Academic literature on the topic 'Iterative parametric runs'

Plant morphology modeling can be done mathematically which includes roots, stems, leaves, to flower. Modeling of plant stems using the Lindenmayer System (L-system) method is a writing returns that are repeated to form a visualization of an object. Deterministic L-system method is carried out by predicting the possible shape of a plant stem using its iterative writing rules based on the original object photo. The purpose of this study is to find a model of the plant stem with Deterministic Lindenmayer System method which will later be divided into two dimensional space three. The research was conducted by identifying objects in the form of pine tree trunks measured by the angle, thickness, and length of the stem. Then a deterministic and parametric model is built with L-system components . The stage is continued by visualizing the model in two dimensions and three dimensions. The result of this research is a visualization of a plant stem model that is close to the original. Addition color, thickness of the stem, as well as the parametric writing is done to get the results resembles the original. The iteration is limited to less than 20 iterations so that the simulation runs optimal.

Buildings have substantial impacts on energy consumption, the environment, and overall comfort of occupants. Rapidly increasing energy use associated with the building sector is a significant and growing problem. Despite advances in energy efficiency and building technology, U.S. energy consumption and resources use per capita continue to increase. This paper examines residential energy performance in a Pennsylvania (PA) single family home, to assess the impact of the most optimal options of building upgrades. Energy consumption in the residential sector has remained relatively steady for several years as increased energy efficiency gains has offset the surge in the number and average size of housing units. To that end, the average area of a U.S. home increased 45% from 1970s. Alternatively, the average number of occupants per household decreased 15% from 1970s. Both of these are alarming trends as it pertains to overall energy use outlooks. As a result, the steady downward energy consumption patterns are threatened to be offset by those trends. Hence, these trends could have negative impacts on energy efficiency gains and greenhouse gas (GHG) emissions. In 2018, the residential sector consumed approximately 21% of the total primary energy produced in the U.S., compared to just 10% in the late 1940’s. Furthermore, total annual U.S. residential energy swelled from a mere 6,000 trillion Btu’s in the 1950’s to almost 22,000 trillion Btu’s in 2016. As a result, 6% of total U.S. GHG emissions are attributed to the residential sector. Given the significant size of this industry, there is tremendous potential to reduce energy use and associated environmental impacts. For example, Pennsylvania could yield a 6.9% reduction of the state’s residential energy market load by 2020 if robust optimal energy conservation measures (ECMs) are adopted in single-family homes. Current and future market trends are projecting a steady increase in home size and population growth, which will inevitably exacerbate environmental and energy use issues further. Left unaddressed, the implications of population growth, rising energy prices, proliferation of modern home appliances and electronics, steadily increasing home sizes, and energy shortages could be profoundly detrimental to overall energy consumption patterns and the environment. This paper reviews the state of residential energy consumption patterns in the US and Pennsylvania specifically, to understand the underlying mechanisms of energy saving mechanisms and methodologies. Furthermore, the paper examines a myriad of energy efficiency measures available to homeowners. Lastly, the study assesses the impacts of building upgrades on energy use in a baseline PA single-family home via a parametric modeling approach, to provide comprehensive energy conservation and efficiency recommendations.       

Abstract State-of-the-art hot stamping processes offer improved material formability and therefore have potential to successfully form challenging components. The feasibility of components to be formed through these processes is dependent on their geometric design and its complex interactions with the hot stamping environment. In industrial practice, trial-and-error approaches are currently used to update non-feasible designs where simulation runs are needed each time a design change is made. These approaches make the design process resource intensive and require considerable numerical and process expertise. To demonstrate a superior approach, this study presents a novel application of a deep-learning-based optimisation platform which adopts a non-parametric geometric modelling strategy. Here, deep drawn corner geometries from different geometry subclasses were optimised to minimise wasted volume due to radii while avoiding excessive post-stamping thinning. A neural network was trained to generate families of deep drawn corner geometries where each geometry was conditioned on an input latent vector. Another neural network was trained to predict the thinning distributions obtained from forming these geometries through a hot stamping process. Guided by these distributions, the latent vector, and therefore geometry, was iteratively updated by a new gradient-based optimisation technique. Overall, it is demonstrated that the platform is capable of optimising geometries, irrespective of complexity, subject to imposed post-stamped thinning constraints.

