Identification of Quadratic Responses of Floating Structures in Waves
|
|
- Marvin French
- 6 years ago
- Views:
Transcription
1 Identification of Quadratic Responses of Floating Structures in Waves im Bunnik, René Huijsmans Maritime Research Institute Netherlands Yashiro Namba National Maritime Research Institute of Japan ABSRAC A formulation for the estimation of the low frequency damping and the quadratic wave drift force transfer function will be presented in this paper. Synthesized time series of the waves and low frequency motions are analyzed. Parameters influencing the stochastical nature of the estimation of the quadratic transfer functions, such as length of time series, number of time segments and frequency resolution, will be discussed. From the simulated low frequency damping and the quadratic transfer function the input signals for the analysis will be reconstructed as a means for a quality check. In this paper two estimation methods will be discussed. One method based on cross-bi-spectral analysis and a method which is based on a minimization scheme involving the quadratic transfer coefficients and the reconstruction of the second order time series. KEY WORDS System Identification non linear processes, Model test analysis. INRODUCION In the day to day practice of performing model tests on moored floating structures in waves one is often faced with the question of the validation of computed motion or force RAO's against the measured ones. Especially for floating structures where non-linear effects can play a significant role, such as semi-submersibles in survival wave conditions. Since the beginning of the 6 s analysis procedures for non-linear identification techniques have been developed (see ick (96)). hese techniques were based on a volterra series expansion of the kernels. he analysis of non-linear processes has been put in a more rigorous mathematical frame work by Brillinger (97), where he introduces the description of poly spectra and higher order transfer functions. A deconvolution technique making it possible to separate linear and higher order responses has been demonstrated by Bendat (99). Later Dalzell (97,975) used cross-bi(tri)-spectral techniques, based on cross-bi-covariance estimators to determine the mean added resistance transfer function and the cubic transfer function for roll of vessels sailing in waves. he quadratic wave drift force transfer function is normally not measured directly. Only in special model test programs such as e.g. reported by Pinkster (98) and Huijsmans et al (99). he quadratic transfer function is estimated directly from force measurements. Stansberg (994, 997) has shown that using a de-convolution process also from low frequency motion responses the underlying quadratic transfer function and the low frequency damping coefficients can be established. In this paper we will focus on the practicality of the developed procedures as well as the statistical relevance of the estimated parameters. Mathematical Background We will shortly explain the basics of linear and non-linear responses. Assume we have a Gaussian distributed input process x(t) with zero mean and a finite r.m.s in a time segment from to. We can describe this as: iπυt x(t) = X ( υ)e dυ, tε(,] () S XX,( υ ) = E X ( υ ) () he linear response to such an input x(t) follows from: () iπυt y(t) = H ( υ)x ( υ)e dυ. (3) From which the cross spectrum can be derived as: S YX,( υ ) = E Y ( υ)x ( υ ) (4) he averaging is taken by splitting the time series into a number of segments. For a quadratic response formally written as: () () y(t) = y (t) + y (t) (5) Paper No. 6-JSC-435 Bunnik
2 Or alternatively: () () i πυ υ ( )t y (t) = H ( υ, υ )X ( υ )X ( υ )e dυdυ (6) Where H is the quadratic (second order) transfer function. A more common way of notation is when we apply a rotation in the integration variables giving: () iπµ t () y (t) = e dµ H ( υ, υ+µ )X ( υ )X ( υ+µ )dυ (7) In the following section we will describe two methods for the estimation of the wave drift force transfer function. Method Cross-bi-spectral analysis Fourier transform of the previous equation gives us: ( ) ( ) * ( ) ( ) ( ) (( )) Y ω = dωh ω, ω X ω X ω ω=ω ω (8) While the left hand side comes from: Y dt y t y e π ω ( ω ) = { () } i t m he quadratic transfer function satisfies the symmetric properties shown as follows: ( ) ( ( ) ) ( )* ( )* H ω, ω = H ( ω, ω ) = H ( ω, ω ) = H ( ω, ω ) () he cross-bi-spectrum between x() t and y() t can be written as: π S, lim E X X Y * ( ω ω ) = ( ω ) ( ω ) ( ω) (( ω=ω ω )) xxy (9) () Where E represents an ensemble average and means the measured time. We can obtain the following expression that allows us to estimate QF: ( ω ω ) ( ω ) S ( ω ) ( ) S, H ( ω, ω ) = S xxy xx xx () Note that we deal with two-sided QF here. If we use the one-sided expression, the right hand side of Eq. should be divided by a factor. Eq. means that we can estimate QF with Eq. and the spectra of the input signal. In the case that the output signal is equal to the squared input signal, QF should be and we can obtain the relation: ( ) ( ) ( ) S ω, ω = S ω S ω (3) xxx xx xx Using this strict relationship we can calibrate the quadratic transfer function by scaling the directly estimated transfer function with the transfer function for the squared operator. Discretization Here we divide the measured time traces of wave and force into M sections respectively to prepare for ensemble averaging. Discretizing Eq. can be transformed into: * ( ) π Sxxy ij = M E msxxy ij = M E lim mxi mxj myk m m where m indicates the considered value that belongs to m th section. E means ensemble average and is defined by: M [ ] (4) E A A (5) M M m M m= m [ ] [ ] Similarly, we write: Sxxy ij = M E msxxy ij π k * ( ) * = ME lim ωmxi mxj Hnp mxn mxp m m (6) where i, j,k,n,p all are discretized frequencies and these frequencies have the following relations: k = i j, n = k+ p Eq. leads to: ( ) Sxxy ij Hij = (7) Sxx isxx j he contents of the square brackets in Eq. 6 consist of self-terms and cross-terms. In the remainder we shall use a Newman s approximation for the estimation of the coefficients of the quadratic transfer function thereby limiting the total amount of unknowns. In the case that it is appropriate to apply the Newman s approximation, an equation ( ) Hij P l, l ( i+ j) (8) can hold, where P l is real and Q l is imaginary and zero. Eq. 7 gives the following formula to estimate P l : Re[S xxy ij] Pl = (9) S S xx i xx j his expression still includes the cross-terms mentioned in the previous section and that makes the accuracy of estimation of QF questionable. But due to the Newman s approximation, we can exclude the cross terms as follows. First of all, Eq. 6 can be rewritten as follows: Sxxy ij = M E msxxy ij k = i j π k * * = ME lim ω mxi mxj Pl mxn mxp n = k+ p m m ( n p )/ l = + π k * * = M E P msxx i msxx j R lim m Xi m Xj m Xn mx l + l ω p m m n i,p j () where R l is a real constant. Similarly, S = ME ms xxx ij xxx ij k = i j π k * * = ME lim ω mxi mxj mxn mxp n = k+ p () m m ( n p )/ l = + π k * * = M E msxx i msxx j lim m Xi m Xj m Xn m X + ω p m m n i,p j Paper No. 6-JSC-435 Bunnik
