient simulation of the proposed controller are also presented.

Humanitarian logistics network design under mixed uncertainty

In this paper, we address a two-echelon humanitarian logistics network design problem involving multiple central warehouses (CWs) and local distribution centers (LDCs) and develop a novel two-stage scenario-based possibilistic-stochastic programming (SBPSP) approach. The research is motivated by the urgent need for designing a relief network in Tehran in preparation for potential earthquakes to cope with the main logistical problems in pre- and post-disaster phases. During the first stage, the locations for CWs and LDCs are determined along with the prepositioned inventory levels for the relief supplies. In this stage, inherent uncertainties in both supply and demand data as well as the availability level of the transportation network's routes after an earthquake are taken into account. In the second stage, a relief distribution plan is developed based on various disaster scenarios aiming to minimize: total distribution time, the maximum weighted distribution time for the critical items, total cost of unused inventories and weighted shortage cost of unmet demands. A tailored differential evolution (DE) algorithm is developed to find good enough feasible solutions within a reasonable CPU time. Computational results using real data reveal promising performance of the proposed SBPSP model in comparison with the existing relief network in Tehran. The paper contributes to the literature on optimization based design of relief networks under mixed possibilistic-stochastic uncertainty and supports informed decision making by local authorities in increasing resilience of urban areas to natural disasters.

A Probabilistic and Interval Hybrid Reliability Analysis Method for Structures with Correlated Uncertain Parameters

This paper proposes a probability-interval mixed uncertainty model considering parametric correlations and a corresponding structural reliability analysis method. First of all, we introduce the sample correlation coefficients to express the correlations between different kinds of uncertain variables including probability and interval variables. Then dependent parameters are transformed into independent ones through a matrix transformation. A reliability analysis model is put forward, and an efficient method is built to obtain the reliability index or failure probability interval of the structure. Finally, four numerical examples are provided to verify the validity of the method.

Multi-fidelity robust aerodynamic design optimization under mixed uncertainty

The objective of this paper is to present a robust optimization algorithm for computationally efficient airfoil design under mixed (inherent and epistemic) uncertainty using a multi-fidelity approach. This algorithm exploits stochastic expansions derived from the Non-Intrusive Polynomial Chaos (NIPC) technique to create surrogate models utilized in the optimization process. A combined NIPC expansion approach is used, where both the design and the mixed uncertain parameters are the independent variables of the surrogate model. To reduce the computational cost, the high-fidelity Computational Fluid Dynamics (CFD) model is replaced by a suitably corrected low-fidelity one, the latter being evaluated using the same CFD solver but with a coarser mesh. The model correction is implemented to the low-fidelity CFD solutions utilized for the construction of stochastic surrogate by using multi-point Output Space Mapping (OSM) technique. The proposed algorithm is applied to the design of NACA 4-digit airfoils with four deterministic design variables (the airfoil shape parameters and the angle of attack), one aleatory uncertain variable (the Mach number) and one epistemic variable (β, a geometry parameter) to demonstrate robust optimization under mixed uncertainties. In terms of computational cost, the proposed technique outperforms the conventional approach that exclusively uses the high-fidelity model to create the surrogates. The design cost reduces to only 34 equivalent high-fidelity model evaluations versus 168 obtained with the conventional method.

Direct and composite iterative neural control for cooperative dynamic positioning of marine surface vessels

This paper considers the cooperative dynamic positioning of multiple marine surface vessels in the presence of dynamical uncertainty and time-varying ocean disturbances. The objective is to enable a group of vessels to automatically position themselves in a desired time-varying formation and track a reference position. By employing a dynamic surface control technique, distributed adaptive controllers are derived on the basis of the information of neighboring vessels. Neural network with iterative updating laws is used to accurately identify the dynamical uncertainty and time-varying ocean disturbances. Two types of adaptive laws are proposed and validated: (1) direct iterative updating laws based on the velocity tracking errors; (2) composite iterative updating laws based on the tracking errors and the prediction errors. For both cases, Lyapunov–Krasovskii functionals are employed to analyze the stability of the closed-loop network, and uniform ultimate boundedness of error signals are established. The key features of the proposed controllers are as follows. First, the information exchanges are reduced by employing a distributed control strategy. Second, by using the iterative updating laws, the mixed uncertainty including the internal model uncertainty and external time-varying ocean disturbances can be compensated. Besides, the proposed controllers are easier to implement in digital processors with the derivative-free updating laws. Third, the prediction errors and tracking errors are combined to construct the composite iterative neural control laws, which are able to achieve faster adaptation and improved performance. Comparison studies are given to show the effectiveness of the proposed methods.

