Modal Assurance Criterion Matrix Research Articles

Modal analysis of key components of crusher based on digital simulation technology

The modal characteristics of the crusher rotor and shell constitute the crucial factors influencing vibration and noise. Based on the principle of simplification, the rotor component model was established. Through mesh optimization, the model accuracy and calculation efficiency can be ensured, and the calculation of natural frequency and modal shapes was completed based on ANSYS. To verify the accuracy of the finite element model, the modal test was carried out by the hammering method. Sensors were set in three different directions to obtain the frequency response function and the modal assurance criterion matrix mode confidence criterion. Using the same research method, the modal characteristics of the shell model were simulated and analyzed. The research results show that the modal parameters identified by the modal test are basically consistent with the simulation model. The natural frequencies of the rotor and the shell are quite different from the excitation frequency of the motor, and resonance problems will not occur when the crusher is proper functioning.

An optimal sparse sensing approach for scanning point selection and response reconstruction in full-field structural vibration testing

Non-contact vibration measurements, such as 3D scanning laser Doppler vibrometry (3D SLDV), are becoming more prevalent in testing next-generation lightweight aerospace structures. This approach reduces the impact of attached sensors and improves measurement reliability. Acquiring precise measurement data for the whole area is feasible, albeit it would demand a considerable amount of time and storage space for testing. The concept of compressed sensing has been recently approved as an effective way to exploit signal sparsity and achieve full response reconstruction with very few measurements. The objective of this work is to enhance the efficiency of non-contact vibration testing by utilizing the state-of-the-art compressive sensing approach. In contrast to conventional sensor placement methods that rely on effective independence, modal kinetic energy, or modal assurance criterion matrix as targets, this paper proposes a novel sensor placement methodology from the perspective of dynamic response reconstruction. The scanning points are chosen with a minimal number to reduce testing time and are well-placed such that full-field vibration responses of the test structure can be reconstructed accurately. This allows for the spatially-detailed vibration responses to be obtained efficiently and accurately with optimal sparse sensing placement and effective response reconstruction through ℓ1 algorithm. Two case studies will be presented in this work to demonstrate and validate the methodology. The first case study is focused on a simplified cantilever beam using the numerical data from the FE analysis to demonstrate the methodology. The second case study is focused on using 3D SLDV experimental testing data from a full-scale industrial fan blade. Based on the results, it is evident that the proposed approach can significantly decrease the scanning points required for a full-field dynamic response reconstruction during full-field vibration testing.

A methodology for sensor number and placement optimization for vibration-based damage detection of composite structures under model uncertainty

Structural health monitoring techniques for composite structures are dependent on the data acquired from sensors; thus, optimal sensor network design is important to provide adequate and reliable information. This paper presents a novel framework for optimizing the number of sensors and sensor placement under model uncertainty for vibration-based damage detection in composite structures. The number of target vibration modes to be identified is first determined, based on the sum of modal effective mass fractions, to sufficiently capture dynamic responses. Since any point on the structure can be a candidate sensor position (causing a large design space), a modal kinetic-energy-based index is proposed to narrow the design space. Design objectives simultaneously minimize the number of sensors and the mean and standard deviation values for the root mean square error of off-diagonal terms in the modal assurance criterion matrix. The nondominated sorting genetic algorithm II is adopted to solve this problem. Monte Carlo simulation (MCS) is applied to evaluate the latter two objective functions. To reduce computation costs, real performance evaluations in MCS are replaced with Gaussian process regression models. To validate the optimized sensors, an optimization-based delamination detection process is applied. Case studies are presented to demonstrate the developed optimization framework.

Optimal sensor placement based on relaxation sequential algorithm

Aiming at the large tension of the solution obtained by sequential algorithm for optimal sensor placement problem, a novel relaxation sequential algorithm is proposed by introducing the idea of edge relaxation operation of Dijkstra’s algorithm into sequential algorithm. An initial solution set is generated by sequential algorithm, and improved by relaxation till the relaxation operation terminates. The proposed algorithm takes modal assurance criterion (MAC) matrix as the objective fitness function. A truss structure and a rigid-framed arch bridge are applied as examples to verify the effectiveness of the new algorithm for optimal sensor placement. The result indicates that the relaxation sequential algorithm requires fewer sensors and can reach better maximum off-diagonal element of MAC matrix in OSP problem.

Partitioned genetic algorithm strategy for optimal sensor placement based on structure features of a high-piled wharf

Health monitoring, detection, and safety assessment of high-piled wharf structures are key problems to be solved urgently in the field of maritime transport engineering. An optimal method for placing accelerometers for monitoring a high-piled wharf structure is presented in this paper. In this method, a partitioned genetic algorithm strategy is proposed based on the frequency and vibration modes of the high-piled wharf obtained by a modal analysis using the finite element method. The modal assurance criterion matrix is used as an evaluation index of sensor placement results. Subsequently, the sensor placement scheme obtained by the proposed method is applied to a reduced-scale model of a high-piled wharf to validate the method. The results demonstrate that the proposed sensor optimal placement method reduces the number of accelerometers and improves the calculation efficiency by ensuring relatively complete information on the high-piled wharf structure.

