Ergonomics,axiomatic design and complexity theory

Ergonomic systems must be designed to be robust and efficient in satisfying their functional requirements (FRs) and constraints. This paper deals with the application of axiomatic design theory and complexity theory to ergonomics. Axiomatic design theory prescribes criteria for the best design and the complexity theory provides means of minimizing the complexity of a system. Axiomatic design divides the design world into four domains and the design activity consists of mapping between the domains. Two axioms?–?the Independence Axiom and the Information Axiom?–?must be satisfied during the mapping process. The highest-level FRs and design parameters are decomposed until the details of the design are completely developed. Uncoupled designs and decoupled designs satisfy the Independence Axiom. The complexity theory shows that there are four different types of complexity: time-independent real and imaginary complexity, and time-dependent combinatorial and periodic complexity. To reduce complexity, the real complexity and imaginary complexity must be eliminated and the time-dependent combinatorial complexity should be transformed into a periodic complexity. Uncoupled designs are the best from the ergonomic point of view, since they do not have imaginary complexity and thus eliminate unnecessary work. Decoupled designs can create imaginary complexity and are thus less desirable than uncoupled designs. Functional periodicity can transform a system with combinatorial complexity to a periodic complexity to reduce complexity and provide a long-term stability to an ergonomic system.     

A Theory of Complexity, Periodicity and the Design Axioms

One of the topics that has received the attention of mathematicians, scientists and engineers is the notion of complexity. The subject is still being debated, as it lacks a common definition of complexity, concrete theories that can predict complex phenomena, and the mathematical tools that can deal with problems involving complexity. In axiomatic design, complexity is defined only when specific functional requirements or the exact nature of the query are defined. Complexity is defined as a measure of uncertainty in achieving a set of specific functions or functional requirements. Complexity is related to information, which is defined in terms of the probability of success of achieving the Functional Requirements (FRs). There are two classes of complexity: time-dependent complexity and time-independent complexity. There are two orthogonal components of time-independent complexity, i.e., real complexity and imaginary complexity. The vector sum is called absolute complexity. Real complexity of coupled design is larger than that of uncoupled or decoupled designs. Imaginary complexity can be reduced when the design matrix is known. As an example of time-independent imaginary complexity, the design of a printing machine based on xerography is discussed. There are two kinds of time-dependent real complexity: time-dependent combinatorial complexity and time-dependent periodic complexity. Using a robot-scheduling problem as an example, it is shown that a coupled design with a combinatorial complexity can be reduced to a decoupled design with periodic complexity. The introduction of periodicity simplifies the design by making it deterministic, which requires much less information. Whenever a combinatorial complexity is converted to a periodic complexity, complexity and uncertainty is reduced and design simplified.     

Using design equations to identify sources of complexity in human–machine interaction

A coupled design is generally more difficult to use than an uncoupled design. It should therefore be replaced by an uncoupled design. The problem described in this paper is to identify sources of couplings and propose new design parameters that uncouple the design. A method based on Suh's axiomatic design (AD) was developed. There are two axioms in AD. The first axiom proclaims that design parameters should be selected so that functional requirements become independent. Based on this, a method for Human Factors Design was devised. It is called Design Equations for Systems Analysis (DESA). Several case studies of human factors design problems were analysed: a refrigerator, hand tools and a driver's compartment. As demonstrated in the case studies, DESA is useful for analysis of existing design solutions as well as for synthesis of new design alternatives. The second axiom in AD aims at minimizing information in design. It should be noted that this is in agreement with Hick's law and Fitts’ law. The calculation of information or entropy in design was demonstrated for an adjustable workstation. The second axiom was adapted to human factors design by taking into account the variability of human attributes, in this case anthropometric measures. If the manufacturer's supplied adjustability range and the users’ desired range are known, the entropy or information of an adjustable workstation can be quantified. In comparing several workstations, the workstation with the least information should be selected.     

Computing the Information Content of Decoupled Designs

The information content of uncoupled designs can be computed by summing the information content associated with each functional requirement. This paper proves that information cannot be summed for decoupled designs. To overcome this problem, this paper presents two algorithms for computing information content of decoupled designs. One algorithm is applicable to any joint probability density function for the design parameters; the second algorithm applies only to uniformly distributed design parameters. The algorithm for uniform distributions is based on a recursive procedure for computing the volume of a convex polytope in n -dimensional real space, where n is the number of design parameters. An engineering application of the algorithms is presented. The example demonstrates that summing information content can significantly over-estimate total information when compared to an algorithm that accounts for correlation. The example also demonstrates that decoupled designs can have lower information content than uncoupled systems with the same functional requirements and similar components.     

