Variation Propagation Research Articles

Stream of Variation Modeling and Monitoring for Heterogeneous Profiles in Multi-Stage Manufacturing Processes

Advanced manufacturing systems typically involve multiple operating stages, where in-process data are observed in the form of profiles that contain rich information for process monitoring. Emerging methodologies have been developed for multi-stage profile monitoring. However, the cases where different stages’ profiles are heterogeneous and variations propagate over stages have not been addressed so far. To this end, this article proposes a heterogeneous profiles-based stream of variation (HP-SoV) framework for multi-stage manufacturing process monitoring. It uses functional decomposition to extract features of heterogeneous profiles from different stages, where the decomposition coefficients are regarded as latent states that propagate along consecutive stages to capture the variation propagation. HP-SoV includes many existing models as its special cases, and enjoys an efficient inference algorithm via maximum likelihood estimation. Based on the one-step-ahead forecast errors of HP-SoV, a group monitoring scheme is further developed for online monitoring. Extensive numerical studies explore the modeling robustness and monitoring effectiveness of HP-SoV under different settings. A case study demonstrates the applicability of HP-SoV in multi-stage process monitoring for heterogeneous profiles.

Process-Oriented Tolerance and Variation Management: Review and Classification

In the context of tolerance management, the consideration of manufacturing and assembly processes is becoming increasingly important. The main drivers for this are, above all, short development times and high-quality requirements, leading to tight tolerances. To overcome the resulting challenges, many publications address the process-oriented tolerance management. However, since multiple terms and definitions for describing activities that link tolerance management with the production process exist, it is hard to obtain a comprehensive overview on the topic. Therefore, this paper presents a review of existing approaches. The aim is to identify similarities and differences of existing approaches and present them with the help of a classification. For this purpose, among others, work from the areas of process-oriented tolerance management, stream of variation, state space modeling, and variation propagation in multistation manufacturing and assembly systems is considered. Based on the definition of the summarizing term “process-oriented tolerance and variation management”, a classification of this thematic area will be introduced.

Application of the heat equation to the study of underground temperature

Modeling underground temperatures provides a practical application of the one-dimensional heat equation. In this work, the one-dimensional heat equation in surface soil is extended to include heat carried by the vertical flow of rainwater through the soil. Analytical solutions, with and without water flow, illustrate the influence of rainwater circulation on the sub-surface propagation of seasonal temperature variations, an important effect that is generally neglected in textbooks. The surface temperature variations are damped by the soil, and this effect was used by the Troglodytae in Egypt or the Petra in South Jordan to insulate against extreme temperatures. For a realistic case of horizontally layered geology, a finite volume Python code was developed for the same purpose. Subsurface temperatures were also measured over a full year at depths up to 1.8 m and used to estimate the thermal skin depth and thermal wavelength. This study provides students with a practical example of how a textbook physics problem can be modified to extract information of contemporary importance in geophysics and global warming.

Comparative Analysis of Meridional and Azimuthal Propagation of Magnetic Variations and Equivalent Current Vortices of Geomagnetic Pc5 Pulsations

Comparative Analysis of Meridional and Azimuthal Propagation of Magnetic Variations and Equivalent Current Vortices of Geomagnetic Pc5 Pulsations

Geometric Deviation Representation and Variation Propagation Modeling in Multistage Machining Processes

Geometric Deviation Representation and Variation Propagation Modeling in Multistage Machining Processes

Study on the Influence of the Joint Angle between Blast Holes on Explosion Crack Propagation and Stress Variation