Experimental facilities for modal testing

PurposeThe experimental modal analysis requires good knowledge of various engineering fields, such as mechanical vibrations, transducers used in vibration measurement, transducers and system calibration methods, data acquisition systems, digital signal processing and system identification. Test facilities constitute a key factor for improving the quality of the estimated modal model. This paper aims to describe the experimental facilities at the Institute of Aeronautics and Space (IAE) Modal Testing Laboratory in terms of associated instrumentation and data acquisition system, metrological aspects and computational resources. The discussion is completed with a practical application showing a ground vibration testing (GVT) of an unmanned aerial vehicle (UAV).Design/methodology/approachThe experimental facilities were evaluated in a typical GVT, using three shakers in both vertical and horizontal excitations and 88 response measurement points. The global excitation method was used to excite all desired modes. The reliability of the experimental modal model was validated by an auto modal assurance criterion matrix for the measured modes of the structure.FindingsThe experimental facilities were successfully used for validating the dynamical characteristics of the UAV under testing.Originality/valueThe modal test facilities of the Modal Testing Laboratory at the IAE, the main research center of the Brazilian Air Force, are described in this paper.

On Crack Detection in Tuned and Mistuned Repeating Structures Using the Modal Assurance Criterion

AbstractRepeating structures in the form of multiple‐bladed rotors are used widely in turbomachinery. Mistuning in turbomachinery is caused by small differences in individual blade properties because of inevitable material and manufacturing variations, resulting in the splitting of vibration modes of the tuned system. Modal characteristics of the blades are quite sensitive to the level of mistuning present inside the structure. In addition, the existence of damage also results in changed dynamics of the complete system. This paper introduces a modal assurance criterion (MAC)‐based approach for the investigation of small defects such as cracks in a repeating structure. In order to understand the key issues involved, initial work involved a numerical study of a simple comb‐like repeating structure, followed by a detailed numerical and experimental investigation of a tuned and mistuned bladed disc. Changes to the system mode shapes 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 follows: material removal, monotonic reduction in the modulus of elasticity of selected elements at the required location and mass modification. Damage indices based on differences in the MAC that give a measure of the change in the mode shapes are introduced. MAC matrices are obtained using a reduced number of data points. The damage index is obtained from the Frobenius norm of the MAC matrix subtracted from the AutoMAC of a reference tuned model without crack. A clear correlation between the damage indices and the crack depth/location is shown. Application of this approach to the limited data obtainable from developing techniques such as blade tip timing is also explained.

A Combined Optimal Sensor Placement Strategy for the Structural Health Monitoring of Bridge Structures

Optimal sensor placement is an important part in the structural health monitoring of bridge structures. However, some defects are present in the existing methods, such as the focus on a single optimal index, the selection of modal order and sensor number based on experience, and the long computation time. A hybrid optimization strategy named MSE-AGA is proposed in this study to address these problems. The approach firstly selects modal order using modal participation factor. Then, the modal strain energy method is adopted to conduct the initial sensor placement. Finally, the adaptive genetic algorithm (AGA) is utilized to determine the optimal number and locations of the sensors, which uses the root mean square of off-diagonal elements in the modal assurance criterion matrix as the fitness function. A case study of sensor placement on a numerically simulated bridge structure is provided to verify the effectiveness of the MSE-AGA strategy, and the AGA method without initial placement is used as a contrast experiment. A comparison of these strategies shows that the optimal results obtained by the MSE-AGA method have a high modal strain energy index, a short computation time, and small off-diagonal elements in the modal assurance criterion matrix.

Optimal sensor placement for structural health monitoring based on multiple optimization strategies

SUMMARYCareful selection and placement of sensors are the critical issue in the construction and implementation of an effective structural health monitoring system. A hybrid method termed the optimal sensor placement strategy (OSPS) based on multiple optimization methods is proposed in this paper. The initial sensor placement is firstly obtained by the QR factorization. Then, using the minimization of the off‐diagonal elements in the modal assurance criterion matrix as a measure of the utility of a sensor configuration, the quantity of the sensors is determined by the forward and backward sequential sensor placement algorithm together. Finally, the locations of the sensor are determined by the dual‐structure coding‐based generalized genetic algorithm (GGA). Taking the scientific calculation software matlab (MathWorks, Natick, MA, USA) as a platform, an OSPS toolbox, which is working as a black box, is developed based on the command‐line compiling and graphical user interface‐aided graphical interface design. The characteristic and operation method of the toolbox are introduced in detail, and the scheme selection of the OSP is carried out on the world's tallest TV tower (Guangzhou New TV Tower) based on the developed toolbox. The results indicate that the proposed method is effective and the software package has a friendly interface, plenty of functions, good expansibility and is easy to operate, which can be easily applied in practical engineering. Copyright © 2011 John Wiley & Sons, Ltd.