3 From this equation, we obtain: π k * * lim ω m Xi m X j mxn m Xp = ms xxx ij msxx i msxx j m m n i,p j Substituting Eq. into Eq., we have: () estimated drift forces. We used a main diagonal of P-matrix shown in Fig. to generate the force numerically. S = E S xxy ij M m xxy ij { xxx ij } = EP S S + R S S S M l m xx i m xx j l m m xx i m xx j he above equations lead to: (3) M ERe[ ms xxy ij] P l = + M E msxx i msxx j M m M E Im[ E Re[ S ] ms xxy ij]. (4) xxx ij ME Im[ ms M E msxx i ms xx j xxx ij ] he first term of the right hand side of this equation is the same as Eq. 9. he nd term indicates the effect of the cross terms. Note that Eq. 4 just depends on l because of the Newman s approximation. In the case that the output signal is purely the squared input signal, Eq. 4 gives us P = l. At the frequencies where MEIm[ ms xxx ij ] =, Eq. 4 cannot hold. In that case, we just use the st term of the right hand side of Eq. 4, which is basically in the frequency range where the group energy is zero. In the practical analysis, we used not only the ensemble averaging but also the spectral window to obtain a smooth P l. In the right hand side of Eq. 4 we just simply applied the Hanning spectral window. Example of the Estimation Procedure Here we show the examples of the estimation. Waves and forces are generated numerically in which we used the Newman s approximation to generate the force from the wave. In the examples, we employed irregular waves with JONSWAP type and BOX type white noise spectrum as shown in Fig.. Fig. : Main diagonal of P-matrix his P matrix corresponds to a barge-shaped FPSO in deep water. he following random waves and variations were used for the simulation. A 3-hour wave realization from a survival wave spectrum (Hs = m, p =.3 s) A 7-hour wave realization from a survival wave spectrum (Hs = m, p =.3 s) A3 3-hour wave realization from a white noise wave spectrum (Hs = m with energy between.4 and. rad/s) A4 7-hour wave realization from a white noise wave spectrum (Hs = m with energy between.4 and. rad/s) A: 3-hour survival wave case Fig. 3 shows the comparison of the estimated and the theoretical main diagonal of the P-matrix. he estimated values were derived using 3- hours survival wave. In the estimation, we divided the time traces into 6 sections ( M = 6). After the ensemble averaging, we applied Hanning spectral window 3 times (NH = 3). wave spectral density [m s] white noise survival wave.5.5 Fig. : heoretical wave spectrums he wave is generated with the time step of.5[s] and total length of time trace was 3 [hours] and 7 [hours]. he 3-hour length was chosen because this is a typical test length used in ocean basins. he 7-hour length was chosen to see the effect of a longer duration on the Fig. 3: Comparison of theoretical and estimated P in 3-hour survival case. he estimated P-matrix was used to calculate the wave drift force. In Fig. 4, we compared wave drift force time trace that were computed with theoretical and with estimated P-matrix. he solid line means the wave drift force generated with the theoretical P-matrix and the dashed line indicates the computed drift force with the estimated P-matrix. hese two lines show a rather good agreement. Paper No. 6-JSC-435 Bunnik 3
4 A3: 3-hour white noise case Fig. 7 and Fig. 8 are for 3-hours white noise case. Here we estimated with M = 6 and NH = 3. In Fig. 7, we observe a considerable difference between the theoretical and the estimated transfer functions. he wave drift force time trace shows a reasonable agreement. Fig. 4: Comparison of time trace of wave drift forces generated with theoretical and with estimated P in 3-hour survival case. A: 7-hour survival case Here the estimated P was obtained using 7-hour survival wave (M = 8, NH = 3). Fig. 5 shows a good agreement between the theoretical and the estimated P-matrix. his figure also shows that we can estimate the P-matrix more accurately and in the wider range in 7-hour case than in the 3-hour case Fig. 6 shows the time traces of the wave drift forces computed with theoretical and the estimated P-matrix. he wave drift force time trace shows very good agreement. Fig. 7: Comparison of theoretical and estimated P in 3-hour white noise case. Fig. 8: Comparison of time trace of wave drift forces generated with theoretical P and with estimated P in 3-hour white noise case. A4: 7-hour white noise case Fig. 5: Comparison of theoretical and estimated P in 7-hour survival case. Fig. 9 shows a comparison between the theoretical and the estimated transfer function in 7-hour white noise case (M = 8, NH = 3). Fig. shows the time traces of the wave drift forces estimated with theoretical and the estimated P-matrix. In Fig. 9, we observe a good agreement between the exact and estimated P values. he wave drift force time trace shows a very good agreement. Fig. 6: Comparison of time trace of wave drift forces generated with theoretical P-matrix and with estimated P-matrix in 7-hour survival case. Fig. 9: Comparison of theoretical and estimated P in 7-hour white noise case. Paper No. 6-JSC-435 Bunnik 4
5 he wave drift forces in an irregular sea can be described by the following formula: N N () t = ζ iζ jpij ( ωi ωj ) t + εi ε j ) + ζiζ jqij sin( ωi ωj ) t + εi ε j ) F i= j= cos (7) Fig. : Comparison of time trace of wave drift forces generated with theoretical P and with estimated P in 7-hour white noise case. Method Estimating wave drift force transfer function by direct simulation In this section, an approach is described with which the wave drift force transfer functions can be estimated from the measured motion response and the wave elevation. he method also offers the possibility to estimate the total mass and linear and quadratic damping. A short description of the method is given by the following steps:. he wave drift force is estimated from the measured motion, velocity and acceleration and the mooring stiffness, and a priori guess on the damping values and total mass.. One value in the P matrix is set to. he remaining values are set to zero. he resulting wave drift force time trace is computed. his is done for all entries and also for the Q matrix. he total wave drift force is a superposition of all these time traces, multiplied by the actual value of the transfer function at the specific P or Q matrix entry. 3. With a least square method, appropriate multiplication coefficients are determined such that the difference between the measured wave drift force and the computed wave drift force is minimized. Estimation of force on vessel he wave forces on the vessel can be estimated from the measured motion, using the following equation of motion (surge is assumed): () () F = Mx & + b x + b x x& + cx (5) Where: F x = wave force [kn] M = total mass (including added mass) [tons] b () = linear damping coefficient [kns/m] b () = quadratic damping coefficient [kns /m ] c = linear mooring stiffness [kn/m] x = surge motion [m] Prior to the analysis, the measured motions are low-pass filtered such that the motion is only caused by the low-frequency wave drift forces. he motion part due to the wave frequency forces is filtered out. Alternatively, the forces excluding the inertia force and damping force can be computed. his way, the total mass and the damping coefficients can be estimated as well, together with the wave drift force transfer function. In this paper, only results are shown based on theoretical wave drift force time