Academic literature on the topic 'Model Assurance Criterion (MAC)'

The modal assurance criterion (MAC) in general measures the degree of proportion between two (modal) vectors, in the form of a correlation coefficient of a least squares ratio estimate. The MAC principle can be extended in several ways, thus increasing its field of applications. The partial MAC (PMAC) correlates parts of (modal) vectors. The spatial MAC (SMAC) allows to compare different vector spaces. Furthermore this paper suggests a way of calculating the MAC sensitivities to model changes. All those extensions are illustrated by their possible uses in correlating measured dynamic data with (finite element) matrix models and in the area of model updating. Those applications might be helpful tools to indicate regions of poor measurement-model correlation, to complete measured vectors, to judge approximate eigenvalue solvers, or to improve model updating procedures.

The coverage intensity of sensors is the most important issue on structural health monitoring technique. The geometric configuration of sensors must be optimized based on coverage intensity with proper objectives. In this article, a novel algorithm for optimal sensor placement in various steel frames was evaluated. These frames including moment-resisting frame, moment-resisting frame with base isolation, and moment-resisting frame with base isolation with steel shear wall were selected for case studies. This approach was proposed based on combination of common optimal sensor placement algorithm and nonlinear time history analysis. A new method called transformed time history to frequency domain approach was evaluated to transform nonlinear time history analysis results to frequency domain and then the effective frequencies according the maximum range of Fourier amplitude were selected. The modified type of modal assurance criterion values can be achieved from modal assurance criterion with the exact seismic displacement. All of novel optimal sensor placement processes were done through FEM-MAC-TTFD code modeled and developed in MATLAB by authors of this article. The results show that there is good relative correlation between the sensors number and coverage intensity obtained with modal and modified modal assurance criterion approaches for moment-resisting frame system, but for integrated frame such as moment-resisting frame with base isolation and moment-resisting frame with base isolation with steel shear wall, the modified modal assurance criterion approach is better approach. There is no significant difference between coverage intensity of sensors for top joints between modal assurance criterion and modified modal assurance criterion approaches for moment-resisting frame, moment-resisting frame with base isolation, and moment-resisting frame with base isolation with steel shear wall systems ( R2 = 0.994, 0.986, and 0.724, respectively). It was found that if reference point is located in center of frame, there is significant difference between modal assurance criterion and modified modal assurance criterion approaches, and modified modal assurance criterion generated slightly better results.

This study proposes a new correlation improvement technique for the optimum node removal location to get improved modal assurance criterion (MAC) matrix. The technique is applied to updating of the finite element model (FEM) of a structure. The developed routine is tried on a utility helicopter. It is proven that it is capable of showing better performance than the coordinate MAC (coMAC), commonly used in such analyses. Commercial software is utilized for the finite element analysis of the helicopter fuselage and tail. Experimental modal analyses are also performed for updating the model for tail of the helicopter to demonstrate the effectiveness of the new technique.

Tracking the aeroelastic modes of an aircraft through changing flight conditions is an essential element of flight flutter testing, which is made difficult by corrupted data and high modal density. The modal assurance criterion (MAC), a method of evaluating the consistency of two modal vectors, is shown to simplify the mode tracking procedure by putting a numerical value on the correlation between pairs of modes identified at consecutive flight conditions. Representation of the resulting MAC values as a colour map gives a clear visual indication of modal consistency. An automated approach to mode tracking is introduced and shown to work on aircraft-type systems, over significant changes in flight condition up to and beyond the flutter speed. Some potential problems of a practical implementation are discussed.

Modern control techniques can improve the performance and robustness of a rotor active magnetic bearing (AMB) system. Since those control methods usually rely on system models, it is important to obtain a precise rotor AMB analytical model. However, the interference fits and shrink effects of rotor AMB cause inaccuracy to the final system model. In this paper, an experiment based model updating method is proposed to improve the accuracy of the finite element (FE) model used in a rotor AMB system. Modelling error is minimized by applying a numerical optimization Nelder-Mead simplex algorithm to properly adjust FE model parameters. Both the error resonance frequencies and modal assurance criterion (MAC) values are minimized simultaneously to account for the rotor natural frequencies as well as for the mode shapes. Verification of the updated rotor model is performed by comparing the experimental and analytical frequency response. The close agreements demonstrate the effectiveness of the proposed model updating methodology.

Model updating techniques are used to modify structural model for more accurate predictions of dynamics behavior. A simple survey on the model updating methods and correlation criteria is presented. Based on the inverse eigensensitivity method (IESM) and modal assurance criterion (MAC), a scheme of model updating for structures is presented and realized by user defined subroutine combined with APDL in commercial software ANSYS®. A four-DOF spring-mass system is assumed and updated, from which the predicted frequencies and MAC values are satisfied compared to the actual dynamics characteristics. This gives evidence that the presented model updating scheme is feasible and efficient. Furthermore, a cylindrical shell structure containing global and local modal information is established to research the updating ability of the scheme on some focused local modal information. The results due to the updated model of cylindrical shell structure show that not only the global modal data but also the local modal data have a good agreement with that of the actual structure.