Response of Arctic Ocean stratification to changing river runoff in a column model

AbstractA one‐dimensional model of the atmosphere‐ice‐ocean column is used to study the effects of changing river runoff to the Arctic Ocean. River runoff is the largest contributor of freshwater to the Arctic and is expected to increase as the hydrological cycle accelerates due to global warming. The column model simulates the stratification of the Arctic Ocean reasonably well, capturing important features such as the fresh surface layer, the salty cold halocline, and the temperature maximum within the Atlantic Water layer. The model is run for 500 years with prescribed boundary conditions to reach steady state solutions. Increasing river runoff is found to strengthen the stratification and to produce a fresher and shallower surface mixed layer with warming (up to ∼1°C for a doubling of present‐day runoff) in the Atlantic Water layer below. An important consequence is that the effect of the larger vertical temperature gradient is able to balance that of the stronger stratification and yield a close to constant vertical heat flux toward the surface. As a result, the sea ice response is small, showing only slight increase (up to ∼15 cm for a doubling of present‐day runoff) in annual mean ice thickness. Limitations of the study include the idealized nature of the column model and uncertainties in the background vertical mixing within the Arctic Ocean.

Multiobjective robust optimization for crashworthiness design of foam filled thin-walled structures with random and interval uncertainties

To improve crashing behavior of aluminum foam-filler columns design optimization has proven rather effective and been extensively used. Nevertheless, an optimal design could become less meaningful or even unacceptable when some uncertainties present. Parametric uncertainties are often treated as random variables in conventional robust optimization. Taking foam filled thin-walled structure as an example, which could also exhibit probabilistic and/or bounded nature of uncertainties, it may be more appropriate to describe them with hybrid uncertainties by using random variables and interval variables. Furthermore, evaluation of product quality often involves a number of criteria which may conflict with each other. To address the issue, this paper presents a multiobjective robust optimization to explore the design problems of parametric uncertainties involving both random and interval variables in foam filled thin-walled tube, in which specific energy absorption (SEA) and peak crushing force are considered as the design objectives and the average crash force is considered as the design constraint. A nesting optimization procedure is proposed here to solve the multiobjective robust optimization problem. In the outer loop, the Non-dominated Sorting Genetic Algorithm II (NSGA-II), is implemented to generate robust Pareto solution. In the inner loop the Monte Carlo simulation is performed to evaluate the impact responses of the mixed uncertainties to the robustness of optimized design. The example demonstrates the effectiveness of the proposed robust crashworthiness optimization involving both random and interval variables.

Quantification of margins and mixed uncertainties using evidence theory and stochastic expansions

The objective of this paper is to implement Dempster–Shafer Theory of Evidence (DSTE) in the presence of mixed (aleatory and multiple sources of epistemic) uncertainty to the reliability and performance assessment of complex engineering systems through the use of quantification of margins and uncertainties (QMU) methodology. This study focuses on quantifying the simulation uncertainties, both in the design condition and the performance boundaries along with the determination of margins. To address the possibility of multiple sources and intervals for epistemic uncertainty characterization, DSTE is used for uncertainty quantification. An approach to incorporate aleatory uncertainty in Dempster–Shafer structures is presented by discretizing the aleatory variable distributions into sets of intervals. In view of excessive computational costs for large scale applications and repetitive simulations needed for DSTE analysis, a stochastic response surface based on point-collocation non-intrusive polynomial chaos (NIPC) has been implemented as the surrogate for the model response. The technique is demonstrated on a model problem with non-linear analytical functions representing the outputs and performance boundaries of two coupled systems. Finally, the QMU approach is demonstrated on a multi-disciplinary analysis of a high speed civil transport (HSCT).