traces. Computation of wave drift force An irregular sea can be described by a sum of harmonic components: N i= ( ) ζ = ζ cos ω t +ε,withζ = S( ω ) δω (6) i i i i i he transfer function is described as a real matrix, the P matrix and an imaginary one called the Q matrix. he P matrix corresponds to the part of the wave drift force in phase with the wave groups, the Q matrix with the part out of phase with the wave groups. Using the Discrete Fourier ransform the number of frequency components is equal to the number of time steps. Instead of defining the transfer function at each discrete frequency ω i and ω j, the transfer functions are defined on a coarser frequency mesh (typically with a spacing of.5 to.5 rads - ), depending on the natural period of the system. he transfer function at in-between frequencies is then found by a D linear interpolation. he present method estimates the P and Q matrix on the coarse mesh. he advantage of the followed approach is that the transfer function is only determined at the relevant resolution and not subject to a resolution prescribed by the direct FF. Due to the limited number of coefficients that need to be estimated, a strict application of a Newman's approximation was not necessary. herefore, all the coefficients of the real and imaginary quadratic transfer function could be estimated. Least squares method By setting one value in the P matrix to one and the others to zero and computing the resulting wave drift force, the influence of one entry in the P matrix to the wave drift force can be found. By doing this for all relevant values in the P matrix (the ones where there is wave group energy present), all the individual influences can be computed. he same can be done for the Q matrix. All these influences are now multiplied by actual P and Q values. he P and Q values are chosen such (using a least squares method) that the difference between the measured wave drift force and the computed wave drift force is minimized in a least squares sense. he method explicitly uses the fact that the P matrix is symmetrical, and the Q matrix asymmetrical. Results In order to test the method several wave drift force time traces were generated. he transfer functions used to compute these time traces were obtained from a diffraction analysis for a loaded barge shaped FPSO in deep water (head seas) as indicated in Figure. As done for the Cross-bi-spectral method, the following random wave realizations were generated B 3-hour wave realization from a survival wave spectrum (Hs = m, p =.3 s) B 7-hour wave realization from a survival wave spectrum (Hs = m, p =.3 s) B3 3-hour wave realization from a white noise wave spectrum (Hs = m with energy between.4 and. rad/s) B4 7-hour wave realization from a white noise wave spectrum (Hs = m with energy between.4 and. rad/s) he wave spectra and realizations of the wave and the wave drift forces were exactly the same as in the cross-bi-spectral method, enabling a direct comparison between the two methods. hese wave realizations were subsequently used, together with the theoretical transfer function, to compute the wave drift force time traces. Newman s approach was used. he wave drift forces were computed up to a difference frequency of. radians per second. Paper No. 6-JSC-435 Bunnik 5
6 he wave elevation and wave drift force time traces were subsequently used to estimate the quadratic transfer function using the method described before. In the estimate a difference frequency of.55 radians per second was used. he theoretical wave drift force time traces contained energy up to. rad/s. herefore, a total of diagonals of the P matrix were estimated (difference frequencies,.5. rad/s). B: 3-hour wave realization from a survival wave spectrum (Hs = m, p =.3 s) Fig. shows the first diagonals of the P matrix (estimated versus theory) using the 3-hour survival wave: difference frequency rad/s difference frequency.5 rad/s Fig.. Estimated Quadratic Wave Drift Force ransfer Function he estimated P matrix was then used (with the wave elevation time trace) to compute the wave drift force time trace. Fig. shows the theoretical wave drift force and the wave drift force according to the estimated P matrix (only first hour): w a v e d rift fo rc e [k N ] theory computed with estimated P time [s] Fig. Wave Drift Force ime Series from Estimated QF hese Figures show that: - A good estimate of the transfer function is obtained in the frequency region where most of the energy is located. In the frequency region with a small amount of energy (tail of the spectrum) there is a considerable scatter in the results, especially on the main diagonal of the P matrix. - he wave drift force time traces show a good agreement. B: 7-hour wave realization from a survival wave spectrum (Hs = m, p =.3 s) Fig. 3 shows the first diagonals of the P matrix (estimated versus theory) using the 7-hour survival wave: difference frequency rad/s difference frequency.5 rad/s Fig. 3 Estimated Quadratic Wave Drift Force ransfer Function Fig. 4 shows the theoretical wave drift force and the wave drift force according to the estimated P matrix (only the first hour is shown): w a v e d rift fo rc e [k N ] x 4 - theory computed with estimated P time [s] Fig. 4 Wave Drift Force ime Series from Estimated QF Paper No. 6-JSC-435 Bunnik 6
7 hese Figures show that: - here is still a large scatter in the estimate of the main diagonal, but smaller than in the 3-hour case - he estimates of the other diagonals become better compared to the 3-hour case but differences can still be observed for the higher frequencies - he wave drift force time trace shows a very good agreement B3: 3-hour wave realization from a white noise wave spectrum hese Figures show that: - A very good agreement between the theoretical and estimated transfer functions is found - he wave drift force time trace shows a very good agreement B4: 7-hour wave realization from a white noise wave spectrum Fig. 7 shows the first diagonals of the P matrix (estimated versus theory) using the 7-hour white noise wave: he following Figure shows the first diagonals of the P matrix (estimated versus theory) using the 3-hour survival white noise wave: 5-5 difference frequency rad/s difference frequency rad/s difference frequency.5 rad/s difference frequency.5 rad/s Fig. 5 Estimated Quadratic Wave Drift Force ransfer Function he estimated P matrix was then used (with the wave elevation time trace) to compute the wave drift force time trace. he following Figure shows the theoretical wave drift force and the wave drift force according to the estimated P matrix: w a v e d rift fo rc e [k N ] theory computed with estimated P time [s] Fig. 6 Wave Drift Force ime Series from Estimated QF Fig. 7 Estimated Quadratic Wave Drift Force ransfer Function - he scatter becomes very small and an excellent agreement is obtained over the complete frequency range of the white noise spectrum. Fig. 8 shows the theoretical wave drift force and the wave drift force according to the estimated P matrix (only the first hour is shown): w a v e d rift fo rc e [k N ] theory computed with estimated P time [s] Fig. 8 Wave Drift Force ime Series from Estimated QF Paper No. 6-JSC-435 Bunnik 7