A measure of correlation between mode shapes is introduced. This measure is a modification of the standard Modal Assurance Criterion (MAC). The new form, called the Modal Correlation Coefficient (MCC), is more sensitive to the existence of kinks in mode shapes. Its advantages are realized in diagnostic and structural health monitoring applications.

In this paper, modal characteristics of self-compacting concrete (SCC) beams were studied through experiment. 3 self-compacting concrete beams were gradually damaged and then subjected to vibration test in free-free boundary conditions after each load step. From analysis, eigenfrequencies could indicate the existence of damage but it could not represent the damage locations. Modal Assurance Criterion (MAC) is lesser reliable to indicate crack damage compare to eigenfrequencies. Next to these, capacity for damage detection and localization of Coordinate Modal Assurance Criterion (COMAC) and the flexibility matrix method are also examined and compared. This paper introduces in detail the dynamic properties and damage localization methods in SCC, which provide basal databases of damage diagnosis for SCC structures and promote the popularization of SCC in civil infrastructures.

In this study, the Tabu search (TS) algorithm is introduced into the optimal sensor placement (OSP) problem in the field of the structural health monitoring and moving force identification. A TS-based OSP procedure is proposed and further evaluated by some numerical simulations on a 2D planar truss model. The mean values of off-diagonal elements in a modal assurance criterion (MAC) matrix are used as the optimization objective function. Based on the criteria of MAC, determinant of fisher matrix, matrix condition number, and the least mean square error, the TS-based OSP procedure is evaluated through comparing with ones due to both of the energy coefficient-effective independence (ECEFI) and the effective independence (EFI) algorithms. The results show that the proposed TS-based OSP procedure is feasible with a higher accuracy.

Mechanical damages in structures changes its geometry in various ways. However, if damage size comparing to structure size is small, thus observation of this damage could be hard or even impossible in some cases. For this reason, changes in structure’s vibration responses are investigated nowadays. The objective of this research is to investigate the influence of damage size to the vibration response of the mechanical structure – aluminum alloy plate. To achieve this aim, modal analysis of a reference, i.e. health, and multiple damaged structures using ANSYS Workbench, and calculation of modal assurance criterion (MAC) using Matlab were carried out in this research. During this research 6 different damage sizes were modelled and its vibration response was compared to the health one. Obtained results revealed that the bending modes rarely shows any trend towards damages scenario. But, when observing the MAC values matrices, the values related to torsional modes even on the diagonal of the matrices decrease as the damage size increases, which indicates that the damage has more influence on the torsional modes.

The dynamic characteristics of a part are highly dependent on geometric and material properties of the part. The identification and tracking of vibrational mode shapes within an iterative design process becomes difficult and time consuming due to the frequently changing part definition. Currently, visual inspection of analysis results is used as the means to identify the shape of each vibrational mode determined by the modal analysis. This thesis investigates the automation of the mode shape identification process through the use of parametric geometry and the Modal Assurance Criterion. Displacement results from finite element modal analysis are used to create parametric geometry templates which can be compared one to another irrespective of part geometry or finite element mesh density. Automation of the mode shape identification process using parametric geometry and the Modal Assurance Criterion allows for the mode shapes from a baseline design to be matched to modified part designs, giving the designer a more complete view of the part's dynamic properties. It also enables the identification process to be completed much more quickly than by visual inspection.

