Mohamed Soula

Multidisciplinary design optimization of stiffened panels using collaborative optimization and artificial neural network

A new method for solving the multidisciplinary design optimization problems with a minimal computational effort is presented. The proposed methodology is based on the combination of artificial neural network model and Improved Multi-Objective Collaborative Optimization. In the artificial neural network–Improved Multi-Objective Collaborative Optimization scheme, the back-propagation algorithm is used for training the artificial neural network metamodel and the Non-dominated Sorting Genetic Algorithm-II is used to search a Pareto optimality set for the objective functions of stiffened panels. The artificial neural network–Improved Multi-Objective Collaborative Optimization algorithm aims firstly to decompose the global optimization problem hierarchically into optimization design problem at system level and several sub-problems at sub-system level and secondly to replace each optimization problem at the system and subsystem levels by artificial neural network model to limit the computational cost. To highlight the efficiency and effectiveness of the proposed artificial neural network–Improved Multi-Objective Collaborative Optimization method, mathematical and engineering examples are presented. Results obtained from the application of the artificial neural network–Improved Multi-Objective Collaborative Optimization approach to an optimization problem of a stiffened panel are compared with those obtained by traditional optimization without using prediction tools. The new method (artificial neural network–Improved Multi-Objective Collaborative Optimization) was proven to be superior to traditional optimization. These results have confirmed the efficiency and effectiveness of the artificial neural network–Improved Multi-Objective Collaborative Optimization method. In addition, it converges at faster rate than traditional optimization. The traditional optimization method converges within 7918 s, while artificial neural network–Improved Multi-Objective Collaborative Optimization requires only 42 s, clearly, the artificial neural network–Improved Multi-Objective Collaborative Optimization method is much more efficient.

Mechanical response of a panel section with a hexagonally tessellated stiffener grid

Stringers are stiffening members of pressurized aircraft fuselage. They provide support to the fuselage’s skin. A new stringer grid concept is proposed for conventional aircraft fuselage. Optimization is used to find the hexagonal grid that best replaces the original while keeping the same total stringer length. A finite element model is built to analyze the optimal hexagonal grid stiffened structure and compare it with the original orthogonally stiffened structure in terms of eigenfrequencies and static response to external loading. The finite element model is validated through Flugge’s analytical expressions for stiffened shells. Results show that the hexagonal grid stiffened structure yields higher eigenfrequencies with stresses and displacements comparable with that of the original structure.

Uncertainty quantification/propagation in nonlinear models: Robust reduction – generalized polynomial chaos

Purpose The purpose of this paper is to develop robust metamodels, which allow propagating parametric uncertainties, in the presence of localized nonlinearities, with reduced cost and without significant loss of accuracy. Design/methodology/approach The proposed metamodels combine the generalized polynomial chaos expansion (gPCE) for the uncertainty propagation and reduced order models (ROMs). Based on the computation of deterministic responses, the gPCE requires prohibitive computational time for large-size finite element models, large number of uncertain parameters and presence of nonlinearities. To overcome this issue, a first metamodel is created by combining the gPCE and a ROM based on the enrichment of the truncated Ritz basis using static residuals taking into account the stochastic and nonlinear effects. The extension to the Craig–Bampton approach leads to a second metamodel. Findings Implementing the metamodels to approximate the time responses of a frame and a coupled micro-beams structure containing localized nonlinearities and stochastic parameters permits to significantly reduce computation cost with acceptable loss of accuracy, with respect to the reference Latin Hypercube Sampling method. Originality/value The proposed combination of the gPCE and the ROMs leads to a computationally efficient and accurate tool for robust design in the presence of parametric uncertainties and localized nonlinearities.

Multi-objective and Multi-physics Optimization of Fully Coupled Complex Structures

This work presents an improved approach for multi-objective and multi-physics optimization based on the hierarchical optimization approach of the typical MOCO (“Multi-objective Collaborative Optimization”) whose objective is to solve multi-objective multi-physics optimization problem. In this document, we propose a new hierarchical optimization approach named Improved Multi-objective Collaborative Optimization (IMOCO) whose goal is to decompose the optimization problems of the complex systems hierarchically in two levels (system and disciplinary level) according to the disciplines. In other words, according to the different physical (mechanical-electrical-acoustical) involved in the mechanical structures design. The presented approach uses a NSGA-II “Non-dominated Sorting Genetic Algorithm II” as an optimizer, and uses a coordinator between the system optimizer and the disciplinary optimizer, which has the role, is to ensure consistency between the various disciplines of the complex system. For the purposes of validation of the proposed method, we chose two examples: (i) numerical problem and (ii) engineering problem. These examples are solved using the proposed IMOCO method and the previous approaches. The obtained results are compared well with those obtained from the previous approaches: (i) non-hierarchically based AAO optimization approach and (ii) hierarchically based MOCO optimization approach, which show the good performance of our proposed IMOCO method.

A new reliability based optimization of tuned mass damper parameters using energy approach

In this work a reliability based optimization (RBO) strategy of Tuned Mass Damper (TMD) parameters is presented. The strategy is based on an energetic approach. The strategy consists to optimize the TMD parameters so that we minimize the failure probability (objective function) characterized by the exceedence of the power dissipated in the primary structure of a certain threshold value during some interval time. The evaluation of the objective function is carried out using the classical Rice’s formula. The strategy is, firstly, applied to linear single-degree of freedom (SDOF) system, subjected to seismic motion, and then extended to linear multi-degree of freedom (MDOF) system. The use of the Rice’s formula requires the knowledge of the joint probability density function (PDF) of the considered processes; to this end, exact expression of the joint PDF is presented for the SDOF system and an approximation is presented for the evaluation of the failure probabilities for the MDOF system. By making use of the obtained joint PDF, for the SDOF system, as the a priori joint PDF, the approximation of the joint PDF, for the MDOF system, has been performed using the Minimum cross-entropy method (MinxEnt). To highlight the good effectiveness of the proposed strategy, a ten-story shear building, subjected to different earthquakes, is considered. The obtained results are compared with other from literature, and it has been shown the superiority of the proposed strategy.