Robust consensus for linear multi-agent systems with mixed uncertainties

This paper studies the robust consensus problem for a class of linear multi-agent systems (MASs) with polytopic uncertainties and external disturbances. The uncertainties appear in both the dynamics of each agent and the topology of the overall network. Based on Lyapunov stability theory, the robust consensus problem is converted to the robust H∞ stabilization of the error system. With the aid of the homogeneous parameter-dependent (HPD) Lyapunov functions and sum of squares (SOS) technique, the robust consensus problem is further formulated as an SOS programming. Sufficient conditions to achieve robust consensus with disturbance rejection capability are presented in terms of SOS constraints. As an extension, the robust consensus problem for discrete-time MASs is studied in a similar way. Numerical examples are provided to illustrate the effectiveness of the approach.

Global Sensitivity Analysis and Uncertainty Quantification for a Hypersonic Shock Interaction Flow

Hypersonic gas flows over concentric double-cone configurations are commonly used to investigate shock–shock and shock wave/boundary-layer interaction phenomena, and are characterized by the formation of interacting flow structures that are highly sensitive to models used in flow simulation. The work presented here is intended to clarify the influence of several modeling parameters and approximations on simulation output quantities through a more general and systematic approach than has previously been employed for this type of flow, with the ultimate goal of improved model validation for simulation of hypersonic shock interactions. Global sensitivity analysis and uncertainty quantification techniques are integrated with a direct simulation Monte Carlo gas flow simulation code, and a large number of these Monte Carlo simulations are performed for a representative hypersonic double-cone flow. Aleatory and epistemic uncertainties are considered in sensitivity analysis/uncertainty quantification calculations, both independently and in combination, through a variety of probabilistic sampling procedures. These procedures include a novel uncertainty quantification technique that combines elements of importance sampling sensitivity analysis with Latin hypercube sampling, as an efficient surrogate-free means of simultaneously considering mixed uncertainty types. Following a strong engineering interest in surface heating augmentation due to hypersonic shock wave/boundary-layer interaction, this paper focuses on surface heat flux at a shock impingement point as an output quantity in sensitivity analysis/uncertainty quantification calculations; other output quantities of interest include impingement point pressure and the integrated force and heat transfer rate over the model surface.

Quantification of Margins and Uncertainties for Integrated Spacecraft Systems Models

The objective of this study was to introduce an efficient and accurate approach to the quantification of margins and uncertainties for integrated spacecraft systems models. In this study, stochastic expansions, based on nonintrusive polynomial chaos, were used for efficient representation of uncertainty both in design metrics and associated performance limits of a system. Additionally, procedures were outlined for analyzing systems that contain different uncertainty types between the performance metrics and performance limits. These methodologies were demonstrated on two model problems, each possessing mixed (epistemic and aleatory) uncertainty, which was propagated through the models using second-order probability. The first was a complex system model of highly nonlinear analytical functions. The second was a coupled multisystem, physics-based model for spacecraft reentry. The performance metrics consisted of two systems used to determine the maximum load, the necessary bank angle correction, and maximum convective heat load along a reentry trajectory. Overall, the methodologies and examples of this work have detailed an efficient approach for measuring the reliability of complex spacecraft systems models, as well as the importance of quantifying margins and uncertainties for the design of reliable systems.

Reliability Analysis in Presence of Random Variables and Fuzzy Variables

For mixed uncertainties of random variables and fuzzy variables in engineering, three indices, that is, interval reliability index, mean reliability index, and numerical reliability index, are proposed to measure safety of structure. Comparing to the reliability membership function for measuring the safety in case of mixed uncertainties, the proposed indices are more intuitive and easier to represent the safety degree of the engineering structure, and they are more suitable for the reliability design in the case of the mixed uncertainties. The differences and relations among three proposed indices are investigated, and their applicability is compared. Furthermore, a technique based on the probability density function evolution method is employed to improve the computational efficiency of the proposed indices. At last, a numerical example and two engineering examples are illustrated to demonstrate the feasibility, reasonability, and efficiency of the computational technique of the proposed indices.

