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One problem in incremental product development is that geometric models are limited in their ability to explore radical alternative design variants. In this publication, a function modeling approach is suggested to increase the amount and variety of explored alternatives, since function models (FM) provide greater model flexibility. An enhanced function-means (EF-M) model capable of representing the constraints of the design space as well as alternative designs is created through a reverse engineering process. This model is then used as a basis for the development of a new product variant. This work describes the EF-M model's capabilities for representing the design space and integrating novel solutions into the existing product structure and explains how these capabilities support the exploration of alternative design variants. First-order analyses are executed, and the EF-M model is used to capture and represent already existing design information for further analyses. Based on these findings, a design space exploration approach is developed. It positions the FM as a connection between legacy and novel designs and, through this, allows for the exploration of more diverse product concepts. This approach is based on three steps – decomposition, design, and embodiment – and builds on the capabilities of EF-M to model alternative solutions for different requirements. While the embodiment step of creating the novel product's geometry is still a topic for future research, the design space exploration concept can be used to enable wider, more methodological, and potentially automated design space exploration.

Groundwater extraction from aquifers is a common practice for human use, and variations in groundwater levels can provide valuable information on the hydrogeological properties of the aquifer. However, reliable data on pumping rates and distribution are often lacking due to unsupervised groundwater pumping activities. This study presents a new mathematical model for transfer function modeling that depicts the drawdown response caused by pumping in an unconfined aquifer system. To account for the dense and unsupervised pumping events, the uniform pumping approach was used to estimate these effects. To more accurately represent unconfined flow, the model first integrates lagging theory into a response function derived from the Boussinesq equation. The lagging theory accounts for the effects of both inertial force and capillary suction. Furthermore, the model has been used to derive both specific yield and transmissivity along with two lagging parameters simultaneously using only groundwater level information from the Choshui River region in Taiwan. The estimated results suggest that this approach provides reliable estimates of hydrogeological parameters, demonstrating its usefulness for water resource management and water budget evaluation. Plain Language Summary This study examines the process of extracting water from underground sources, known as aquifers, and how monitoring changes in water levels can provide valuable insights into the characteristics of the aquifer. It can be challenging to obtain accurate information on the amount of water being pumped out due to inadequate monitoring. The researchers have developed a novel approach to comprehending the impact of water extraction on the water levels in these subterranean regions. This method considers the general pattern of water use to pump out water without close monitoring. It also incorporates realistic ideas about how water moves through the ground, taking into account factors such as the delay in water movement and the role of different forces in the soil. The study applied this method to data from Taiwan's Choshui River area and was able to determine important details about the aquifer using only water level information. These findings hold promise for effective water resource management and the wise use of water. A novel mathematical model for groundwater extraction in unconfined aquifer systems. The model captures drawdown response due to pumping, integrates insights from uniform pumping approach for reflecting heavy pumping activities, the Boussinesq equation for formulating the unconfined flow, and lagging theory for capturing the effect from capillary fringe.

Background Intraclass correlation coefficients (ICC) are recommended for the assessment of the reliability of measurement scales. However, the ICC is subject to a variety of statistical assumptions such as normality and stable variance, which are rarely considered in health applications. Methods A Bayesian approach using hierarchical regression and variance-function modeling is proposed to estimate the ICC with emphasis on accounting for heterogeneous variances across a measurement scale. As an application, we review the implementation of using an ICC to evaluate the reliability of Observer OPTION 5 , an instrument which used trained raters to evaluate the level of Shared Decision Making between clinicians and patients. The study used two raters to evaluate recordings of 311 clinical encounters across three studies to evaluate the impact of using a Personal Decision Aid over usual care. We particularly focus on deriving an estimate for the ICC when multiple studies are being considered as part of the data. Results The results demonstrate that ICC varies substantially across studies and patient-physician encounters within studies. Using the new framework we developed, the study-specific ICCs were estimated to be 0.821, 0.295, and 0.644. If the within- and between-encounter variances were assumed to be the same across studies, the estimated within-study ICC was 0.609. If heteroscedasticity is not properly adjusted for, the within-study ICC estimate was inflated to be as high as 0.640. Finally, if the data were pooled across studies without accounting for the variability between studies then ICC estimates were further inflated by approximately 0.02 while formerly allowing for between study variation in the ICC inflated its estimated value by approximately 0.066 to 0.072 depending on the model. Conclusion We demonstrated that misuse of the ICC statistics under common assumption violations leads to misleading and likely inflated estimates of interrater reliability. A statistical analysis that overcomes these violations by expanding the standard statistical model to account for them leads to estimates that are a better reflection of a measurement scale’s reliability while maintaining ease of interpretation. Bayesian methods are particularly well suited to estimating the expanded statistical model.

This work is aimed at establishing a common frame and understanding of function modeling (FM) for our ongoing research activities. A comparative review of the literature is performed to grasp the various FM approaches with their commonalities and differences. The relations of FM with the research fields of artificial intelligence, design theory, and maintenance are discussed. In this discussion the goals are to highlight the features of various classical approaches in relation to FM, to delineate what FM introduces to these fields, and to discuss the applicability of various FM approaches in these fields. Finally, the basic ideas underlying our projects are introduced with reference to the general framework of FM.

