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Linearization of the eigenvalue problem has been widely used in vibration-based damage detection utilizing the change of natural frequencies. However, the linearization method introduces bias in the estimation of damage parameters. Moreover, the commonly employed regularization method may render the estimation different from the true underlying solution. These issues may cause wrong estimation in the damage severities and even wrong damage locations. Limited work has been done to address these issues. It is found that particular combinations of natural frequencies will result in less biased estimation using linearization approach. In this paper, we propose a measurement selection algorithm to select an optimal set of natural frequencies for vibration-based damage identification. The proposed algorithm adopts L1-norm regularization with iterative matrix randomization for estimation of damage parameters. The selection is based on the estimated bias using the least square method. Comprehensive case analyses are conducted to validate the effectiveness of the method.

Finite element model (FEM) is a broadly used numerical tool in structural damage detection. In such applications, damage parameters in FEM are estimated by minimizing the differences between experimental modal analysis data and the corresponding FEM model prediction. Very limited works exist on analyzing the identifiability of the FEM used in such applications. In this paper, the identifiability of FEM-based structural damage detection is investigated for undamped elastic beams. We theoretically proved that damage severity at a given location in a uniform beam is identifiable by reformulating the FEM into a linear time invariant (LTI) system. A numerical algorithm is also proposed for checking the identifiability issue of multiple damage locations. Numerical case studies are provided to validate the effectiveness and usefulness of the proposed framework.

Ultrasonic testing is a promising alternative quality inspection technique to the expensive microscopic imaging to characterize metal matrix nanocomposites. However, due to the complexity of the wave–microstructure interaction, and the difficulty in fabricating nanocomposites of different microstructural features, it is very challenging to build reliable relationships between ultrasonic testing results and nanocomposites quality. In this research, we propose a microstructure modeling and wave propagation simulation method to simulate ultrasonic attenuation characteristic for A206–Al2O3 metal matrix nanocomposites (MMNCs). In particular, a modified Voronoi diagram is used to reproduce the microstructures and the numeric method elastodynamic finite integration technique (EFIT) is used to simulate the wave propagation through the generated microstructures. Linear mixed effects model (LME) is used to quantify the between-curve variation of ultrasonic attenuation from both experiment and simulation. Permutation test is employed to quantify the similarity of the quantified variation between experiment and simulation. This research supports the experimental results through the simulation approach and provides a better understanding of the relationship between attenuation curves and the microstructures.

A206–Al2O3 metal matrix nanocomposite (MMNC) is a promising high performance material with potential applications in various industries, such as automotive, aerospace, and defense. Al2O3 nanoparticles dispersed into molten Al using ultrasonic cavitation technique can enhance the nucleation of primary Al phase to reduce its grain size and modify the secondary intermetallic phases. To enable a scale-up production, an effective yet easy-to-implement quality inspection technique is needed to effectively evaluate the resultant microstructure of the MMNCs. At present the standard inspection technique is based on the microscopic images, which are costly and time-consuming to obtain. This paper investigates the relationship between the ultrasonic attenuation and the microstructures of pure A206 and Al2O3 reinforced MMNCs with/without ultrasonic dispersion. A hypothesis test based on an estimated attenuation variance was developed and it could accurately differentiate poor samples from good ones. This study provides useful guidelines to establish a new quality inspection technique for A206–Al2O3 nanocomposites using ultrasonic nondestructive testing method.

Variation source identification is a critical step in the quality and productivity improvement of manufacturing processes and draws significant attention recently. In this article we present a robust pattern-matching technique for variation source identification. In this paper, a multiple variation sources identification technique is developed by adopting the linear relationship between variation sources and product quality characteristics, which is described by a coefficient matrix. The columns of the coefficient matrix are treated as the signatures of corresponding variation sources. The matching is conducted between the signature vectors and the eigenvectors of the sample covariance matrix of the product quality measurements. Multiple faults are allowed in the matching. Further, both the perturbation of unstructured noise and the sample uncertainties are considered in this matching method. A comprehensive case study illustrates the effectiveness of this method. This robust method can be used for root cause identification of manufacturing processes. The application of this method can significantly reduce the troubleshooting time and hence improve the quality and productivity of manufacturing processes. DOI: 10.1115/1.2117447

This paper presents a supervisory generalized predictive control (GPC) by combining GPC with statistical process control (SPC) for the control of the thin film deposition process. In the supervised GPC, the deposition process is described as an ARMAX model for each production run and GPC is applied to the in situ thickness-sensing data for thickness control. Supervisory strategies, developed from SPC techniques, are used to monitor process changes and estimate the disturbance magnitudes during production. Based on the SPC monitoring results, different supervisory strategies are used to revise the disturbance models and the control law in the GPC to achieve a satisfactory control performance. A case study is provided to demonstrate the developed methodology.

Dimensional variation reduction is critical to assure high product quality in discrete-part manufacturing. Recent innovations in sensor technology enable in-process implementation of laser-optical coordinate sensors and continuous monitoring of product dimensional quality. The abundance of measurement data provides an opportunity to develop next generation process control technologies that not only detect process change, but also provide guidelines respective of root cause identification. Given continuous product dimensional measurements, a critical step leading to root cause identification is the variance estimation of process variation sources. A few on-line variance estimators are available. The focus of this paper is to study the interrelationships and properties of the available variance estimators and compare their performance. An operating characteristics curve is developed as a convenient tool to guide the appropriate use of on-line variance estimators under specific circumstances. The method is illustrated using examples of dimensional control for a panel assembly process.

