Stochastic numerical treatment for solving Falkner–Skan equations using feedforward neural networks

Multidisciplinary design optimization (MDO) was performed on a helicopter rotor blade. The blade was modeled as a rigid flapping blade for dynamics; Blade Element Theory (BET) was the analysis approach to model the aerodynamic loading, and a simple linearly elastic hollowed rectangular section was the main structural component. MATLAB was used to solve the flapping differential equations and its Sequential Quadratic Programming (SQP) and Genetic Algorithm (GA) were used for the optimization. A Particle Swarm Optimization (PSO) routine was also tested. The optimization process consisted of three cases. The first case was a simple cantilever beam under centrifugal and an assumed bending loads. The optimization was performed using the SQP, GA, and PSO algorithms. The SQP resulted in the superior design with 75.45 compared to the GA's 87.1 and the PSO's 79.2, but a local minimum was present. The second case was an expansion of the first case by turning it into multidisciplinary problem. Aerodynamics was included in the design variables and objective function. Only the SQP algorithm was used and there was a reduction in hub vertical shear by 33.6%. The blade mass increased by 36.84%. The last case was an improvement to the second by creating a multiobjective problem by including the hub radial shear and the results were improved significantly by reducing the hub vertical shear by 34.06% and radial shear by 17.87% with a reduction of blade mass by 23.86%.

An optimization procedure is developed for the design of structural components under crashworthiness requirements. The optimization procedure consists of first developing a system of parallel neural networks able to reproduce the structural behavior during the crash phenomena. Training and test sets are generated by finite element analyses. Then, to find the optimal configuration, both sequential quadratic programming and genetic algorithms are implemented to evaluate the objective and constraint functions using the response surfaces generated by the neural networks. The procedure is applied for the optimization of helicopter subfloor components. In this application, the objective function is taken equal to the sum of two terms: the crush force efficiency and the specific absorbed energy. The values of maximum and mean forces are constrained to meet crashworthiness requirements, whereas other constraints are applied to define the feasibility of the structural solution. The optimal configuration, obtained measuring orders of magnitude savings in the CPU time, allows an increase of the crush force efficiency equal to 18% and a decrease of the mass equal to 8%.

The sequential quadratic programming and genetic algorithms are finely tuned on the optimal design of a brushless DC wheel motor. Combining both methods, a hybrid approach is tested. Multiobjective optimizations are performed using Nondominated Sorting Genetic Algorithm, Strength Pareto Evolutionary Algorithm, and a variable weighted sum of objectives with the sequential quadratic programming. The Pareto fronts are compared in term of accuracy, uniformity, and coverage criteria using some quality indicators.

The idea of multidisciplinary design optimization (MDO) is applied to synthesize optimum robots. The main idea and frame of collaborative optimization are introduced. Three disciplines of working stroke L driving performance and hydraulic component are involved in the design optimization of a 3-RRS robot. The optimization model of system-level and optimization model of subsystem are established. Sequential quadratic programming (SQP) and genetic algorithm (GA) are respectively used to execute the optimization of system-level and the optimization of subsystems using popular commercialized MATLAB. The numerical results indicate that the collaborative optimization can be successfully applied to dealing with the complex robot system, and lay a foundation to solve more complex mechanical system. (5 pages)

The authors present a general framework of the construction of biorthogonal wavelets based on Bernstein bases along with theory analysis and application. The presented framework possesses the largest possible regularity, the required vanishing moments and the passband flatness of frequency response of filters. Based on this concept, the authors establish explicit formulas for filters of biorthogonal wavelets with arbitrary odd lengths. Meanwhile, a new family of parametric filters with symmetry is constructed. The choice of filter bank in wavelet compression is a critical issue that affects image quality. In this study, an optimal model of FIR aiming at image compression is brought forward, and the optimal finite impulse response (FIR) filters can be obtained correspondingly through sequential quadratic programming (SQP) and genetic algorithm (GA). The authors demonstrate the performance of the new family of filters given in this study for image compression with very encouraging results.

Attainment of Kinetic Parameters and Model Validation for Nylon-6 Process

The objective of this study is to propose the effective method of reducing the maximum contact pressure at the contact edge of press-fitted shaft by optimizing the location and the size of stress relief groove in hub face. Finite element analysis was performed in order to determine the contact pressure and stress state on a press-fitted assembly and optimization were applied to select optimal size and location of stress relief groove. In order to reduce the cost of optimization design, approximation optimization method is used and the optimum results obtained by Sequential Quadratic Programming and genetic algorithm are compared. Optimized results show that the maximum contact pressure at the contact edge of press-fitted shaft with optimal stress relief groove decreased about 30%. And the both optimization algorithms can effectively reduced the maximum contact pressure at the contact edge of press-fitted shaft.

This work aims to evaluate the efficiency and robustness of the cross-entropy (CE) method in the context of structural optimization. A two-dimensional truss subject to vertical loads is used as a benchmark test, where one seeks to minimize the structure weight, respecting a structural integrity criterion. The optimal results obtained via CE are compared with reference solutions, obtained via sequential quadratic programming and genetic algorithm. Numerical experiments demonstrate that CE offers a solution or structural optimization that can be very competitive in terms of accuracy and computational efficiency.

A machine learning approach for modeling and optimization of a CO2 post-combustion capture unit

This paper discusses a kind of optimization problem with linear complementarity constraints, and presents a sequential quadratic programming (SQP) algorithm for solving a stationary point of the problem. The algorithm is a modification of the SQP algorithm proposed by Fukushima et al. [Computational Optimization and Applications, 10 (1998), 5-34], and is based on a reformulation of complementarity condition as a system of linear equations. At each iteration, one quadratic programming and one system of equations needs to be solved, and a curve search is used to yield the step size. Under some appropriate assumptions, including the lower-level strict complementarity, but without the upper-level strict complementarity for the inequality constraints, the algorithm is proved to possess strong convergence and superlinear convergence. Some preliminary numerical results are reported.

Performance analysis of support vector machine, Gaussian Process Regression, sequential quadratic programming algorithms in modeling hydrogen-rich syngas production from catalyzed co-gasification of biomass wastes from oil palm

The presence of microcalcification clusters in digital mammograms is a primary indicator of early stages of malignant types of breast cancer and its detection is important to prevent the disease. This paper uses a procedure for the classification of microcalcification clusters in mammograms using sequential Difference of Gaussian filters (DoG) and feedforward Neural Networks (NN). Three methods using class separability, forward sequential search and genetic algorithms for feature selection are compared. We found that the use of Genetic Algorithms (GAs) for selecting the features from microcalcifications and microcalcification clusters that will be the inputs of a feedforward Neural Network (NN) results mainly in improvements in overall accuracy, sensitivity and specificity of the classification.

The present study investigate the numerical solution of nonlinear singular system represented with sixth Painleve equation by the strength of artificial intelligence using feed-forward artificial neural networks (ANNs) optimized with genetic algorithms (GAs), interior point technique (IPT), sequential quadratic programming (SQP), and their hybrids. The ANN provided a compatible method for finding nature-inspired mathematical model based on unsupervised error for sixth Painleve equation and adaptation of weights of these networks is carried out globally by the competency of GA aided with IPT or SQP algorithms. Moreover, a hybrid approach has been adopted for better proposed numerical results. An extensive statistical analysis has been performed through several independent runs of algorithms to validate the accuracy, convergence, and exactness of the proposed scheme.

Comparison of SQP and AL algorithms for deterministic constrained production optimization of hydrocarbon reservoirs

Optimal Design of Heat Exchanger Networks by Using SQP Algorithm Based on GPU Acceleration