Fault Diagnosis in Multistation Assembly Systems Using Spatially Correlated Bayesian Learning Algorithm

The problem of fault diagnosis for dimensional integrity in multistation assembly systems is addressed in this paper. Fault diagnosis under this context is to identify the process errors which significantly contribute to the large product dimensional variation based on sensor data. The main challenges to be resolved in this paper include (1) the number of measurements is less than the process errors, which is typical in practice, but results in an ill-posed estimation problem, and (2) there exists spatial correlation among the dimensional variation of process errors, which has not been addressed yet by existing literature. A spatially correlated Bayesian learning (SCBL) algorithm to address these challenges is developed. The SCBL algorithm is based on the relevance vector machine (RVM) by exploiting the spatial correlation of dimensional variation from various process errors, which occurs in some circumstances of assembled parts and is well defined in GD&T standards. The proposed algorithm relies on a parametrized prior including the spatial correlation, and eventually leads sparsity in fault diagnosis; hence, the issues with ill-posedness and structured process errors will be addressed. A number of simulation studies are performed to illustrate the superiority of SCBL algorithm over state-of-the-art algorithms in sparse estimation problems when spatial correlation exists among the nonzero elements. A real autobody assembly process is also used to demonstrate the effectiveness of proposed SCBL algorithm.

Stream of Variation Modeling and Analysis for Compliant Composite Part Assembly— Part II: Multistation Processes

Part I of this paper (Zhang and Shi, 2015, “Stream of Variation Modeling and Analysis for Compliant Composite Part Assembly—Part I: Single-Station Processes,” ASME J. Manuf. Sci. Eng.,) has studied the variation modeling and analysis of compliant composite part assembly in a single-station process. In practice, multiple assembly stations are involved in assembling the final product. This paper aims to develop a variation propagation model for stream of variation analysis in a multistation assembly process for composite parts. This model takes into account major variation factors, including part manufacturing error (PME), fixture position error (FPE), and relocation-induced error (RIE). With the help of a finite element method (FEM), a state space model (SSM) is established to represent the relationships between the sources of variation and the final assembly variation. The developed methodology is illustrated by using a case study of three composite laminated plates assembled in a two-station assembly system. The validity of the developed SSM is verified by Monte Carlo simulation (MCS), which is implemented on the basis of FEM. The SSM provides a potential application for diagnosis of variation sources and variation reduction.

Fixture Fault Diagnosis in Multistation Assembly of Sheet Metal

This paper presents a methodology for diagnostics of fixture failures in multistation assembly processes. Diagnosis matrix equation is established by state space equation and measurement equation, which study the conditions of deviation source diagnosis. The determination method of deviation source diagnosis is obtained. 3-D scanner is used to measure the key data. A case study illustrates the proposed method.

Method for Handling Model Growth in Nonrigid Variation Simulation of Sheet Metal Assemblies

In automotive industry, virtual tools and methods are becoming increasingly important to ensure robust solutions as early as possible in the development processes. Today, techniques exist that combine Monte Carlo simulations (MCS) with finite element analysis (FEA) to capture the part's nonrigid geometric behavior when predicting variation in a critical dimension of a subassembly or product. A direct combination of MCS with full FEA requires high computational power and the calculations tend to be very time consuming. To overcome this problem, the method of influence coefficients (MIC) was proposed by Liu and Hu in the late 1990s. This well-known technique has since then been used in several studies of nonrigid assemblies and sensitivity analysis of the geometric fault propagation in multistation assembly processes. In detailed studies of the resulting subassemblies and levels of variation, functionality for color plots and the ability to study the geometry in arbitrary sections are desired to facilitate the analysis of the simulation results. However, when including all part nodes in combination with methods for contact and spot weld sequence modeling, the required sensitivity matrices grow exponentially. In this paper, a method is proposed, describing how traditional MIC calculations can be combined with a separate detailed subassembly analysis model, keeping the model sizes down and thus facilitating detailed studies of larger assembly structures.

