• Journal of Institute of Control, Robotics and Systems
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• v.8 no.8
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• pp.682-690
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• 2002

This paper presents an output feedback controller design method for uncertain linear systems with sinusoidal disturbance of uncertain frequencies. The controller needs to compensate for the performance deterioration due to the uncertain frequencies of sinusoidal disturbance. To this end, we introduce a virtual system including the dynamics corresponding to the uncertain frequencies and design a controller which minimizes the output difference between the virtual system and the closed-loop system. In other words, the controller is designed so that the closed-loop system approximates the virtual system. The feedback controller is achieved by solving an LMI optimization problem involving a robust $H_{\infty}$ constraint. The advantages of the proposed design method are examined by comparing it with a design method that only minimizes the $H_{\infty}$ norm of the transfer function between the sinusoidal disturbance and the output. The proposed design method is applied to the track-following system of rewritable optical disk drives and is evaluated through an experiment.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2014.10a
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• pp.467-471
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• 2014

The natural frequencies of a mechanical system are determined by the system parameters such as masses and stiffness of the system. Since material irregularities and manufacturing tolerances always exist in most of practical engineering situations, the system parameters always have uncertainties. As the uncertainties of the parameters increase, the uncertainties of the system natural frequencies also increases. Then, the reliability of the system deteriorates. So, the uncertainty of the system natural frequencies should be analyzed accurately and considered in the design of the system. In order to analyze the uncertainty of the system natural frequencies employing most of existing uncertainty analysis methods, the probability distributions of the uncertain system parameters should be identified. In most practical situations, however, identification of the probability distributions is almost impossible because of limited time and cost. For that case, the reliability should be estimated based on finite samples of the system parameters. In this paper, sample based reliability estimation method employing extreme value theory was proposed. Using the proposed estimation method, sample based reliability design of the system natural frequencies was conducted.

• International Journal of Aerospace System Engineering
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• v.6 no.2
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• pp.1-10
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• 2019

In this paper, the probabilistic free vibration analysis of a geometrically coupled cantilever wing with uncertain material properties is carried out using stochastic finite element (SFEM) based on first order perturbation technique. Here, both stiffness and damping of the system are considered as random parameters. The bending and torsional rigidities are assumed as spatially varying second order Gaussian random fields and represented by Karhunen Loeve (K-L) expansion. Here, the expected value, standard deviation, and probability distribution of random natural frequencies and damping ratios are computed. The results obtained from the present approach are also compared with Monte Carlo simulations (MCS). The results show that the uncertain bending rigidity has more influence on the damping ratio and frequency of modes 1 and 3 while uncertain torsional rigidity has more influence on the damping ratio and frequency of modes 2 and 3.

• Journal of Ocean Engineering and Technology
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• v.22 no.1
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• pp.75-82
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• 2008

A vibration-based damage-monitoring scheme is proposed that would generate an alarm showing the occurrence and location of damage under temperature-induced uncertainty conditions. Experiments on a model plate-girder bridge are described, for which a set of modal parameters was measured under uncertain temperature conditions. A damage-alarming model is formulated to statistically identify the occurrence of damage by recognizing the patterns of damage-driven changes in the natural frequencies of the test structure and by distinguishing temperature-induced off-limits. A damage index method based on the concept of modal strain energy is implemented in the test structure to predict the location of damage. In order to adjust for the temperature-induced changes in the natural frequencies that are used for damage detection, a set of empirical frequency correction formulas is analyzed from the relationship between the temperature and frequency ratio.

• Journal of Advanced Marine Engineering and Technology
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• v.4 no.1
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• pp.2-22
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• 1980

In the earlier days, when the diesel engine was used for ship propulsion, its shaft had often been broken by uncertain causes. Bauer suggested, for the first time in 1900, that it resulted from the torsional vibration of the shaft system. From 1901 to 1902, Gumbel and Frahm found out that shaft failures were caused by the resonance of the shaft system in critical speed. Since that time, valuable theories, empirical formulae and methods of vibration analysis were introduced by many investigators such as Geiger, Holzer, Lewis, Carter, Porter, Constant, Timoshenko, Dorey, Den Hartog, Tuplin, Ker Wilson, Bradbury etc. But, as the calculation of the damping energy involves very complicated and uncertain factors, the estimated amplitude of the torsional vibration is incorrect and uncertain. Besides, as high-powered engines have been installed on large vessels or special vessels and exciting force has been increased, new problems of the torsional vibration have continuously occurred. Although we can calculate the approximate natural frequencies or estimate their amplitude and additional stress in the design stage, through the above mentioned studies, the results of the calculations are unsatisfactory, and so much time is needed to carry out the calculation by hand. The authors have developed a computer program to calculate its natural frequencies, the amplitudes and additional stresses of the torsional vibration in the marine diesel engine shafting. In developing the computer program, the authors have paid the special attention to the calculation of the damping energy. To verify the reliability of the developed computer program, the torsional vibration of several propulsion shaftings which are driven by the diesel engine has been analyzed. The results calculted by the authors' computer program show good agreements with those of the actual measurements and are better than the results of engine maker's calculation.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.9
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• pp.1931-1942
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• 2002