A MIXED UNCERTAINTY QUANTIFICATION APPROACH USING EVIDENCE THEORY AND STOCHASTIC EXPANSIONS

Uncertainty quantification (UQ) is the process of quantitative characterization and propagation of input uncertainties to the response measure of interest in experimental and computational models. The input uncertainties in computational models can be either aleatory i.e. irreducible inherent variations or epistemic i.e. reducible variability which arises from lack of knowledge. Previously, it has been shown that Dempster-Shafer Theory of Evidence (DSTE) can be applied to model epistemic uncertainty in case of uncertainty information coming from multiple sources. The objective of this paper is to model and propagate mixed uncertainty (aleatory and epistemic) using DSTE. In specific, the aleatory variables are modeled as Dempster-Shafer structures by discretizing them into sets of intervals according to their respective probability distributions. In order to avoid excessive computational cost associated with large scale applications, a stochastic response surface based on point-collocation non-intrusive polynomial chaos has been implemented as the surrogate model for the response. A convergence study for accurate representation of aleatory uncertainty in terms of minimum number of subintervals required is presented. The mixed UQ approach is demonstrated on a numerical example and high fidelity computational fluid dynamics study of transonic flow over RAE 2822 airfoil.

An ensemble classification approach for improved Land use/cover change detection

Abstract. Change Detection (CD) methods based on post-classification comparison approaches are claimed to provide potentially reliable results. They are considered to be most obvious quantitative method in the analysis of Land Use Land Cover (LULC) changes which provides from - to change information. But, the performance of post-classification comparison approaches highly depends on the accuracy of classification of individual images used for comparison. Hence, we present a classification approach that produce accurate classified results which aids to obtain improved change detection results. Machine learning is a part of broader framework in change detection, where neural networks have drawn much attention. Neural network algorithms adaptively estimate continuous functions from input data without mathematical representation of output dependence on input. A common practice for classification is to use Multi-Layer-Perceptron (MLP) neural network with backpropogation learning algorithm for prediction. To increase the ability of learning and prediction, multiple inputs (spectral, texture, topography, and multi-temporal information) are generally stacked to incorporate diversity of information. On the other hand literatures claims backpropagation algorithm to exhibit weak and unstable learning in use of multiple inputs, while dealing with complex datasets characterized by mixed uncertainty levels. To address the problem of learning complex information, we propose an ensemble classification technique that incorporates multiple inputs for classification unlike traditional stacking of multiple input data. In this paper, we present an Endorsement Theory based ensemble classification that integrates multiple information, in terms of prediction probabilities, to produce final classification results. Three different input datasets are used in this study: spectral, texture and indices, from SPOT-4 multispectral imagery captured on 1998 and 2003. Each SPOT image is classified individually to produce the classified output and used for comparison. A MLP is trained with the input datasets separately using a backpropagation learning algorithm and prediction probabilities are produced for each pixel as evidence against each LU/LC class. An integration rule based on Endorsement Theory is applied to these multiple evidence by considering their individual contribution and the most probable class of a pixel is identified. Integration of the three datasets by the proposed method is found to produce 88.4 % and 84.6 % for individual image. The proposed method improves the potential of using SPOT satellite imagery for change detection.

Uncertainty Quantification of Hypersonic Reentry Flows with Sparse Sampling and Stochastic Expansions

The objective of this study was to introduce a combined sparse sampling and stochastic expansion approach for efficient and accurate uncertainty quantification. The new techniques are applied to high-fidelity, hypersonic reentry flow simulations, which may contain large numbers of aleatory and epistemic uncertainties. Stochastic expansion coefficients were obtained using the point-collocation nonintrusive polynomial chaos technique with a number of samples less than the minimum number required for a total-order expansion. This study introduced two methods of measuring the accuracy of the expansion coefficients, as well as their convergence with iteratively increasing sample size. The newly developed approaches were demonstrated on two model problems. The first was a model for stagnation point, convective heat transfer in hypersonic flow. Mixed uncertainty quantification analysis results showed that accurate expansion coefficients could be obtained with half of the minimum number of samples required for a total-order expansion. The second problem was a high-fidelity, computational fluid dynamics model for radiative heat flux prediction on a hypersonic inflatable aerodynamic decelerator during Mars entry. The model consisted of 93 uncertain parameters, coming from both flowfield and radiation modeling. Results indicated that an accurate surrogate model could be obtained with only about 15% of the number of samples required for a total-order expansion when compared with previous work.