La protezione del patrimonio culturale e architettonico rappresenta una sfida interdisciplinare dovuta alla coesistenza di problemi storici, artistici e strutturali. Notevoli terremoti storici hanno evidenziato l'intrinseca vulnerabilità degli edifici in muratura, in particolare quelli appartenenti a complessi architettonici sotto forma di aggregati di edifici. L'attività delle autorità italiane ha mostrato un forte impegno in questo campo con il rilascio di un programma completo volto a valutare la vulnerabilità sismica di edifici e infrastrutture critiche, compresi i beni storici e architettonici. Alla luce delle incertezze derivanti dalla caratterizzazione materiale e dal comportamento strutturale, la prevenzione e la conservazione sono diventate un compito complesso nelle regioni sismiche. Le questioni relative alla definizione di un modello strutturale e dinamico appropriato spesso mettono a repentaglio l'affidabilità dell'analisi sismica. Una preoccupazione primaria è la discriminazione tra la risposta locale di macroelementi selezionati e la risposta globale della struttura. In tale contesto, le tecniche di identificazione dinamica basate sulle vibrazioni hanno visto l’ implementazione delle loro attrattiva grazie alla definizione di procedure automatizzate ed efficaci, in grado di estrarre i parametri modali dai record di misurazioni disponibili. Questo processo è fondamentalmente ben definito per queste strutture, in cui il comportamento dinamico è chiaramente definito mediante un ragionevole numero di gradi di libertà. Con riferimento a quanto descritto, viene presentata una nuova procedura basata su un indice di correlazione vettoriale ben consolidata (Modal Assurance Criterion - MAC), frequentemente utilizzato nel campo dell'analisi modale sperimentale, ed in grado di supportare la discriminazione razionale dei modi globali e locali nel campo dell'identificazione strutturale e del monitoraggio dinamico. La metodologia proposta è validata sulla base dei risultati ottenuti da un numero di casi studio numerici e attraverso un caso sperimentale. Nel processo di tutela del patrimonio esistente , la valutazione delle condizioni strutturali è necessaria per pianificare misure correttive efficaci in termini di costi, prima che l'estensione del danno porti i sistemi a interrompere lo stato di operabilità, richiedendo maggiori costi di intervento. In questo contesto, l'identificazione del danno strutturale in una fase iniziale svolge un ruolo importante nello sviluppo di procedure efficaci e affidabili per la valutazione delle prestazioni delle strutture storiche nelle aree sismiche. I danni sulle strutture in muratura si riferiscono principalmente a fessurazioni, insediamenti di fondazione, degrado del materiale e spostamenti. I metodi basati sulla dinamica per valutare il danno rappresentano uno strumento allettante per questo tipo di strutture, perché sono metodi non distruttivi e sono in grado di catturare il comportamento strutturale globale. Un affidabile algoritmo spettrale, adatto sia per tecniche di identificazione dinamica in uscita che in entrata, in grado di rilevare, localizzare e valutare il danno strutturale, viene validato mediante campagne esplicative numeriche e sperimentali eseguite sulla replica di un arco storico in muratura.
Protection of cultural and architectural heritage represents an interdisciplinary challenge due to the coexistence of historical, artistic and structural issues. Notable historical earthquakes pointed out the inherent vulnerability of the masonry buildings, in particular those belonging to architectural complexes in the form of building aggregates. The activity of the Italian Authorities showed a strong effort in this field with the release of a comprehensive program aimed at assessing the seismic vulnerability of critical buildings and infrastructures including historical and architectural assets. In the light of the uncertainties arising from material characterization and structural behaviour, prevention and preservation has become a complex task in seismic regions. The issues related to the definition of an appropriate structural and dynamic model often jeopardize the reliability of seismic analysis. A primary concern is the discrimination between the local response of selected macro elements and the global response of the structure. In such a context, vibration based dynamic identification techniques deployed their attractiveness due to definition of automated and effective procedures able to extracted modal parameters from available measurements records. This process is basically well established for these structures, where dynamics is clear and discussed by a reasonable number of degrees of freedom. In this framework, a new procedure based on well-established vector correlation ( Modal Assurance Criterion - MAC index), frequently used in the field of experimental modal analysis, point out how it can support a rational discrimination of the global and local mode, in the field of dynamic structural identification and monitoring is presented. The proposed methodology is validated based on the results obtained from a number of simulated case studies and by an experimental validation case. In the protection process of the cultural and architectural heritage, the assessment of the structural conditions is needed to plan cost-effective remedial measures, before the extension of damage leads the systems to stop operation, requiring expensive in depth interventions. In this context, structural damage identification at an early stage plays an important role for developing effective and reliable procedures for performance assessment of historical structures in seismic areas. Damage on masonry structures mainly relates to cracks, foundation settlements, material degradation and displacements. Dynamic based methods to assess the damage are an attractive tool to this type of structures because they are non-destructive methods and are able to capture the global structural behaviour. An existing robust spectral-based algorithm able to detect, locate and assess the structural damage, suitable for both output-only and input-output dynamic identification techniques, is validated by means of numerical and experimental explanatory campaign carried out on the masonry arch replica.

Existing methods of evaluating the structural system of a building after a seismic event consist of removing architectural elements such as drywall, cladding, insulation, and fireproofing. This method is destructive and costly in terms of downtime and repairs. This research focuses on removing the guesswork by using forced vibration testing (FVT) to experimentally determine the health of a building. The experimental structure is a one-story, steel, bridge-like structure with removable braces. An engaged brace represents a nominal and undamaged condition; a dis-engaged brace represents a brace that has ruptured thus changing the stiffness of the building. By testing a variety of brace configurations, a set of experimental data is collected that represents potential damage to the building after an earthquake. Additionally, several unknown parameters of the building’s substructure, lateral-force-resisting-system, and roof diaphragm are determined through FVT. A suite of computer models with different levels of damage are then developed. A quantitative analysis procedure compares experimental results to the computer models. Models that show high levels of correlation to experimental brace configurations identify the extent of damage in the experimental structure. No testing or instrumentation of the building is necessary before an earthquake to identify if, and where, damage has occurred.

