Recognizing expected utility as a valid design criterion, there are cases where uncertainty is such that this criterion fails to distinguish clearly between design alternatives. These cases may be characterized by broad and significantly overlapping utility probability distributions. Not uncommonly in such cases, the utility distributions of the alternatives may be highly correlated as the result of some uncertain variables being shared by the alternatives, because modeling assumptions may be the same across alternatives, or because difference information may be obtained by means of an independent source. Because expected utility is evaluated for alternatives independently, maximization of expected utility typically fails to take these correlations into account, thus failing to make use of all available design information. Correlation in expected utility across design alternatives can be taken into account only by computing the expected utility difference, namely the “differential expected utility,” between pairs of design alternatives. However, performing this calculation can present significant difficulties of which excessive computing times may be key. This paper outlines the mathematics of differential utility and presents an example case, showing how a few simplifying assumptions enabled the computations to be completed with approximately 24 hours of desktop computing time. The use of differential utility in design decision making can, in some cases, provide significant additional clarity, assuring better design choices.

This paper brings together rigid body kinematics and machine learning to create a novel approach to path synthesis of linkage mechanisms under practical constraints, such as location of pivots. We model the coupler curve and constraints as probability distributions of image pixels and employ a Convolutional Neural Network (CNN) based Variational AutoEncoder (VAE) architecture to capture and predict the features of the mechanism. Plausible solutions are found by performing informed latent space exploration so as to minimize the changes to the input coupler curve while seeking to find user-defined pivot locations. Traditionally, kinematic synthesis problems are solved using precision point approach, wherein the input path is represented as a set of points and a set of equations in terms of design parameters are formulated. Generally, this problem is solved via optimization, wherein a measure of error between the given path and the coupler curve is minimized. A limitation of this approach is that the existing formulations depend on the type of mechanism, do not admit practical constraints in a unified way, and provide a limited number of solutions. However, in the machine design pipeline, kinematic synthesis problems are concept generation problems, where designers care more about a large number of plausible and practical solutions rather than the precision of input or the solutions. The image-based approach proposed in this paper alleviates the difficulty associated with inherently uncertain inputs and constraints.

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.

An exact constraint scheme based on the physical contacting constraints of real part mating features is used to represent the process of assembling the parts. To provide useful probability information about how assembly dimensions are distributed when the parts are assembled as intended, the real world constraints that would prevent interference are ignored. This work addresses some limitations in the area of three dimensional assembly tolerance analysis. As a result of this work, the following were demonstrated: 1. Assembly of parts whose assembly mating features are subjected to variation; 2. Assemble parts using a real world set of exact constraints; 3. Provide probability distributions of assembly dimensions.

The modeling of manufacturing errors in mechanisms is a significant task to validate practical designs. The use of probability distributions for errors can simulate manufacturing variations and real world operations. This paper presents the mechanical error analysis of universal joint drivelines. Each error is simulated using a probability distribution, i.e., a design of the mechanism is created by assigning random values to the errors. Each design is then evaluated by comparing the output error with a limiting value and the reliability of the universal joint is estimated. For this, the design is considered a failure whenever the output error exceeds the specified limit. In addition, the problem of synthesis, which involves the allocation of tolerances (errors) for minimum manufacturing cost without violating a specified accuracy requirement of the output, is also considered. Three probability distributions — normal, Weibull and beta distributions — were used to simulate the random values of the errors. The similarity of the results given by the three distributions suggests that the use of normal distribution would be acceptable for modeling the tolerances in most cases.

Due to material, geometric and manufacturing irregularities, a structure designed to be spatially periodic cannot be exactly periodic. The departure from perfect periodicity is referred to as disorder, and it is known to cause spatial localization of normal modes and attenuation of wave propagation even if the structure is undamped. In this paper, another effect of disorder is investigated; namely, possible energy concentration near where a excitation is applied, thus, inducing higher level of structure response, A computational procedure is developed for calculating the mobility, or mechanical admittance, of deterministically disordered periodic structures based on wave propagation theory, and then extended to the case of randomly disordered periodic structures. It is shown that, given the probability distribution of the disordered parameters of a periodic structure, the mean and standard deviation of the mobility magnitude can be obtained. The results are exact if the number of the periodic cell units is not large, and approximate if the number is large. Depending on the excitation frequency, the mean mobility magnitude of a disordered system may be either greater or smaller than that of the perfectly periodic counterpart.

The allowable bending stress S e of a gear tooth is one of the basic factors in gear design. It can be determined by either the pulsating test or the gear-running test. However, some differences exist between the allowable bending stress S e obtained from these different test methods. In this paper, the probability distribution functions corresponding to each test method are analyzed and the expressions for the minimum extreme value distribution are presented. By using numerical integration, S e values from the population of the same tested gear tooth are obtained. Based on this investigation it is shown that the differences in S e obtained from the different test methods are significant. A proposed correction factor associated with the different experimental approaches is also presented.