Evaluation of noise annotation lines: using noise to represent thematic uncertainty in maps

Noise annotation lines are a promising technique to visualize thematic uncertainty in maps. However, their potential has not yet been evaluated in user studies. In two experiments, we assessed the usability of this technique with respect to a different number of uncertainty levels as well as the influence of two design aspects of noise annotation lines: the grain and the width of the noise grid. We conducted a web-based study utilizing a qualitative comparison of 2 areas in 150 different maps. We recruited participants from Amazon Mechanical Turk with the majority being nonexperts with respect to the use of maps. Our findings suggest that for qualitative comparisons of “constant uncertainty” (i.e., constant uncertainty per area) in thematic maps, noise annotation lines can be used for up to six uncertainty levels. During comparison of four, six, and eight levels, the different designs of the technique yielded significantly different accuracies. We propose to use the “large noise width, coarse grain” design that was most successful. For “mixed uncertainty” (i.e., uncertainty is not constant per area) we observed a significant decrease in accuracy, but for four levels the technique can still be recommended. This article is a follow-up to our conference paper reporting on preliminary results of the first of the two experiments.

Distributed robust H∞ rotating consensus control for directed networks of second-order agents with mixed uncertainties and time-delay

In this paper, distributed robust H∞ rotating consensus control is investigated for a class of second-order multi-agent systems with mixed uncertainties and time-delay. Firstly, the rotating consensus is defined in the real field. To solve the consensus problem, two distributed protocols are introduced for networks with and without time-delay respectively. Then by employing Lyapunov approach and H∞ control theory, two sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to make all agents asymptotically reach rotating consensus with the desired H∞ performance. Finally, simulation results are provided to illustrate the effectiveness of our theoretical results.

Response-surface-based structural reliability analysis with random and interval mixed uncertainties

Traditional reliability analysis requires probability distributions of all the uncertain parameters. However, in many practical applications, the variation bounds can be only determined for the parameters with limited information. A complex hybrid reliability problem then will be caused when the random and interval variables coexist in a same structure. In this paper, by introducing the response surface technique, we develop a new hybrid reliability method to efficiently compute the interval of the failure probability of the structure due to the probability-interval hybrid uncertainty. The present method consists of a sequence of iterations. At each step, a response surface model is constructed for the limit-state function by using a quadratic polynomial and a modified axial experimental design method. An approximate hybrid reliability problem is created based on the response surface model, which is subsequently solved by an efficient decoupling approach. An updating strategy is suggested to improve the quality of the response surface and whereby ensure the reliability analysis precision. A computational procedure is then summarized for the whole iterations. Four numerical examples and also a practical application are provided to demonstrate the effectiveness of the present method.

Exponential synchronization for fractional‐order chaotic systems with mixed uncertainties

This article focuses on the problem of exponential synchronization for fractional‐order chaotic systems via a nonfragile controller. A criterion for α‐exponential stability of an error system is obtained using the drive‐response synchronization concept together with the Lyapunov stability theory and linear matrix inequalities approach. The uncertainty in system is considered with polytopic form together with structured form. The sufficient conditions are derived for two kinds of structured uncertainty, namely, (1) norm bounded one and (2) linear fractional transformation one. Finally, numerical examples are presented by taking the fractional‐order chaotic Lorenz system and fractional‐order chaotic Newton–Leipnik system to illustrate the applicability of the obtained theory. © 2014 Wiley Periodicals, Inc. Complexity 21: 114–125, 2015