Finding optimal operating conditions fast with a scarce budget of experimental runs is a key problem to speed up the development and scaling up of innovative bioprocesses. In this paper, a novel iterative methodology for the model-based design of dynamic experiments in modeling for optimization is developed and successfully applied to the optimization of a fed-batch bioreactor related to the production of r-interleukin-11 (rIL-11) whose DNA sequence has been cloned in an Escherichia coli strain. At each iteration, the proposed methodology resorts to a library of tendency models to increasingly bias bioreactor operating conditions towards an optimum. By selecting the ‘most informative’ tendency model in the sequel, the next dynamic experiment is defined by re-optimizing the input policy and calculating optimal sampling times. Model selection is based on minimizing an error measure which distinguishes between parametric and structural uncertainty to selectively bias data gathering towards improved operating conditions. The parametric uncertainty of tendency models is iteratively reduced using Global Sensitivity Analysis (GSA) to pinpoint which parameters are keys for estimating the objective function. Results obtained after just a few iterations are very promising.

ABSTRACTThe displacement response of a building structure to earthquake excitations is crucial for assessing its seismic damage, which is usually accompanied by structural nonlinear behavior. This study proposes an efficient method of quickly estimating the nonlinear displacement responses of seismically damaged buildings. By designing a set of sparsely and uniformly distributed samples in the multi‐dimensional parameter space, this method traverses all these samples to find the best set of parameters for a parametric numerical model of the building that minimizes the error between the simulated and the measured responses. Compared to existing model‐driven methods, the proposed method can efficiently match the high‐dimensional parameters of the assumed parametric model without tedious and less robust iterative optimization, even if the instrumented building sustains severe seismic damage and deviates significantly from its initial state. The shaking table test data of a full‐scale four‐story reinforced concrete moment‐resisting frame structure is used to justify the advantage of the method over the state‐of‐the‐art optimization‐based model‐driven method. The proposed method successfully estimated the structural responses of all the stories of the building with an average error of 4.6% for the maximum inter‐story drift across the five earthquake loading runs. It took only approximately 19 min to complete the calculation on a personal computer, which could be greatly accelerated given more computation cores because the traversal is inherently friendly to parallel computation.

We present an accelerated or “look-ahead” version of the Newton–Dinkelbach method, a well-known technique for solving fractional and parametric optimization problems. This acceleration halves the Bregman divergence between the current iterate and the optimal solution within every two iterations. Using the Bregman divergence as a potential in conjunction with combinatorial arguments, we obtain strongly polynomial algorithms in three applications domains. (i) For linear fractional combinatorial optimization, we show a convergence bound of [Formula: see text] iterations; the previous best bound was [Formula: see text] by Wang, Yang, and Zhang from 2006. (ii) We obtain a strongly polynomial label-correcting algorithm for solving linear feasibility systems with two variables per inequality (2VPI). For a 2VPI system with n variables and m constraints, our algorithm runs in O(mn) iterations. Every iteration takes O(mn) time for general 2VPI systems and [Formula: see text] time for the special case of deterministic Markov decision processes (DMDPs). This extends and strengthens a previous result by Madani from 2002 that showed a weakly polynomial bound for a variant of the Newton–Dinkelbach method for solving DMDPs. (iii) We give a simplified variant of the parametric submodular function minimization result from 2017 by Goemans, Gupta, and Jaillet. Funding: This project received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme [Grants 757481-ScaleOpt and 805241-QIP].

