Reliability-based design optimization of shells with uncertain geometry using adaptive Kriging metamodels

Optimal design under uncertainty has gained much attention in the past ten years due to the ever increasing need for manufacturers to build robust systems at the lowest cost. Reliability-based design optimization (RBDO) allows the analyst to minimize some cost function while ensuring some minimal performances cast as admissible failure probabilities for a set of performance functions. In order to address real-world engineering problems in which the performance is assessed through computational models (e.g., finite element models in structural mechanics) metamodeling techniques have been developed in the past decade. This paper introduces adaptive Kriging surrogate models to solve the RBDO problem. The latter is cast in an augmented space that "sums up" the range of the design space and the aleatory uncertainty in the design parameters and the environmental conditions. The surrogate model is used (i) for evaluating robust estimates of the failure probabilities (and for enhancing the computational experimental design by adaptive sampling) in order to achieve the requested accuracy and (ii) for applying a gradient-based optimization algorithm to get optimal values of the design parameters. The approach is applied to the optimal design of ring-stiffened cylindrical shells used in submarine engineering under uncertain geometric imperfections. For this application the performance of the structure is related to buckling which is addressed here by means of a finite element solution based on the asymptotic numerical method

Stochastic multi-objective optimisation of the cure process of thick laminates

A stochastic multi-objective cure optimisation methodology is developed in this work and applied to the case of thick epoxy/carbon fibre laminates. The methodology takes into account the uncertainty in process parameters and boundary conditions and minimises the mean values and standard deviations of cure time and temperature overshoot. Kriging is utilised to construct a surrogate model of the cure substituting Finite Element (FE) simulation for computational efficiency reasons. The surrogate model is coupled with Monte Carlo and integrated into a stochastic multi-objective optimisation framework based on Genetic Algorithms. The results show a significant reduction of about 40% in temperature overshoot and cure time compared to standard cure profiles. This reduction is accompanied by a reduction in variability by about 20% for both objectives. This highlights the opportunity of replacing conventional cure schedules with optimised profiles achieving significant improvement in both process efficiency and robustness

Application of Surrogate Based Optimisation in the Design of Automotive Body Structures