Variation Propagation Analysis for Multistation Assembly Process With Consideration of GD&T Factors

Modeling of variation propagation in multistation assembly processes is crucial in predicting product dimensional quality and general performance of manufacturing systems. Based on the state space modeling, this paper develops a variation propagation model, which can be applied for analysis of various tolerances such as size tolerance, bonus tolerance, floating tolerance, etc. The nonstationary tolerance/variation (varying variance) caused by bonus tolerance and floating tolerance is properly handled by the proposed method. Thus, by using the developed variation propagation model, the variations on key product characteristics (KPCs) can be accurately predicted. This enables broad applications of the proposed method in actual manufacturing processes. The results of the case study also validated the proposed model.

Robust Fixture Layout Design for a Product Family Assembled in a Multistage Reconfigurable Line

Reconfigurable assembly systems enable a family of products to be assembled in a single system by adjusting and reconfiguring fixtures according to each product. The sharing of fixtures among different products impacts their robustness to fixture variation due to trade offs in fixture design (to allow the accommodation of the family in the single system) and to frequent reconfigurations. This paper proposes a methodology to achieve robustness of the fixture layout design through an optimal distribution of the locators in a multistation assembly system for a product family. This objective is accomplished by (1) the use of a multistation assembly process model for the product family, and (2) minimizing the combined sensitivity of the products to fixture variation. The optimization considers the feasibility of the locator layout by taking into account the constraints imposed by the different products and the processes (assembly sequence, data scheme, and reconfigurable tools’ workspace). A case study where three products are assembled in four stations is presented. The sensitivity of the optimal layout was benchmarked against the ones obtained using dedicated assembly lines for each product. This comparison demonstrates that the proposed approach does not significantly sacrifice robustness while allowing the assembly of all products in a single reconfigurable line.

Process Yield Improvement Through Optimum Design of Fixture Layouts in 3D Multistation Assembly Systems

Fixtures control the positions and orientations of parts in an assembly process. Inaccuracies of fixture locators or nonoptimal fixture layouts can result in the deviation of a workpiece from its design nominal and lead to overall product dimensional variability and low process yield. Major challenges involving the design of a set of fixture layouts for multistation assembly system can be enumerated into three categories: (1) high-dimensional design space since a large number of locators are involved in the multistation system, (2) large and complex design space for each locator since the design space represents the area of a particular part or subassembly surfaces on which a locator is placed, (here, the design space varies with a particular part design and is further expanded when parts are assembled into subassemblies), and (3) the nonlinear relations between locator nominal positions and key product characteristics. This paper presents a new approach to improve process yield by determining an optimum set of fixture layouts for a given multistation assembly system, which can satisfy (1) the part and subassembly locating stability in each fixture layout and (2) the fixture system robustness against environmental noises in order to minimize product dimensional variability. The proposed methodology is based on a two-step optimization which involves the integration of genetic algorithm and Hammersley sequence sampling. First, genetic algorithm is used for design space reduction by estimating the areas of optimal fixture locations in initial design spaces. Then, Hammersley sequence sampling uniformly samples the candidate sets of fixture layouts from those predetermined areas for the optimum. The process yield and part instability index are design objectives in evaluating candidate sets of fixture layouts. An industrial case study illustrates and validates the proposed methodology.

A Simplified Method for Optimal Sensor Distribution for Process Fault Diagnosis in Multistation Assembly Processes

The fault diagnosis plays an important role for product quality improvement in the multistation assembly processes (MAPs) and the efficiency of diagnosis significantly depends on the sensor distribution strategy, such as the number and location of the sensor. The diagnosis-oriented sensor distribution optimization in MAP has been studied for the purpose of a full diagnosis of the process faults with the minimum sensing stations number as well as the minimum sensor number. However, the existing studies are time consuming with the complex analysis and calculation processes, and no intuitive principles are given directly according to the process configuration. In this paper, a simplified method for the optimal sensor distribution is presented for a fully diagnosis of the process faults. First, two different types of assembly modes are defined and the variation transmissibility ratios for these two assembly modes are discussed based on the process configuration. Then, the conditions for between-station diagnosability and within-station diagnosability are analyzed, respectively. Based on the results, the optimal sensor distribution method is derived finally. After comparing with the former methods, the optimal sensor distribution in this paper is based only on the process configuration without using for model-based matrix computation. Therefore, the proposed method greatly simplified the process.