The joints and fissures in a natural rock mass can affect the mechanical properties of the rock mass, the propagation of a blasting stress wave, and the blasting effect of the smooth surface of roadways. In the process of roadway drilling and blasting, there will inevitably be some joints between the two blast holes. Taking the joint angle as the starting point, this paper studies the rule of rock explosion crack propagation and stress variation when there are joints with different angles between two blast holes and analyzes the influence of joints on rock mechanical properties and blasting effects. The numerical simulation method and the software ANSYS/LS-DYNA are used to establish 7 rock mass models with various joint angles. When there is no joint between two holes and joints of 15°, 30°, 45°, 60°, 75°, and 90°, the propagation of explosive cracks and stress variations in the rock mass are discussed. The results show that the joints at different angles have obvious guiding and blocking effects on the propagation of explosive cracks, and as joint angles increase, the guiding effect becomes more apparent and the blocking effect becomes weaker. The effective stress of the rock mass will vary depending on the angles of the joints between the hole and the joint. As the joint angle increases, the joint’s influence on the reflection and superposition of stress waves gradually weakens, and the peak value of the effective stress of the rock mass gradually decreases. The peak effective stress of the rock mass on the blasting side of the joint is similarly impacted by the superposition of stress waves, and the extreme value may be seen at the critical node of each change curve. The explosive crack will break through at the critical location because the maximal effective stress of the rock mass is distributed in a “W” form on the blasting side of the joint.

Modeling and analysis of assembly variation with non-uniform stiffness condensation for large thin-walled structures

The increase of thickness for large thin-walled structure causes the nonlinear enhancement of local structural stiffness, which leads to that the variation is concentrated on the local assembled area. The strong geometrical nonlinearity exists in the assembly process, which causes the non-uniform constraint for the material in assembled area and the variation of assembled large thin-walled structure is difficultly predicted. In this paper, the large thin-walled structure is partitioned into the assembled area and non-assembled area. The nonlinear stiffness matrix of each area is constructed based on continuum mechanics theory. The large non-assembled area is condensed as the nonlinear stiffness constraint and attached on the small assembled area. The non-uniform stiffness condensation method is developed and a new assembly variation model is proposed for large thin-walled structure with high local stiffness. The initial bending and torsional variations are constructed according to the manufacturing process of thin-walled structure and the assembly variations of two large cylindrical thin-walled structures are calculated. The predicted results by using the non-uniform condensation model are compared with that by the commercial software and the classic method of influence coefficients, in which the accuracy of the proposed model is verified. The proposed model may predict the local variation characteristics of large thin-walled structures effectively and is significant for the analysis of variation propagation in the series assembly process of large thin-walled structures.

Production quality prediction of multistage manufacturing systems using multi-task joint deep learning

A multistage manufacturing system with multiple manufacturing stages is the key and main production mode for enterprises to achieve lean production. Due to the variation propagation between stages and multiple related quality prediction tasks, it is difficult to accurately predict the quality of multistage manufacturing systems with multiple tasks. Traditional single stage and single task quality prediction methods permit the multi stages and multiple tasks separately, which ignore multi-stage effects or the quality-related relationship between multiple quality output indicators and reduce the efficiency of quality prediction. In this paper, a production quality prediction framework based on multi-task joint deep learning is proposed to simultaneously evaluate the multi-task quality of all stages in a multistage manufacturing system. To be specific, variation propagation cumulative impact between multiple manufacturing stages is innovatively expressed by designing a multi-scale convolutional neural network with control gates (MCNN-CG) to extract and propagate data features. Production quality with multi-tasks at all stages is jointly predicted by designing a multi-layer multi-gate mixture-of-experts multi-task (ML-MMoE) model with reducing multi-task predictive loss simultaneously. The soft parameter-sharing strategy and multi-gate attention strategy are separately designed to ensure information sharing while learning personalized features of tasks to improve quality prediction accuracy of each task. In addition, a loss function based on homoscedastic uncertainty and regularization is designed to automatically learn the weight between multi-stage and multi-task losses. Experiments on multistage assembly test data of an inertial navigation manufacturing system show that the proposed method performs better than traditional models. Compared to the single-stage model, the proposed multistage model has an average improvement of 8.5%, 20.0% and 23.3% in R2, MAE and RMSE respectively in the second stage. Compared with the traditional multi-stage model, the proposed model has an average improvement of 1.7%, 6.2% and 9.8% in R2, MAE and RMSE respectively in the second stage.

