Tolerancing began with the notion of limits imposed on the dimensions of realized parts both to maintain functional geometric dimensionality and to enable cost-effective part fabrication and inspection. Increasingly however, component fabrication depends on more than part geometry as many parts are fabricated as a result of a “recipe” rather than dimensional instructions for material addition or removal. Referred to as process tolerancing, this is the case, for example, with IC chips. There has emerged an extensive literature on both geometric and process tolerancing, much of it with a focus on tolerance optimization. In the case of tolerance optimization, a typical objective is cost minimization while achieving required functionality or “quality.” This paper takes a different look at tolerances, suggesting that rather than ensuring merely that parts achieve a desired functionality at minimum cost, the underlying goal of product design is to make money, and tolerances comprise additional design variables amenable to optimization in a decision theoretic framework. We recognize that a theory of tolerancing must apply equally to processes and procedures, and note that tolerances introduce additional product attributes that relate to product characteristics such as consistency, quality, reliability and durability. These important attributes complicate the computation of the expected utility of candidate designs, requiring additional computational steps for their determination. Nonetheless, their proper consideration is an important element in the evaluation of product design alternatives. The resulting theory of tolerancing presented here is illustrated using the example of tolerancing for an apple pie.

This paper presents the gravity balancing reliability and sensitivity analysis of robotic manipulators with uncertainties. The gravity balancing reliability of the robot is defined as the probability that the reduction torque ratio of the robot reduces below a specified threshold. This index is of great importance for assessing and guaranteeing the balancing performance of the robot in the presence of uncertainties in input parameters. In this work, the balancing design for an industrial robot using the gear-spring modules (GSMs) is proposed with the adoption of a simulation-based analysis of the gravity effect of the robot. The Monte Carlo Simulation (MCS) method with normally distributed variables (i.e., link dimensions, masses, and spring stiffness coefficients) is employed to analyze and simulate the reliability. A case study with an industrial robot is then given to illustrate the reliability performance and the sensibility of the uncertain parameters. It is found that the gravity balancing behavior is achieved even when the uncertainties are applied. The uncertainties could deteriorate the balancing performance when increasing the standard deviations by more than seven percent of their means. The dimensional parameters enjoy the most critical influence on the balancing performance.

Power systems are designed to meet power demands of the communities with high reliability. Distributed generators (DGs) could play an essential role in improving the power system reliability and resilience. To date, influence of the uncertainty of the DGs to power system reliability has not been well addressed. Consequently, placement of the DGs considering reliability constraints may not be optimally conducted. This paper proposes reliability analysis and design of power systems under time-dependent load uncertainty and wind power generation uncertainty using an efficient uncertainty quantification (UQ) method, i.e., the eigenvector dimension reduction (EDR) method. Furthermore, binary particle swarm optimization (B-PSO) is proposed to address the optimal placement of DGs considering the reliability constraint. Two case studies, including an IEEE 14-bus power system and an IEEE 57-bus power system, are used to demonstrate the effectiveness of the proposed methodology.

As enablers of electric vehicles, lithium-ion batteries are drawing much attention for their high energy density and low self-discharging rate. However, “range anxiety” has remained a significant hindrance to its further development. Of the many design objectives, minimizing the charging time and maximizing the cycle life are conflicting design objectives. In the past, enormous efforts have been carried out to resolve the dispute between high charging rates and large capacity losses by either improving the battery design or optimizing the charging/discharging protocols. However, the battery design and the control are usually coupled that integration of the two discipline, or control co-design, may offer improved performances as compared with traditional sequential optimization approaches. In an previous study, we have shown that efficient control co-design is achievable for Lithium-ion batteries through surrogate modeling. In this work, a reliability-based design optimization framework is integrated to guarantee the performances under parametric uncertainties. The challenges, such as simultaneous model update for the dynamic system and excessive computation burden due to optimal control and reliability assessment, are resolved through coupling the first principle model and the empirical models by an adaptive surrogate modeling process. Such a combination captures the multi-scale nature of the battery and allows efficient numerical analysis for the reliability-based co-design (RBCD) problem. A nested co-design approach and a double-loop reliability assessment method were implemented. The results show that the algorithm can shorten the charging time while satisfying the probability constraint on the cycle-life performances under parametric uncertainties.