Dynamic Relaxation Coordination Based Collaborative Optimization for Optimal Design of Multi-physics Systems

To solve problems of higher computational burden in standard collaborative optimization (CO) approach during the processing of design problem of the multi-physics systems with multiples disciplines, a Dynamic Relaxation Coordination based Collaborative Optimization (DRC-CO) method is presented. The main concept of DRC-CO method is to decompose the global design problem into one optimization problem at the system level and several autonomous sub-problems at disciplinary level. At the system level, the dynamic relaxation coordination aims to solve the inconsistency between all disciplines, which leads the optimization process converging to the feasible optimum efficiently. To demonstrate the efficiency and accuracy of the proposed DRC-CO method, a safety isolation transformer is considered. The obtained results of the engineering multi-physics system show the effectiveness of the proposed DRC-CO process compared to Single Level Optimization (SLO) and standard CO methods. The obtained optimal configuration of the safety isolation transformer in terms of total mass using DRC-CO method (2.30 kg) is close to the result obtained from SLO method (2.31 kg) with an absolute percentage error is less than 0.5%. Moreover, our approach requires 3 system iterations to find realizable designs. However, an important number of disciplinary design problems were evaluated at the disciplinary level optimizer.

Robust Multi-objective Collaborative Optimization of Complex Structures

This paper presents a new approach aims to solve robust multidisciplinary design optimization MDO problem called Improved Multi-objective Robust Collaborative Optimization . This method combines the Multi-objective Robust Collaborative Optimization method, the Worst Possible Point constraint cuts and the Genetic algorithm NSGA-II type as an optimizer to solve the robust optimization problem of complex structure named Y-stiffened panel under interval uncertainty . The proposed approach hierarchically decomposes the optimization problem into a structure level considered as an upper level in the Y-stiffened panel and a second level considered as a lower level of the studied panel. A robust multi-objective optimization problem intended to optimize the eigenfrequency, the global mass and the displacement at a fixed point of the Y-stiffened panel at the first level and each structure’s robust optimization problem allows optimizing its eigenfrequency and mass limited by their local constraint functions at the second one. Tor demonstrate our method, an engineering example of Y-stiffened panel is treated. A good performance of proposed method is proved by a comparison between obtained results and Non-Distributed Multi-objective Robust Optimization .

Investigations on the Validity of the Poisson Assumption in Reliability Based Optimization of TMD Parameters

The purpose of the present work is to investigate the validity of the Poisson assumption used in the failure analysis, which is in turn required for the reliability based optimization (RBO) of tuned mass dampers (TMD) parameters. The TMD is a widely used device aiming to mitigate induced vibrations into structures under stochastic loading. The performance of this device is deeply related to its parameters that should be carefully chosen and in this context the RBO strategy can be used. The RBO problem required failure analysis, usually, performed based on analytical approximations and among them we can find: the Poisson, the Vanmarcke and the modified Vanmarcke approximations. The failure analysis based on Poisson assumption is very simple and widely used for its lower computational cost compared with the other approximations. Nevertheless, it’s also known that the Poisson approximation is inappropriate for narrowband process and/or for low threshold values, whereas, the other approximations could be used in such conditions. By studying a single degree of freedom system (SDOF), submitted to stochastic base acceleration, we investigate the relative error, in the optimum TMD parameters, induced by these approximations and we show that the Poisson assumption is relatively accurate and valid for high threshold level, even for narrowband excitations.

Surrogate-Based Multidisciplinary Design Optimization for Stiffened Panels Application

This paper is devoted to propose and apply a surrogate-based multidisciplinary design optimization (MDO) method on stiffened panels with several substructures and objectives. This method combines Kriging Surrogate Model (KSM), which is used to predict the exact responses of objectives and constraint functions, and an Improved Multi-Objective Collaborative Optimization (IMOCO) to solve the MDO problems. In the KSM-IMOCO scheme, each exact optimization problem at structure and substructure level is replaced by a metamodel to limit the computational burden. To demonstrate the applicability of the proposed KSM-IMOCO method, we treat an engineering example of kind stiffened panel. Results obtained from the application of the KSM-IMOCO approach on optimization problem of a stiffened panel kind L are compared with the traditional optimization (TO), without passing by the approximation tools, and it has been shown the sovereignty of the proposed KSM-IMOCO method. These results indicate that the proposed KSM-IMOCO method significantly reduces computational burden, and improves the convergence rate for solving the exact multidisciplinary optimization problem.

Stochastic Optimal Design of Tuned Mass Damper Parameters Using Energetic Approaches

The present work is intended to introduce a new reliability based optimization strategy (RBO) of single-tuned mass damper (TMD) parameters. The strategy uses an energetic approach and consists to obtain the optimum TMD parameters so that a failure probability is minimized. The failure probabilityis related to the dissipated power process in the primary structure (DPP) and it’s characterized by the out-crossing, for the first time, of the DPP across a certain threshold value during a time interval. The introduced RBO strategy is then compared with another related to the mean value of the DPP. The obtained results show a strong correlation between the presented strategies and equivalence can be made. The effectiveness of the TMD with the proposed optimum parameters is also investigated and compared with Bi-tuned mass dampers (Bi-TMDs). The results showed that the TMD optimized using the proposed strategy is more effective than the Bi-TMDs.