Variation Propagation Analysis of Hull Flat Block Construction Process Based on State Space Model

_ Hull flat block (HFB) construction is a typical discrete manufacturing process, during which block deviation is accumulated. To satisfy the dimensional requirements of shipowners, the variation propagation during HFB construction must be modeled and analyzed. Based on the stream of variation theory, the construction process is analyzed to provide a reference for controlling the deviation. In the hull construction process, the deviation is categorized into part deviation, location deviation, and welding deviation. By analyzing the causes of the different deviations, the different deviations and their accumulations can be calculated. A HFB is used to verify the proposed model, and the results show that the method can be used to calculate the deviation to the HFB. Introduction As a typical large-scale complex equipment, the hull construction process is extremely time-consuming and laborious. The final hull is composed of intermediate products, such as subassemblies, unit assemblies, and grand-assemblies (Cho et al. 1999). Since the group technology was applied in hull construction, a series of production lines has been established based on the process similarity of parts, components, blocks, and grand blocks. The actual dimension of parts would inevitably deviate from the theoretical dimension (Mandal 2017), i.e., dimensional and shape deviations will occur owing to many factors (Okumoto 2002). In the hull construction process, the deviation from the previous process will be propagated to the current process and coupled with the deviation in the current process, thereby affecting the accuracy of the product. Hence, the product must be repaired to satisfy the design requirements (Takechi et al. 1998). This will prolong the production cycle and reduce the production efficiency (Heo et al. 2015). It was discovered that the man-hours of the main operations during hull assembly constituted only one-sixth of the total assembly manhours, whereas the man-hours used for adjustment constituted one-third (Chen et al. 2020). Currently, shipyards need to eliminate the adjustment operation to avoid unnecessary rework, as well as reduce human and material resources in subsequent processes. Tanigawa (2003) estimated that an ideal ship construction accuracy control plan can reduce the production cost by 5%. Therefore, the accuracy of the hull construction process must be controlled and improved in shipyards, and a reasonable accuracy control plan should be devised to improve the product quality.

Modeling Variation in Multi-Station Compliant Assembly Using Parametric Space Envelope

Abstract Compliant parts have different characteristics from rigid parts and are used frequently in industries. One of the biggest challenges facing by industries is geometric variation management of these compliant parts which can directly impact product quality and functionality. Existing rigid body-based variation modeling approaches are not suitable for compliant assembly while finite element analysis-based methods have the disadvantages of requiring heavy computation efforts and detailed design information which is unavailable during preliminary design phase. Hence, this paper proposes a novel geometric variation propagation model of multi-station compliant assembly based on parametric space envelope. Three sources of variation: location-led positional variation, assembly deformation-induced variation, and station transition caused variation are analyzed. In this study, geometric variations are modeled indirectly through control points of constructed variation tool. Compared with existing methods where geometric variation is modeled by tracking key feature points on the manufacturing part, the proposed approach brings unique benefits. It can deal with arbitrary complex compliant part, and it provides a unified modeling framework for different types of variation. The method is illustrated and verified through a two-station three parts case study on a multi-station compliant panel assembly. The proposed method provides industries with a new way to manage geometric variation from compliant assembly.

Modeling of the Variation Propagation for Complex-Shaped Workpieces in Multi-Stage Machining Processes

Variation prediction and quality control for complex-shaped workpieces in automotive and aerospace fields with multi-stage machining processes have drawn significant attention because of the widespread application and increasing diversity of these kinds of workpieces. To finish the final workpieces with complex shapes, multiple setups and operations are often applied in machining processes. However, sources of geometric error, such as fixture error, datum error, machine tool path error, and the dimensional quality of the product, interact complicatedly at different stages. These complex interactions pose significant challenges to final product error prediction and reduction. Manufacturing error prediction based on stream of variation is an effective way to control the machining quality. However, there are few integrated models that can describe the interactions among types of geometric error sources from different stages for different kinds of complex workpieces. This paper proposes a modified error prediction model to systematically capture the interactions of different error sources among different operations for complex-shaped workpieces in multi-stage machining processes. Using differential motion vectors, the connection of all key variations from machine, fixture, and workpiece is established. This modified model can not only handle general fixture layouts for complex workpieces, but also introduce machining-induced variations. Based on this model, the main error sources identification method and error compensation method are proposed. In order to evaluate the effectiveness of the proposed method, engine blocks are used to be machined as an example. Compared with a machining process without a compensating strategy, the average machining error of the key feature is reduced by 80.5% after compensating for the main error sources.

