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Technipfmc Plc Rises 5.48% on Heavy Volume: Watch For Potential Pullback
Technipfmc Plc (NYSE:FTI) traded in a range yesterday that spanned from a low of $22.91 to a high of $23.10. Yesterday, the shares gained 5.5%, which took the trading range above the 3-day high of $22.14 on volume of 5.3 million shares. Often times after large one-day gains, short term traders will seek to take profits and, as such, investors should be cautious.
In the past 52 weeks, shares of Technipfmc Plc have traded between a low of $18.20 and a high of $34.39 and are now at $23.10, which is 27% above that low price. The 200-day and 50-day moving averages have moved 0.66% lower and 0.56% higher over the past week, respectively.
SmarTrend is monitoring the recent change of momentum in Technipfmc Plc. Please refer to our Company Overview for the results of our proprietary technical indicators that have been scanning shares of Technipfmc Plc in search of a potential trend change.
Keywords: rebounders technipfmc plc
Ticker(s): FTI


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Tazo Iced Green Tea$3.50
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Fried Mozzarella
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Food at La Maison for me is just ok. Not that special for me. Tastes like just "so-so". It has the same taste as how my mother cooks these kind of dishes at home(LOL). We took advantage of their group menu which is good for 6 pax already, priced at 1k+. We just added additional food with it coz we felt it's not enough for the 6 of us.
With regards to the place, well it's an ok place with nice interiors. The service is ok as well, we don't usually complain (tsk tsk tsk) when eating in fancy restos.
A bit expensive as well for me, because servings are very little. Good that I'm with a company of good friends. I tend to forget my disappointment with their food. A good company really do makes a difference.
Will I go back to La Maison? Probably not if it'd be my expense 'coz I really find it expensive and servings is not justifiable.


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Date: 11/20/2018
Duration: 09:03
Lots of snow and very cold..gloomy! The sun, when we see it setting, is edging slowly from it's westerly position on the horizon ..southward.
Gowganda, ON
Latitude: 47.7 Longitude: -80.8
Observed by: Gert
Contact Observer
The observer's e-mail address will not be disclosed.
Contact will be made through a web-based form.


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I just love a Tiki Bar. I think they are so much fun and create the perfect ambiance for a Luau party. Here's how you can make your own home tiki bar complete with pictured instructions and tips and tricks along the way. Since I was in a rush and graduation blur with my first […] More
Easter bread is such a fun way to add a little fun to your Easter dinner table. These Easter bead recipes include fun Spring shapes like the Easter bunny, chicks, lamb, and on the spiritual side resurrection rolls. I even threw in a nursery rhyme with some hot cross buns. {giggle} The cutest shapes and […] More
Easter brunch is such a fun family tradition and what a great way to start out Easter Sunday celebrations with some delicious comfort food. These Easter brunch recipes include hard boiled eggs, frittata, carrot crescent rolls, french toast recipes, and hasbrown recipes. All breakfast and lunch recipes combined that are perfect to cook for your […] More
Baking Easter desserts is such a fun tradition that you can do with your family or to gift for neighbors and friends. These Easter desserts include rainbow jello, Easter chocolate, Easter cookies as well as free printable Easter treats. Easter Sunday is around the corner and these yummy Easter desserts are perfect for a Spring […] More
Basket liners can bring an old wicker basket from drab to fab in an instant. I've listed a variety of sewing tutorials from easy basket liners to super frilly to how to grow your own grass liner. {snicker} I've already featured several Easter baskets for girls and Easter basket ideas for boys and even some […] More
Easter Baskets make the cutest party favors and these DIY Easter basket ideas are so adorable and perfect for Easter Sunday. These party favors are perfect for Spring and include Easter basket templates, free printables, and Easter gift baskets as a hostess gift or little gift for your Easter Sunday table. Easter Box Party Favors […] More
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Put a pink tutu on your jewelry box. Add shimmery gems, jewels and glitter. Then fill it with your precious jewelry. Your ballerina dances to Swan Lake each tim...(more)
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For the first time in the series, Chicago has the lead and this time they need a single victory to lift the Stanley Cup. Boston returns home confident that the support of their fans will propel them to a series tying victory, before they return to Chicago for a decisive game seven.