Imbalance-induced vibration of rotating machineries is an important factor limiting the performance and fatigue life of a rotor system. Particularly, the severe resonant vibration of a rotor when it passes through its critical speeds could damage the rotor system. To avoid this peak vibration, this paper presents an active balancing method to offset the imbalance of the rotor system during acceleration by using an electromagnetic balancer. In this method, “instantaneous” influence coefficients at different speeds are obtained and stored in a look-up table. Then, a gain scheduling strategy is adopted to suppress the imbalance-induced vibration during acceleration based on the “instantaneous” influence coefficient table. A comprehensive testbed is built to validate this scheme, and the validation results are presented.

The characteristics of the transition vibration of a rotor system when it passes its critical speeds during acceleration are of great interest for active vibration control, active real-time balancing @1#, and rotor design. In the past, a few analyses @2‐8# have dealt with speed varying transient rotor dynamics. These researchers used numerical integration techniques to calculate numerical solutions to the transient dynamic model. Although these models can be used to predict the transient vibration for a complicated rotor system, it remains hard to obtain the quantitative characteristics of the transient vibration. Lewis @9# and Dimentberg @10# presented an analytical solution of the problem of running a rotor system through its critical speeds at a uniform acceleration. The basic characteristic of the ‘‘envelope’’ ~amplitude! of the transient vibration was studied by an approximation method. In this paper, their work is extended. An analytical expression of the motion of the geometric center of a simple Jeffcott rotor is derived. The exact ‘‘envelope’’ and ‘‘phase’’ of the transient vibration are presented. As stated in Dimentberg @10#, it is found that the transient vibration through critical speeds consists of free vibration and synchronous vibration. Explicit expressions of these two components are presented in this paper.

Rigid rotor dynamic model is widely used to model rotating machinery. In this paper, a speed-varying transient rigid rotor model is developed in the state space form. The states of this model are augmented to include imbalance forces and moments. A time-varying observer can then be designed for the augmented system by using canonical transformation. After obtaining an estimation of the imbalance forces and moments as the states of the augmented system, the estimated imbalance can be directly calculated. This estimation method can be used in the active vibration control or active balancing schemes for a rigid rotor.

Recently, the importance of metrics on the group of rigid body motions has been addressed in a number of works in the kinematics and robotics literature. This paper defines new metrics on motion which are particularly easy to compute. It is shown how these metrics are applicable to path generation for rigid body motions, and also as a means for generating interpolated sequences of deformed solid models. In order to address both problems in a unified framework, general metrics on Lie groups are discussed.

In the manufacturing of micro/nanocomposite materials, micro/nanoparticles need to be dispersed evenly into the base materials. However, due to their high surface-to-volume ratio and high surface energy, the micro/nanoparticles tend to agglomerate and cluster together. Ultrasonic cavitation is effective to disperse micro/nanoparticles. However, works on correlating the cavitation parameters with the micro/nanoparticle dispersion are limited. This paper presents a real-time acoustic monitoring method based on cavitation noises to monitor the micro/nanoparticle dispersion status. In this paper, two types of cavitation noise power indices computed based on the raw cavitation noise signals are used to monitor the cavitation status. Both off-line and on-line steady state detection algorithms are developed. These algorithms can be used to determine the critical process parameters including the power of the ultrasonic sound and the dispersion time. Extensive experiments have been conducted to illustrate the effectiveness of the developed methods. [DOI: 10.1115/1.4024041]

Metal matrix nanocomposites (MMNCs) are produced by dispersing reinforcing nanoparticles into metal matrix. It is a type of emerging materials with high strength and light weight and draws significant attentions in recent years. If the particles are not well dispersed, they will form particle clusters in the metal matrix. These clusters will detrimentally impact on the final quality of MMNCs. This paper proposes a statistical approach to estimating the parameters of the size distribution of clusters in MMNCs. One critical challenge is that the clusters are distributed in a three-dimensional (3D) space, while the observations we have are two-dimensional (2D) cross-section microscopic images of these clusters. In the proposed approach, we first derived the probability distribution of the observed sizes of the 2D cross sections of the clusters and then a maximum likelihood estimation (MLE) method is developed to estimate the 3D cluster size distribution. Computational efficient algorithms are also established to make computational load manageable. The case studies based on simulation and real observed data are conducted, which demonstrates the effectiveness of the proposed approach.

B-spline surfaces are widely used in engineering practices as a flexible and efficient mathematical model for product design, analysis, and assessment. In this paper, we propose a new sequential B-spline surface construction procedure using multiresolution measurements. At each iterative step of the proposed procedure, we first update knots vectors based on bias and variance decomposition of the fitting error and then incorporate new data into the current surface approximation to fit the control points using Kalman filtering technique. The asymptotical convergence property of the proposed procedure is proved under the framework of sieves method. Using numerical case studies, the effectiveness of the method under finite sample is tested and demonstrated.

Variation source identification for manufacturing processes is critical for product dimensional quality improvement, and various techniques have been developed in recent years. Most existing variation source identification techniques are based on a linear fault-quality model, in which the relationships between process faults and product dimensional quality measurements are linear. In practice, many dimensional measurements are actually nonlinearly related to the process faults: For example, relational dimension measurements such as the relative distance between features are used to monitor composite tolerances. This paper presents a variation source identification methodology in the presence of these relational dimension measurements. In the proposed methodology, the joint probability density of the measurements is determined as a function of the process parameters; then, series of statistical comparisons are performed to differentiate and identify the variation source. A case study is also presented to illustrate the effectiveness of the methodology.