A methodology for data-driven adjustment of variation propagation models in multistage manufacturing processes

In the current paradigm of Zero Defect Manufacturing, it is essential to obtain mathematical models that express the propagation of manufacturing deviations along Multistage Manufacturing Processes (MMPs). Linear physical-based models such as the Stream of Variation (SoV) model are commonly used, but its accuracy may be limited when applied to MMPs with a large amount of stages, mainly because of the modeling errors at each stage that are accumulated downstream.In this paper we propose a methodology to calibrate the SoV model using data from the inspection stations and prior engineering-based knowledge. The data used for calibration does not contain information about the sources of variation, and they must be estimated as part of the model adjustment procedure. The proposed methodology consists of a recursive algorithm that minimizes the difference between the sample covariance of the measured Key Product Characteristic (KPC) deviations and its estimation, which is a function of a variation propagation matrix and the covariance of the deviation of the variation sources. To solve the problem with standard convex optimization tools, Schur complements and Taylor series linearizations are applied. The output of the algorithm is an adjusted model, which consists of a variation propagation matrix and an estimation of the aforementioned variation source covariance.In order to validate the performance of the algorithm, a simulated case study is analyzed. The results, based on Monte Carlo simulations, show that the estimation errors of the KPC deviation covariances are proportional to the measurement noise variance and inversely proportional to the number of processed parts that have been used to train the algorithm, similarly to other process estimators in the literature.

Reduced Order Model of Common Battery Pack Architectures for Assessment of Cell Parameter Variation Propagation

Reduced Order Model of Common Battery Pack Architectures for Assessment of Cell Parameter Variation Propagation

Observation of Abyssal Circulation to the West of the Luzon Strait, South China Sea

Abstract South China Sea (SCS) abyssal circulation largely contributes to water renewal, energy budget, and sedimentary processes in the deep ocean. The three-dimensional abyssal circulation west of the Luzon Strait (LS) in the northern SCS was investigated using an array comprising 27 current- and pressure-recording inverted echo sounders. Over 400 days of measurements from June 2018 to July 2019 showed a narrow and strong (∼70 km, ∼2.3 cm s−1 at 2500 dbar) northward current near the steep eastern boundary, while a wide and weak (∼180 km, ∼1.5 cm s−1 at 2500 dbar) southwestward current lies along the subdued western boundary. The circulation showed conspicuous cyclonic patterns with a volume transport of ∼1.21 ± 0.93 Sv (1 Sv ≡ 106 m3 s−1) and ∼1.59 ± 0.95 Sv below 2500 dbar along the eastern and western boundaries, respectively. The current near the LS was strong in late autumn and early winter but weak in late winter and spring, following the seasonal variation of LS deep-water overflow. However, the southwestward current in the interior SCS was stronger in summer and early autumn but weaker in late winter and early spring. The different seasonal patterns identified near the LS and the interior SCS are attributed to the propagation of seasonal variation. The weak current along the western boundary in August 2018 and February 2019 was dominated by LS deep-water overflow with a time lag of ∼7.5 months. Although eddies in the upper ocean may also contribute to such variation through pressure work, the effect is minor. Significance Statement Cyclonic circulation in the deep South China Sea (SCS) largely contributes to water renewal, energy budget, and sedimentary processes and influences the transport of dissolved elements, minerals, and pollutants. As an important part of the SCS throughflow, an in-depth analysis of the SCS abyssal circulation may also contribute to understanding Indonesian Throughflow and global climate change. The three-dimensional abyssal circulation west of the Luzon Strait was investigated using large-scale data from June 2018 to July 2019, which provided unprecedented coverage of abyssal circulation in the northeast SCS. The study provides important observational evidence for the existence of SCS abyssal cyclonic circulation. Detailed spatiotemporal structure of abyssal circulation and its variations are presented, and related dynamic processes are discussed.

