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This paper presents a new topology optimization approach based on the so-called Moving Morphable Components (MMC) solution framework. The proposed method improves several weaknesses of the previous approach (e.g., Guo et al. in J Appl Mech 81:081009, 2014a ) in the sense that it can not only allow for components with variable thicknesses but also enhance the numerical solution efficiency substantially. This is achieved by constructing the topological description functions of the components appropriately, and utilizing the ersatz material model through projecting the topological description functions of the components. Numerical examples demonstrate the effectiveness of the proposed approach. In order to help readers understand the essential features of this approach, a 188 line Matlab implementation of this approach is also provided.

This article brings forward a new computational method for reliability-based design optimization (RBDO) of complex mechanical systems subject to input random variables following arbitrary, dependent probability distributions. It involves a generalized polynomial chaos expansion (GPCE) for reliability analysis subject to dependent input random variables, a novel fusion of the GPCE approximation and score functions for estimating the sensitivities of the failure probability with respect to design variables, and standard gradient-based optimization algorithms, resulting in a multi-point single-step design process. The method, designated as the multi-point single-step GPCE method or simply the MPSS-GPCE method, yields analytical formulae for computing the failure probability and its design sensitivities concurrently from a single stochastic simulation or analysis. For this reason, the MPSS-GPCE method affords the ability to solve industrial-scale problems with large design spaces. Numerical results stemming from mathematical functions or elementary engineering problems indicate that the new method provides more accurate or computationally efficient design solutions than existing methods or reference solutions. Furthermore, the shape design optimization of a jet engine compressor blade root was successfully conducted, demonstrating the power of the new method in confronting practical RBDO problems.

Even though the conventional finite element analysis (FEA)-based boundary method for shape design sensitivity analysis (DSA) has the advantage of low computation costs, the accuracy of computed sensitivity is not satisfactory due to the inaccurate consideration of boundary geometry. To overcome this difficulty, employing an efficient adjoint method, we propose an isogeometric analysis (IGA)-based boundary method for shape DSA that can exactly handle the normal and curvature on a non-smooth boundary. The required computational costs for the boundary method is much less than that of the domain method since the computation is performed only on the boundary. Furthermore, the shape sensitivity of performance measure defined by a boundary functional on the non-smooth boundary can be precisely obtained using the curvature of boundary, the normal component of design velocity, and the tangential divergence of design velocity. Through numerical examples, the accuracy and efficiency of the IGA-based boundary method for DSA are compared with other methods such as FEA-based boundary and domain methods. It is demonstrated that the IGA-based shape design sensitivity of the boundary functional could accurately represent the tangential divergence on the boundary that the linear shape function in the FEA-based one cannot properly represent.

Reliability analysis and reliability-based design optimization (RBDO) require an exact input probabilistic model to obtain accurate probability of failure (PoF) and RBDO optimum design. However, often only limited input data is available to generate the input probabilistic model in practical engineering problems. The insufficient input data induces uncertainty in the input probabilistic model, and this uncertainty forces the PoF to be uncertain. Therefore, it is necessary to consider the PoF to follow a probability distribution. In this paper, the probability of the PoF is obtained with consecutive conditional probabilities of input distribution types and parameters using the Bayesian approach. The approximate conditional probabilities are obtained under reasonable assumptions, and Monte Carlo simulation is applied to calculate the probability of the PoF. The probability of the PoF at a user-specified target PoF is defined as the conservativeness level of the PoF. The conservativeness level, in addition to the target PoF, will be used as a probabilistic constraint in an RBDO process to obtain a conservative optimum design, for limited input data. Thus, the design sensitivity of the conservativeness level is derived to support an efficient optimization process. Using numerical examples, it is demonstrated that the conservativeness level should be involved in RBDO when input data is limited. The accuracy and efficiency of the proposed design sensitivity method is verified. Finally, conservative RBDO optimum designs are obtained using the developed methods for limited input data problems.

Polynomial chaos (PC) methods with Gauss-type quadrature formulae have been widely applied for robust design optimization. During the robust optimization, gradient-based optimization algorithms are commonly employed, where the sensitivities of the mean and variance of the output response with respect to design variables are calculated. For robust optimization with computationally expensive response functions, although the PC method can significantly reduce the computational cost, the direct application of the classical finite difference method for the analysis of the design sensitivity is impractical with a limited computational budget. Therefore, in this paper, a semi-analytical design sensitivity analysis method based on the PC method is proposed, in which the sensitivity is directly derived based on the Gauss-type quadrature formula without additional function evaluations. Comparative studies conducted on several mathematical examples and an aerodynamic robust optimization problem revealed that the proposed method can reduce the computational cost of robust optimization to a certain extent with comparable accuracy compared with the finite difference-based PC method.