Sound and vibration transmission modeling methods are important to the design process for high quality automotive vehicles. Statistical Energy Analysis (SEA) is an emerging design tool for the automotive industry that was initially developed in the 1960’s to estimate root-mean-square sound and vibration levels in structures and interior spaces. Although developed to estimate statistical mean values, automotive design application of SEA needs the additional ability to predict statistical variances of the predicted mean values of sound and vibration. This analytical ability would allow analysis of vehicle sound and vibration response sensitivity to changes in vehicle design specifications and their statistical distributions. This paper will present an algorithm to extend the design application of the SEA method through prediction of the variances of RMS responses of vibro-acoustic automobile structures and interior spaces from variances in SEA automotive model physical parameters. The variance analysis is applied to both a simple, complete illustrative example and a more complex automotive vehicle example. Example variance results are verified through comparison with a Monte Carlo test of 2,000 SEA responses whose physical parameters were given Gaussian distributions with means at design values. Analytical predictions of the response statistics agree with the statistics generated by the Monte Carlo method but only require about 1/300 of the computational effort.

Traditionally, most engineering problems are modeled in such a manner that all the variables involved in the design equations are deterministic. By nature, however, seldom does such a phenomenon exist. Most of the variables involved are randomly distributed with a certain mean and standard deviation and follow a certain type of statistical distribution. This investigation compares two such statistical based design processes to evaluate failure probabilities of a one dimensional heat transfer problem with various statistically distributed parameters in its performance function. The methods developed are the Monte Carlo simulation and First Order Reliability Method (FORM). Comparison is made between the Monte Carlo simulation and FORM based upon the investigated problem and the relative advantages and disadvantages of both methods are noted at the end of the investigation. The investigation demonstrates that FORM can be used effectively to determine failure probabilities and sensitivity factors in a manner better than Monte Carlo simulation.

We describe research efforts to implement a Bayesian belief network based expert system to solve a real-world diagnostic problem — the diagnosis of integrated circuit (IC) testing machines. We describe the development of several models of the IC tester diagnostic problem in belief networks, the implementation of one of these models using Symbolic Probabilistic Inference (SPI), and discuss the difficulties and advantages encountered in the process. We observe that modelling with interdependencies in belief networks simplified the knowledge engineering task for the IC tester diagnosis problem, by avoiding procedural knowledge and focusing on diagnostic component’s interdependencies. Several general model frameworks evolved through knowledge engineering to capture diagnostic expertise that facilitated expanding and modifying the networks. However, model implementation was restricted to a small portion of the modelling, contact resistance failures, because evaluation of the probability distributions could not be made fast enough to expand to a complete model with real-time diagnosis. Further research is recommended to create new methods, or refine existing methods, to speed evaluation of the models created in this research. With this accomplished, a more complete diagnosis can be achieved.

Polyharmonic oscillation with multiple frequencies is inherent in many applied problems. However, it rarely exists in the pure form and is often accompanied by a random vibration. Separation of the periodic signal from the actual record measured is usually restricted to determining the harmonic amplitudes only. The paper presents a method for complete identification of polyharmonic process including the phase angles that were unattainable when its period is unknown a priori. The approach is based on the fact that the presence of a periodic component transforms the instantaneous-value probability distribution of the combined signal to the non-Gaussian form. The solution obtained is compared with the results of time domain averaging.

Changing customer preferences, demand for quality and new technologies have led to very short product life cycles. This requires firms to have short product development lead times while keeping product cost low and quality high in order to stay competitive. In this context, we focus on improved understanding of design iterations. We are creating tools for modeling product development projects in order to predict the performance of product development organizations. In this paper, signal flow graphs are presented as a flexible tool for design process modeling. Illustrated using an industrial example, key project performance metrics including the probability distribution of lead time, and to identify key drivers of lead time.

Yield stresses, allowable stresses, moment capacities (plastic moments), external loadings, manufacturing errors are not given fixed quantities in practice, but have to be modelled as random variables with a certain joint probability distribution. Hence, problems from limit (collapse) load analysis or plastic analysis and from plastic and elastic design of structures are treated in the framework of stochastic optimization. Using especially reliability-oriented optimization methods, the behavioral constraints are quantified by means of the corresponding probability p s of survival. Lower bounds for p s are obtained by selecting certain redundants in the vector of internal forces; moreover, upper bounds for p s are constructed by considering a pair of dual linear pro-prams for the optimizational representation of the yield or safety conditions. Whereas p s can be computed e.g. by sampling methods or by asymptotic expansion techniques based on Laplace integral representations of certain multiple integrals, efficient techniques for the computation of the sensitivities (of various orders) of p s with respect to input or design variables have yet to be developed. Hence several new techniques are suggested for the numerical computation of derivatives of p s .

Two of the latest developments concerning the spectral representation method (used to simulate stochastic processes and fields) are presented in this paper. The first one introduces an extension of the spectral representation method to simulate non-stationary stochastic vector processes with evolutionary power. The proposed simulation formula is simple and straightforward and generates sample functions of the vector process according to a prescribed non-stationary cross-spectral density matrix. The second development introduces another extension of the spectral representation method to simulate multi-dimensional, multi-variate, non-Gaussian stochastic fields. In this case, sample functions are generated according to a prescribed cross-spectral density matrix and prescribed (non-Gaussian) probability distribution functions. Numerical examples are provided for both developments.