Numerical model usage has substantially increased in many industries. It is the aerospace industry that numerical models play possibly the most important role for development of optimum design. However, numerical models need experimental verification. This experimental verification is used not only for validation, but also updating numerical model parameters. Verified and updated models are used to analyze a vast amount of cases that structure is anticipated to face in real life. In this thesis, structural finite element model updating of a utility helicopter fuselage was performed as a case study. Initially, experimental modal analyses were performed using modal shakers. Modal analysis of test results was carried out using LMS Test.lab software. At the same time, finite element analysis of the helicopter fuselage was performed by MSC.Patran &
Nastran software. v Initial updating was processed first for the whole helicopter fuselage then, tail of the helicopter was tried to be updated. Furthermore, a new method was proposed for the optimum node removal location for getting better Modal Assurance Criterion (MAC) matrix. This routine was tried on the helicopter case study and it showed better performance than the Coordinate Modal Assurance Criterion (coMAC) that is often used in such analyses.

Complex systems can be divided into simpler substructures. Determining the properties of each subcomponent by experimental procedures is practical and can serve to verify or calibrate finite element models. In this work, an existing model of a wind turbine blade was improved by use of experimental data. Such a blade is a subpart of a complete wind turbine. For calibration purpose, several material tests were made in order to determine the stiffness and mass properties. Later on, vibration tests of the blades were conducted and compared with simulation results of the improved model. Geometry variability within sets of blades was also studied. The blade twist angles and the center of gravity positions were found to vary moderately, which accounts for differences in blades’ dynamic behavior. Correlations between experimental data and analytical model results were very high for the first eight modeshapes. That is, according to the Model Assurance Criterion the calibrated model achieves a high-quality representation of reality. However, torsional modes in the computer model occur at a higher frequency than the experimental ones. Substructuring of the turbine allows the blades to be modeled and validated independently of the other substructures and can later be incorporated into a complete model of the turbine.

Dissertação de mestrado integrado em Engenharia Mecânica
A presente dissertação tem como principal objectivo a “Optimização do comportamento dinâmico de um componente estrutural de um Auto-Rádio” através de uma metodologia desenvolvida anteriormente, “updating” (melhoramento) do comportamento dinâmico do componente. O componente estrutural é o painel traseiro de um Auto-Rádio, que tem como função fazer o suporte e ligação da consola à caixa de componentes. O seu comportamento dinâmico é caracterizado pelos modos de vibração e frequências naturas, procura-se melhorar a geometria da peça para aperfeiçoar o seu comportamento na aplicação em que está previsto e se possível reduzir o seu custo. A ferramenta numérica de apoio para “updating” desenvolvida por Meireles em 2007, executa a optimização de um modelo numérico por minimização de uma função objectivo, de forma a melhorar o comportamento dinâmico de estruturas; esta técnica utiliza um modelo de referência e um modelo numérico do componente, por alterações de parâmetros definidos, que variam ao longo da optimização. Os parâmetros a variar estão relacionados com a geometria ou com o material do qual o componente estrutural é fabricado. O algoritmo utilizado recorre ao MAC (“Modal Assurance Criterion”) afectado do ASMAC (“Alternated Modal Search Assurance Criteria”), que estão interligados por uma função objectivo. O desenvolvimento do trabalho implica a utilização de um programa de elementos finitos, ANSYS, onde se obtêm as características dinâmicas dos modelos envolvidos e do algoritmo para execução da optimização, desenvolvido para o efeito, em linguagem MATLAB. O algoritmo de optimização varia os parâmetros definidos no problema por iterações sucessivas interagindo com o programa de elementos finitos com o objectivo de se atingir uma solução melhor que a inicial.
The present dissertation has as main objective the "Optimization of dynamic behavior of a structural component of a car radio" through a methodology developed previously, updating the dynamic behavior of the component. The structural component is the back panel of a car radio, which function is to support and connect the console to the box components. The dynamic behavior is characterized by the mode shapes and natural frequencies, wich aims to improve the geometry of the piece to improve it’s behavior in the application that is provided and if possible reduce their cost. The numerical tool support for updating developed by Meireles in 2007, performs the optimization of a numerical model by minimizing an objective function, to improve the dynamic behavior of structures, this technique uses a reference model and a numerical model component, by changes of parameters defined, which vary along of the optimization. The parameters to vary are related to the geometry or the material from which the structural component is manufactured. The algorithm uses the MAC (Modal Assurance Criterion) affected the ASMAC (Search Alternated Modal Assurance Criteria) that are interconnected by an objective function. The development of the work involves the use of a finite element program, ANSYS, where obtained the dynamic characteristics of the models involved and the algorithm to perform the optimization, developed for this purpose in MATLAB language. The optimization algorithm varies the parameters defined by successive iterations on the problem interacting with the finite element program with the aim of reaching a better solution than the original.

Quality assurance tasks such as testing, verification and validation, fault tolerance, and fault prediction play a major role in software engineering activities. Fault prediction approaches are used when a software company needs to deliver a finished product while it has limited time and budget for testing it. In such cases, identifying and testing parts of the system that are more defect prone is reasonable. In fact, prediction models are mainly used for improving software quality and exploiting available resources. Software fault prediction is studied in this chapter based on different criteria that matters in this research field. Usually, there are certain issues that need to be taken care of such as different machine-learning techniques, artificial intelligence classifiers, variety of software metrics, distinctive performance evaluation metrics, and some statistical analysis. In this chapter, the authors present a roadmap for those researchers who are interested in working in this area. They illustrate problems along with objectives related to each mentioned criterion, which could assist researchers to build the finest software fault prediction model.

