Statistical evaluation of performance impact of manufacturing variability by an adjoint method

Luo, Jiaqi; Liu, Feng

doi:10.1016/j.ast.2018.03.030

Cited by 46 publications

(17 citation statements)

References 25 publications

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“…33 This approach is closely similar to Principal Component Analysis (PCA). 2,9,15–16,29–31 The K–L expansion of truncated Normal random fields can be generalized from that of Normal random fields obtained by Mercer’s theorem. 34 For the random fields ev(s,ω), the K–L expansion iswhere λi denotes the geometric variability attributable to the i -th mode and ϕi(s) denotes the normalized geometric mode shape.…”

Section: Modeling Geometric Variations Caused By Manufacturing Errorsmentioning

confidence: 99%

“…33 This approach is closely similar to Principal Component Analysis (PCA). 2,9,[15][16][29][30][31] The K-L expansion of truncated Normal random fields can be generalized from that of Normal random fields obtained by Mercer's theorem. 34 For the random fields e v ðs,ωÞ, the K-L expansion is…”

Section: Dimensionality Reduction Model For Describing Geometric Vari...mentioning

confidence: 99%

“…Because numerous samples are necessary for MCS to obtain enough accurate results, adjoint methods and polynomial chaos (PC) methods have been developed rapidly to further improve the efficiency of MCS. Giebmanns et al 13 and Luo et al [14][15][16] applied the first-order (FO) and second-order (SO) adjoint sensitivity methods to stochastic aerodynamic problems, respectively. However, the FO adjoint method is difficult to capture the nonlinear relationship resulting from geometrical variations.…”

Section: Introductionmentioning

confidence: 99%

“…However, the FO adjoint method is difficult to capture the nonlinear relationship resulting from geometrical variations. 13 Although the nonlinear dependence of performance variations on geometric variations were successfully captured by SO adjoint method, [14][15][16] the method is suitable for small-scale uncertainty problems. With the decrease of machining precision, the local geometric change scale of blades may increase.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic aerodynamic analysis for compressor blades with manufacturing variability based on a mathematical dimensionality reduction method

Guo

Chu

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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It is essential for engineering manufacture and robust design to evaluate the impact of manufacturing variability on the aerodynamics of compressor blades efficiently and accurately. In the paper, a novel quadratic curve approximation method based on the scanning points of blade design profiles was introduced and combined with Karhunen–Loève expansion, a mathematical dimensionality reduction method for modeling manufacturing variability as truncated Normal process was proposed. Subsequently, Sparse Approximation of Moment-based Arbitrary Polynomial Chaos (SAMBA PC) and computational fluid dynamics (CFD) were applied to build a computational framework for stochastic aerodynamic analysis considering manufacturing variability. Finally, the framework was adopted to evaluate the aerodynamic variations of a high subsonic compressor cascade under the design incidence. The results illustrate that the SAMBA PC method is more efficient than the traditional methods such as Monte Carlo simulation (MCS) for stochastic aerodynamic analysis. Through uncertainty quantification, the impact of manufacturing variability on the global aerodynamic performance is primarily reflected in the fluctuation of aerodynamic losses, and the fluctuation of the total losses is mainly contributed by the fluctuation of the separation loss after the suction peak (a negative pressure spike near the leading edge (LE)) and the boundary-layer loss on the suction surface (SS). With sensitivity analysis, the most important geometric modes to aerodynamics can be revealed, which provides a useful reference for manufacturing inspection process and helps reduce computational cost in robust design.

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Section: Modeling Geometric Variations Caused By Manufacturing Errorsmentioning

confidence: 99%

Section: Dimensionality Reduction Model For Describing Geometric Vari...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stochastic aerodynamic analysis for compressor blades with manufacturing variability based on a mathematical dimensionality reduction method

Guo

Chu

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…Engels-Putzka et al 23 used the IMC model to estimate the mass flow rate, total-pressure ratio and total-temperature ratio in the two-stage Darmstadt Transonic Compressor using the TRACE flow and adjoint solver developed at DLR for use in robust design. Luo et al 24 adopted a similar approach of using the adjoint and higher order sensitivities to approximately evaluate the aerodynamic performance of a turbine subject to manufacturing variability using Taylor expansion. The authors used a continuous adjoint approach based on inviscid Euler equations to obtain the adjoint sensitivity and Hessian solutions.…”

Section: Introductionmentioning

confidence: 99%

An adjoint‐assisted multilevel multifidelity method for uncertainty quantification and its application to turbomachinery manufacturing variability

Mohanamuraly

Müller

2021

Numerical Meth Engineering

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In this work we propose, analyse, and demonstrate a new adjoint-based multilevel multifidelity Monte Carlo framework called FastUQ. The framework unifies the multifidelity analysis of Ng 1 , multilevel multifidelity analysis of Geraci 2 and an adjoint error correction surrogate model due to Ghate 3. The optimal mean squared error estimator shows that introducing multilevel in a multifidelity framework guarantees reduction in computational cost. Moreover, unlike the surrogate model of Ghate 3 , the method does not suffer from the curse of dimensionality. FastUQ is demonstrated here to quantify uncertainties in aerodynamic parameters due to surface variations caused by the manufacturing processes for a highly loaded turbine cascade. A stochastic model for surface variations on the cascade is proposed and optimal dimensionality reduction of model parameters is realised using goal-based principal component analysis considering the adjoint sensitivities of multiple quantities of interest (QoI). The proposed method achieves a reduction of 70% in computational cost in predicting the mean quantities like total-pressure loss and mass flow rate compared to state-of-art MLMC method. The robustness of the method is shown in application to the highly non-linear case of a heavily loaded turbine cascade operating at off-design conditions.

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Parametric modeling method for integrated design and manufacturing of radial compressor impeller

Zhou

Song

Xing

et al. 2020

Int J Adv Manuf Technol

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Statistical evaluation of performance impact of manufacturing variability by an adjoint method

Cited by 46 publications

References 25 publications

Stochastic aerodynamic analysis for compressor blades with manufacturing variability based on a mathematical dimensionality reduction method

Stochastic aerodynamic analysis for compressor blades with manufacturing variability based on a mathematical dimensionality reduction method

An adjoint‐assisted multilevel multifidelity method for uncertainty quantification and its application to turbomachinery manufacturing variability

Parametric modeling method for integrated design and manufacturing of radial compressor impeller

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