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### Research Papers: Design Theory and Methodology

J. Mech. Des. 2016;138(9):091101-091101-9. doi:10.1115/1.4033989.

Complex, large-scale engineered systems are an integral part of modern society. The cost of these systems is often high, while their ability to react to emergent requirements can be low. This paper proposes evolvability, based on usable excess, as a possible metric to promote system longevity. An equation for the usability of excess, previously defined only in terms of quantity, is improved to include the attributes of type, location, and form as well as quantity. A methodology for evaluating a system's evolvability is also presented. Using an automated assembly line as an example, we show that system evolvability can be modeled as a function of usable excess.

Commentary by Dr. Valentin Fuster

### Research Papers: Design Automation

J. Mech. Des. 2016;138(9):091401-091401-10. doi:10.1115/1.4034035.

In engineering design optimization, evaluation of a single solution (design) often requires running one or more computationally expensive simulations. Surrogate assisted optimization (SAO) approaches have long been used for solving such problems, in which approximations/surrogates are used in lieu of computationally expensive simulations during the course of search. Existing SAO approaches often use the same type of approximation model to represent all objectives and constraints in all regions of the search space. The selection of a type of surrogate model over another is nontrivial and an a priori choice limits flexibility in representation. In this paper, we introduce a multi-objective evolutionary algorithm (EA) with multiple adaptive spatially distributed surrogates. Instead of a single global surrogate, local surrogates of multiple types are constructed in the neighborhood of each offspring solution and a multi-objective search is conducted using the best surrogate for each objective and constraint function. The proposed approach offers flexibility of representation by capitalizing on the benefits offered by various types of surrogates in different regions of the search space. The approach is also immune to illvalidation since approximated and truly evaluated solutions are not ranked together. The performance of the proposed surrogate assisted multi-objective algorithm (SAMO) is compared with baseline nondominated sorting genetic algorithm II (NSGA-II) and NSGA-II embedded with global and local surrogates of various types. The performance of the proposed approach is quantitatively assessed using several engineering design optimization problems. The numerical experiments demonstrate competence and consistency of SAMO.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2016;138(9):091402-091402-10. doi:10.1115/1.4033990.

The continuous pursuits of developing a better, safer, and more sustainable system have pushed systems to grow in complexity. As complexity increases, challenges consequently arise for system designers in the early design stage to take account of all potential failure modes in order to avoid future catastrophic failures. This paper presents a resilience allocation framework for resilience analysis in the early design stage of complex engineering systems. Resilience engineering is a proactive engineering discipline that focuses on ensuring the performance success of a system by adapting to changes and recovering from failures under uncertain operating environments. Utilizing the Bayesian network (BN) approach, the resilience of a system could be analyzed and measured quantitatively in a probabilistic manner. In order to ensure that the resilience of a complex system satisfies the target resilience level, it is essential to identify critical components that play a key role in shaping the top-level system resilience. Through proper allocation of resilience attributes to these critical components, not only target could resilience requirements be fulfilled, global cascading catastrophic failure effects could also be minimized. An electrical distribution system case study was used to demonstrate the developed approach, which can also be used as a fundamental methodology to quantitatively evaluate resilience of engineered complex systems.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2016;138(9):091403-091403-9. doi:10.1115/1.4033987.

In the early-phase design of complex systems, a model of design performance is coupled with visualizations of competing designs and used to aid human decision-makers in finding and understanding an optimal design. This consists of understanding the tradeoffs among multiple criteria of a “good” design and the features of good designs. Current visualization techniques are limited when visualizing many performance criteria and/or do not explicitly relate the mapping between the design space and the objective space. We present a new technique called Cityplot, which can visualize a sample of an arbitrary (continuous or combinatorial) design space and the corresponding single or multidimensional objective space simultaneously. Essentially a superposition of a dimensionally reduced representation of the design decisions and bar plots representing the multiple criteria of the objective space, Cityplot can provide explicit information on the relationships between the design decisions and the design criteria. Cityplot can present decision settings in different parts of the space and reveal information on the decision → criteria mapping, such as sensitivity, smoothness, and key decisions that result in particular criteria values. By focusing the Cityplot on the Pareto frontier from the criteria, Cityplot can reveal tradeoffs and Pareto optimal design families without prior assumptions on the structure of either. The method is demonstrated on two toy problems and two real engineered systems, namely, the NASA earth observing system (EOS) and a guidance, navigation and control (GNC) system.

Topics: Design , Visualization
Commentary by Dr. Valentin Fuster
J. Mech. Des. 2016;138(9):091404-091404-12. doi:10.1115/1.4033991.

