Uncertainty Quantification and Robust Optimization in Engineering
Lecture Notes in Mechanical Engineering, 2019
The application and use of engineering components such as engines, wings, or complete airplanes a... more The application and use of engineering components such as engines, wings, or complete airplanes are all subject to uncertainties, either of operational nature (variations in speed, angle of attack, pressure, etc) or of geometrical nature (manufacturing tolerances or uncertainties due to wearing). These uncertainties can have an important effect on the performance (output) of these components. The effect of these uncertain parameters should be quantified and included in the final solution to assure and improve the quality of the results. Polynomial chaos is a recent methodology to account for uncertainties that can be described by a distribution function. The method allows to obtain the distribution of the output for given input distributions. Over the last decade, with increasing computational resources and hardware power, design optimization is receiving more and more interest in aeronautical applications. Due to the uncertainties in a design process, the objective is also uncertain. Robust optimization is an extension of conventional optimization where uncertainties are also included in the design procedure. Using polynomial chaos expansion, the uncertain objective can be characterized by its mean and its variance. Therefore, it becomes a multi-objective problem and gradient based optimization requires the gradient of both quantities. These gradients can be obtained from the polynomial chaos expansion of the gradient of the objective. In this chapter, first, a brief introduction to polynomial chaos approach for uncertainty quantification is provided. Further its formulation with adjoint methods is described for gradient based robust optimization. The approach is applied to the optimal shape design of a transonic airfoil under uncertainties.
WIT Transactions on Information and Communication Technologies, 1970
In this paper we discuss the application of the Object Oriented Programming (OOP) paradigm to the... more In this paper we discuss the application of the Object Oriented Programming (OOP) paradigm to the development and implementation of a software system for the interactive visualization of CFD data. We show that OOP provides both a powerful framework to analyze and design the system as well as an efficient implementation tool.In particular we show how a high degree of interactivity and user-friendliness can be achieved through the use of class libraries encapsulating graphics, networking and interfacing. We illustrate our approach with examples taken from the development of CFView, which is an advanced interactive visualization tool capable of handling both structured and unstructured meshes. We include a discussion of how OOP facilitates parallelization.
Universal generator of irregular multidimensional multiextremal functions
2017 IEEE East-West Design & Test Symposium (EWDTS), 2017
The paper describes the development of a universal test functions generator to validate and setup... more The paper describes the development of a universal test functions generator to validate and setup the algorithms for investigating multiextremal systems characteristics. The main difference between the proposed functions and the set of known multiextremal test functions is their irregularity related to the extremes coordinate location and their respective quantitative values, since all known test functions are based on the analytical functions. The functionality of the developed “Lambda Function” software is described in details to validate such approach, supporting the test functions controlled generation, their editing and studying the multi-dimensional, multi-extremal test functions characteristics. Its fundamental novelty is that these functions are based on the multiplicative functions, developed by R. Neudorf, which extreme and multidimensionality characteristics enable to completely exclude the influence of their structure patterns when the results are computed. The “Lambda Function” software provides a wide range of possibilities to develop and investigate the test functions being created. Such results can be applied in variety of research domains, and the developed software can be easily integrated with third-party software, based on its extensive modular design.
“Cut-Glue” Approximation Based on Pseudo-genetic Algorithm for Strongly Nonlinear Parametric Dependencies of Mathematical Models
In the present work we consider one of the basic methods of Cut-Glue approximation—the approximat... more In the present work we consider one of the basic methods of Cut-Glue approximation—the approximation method for fragments with essentially nonlinear dependencies. As an instrument of approximation, a hybrid application of the classical regression analysis is used and specially developed for the evolutionarily modified genetic algorithm. The proposed approach allows finding the optimal dependence of the specified fragment.
A high-speed hybrid algorithm of monochrome multitone images approximation
2017 IEEE East-West Design & Test Symposium (EWDTS), 2017
The paper considers the problem of increasing the speed of monochrome multitone image (MMI) appro... more The paper considers the problem of increasing the speed of monochrome multitone image (MMI) approximation, which consists in replacement of original palette with palette that has less number of tones. Often, for solving such a problem, the heuristic optimization-search algorithms are used. Their drawback is that, they cannot guarantee to find the solution for the given optimization criteria, which motivates to find the approximating palette of the potential extreme. The solution of this problem is to define the deterministic algorithm, that guarantees finding the extreme, through the integration with the heuristic algorithm. Such hybridization takes in consideration the main advantage of these 2 approaches: (1) speed of the heuristic algorithm and (2) accuracy of the deterministic one. The hybrid algorithm applies the heuristic approach to decrease the search area and the deterministic approach guarantees to find extremes within this area. This approach defines the time, as the opti...
The use of piezoelectric ceramics as actuators in flapping plate systems is interesting due to th... more The use of piezoelectric ceramics as actuators in flapping plate systems is interesting due to the low power consumption and high energy efficiency. Fluid flow is induced by these piezoelectric fans by converting electric energy into mechanical vibrations with the use of piezoelectric patches bonded to a passive elastic plate. By applying an alternating voltage the patch will periodically start to contract and expand. If the frequency of the AC voltage is equal to the first resonance frequency of the structure, a sufficiently large dynamic tip deflection can be obtained, which is required to induce an air flow by the flapping plate. A considerable increase in heat transfer could be obtained by using these piezo fans for cooling of electronic devices [2]. Another application is applying these piezoelectric oscillating mechanical systems as flapping wings for MAVs [6]. The motion of the piezo fan is determined by the actuation frequency and the modal parameters. The structural optimiz...