Reliability-based optimization methods in optimal structural design use mostly the following basic design criteria: I) Minimal weight (volume or costs) and II) high or reliability of the structure. Since, in practice, several parameters of the structure, e.g. elastic moduli, tolerances of structural dimensions, loads, are not given, fixed quantities, but random variables having a certain probability distribution P, a stochastic optimization problem will result from criteria (I), (II), which can be represented min F(x) with F(x) := Ef(ω, x). (1) x∇D Stochastic approximation methods are considered for solving (1): The gradient estimators are obtained by the response surface methodology (RSM) where especially the improvement of the estimators by using so-called “intermediate” or “intervening” variables is considered.

Random vibration analysis (RVA) of structural systems is a rapidly growing branch of engineering mechanics. The theory of random vibration is central to the analysis and design of structures in a variety of engineering fields. In recent years, RVA in conjunction with finite element methods has been available in several commercial computer-aided-engineering software, such as ANSYS, NASTRAN, etc. The finite element-based RVA is being widely adopted for computing stochastic responses, such as displacements, stresses and strains in terms of statistical quantities, i.e., root-mean-square responses. However, these statistical responses from RVA are limited to Cartesian responses which depend on the coordinate system of use. In structural design, a failure criterion using distortion energy known as the von Mises theory is more appropriate and of interest in this paper. The statistics of von Mises stress can not be obtained in terms of the statistics of Cartesian stresses. Simulation-based von Mises stress responses corresponding to a covariance matrix of Cartesian stresses are used to perform scatter and failure analyses. Based on a sufficient number of stress samples, a probability distribution of von Mises stress response may be obtained. Given a specified design criterion, statistical moments of safety margin as well as a safety index can be computed. In addition, a required design strength corresponding to a desired probability of failure can be provided in this study.

Industrial companies are being more and more interested in the non-deterministic aspects of system, structure and process design, and beyond, in the non-deterministic analysis and optimisation outcomes. The main difficulties of stochastic approaches lie in the evaluation of the statistical distributions of the structural responses. Current methods fall in two categories, with Monte-Carlo methods whose computational costs become prohibitive as the number of parameters increases or the expected confidence levels are high and Stochastic Finite Element methods whose assumptions may be restrictive. In order to calculate the statistical distributions of structural responses, an original method is proposed. The method, which uses interval arithmetics, seems promising in terms of performance and suitability for intensive numerical treatment.

The product architecture developed by a design team will have a tremendous impact upon customer satisfaction and market acceptance of a product. Yet most work in product architecture centers around configuring them for cost savings, manufacturability, and other production-driven concerns. Here, we propose a customer need basis for defining a product architecture. Customer needs analysis can provide a list of requirements for a product to sell. At any moment in time, one can assess a market population to establish target values for product features and represent those targets as probability distributions. Alternatively, one can also trace a few products through their use in time, and establish desired target values as a set of different distributions. Comparing these two distribution sets for every important customer need can point to the type of architecture a market population desires. When population and time distributions match, feature adjustability is required. When these distributions are different but constant in time, a family of product variants is more appropriate. When the population distribution changes over time, the feature must be isolated so it can be upgraded over time. If the distributions across both time and population are narrow, a single offering will supply the needs of the market. An instant film camera product is used as an example of the relationship between customer need distributions and appropriate product architecture.

Quality improvement methods such as robust design, statistical process control (SPC), and inspection have received significant attention over the past decade. Despite the plethora of research, there is very little work that describes how to allocate quality control methods in a complex system. This paper focuses on how to choose an inspection plan to remove the most variation at the lowest cost. This paper describes how to quantitatively allocate inspection locations in a complex assembly using a combination of modeling, simulation, and simulated annealing. It demonstrates the functionality of the theory using an example from the aircraft industry. The model provides three improvements over current methods: 1) methods to optimize both inspection limits and inspection locations, 2) the ability to mix both rework and scrap, 3) explicit calculation of the probability distributions for each point in the assembly.

In this work, a Deep Reinforcement Learning (RL) approach is proposed for Procedural Content Generation (PCG) that seeks to automate the generation of multiple related virtual reality (VR) environments for enhanced personalized learning. This allows for the user to be exposed to multiple virtual scenarios that demonstrate a consistent theme, which is especially valuable in an educational context. RL approaches to PCG offer the advantage of not requiring training data, as opposed to other PCG approaches that employ supervised learning approaches. This work advances the state of the art in RL-based PCG by demonstrating the ability to generate a diversity of contexts in order to teach the same underlying concept. A case study is presented that demonstrates the feasibility of the proposed RL-based PCG method using examples of probability distributions in both manufacturing facility and grocery store virtual environments. The method demonstrated in this paper has the potential to enable the automatic generation of a variety of virtual environments that are connected by a common concept or theme.