Abstract A full scale experimental beam expander structure is modeled and correlated with modal test results on a component and system level. Correlation of the FE models is completed using the LINK module of the Leuven Measurement Systems (LMS) software which is also used to acquire and reduce the modal test data. The correlation tools used to measure the agreement between test and analytic mode shapes are the Modal Assurance Criterion (MAC), Coordinate Modal Assurance Criterion (CoMAC), and mass cross-orthogonality. In addition to the tools used to measure agreement between test and analysis modal parameters, sensitivity and optimization algorithms are used to identity structural parameters which influence a particular mode and what the minimum change(s) must be in the parameter(s) to bring about the desired agreement. As part of a system level pre-test analysis, the theoretical mode shapes along with a normalized line-of-sight error associated with each mode are used to select the best measurement and excitation locations.

We perform nonlinear system identification (NSI) on the acceleration signals that were experimentally measured at ten, almost evenly spaced positions along a cantilever beam undergoing vibro-impacts between two rigid stops with clearances. The NSI methodology is based on the correspondence between analytical and empirical slow-flow dynamics, with the first step requiring empirical mode decomposition (EMD) analysis of the measured time series leading to sets of intrinsic modal oscillators (IMOs) governing the vibro-impact dynamics at different time scales. By comparing the spatiotemporal variations of the nonlinear modal interactions (and hence the IMOs), we examine how vibro-impacts influence the low- and high-frequency modes in global and local senses. In applications of the NSI results to structural health monitoring and damage detection (SHM / DD), we calculate typical measures such as the modal assurance criterion (MAC) and the coordinate modal assurance criterion (COMAC) by extracting information about the mode shape functions from the spatiotemporal IMO solutions. Whereas the MAC provides a global aspect of damage occurrence (i.e., which modes are more affected by induced defects), the COMAC can narrow down the damage locations (i.e., where in the structure defects exist that yield low correlation values in specific modes). Finally, we discuss the use of the 2-dimensional correlation spectroscopy technique to SHM / DD, which is frequently used in optical chemistry areas. With the spatiotemporal IMOs the 2-D correlation intensity for the linear beam is proportional to the product of the two mode shape functions at the respective positions; hence any deviations from that may indicate the occurrence and locations of damage in the structure.

<p>A large part of the European bridge stock is reaching the end of its design service life. Currently, several applications for numerical models have been emerged, such as damage detection or structural safety assessment, among others. However, accurate numerical modeling is still a challenge. Model input uncertainties can cause large differences between numerical model predictions and actual measured responses from the structure. This fact makes model updating or calibration techniques essential for the aim of reducing such discrepancies. In this study, a model updating methodology is developed and implemented in an aging steel bridge located in a corrosive environment. An extensive and multidisciplinary experimental campaign was first carried out for collecting the necessary geometrical and material properties as well as dynamic data that will be used as a reference for the calibration process. A good agreement was found between the updated numerical model and the experimental modal data obtaining an average frequency error of 2.09% and average MAC (Modal Assurance Criterion) of 0.97.</p>

This work represents an investigation of the complex modes of continuous vibration systems with nonmodal damping. As an example, a cantilevered beam with damping at the free end is studied. Traditional separation of variables for this problem leads to a differential eigenvalue problem which requires a numerical solution. In this paper, assumed modes are applied to discretize the eigenvalue problem in state-variable form, to then obtain estimates of the frequencies and modes. The finite-element method (FEM) is also utilized to get the mass, stiffness, and damping matrices and further to solve a state-variable eigenproblem. A comparison between the assumed-mode and finite-element eigenvalues and modal vectors shows that the methods produce consistent results. The comparison of the modes was done visually and also by using the modal assurance criterion (MAC) on the modal vectors. The assumed-mode method is then used to study the effects of the damping coefficient on mode shapes and modal damping.

Ultrasonic flip chip bonding is one of the widely used methods in semiconductor chip or microsystem packaging and ultrasonic (US) bonding tool is important part for the bonding machine. To perform the proper operation of US bonding, the adequate vibration frequency and mode of US tool is required and the vibration design of the tool is very important. Until recent days, however, the most of practical aspect of the tool design follows the trial-and-error approach. In this study, we introduce the method of topology optimization for US bonding tools. The solid isotropic material with penalization (SIMP) method is used to formulate topology optimization and optimal criteria (OC) method is introduced for the update scheme. The objective resonance frequency and longitudinal mode is tracked using Modal Assurance Criterion (MAC). We compare between 2D and 3D finite element models, and realize two types of US tools which are based on 3D optimization results. To ensure the validity of topology optimization applied to the high frequency and tough devices such as US bonding tools, the vibration displacements at anti-nodal points of the optimized US tools are measured by laser vibrometer.