Functional modeling is an analytical approach to design problems that is widely taught in certain academic communities but not often used by practitioners. This approach can be applied in multiple ways to formalize the understanding of the systems, to support the synthesis of the design in the development of a new product, or to support the analysis and improvement of existing systems incrementally. The type of usage depends on the objectives that are targeted. The objectives can be categorized into two key groups: discovering a totally new solution, or improving an existing one. This article proposes to use the functional modeling approach to achieve three goals: to support the representation of physics-based reasoning, to use this physics-based reasoning to assess design options, and finally to support innovative ideation. The exemplification of the function-based approach is presented via a case study of a glue gun proposed for this Special Issue. A reverse engineering approach is applied, and the authors seek an incremental improvement of the solution. As the physics-based reasoning model presented in this article is heavily dependent on the quality of the functional model, the authors propose a general approach to limit the interpretability of the functional representations by mapping the functional vocabulary with elementary structural blocks derived from bond graph theory. The physics-based reasoning approach is supported by a mathematical framework that is summarized in the article. The physics-based reasoning model is used for discovering the limitations of solutions in the form of internal contradictions and guiding the design ideation effort.

This paper focuses on the modeling and analysis of a high-voltage layer heater (HVLH) designed for environmentally friendly vehicles, including electric vehicles (EVs) and plug-in hybrid electric vehicles (PHEVs), through multiphysics simulations that cover electrical, thermal, and fluid dynamics aspects. Due to the significant expenses and extensive time needed for producing and experimentally characterizing HVLHs, simulation and physical modeling methods are favored in the development stage. This research pioneers the separate modeling of thermal boundary conditions for the heating element (TFE) within the electrical domain, enabling the calculation of Joule heating and the analysis of transient conjugate heat transfer. Moreover, this research initiates the application of transfer function modeling for the HVLH component, expanding its use to the broader context of heating, ventilation, and air conditioning (HVAC) systems. The simulation results, which include calculations for Joule heating and temperature fields based on input voltage and flow conditions, closely follow experimental data. The derived transfer function, along with the regression parameters, precisely predicts the dynamic behavior of the system. The simulation-based modeling approach presented in this study significantly advances the design and control of environmentally friendly electric heating systems, providing a sustainable and cost-effective solution.

This paper introduces a rigorous framework for function modeling of complex multidisciplinary systems based on the system state flow diagram (SSFD). The work addresses the need for a consistent methodology to support solution-neutral function-based system decomposition analysis, facilitating the design, modeling, and analysis of complex systems architectures. A rigorous basis for the SSFD is established by defining conventions for states and function definitions and a representation scheme, underpinned by a critical review of existing literature. A set of heuristics are introduced to support the function decomposition analysis and to facilitate the deployment of the methodology with strong practitioner guidelines. The SSFD heuristics extend the existing framework of Otto and Wood (2001) by introducing a conditional fork node heuristic, to facilitate analysis and aggregation of function models across multiple modes of operation of the system. The empirical validation of the SSFD function modeling framework is discussed in relation to its application to two case studies: a benchmark problem (glue gun) set for the engineering design community; and an industrial case study of an electric vehicle powertrain. Based on the evidence from the two case studies presented in the paper, a critical evaluation of the SSFD function modeling methodology is discussed based on the function benchmarking framework established by Summers et al. (2013), considering the representation, modeling, cognitive, and reasoning characteristics. The significance of this paper is that it establishes a rigorous reference framework for the SSFD function representation and a consistent methodology to guide the practitioner with its deployment, facilitating its impact to industrial practice.

The main focus of this paper is the integration of an integrated function modeling (IFM) framework in an engineering framework based on graph-based design languages (GBDLs). Over the last decade, GBDLs have received increasing attention as they offer a promising approach for addressing several important challenges in engineering, such as the frequent and time-consuming transfer of data between different computer aided engineering (CAE) tools. This absorbs significant amounts of manual labor in engineering design projects. GBDLs create digital system models at a meta level, encompassing all relevant information concerning a certain product design and feeding this into the relevant simulation tools needed for evaluating the impact of possible design variations on the performance of the resulting products/parts. It is possible to automate this process using digital compilers. Because of this, it is also possible to realize systematic design variations for a very large number of parameters and topological variants. Therefore, these kinds of graph-based languages are a powerful means for creating a large number of viable design alternatives and for permitting fast evaluation processes against the given specifications. While, thus far, such analyses tend to be based on a more or less fully defined system, this paper proposes an expansion of the applicability of GBDLs into the domain of product functions to cohesively link conceptual with embodiment design stages. This will also help with early systematic, automated generation and the validation of design alternatives through relevant simulation tools during embodiment design. Further, it will permit the automated exploration of function paths and enable extended analysis possibilities, such as the detection of functional bottlenecks, while enhancing the traceability of the design over the development process. For these extended analysis possibilities, a function analysis tool was developed that adopts core ideas of the failure mode and effects analysis (FMEA). In this, the functional distinction between function carriers and function-related processes allows the goal-directed assessment of component reliabilities and the detectability and importance of processes in a technical system. In the paper, the graph-based modeling of functions and the function analysis tools are demonstrated on the example of a multicopter.

Research and industrial practice have produced a host of function models and modeling approaches over the last decades. Each of these is meant to support designers in their design endeavors. Industrial practice is excessively diversified in terms of contextual requirements, aims, and adopted processes; this automatically begs the question which of the existing models should be selected for application in a specific situation. This paper sets out to contribute to this discourse. It strives to benchmark the fairly novel integrated function modeling (IFM) framework against the well-established function structures modeling approach. The paper comparatively investigates the respective capabilities of the approaches, following the benchmarking protocol used earlier in relation to this Special Issue. Function structures are used as reference as they represent one of the most widespread function modeling approaches in research and practice. Both function structures and the IFM framework are exemplarily applied for modeling a glue gun. The gradual generation and refinement of the models is used to showcase their respective benefits and shortcomings. Eventually, the IFM framework is found to excel over function structures in terms of comprehensiveness and support for different types of function analyses. Finally, future research directions are proposed.