8 DISCUSSION AND CONCLUSIONS wo methods of estimating the wave drift force quadratic transfer function have been presented. Both the estimation procedure based on a cross-bi-spectral analysis techniques and the estimation procedure based on direct simulation can give larger scatter in the QF coefficients on the diagonal. his behaviour is known since in order to estimate the diagonal (i.e. the mean) of the QF as a limiting case of the group frequency going to zero. his leads to coefficients with a limited number of statistical relevance. he agreement already becomes much better once the difference frequency is larger than.5 rad/sec. In case of a white noise excitation the resulting estimates of the coefficients become much more scattered using the cross-bi-spectral analysis. It seems therefore that applying wave spectra give much more band limited effects than a white noise excitation, which covers a larger range of group frequencies. However, the use of a white noise spectrum gives much better results compared to using a survival spectrum when the direct simulation is used. his is most likely related to the conditioning of the least squares matrix in this method, but this needs to be investigated further. Also in both methods it becomes apparent that a substantial increase in the length of the time series leads to better estimates of the QF. he rms of the resulting coefficients for both methods is in this case the same. his is obvious since more statistical information is gathered (number of long-period oscillations in the time traces). In this paper it (at least in of the methods) it has been assumed that Newman s approximation can be applied. his is of course a non-valid approach in case of shallow water and for several types of floating structures (semi-submersibles). his method, therefore, needs to be extended further. REFERENCES Bendat, J. and L.Piersol (): Random Data: Analysis and Measurement procedures. Wiley Interscience 3 rd edition. Bendat, J. (99): Non Linear System Analysis and Identification from Random Data. Wiley Interscience USA. Brillinger D.R. (98): ime Series: Data Analysis and heory SF Holden USA. Dalzell, J.F. (97): Application of cross-bi-spectral analysis to ship resistance in waves, Stevens Institute of echnology NJ, Report SI-DL-7-66 Dalzell, J.F. (975): he applicability of the functional polynomial input-output model to ship responses in waves. Stevens Institute of echnology NJ,SI-DL , Huijsmans, R.H.M. and J.A. Pinkster (99). he Wave Drift Forces on Ships in Shallow Water. Proceedings of the Boss Conference London. Kim, Y. and Powers (979) : Digital Bispectral Analysis and its application to non-linear wave interaction. IEEE rans. on Plasma vol. pp -3. Stansberg, C. (997) : Linear and non-linear System Identification in Pinkster, J.A. (98): he low frequency second order wave drift forces on ships. PhD hesis Delft Model esting. Proceedings of the int. Conf. on Non-linear Aspects of Physical Model ests. Stansberg, C.. (994): Low frequency excitation and damping characteristics of a moored semi-submersible in irregular seas. Estimation from model test data. Proceedings of the Boss 994 Conf. MI USA. ick,l.j. (96): he estimation of ransfer Functions of Quadratic Systems. echnometrics, 4(7) Paper No. 6-JSC-435 Bunnik 8
Seakeeping Models in the Frequency Domain
Seakeeping Models in the Frequency Domain (Module 6) Dr Tristan Perez Centre for Complex Dynamic Systems and Control (CDSC) Prof. Thor I Fossen Department of Engineering Cybernetics 18/09/2007 One-day
More informationViscous Damping of Vessels Moored in Close Proximity of Another Object
Proceedings of The Fifteenth (5) International Offshore and Polar Engineering Conference Seoul, Korea, June 9 4, 5 Copyright 5 by The International Society of Offshore and Polar Engineers ISBN -885-4-8
More informationIDENTIFICATION OF MULTI-DEGREE-OF-FREEDOM NON-LINEAR SYSTEMS UNDER RANDOM EXCITATIONS BY THE REVERSE PATH SPECTRAL METHOD
Journal of Sound and Vibration (1998) 213(4), 673 78 IDENTIFICATION OF MULTI-DEGREE-OF-FREEDOM NON-LINEAR SYSTEMS UNDER RANDOM EXCITATIONS BY THE REVERSE PATH SPECTRAL METHOD Acoustics and Dynamics Laboratory,
More informationA Preliminary Analysis on the Statistics of about One-Year Air Gap Measurement for a Semi-submersible in South China Sea
Proceedings of the Twenty-sixth (2016) International Ocean and Polar Engineering Conference Rhodes, Greece, June 26-July 1, 2016 Copyright 2016 by the International Society of Offshore and Polar Engineers
More informationMultiple Wave Spectra. Richard May Team Lead, Aqwa development
Multiple Wave Spectra Richard May Team Lead, Aqwa development . Introduction Ocean waves with different frequencies and directions are very difficult to model mathematically Various simplified theories
More information13. Power Spectrum. For a deterministic signal x(t), the spectrum is well defined: If represents its Fourier transform, i.e., if.
For a deterministic signal x(t), the spectrum is well defined: If represents its Fourier transform, i.e., if jt X ( ) = xte ( ) dt, (3-) then X ( ) represents its energy spectrum. his follows from Parseval
More informationNON-LINEAR PARAMETER ESTIMATION USING VOLTERRA AND WIENER THEORIES
Journal of Sound and Vibration (1999) 221(5), 85 821 Article No. jsvi.1998.1984, available online at http://www.idealibrary.com on NON-LINEAR PARAMETER ESTIMATION USING VOLTERRA AND WIENER THEORIES Department
More information2.161 Signal Processing: Continuous and Discrete
MI OpenCourseWare http://ocw.mit.edu.6 Signal Processing: Continuous and Discrete Fall 8 For information about citing these materials or our erms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSES INSIUE
More informationAnalytical Predictions of the Air Gap Response of Floating Structures
Lance Manuel Department of Civil Engineering, University of Texas at Austin, Austin, TX 78712 e-mail: lmanuel@mail.utexas.edu Bert Sweetman Steven R. Winterstein Department of Civil and Environmental Engineering,
More informationA numerical investigation of second-order difference-frequency forces and motions of a moored ship in shallow water
J. Ocean Eng. Mar. Energy (205) :57 79 DOI 0.007/s40722-05-004-6 RESEARCH ARTICLE A numerical investigation of second-order difference-frequency forces and motions of a moored ship in shallow water Jikun
More information[ ], [ ] [ ] [ ] = [ ] [ ] [ ]{ [ 1] [ 2]
4. he discrete Fourier transform (DF). Application goal We study the discrete Fourier transform (DF) and its applications: spectral analysis and linear operations as convolution and correlation. We use
More informationSimple Estimation of Wave Added Resistance from Experiments in Transient and Irregular Water Waves
Simple Estimation of Wave Added Resistance from Experiments in Transient and Irregular Water Waves by Tsugukiyo Hirayama*, Member Xuefeng Wang*, Member Summary Experiments in transient water waves are
More informationA DERIVATION OF HIGH-FREQUENCY ASYMPTOTIC VALUES OF 3D ADDED MASS AND DAMPING BASED ON PROPERTIES OF THE CUMMINS EQUATION
Journal of Maritime Research, Vol. V. No., pp. 65-78, 8 Copyright 8. SEECMAR Printed in Santander (Spain). All rights reserved ISSN: 697-484 A DERIVATION OF HIGH-FREQUENCY ASYMPTOTIC VALUES OF 3D ADDED
More informationDevelopment of formulas allowing to predict hydrodynamic responses of inland vessels operated within the range of navigation 0.6 Hs 2.
