Although robustness is an important consideration to guarantee the performance of designs under deviation, systems are often engineered by evaluating their performance exclusively at nominal conditions. Robustness is sometimes evaluated a posteriori through a sensitivity analysis, which does not guarantee optimality in terms of robustness. This article introduces an automated design framework based on multiobjective optimisation to evaluate robustness as an additional competing objective. Robustness is computed as a sampled hypervolume of imposed geometrical and operational deviations from the nominal point. In order to address the high number of additional evaluations needed to compute robustness, artificial neutral networks are used to generate fast and accurate surrogates of high-fidelity models. The identification of their hyperparameters is formulated as an optimisation problem. In the frame of a case study, the developed methodology was applied to the design of a small-scale turbocompressor. Robustness was included as an objective to be maximised alongside nominal efficiency and mass-flow range between surge and choke. An experimentally validated 1D radial turbocompressor meanline model was used to generate the training data. The optimisation results suggest a clear competition between efficiency, range and robustness, while the use of neural networks led to a speed-up by four orders of magnitude compared to the 1D code.

Seasonal effects can significantly impact the robustness of socio-technical systems (STS) to demand fluctuations. There is an increasing need to develop novel design approaches that can support capacity planning decisions for enhancing the robustness of STS against seasonal effects. This paper proposes a new network motif-based approach to supporting capacity planning in STS for an improved seasonal robustness. Network motifs are underlying nonrandom subgraphs within a complex network. In this approach, we introduce three motif-based metrics for system performance evaluation and capacity planning decision-making. The first one is the imbalance score of a motif (e.g., a local service network), the second one is the measurement of a motif’s seasonal robustness, and the third one is a capacity planning decision criterion. Based on these three metrics, we validate that the sensitivity of STS performance against seasonal effects is highly correlated with the imbalanced capacity between service nodes in an STS. Correspondingly, we formulate a design optimisation problem to improve the robustness of STS by rebalancing the resources at critical service nodes. To demonstrate the utility of the approach, a case study on Divvy bike-sharing system in Chicago is conducted. With a focus on the size-3 motifs (a subgraph consisting three docked stations), we find that there is a significant correlation between the difference of the number of docks among the stations in a motif and the return/rental performance of such a motif against seasonal changes. Guided by this finding, our design approach can successfully balance out the number of docks between those stations that have caused the most severe seasonal perturbations. The results also imply that the network motifs can be an effective local structural representation in support of STS robust design. Our approach can be generally applied in other STS where the system performances are significantly impacted by seasonal changes, for example, supply chain networks, transportation systems and power grids.

Along with the ever-increasing customer demands, early consideration of variation in terms of robust design is important to avoid expensive iterations in the product development. However, existing methods are detached from the development process and can therefore only be applied at a late stage or only with comprehensive expert knowledge. Especially in the concept stage, where the geometry of a product is not yet defined and the optimisation potential is high, effective solution proposals for systematic consideration of variation are lacking. Therefore, this paper describes a new integrated approach facilitating robust and tolerance design in the concept stage. The novelty of the approach using ontologies and graph-based visualisation is the close linkage of product development and tolerance knowledge, which allows automation and helps to avoid time- and cost-intensive iteration loops. As a result, a robust and tolerance-compliant concept design, an initial qualitative tolerance specification and instructions for the further tolerancing process are already available at the end of the concept stage. The applicability and the benefits of the approach are illustrated by representative case studies and a user study allowing a critical comparison between the conventional, mostly subjective procedure and the presented approach.

Sensing machine elements offer the potential to upgrade conventional machine elements by extending their primary function to be able to measure a quantity of interest at its point of origin in a technical system, the so-called in situ measurement. To ensure the functionality of these next generation machine elements, special attention must be paid to uncertainty in terms of modelling to be able to correctly evaluate the provided signal and obtain reliable information. Consequently, this contribution describes an approach to classify uncertainty in sensing technology, especially in SMEs, based on the amount of available information, which can be used as a point of departure to reduce the impact of occurring uncertainty to improve the robustness of the obtained signal. Starting from the understanding of uncertainty and the corresponding classification scheme as well as its linkage to robust design from the Collaborative Research Centre 805, a quantitative model is presented to determine the impact of uncertainty on a measuring signal. The applicability of the proposed approach is demonstrated using the example of a sensing timing belt by taking into account the uncertainty from the SME itself and also from the surrounding technical system.