This paper discusses the approach of cooling design optimization of a high-pressure turbine (HPT) endwall with applied 3D conjugate heat transfer (CHT) computational fluid dynamics (CFD). This study involved the optimization of the spacing of impingement jet array and the exit width of shaped holes, which are different for each cooling cavity. The optimization objectives were to reduce the wall-temperature level and to increase the aerodynamic performance. The optimization methodology consisted of an in-house parametric design and CFD mesh generation tool, a CHT CFD solver, a database of CFD results, a metamodel, and an algorithm for multi-objective optimization. The CFD tool was validated against experimental data of an endwall at CHT conditions. The metamodel, which could efficiently estimate the optimization objectives of new individuals without CFD runs, was developed and coupled with nondominated sorting genetic algorithm II (NSGA II) to accelerate the optimization process. Through the optimization search, the Pareto front of the problem was found in each iteration. The accuracy of metamodel with more iterations was improved by enriching database. But optimal designs found by the last iteration are almost identical with those of the first iteration. Through analyzing extra CFD results, it was demonstrated that the design variables in the Pareto front successfully reached the optimal values. The optimal pitches of impingement arrays could be decided accommodating the local thermal load while avoiding jet lift-off of film coolant. It was also suggested that cylindrical film holes near throat should be beneficial to both aerodynamic and cooling performances.

The success of shape optimisation depends significantly on the parametrisation of the shape. Ideally, it defines a very rich variation in shape, allows for rapid grid generation of high quality, and expresses the shape in a standard Computer Aided Design (CAD) representation. While most existing parametrisation methods fail at least one of these criteria, this work introduces a novel parametrisation method, which satisfies all three. A tri-variate B-spline volume is used to define the volume to be optimised. The position of the external control points are used as design parameters, while the internal control points are repositioned to ensure regularity of the transformation. The grid generation process transforms a Cartesian grid (defined in parametric space) to the physical space using the tri-variate net of control points. This process guarantees a high grid quality even for large deformations, and has extremely low computational cost as it only involves a transformation from parameter space to physical space. This allows the computation of the grid sensitivities with respect to the design variables at a fraction of the cost of a Computational Fluid Dynamics (CFD) iteration, therefore allowing the use of one-shot methods. This novel parametrisation is applied to the shape optimisation of a U-bend passage of a turbine-blade serpentine-cooling channel with the objective to minimise pressure losses. A steady state, Reynolds-Averaged, density-based Navier-Stokes solver is used to predict the pressure losses at a Reynolds number of 40,000. The sensitivities of the objective function with respect to the control points are computed using a hand-derived adjoint solver and geometry generation system. A one-shot approach is used to simultaneously converge flow, gradient and design, resulting in a rapid design approach with a design time equivalent to approximately 10 normal CFD runs, while still maintaining a CAD representation of the geometry. A large reduction in pressure loss is obtained, and the flow in the optimal geometry is analysed in detail.  

<strong>Abstract:</strong> The success of shape optimisation depends significantly on the parametrisation of the shape. Ideally, it defines a very rich variation in shape, allows for rapid grid generation of high quality, and expresses the shape in a standard Computer Aided Design (CAD) representation. While most existing parametrisation methods fail at least one of these criteria, this work introduces a novel parametrisation method, which satisfies all three. A tri-variate B-spline volume is used to define the volume to be optimised. The position of the external control points are used as design parameters, while the internal control points are repositioned to ensure regularity of the transformation. The grid generation process transforms a Cartesian grid (defined in parametric space) to the physical space using the tri-variate net of control points. This process guarantees a high grid quality even for large deformations, and has extremely low computational cost as it only involves a transformation from parameter space to physical space. This allows the computation of the grid sensitivities with respect to the design variables at a fraction of the cost of a Computational Fluid Dynamics (CFD) iteration, therefore allowing the use of one-shot methods. This novel parametrisation is applied to the shape optimisation of a U-bend passage of a turbine-blade serpentine-cooling channel with the objective to minimise pressure losses. A steady state, Reynolds- Averaged, density-based Navier-Stokes solver is used to predict the pressure losses at a Reynolds number of 40,000. The sensitivities of the objective function with respect to the control points are computed using a hand-derived adjoint solver and geometry generation system. A one-shot approach is used to simultaneously converge flow, gradient and design, resulting in a rapid design approach with a design time equivalent to approximately 10 normal CFD runs, while still maintaining a CAD representation of the geometry. A large reduction in pressure loss is obtained, and the flow in the optimal geometry is analysed in detail.