Collaboration and complexity: an experiment on the effect of multi-actor coupled design

Design of complex systems requires collaborative teams to overcome limitations of individuals; however, teamwork contributes new sources of complexity related to information exchange among members. This paper formulates a human subjects experiment to quantify the relative contribution of technical and social sources of complexity to design effort using a surrogate task based on a parameter design problem. Ten groups of 3 subjects each perform 42 design tasks with variable problem size and coupling (technical complexity) and team size (social complexity) to measure completion time (design effort). Results of a two-level regression model replicate past work to show completion time grows geometrically with problem size for highly coupled tasks. New findings show the effect of team size is independent from problem size for both coupled and uncoupled tasks considered in this study. Collaboration contributes a large fraction of total effort, and it increases with team size: about 50–60 % of time and 70–80 % of cost for pairs and 60–80 % of time and 90 % of cost for triads. Conclusions identify a role for improved design methods and tools to anticipate and overcome the high cost of collaboration.     

An integration design optimization framework of robust design,axiomatic design,and reliability‐based design

Robust design, axiomatic design, and reliability‐based design provide effective approaches to deal with quality problems, and their integration will achieve better quality improvement. An integration design optimization framework of robust design, axiomatic design, and reliability‐based design is proposed in this paper. First, the fitted response model of each quality characteristic is obtained by response surface methodology and the mean square error (MSE) estimation is given by a second‐order Taylor series approximation expansion. Then the multiple quality characteristics robust design model is developed by the MSE criteria. Finally, the independence axiom constraints for decoupling and reliability constraints are integrated into the multiple quality characteristics robust design model, and the integration design optimization framework is formulated, where the weighted Tchebycheff approach is adopted to solve the multiple objective programming. An illustrative example is presented at the end, and the results show that the proposed approach can obtain better trade‐offs among conflicting quality characteristics, variability, coupling degree and reliability requirements. Copyright © 2011 John Wiley & Sons, Ltd.     

On the consistency of risk acceptance criteria with normative theories for decision-making

In evaluation of safety in projects it is common to use risk acceptance criteria to support decision-making. In this paper, we discuss to what extent the risk acceptance criteria is in accordance with the normative theoretical framework of the expected utility theory and the rank-dependent utility theory. We show that the use of risk acceptance criteria may violate the independence axiom of the expected utility theory and the comonotonic independence axiom of the rank-dependent utility theory. Hence the use of risk acceptance criteria is not in general consistent with these theories. The level of inconsistency is highest for the expected utility theory.     

Root cause analysis strategy for robust design domain recognition

Design domain identification with desirable attributes (e.g. feasibility, robustness and reliability) provides advantages when tackling large-scale engineering optimization problems. For the purpose of dealing with feasibility robustness design problems, this article proposes a root cause analysis (RCA) strategy to identify desirable design domains by investigating the root causes of performance indicator variation for the starting sampling initiation of evolutionary algorithms. The iterative dichotomizer 3 method using a decision tree technique is applied to identify reduced feasible design domain sets. The robustness of candidate domains is then evaluated through a probabilistic principal component analysis-based criterion. The identified robust design domains enable optimal designs to be obtained that are relatively insensitive to input variations. An analytical example and an automotive structural optimization problem are demonstrated to show the validity of the proposed RCA strategy.     

Probabilistic collocation for simulation-based robust concept exploration

In the early stages of an engineering design process it is necessary to explore the design space to find a feasible range that satisfies design requirements. When robustness of the system is among the requirements, the robust concept exploration method can be used. In this method, a global metamodel, such as a global response surface of the design space, is used to evaluate robustness. However, for large design spaces, this is computationally expensive and may be relatively inaccurate for some local regions. In this article, a method is developed for successively generating local response models at points of interest as the design space is explored. This approach is based on the probabilistic collocation method. Although the focus of this article is on the method, it is demonstrated using an artificial performance function and a linear cellular alloy heat exchanger. For these problems, this approach substantially reduces computation time while maintaining accuracy.     

Aktive Luftfederung – Modellierung,Regelung und Hardware-in-the-Loop-Experimente

It is assumed that autonomous driving is the key technology for our future transportation system. However, studies have shown that the incidence of kinetosis, i. e. motion sickness, is significantly higher in autonomous driving cars than in conventional vehicles. Since especially vertical dynamic oscillations (heave) in the frequency range from 0.1?Hz to approx. 1?Hz are perceived as particularly disturbing, active spring-damper systems can provide a remedy. The active air spring, which we develop at the Institute for Fluid Systems at TU Darmstadt, is such a system. It combines the advantages of an air spring (level control, load independent body natural frequency, etc.), which result from the separation of the functions “load carrying” and “energy storing”, with those of an active system. The actuating force is generated by adjusting the load-carrying (pressure-effective) area of the air spring during operation with an edge frequency of more than 5?Hz. This is realized by adjusting the air spring rolling piston diameter with four radially adjustable segments. For this purpose, a compact hydraulic linear actuator was developed which is integrated into the air spring piston.In this article, we describe the concept of the active air spring and introduce the functional prototype. Thereafter, the general optimal vertical dynamic design of an active system is discussed using the example of a quarter car model and the influence of system variables such as actuating force and actuating frequency is addressed. In the next step, a simple modeling of the overall system is carried out with regard to the \(\text{H}_{2}\)-optimal controller design and the suitability of the actuator concept for use in an active chassis as well as the robustness of the controller is shown exemplarily. In order to optimally tune the system to reduce oscillations that cause kinetosis and decrease driving comfort, frequency-specific weighting filters in accordance with VDI Guideline 2057 are used for the control design. Finally, the functional performance of the active air spring is demonstrated in hardware-in-the-loop experiments in which the functional prototype is coupled with a virtual quarter vehicle in a real-time simulation environment.     