Edge crush testing methods and box compression modeling

While multiple test procedures have been developed to assess the inherent compressive strength of corrugated materials (edge crush test, ECT), limited work has explored the appropriateness of each in the context of box compression modeling. This study incorporates a variety of real-world samples, highlighting the varying challenges different ECT methods face in measuring the intrinsic compressive resistance of combined corrugated board. We examine each of these methods as inputs for different types of models, as well as discuss the propagation of measurement variation through the modeling effort. By highlighting the cases in which a given ECT method no longer proves to be an optimal parameter in box compression strength modeling, we explore how we might better measure this material property.

Sensor Optimization for Variation Diagnosis in Multistation Assembly Processes

Appropriate sensor deployment is the key to the efficient diagnosis of product variation. Yet, optimizing sensor placement in complex manufacturing systems remains challenging. We propose a variation propagation analysis (VPA)-based sensor deployment strategy for variation diagnosis in multistation assembly processes. A state-space model is employed to analyze the influences of fixture faults and workpiece dimensional deviations on assembly variation. Based on matrix transformation, the assembly variation propagation characteristics are quantified and a VPN-based causal graph is constructed to represent the causality between assembly variation and sensor measurement. To ensure the diagnosability of over-tolerance of assembly variation (OAV) and the economics of the sensor system, an optimal sensor deployment scheme is presented. It uses the enhanced shuffled frog-leaping algorithm to minimize the OAV unobservability per unit cost and the sensor cost under the constraint of detectability. Finally, the effectiveness of the proposed approach is illustrated by a case study of sensor deployment for variation diagnosis in a multistation automobile differential assembly process.

Variation Analysis Considering the Partial Parallel Connection in Aero-Engine Rotor Assembly

The rotation precision of rotors determines the efficiency and quality of the overall aero-engine, as well as its long-term and reliable operation ability. As the terminal link of aero-engine manufacturing, the assembly is the last guarantee of precision control. Rotor assembly relates to the accurate expression of the connection form and design optimization of the assembly scheme. The existing variation model cannot adequately handle the partial parallel chain problem, ignoring the bayonet circular connector between the rotor parts, and it is still deficient in multistage gyration error control. In this paper, the partial parallel connection and multistage revolving characteristics of rotors were discussed, and a novel modeling and optimizing method for a partial parallel dimension chain was proposed. On the one hand, the variation expression of the connection features for the revolving components considering the partial parallel structure was researched. Contact point-based torsors were represented, and a system for locating points was regarded as an assembly to describe the partial parallel chain. On the other hand, the variation propagation modeling and control for the stacking of the multistage revolving components was researched. A revolution joint was introduced in the unified Jacobian–Torsor model, and a novel assembly technique for concentricity control was proposed. Therefore, a unified variation analysis and control method for rotor assembly has been developed. Experimental results show that through this method, the final concentricity variation is 0.0539 mm, far less than the 0.1595 mm of the traditional model, and is closer to the true value range of 0.030–0.040 mm. Moreover, the optimum installed angles can be calculated as 3.153 rad, 6.025 rad, and 2.590 rad, to obtain the highest concentricity of 0.040 mm, which has strong practical guiding significance.