Advances in additive manufacturing enable the fabrication of complex structures with intricate geometric details. It also escalates the potential for high-resolution structure design. However, the increasingly finer design brings computational challenges for structural optimization approaches such as topology optimization (TO) since the number of variables to optimize increases with the resolutions. To address this issue, two-scale TO paves an avenue for high-resolution structural design. The design domain is first discretized to a coarse scale, and the material property distribution is optimized, then using micro-structures to fill each property field. In this paper, instead of finding optimal properties of two scales separately, we reformulate the two-scale TO problem and optimize the design variables concurrently in both scales. By introducing parameterized periodic cellular structures, the minimal surface level-parameter is defined as the material design parameter and is implemented directly in the optimization problem. A numerical homogenization method is employed to calculate the elasticity tensor of the cellular materials. The stiffness matrices of the cellular structures derived as a function of the level parameters, using the homogenization results. An additional constraint on the level parameter is introduced in the structural optimization framework to enhance adjacent cellulars interfaces’ compatibility. Based on the parameterized micro-structure, the optimization problem is solved concurrently with an iterative solver. The reliability of the proposed approach has been validated with different engineering design cases. Numerical results show a noticeable increase in structure stiffness using the level parameter directly in the optimization problem than the state-of-art mapping technique.

The unstructured data available on the websites of manufacturing suppliers can provide useful insights into the technological and organizational capabilities of manufacturers. However, since the data is often represented in an unstructured form using natural language text, it is difficult to efficiently search and analyze the capability data and learn from it. The objective of this work is to propose a set of text analytics techniques to enable automated classification and ranking of suppliers based on their capability narratives. The supervised classification and semantic similarity measurement methods used in this research are supported by a formal thesaurus that uses SKOS (Simple Knowledge Organization System) for its syntax and semantics. Normalized Google Distance (NGD) was used as a metric for measuring the relatedness of terms. The proposed framework was validated experimentally using a hypothetical search scenario. The results indicate that the generated ranked list shows a high correlation with human judgment specially if the query concept vector and supplier concept vector belong to the same class. However, the correlation decreases when multiple overlapping classes of suppliers are mixed together. The findings of this research can be used to improve the precision and reliability of Capability Language Processing (CLP) tools and methods.

Functional electrical stimulation (FES) in stroke rehabilitation is hindered by early patient fatigue. Therefore the study of FES-elicited fatigue is needed to optimise its therapeutic impact. In this study, the reliability of evoked electromyography (EMG) median frequency (MDF) and peak-to-peak (PTP) fatigue indices were investigated during stimulation of the forearm. During isometric constant stimulation the MDF-time and PTP-time waveforms exhibited negative gradients in the ranges (−1.3 to −3.6) Hz · s −1 and (−0.013 to −0.016) V · s −1 respectively, most with coefficients of determination (R 2 ) greater than 0.83. During vEMG-controlled stimulation the MDF-contraction waveforms exhibited negative gradients in the range (−2.4 to −9.0) Hz · Cont −1 while the PTP gradients ranged from (0.0070 to −0.019) V · Cont −1 . For these datasets the MDF waveforms’ R 2 > 0.62 and most PTP waveforms’ R 2 < 0.35. These findings suggest that the MDF and PTP amplitude are suitable fatigue indices during isometric constant stimulation but the PTP-based index becomes unreliable during vEMG-controlled stimulation.

We present an efficient data-driven sparse identification of dynamical systems. The work aims at reconstructing the different sets of governing equations and identify discontinuity surfaces in hybrid systems when the number of discontinuities is known a priori. In our approach, we first focus to identify the switches between the separate vector fields. Then, the dynamics among the manifolds are regressed by making use of the model discovery algorithm of Brunton et al. [1]. The reconstruction of the discontinuity surfaces comes as the outcome of a statistical analysis implemented via symbolic regression with small clusters (micro-clusters) and a rigid library of models. This allows to identify all the many possible switch points that are clustered to determine the actual discontinuity surfaces. The performances of the method are tested on two numerical examples, namely, a canonical spring–mass hopper and a free/impact electromagnetic energy harvester. These applications are characterized by the presence of a single and double discontinuity, respectively. The analyses demonstrate that in the supervised approach, i.e. where the number of discontinuities is preassigned, we are capable to determine accurately both discontinuities and set of governing equations. It is found a great improvement in time of computation reaching the maximum achievable reliability that outperform existing data-driven identification approaches for hybrid systems.