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Application of Independent Component Analysis and Blind Source Separation Techniques to Operational Modal Analysis
Application of Independent Component Analysis and Blind Source Separation Techniques to Operational Modal Analysis S. Chauhan, R.J. Allemang, R. Mart...
John Lawrence
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Application of Independent Component Analysis and Blind Source Separation Techniques to Operational Modal Analysis
S. Chauhan, R.J. Allemang, R. Martell, D.L. Brown, Structural Dynamics Research Laboratory University of Cincinnati, Cincinnati, OH Email:
[email protected]
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Nomenclature t x(t) A s(t) n
Time Vector of output observations Mixing system or mixing matrix Source signals Number of sources
Rˆ x
Covariance matrix
Λ Vs Vn
Eigenvalues of covariance matrix Eigenvectors associated with principle eigenvalues Eigenvectors associated with noise Pre-whitened vector of output observations Quadricovariance Matrix Number of time lag Modal vector associated with rth mode Modal coordinates associated with rth mode Modal filter matrix Independent and identically distributed
x C p Φr ηr Ψ i.i.d.
Abstract Independent Component Analysis (ICA) / Blind Source Separation (BSS) is an emerging research area in the field of signal processing. The goal of ICA / BSS techniques is to identify statistically independent and non-Gaussian sources from a linear mixture of such sources. It also extracts the unknown mixture matrix in the process. The purpose of this paper is to explore the possibilities of utilizing this concept of ICA for the purpose of Operational Modal Analysis in which the system is identified only on the basis of output responses which are a function of unknown input forces and underlying system characteristics. Four different ICA algorithms are used in this study by applying them on a 15 degrees-of-freedom analytical system. These algorithms differ from each other on the basis of the optimizing techniques implemented and by utilization of second or higher order statistics. The modal parameters estimated using these methods are compared with true system parameters and also with one of the Operational Modal Analysis techniques.
1. Introduction Experimental Modal Analysis (EMA) has been the most prominent tool for characterizing the dynamics of a structure. Modal parameter estimation is one of the key stages of overall EMA process where modal parameters namely natural frequency, associated damping, mode shapes and scaling factors that characterize the structure
are estimated. In past, several algorithms have been developed to estimate the modal parameters. Details of these algorithms can be found in [1-4]. However, difficulties in characterizing large structures (such as bridges and buildings) and simulating exact operating conditions (such as those encountered by vehicles on road) led to the development of Operational Modal Analysis in which the system parameters are identified on the basis of the output responses only. This approach is different from the traditional EMA in which both the output responses and the input forces are required to be measured. As in case of EMA, there are several OMA parameter estimation techniques, most of which are basically the extension of popular EMA algorithms to OMA domain [5]. The focus of this paper is Independent Component Analysis (ICA) and its applicability to Operational Modal Analysis. Independent component analysis and other related problems such as Blind Source Separation (BSS), Blind Signal Extraction (BSE) and Multichannel Blind Deconvolution (MBD) share the same generalized blind signal processing problem where the aim is to estimate the original source signal and corresponding mixing matrix based only on the knowledge of mixed output signals. There are several good resources that explain the concept of ICA, BSS and other related problems [6-10]. ICA based methods have found application in diverse areas such as biomedical signal analysis (EEG, MMG etc.), speech enhancement, image processing, wireless communication etc. ICA based methods have also found application in structural dynamics related areas such as damage detection and fault diagnosis [11, 12], rotating machinery vibration [13] etc. Recently, Kerschen et al [14, 15] showed that ICA can also be used for parameter estimation purposes. The work in this paper, illustrates the effectiveness of ICA techniques for the purpose of output only OMA applications. Four different ICA algorithms namely, AMUSE [16], Second Order Blind Identification (SOBI) [17], Joint Approximate Diagonalization (JADE) [18] and Fourth Order Blind Identification (FOBI) [19, 20] are applied to an analytical system and their performance is compared with theoretical and OMA based results. The paper is organized in the following manner. Section 2 describes the general ICA problem and the various ICA algorithms as listed above briefly. Extension of ICA techniques to OMA and related issues are discussed next. In section 3, a case study, an analytical system, is presented and associated results are discussed. Finally, based on the obtained results, conclusions are presented along with the scope of ICA techniques in the field OMA.