Gian Carlo Matheus Torres 6 th EMship cycle: October 2015 February 2017 Master Thesis Development of formulas allowing to predict hydrodynamic responses of inland vessels operated within the range of navigation
More informationClassification of offshore structures
Classification: Internal Status: Draft Classification of offshore structures A classification in degree of non-linearities and importance of dynamics. Sverre Haver, StatoilHydro, January 8 A first classification
More informationInternational Journal of Scientific & Engineering Research Volume 9, Issue 2, February ISSN
International Journal of Scientific & Engineering Research Volume 9, Issue, February-8 48 Structural Response of a Standalone FPSO by Swell Wave in Offshore Nigeria Abam Tamunopekere Joshua*, Akaawase
More informationTIME DOMAIN COMPARISONS OF MEASURED AND SPECTRALLY SIMULATED BREAKING WAVES
TIME DOMAIN COMPARISONS OF MEASRED AND SPECTRAY SIMATED BREAKING WAVES Mustafa Kemal Özalp 1 and Serdar Beji 1 For realistic wave simulations in the nearshore zone besides nonlinear interactions the dissipative
More informationTransfer Function Identification from Phase Response Data
ransfer Function Identification from Phase Response Data Luciano De ommasi, Dir Deschrijver and om Dhaene his paper introduces an improved procedure for the identification of a transfer function from phase
More informationCONTRIBUTION TO THE IDENTIFICATION OF THE DYNAMIC BEHAVIOUR OF FLOATING HARBOUR SYSTEMS USING FREQUENCY DOMAIN DECOMPOSITION
CONTRIBUTION TO THE IDENTIFICATION OF THE DYNAMIC BEHAVIOUR OF FLOATING HARBOUR SYSTEMS USING FREQUENCY DOMAIN DECOMPOSITION S. Uhlenbrock, University of Rostock, Germany G. Schlottmann, University of
More informationModeling nonlinear systems using multiple piecewise linear equations
Nonlinear Analysis: Modelling and Control, 2010, Vol. 15, No. 4, 451 458 Modeling nonlinear systems using multiple piecewise linear equations G.K. Lowe, M.A. Zohdy Department of Electrical and Computer
More information14 - Gaussian Stochastic Processes
14-1 Gaussian Stochastic Processes S. Lall, Stanford 211.2.24.1 14 - Gaussian Stochastic Processes Linear systems driven by IID noise Evolution of mean and covariance Example: mass-spring system Steady-state
More informationTutorial Sheet #2 discrete vs. continuous functions, periodicity, sampling
2.39 utorial Sheet #2 discrete vs. continuous functions, periodicity, sampling We will encounter two classes of signals in this class, continuous-signals and discrete-signals. he distinct mathematical
More informationStochastic Processes. M. Sami Fadali Professor of Electrical Engineering University of Nevada, Reno
Stochastic Processes M. Sami Fadali Professor of Electrical Engineering University of Nevada, Reno 1 Outline Stochastic (random) processes. Autocorrelation. Crosscorrelation. Spectral density function.
More informationA STRATEGY FOR IDENTIFICATION OF BUILDING STRUCTURES UNDER BASE EXCITATIONS
A STRATEGY FOR IDENTIFICATION OF BUILDING STRUCTURES UNDER BASE EXCITATIONS G. Amato and L. Cavaleri PhD Student, Dipartimento di Ingegneria Strutturale e Geotecnica,University of Palermo, Italy. Professor,
More informationEXPERIMENTAL IDENTIFICATION OF A NON-LINEAR BEAM, CONDITIONED REVERSE PATH METHOD
EXPERIMENAL IDENIFICAION OF A NON-LINEAR BEAM, CONDIIONED REVERSE PAH MEHOD G. Kerschen, V. Lenaerts and J.-C. Golinval Université de Liège, LAS Vibrations et identification des structures, Chemin des
More informationTRUNCATED MODEL TESTS FOR MOORING LINES OF A SEMI-SUBMERSIBLE PLATFORM AND ITS EQUIVALENT COMPENSATED METHOD
Journal of Marine Science and Technology, Vol., No., pp. 5-36 (4) 5 DOI:.69/JMST-3-8- TRUNCATED MODEL TESTS FOR MOORING LINES OF A SEMI-SUBMERSIBLE PLATFORM AND ITS EQUIVALENT COMPENSATED METHOD Dong-Sheng
More informationERRATA TO: STRAPDOWN ANALYTICS, FIRST EDITION PAUL G. SAVAGE PARTS 1 AND 2 STRAPDOWN ASSOCIATES, INC. 2000
ERRATA TO: STRAPDOWN ANAYTICS, FIRST EDITION PAU G. SAVAGE PARTS 1 AND 2 STRAPDOWN ASSOCIATES, INC. 2000 Corrections Reported From April 2004 To Present Pg. 10-45 - Section 10.1.3, first paragraph - Frequency
More informationOSE801 Engineering System Identification. Lecture 09: Computing Impulse and Frequency Response Functions
OSE801 Engineering System Identification Lecture 09: Computing Impulse and Frequency Response Functions 1 Extracting Impulse and Frequency Response Functions In the preceding sections, signal processing
More informationChapter 2: The Fourier Transform
EEE, EEE Part A : Digital Signal Processing Chapter Chapter : he Fourier ransform he Fourier ransform. Introduction he sampled Fourier transform of a periodic, discrete-time signal is nown as the discrete
More informationContinuous Fourier transform of a Gaussian Function
Continuous Fourier transform of a Gaussian Function Gaussian function: e t2 /(2σ 2 ) The CFT of a Gaussian function is also a Gaussian function (i.e., time domain is Gaussian, then the frequency domain
More informationSimplified formulas of heave added mass coefficients at high frequency for various two-dimensional bodies in a finite water depth
csnak, 2015 Int. J. Nav. Archit. Ocean Eng. (2015) 7:115~127 http://dx.doi.org/10.1515/ijnaoe-2015-0009 pissn: 2092-6782, eissn: 2092-6790 Simplified formulas of heave added mass coefficients at high frequency
More informationANNEX A: ANALYSIS METHODOLOGIES
ANNEX A: ANALYSIS METHODOLOGIES A.1 Introduction Before discussing supplemental damping devices, this annex provides a brief review of the seismic analysis methods used in the optimization algorithms considered
More informationFrequency Resolution Effects on FRF Estimation: Cyclic Averaging vs. Large Block Size
Frequency Resolution Effects on FRF Estimation: Cyclic Averaging vs. Large Block Size Allyn W. Phillips, PhD Andrew. Zucker Randall J. Allemang, PhD Research Assistant Professor Research Assistant Professor
More informationOn the evaluation quadratic forces on stationary bodies
On the evaluation quadratic forces on stationary bodies Chang-Ho Lee AMIT Inc., Chestnut Hill MA, USA June 9, 006 Abstract. Conservation of momentum is applied to finite fluid volume surrounding a body
More informationAlgorithm for Multiple Model Adaptive Control Based on Input-Output Plant Model
BULGARIAN ACADEMY OF SCIENCES CYBERNEICS AND INFORMAION ECHNOLOGIES Volume No Sofia Algorithm for Multiple Model Adaptive Control Based on Input-Output Plant Model sonyo Slavov Department of Automatics
More informationLECTURE 12 Sections Introduction to the Fourier series of periodic signals
Signals and Systems I Wednesday, February 11, 29 LECURE 12 Sections 3.1-3.3 Introduction to the Fourier series of periodic signals Chapter 3: Fourier Series of periodic signals 3. Introduction 3.1 Historical
More informationChapter 7 Vibration Measurement and Applications
Chapter 7 Vibration Measurement and Applications Dr. Tan Wei Hong School of Mechatronic Engineering Universiti Malaysia Perlis (UniMAP) Pauh Putra Campus ENT 346 Vibration Mechanics Chapter Outline 7.1
More informationLecture 27 Frequency Response 2
Lecture 27 Frequency Response 2 Fundamentals of Digital Signal Processing Spring, 2012 Wei-Ta Chu 2012/6/12 1 Application of Ideal Filters Suppose we can generate a square wave with a fundamental period
More informationIdentification of nonlinear mechanical systems: Comparison between Harmonic Probing and Volterra-Kautz methods.
