Two-stage size-layout optimization of axially compressed stiffened panels

In this study, a two-stage optimization framework is proposed for cylindrical or flat stiffened panels under uniform or non-uniform axial compression, which are extensively used in the aerospace industry. In the first stage, traditional sizing optimization is performed. Based on the buckling or collapse-like deformed shape evaluated for the optimized design, the panel can be divided in sub-regions each of which shows characteristic deformations along axial and circumferential directions. Layout optimization is then performed using a stiffener spacing distribution function to represent the location of each stiffener. A layout coefficient is assigned to each sub-region and the overall layout of the panel is optimized. Three test problems are solved in order to demonstrate the validity of the proposed optimization framework: remarkably, the load-carrying capacity improves by 17.4 %, 66.2 % and 102.2 % with respect to the initial design.     

Reliability-based design optimization of composite stiffened panels in post-buckling regime

This paper focuses on Deterministic and Reliability Based Design Optimization (DO and RBDO) of composite stiffened panels considering post-buckling regime and progressive failure analysis. The ultimate load that a post-buckled panel can hold is to be maximised by changing the stacking sequence of both skin and stringers composite layups. The RBDO problem looks for a design that collapses beyond the shortening of failure obtained in the DO phase with a target reliability while considering uncertainty in the elastic properties of the composite material. The RBDO algorithm proposed is decoupled and hence separates the Reliability Analysis (RA) from the deterministic optimization. The main code to drive both the DO and RBDO approaches is written in MATLAB and employs Genetic Algorithms (GA) to solve the DO loops because discrete design variables and highly nonlinear response functions are expected. The code is linked with Abaqus to perform parallel explicit nonlinear finite element analyses in order to obtain the structural responses at each generation. The RA is solved through an inverse Most Probable failure Point (MPP) search algorithm that benefits from a Polynomial Chaos Expansion with Latin Hypercube Sampling (PCE-LHS) metamodel when the structural responses are required. The results led to small reductions in the maximum load that the panels can bear but otherwise assure that they will collapse beyond the shortening of failure imposed with a high reliability.

     

Adaptive gradient-enhanced kriging model for variable-stiffness composite panels using Isogeometric analysis

A vibration isolation system is designed using novel hybrid optimization techniques, where locations of machines, locations of isolators and layout of supporting structure are all taken as design variables. Instead of conventional parametric optimization model, the 0-1 programming model is established to optimize the locations of machines and isolators so that the time-consuming remeshing procedure and the complicated sensitivity analysis with respect to position parameters can be circumvented. The 0-1 sequence for position design variables is treated as binary bits so as to reduce the actual number of design variables to a great extent. This way the 0-1 programming can be solved in a quite efficient manner using a special version of genetic algorithm(GA) that has been published by the authors. The layout of supporting structure is optimized using SIMP based topology optimization method, where the fictitious elemental densities are taken as design variables ranging from 0 to 1. Influence of different design variables is firstly investigated by numerical examples. Then a hybrid multilevel optimization method is proposed and implemented to simultaneously take all design variables into account.     

Finite element free vibration analysis of damped stiffened panels

Free vibration characleristics of a damped stiffened panel with applied viscoelastic damping on the flanges of the stiffeners are studied using finite element method. The complex nature of the rotational and transverse stiffnesses of the stringers is taken into consideration while deriving the stiffness and mass matrices of the damped stiffener element. The finite element method consists of representing the panel by rectangular plate elements of 12 d.o.f. and the stiffeners by beam elements of 8 d.o.f. which allow for bending, torsional and warping effects. Numerical results showing the effect of the geometric and material properties of the damping layer treatment on the resonant frequencies and loss factors of the composite panel are presented.     

A cellular framework for structural analysis and optimization

The present paper describes the implementation of a cellular automata based computational approach in structural analysis and design. This approach assumes that a computational domain can be subdivided into a number of discrete cells, with state variables associated with each cell. Collectively, these cell states define the state of the entire domain, and which may be evolved through application of local rules of interaction that apply to a defined neighborhood around each cell. The computational process is intrinsically parallel in nature, and allows for a natural implementation on parallel computers. The paper describes an overview of this computational model for the analysis of structural systems, and demonstrates how it can be extended for a fine-grained parallel implementation of the genetic algorithm based optimization strategy. The paper also illustrates an extension of the proposed model in solving problems of simultaneous analysis and optimization.     