Turbomachinery blade design improvement and optimization by CFD is a time-consuming engineering challenge. Such an optimization process, which requires advanced numerical simulations, uses a large amount of computational resources to provide the required solutions. This paper presents a turbine blade optimization process which uses an algorithm based on response surface methodology (RSM) to increase the simulation speed. The main idea of RSM is to start with a lower number of sample points to generate an analytical model that describes the relationship between the pre-defined numbers of design parameters. In this study, the Kriging approximation is used to generate the surface model. The global minimum on the surface is searched by applying a gradient method. The increase in the convergence speed is achieved by using an adaptive scheme, which creates additional points around the previous minimum while reducing the solution space at each iteration step, until convergence is achieved. Each iteration step is composed of several CFD simulation runs where each point represents different designed geometries inside the n-dimensional parameter space. The process combines a Bezier-spline based airfoil-generator with a parametric meshing tool —G3DMESH— and a CFD solver —TRACE—, both developed and provided by DLR, into a MATLAB script function. A particular characteristic of this optimization method is its lower evaluation number requirement to reach convergence, as well as its capability to run multiple simultaneous RANS. The optimizer process was initially tested by using basic functions to analyze its solution behavior and its performance in comparison to a genetic algorithm (GA) type optimizer. It is observed from this comparison that RSM optimization reaches the convergence faster and more stable than the GA method applied on the test case. Preliminary optimization results show an improvement in function evaluation requirements by up to 50%, which depends on the complexity of the respective surface model of the test case. As an application, a 4-stage low pressure turbine for a turboprop engine is designed by multi-streamline analysis. 2D mid-span cross-sections from both rotor and stator are produced by the Bezier-spline based airfoil-generator. The basis tool requires input parameters as leading and trailing edge blade angles and maximum thickness position. The blade generator is further improved by the additional ability to work with high values of deviation angles between the leading and trailing edges, up to 90°. 6 control points are used to define the two curves, for pressure and suction sides, which encompass the cross-section geometry. Optimization process runs to improve these airfoil parameters. The 2D airfoils of the first stage are optimized by an objective function based on total pressure loss coefficient at the engine on-design point. The same geometry is also optimized using the GA method as a comparison case.

Shaped film holes can achieve higher film cooling effectiveness compared with the simple cylindrical film holes. According to former studies, the geometry of the shaped film holes has significant influence on the cooling performance. In order to maximize the film cooling effectiveness of the shaped holes, a two-level design optimization methodology of the hole exit shaping is developed in the present study. The optimization methodology consists of a parametric design and CFD mesh generation tool called Coolmesh, a RANS CFD solver, a database of film cooling effectiveness distributions, a metamodel, and a genetic algorithm (GA) for evolutionary optimization. A binary parametric representation of the 2D hole exit shaping is initiated based on the B-spline methods. The metamodel can efficiently predict the detailed distribution of film cooling effectiveness using the CFD results in the database, which is continuously updated for higher accuracy. In each first-level iteration, a second-level GA optimization search is carried out coupled with the metamodel, and then the optimal geometry is evaluated using CFD methods and added to the database. An anisotropic turbulence model is applied to the CFD solver for higher accuracy according to a detailed experimental validation using PSP measurements. In the present study, three design optimizations of the shaped holes without and with compound angles are carried out on a flat plate. The optimization methodology can efficiently find the optimal geometries of shaped holes using only hundreds of CFD runs. For the shaped holes with compound angle, the optimized geometry can generate a back flow vortex which interacts with the shear vortex and weakens the mixing of coolant and hot gas, resulting in a higher film cooling effectiveness on the plate.