The rapid development of automotive industry requires manufacturers to continuously reduce the development cost and time and to enhance the product quality. Thus, modern automotive design pays more attention to using CAE analysis based optimisation techniques to drive the entire design flow. This thesis focuses on the optimisation design to improve the automotive crashworthiness and fatigue performances, aiming to enhance the optimisation efficiency, accuracy, reliability, and robustness etc. The detailed contents are as follows: (1) To excavate the potential of crash energy absorbers, the concept of functionally graded structure was introduced and multiobjective designs were implemented to this novel type of structures. First, note that the severe deformation takes place in the tubal corners, multi-cell tubes with a lateral thickness gradient were proposed to better enhance the crashworthiness. The results of crashworthiness analyses and optimisation showed that these functionally graded multi-cell tubes are preferable to a uniform multi-cell tube. Then, functionally graded foam filled tubes with different gradient patterns were analyzed and optimized subject to lateral impact and the results demonstrated that these structures can still behave better than uniform foam filled structures under lateral loading, which will broaden the application scope of functionally graded structures. Finally, dual functionally graded structures, i.e. functionally graded foam filled tubes with functionally graded thickness walls, were proposed and different combinations of gradients were compared. The results indicated that placing more material to tubal corners and the maximum density to the outmost layer are beneficial to achieve the best performance. (2) To make full use of training data, multiple ensembles of surrogate models were proposed to maximize the fatigue life of a truck cab, while the panel thicknesses were taken as design variables and the structural mass the constraint. Meanwhile, particle swarm optimisation was integrated with sequential quadratic programming to avoid the premature convergence. The results illustrated that the hybrid particle swarm optimisation and ensembles of surrogates enable to attain a more competent solution for fatigue optimisation. (3) As the conventional surrogate based optimisation largely depends on the number of initial sample data, sequential surrogate modeling was proposed to practical applications in automotive industry. (a) To maximize the fatigue life of spot-welded joints, an expected improvement based sequential surrogate modeling method was utilized. The results showed that by using this method the performance can be significantly improved with only a relatively small number of finite element analyses. (c) A multiojective sequential surrogate modeling method was proposed to address a multiobjective optimisation of a foam-filled double cylindrical structure. By adding the sequential points and updating the Kriging model adaptively, more accurate Pareto solutions are generated. (4) While various uncertainties are inevitably present in real-life optimisations, conventional deterministic optimisations could probably lead to the violation of constraints and the instability of performances. Therefore, nondeterministic optimisation methods were introduced to solve the automotive design problems. (a) A multiobjective reliability-based optimisation for design of a door was investigated. Based on analysis and design responses surface models, the structural mass was minimized and the vertical sag stiffness was maximized subjected to the probabilistic constraint. The results revealed that the Pareto frontier is divided into the sensitive region and insensitive region with respect to uncertainties, and the decision maker is recommended to select a solution from the insensitive region. Furthermore, the reduction of uncertainties can help improve the reliability but will increase the manufacturing cost, and the tradeoff between the reliability target and performance should be made. (b) A multiobjective uncertain optimisation of the foam-filled double cylindrical structure was conducted by considering randomness in the foam density and wall thicknesses. Multiobjective particle swarm optimisation and Monte Carlo simulation were integrated into the optimisation. The results proved that while the performances of the objectives are sacrificed slightly, the nondeterministic optimisation can enhance the robustness of the objectives and maintain the reliability of the constraint. (c) A multiobjective robust optimisation of the truck cab was performed by considering the uncertainty in material properties. The general version of dual response surface model, namely dual surrogate model, was proposed to approximate the means and standard deviations of the performances. Then, the multiobjective particle optimisation was used to generate the well-distributed Pareto frontier. Finally, a hybrid multi-criteria decision making model was proposed to select the best compromise solution considering both the fatigue performance and its robustness. During this PhD study, the following ideas are considered innovative: (1) Surrogate modeling and multiobjective optimisation were integrated to address the design problems of novel functionally graded structures, aiming to develop more advanced automotive energy absorbers. (2) The ensembles of surrogates and hybrid particle swarm optimisation were proposed for the design of a truck cab, which could make full use of training points and has a strong searching capacity. (3) Sequential surrogate modeling methods were introduced to several optimisation problems in the automotive industry so that the optimisations are less dependent on the number of initial training points and both the efficiency and accuracy are improved. (4) The surrogate based optimisation method was implemented to address various uncertainties in real life applications. Furthermore, a hybrid multi-criteria decision making model was proposed to make the best compromise between the performance and robustness

Solving optimisation problems in metal forming using FEM: A metamodel based optimisation algorithm

During the last decades, Finite Element (FEM) simulations of metal forming processes have\ud become important tools for designing feasible production processes. In more recent years,\ud several authors recognised the potential of coupling FEM simulations to mathematical opti-\ud misation algorithms to design optimal metal forming processes instead of only feasible ones.\ud This report describes the selection, development and implementation of an optimisa-\ud tion algorithm for solving optimisation problems for metal forming processes using time\ud consuming FEM simulations. A Sequential Approximate Optimisation algorithm is pro-\ud posed, which incorporates metamodelling techniques and sequential improvement strate-\ud gies for enhancing the e±ciency of the algorithm. The algorithm has been implemented in\ud MATLABr and can be used in combination with any Finite Element code for simulating\ud metal forming processes.\ud The good applicability of the proposed optimisation algorithm within the ¯eld of metal\ud forming has been demonstrated by applying it to optimise the internal pressure and ax-\ud ial feeding load paths for manufacturing a simple hydroformed product. Resulting was\ud a constantly distributed wall thickness throughout the ¯nal product. Subsequently, the\ud algorithm was compared to other optimisation algorithms for optimising metal forming\ud by applying it to two more complicated forging examples. In both cases, the geometry of\ud the preform was optimised. For one forging application, the algorithm managed to solve\ud a folding defect. For the other application both the folding susceptibility and the energy\ud consumption required for forging the part were reduced by 10% w.r.t. the forging process\ud proposed by the forging company. The algorithm proposed in this report yielded better\ud results than the optimisation algorithms it was compared to