A framework for coupled deformation–diffusion analysis with application to degradation/healing

This paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformation–diffusion in linearized elastic solids. The mathematical model takes into account the effect of the deformation on the diffusion process, and the affect of the transport of an inert chemical species on the deformation of the solid. We then present a robust computational framework for solving the proposed mathematical model, which consists of coupled non‐linear partial differential equations. It should be noted that many popular numerical formulations may produce unphysical negative values for the concentration, particularly, when the diffusion process is anisotropic. The violation of the non‐negative constraint by these numerical formulations is not mere numerical noise. In the proposed computational framework, we employ a novel numerical formulation that will ensure that the concentration of the diffusant be always snon‐negative, which is one of the main contributions of this paper. Representative numerical examples are presented to show the robustness, convergence, and performance of the proposed computational framework. Another contribution of this paper is to systematically study the affect of transport of the diffusant on the deformation of the solid and vice versa, and their implication in modeling degradation/healing of materials. We show that the coupled response is both qualitatively and quantitatively different from the uncoupled response. Copyright © 2011 John Wiley & Sons, Ltd.     

Aspects of finite element implementation of critical state models

 In this paper, some practical aspects of the finite element implementation of critical state models are discussed. Improved automatic algorithms for stress integration and load and time stepping are presented. The implementation of two generalized critical state soil models, with one described first in this paper and the other recently published elsewhere, is discussed. The robustness and correctness of the proposed numerical algorithms are illustrated through both coupled and uncoupled analyses of geotechnical problems.     

Robust optimal Robin boundary control for the transient heat equation with random input data

The problem of robust optimal Robin boundary control for a parabolic partial differential equation with uncertain input data is considered. As a measure of robustness, the variance of the random system response is included in two different cost functionals. Uncertainties in both the underlying state equation and the control variable are quantified through random fields. The paper is mainly concerned with the numerical resolution of the problem. To this end, a gradient‐based method is proposed considering different functional costs to achieve the robustness of the system. An adaptive anisotropic sparse grid stochastic collocation method is used for the numerical resolution of the associated state and adjoint state equations. The different functional costs are analysed in terms of computational efficiency and its capability to provide robust solutions. Two numerical experiments illustrate the performance of the algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Conditions for connectivity of incomplete block designs

In experimental situations where observation loss is common, it is important for a design to be robust against breakdown. For incomplete block designs, with one treatment factor and a single blocking factor, conditions for connectivity and robustness are developed using the concepts of treatment and block partitions, and of linking blocks. Lower bounds are given for the block breakdown number in terms of parameters of the design and its support. The results provide guidance for construction of designs with good robustness properties.     

A new decoupling method for phased arrays in magnetic resonance imaging: an experimental approach

A new decoupling method for magnetic resonance imaging (MRI) phased arrays is studied by experimental measurements. A laboratory measurement setup is built to characterise the signal coupling paths and their coupling strengths. A new concept, the receiving mutual impedance, is introduced to measure the coupled signals between the phased array elements. Measured values of the receiving mutual impedances for a typical two-element surface-coil array are obtained and used in other experiments to find the uncoupled voltages from the received voltages. Results show that the new decoupling method is both accurate and robust over a wide frequency range. Comparison of the uncoupled voltages with the actual ideal uncoupled voltages confirms that if the position of the signal source is known, almost error-free uncoupled voltages can be obtained. The errors resulted from a change of the position of the signal source are also measured and it is found that they generally increase with the deviation of the signal source from its position where the receiving mutual impedances are measured. The maximum % error of the uncoupled voltages is found to be below 10% when the signal source changes its position over a distance of half the length of a surface coil. Over this distance change, the signal isolation between the two surface coils is found to be at least 20 dB, whereas the maximum is more than 300 dB. The results demonstrate the effectiveness and the feasibility of the new decoupling method for use in MRI phased arrays.     