Abstract A machine learning (ML) approach is developed to predict the effect of blend repairs on airfoil frequency, modal assurance criterion (MAC), and modal displacement vectors. The method is demonstrated on a transonic research rig compressor rotor airfoil. A parametric definition of blend geometry is developed and shown to be capable of encompassing a large range of blend geometry. This blend repair geometry is used to modify the airfoil surface definition and a mesh morphing process transforms the nominal finite element model (FEM) to the repaired configuration. A multi-level full factorial sampling of the blend repair design space provides training data to a Guassian stochastic process (GSP) regressor. The frequency and MAC results create a vector of training data for GSP calibration, but the airfoil mode shapes require further mathematical manipulation to avoid creating GSP models for each nodal displacement. This paper develops a method to significantly reduce blended airfoil mode shape emulation cost by transforming the mode shape training data into a reduced basis space using principal component analysis (PCA). The coefficients of this reduced basis are used to train a GSP that can then predict the values for new blended airfoils. The emulated coefficients are used with the reduced basis vectors in a reconstruction of blended airfoil mode shape. Validation data is computed at a full-factorial design that maximizes the distance from training points. It is found that large variations in modal properties from large blend repairs can be accurately emulated with a reasonable number of training points. The reduced basis approach of mode shape variation is shown to more accurately predict MAC variation when compared to direct MAC emulation. The added benefit of having the full modal displacement field also allows determination of other influences such as tip-timing limits and modal force values.

Repeating structures in the form of multiple-bladed rotors are used widely in turbomachinery. Damage to blades can have significant consequences but can be difficult to identify in normal operation. This paper introduces an approach for identifying small defects such as cracks in a repeating structure that may be applicable to the limited data obtainable from developing techniques such as blade tip-timing. In order to understand the key issues involved, this initial work involves a numerical study of a simple comb-like repeating structure rather than a bladed rotor. Changes to the system modeshapes and mode order arising from damage are related to the location and severity of damage. Damage, in the form of small, open cracks, is modelled using different techniques such as material removal, periodic reduction in modulus of elasticity of selected elements at the required location and mass modification. Damage indices based on differences in the Modal Assurance Criterion (MAC) that give a measure of the change in the modeshapes are introduced. MAC matrices are obtained using a reduced number of data points. The damage index is obtained from the Frobenius norm of MAC matrix subtracted from (1) the AutoMAC of reference model without crack and (2) the identity matrix. A clear correlation between the damage indices and crack depth / location is shown. In order to account for mistuning in real repeating structures, the performance when the assembly is subjected to inhomogeneous temperature distributions is also considered.

This work explores the application of reduced-order mass-weighted proper orthogonal decomposition (RMPOD), state variable modal decomposition (SVMD), and smooth orthogonal decomposition (SOD) for extracting approximations of linear normal modes (LNMs) of a free vibrating thin lightly damped nonuniform beam experiment. The application of these decomposition methods involves organizing sensed outputs into ensemble matrices. The ensemble matrices are utilized to create correlation matrices, which are used in solving an eigenvalue problem. This is realized experimentally by sensing a thin nonuniform cantilevered beam, a saw blade, with eleven equally spaced accelerometers, during free vibration. The first mode was filtered out since its frequency was below the threshold of reliable accelerometers performance. RMPOD was able to extract the second, third, and fourth mode as implied by modal assurance criterion (MAC) in a comparison with an analytical approximation of the nonuniform Euler-Bernoulli beam modes. SVMD was able to extract an approximation to the LNMs and natural frequencies for the second, third, and fourth modes. SOD was able to extract the second, third, and fourth modes and natural frequencies successfully.

The dynamic control of stacked-plate mechanical systems such as circuit board assemblies is a common technical problem that often requires a complete description of the open loop system dynamics prior to controller development. Often, a preliminary finite element model (FEM) of the test article is developed to understand the dynamics of the system to perform a modal test. The results of this modal test must then be used to update the stiffness, mass and damping matrices to yield correct FEM frequencies mode shapes and damping. This work describes the mathematical development of a finite element model of a multi-plate test article and proceeds with a model update using differentiated velocity data collected at discrete points on the structure with a laser Doppler vibrometer (LDV) and drive point measurements collected at the excitation location with an impedance head. Using these data, accelerance FRFs were computed and the first three flexible mode shapes were estimated and these shapes were compared to the corresponding FEM shapes using both percent frequency difference and modal assurance criterion (MAC). Several parameters of the system model were modified yielding improved correlation with the experimental results.