Optimisation of the Filament Winding Approach Using a Newly Developed In-House Uncertainty Model

The device under investigation in this paper consists of a float used to capture tidal energy, which is tethered by multiple flexible cables to a large barge-like reactor. The proposed float is made of a continuously wound glass-reinforced composite shell with stainless steel bolting plates integrated into the float walls to allow the connection of 5 stainless steel cables. Numerical computations are required to assess whether a delamination of the composite layers in the float is likely. The manufacturing of the device has various potential uncertainties that should be investigated, such as the number of the plies, the bond strength between the composite layers, and the fibre orientations of the composite material relative to the applied load. This paper provides a multi-level strategy to optimise the composite float system, which is manufactured from glass-reinforced plastic (GRP). In contrast to previous publications on the topic, the current work uses an efficient link between ANSYS Workbench and MATLAB through an in-house code that has been developed over 3 years. This allowed the whole process to be fully automated and to reduce the time and cost of the simulations. Previously, ANSYS APDL was linked to MATLAB, but limitations in terms of the geometry and boundary conditions made it impractical when compared to ANSYS Workbench for the simulation of complex features. This makes the current approach unique and rare when compared to the published work in the field. This approach allows the use of a huge number of trials and is able to reduce the number of parameters to be studied by selecting the most sensitive ones. Additionally, the developed tools may be used for the efficient, robust optimisation of the proposed structure. The current study has focused on exploring the effects of the fibre orientations and the optimum number of plies on the overall performance of the structure

Dynamic data driven applications systems (DDDAS) for multidisciplinary optimisation (MDO)

[ES] Nowadays, the majority of optimisation processes that are followed to obtain new optimum designs involve expensive simulations that are costly and time comsuming. Besides, designs involving aerodynamics are usually highly constrained in terms of infeasible geometries to be avoided so that it is really important to provide the optimisers effective datum or starting points that enable them to reach feasible solutions. This MSc Thesis aims to continue the development of an alternative design methodology applied to a 2D airfoil at a cruise flight condition by combining concepts of Dynamic Data Driven Application Systems (DDDAS) paradigm with Multiobjec- tive Optimisation. For this purpose, a surrogate model based on experimental data has been used to run a multiobjective optimisation and the given optimum designs have been considered as starting points for a direct optimisation, saving number of evaluations in the process. Throughout this work, a technique for retrieving experi- mental airfoil lift and drag coefficients was conducted. Later, a new parametrisation technique using Class-Shape Transformation (CST) was implemented in order to map the considered airfoils into the design space. Then, a response surface model considering Radial Basis Functions (RBF) and Kriging approaches was constructed and the multiobjective optimisation to maximise lift and minimise drag was under- taken using stochastic algorithms, MOTSII and NSGA. Alternatively, a full direct optimisation from datum airfoil and a direct optimisation from optimum surrogate- based optimisation designs were performed with Xfoil and the results were compared. As an outcome, the developed design methodology based on the combination of surrogate-based and direct optimisation was proved to be more effective than a single full direct optimisation to make the whole process faster by saving number of evaluations. In addition, further work guidelines are presented to show potential directions in which to expand and improve this methodology.Patón Pozo, PJ. (2016). Dynamic data driven applications systems (DDDAS) for multidisciplinary optimisation (MDO). Universitat Politècnica de València. http://hdl.handle.net/10251/142210TFG

The use of geometric uncertainty data in aero engine structural analysis and design