Abstract An underwater vehicle’s design and operation requires prediction of its performance at various velocities and angles-of-attack or of sideslip. Traditional models based upon headway motion at substantial speeds use coefficient-based equations of motion. Simulations based upon these coefficients are not valid for hover, low speeds, or high angles-of-attack or of sideslip. To remedy this severe limitation, nonlinear hydrodynamic models valid for all attitudes of underwater vehicles have been developed and are presented here. These models are derived from the physics of hydrodynamic phenomena. Forces and moments for the total vehicle are obtained by relying on body-buildup techniques. For the vehicle’s hull, the models are profile drag, lift, crossflow force, and added mass. For appendages such as fins, the models are lift and drag when unstalled, normal force when stalled, transition between unstalled and stalled conditions, and hull interference effects. Whenever the equations contain parametric coefficients such as added-mass, drag, and lift, values are specified for all angles-of-attack and sideslip with a minimal use of empirical look-up tables. These models represent the state-of-the-art in low speed hydrodynamics at all angles-of-attack. The hydrodynamic models presented here have been improved and validated by analysis and comparison with test data. Sub-scale versions of two different vehicles have been tested in tow-tanks at all angles-of-attack. The models have been implemented in a C language computer code which runs at high speed with no iteration required. This code is utilized regularly in faster-than-real-time vehicle performance simulations.

Today market requires machinery with ever larger performance increasing compression system vibrations risks. Knowledge of dampers pulsation-forces phenomena and best practices allows their minimization. Loads acting on foundation are early defined allowing a proper design, while “Cylinder-Gas-loads” depending upon compressor data-sheet cannot be adjusted unless to change requirements. Considering their high amplitudes and frequencies spectrum, some exciting frequencies often coincides with system mechanical natural frequencies. This involves expensive efforts in preliminary Cylinder Manifold response studies to guide compressor General Arrangement design. Specific software that includes Compressor standard elements selection and that allow building dampers by parametric inputs is cost effective in model creation. Together with the cost benefits it facilitates the designer to simulate multiple configurations rebuilding the model in a short time and exploring several solutions to optimize the system vibration control. A FEM specialist is not required for the Model build-up, the Software allow automatically applying cylinder gas loads, run analysis and compare results vs allowable ones. In case of allowable limits exceeding or design changes, G&amp;A Designer can easily change input and iterate the loop till satisfactory results are achieved in a timely and quality manner, optimizing dampers and supports.

Cooled turbine blades represent a major component of gas turbine technology due their potential for enhancing overall cycle performance. Due to the difficulty of performing detailed experiments on these complex internal configurations, the only option is to rely intensively on high fidelity CFD modeling and subsequent optimization to enhance the heat transfer coefficient (HTC) by exploration of a broad design space. The optimization strategy relies on the following steps: parametric modeling of cooling passages; automatic grid generation; validation of the most reliable turbulence models and boundary conditions; optimization process based on genetic algorithms. The parametric blade modeler AutoBlade™ has been upgraded to generate CAD geometries of cooling channels, including ribs, different section shapes, U-turns. From those geometries, the full hexahedral mesher HEXPRESS™ is able to automatically generate high quality unstructured meshes with the possibility to insert viscous sublayers to provide adequate resolution in boundary layer regions. The mesh generator can also deal with multi-domain problems allowing conjugate heat transfer (CHT) method. CFD options were analyzed in order to obtain numerical results as accurate as possible for the optimization process. It appears that low Reynolds grids were necessary to reproduce the thermal effects due to the strong temperature gradient near solid walls. The preconditioning technique seems to be essential for density based flow to obtain realistic results for flows at low Mach number. The anisotropic EARSM turbulence model appears to provide good heat transfer predictions. In addition, the question to include or not CHT is raised: the study also compares the heat transfer obtained in case of imposed static temperature conditions on the coolant to the ones obtained by means of CHT. The results highlight that CHT is more realistic. Optimization of HTC is performed on three baseline configurations by variation of geometric parameters including the aspect ratio of the channel cross section, the shape, position and size of the ribs. The main objective consists in maximization the heat fluxes while limiting the head loss. The optimization process starts from an initial database of high-fidelity CHT simulations obtained by design of experiment methods. To predict a potential optimum, an evolutionary algorithm is run on an artificial neural network for a very quick evaluation of the objectives from the database. The process is iterative: starting from potential candidates, the CFD process is launched to validate the guess and populate the database. Results and optimized geometries will be presented in the full paper.