The recently developed state-variable modal decomposition method provides a quick and efficient way to estimate modal parameters from data for a multi-degree-of-freedom vibratory system without having the need to measure inputs. Associated with the decomposition method are the state-variable modal coordinates (SVMC), which can be used to determine the quality of decomposition. In present work, a systematic way is established to distinguish a true mode from a spurious one from features of the modal coordinates. In an approach similar, in principle, to the modal assurance criterion (MAC) for assessing mode shapes, a value is directly obtained by comparing the fast Fourier transform (FFT) of the impulse response of the modal coordinate, to the sampled ideal frequency response generated by the modal parameters obtained from the decomposition. Also, the norm of the difference between the FFT magnitude of the SVMC impulse response and the sampled identified ideal frequency response is used to distinguish the true modes. Various case studies using combinations of frequency and damping values are obtained in numerically simulated results. Actual modes are also distinguished from the spurious modes using test data from a uniform thin beam.

Background Lung cancer is the number one cause of cancer death worldwide.(1) It is the fifth most commonly diagnosed cancer in Australia (12,741 cases diagnosed in 2018) and the leading cause of cancer death.(2) The number of years of potential life lost to lung cancer in Australia is estimated to be 58,450, similar to that of colorectal and breast cancer combined.(3) While tobacco control strategies are most effective for disease prevention in the general population, early detection via low dose computed tomography (LDCT) screening in high-risk populations is a viable option for detecting asymptomatic disease in current (13%) and former (24%) Australian smokers.(4) The purpose of this Evidence Check review is to identify and analyse existing and emerging evidence for LDCT lung cancer screening in high-risk individuals to guide future program and policy planning. Evidence Check questions This review aimed to address the following questions: 1. What is the evidence for the effectiveness of lung cancer screening for higher-risk individuals? 2. What is the evidence of potential harms from lung cancer screening for higher-risk individuals? 3. What are the main components of recent major lung cancer screening programs or trials? 4. What is the cost-effectiveness of lung cancer screening programs (include studies of cost–utility)? Summary of methods The authors searched the peer-reviewed literature across three databases (MEDLINE, PsycINFO and Embase) for existing systematic reviews and original studies published between 1 January 2009 and 8 August 2019. Fifteen systematic reviews (of which 8 were contemporary) and 64 original publications met the inclusion criteria set across the four questions. Key findings Question 1: What is the evidence for the effectiveness of lung cancer screening for higher-risk individuals? There is sufficient evidence from systematic reviews and meta-analyses of combined (pooled) data from screening trials (of high-risk individuals) to indicate that LDCT examination is clinically effective in reducing lung cancer mortality. In 2011, the landmark National Lung Cancer Screening Trial (NLST, a large-scale randomised controlled trial [RCT] conducted in the US) reported a 20% (95% CI 6.8% – 26.7%; P=0.004) relative reduction in mortality among long-term heavy smokers over three rounds of annual screening. High-risk eligibility criteria was defined as people aged 55–74 years with a smoking history of ≥30 pack-years (years in which a smoker has consumed 20-plus cigarettes each day) and, for former smokers, ≥30 pack-years and have quit within the past 15 years.(5) All-cause mortality was reduced by 6.7% (95% CI, 1.2% – 13.6%; P=0.02). Initial data from the second landmark RCT, the NEderlands-Leuvens Longkanker Screenings ONderzoek (known as the NELSON trial), have found an even greater reduction of 26% (95% CI, 9% – 41%) in lung cancer mortality, with full trial results yet to be published.(6, 7) Pooled analyses, including several smaller-scale European LDCT screening trials insufficiently powered in their own right, collectively demonstrate a statistically significant reduction in lung cancer mortality (RR 0.82, 95% CI 0.73–0.91).(8) Despite the reduction in all-cause mortality found in the NLST, pooled analyses of seven trials found no statistically significant difference in all-cause mortality (RR 0.95, 95% CI 0.90–1.00).(8) However, cancer-specific mortality is currently the most relevant outcome in cancer screening trials. These seven trials demonstrated a significantly greater proportion of early stage cancers in LDCT groups compared with controls (RR 2.08, 95% CI 1.43–3.03). Thus, when considering results across mortality outcomes and early stage cancers diagnosed, LDCT screening is considered to be clinically effective. Question 2: What is the evidence of potential harms from lung cancer screening for higher-risk individuals? The harms of LDCT lung cancer screening include false positive tests and the consequences of unnecessary invasive follow-up procedures for conditions that are eventually diagnosed as benign. While LDCT screening leads to an increased frequency of invasive procedures, it does not result in greater mortality soon after an invasive procedure (in trial settings when compared with the control arm).(8) Overdiagnosis, exposure to radiation, psychological distress and an impact on quality of life are other known harms. Systematic review evidence indicates the benefits of LDCT screening are likely to outweigh the harms. The potential harms are likely to be reduced as refinements are made to LDCT screening protocols through: i) the application of risk predication models (e.g. the PLCOm2012), which enable a more accurate selection of the high-risk population through the use of specific criteria (beyond age and smoking history); ii) the use of nodule management algorithms (e.g. Lung-RADS, PanCan), which assist in the diagnostic evaluation of screen-detected nodules and cancers (e.g. more precise volumetric assessment of nodules); and, iii) more judicious selection of patients for invasive procedures. Recent evidence suggests a positive LDCT result may transiently increase psychological distress but does not have long-term adverse effects on psychological distress or health-related quality of life (HRQoL). With regards