Virtual shimming simulation for smart assembly of aircraft skin panels based on a physics-driven digital twin

A leading challenge in the assembly process of aircraft skin panels is the precise control of part-to-part gaps to avoid excessive pre-tensions of the fastening element which, if exceeded, impair the durability and the response under dynamics loads of the whole skin assembly. The current practice is to measure the gap in specific points of the assembly with parts already at their final location, and then be-spoke shims are machined and inserted between the mating components to fill the gap. This process involves several manual measurement-fit-adjust quality loops, such as loading parts on the assembly frame, measuring gaps, off-loading parts, adding be-spoke shims and re-positioning parts ready for the fastening operation—as a matter of fact, the aircraft is re-assembled at least twice and therefore the current practice has been proved highly cost and time ineffective. Additionally, the gap measurement relies on manual gauges which are inaccurate and unable to follow the actual 3D profile of the gap. Taking advantage of emerging tools such as in-line measurement systems and large-scale physics-based simulations, this paper proposes a novel methodology to predict the part-to-part gap and therefore minimise the need for multiple quality loops. The methodology leverages a physics-driven digital twin model of the skin assembly process, which combines a physical domain (in-line measurements) and a digital domain (physics-based simulation). Central to the methodology is the variation model of the multi-stage assembly process via a physics-based simulation which allows to capture the inherent deformation of the panels and the propagation of variations between consecutive assembly stages. The results were demonstrated during the assembly process of a vertical stabiliser for commercial aircraft, and findings showed a significant time saving of 75% by reducing costly and time-consuming measurement-fit-adjust quality loops.

T-Maps-Based Tolerance Analysis of Composites Assembly Involving Compensation Strategies

Abstract Clamping force and shimming are two important compensation processes in the composite assembly. Their effects on variation propagation should be investigated in tolerance analysis. The paper presents a tolerance analysis method for composites assembly based on the T-Maps method, mainly concerning the anisotropic variations accumulation and propagation where there is the clamping force modification and the shimming. Variations of the composite parts in different directions are represented by the T-Maps. Since the different axial deviations are represented in the same Euclidean point-space, the T-Maps-based tolerance analysis of the composite parts assembly provides more accurate and reliable results. Compensation processes, the clamping force, and the shimming, on assembly tolerance synthesis of the composite parts, are analyzed clearly in the T-Map. This procedure is found to be effective for the anisotropy-oriented assembly tolerance analysis, especially concerning about effect of the clamping force and the shimming on variations accumulation and propagation. The assembly of an aircraft composite elevator is considered to demonstrate the effectiveness of the T-Maps-based method. The procedures outlined in the paper are quite general and can be used for assembly tolerance analysis of anisotropic parts.

Proof of Concept in Assignment of Within-Subject Variability During Virtual Bioequivalence Studies: Propagation of Intra-Subject Variation in Gastrointestinal Physiology Using Physiologically Based Pharmacokinetic Modeling

While the concept of ‘Virtual Bioequivalence’ (VBE) using a combination of modelling, in vitro tests and integration of pre-existing data on systems and drugs is growing from its infancy, building confidence on VBE outcomes requires demonstration of its ability not only in predicting formulation-dependent systemic exposure but also the expected degree of population variability. The concept of variation influencing the outcome of BE, despite being hidden with the cross-over nature of common BE studies, becomes evident when dealing with the acceptance criteria that consider the 90% confidence interval (CI) around the relative bioavailability. Hence, clinical studies comparing a reference product against itself may fail due to within-subject variations associated with the two occasions that the individual receives the same formulation. In this proof-of-concept study, we offer strategies to capture the most realistic predictions of CI around the pharmacokinetic parameters by propagating physiological variations through physiologically based pharmacokinetic modelling. The exercise indicates feasibility of the approach based on comparisons made between the simulated and observed WSV of pharmacokinetic parameters tested for a clinical bioequivalence case study. However, it also indicates that capturing WSV of a large array of physiological parameters using backward translation modelling from repeated BE studies of reference products would require a diverse set of drugs and formulations. The current case study of delayed-release formulation of posaconazole was able to declare certain combinations of WSV of physiological parameters as ‘not plausible’. The eliminated sets of WSV values would be applicable to PBPK models of other drugs and formulations.Graphical