Real-life design problems often require simultaneous optimization of multiple conflicting criteria resulting in a set of best trade-off solutions. This best trade-off set of solutions is referred to as Pareto optimal front (POF) in the outcome space. Obtaining the complete POF becomes impractical for problems where evaluation of each solution is computationally expensive. Such problems are commonly encountered in several fields, such as engineering, management, and scheduling. A practical approach in such cases is to construct suitable POF approximations, which can aid visualization, decision-making, and interactive optimization. In this paper, we propose a method to generate piecewise linear Pareto front approximation from a given set of N Pareto optimal outcomes. The approximations are represented using geometrical linear objects known as polytopes, which are formed by triangulating the given M-objective outcomes in a reduced $(M−1)$-objective space. The proposed approach is hence referred to as projection-based Pareto interpolation (PROP). The performance of PROP is demonstrated on a number of benchmark problems and practical applications with linear and nonlinear fronts to illustrate its strengths and limitations. While being novel and theoretically interesting, PROP also improves on the computational complexity required in generating such approximations when compared with existing Pareto interpolation (PAINT) algorithm.

Commentary by Dr. Valentin Fuster

### Research Papers: Design of Mechanisms and Robotic Systems

J. Mech. Des. 2016;138(9):092301-092301-13. doi:10.1115/1.4033988.

This paper introduces a position-space-based reconfiguration (PSR) approach to the reconfiguration of compliant mechanisms. The PSR approach can be employed to reconstruct a compliant mechanism into many new compliant mechanisms, without affecting the mobility of the compliant mechanism. Such a compliant mechanism can be decomposed into rigid stages and compliant modules. Each of the compliant modules can be placed at any one permitted position within its position space, which does not change the constraint imposed by the compliant module on the compliant mechanism. Therefore, a compliant mechanism can be reconfigured through selecting different permitted positions of the associated compliant modules from their position spaces. The proposed PSR approach can be used to change the geometrical shape of a compliant mechanism for easy fabrication, or to improve its motion characteristics such as cross-axis coupling, lost motion, and motion range. While this paper focuses on reducing the parasitic motions of a compliant mechanism using this PSR approach, the associated procedure is summarized and demonstrated using a decoupled XYZ compliant parallel mechanism as an example. The parasitic motion of the XYZ compliant parallel mechanism is modeled analytically, with three variables which represent any permitted positions of the associated compliant modules in their position spaces. The optimal positions of the compliant modules in the XYZ compliant parallel mechanism are finally obtained based on the analytical results, where the parasitic motion is reduced by approximately 50%. The reduction of the parasitic motion is verified by finite-element analysis (FEA) results, which differ from the analytically obtained values by less than 7%.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2016;138(9):092302-092302-8. doi:10.1115/1.4034111.
OPEN ACCESS

Compliant members come in a variety of shapes and sizes. While thin beam flexures are commonly used in this field, they can be replaced by soft members with lower aspect ratio. This paper looks to study the behavior of such elements by analyzing them from the view of beam theory for 2D cases. A modified version of the Timoshenko beam theory is presented which incorporates extension and Poisson's effects. The utility and validity of the new approach are demonstrated by comparing against Euler–Bernoulli beam theory, Timoshenko beam theory, and finite-element analysis (FEA). The results from this are then used to study the performance of pseudo-rigid-body models (PRBMs) for the analysis of low aspect ratio soft compliant joints for 2D quasi-static applications. A parallel-guiding mechanism comprised of similar compliant elements is analyzed using the new results to validate the contribution of this work.

Commentary by Dr. Valentin Fuster

### Research Papers: Design of Direct Contact Systems

J. Mech. Des. 2016;138(9):093301-093301-9. doi:10.1115/1.4033992.

Trial and error experiments are the dominant approaches to select machining settings and also cutting system design in face-hobbing of bevel gears. These time-consuming experimental tests impose undesired costs to industries. In the present paper, an integrated method is proposed to find optimum machining settings in face-hobbing based on minimum machining time and allowable cutting force and tool wear. Cutting blades in face-hobbing are converted to many infinitesimal oblique elements along the cutting edge, and the cutting forces and the tool wear are predicted on all these small elements. The constructed optimization problem seeks a face-hobbing scenario with minimum plunge time which meets the cutting force or crater wear depth constraints. The proposed method is applied in two case studies successfully to show the capability of the approach.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2016;138(9):093302-093302-13. doi:10.1115/1.4034175.

This paper investigates the influences of tooth indexing errors on dynamic factors of spur gears. An experimental study is performed using root strain measurements to (i) establish baseline dynamic behavior of gears having negligible indexing errors and (ii) characterize changes caused by tightly controlled intentional indexing errors to this baseline dynamic behavior. For this, test gears having different forms of indexing errors are paired with an instrumented gear having negligible indexing error. Dynamic root strains of teeth in the neighborhood of teeth with indexing error are measured. A dynamic gear load distribution model is employed to simulate these experiments. Both measurements and predictions indicate clearly that the baseline dynamic response, dominated by well-defined resonance peaks, is altered significantly by transient vibrations induced by indexing errors, in the process increasing dynamic factors significantly in comparison to the case of negligible indexing error.

Commentary by Dr. Valentin Fuster