to smoking cessation, there is no evidence to suggest screening participation invokes a false sense of assurance in smokers, nor a reduction in motivation to quit. The NELSON and Danish trials found no difference in smoking cessation rates between LDCT screening and control groups. Higher net cessation rates, compared with general population, suggest those who participate in screening trials may already be motivated to quit. Question 3: What are the main components of recent major lung cancer screening programs or trials? There are no systematic reviews that capture the main components of recent major lung cancer screening trials and programs. We extracted evidence from original studies and clinical guidance documents and organised this into key groups to form a concise set of components for potential implementation of a national lung cancer screening program in Australia: 1. Identifying the high-risk population: recruitment, eligibility, selection and referral 2. Educating the public, people at high risk and healthcare providers; this includes creating awareness of lung cancer, the benefits and harms of LDCT screening, and shared decision-making 3. Components necessary for health services to deliver a screening program: a. Planning phase: e.g. human resources to coordinate the program, electronic data systems that integrate medical records information and link to an established national registry b. Implementation phase: e.g. human and technological resources required to conduct LDCT examinations, interpretation of reports and communication of results to participants c. Monitoring and evaluation phase: e.g. monitoring outcomes across patients, radiological reporting, compliance with established standards and a quality assurance program 4. Data reporting and research, e.g. audit and feedback to multidisciplinary teams, reporting outcomes to enhance international research into LDCT screening 5. Incorporation of smoking cessation interventions, e.g. specific programs designed for LDCT screening or referral to existing community or hospital-based services that deliver cessation interventions. Most original studies are single-institution evaluations that contain descriptive data about the processes required to establish and implement a high-risk population-based screening program. Across all studies there is a consistent message as to the challenges and complexities of establishing LDCT screening programs to attract people at high risk who will receive the greatest benefits from participation. With regards to smoking cessation, evidence from one systematic review indicates the optimal strategy for incorporating smoking cessation interventions into a LDCT screening program is unclear. There is widespread agreement that LDCT screening attendance presents a ‘teachable moment’ for cessation advice, especially among those people who receive a positive scan result. Smoking cessation is an area of significant research investment; for instance, eight US-based clinical trials are now underway that aim to address how best to design and deliver cessation programs within large-scale LDCT screening programs.(9) Question 4: What is the cost-effectiveness of lung cancer screening programs (include studies of cost–utility)? Assessing the value or cost-effectiveness of LDCT screening involves a complex interplay of factors including data on effectiveness and costs, and institutional context. A key input is data about the effectiveness of potential and current screening programs with respect to case detection, and the likely outcomes of treating those cases sooner (in the presence of LDCT screening) as opposed to later (in the absence of LDCT screening). Evidence about the cost-effectiveness of LDCT screening programs has been summarised in two systematic reviews. We identified a further 13 studies—five modelling studies, one discrete choice experiment and seven articles—that used a variety of methods to assess cost-effectiveness. Three modelling studies indicated LDCT screening was cost-effective in the settings of the US and Europe. Two studies—one from Australia and one from New Zealand—reported LDCT screening would not be cost-effective using NLST-like protocols. We anticipate that, following the full publication of the NELSON trial, cost-effectiveness studies will likely be updated with new data that reduce uncertainty about factors that influence modelling outcomes, including the findings of indeterminate nodules. Gaps in the evidence There is a large and accessible body of evidence as to the effectiveness (Q1) and harms (Q2) of LDCT screening for lung cancer. Nevertheless, there are significant gaps in the evidence about the program components that are required to implement an effective LDCT screening program (Q3). Questions about LDCT screening acceptability and feasibility were not explicitly included in the scope. However, as the evidence is based primarily on US programs and UK pilot studies, the relevance to the local setting requires careful consideration. The Queensland Lung Cancer Screening Study provides feasibility data about clinical aspects of LDCT screening but little about program design. The International Lung Screening Trial is still in the recruitment phase and findings are not yet available for inclusion in this Evidence Check. The Australian Population Based Screening Framework was developed to “inform decision-makers on the key issues to be considered when assessing potential screening programs in Australia”.(10) As the Framework is specific to population-based, rather than high-risk, screening programs, there is a lack of clarity about transferability of criteria. However, the Framework criteria do stipulate that a screening program must be acceptable to “important subgroups such as target participants who are from culturally and linguistically diverse backgrounds, Aboriginal and Torres Strait Islander people, people from disadvantaged groups and people with a disability”.(10) An extensive search of the literature highlighted that there is very little information about the acceptability of LDCT screening to these population groups in Australia. Yet they are part of the high-risk population.(10) There are also considerable gaps in the evidence about the cost-effectiveness of LDCT screening in different settings, including Australia. The evidence base in this area is rapidly evolving and is likely to include new data from the NELSON trial and incorporate data about the costs of targeted- and immuno-therapies as these treatments become more widely available in Australia.