Robust design methods have expanded from experimental techniques to include sampling methods, sensitivity analysis and probabilistic optimisation. Such methods typically require many evaluations. We study design and noise variable cross-term second derivatives of a response to quickly identify design variables that reduce response variability. We first compute the response uncertainty and variance decomposition to determine contributing noise variables of an initial design. Then we compute the Hessian second-derivative matrix cross-terms between the variance-contributing noise variables and proposed design change variables. Design variable with large Hessian terms are those that can reduce response variability. We relate the Hessian coefficients to reduction in Sobol indices and response variance change. Next, the first derivative Jacobian terms indicate which design variable can shift the mean to maintain a desired nominal target value. Thereby, design changes can be proposed to reduce variability while maintaining a targeted nominal value. This workflow finds changes that improve robustness with a minimal four runs per design change. We also explore further computation reductions achieved through compounding variables. An example is shown on a Stirling engine where the top four variance-contributing tolerances and design changes identified through 16 Hessian terms generated a design with 20% less variance.

Over the last decades, finite element analysis (FEA) has become a standard tool in industrial product development, allowing for virtual analysis of designs, quick turnaround times and prompt implementation of results. Although academic research also provides numerous approaches for evaluating a product’s robustness towards geometrical, material and load variations based on FEA analyses, this, however, stands in striking contrast to the limited use of these FEA-based variation simulations in industry. In order to bridge the existing gap between academic research and industrial application, this paper explores the barriers that limit the adoption of FEA-based variation simulation. The investigation is based on interviews with five lead engineers, followed by a case study that details the underlying technical challenges and allows for some initial suggestions for future solutions. The case study involves a sterile canister with seven geometrical variables. The design objective is to ensure sufficient sealing within the range of expected probabilistic variation. The combined study details the identified main barriers for a wider application, that is, the lack of robust CAD, practical guidelines to select an efficient design of experiments for design purposes, and the complexity of the automated processes. From a technical perspective, the case study results in estimations for main and interaction effects, an accurate metamodel and Monte Carlo simulations of 100,000 samples providing the design engineer with more detailed and actionable insights on the performance of the product compared with the traditional nominal or best/worst case simulations.

The design of a connected engineered system requires numerous design decisions that influence one another. In a connected system that comprises numerous interacting decisions involving concurrency and hierarchy, accounting for interactions while also managing uncertainties, it is imperative to make robust decisions. In this article, we present a method for robust design using coupled decisions to identify design decisions that are relatively insensitive to uncertainties. To account for the influence among decisions, design decisions are modelled as coupled decisions. They are defined using three criteria: the types of decisions, the strength of interactions and the decision levels. In order to make robust decisions, robust design methods are classified based on sources of uncertainty, namely, Type I (noise factors), Type II (design variables) and Type III (function relationship between design variables and responses). The design of a one-stage reduction gearbox is used as a demonstration example. To illustrate the proposed method for robust design using coupled decisions, we present the simultaneous selection of gear material and gearbox geometry in a coupled decision environment while managing the uncertainties involved in designing gearboxes.

This paper develops theoretical foundations for extending Gauss–Hermite quadrature to robust design with computer experiments. When the proposed method is applied with m noise variables, the method requires 4m + 1 function evaluations. For situations in which the polynomial response is separable, this paper proves that the method gives exact transmitted variance if the response is a fourth-order separable polynomial response. It is also proven that the relative error mean and variance of the method decrease with the dimensionality m if the response is separable. To further assess the proposed method, a probability model based on the effect hierarchy principle is used to generate sets of polynomial response functions. For typical populations of problems, it is shown that the proposed method has less than 5% error in 90% of cases. Simulations of five engineering systems were developed and, given parametric alternatives within each case study, a total of 12 case studies were conducted. A comparison is made between the cumulative density function for the hierarchical probability models and a corresponding distribution function for case studies. The data from the case-based evaluations are generally consistent with the results from the model-based evaluation.