The effect of membrane load on the behaviour of axisymmetric bistable circular curved microplates on Berger’s based axisymmetric reduced order (RO) model, incorporating radial prestress, is studied. The model is first validated for a “mechanical” load, against a Föppl-von-Kármán’s RO model with twenty degrees of freedom (DOF), a finite differences (FD) solution and a finite elements (FE) model, serving as the reference. All solutions implement the “Riks” method to track possible unstable branches, which can swerve in due to the presence of higher buckling modes. A convergence study is carried out for the snap-through location and load, as well as for the critical elevation and prestress required for bistability. Based on validated results of the analysis, the reliability of the model for predicting the effect of prestress on the plate behaviour under nonlinear electrostatic load is then investigated while using FD solutions as the reference. The study furnishes a reliable expended RO model, which includes prestress on the as-fabricated curved plate. The resulting model can further be used to estimate the value of residual prestress, present in an electrostatically actuated curved plate, based on its response.

Reliability analysis is usually a core element in engineering design, during which reliability is predicted with physical models (limit-state functions). Reliability analysis becomes computationally expensive when the dimensionality of input random variables is high. This work develops a high dimensional reliability analysis method by a new dimension reduction strategy so that the contributions of both important and unimportant input variables are accommodated by the proposed dimension reduction method. The consideration of the contributions of unimportant input variables can certainly improve the accuracy of the reliability prediction, especially where many unimportant input variables are involved. The dimension reduction is performed with the first iteration of the first order reliability method (FORM), which identifies important and unimportant input variables. Then a higher order reliability analysis, such as the second order reliability analysis and metamodeling method, is performed in the reduced space of only important input variables. The reliability obtained in the reduced space is then integrated with the contributions of unimportant input variables, resulting in the final reliability prediction that accounts for both types of input variables. Consequently, the new reliability method is more accurate than the traditional method, which fixes unimportant input variables at their means. The accuracy is demonstrated by three examples.

Design for Remanufacturing (DfRem) is an attractive approach for sustainable product development. Evaluation of DfRem strategies, from both economic and environmental perspectives, at an early design stage can allow the designers to make informed decisions when choosing the best design option. Studying the long-term implications of a particular design scenario requires quantifying the benefits of remanufacturing for multiple life cycles while considering the reliability of the product. In addition to comparing designs on a one-to-one basis, we find that including reliability provides a different insight into comparing design strategies. We present a reliability-informed cost and energy analysis framework that accounts for product reliability for multiple remanufacturing cycles within a certain warranty policy. The variation of reuse rate over successive remanufacturing cycles is formulated using a branched power-law model which provides probabilistic scenarios of reusing or replacing with new units. To demonstrate the utility of this framework, we use the case study of a hydraulic manifold, which is a component of a transmission used in some agricultural equipment, and use real-world field reliability data to quantify the transmission’s reliability. Three design improvement changes are proposed for the manifold and we quantify the costs and energy consumption associated with each of the design changes for multiple remanufacturing cycles.

Predicting system reliability is often a core task in systems design. System reliability depends on component reliability and dependence of components. Component reliability can be predicted with a physics-based approach if the associated physical models are available. If the models do not exist, component reliability may be estimated from data. When both types of components coexist, their dependence is often unknown, and the component states are therefore assumed independent by the traditional method, which can result in a large error. This work proposes a new system reliability method to recover the missing component dependence, thereby leading to a more accurate estimate of the joint probability density (PDF) of all the component states. The method works for series systems whose load is shared by its components that may fail due to excessive loading. For components without physical models available, the load data are recorded upon failure, and equivalent physical models are created; the model parameters are estimated by the proposed Bayesian approach. Then models of all component states become available, and the dependence of component states, as well as their joint PDF, can be estimated. Four examples are used to evaluate the proposed method, and the results indicate that the proposed method can produce more accurate predictions of system reliability than the traditional method that assumes independent component states.

Reliability-based mission planning aims to identify an optimal path for off-road autonomous ground vehicles (AGVs) under uncertain terrain environment, while satisfying specific mission mobility reliability (MMR) constraints. The evaluation of MMR during path planning poses computational challenges for practical applications. This paper presents an efficient reliability-based mission planning using an outcrossing approach that has the same computational complexity as deterministic mission planning. A Gaussian random field is employed to represent the spatially dependent uncertainty sources in the terrain environment. The latter are then used in conjunction with a vehicle mobility model to generate a stochastic mobility map. Based on the stochastic mobility map, outcrossing rate maps are generated using the outcrossing concept which is widely used in time-dependent reliability. Integration of the outcrossing rate map with a rapidly-exploring random tree (RRT*) algorithm, allows for efficient path planning of AGVs subject to MMR constraints. A reliable RRT* algorithm using the outcrossing approach (RRT*-OC) is developed to implement the proposed efficient reliability-based mission planning. Results of a case study verify the accuracy and efficiency of the proposed algorithm.