2. Independent Component Analysis Independent Component Analysis (ICA) or Blind Source Separation (BSS) can be seen as an extension to Principal Component Analysis (PCA) which aims at recovering the source signals from the set observed instantaneous linear mixtures without any a priori knowledge of the mixing system. Mathematically, ICA problem can be formulated as x(t ) = As (t ) (01) where x(t) is a column vector of m output observations representing an instantaneous linear mixture of source signals s(t) which is a column vector of n sources at time instant t. A is an m X n matrix referred to as "mixing system" or more commonly as "mixing matrix". Although ICA and BSS techniques claim to identify both the source signals and the mixing matrices, they do so within certain indeterminacies that include arbitrary scaling, permutation and delay of estimated source signals. However, in spite of these limitations the waveform of the original signal is preserved and in many applications knowledge of source waveform is the most relevant information. The task of estimating both s and A, the two unknowns in the above mentioned problem requires certain assumptions to be made about the statistical properties of the sources si. ICA assumes that the sources si are statistically independent and that they have non-Gaussian distribution. A detailed discussion of the subject of ICA is beyond the scope of this paper; interested readers can refer to [6-10,21-22] for general introduction and details of the various aspects of ICA. In addition to these resources readers can also refer to the special issue on ICA and BSS published by Mechanical Systems and Signal Processing in 2005 [23].
2.1 ICA / BSS Algorithms A wide variety of ICA algorithms are available in the literature [6-8]. These algorithms differ from each other on the basis of the choice of objective function and selected optimization scheme. Although the assumption about statistical independence requires the sources to be non-Gaussian in order to utilize the higher-order statistics (HOS) based BSS methods, several second-order statistics (SOS) based techniques are also available. SOS methods exploit weaker conditions for separating the sources assuming that they have a temporal structure with different autocorrelation functions (or power spectra). In this section, four ICA / BSS methodologies are briefly discussed.
2.1.1 Algorithm for Multiple Unknown Signals Extraction (AMUSE) [6, 16 ] SOS based algorithms like AMUSE assume that: 1. The mixing matrix A is of full column rank. 2. Sources are spatially uncorrelated with different autocorrelation functions but are temporally correlated (colored) stochastic signals with zero-mean. 3. Sources are stationary signals and / or second order non-stationary signals i.e. their variances are time varying. The AMUSE algorithm is outlined below [6]: 1. Estimate the covariance (mean removed correlation) matrix of the output observations 1 N (02) Rˆ x (0) = ∑ x(k )xT (k ) N k =1 where Rˆ x (0 ) is the covariance matrix at zero time lag and N is the total number of time samples taken.
2. Compute EVD (or SVD) of Rˆ x (0 )
Rˆ x (0 ) = U x ∑ x V xT = V x Λ xV xT = Vs Λ sVsT + V N Λ N V NT
where Vs is m X n matrix of eigenvectors associated with n principal eigenvalues of Λs = diag{λ1, λ2, ….., λn} in descending order. Vn is m X (m-n) matrix containing the (m-n) noise eigenvectors associated with noise eigenvalues Λn = diag{λn+1, λn+2, ….., λm}. The number of sources n are thus estimated based on the n most significant eigenvalues (or singular values in case of SVD). 3. Perform pre-whitening transformation
x (k ) = Λ s 2VsT x(k ) = Qx(k ) −1
( ) 4. Estimate the covariance matrix of the vector x k for specific time lag other than p=0 (say p=1). Perform SVD on the estimated covariance matrix. 1 Rˆ x ( p ) = N
∑ x (k ) k =1
x T (k − p ) = U x ∑ x V xT (05)
5. The mixing matrix and source signals can be estimated as 1 Aˆ = Q +U x = Vs Λ s2U x
y (k ) = sˆ(k ) = U x (k )
T x
(07) AMUSE performs well for colored sources with different power spectra shapes which means that the eigenvalues of the time-delayed covariance matrix are distinct. The accuracy of AMUSE however deteriorates in presence of additive noise.