The design cycle of a launch vehicle combines a variety of disciplines that each require expertise and dedicated tools in the development. A significant improvement in development efficiency can be achieved having one coherent toolchain that can cover all the different topics. The framework presented in this abstract comprises a set of interoperable, reconfigurable, and flexible tools based on ASTOS and MATLAB/Simulink. It allows for the rapid and agile high-fidelity simulation of launch vehicles trajectories and easy prototyping of GNC algorithms up to detailed design and V&amp;V of GNC Flight Software. The toolchain is centred around the ASTOS scenarios that contain the definition of the vehicle characteristics (e.g., propulsion and structural design parameters), environmental (e.g., gravity and atmospheric models), and dynamic models (e.g., equations of motion). This allows the user to adapt the level of fidelity of their models depending on the task and development stage. With a few simple changes the user can modify their 3DoF scenario - used for trajectory and vehicle optimization as well as design of guidance and navigation algorithms - to a 6DoF scenario – used for detailed model-based control design and V&amp;V of GNC algorithms. The simulator is automatically configured based on the underlying scenario guaranteeing consistency and data integrity. This enables users to focus their efforts on the actual development of GNC methods, saving precious time and resources developing and setting up simulators that need to be updated with every iteration and change of the launch vehicle. The simulations can be performed either within the ASTOS software itself or in MATLAB/Simulink making use of the ASTOS Simulink interface. The ASTOS toolchain proved its merits on a variety of activities ranging from early design to spacecraft checkout and operational support. While most use cases address expendable launcher configurations, also reusable concepts are strongly supported such as first stage return flights making use of retro engines and aerodynamic control flaps, towing of a fly-back booster as studied in the FALCon project, air-launch concepts or hypersonic flight vehicles. Flexible structures can be simulated in an ASTOS scenario via Linearized Flexible Dynamics (LFD) or Multi-Body Simulation (MBS). This allows to setup the flexible model in an agile way and capture the impact from the flexible deflection of launch vehicle structural components and sloshing on navigation and control algorithms. In addition, MBS allows for detailed analysis of stage and payload separation. ASTOS is well known for its trajectory optimization capabilities which is an important step in the GNC development. The optimized reference trajectory serves as a basis for both guidance and control development. Linearized models of the dynamics of the launch vehicle form the basis of all model-based control design methods and open the door to advanced (robust) analysis tools providing quick insight into the performance of a controller. The proposed toolchain provides a tool to linearise the user-defined scenario at chosen time instances along the optimized reference trajectory. The user is also free to select the range of physical effects to include in the linearised dynamics among launcher flexibility, sloshing, sensor dynamics, tail-wag-dog effect, local aerodynamics, jet damping and pitch-yaw coupling. This modularity allows the user to work with simpler linearised launcher dynamics in the initial analysis phases and progressively increase the complexity of the linear model, up to validation and verification. A Verification tool allows to validate the obtained linearized models against the nonlinear simulator, giving insights into their correctness and domain of validity about the chosen grid. To validate the performance and robustness of the developed GNC strategies in a high-fidelity non-linear simulation, a Monte-Carlo (MC) environment is included within the toolchain. This environment is responsible for configuring the simulator to perform the desired tests, either single runs or full MC campaigns, with the target launch scenario, GNC algorithms and the GNC parameterization. The MC environment allows to, not only disperse the “real-world” parameters according to the user inputs and scenario specification, but also change the configuration of the GNC programmatically to perform sensitivity and parametric analysis to aid the algorithms tuning. The MC environment employs several desired features, identified in previous activities. It separates the generation of the configuration files for the MC campaigns from the execution of the simulations. In this way, the execution of the simulation is not hindered by the configuration and the repeatability of the test is ensured. It allows the user to select which simulation outputs to store and at which rate. It is possible for the user to reconfigure the simulator with the parameters of a specific MC run to easily reproduced identified behaviours. It implements plotting and reporting utilities to expedite the post-processing and analysis of the results by the automated generation of plots and reports.