Trabalho apresentado no DINCON, Natal - RN, 215. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics Identification of nonlinear mechanical systems: Comparison between Harmonic
More informationSystem Modeling and Identification CHBE 702 Korea University Prof. Dae Ryook Yang
System Modeling and Identification CHBE 702 Korea University Prof. Dae Ryook Yang 1-1 Course Description Emphases Delivering concepts and Practice Programming Identification Methods using Matlab Class
More informationInverse problems in theory and practice of measurements and metrology
University of Texas at El Paso DigitalCommons@UTEP Departmental Technical Reports (CS) Department of Computer Science 1-2015 Inverse problems in theory and practice of measurements and metrology Konstantin
More informationAA242B: MECHANICAL VIBRATIONS
AA242B: MECHANICAL VIBRATIONS 1 / 50 AA242B: MECHANICAL VIBRATIONS Undamped Vibrations of n-dof Systems These slides are based on the recommended textbook: M. Géradin and D. Rixen, Mechanical Vibrations:
More informationA NUMERICAL IDENTIFICATION OF EXCITATION FORCE AND NONLINEAR RESTORING CHARACTERISTICS OF SHIP ROLL MOTION
ournal of Marine Science and Technology Vol. 5 No. 4 pp. 475-481 (017 475 DOI: 10.6119/MST-017-0418-1 A NUMERICAL IDENTIFICATION OF EXCITATION FORCE AND NONNEAR RESTORING CHARACTERISTICS OF SHIP ROLL MOTION
More informationELEG 3143 Probability & Stochastic Process Ch. 6 Stochastic Process
Department of Electrical Engineering University of Arkansas ELEG 3143 Probability & Stochastic Process Ch. 6 Stochastic Process Dr. Jingxian Wu wuj@uark.edu OUTLINE 2 Definition of stochastic process (random
More informationNonlinear Tracking Control of Underactuated Surface Vessel
American Control Conference June -. Portland OR USA FrB. Nonlinear Tracking Control of Underactuated Surface Vessel Wenjie Dong and Yi Guo Abstract We consider in this paper the tracking control problem
More informationSpectral methods for fuzzy structural dynamics: modal vs direct approach
Spectral methods for fuzzy structural dynamics: modal vs direct approach S Adhikari Zienkiewicz Centre for Computational Engineering, College of Engineering, Swansea University, Wales, UK IUTAM Symposium
More informationDynamics of Structures
Dynamics of Structures Elements of structural dynamics Roberto Tomasi 11.05.2017 Roberto Tomasi Dynamics of Structures 11.05.2017 1 / 22 Overview 1 SDOF system SDOF system Equation of motion Response spectrum
More informationROLL MOTION OF A RORO-SHIP IN IRREGULAR FOLLOWING WAVES
38 Journal of Marine Science and Technology, Vol. 9, o. 1, pp. 38-44 (2001) ROLL MOTIO OF A RORO-SHIP I IRREGULAR FOLLOWIG WAVES Jianbo Hua* and Wei-Hui Wang** Keywords: roll motion, parametric excitation,
More informationAppendix A Satellite Mechanical Loads
Appendix A Satellite Mechanical Loads Mechanical loads can be static or dynamic. Static loads are constant or unchanging, and dynamic loads vary with time. Mechanical loads can also be external or self-contained.
More informationAdvanced Digital Signal Processing -Introduction
Advanced Digital Signal Processing -Introduction LECTURE-2 1 AP9211- ADVANCED DIGITAL SIGNAL PROCESSING UNIT I DISCRETE RANDOM SIGNAL PROCESSING Discrete Random Processes- Ensemble Averages, Stationary
More informationIdentification Methods for Structural Systems. Prof. Dr. Eleni Chatzi Lecture March, 2016
Prof. Dr. Eleni Chatzi Lecture 4-09. March, 2016 Fundamentals Overview Multiple DOF Systems State-space Formulation Eigenvalue Analysis The Mode Superposition Method The effect of Damping on Structural
More information13.42 READING 6: SPECTRUM OF A RANDOM PROCESS 1. STATIONARY AND ERGODIC RANDOM PROCESSES
13.42 READING 6: SPECTRUM OF A RANDOM PROCESS SPRING 24 c A. H. TECHET & M.S. TRIANTAFYLLOU 1. STATIONARY AND ERGODIC RANDOM PROCESSES Given the random process y(ζ, t) we assume that the expected value
More informationKernel Machine Based Fourier Series
Kernel Machine Based Fourier Series Masoumeh Abbasian, Hadi Sadoghi Yazdi, Abedin Vahedian Mazloom Department of Communication and Computer Engineering, Ferdowsi University of Mashhad, Iran massomeh.abasiyan@gmail.com,
More informationLecture notes on Waves/Spectra Noise, Correlations and.