One of the most important assemblies in any computer disk drive is the actuator which positions the read/write coil over the disk. Historically, actuators have been of the linear type, but in recent years the rotary actuator has become more popular because of its lower inertia and higher reliability. In this paper we describe the optimization of the rotary actuator geometry to achieve a minimum seek time. An objective function which approximates seek-time is derived based on the polar moment of inertia and the sweep of the actuator. A set of constraints is also developed which control mechanical resonances, skew angles, and physical position of the actuator. An optimal solution is presented as well as a sensitivity study of the final design. It is shown that the final design is relatively insensitive to changes in the problem parameters. Additionally, the sensitivity analysis reveals that a static balance constraint which is originally ignored, is not necessary.

The application of fault tree techniques to the analysis of gear trains is considered. The techniques involve the decomposition of the system into a logic diagram or fault tree in which certain basic or primary events lead to a specified top event which signifies the total failure of the system. The fault trees are used to obtain minimal cut sets from which the modes of system failure and, hence, the reliability measure for the top event can be calculated. The method of constructing fault trees and the subsequent estimation of reliability of the system is illustrated through a nine speed compound gear train and a five speed epicyclic gear train.

Due to normal variations in dimensions inherent in the manufacture of the components of a mechanism, there is a small probability of not meeting the accuracy predicted by a deterministic representation of the mechanism. The reliability of a mechanism can be defined as the probability of deviation from its specified function. This paper presents a Monte Carlo simulation approach for the reliability analysis of function generating mechanisms. The approach is illustrated by considering the reliability analysis of a four-bar straight-line mechanism. The effect of the probability distribution of the random parameters on the overall reliability is also investigated. The Monte Carlo approach can be coupled with the known statistical properties of the production techniques to significantly increase the production yield of mechanisms that satisfy specified reliability requirements.

The use of a computer-controlled multirobot system with sensors in batch manufacturing and assembly tasks offers a number of significant advantages. These include cost savings, reliability, tolerance of working environments unacceptable to humans, and an adaptability to both structured and unstructured environments through simple reprogramming. The end results are improved productivity, efficiency, and flexibility in manufacturing and automation. However, the use of two or more cooperating robots has not been fully exploited to date. Current industrial practice employs simple time-space coordination which does not allow more than one robot working in a common workspace, such coordination and control results in under-utilization of robots. With the increasing demand for high performance manipulators and efficient multirobot manufacturing cells, there is a vital need to develop theoretical and design methodologies that will solve the generic problems faced by industrial robots working cooperatively. If multirobot systems are to be used in manufacturing and assembly tasks, a thorough knowledge of the dynamics of such systems is essential. This paper formulates the dynamics of two robots cooperating to move a rigid body object. The analysis is based on Newtonian mechanics with screw calculus and dual transformation matrices.

In this paper, design optimization of aircraft wing structures with multiple frequency constraints is considered. An optimality criterion algorithm along with a scaling procedure has been used. Large scale structural design problems were considered for demonstrating the reliability and efficiency of the algorithm. A simplified fighter wing, an intermediate complexity wing, and a large wing typical of a transport aircraft were considered as design examples. Design histories and the first few frequencies at the initial and final conditions are presented.

A probabilistic approach to robot kinematics is presented and the concept of manipulator reliability is introduced to obtain a better evaluation of the performance of manipulators. Techniques are presented to compute this reliability and its relationship to the geometric parameters such as tolerances and arm configuration are discussed. The aspects of accuracy and repeatability of manipulators are explained in terms of manipulator reliability. The reliability of a two-link planar manipulator and the Stanford arm are considered for numerical illustration.

The application of fault tree techniques to the analysis of gear trains is considered. The techniques involve the decomposition of the system into a logic diagram or fault tree in which certain basic or primary events lead to a specified top event which signifies the total failure of the system. The fault trees are used to obtain minimal cut sets from which the modes of system failure and hence the reliability measure for the top event can be calculated. The method of constructing fault trees and the subsequent estimation of reliability of the system is illustrated through a nine speed compound gear train and a five speed epicyclic gear train.