Monochrome multitone image approximation with low-dimensional palette
2016 IEEE East-West Design & Test Symposium (EWDTS), 2016
The report is devoted to the problem of suboptimal approximation of monochrome multitone image. T... more The report is devoted to the problem of suboptimal approximation of monochrome multitone image. The proposed approximation consists in replacing the original image tone palette with a reduced size tone palette. The suboptimum approximation is based on the evolutionarily genetic algorithm. The algorithm provides the suboptimal selection of tones for the new palette and its covering range. The weight-dividing strategy of the original monochrome multitone image's frequency diagram of brightness is used to define the initial tones of the new palette and its covering range. These numerical vectors, considered as chromosomes, define the approximated image created by 2 respective chromosomes. The standard genetic operators of mutation is crossed over with the selection strategy, which provides an effective approximation optimization according to the criteria of the least square deviation between pixels of their original tones, when related to the new palette tones. The developed algori...
“Cut-Glue” Approximation Method for Strongly Nonlinear and Multidimensional Object Dependencies Modeling
The main difficulties in modeling a variety of technical systems are experienced when creating ap... more The main difficulties in modeling a variety of technical systems are experienced when creating appropriate mathematical objects to simulate their behavior. It is well known that such inter-objects dependences are defined with their variable with strong nonlinear and multidimensional characteristics. The mathematical models (MM) dependences are approximated with advance numerical methods, such as polynomial decomposition, spline functions, etc., which are today still very time-consuming and laborious to be correctly created and applied, also considering their precision. In this paper, the authors have created and investigated the high-precision analytical approximation method to model the nonlinear MM dependences, which are defined only by appropriate analytical functions. These approaches have been already studied in details, where the Cut-Glue approximation method defines 1-dimensional dependences, and to 2-dimensional dependences were approximated with analytical functions of 2 ar...
“Cut-Glue” Approximation Based on Particle Swarm Sub-optimization for Strongly Nonlinear Parametric Dependencies of Mathematical Models
The difficulties in the experimental and computer modeling of the static and dynamic transport me... more The difficulties in the experimental and computer modeling of the static and dynamic transport media are associated with a significant non-linearity of the present model dependencies. This is due to the mechanical friction effects, backlash, aerodynamic effects and other physical phenomena. The construction of the mathematical models (MM) for such objects is most often associated with the mathematical treatment of the experimental data. The point-like dependencies of the output variables linked to the input are essentially non-linear, piecewise and sometimes discontinuous. These dependencies, when approximated with polynomial or spline functions, are difficult to control, and thus associated with large errors. The radically new solution to this problem is proposed in paper [1]. This method is called the «cut-glue» approximation (CGA) method. It is based on partitioning the simulated dependence within specified areas; approximating each fragment with the polynomial dependencies; mult...
Human Heart Blood Flow Numerical Modelling and Simulations
Lecture Notes in Mechanical Engineering, 2019
In order to make a correct choice of the artificial heart valve for curing patients with cardio v... more In order to make a correct choice of the artificial heart valve for curing patients with cardio vascular disorder it is very important to know in detail the blood flow in the heart of the specific patient. In this book chapter, two separate approaches are presented on how to model the blood flow within the real human heart. The first approach is based on Magnetic Resonance Imaging/Tomography to get shape (“geometry”) of internal heart volumes in time (tens or hundreds of frames for one heartbeat), and applies a Computational Fluid Dynamics (CFD) tool for simulating and visualizing a blood flow. The second approach is based on the SIMULIA Abaqus LHHM model, combining the structural heart Finite Element Model (FEM) with the CFD simulation to solve the fluid structure interaction problem. The blood flow circulation through the heart is numerically simulated with a modern FlowVision code that has a fully automatic mesh generation using arbitrary cell shapes for dynamic mesh refinement and taking into account the motion of the heart surface, applying the Euler coordinates. The second approach solves the bidirectional fluid-structure interaction problem applying the general purpose CFD code FlowVision and the SIMULIA Living Heart Human Model (LHHM), a dynamic, anatomically realistic, 4-chamber heart model with mechanical valves that considers the interplay and coupling of electrical and mechanical fields, which are acting simultaneously to regulate the heart filling, ejection, and overall like pump functions. LHHM natively includes a 1D fluid network model capable of representing dynamic pressure/volume changes in the intra- and extra-cardiac circulation. In the current work, this network model is first replaced with a full 3D blood model (solved in FlowVision) that provides detailed spatial and temporal resolution of cardiac hemodynamic driven by motions of the beating heart and constrained with appropriate time-varying boundary conditions derived from the literature. After validating this approach, the bidirectional coupling between the blood flow CFD model and the LHHM electromechanical model is activated by using the SIMULIA co-simulation engine and in conclusion the modelling details and results of interest are discussed. Using the real heart MRI/MRT has tested the described approaches of simulating the blood flow and SIMULIA Abaqus LHHM and the simulation results are presented.
This work presents an innovative approach adopted for the development of a new numerical software... more This work presents an innovative approach adopted for the development of a new numerical software framework for accelerating dense linear algebra calculations and its application within an engineering context. In particular, response surface models (RSM) are a key tool to reduce the computational effort involved in engineering design processes like design optimization. However, RSMs may prove to be too expensive to be computed when the dimensionality of the system and/or the size of the dataset to be synthesized is significantly high or when a large number of different response surfaces has to be calculated in order to improve the overall accuracy (e.g. like when using ensemble modelling techniques). On the other hand, the potential of modern hybrid hardware (e.g. multicore, GPUs) is not exploited by current engineering tools, while they can lead to a significant performance improvement. To fill this gap, a software framework is being developed that enables the hybrid and scalable a...
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