A gas turbine disc has three critical regions for which lifing calculations are essential: the assembly holes or weld areas, the hub region, and the blade-disc attachment area. Typically, a firtree joint is used to attach the blades to the turbine disc instead of a dove-tail joint, which is commonly used for compressor discs. A firtree joint involves contact between two surfaces at more than one location which makes the joint more difficult to design. Large loads generated due to the centrifugal action of the disc and associated blades are distributed over multiple areas of contact within the joint. All of the contacts in a firtree joint are required to be engaged simultaneously when the blades are loaded. However, slight variations in the manufacture of these components can have an impact on this loading. It is observed that small changes in the geometric entities representing contact between the two bodies can result in variations in the stress distribution near contact edges and the notch regions. Even though manufacturing processes have advanced considerably in the last few decades, the variations in geometry due to these processes cannot be completely eliminated. Hence, it is necessary to design such components in the presence of uncertainties in order to minimise the variation observed in their performance. In this work, the variations in geometry due to the manufacturing processes used to produce firtree joints between a gas turbine blade and the disc are evaluated. These variations are represented in two different ways using measurement data of firtree joints obtained from a coordinate measuring machine (CMM): (i) the variation for the pressure angle in the firtree joint is extracted from a simple curve fit and (ii) using the same measurement data, the unevenness of the pressure surfaces is represented using a Fourier series after filtering noise components. A parametric computer aided design (CAD) model which represents the manufacturing variability is implemented using Siemens NX. Non-smooth surfaces are also numerically generated by assuming the surface profile to be a random process. Two- and three-dimensional elastic stress analysis is carried out on the firtree joint using the finite element code, Abaqus and the variations observed in the notch stresses with changing pressure angle are extracted. A surrogate assisted multiobjective optimisation is performed on the firtree joint based on the robustness principles. Kriging based models are used to build a surrogate for notch stresses and the non-dominated sorting genetic algorithm-II (NSGA-II) is implemented to perform a multiobjective optimisation in order to minimise the mean and standard deviation of the notch stresses. An iterative search algorithm that updates the Kriging models with equally spaced infill points from the predicted Pareto front is adopted. Finally, a new design of the firtree joint is obtained which has better performance with respect to the variation in the notch stresses due to manufacturing uncertainties

UQ and AI: data fusion, inverse identification, and multiscale uncertainty propagation in aerospace components

A key requirement for engineering designs is that they offer good performance across a range of uncertain conditions while exhibiting an admissibly low probability of failure. In order to design components that offer good performance across a range of uncertain conditions, it is necessary to take account of the effect of the uncertainties associated with a candidate design. Uncertainty Quantification (UQ) methods are statistical methods that may be used to quantify the effect of the uncertainties inherent in a system on its performance. This thesis expands the envelope of UQ methods for the design of aerospace components, supporting the integration of UQ methods in product development by addressing four industrial challenges. Firstly, a method for propagating uncertainty through computational models in a hierachy of scales is described that is based on probabilistic equivalence and Non-Intrusive Polynomial Chaos (NIPC). This problem is relevant to the design of aerospace components as the computational models used to evaluate candidate designs are typically multiscale. This method was then extended to develop a formulation for inverse identification, where the probability distributions for the material properties of a coupon are deduced from measurements of its response. We demonstrate how probabilistic equivalence and the Maximum Entropy Principle (MEP) may be used to leverage data from simulations with scarce experimental data- with the intention of making this stage of product design less expensive and time consuming. The third contribution of this thesis is to develop two novel meta-modelling strategies to promote the wider exploration of the design space during the conceptual design phase. Design Space Exploration (DSE) in this phase is crucial as decisions made at the early, conceptual stages of an aircraft design can restrict the range of alternative designs available at later stages in the design process, despite limited quantitative knowledge of the interaction between requirements being available at this stage. A histogram interpolation algorithm is presented that allows the designer to interactively explore the design space with a model-free formulation, while a meta-model based on Knowledge Based Neural Networks (KBaNNs) is proposed in which the outputs of a high-level, inexpensive computer code are informed by the outputs of a neural network, in this way addressing the criticism of neural networks that they are purely data-driven and operate as black boxes. The final challenge addressed by this thesis is how to iteratively improve a meta-model by expanding the dataset used to train it. Given the reliance of UQ methods on meta-models this is an important challenge. This thesis proposes an adaptive learning algorithm for Support Vector Machine (SVM) metamodels, which are used to approximate an unknown function. In particular, we apply the adaptive learning algorithm to test cases in reliability analysis.Open Acces