2.1.2 Fourth Order Blind Identification Algorithm (FOBI) [6, 7, 19-20] FOBI is an extension of the AMUSE algorithm which uses contracted quadricovariance matrices instead of covariance matrices. This technique is aimed at separating independent non-Gaussian source signals. The quadricovariance matrices are defined as
C x (E ) = C x x T (k )Ex (k )x (k )x T (k )
= E x (k )Ex (k )x (k )x (k ) − R x (0 )ER x (0 ) − tr (ER x (0 ))R x (0 ) − R x (0 )E T R x (0 )
where R x (0 ) = E x (k )x
(k )} and E is an
m X n freely chosen matrix called eigenmatrix (typically E = In or
E = e q e Tq , where eq are vectors of some unitary matrix). The eigenvalue decomposition of the quadricovariance matrix is of the following form
C x (E ) = UΛ EU T
with Λ E = diag (λ1u1 Eu1 ,........., λ n u n Eu n ) , T
λi = κ 4 (si ) = E {si4 }− 3E 2 {si2 }
is the kurtosis of the zero-mean
i source and ui is the i-th column of the orthogonal eigenvector matrix U. The main advantage of the FOBI algorithm is that it is insensitive to arbitrary Gaussian noise and that it allows the mixing system to be identified when sources are i.i.d. and mutually independent. However, it should be noted that quadricovariance matrices require many more time samples for correct estimates in comparison to covariance matrices. FOBI also has a restriction that it only works for sources having different kurtosis; thus it will not give good results in cases where sources have identical distributions.
2.1.3 Second Order Blind Identification (SOBI) [6, 17] SOBI algorithm utilizes the joint diagonalization procedure [6, 18, 24] unlike AMUSE and FOBI which use EVD / SVD techniques. SOBI works well for simple colored sources with distinct power spectra (or distinct autocorrelation functions). Like AMUSE, it operates on time delayed covariance matrices. SOBI utilizes the pre-whitening transformation similar to that described in case of AMUSE. This is followed by estimation of set of covariance matrices for a preselected set of time lags (p1, p2, ….., pL)
1 Rˆ x ( pi ) = N
∑ x (k )x (k − p ) = QRˆ ( p )Q T
k =1
Joint approximate diagonalization (JAD) is performed on the above matrices; R x ( pi ) = UDiU , to estimate the T
orthogonal matrix U that diagonalizes a set of covariance matrices. Several efficient algorithms are available for this purpose including Jacobi techniques, Alternating Least Squares, Parallel Factor Analysis etc. [18, 24]. Finally the sources and signals can be estimated using the same equations as explained earlier with AMUSE. It should be noted that Di(pi) is a diagonal matrix that has distinct diagonal entries. However, it is difficult to determine a priori a single time lag p at which the above criterion is satisfied. Joint diagonalizaton procedure avoids this difficulty by providing an optimum solution considering a number of time lags.
2.1.4 Joint Approximate Diagonalization of Eigenmatrices (JADE) [6, 25] JADE can be considered as an extension of SOBI and FOBI algorithms. Like FOBI, JADE works on the contacted quadricovariance matrices but instead of employing EVD / SVD it jointly diagonalizes a set of such matrices just like SOBI. The aim of JADE is to estimate an orthogonal matrix U which diagonalizes a set of quadricovariance matrices. JADE is a mathematically intensive algorithm and the complete explanation is beyond the scope of this paper. Interested readers can refer the above mentioned references for more details.
3. ICA and BSS in Vibrations Due to the tremendous potential of ICA / BSS techniques, it is not a surprise that research community in the vibration associated field have also started looking at utilizing them for variety of purposes. In [13], second order ICA techniques were utilized for rotating machinery vibration analysis. ICA of vibration signals was also used for fault diagnosis of an induction motor [12]. ICA was used along with Artificial Neural Network (ANN) for data reduction purposes while detecting structural damage [11]. However in spite of their tremendous potential, use of ICA and BSS techniques in vibration and related areas has been slow in comparison to some of the other areas. Antoni [26] has discussed the issues associated with application of ICA / BSS techniques for vibration signals in detail. One of the major issues with the application of ICA / BSS techniques to vibrations, particularly structural identification related applications, is the fact that vibrating systems are dynamic or convolutive in nature as opposed to static (instantaneous linear) mixtures for which the ICA / BSS theory is originally designed. One obvious way to tackle the convolutive mixtures is to deal with them in the frequency domain as convolution in time domain is equivalent to multiplication in frequency domain. However, there are two other problems which are inherent to ICA / BSS techniques; scaling of sources and the order in which they are identified, often referred as 'permutation problem'. This is the same problem encountered in estimating partial coherence and/or conditioned partial coherence over 20 years ago with respect to partially dependent sources in acoustics (general MIMO problem) and in multiple input excitation problems in structural dynamics (MIMO-FRF estimation). In the case of frequency domain ICA / BSS, these two problems become much more severe as they now become a function of each frequency bin. Frequency domain ICA / BSS is a topic of ongoing research and lots of efforts are being made to understand it [27-30]. Most of these algorithms were based on the fact that convolved mixing in time domain corresponds to instantaneous mixing in frequency domain. The work done in this aspect deals with
handling of the scaling and permutation problems. However so far no significant success has been achieved in this aspect and research is still going on.