Lecture notes on Waves/Spectra Noise, Correlations and. References: Random Data 3 rd Ed, Bendat and Piersol,Wiley Interscience Beall, Kim and Powers, J. Appl. Phys, 53, 3923 (982) W. Gekelman Lecture 6,
More informationProceedings of the ASME 27th International Conference on Offshore Mechanics and Arctic Engineering OMAE2008 June 15-20, 2008, Estoril, Portugal
Proceedings of the ASME 7th International Conference on Offshore Mechanics and Arctic Engineering OMAE8 June 15-, 8, Estoril, Portugal OMAE8-57935 DISTRIBUTION OF MAXIMA OF NON-LINEAR ROLLING IN CASE OF
More informationDynamic response and fluid structure interaction of submerged floating tunnels
Fluid Structure Interaction and Moving Boundary Problems 247 Dynamic response and fluid structure interaction of submerged floating tunnels S. Remseth 1, B. J. Leira 2, A. Rönnquist 1 & G. Udahl 1 1 Department
More information2.161 Signal Processing: Continuous and Discrete Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 2.6 Signal Processing: Continuous and Discrete Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Massachusetts
More informationA quantative comparison of two restoration methods as applied to confocal microscopy
A quantative comparison of two restoration methods as applied to confocal microscopy Geert M.P. van Kempen 1, Hans T.M. van der Voort, Lucas J. van Vliet 1 1 Pattern Recognition Group, Delft University
More informationOTG-13. Prediction of air gap for column stabilised units. Won Ho Lee 01 February Ungraded. 01 February 2017 SAFER, SMARTER, GREENER
OTG-13 Prediction of air gap for column stabilised units Won Ho Lee 1 SAFER, SMARTER, GREENER Contents Air gap design requirements Purpose of OTG-13 OTG-13 vs. OTG-14 Contributions to air gap Linear analysis
More informationUp-Sampling (5B) Young Won Lim 11/15/12
Up-Sampling (5B) Copyright (c) 9,, Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version. or any later version
More informationEstimation of Variance and Skewness of Non-Gaussian Zero mean Color Noise from Measurements of the Atomic Transition Probabilities
International Journal of Electronic and Electrical Engineering. ISSN 974-2174, Volume 7, Number 4 (214), pp. 365-372 International Research Publication House http://www.irphouse.com Estimation of Variance
More informationNew Developments in Tail-Equivalent Linearization method for Nonlinear Stochastic Dynamics
New Developments in Tail-Equivalent Linearization method for Nonlinear Stochastic Dynamics Armen Der Kiureghian President, American University of Armenia Taisei Professor of Civil Engineering Emeritus
More informationECE 636: Systems identification
ECE 636: Systems identification Lectures 3 4 Random variables/signals (continued) Random/stochastic vectors Random signals and linear systems Random signals in the frequency domain υ ε x S z + y Experimental
More informationSimulation of a Class of Non-Normal Random Processes
Simulation of a Class of Non-Normal Random Processes Kurtis R. Gurley *, Ahsan Kareem, Michael A. Tognarelli Department of Civil Engineering and Geological Sciences University of Notre Dame, Notre Dame,
More informationGeotechnical Earthquake Engineering
Geotechnical Earthquake Engineering by Dr. Deepankar Choudhury Professor Department of Civil Engineering IIT Bombay, Powai, Mumbai 400 076, India. Email: dc@civil.iitb.ac.in URL: http://www.civil.iitb.ac.in/~dc/
More informationTIME-FREQUENCY ANALYSIS: TUTORIAL. Werner Kozek & Götz Pfander
TIME-FREQUENCY ANALYSIS: TUTORIAL Werner Kozek & Götz Pfander Overview TF-Analysis: Spectral Visualization of nonstationary signals (speech, audio,...) Spectrogram (time-varying spectrum estimation) TF-methods
More informationIn-Structure Response Spectra Development Using Complex Frequency Analysis Method
Transactions, SMiRT-22 In-Structure Response Spectra Development Using Complex Frequency Analysis Method Hadi Razavi 1,2, Ram Srinivasan 1 1 AREVA, Inc., Civil and Layout Department, Mountain View, CA
More informationTherefore the new Fourier coefficients are. Module 2 : Signals in Frequency Domain Problem Set 2. Problem 1
Module 2 : Signals in Frequency Domain Problem Set 2 Problem 1 Let be a periodic signal with fundamental period T and Fourier series coefficients. Derive the Fourier series coefficients of each of the
More informationUniversity of Athens School of Physics Atmospheric Modeling and Weather Forecasting Group
University of Athens School of Physics Atmospheric Modeling and Weather Forecasting Group http://forecast.uoa.gr Data Assimilation in WAM System operations and validation G. Kallos, G. Galanis and G. Emmanouil
More informationNONLINEAR ROLLING MOTION OF SHIP IN RANDOM BEAM SEAS
Journal of Marine Science and Technology, Vol., No. 4, pp. 73-79 (4) 73 NONLINEAR ROLLING MOTION OF SHIP IN RANDOM BEAM SEAS Jia-Yang Gu* Key words: nonlinear roll, melnikov function, phase space flux,
More informationIMPROVEMENTS IN MODAL PARAMETER EXTRACTION THROUGH POST-PROCESSING FREQUENCY RESPONSE FUNCTION ESTIMATES
IMPROVEMENTS IN MODAL PARAMETER EXTRACTION THROUGH POST-PROCESSING FREQUENCY RESPONSE FUNCTION ESTIMATES Bere M. Gur Prof. Christopher Niezreci Prof. Peter Avitabile Structural Dynamics and Acoustic Systems
More informationSEAKEEPING AND MANEUVERING Prof. Dr. S. Beji 2
SEAKEEPING AND MANEUVERING Prof. Dr. S. Beji 2 Ship Motions Ship motions in a seaway are very complicated but can be broken down into 6-degrees of freedom motions relative to 3 mutually perpendicular axes
More informationS S D C. LSubmitted by: 0Contract. Lfl ELEC E DEC (o NONLINEAR DIGITAL SIGNAL PROCESSING TO I- N " > "FINAL REPORT
" > "FINAL REPORT Lfl N APPLICATIONS OF FREQUENCY AND WAVENUMBER (o NONLINEAR DIGITAL SIGNAL PROCESSING TO I- N NONLINEAR HYDRODYNAMICS RESEARCH 0Contract N00167-88-K-0049 Office of Naval Research Applied
More information1 The frequency response of the basic mechanical oscillator
Seismograph systems The frequency response of the basic mechanical oscillator Most seismographic systems are based on a simple mechanical oscillator really just a mass suspended by a spring with some method
More informationChapter 2 Formulas and Definitions:
Chapter 2 Formulas and Definitions: (from 2.1) Definition of Polynomial Function: Let n be a nonnegative integer and let a n,a n 1,...,a 2,a 1,a 0 be real numbers with a n 0. The function given by f (x)
More informationCorrelator I. Basics. Chapter Introduction. 8.2 Digitization Sampling. D. Anish Roshi
Chapter 8 Correlator I. Basics D. Anish Roshi 8.1 Introduction A radio interferometer measures the mutual coherence function of the electric field due to a given source brightness distribution in the sky.