In this paper a formulation of robust optimization is presented and illustrated by a design example of vibratory micro gyroscopes in order to reduce the effect of variations due to uncertainties in MEMS fabrication processes. For the vibratory micro gyroscope considered it is important to match the resonance frequencies of the vertical (sensing) and lateral (driving) modes as close as possible to attain a high sensing sensitivity. A deterministic optimization in which the difference of both the sensing and driving natural frequencies is minimized as an objective function results in highly enhanced performance but apt to be very sensitive to fabrication errors. The formulation proposed is to attain robustness of the performance by including the sensitivity of the response with respect to uncertain variables as a term of objective function to be minimized. This formulation is simple and practically applicable since no detail statistical information on fabrication errors is required. The geometric variables, beam width, length and thickness of vibratory micro gyroscopes are adopted as design variables and at the same time considered as uncertain variables because here occur the fabrication errors. A robustness test in terms of a percentage yield by using the Monte Carlo simulation has shown that the robust optimum produces twice more acceptable designs than the deterministic optimum. Improvement of robustness becomes bigger as the amount of fabrication errors is assumed larger. Considering that the magnitude of fabrication errors and uncertainties in a MEMS structure are comparatively large, the present method is illustrated to be a viable approach for a robust MEMS design.

• Journal of Advanced Marine Engineering and Technology
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• v.5 no.1
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• pp.34-51
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• 1981

Lately, due to increasing engine output by high supercharging, heavy crankshaft and propeller mass, as well as long strokes attended with the reduced crankshaft axial stiffness, the critical crankshaft axial vibration has frequently appeared in maneuvering range of the engine. Some investigators have developed calculating methods of natural frequencies and resonant amplitudes for crankshaft axial vibrations. But their reliabilities are uncertain as the estimated crankshaft axial stiffness are incorrect. The calculating procedure of these natural frequencies is practically analogous to the classical calculation of torsional vibration frequencies, except for an important difference due to the relationship of the axial stiffness of a crank and the angle between the crank and other, especially the adjacent, cranks. In this paper, 6 calculation formulae of crankshaft axial stiffness already published and a theoretically- developed one by authors are checked by comparing their calculating results with those measured values of one model crankshafat and three full-scale actual crankshafts. Also, the calculating methods of the crankshaft axial free vibration are investigated and their computer programs are developed. Finally, those developed computer programs are applied to calculating one model crankshaft and two full-scale actual crankshafts of ship's propulsion engines and their calculated results are compared with those measured values.

• Structural Engineering and Mechanics
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• v.17 no.3_4
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• pp.467-482
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• 2004

One of the uncertain damage parameters to jeopardize the safety of existing PSC bridges is the loss of the prestress force. A substantial prestress-loss can lead to severe problems in the serviceability and safety of the PSC bridges. In this paper, a nondestructive method to detect prestress-loss in beam-type PSC bridges using a few natural frequencies is presented. An analytical model is formulated to estimate changes in natural frequencies of the PSC bridges under various prestress forces. Also, an inverse-solution algorithm is proposed to detect the prestress-loss by measuring the changes in natural frequencies. The feasibility of the proposed approach is evaluated using PSC beams for which a few natural frequencies were experimentally measured for a set of prestress-loss cases. Numerical models of two-span continuous PSC beams are also examined to verify that the proposed algorithm works on more complicated cases.

• Journal of Ocean Engineering and Technology
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• v.17 no.6
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• pp.58-64
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• 2003

The performance of vibration-based damage detection methods is dependent upon the accuracy of modal parameters measured from structures of interest. Vibration monitoring, performed on a structure under uncertain temperature conditions, results in the uncertainty in model parameters of the structure. In this study, an experiment on the effect of various temperatures on modal characteristics of steel plate-girders is presented. First, the model plate-girder used for the experiment is described. Second, natural frequencies measured from the structure, using two different excitation sources, are described. Third, natural frequencies measured from the structure, under various temperatures, are described. Finally, the relationship between measurement temperature and natural frequency is analyzed.

• Journal of Wind Energy
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• v.13 no.3
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• pp.13-21
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• 2022

When a wind turbine is designed, the dynamic stability of the system as well as the dynamic characteristics of the main components such as blades, hub, main shaft and tower must be evaluated. In particular, the natural frequencies of a blade, as a main load-generating component, need to be measured and assessed by component level testing. In conventional practice, the natural frequencies of a blade are determined as the measured frequencies near the reference frequencies provided by FE analysis results. But the reference frequencies are also uncertain since designers have difficulty distinguishing the torsional mode shape among the analysis results due to the complexity of its mode shape. So, in conventional practice, the determination of a measured torsional frequency inevitably contains uncertainty. Therefore, a novel method to definitely determine the torsional frequencies from the experimental data itself is necessary. In this paper, a new methodology to measure the torsional frequency of a blade was studied from the perspective of a modal test procedure, data processing method and mode determination logic. Finally, the validity of the method that can measure torsional frequency without reference FE analysis results was verified by applying it to an actual large wind turbine blade