Design and analysis of stiffened composite panels including post-buckling and collapse

The European aircraft industry demands reduced development and operating costs, by 20% and 50% in the short and long term, respectively. Contributions to this aim are provided by the completed project POSICOSS (5th FP) and the running follow-up project COCOMAT (6th FP), both supported by the European Commission. As an important contribution to cost reduction a decrease in structural weight can be reached by exploiting considerable reserves in primary fibre composite fuselage structures through an accurate and reliable simulation of post-buckling up to collapse. The POSICOSS team developed fast procedures for the post-buckling analysis of stiffened fibre composite panels, created comprehensive experimental data bases and derived suitable design guidelines. COCOMAT builds up on the POSICOSS results and considers in addition the simulation of collapse by taking degradation into account. The results comprise an extended experimental data base, degradation models, and improved certification and design tools as well as extended design guidelines.One major task of POSICOSS and COCOMAT is the development of improved analysis tools that are validated by experiments performed within the framework of the projects. Because the new tools must comprise a wide range of various aspects a considerable number of different structures had to be tested. These structures were designed under different objectives (e.g. large post-buckling region). For the design process, the consortiums applied state-of-the-art simulation tools and brought in their own design experience. This paper deals with the design process as performed within both projects and with the applied analysis procedures. It is focused on the DLR experience in the design and analysis of stringer-stiffened CFRP panels gained within the scope of these two projects.     

A unidirectionally stiffened panels database for structural synthesis on microcomputer networks

In this paper, the size-inertia database approach and the computerized record-keeping database approach to the Tables for the Design and Analysis of (Unidirectionally) Stiffened Steel Plates (N. W. Murray and G. Thierauf; Vieweg, Braunschweig, 1981) are examined. This is done in order to establish the fact that Isreb's integrated database for mainframe computers, published in volume 10 of Computers and Structures, is still the only synthesis-oriented-database in the literature which deals with uni-directionally stiffened panels. Next the paper studies the topic of database organization within a typical structural optimization program on a microcomputer network.     

A fuzzy evolutionary framework for combining ensembles

We propose an evolutionary framework for the production of fuzzy rule bases where each rule executes an ensemble of predictors. The architecture, the rule base and the composition of the ensembles are evolved over time. To achieve this, we employ a context-free grammar within a hybrid genetic programming system using a multi-population model. As base predictors, multilayer perceptron neural networks and support vector machines are available. We apply the system to several function approximation and regression tasks and compare the results with recent research and state-of-the-art models. We conclude that the proposed architecture is competitive and has a number of very desirable features supporting automation of predictive model building and their adaptation over time. Finally, we suggest further potential research directions.     

A gradient-based uncertainty optimization framework utilizing dimensional adaptive polynomial chaos expansion

To improve the efficiency of solving uncertainty design optimization problems, a gradient-based optimization framework is herein proposed, which combines the dimension adaptive polynomial chaos expansion (PCE) and sensitivity analysis. The dimensional adaptive PCE is used to quantify the quantities of interest (e.g., reliability, robustness metrics) and the sensitivity. The dimensional adaptive property is inherited from the dimension adaptive sparse grid, which is used to evaluate the PCE coefficients. Robustness metrics, referred to as statistical moments, and their gradients with respect to design variables are easily derived from the PCE, whereas the evaluation of the reliability and its gradient require integrations. To quantify the reliability, the framework uses the Heaviside step function to eliminate the failure domain and calculates the integration by Monte Carlo simulation with the function replaced by PCE. The PCE is further combined with Taylor’s expansion and the finite difference to compute the reliability sensitivity. Since the design vector may affect the sample set determined by dimension adaptive sparse grid, the update of the sample set is controlled by the norm variations of the design vector. The optimization framework is formed by combining reliability, robustness quantification and sensitivity analysis, and the optimization module. The accuracy and efficiency of the reliability quantification, as well as the reliability sensitivity, are verified through a mathematical example, a system of springs, and a cantilever beam. The effectiveness of the framework in solving optimization problems is validated by multiple limit states example, a truss optimization example, an airfoil optimization example, and an ONERA M6 wing optimization problem. The results demonstrate that the framework can obtain accurate solutions at the expense of a manageable computational cost.

     

A multi-point sampling method based on kriging for global optimization

In general, sampling strategy plays a very important role in metamodel based design optimization, especially when computationally expensive simulations are involved in the optimization process. The research on new optimization methods with less sampling points and higher convergence speed receives great attention in recent years. In this paper, a multi-point sampling method based on kriging (MPSK) is proposed for improving the efficiency of global optimization. The sampling strategy of this method is based on a probabilistic distribution function converted from the expected improvement (EI) function. It can intelligently draw appropriate new samples in an area with certain probability according to corresponding EI values. Besides, three strategies are also proposed to speed up the sequential sampling process and the corresponding convergence criterions are put forward to stop the searching process reasonably. In order to validate the efficiency of this method, it is tested by several numerical benchmark problems and applied in two engineering design optimization problems. Moreover, an overall comparison between the proposed method and several other typical global optimization methods has been made. Results show that the higher global optimization efficiency of this method makes it particularly suitable for design optimization problems involving computationally expensive simulations.     

