Aerodynamic Efficiency Optimization of the 1st Stage of Transonic High Pressure Turbine through Lean and Sweep Angles

The purpose of this study is to optimize the 1st stage of the transonic high pressure turbine (HPT) for enhancement of aerodynamic performance. Isentropic total-to-total efficiency is designated as the objective function. Since the isentropic efficiency can be improved through modifying the geometry of vane and rotor blade, lean angle and sweep angle are chosen as design variables, which can effectively alter the blade geometry. The sensitivities of each design variable are investigated by applying lean and sweep angles to the base nozzle and rotor, respectively. The design space is also determined based on the results of the parametric study. For the design of experiment (DoE), Optimal Latin Hypercube sampling is adopted, so that 25 evenly distributed samples are selected on the design space. Sequentially, based on the values from the CFD calculation, Kriging surrogate model is constructed and refined using Expected Improvement (EI). With the converged surrogate model, optimum solution is sought by using the Genetic Algorithm. As a result, the efficiency of optimum turbine 1st stage is increased by 1.07 % point compared to that of the base turbine 1st stage. Also, the blade loading, pressure distribution, static entropy, shock structure, and secondary flow are thoroughly discussed.

Airfoil Optimization Design Based on the Pivot Element Weighting Iterative Method

Class function/shape function transformation (CST) is an advanced geometry representation method employed to generate airfoil coordinates. Aiming at the morbidity of the CST coefficient matrix, the pivot element weighting iterative (PEWI) method is proposed to improve the condition number of the ill-conditioned matrix in the CST. The feasibility of the PEWI method is evaluated by using the RAE2822 and S1223 airfoil. The aerodynamic optimization of the S1223 airfoil is conducted based on the Isight software platform. First, the S1223 airfoil is parameterized by the CST with the PEWI method. It is very significant to confirm the range of variables for the airfoil optimization design. So the normalization method of design variables is put forward in the paper. Optimal Latin Hypercube sampling is applied to generate the samples, whose aerodynamic performances are calculated by the numerical simulation. Then the Radial Basis Functions (RBF) neural network model is trained by these aerodynamic performance data. Finally, the multi-island genetic algorithm is performed to achieve the maximum lift-drag ratio of S1223. The results show that the robustness of the CST can be improved. Moreover, the lift-drag ratio of S1223 increases by 2.27% and the drag coefficient decreases by 1.4%.

Optimal Latin hypercube sampling-based surrogate model in NAPLs contaminated groundwater remediation optimization process

A surrogate model based groundwater optimization model was developed to solve the non-aqueous phase liquids (NAPLs) contaminated groundwater remediation optimization problem. To illustrate the impact of sampling method improvement to the surrogate model performance improvement, aiming at a nitrobenzene contaminated groundwater remediation problem, optimal Latin hypercube sampling (OLHS) method was introduced to sample data in the input variables feasible region, and a radial basis function artificial neural network was used to construct a surrogate model. Considering the surrogate model's uncertainty, a chance-constrained programming (CCP) model was constructed, and it was solved by genetic algorithm. The results showed the following, for the problem considered in this study. (1) Compared with the Latin hypercube sampling (LHS) method, the OLHS method improves the space-filling degree of sample points considerably. (2) The effects of the two sampling methods on surrogate model performance were analyzed through comparison of goodness of fit, residual and uncertainty. The results indicated that the OLHS-based surrogate model performed better than the LHS-based surrogate model. (3) The optimal remediation strategies at 99%, 95%, 90%, 85%, 80% and 50% confidence levels were obtained, which showed that the remediation cost increased with the confidence level. This work would be helpful for increasing surrogate model performance and lowering the risk of a groundwater remediation strategy.

Surrogating for High Dimensional Computationally Expensive Multi-Modal Functions with Elliptical Basis Function Models

In the engineering design process, approximation Technique could guarantee the fitting precision, speed up the design process and reduce design costs. To a certain extent, surrogate models could replace time-consuming and highly accurate computational fluid dynamics analysis gradually. In this paper, we take Optimal Latin Hypercube Sampling experimental design strategies to determine the sample space and error analysis test sample, adopt the principle of infilling criteria based on the maximum error to improve the accuracy of the surrogate model, test the unimodal and multimodal expensive functions of 10 dimension, 20 dimensions and 30 dimensions, study the performance and scope of EBF-NN surrogate model based on infilling criteria by comparing the RBF-NN surrogate model.

Structure and System Nonprobabilistic Reliability Solution Method Based on Enhanced Optimal Latin Hypercube Sampling

Using the convex model approach, the bounds of uncertain variables are only required rather than the precise probability distributions, based on which it can be made possible to conduct the reliability analysis for many complex engineering problems with limited information. This paper aims to develop a novel nonprobabilistic reliability solution method for structures with interval uncertainty variables. In order to explore the entire domain represented by interval variables, an enhanced optimal Latin hypercube sampling (EOLHS) is used to reduce the computational effort considerably. Through the proposed method, the safety degree of a structure with convex modal uncertainty can be quantitatively evaluated. More importantly, this method can be used to deal with any general problems with nonlinear and black-box performance functions. By introducing the suggested reliability method, a convex-model-based system reliability method is also formulated. Three numerical examples are investigated to demonstrate the efficiency and accuracy of the method.

Approximations for Safety Optimization of Large Systems

This paper presents four approximation methods for the construction of safety related functions. These methods are: Enhanced Multivariate Adaptive Regression Splines, Stepwise Regression, Artificial Neural Network, and the Moving Least Square. The optimal Latin Hypercube Sampling method is used to distribute the sampling points uniformly over the entire design space. Four benchmark problems used in crash and occupant simulation are employed to investigate the accuracy of the approximate or surrogate models. An occupant safety optimization problem is solved using these four response surfaces. Based on numerical results, a best, applicable approximation strategy for safety optimization is proposed in the end.

Computer Aided Reliability and Robustness Assessment

The competitive pressure to shorten product development time has necessitated the automotive industry to rely more on Computer Aided Engineering (CAE) for analyzing and proving product reliability and robustness. The challenge of this approach is the incorporation of product variability, due to manufacturing and customer usage variations in the analysis, requires a massive computation process which may be prohibitive even with today's advanced computers. In this paper, we demonstrate the use of an efficient computational procedure based on optimal Latin Hypercube Sampling (LHS) and a "cheap-to-compute" nonlinear surrogate model using Multivariate Adaptive Regression Splines (MARS) to emulate a computationally intensive complex CAE model. The result of the analysis is the identification of sensitivity of design parameters, in addition to a computationally affordable reliability assessment. Fatigue life durability of automotive shock tower is presented as an example to demonstrate the methodology.