Robust optimal design using a second-order tolerance model

In this paper we present a general, quantitative method for developing designs that are robust to variation in design variables and parameters. Variation is defined in terms of tolerances which bracket the expected deviation of uncertain quantities about nominal values. We specifically address the case where input variations are assumed to be random variables that are normally distributed. The method incorporates a second-order tolerance model as part of a nonlinear optimization process. The second-order tolerance model makes it possible to estimate the skewness of function distributions, which are modeled with a three-parameter gamma distribution. We apply the method to determine robust designs for 11 test cases that span a variety of problems; robustness is verified with Monte Carlo simulation. The method enables a designer to understand and account for the effects of tolerances, making it possible to build robustness into an engineering design.     

Ist eine Über-Carnot-Maschine möglich?

A hyper-Carnot engine, i.e. a heat engine with a conversion coefficient exceeding the Carnot value, is forbidden by the second law. However, this law is not proven and, by principle, cannot be proven. It is an axiom. It is only based on all earlier unsuccessful attempts to circumvent it. In this paper, concept and calculation of a hyper-Carnot engine are presented the individual components of which all operate in agreement with all known physical laws. The crucial point is generating high phase space density synchrotron radiation by low phase space density thermal electron radiation.     

Dynamic reliability-based robust design optimization with time-variant probabilistic constraints

With the increasing complexity of engineering systems, ensuring high system reliability and system performance robustness throughout a product life cycle is of vital importance in practical engineering design. Dynamic reliability analysis, which is generally encountered due to time-variant system random inputs, becomes a primary challenge in reliability-based robust design optimization (RBRDO). This article presents a new approach to efficiently carry out dynamic reliability analysis for RBRDO. The key idea of the proposed approach is to convert time-variant probabilistic constraints to time-invariant ones by efficiently constructing a nested extreme response surface (NERS) and then carry out dynamic reliability analysis using NERS in an iterative RBRDO process. The NERS employs an efficient global optimization technique to identify the extreme time responses that correspond to the worst case scenario of system time-variant limit state functions. With these extreme time samples, a kriging-based time prediction model is built and used to estimate extreme responses for any given arbitrary design in the design space. An adaptive response prediction and model maturation mechanism is developed to guarantee the accuracy and efficiency of the proposed NERS approach. The NERS is integrated with RBRDO with time-variant probabilistic constraints to achieve optimum designs of engineered systems with desired reliability and performance robustness. Two case studies are used to demonstrate the efficacy of the proposed approach.     

Structure and Matrix Models for Tolerance Analysis from Configuration to Detail Design

A substantial amount of all quality problems that arise during assembly can be referred back to the geometrical design, and especially the geometrical concept of the product, i.e. the way in which parts are designed and located with each other. Special emphasis should thus be put on geometry design, especially during the early design phases, to try to find robust concepts and avoid solutions that may cause down-stream production problems.  This paper presents a generic set of evaluation tools for robust geometry design encountering (i) potential tolerance chain detection in configuration design, (ii) assembly robustness evaluation in concept design, and (iii) tolerance sensitivity analysis in detail design. Special attention is given to the development of a new matrix-based evaluation tool for the configuration design part. The tool presented is based on a new way of representing geometry variation constraints in an enhanced function-means tree structure model. Different parts of the function-means tree that are of interest for analysis purposes are then extracted and converted to matrix representation. The reason for doing this is that the structure model is most suitable for modeling, but becomes unsuitable for analysis as the model complexity increases. For this latter purpose, the matrix representation is far better. The use of the different tools is demonstrated in the design of a new vehicle front system for which the geometry a priori is unknown.     

Multi-objective gearbox design optimization for xEV-axle drives under consideration of package restrictions

In the design process of electric powertrains, consisting of electric machine, gearbox and power electronics, the requirements regarding performance, package and costs are typically set on system level. This imposes that deduction of component requirements is not unique and component properties interfere with each other. As a component of the powertrain system, the gearbox represents a linking element between the electric machine and drive shafts to the wheels. Through this the available installation space of the gearbox shows manifold characteristics due to multiple possible motor- and power electronics variants as also versatile system installation positions and angles. This space can be utilized by different gearbox variants, which are characterized by gearbox-internal design parameters. They affect gear ratio, configuration of gear wheels, outer shape of the gearbox and therefore the package as well as efficiency and production costs. The high variability of gearbox design parameters and packaging-related aspects lead to a complex problem in the design process.In this context, the present contribution introduces a gearbox design optimization process to support decision-making in the early development phase. For given load-, lifetime- and package-requirements, the introduced differential-evolution-based process delivers design parameters for shafts, gears, bearings and their arrangement to handle efficiency, package and costs in a multi-objective manner. The results are represented by a Pareto front of gearbox designs variants, from which decision makers are able to choose the best and most suitable trade-off. The new approach is exemplarily demonstrated on a single-speed, two-stage helical gearbox with an integrated differential drive, which represents a common gearbox topology for xEV-axle drives.