Numerical method for shape optimization using meshfree method

A numerical method for continuum-based shape design sensitivity analysis and optimization using the meshfree method is proposed. The reproducing kernel particle method is used for domain discretization in conjunction with the Gauss integration method. Special features of the meshfree method from a sensitivity analysis viewpoint are discussed, including the treatment of essential boundary conditions, and the dependence of the shape function on the design variation. It is shown that the mesh distortion that exists in the finite element-based design approach is effectively resolved for large shape changing design problems through 2-D and 3-D numerical examples. The number of design iterations is reduced because of the accurate sensitivity information.     

Topology optimization of stiffened plate/shell structures based on adaptive morphogenesis algorithm

This article proposes an adaptive morphogenesis algorithm to design stiffened plate/shell structures in a growth manner. The idea of this work is inspired by researches in leaf venation which indicates that the adaptive growth of leaf vein provides the relatively large structure with an effective reinforcement. This excellent performance is regarded as the contribution of two primary morphological features: branching and hierarchy. To apply the growth mechanism of leaf venation into stiffened plate/shell structures, a mathematical model describing the growth process is established. Based on this, the adaptive morphogenesis algorithm is developed to make stiffeners “grow” step by step. Besides, the “stiffness transforming operation”, a numerical treatment, is introduced to enable stiffeners to grow along arbitrary directions in the FEM model, which guarantees the design more optimized than previous methods. To obtain a further verification of the proposed method, a comparison between the proposed method and three typical methods is implemented. This comparison shows that the proposed method endows the designed object with a more excellent performance than others. Therefore, the proposed method is competent in the stiffened plate/shell structure design.     

A general framework for analysis and comparison of surface mesh optimization techniques

Many different algorithms for surface mesh optimization (including smoothing, remeshing, simplification and subdivision), each giving different results, have recently been proposed. All these approaches affect vertices of the mesh. Vertex coordinates are modified, new vertices are added and some original ones are removed, with the result that the shape of the original surface is changed. The important question is how to evaluate the differences in shape between the input and output models. In this paper, we present a novel and versatile framework for analysis of various mesh optimization algorithms in terms of shape preservation. We depart from the usual strategy by measuring the changes in the approximated smooth surfaces rather than in the corresponding meshes. The proposed framework consists of two error metrics: normal-based and physically based. We demonstrate that our metrics allow more subtle changes in shape to be captured than is possible with some commonly used measures. As an example, the proposed tool is used to compare three different techniques, reflecting basic ideas on how to solve the surface mesh improvement problem.     

An alternate stability analysis framework for adaptive control

A proof is given for the uniform asymptotic stability of a class of pointwise-in-time stable systems of time-varying ordinary differential equations. The sufficient conditions for stability are shown to be naturally testable in a general adaptive control context. A weak form of robust identification is found to imply robust stability of the overall closed-loop adaptive control system.     

A novel real time video tracking framework using adaptive discrete swarm optimization

This paper has proposed a new adaptive discrete swarm optimization (ADSO) for the video tracking framework. Each target object is first presented by a search window with four-dimensional features, which include 2D coordinates of the search window, its width and height. The image in the search window of a target object is extracted to calculate the HSV histograms, which are used to establish a feature model for the target object. Then the particles fly in a sub-search-space to find an optimal match of the target. If any occlusion or disappearance of the target object is detected, the particles will adaptively update their searching strategies in order to recapture the target. The experimental results demonstrate that the ADSO can out-perform the traditional PSO algorithm in the aspects of high accuracy rate and fast tracking and relocating speed.     

Optimum design and evaluation of stiffened panels with practical loading

Optimum design of a blade-stiffened panel of composite/honeycomb sandwich construction and a metal T-stiffened panel is considered using the buckling and strength constraint program VICONOPT. Both panels have practical loadings which produce a nonlinear out-of-plane bending moment, calculated using beam-column expressions. Large deflection finite element analysis of the optima shows that modifications to these expressions are necessary when the panels are shear loaded. The use of integrally machined stiffeners, as opposed to a conventional, built-up panel designed using PANDA2, is shown to permit 20% mass saving when the latter has no postbuckling strength and 3% saving when postbuckling strength is allowed for.     

A mixture-of-experts framework for adaptive Kalman filtering

This paper proposes a modular and flexible approach to adaptive Kalman filtering using the framework of a mixture-of-experts regulated by a gating network. Each expert is a Kalman filter modeled with a different realization of the unknown system parameters such as process and measurement noise. The gating network performs on-line adaptation of the weights given to individual filter estimates based on performance. This scheme compares very favorably with the classical Magill filter bank, which is based on a Bayesian technique, in terms of: estimation accuracy; quicker response to changing environments; and numerical stability and computational demands. The proposed filter bank is further enhanced by periodically using a search algorithm in a feedback loop. Two search algorithms are considered. The first algorithm uses a recursive quadratic programming approach which extremizes a modified maximum likelihood function to update the parameters of the best performing filter in the bank. This particular approach to parameter adaptation allows a real-time implementation. The second algorithm uses a genetic algorithm to search for the parameter vector and is suited for post-processed data type applications. The workings and power of the overall filter bank and the suggested adaptation schemes are illustrated by a number of examples.