More informationITTC Recommended Procedures and Guidelines. Testing and Extrapolation Methods Loads and Responses, Ocean Engineering,
Multidirectional Irregular Wave Spectra Page 1 of 8 25 Table of Contents Multidirectional Irregular Wave Spectra... 2 1. PURPOSE OF GUIDELINE... 2 2. SCOPE... 2 2.1 Use of directional spectra... 2 2.2
More informationAn Estimation of Error-Free Frequency Response Function from Impact Hammer Testing
85 An Estimation of Error-Free Frequency Response Function from Impact Hammer Testing Se Jin AHN, Weui Bong JEONG and Wan Suk YOO The spectrum of impulse response signal from the impact hammer testing
More informationSeismic analysis of structural systems with uncertain damping
Seismic analysis of structural systems with uncertain damping N. Impollonia, G. Muscolino, G. Ricciardi Dipartirnento di Costruzioni e Tecnologie Avanzate, Universita di Messina Contrada Sperone, 31 -
More informationTransform Representation of Signals
C H A P T E R 3 Transform Representation of Signals and LTI Systems As you have seen in your prior studies of signals and systems, and as emphasized in the review in Chapter 2, transforms play a central
More informationFourier Analysis and Power Spectral Density
Chapter 4 Fourier Analysis and Power Spectral Density 4. Fourier Series and ransforms Recall Fourier series for periodic functions for x(t + ) = x(t), where x(t) = 2 a + a = 2 a n = 2 b n = 2 n= a n cos
More informationNonlinear Observer Design for Dynamic Positioning
Author s Name, Company Title of the Paper DYNAMIC POSITIONING CONFERENCE November 15-16, 2005 Control Systems I J.G. Snijders, J.W. van der Woude Delft University of Technology (The Netherlands) J. Westhuis
More information3. ESTIMATION OF SIGNALS USING A LEAST SQUARES TECHNIQUE
3. ESTIMATION OF SIGNALS USING A LEAST SQUARES TECHNIQUE 3.0 INTRODUCTION The purpose of this chapter is to introduce estimators shortly. More elaborated courses on System Identification, which are given
More information08. Brownian Motion. University of Rhode Island. Gerhard Müller University of Rhode Island,
University of Rhode Island DigitalCommons@URI Nonequilibrium Statistical Physics Physics Course Materials 1-19-215 8. Brownian Motion Gerhard Müller University of Rhode Island, gmuller@uri.edu Follow this
More informationseries of ship structural stresses
TimeWhipping/springing response in the time series analysis series of ship structural stresses in marine science and applicat Wengang Mao*, Igor Rychlik ions for industry Chalmers University of Technology,
More informationWAMIT-MOSES Hydrodynamic Analysis Comparison Study. JRME, July 2000
- Hydrodynamic Analysis Comparison Study - Hydrodynamic Analysis Comparison Study JRME, Prepared by Hull Engineering Department J. Ray McDermott Engineering, LLC 1 - Hydrodynamic Analysis Comparison Study
More informationElec4621 Advanced Digital Signal Processing Chapter 11: Time-Frequency Analysis
Elec461 Advanced Digital Signal Processing Chapter 11: Time-Frequency Analysis Dr. D. S. Taubman May 3, 011 In this last chapter of your notes, we are interested in the problem of nding the instantaneous
More informationSystem Parameter Identification for Uncertain Two Degree of Freedom Vibration System
System Parameter Identification for Uncertain Two Degree of Freedom Vibration System Hojong Lee and Yong Suk Kang Department of Mechanical Engineering, Virginia Tech 318 Randolph Hall, Blacksburg, VA,
More informationMA 323 Geometric Modelling Course Notes: Day 07 Parabolic Arcs
MA 323 Geometric Modelling Course Notes: Day 07 Parabolic Arcs David L. Finn December 9th, 2004 We now start considering the basic curve elements to be used throughout this course; polynomial curves and
More informationTime Series Analysis: 4. Digital Linear Filters. P. F. Góra
Time Series Analysis: 4. Digital Linear Filters P. F. Góra http://th-www.if.uj.edu.pl/zfs/gora/ 2018 Linear filters Filtering in Fourier domain is very easy: multiply the DFT of the input by a transfer
More informationNumerical model validation for mooring systems: Method and application for wave energy converters
1 Renewable Energy March 2015, Volume 75 Pages 869-887 http://dx.doi.org/10.1016/j.renene.2014.10.063 http://archimer.ifremer.fr/doc/00233/34375/ 2014 Published by Elsevier Ltd. All rights reserved. Achimer
More informationStochastic Processes. A stochastic process is a function of two variables:
Stochastic Processes Stochastic: from Greek stochastikos, proceeding by guesswork, literally, skillful in aiming. A stochastic process is simply a collection of random variables labelled by some parameter:
More informationSAMPLE EXAMINATION PAPER (with numerical answers)
CID No: IMPERIAL COLLEGE LONDON Design Engineering MEng EXAMINATIONS For Internal Students of the Imperial College of Science, Technology and Medicine This paper is also taken for the relevant examination
More informationIntroduction to Path Integrals
Introduction to Path Integrals Consider ordinary quantum mechanics of a single particle in one space dimension. Let s work in the coordinate space and study the evolution kernel Ut B, x B ; T A, x A )
More informationMedical Image Analysis
Medical Image Analysis CS 593 / 791 Computer Science and Electrical Engineering Dept. West Virginia University 20th January 2006 Outline 1 Discretizing the heat equation 2 Outline 1 Discretizing the heat
More informationNoise - irrelevant data; variability in a quantity that has no meaning or significance. In most cases this is modeled as a random variable.
1.1 Signals and Systems Signals convey information. Systems respond to (or process) information. Engineers desire mathematical models for signals and systems in order to solve design problems efficiently
More informationSignals and Spectra (1A) Young Won Lim 11/26/12
Signals and Spectra (A) Copyright (c) 202 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version.2 or any later
More informationFrequency Response and Continuous-time Fourier Series
Frequency Response and Continuous-time Fourier Series Recall course objectives Main Course Objective: Fundamentals of systems/signals interaction (we d like to understand how systems transform or affect
More informationStabilization and Acceleration of Algebraic Multigrid Method
Stabilization and Acceleration of Algebraic Multigrid Method Recursive Projection Algorithm A. Jemcov J.P. Maruszewski Fluent Inc. October 24, 2006 Outline 1 Need for Algorithm Stabilization and Acceleration
More informationReview of Fundamental Equations Supplementary notes on Section 1.2 and 1.3
Review of Fundamental Equations Supplementary notes on Section. and.3 Introduction of the velocity potential: irrotational motion: ω = u = identity in the vector analysis: ϕ u = ϕ Basic conservation principles:
More information