An accurate mathematical model for the tooth surface of spiral bevel gears incorporating manufacturing errors has been developed. A gear pair meshing model with consideration of assembly error has been derived. The impact of comprehensive errors of manufacturing and assembling on the tooth surface contact patterns has been investigated. A low sensitivity design method for tooth surfaces considering comprehensive errors of manufacture and assemble has been proposed. The results show that with the error changing from negative to positive, the tooth surface contact pattern of the cutter mean radius, ratio of roll, and the pinion axial displacement error move from toe-top to heel-root sides. The tooth surface contact pattern of the radial distance, horizontal, work offset error move from heel-root to the toe-top sides. For the comprehensive errors, the five parameters of the cutter mean radius, radial distance, horizontal, ratio of roll, and pinion axial displacement error have the most significant impact on the tooth surface contact pattern, directly leading to severe edge contact. With surface modification, the movement of parameters under error conditions decreases substantially, and except for a little edge contact in the ratio of rolling error, no edge contact occurs in other parameter errors.

Conventionally, the construction of a pair-matched sample selects treated and control units and pairs them in a single step with a view to balancing observed covariates x and reducing the heterogeneity or dispersion of treated-minus-control response differences, Y. In contrast, the method of cardinality matching developed here first selects the maximum number of units subject to covariate balance constraints and, with a balanced sample for x in hand, then separately pairs the units to minimize heterogeneity in Y. Reduced heterogeneity of pair differences in responses Y is known to reduce sensitivity to unmeasured biases, so one might hope that cardinality matching would succeed at both tasks, balancing x, stabilizing Y. We use cardinality matching in an observational study of the effectiveness of for-profit and not-for-profit private high schools in Chile—a controversial subject in Chile—focusing on students who were in government run primary schools in 2004 but then switched to private high schools. By pairing to minimize heterogeneity in a cardinality match that has balanced covariates, a meaningful reduction in sensitivity to unmeasured biases is obtained.

A sensitivity analysis for an observational study assesses how much bias, due to nonrandom assignment of treatment, would be necessary to change the conclusions of an analysis that assumes treatment assignment was effectively random. The evidence for a treatment effect can be strengthened if two different analyses, which could be affected by different types of biases, are both somewhat insensitive to bias. The finding from the observational study is then said to be replicated. Evidence factors allow for two independent analyses to be constructed from the same dataset. When combining the evidence factors, the Type I error rate must be controlled to obtain valid inference. A powerful method is developed for controlling the familywise error rate for sensitivity analyses with evidence factors. It is shown that the Bahadur efficiency of sensitivity analysis for the combined evidence is greater than for either evidence factor alone. The proposed methods are illustrated through a study of the effect of radiation exposure on the risk of cancer. An R package, evidenceFactors, is available from CRAN to implement the methods of the paper.

Weak instruments produce causal inferences that are sensitive to small failures of the assumptions underlying an instrumental variable, so strong instruments are preferred. The possibility of strengthening an instrument at the price of a reduced sample size has been proposed in the statistical literature and used in the medical literature, but there has not been a theoretical study of the trade-off of instrument strength and sample size. This trade-off and related questions are examined using the Bahadur efficiency of a test or a sensitivity analysis. A moderate increase in instrument strength is worth more than an enormous increase in sample size. This is true with a flawless instrument, and the difference is more pronounced when allowance is made for small unmeasured biases in the instrument. A new method of strengthening an instrument is proposed: it discards half the sample to learn empirically where the instrument is strong, then discards part of the remaining half to avoid areas where the instrument is weak; however, the gains in instrument strength can more than compensate for the loss of sample size. The example is drawn from a study of the effectiveness of high-level neonatal intensive care units in saving the lives of premature infants.

We discuss observational studies that test many causal hypotheses, either hypotheses about many outcomes or many treatments. To be credible an observational study that tests many causal hypotheses must demonstrate that its conclusions are neither artifacts of multiple testing nor of small biases from nonrandom treatment assignment. In a sense that needs to be defined carefully, hidden within a sensitivity analysis for nonrandom assignment is an enormous correction for multiple testing: In the absence of bias, it is extremely improbable that multiple testing alone would create an association insensitive to moderate biases. We propose a new strategy called \"cross-screening,\" different from but motivated by recent work of Bogomolov and Heller on replicability. Cross-screening splits the data in half at random, uses the first half to plan a study carried out on the second half, then uses the second half to plan a study carried out on the first half, and reports the more favorable conclusions of the two studies correcting using the Bonferroni inequality for having done two studies. If the two studies happen to concur, then they achieve Bogomolov-Heller replicability; however, importantly, replicability is not required for strong control of the family-wise error rate, and either study alone suffices for firm conclusions. In randomized studies with just a few null hypotheses, cross-screening is not an attractive method when compared with conventional methods of multiplicity control. However, cross-screening has substantially higher power when hundreds or thousands of hypotheses are subjected to sensitivity analyses in an observational study of moderate size. We illustrate the technique by comparing 46 biomarkers in individuals who consume large quantities of fish versus little or no fish. The R package CrossScreening on CRAN implements the cross-screening method. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.