3.1 ICA / BSS techniques for Operational Modal Analysis Operational Modal Analysis is an emerging technique in the field of modal analysis where dynamic characteristics of a system are identified based only on the output responses. OMA has found applications in the areas of civil structures, automobile, rotating machinery etc. Since, by definition, ICA / BSS techniques works only on system outputs to identify either the sources or the system (mixing matrix) without any a priori (or very little) information about them, it is logical to believe that these techniques can also be used for OMA purposes. Recently, it was shown how ICA / BSS techniques can be utilized for the purpose of modal analysis [14-15, 31]. The basic fundamentals behind application of ICA / BSS techniques to modal analysis goes back to the concept of expansion theorem [32] and modal filters [33-35]. According to the expansion theorem the response of a distributed parameter structure can be expressed as
x (t ) =
∑φ η r =1
(t )
where Φr are the modal vectors weighted by the modal coordinates ηr. For real systems, however, the response of the system can be represented as a finite sum of modal vectors weighted by the modal coordinates. To obtain a particular modal coordinate ηi from response vector x, a modal filter vector ψi is required such that
ψ iT φi = 0,
for i ≠ j
ψ iT φi ≠ 0,
for i = j
and so that N
ψ iT x(t ) = ψ iT ∑ φ rη r (t )
= ψ iT φiη i
r =1
or Thus modal filter performs a coordinate transformation from physical to modal coordinates. Multiplying the system response x with modal filter matrix ΨT results in uncoupling of the system response into single degree of freedom (SDOF) modal coordinate responses (η). In order for ψi to exist, the associated modal vector Φi must be linearly independent with respect to all other modal vectors [33]. This is also the reason why ICA / BSS based techniques can be utilized for the purpose of decomposing the output system response into a product of modal vectors and corresponding modal coordinate responses. Also, a modal filter vector is unique if and only if the number of sensors used for the modal filter implementation is equal to the number of linearly independent modal vectors contributing to the system response. In the past, SDOF modal coordinate responses have been obtained by utilizing modal filters calculated using FRF based data. The ICA / BSS based techniques differ from this approach in the sense that they directly work on output system response to obtain the modal coordinate responses (η). This approach is similar to that in [14, 15] where modal coordinates are treated as virtual sources. In the following section, four different ICA algorithms as described in Section 2.1 are applied to a 15 degrees of freedom system.
4. Analytical 15 Degree of Freedom System Figure 1 shows a 15 degree of freedom system which is excited at all 15 degrees of freedom by means of a white random uncorrelated set of inputs. The chosen system has some closely spaced modes (around 53 Hz), some modes that are lightly damped, other modes that are moderately damped and also some local modes that are well separated from each other. This makes it a good system to investigate the various ICA / BSS algorithms described in Section 2. Figure 2-5 show the plot of the auto-power spectrums of the modal coordinate responses (η) obtained using various algorithms. The Second Order Statistics (SOS) based algorithms, AMUSE and SOBI, uncouple the
system response into SDOF modal coordinate responses. However, both Higher Order Statistics (HOS) based methods, JADE and FOBI, fail to successfully separate the response into corresponding modal coordinate response. Possible reasons for the inferior behavior of the HOS based methods can be that quadricovariance matrices are not correctly estimated and also the fact that SOS based methods better exploit the temporal coherence (uniqueness of autopower spectra) of various modal coordinate responses. Modal parameters obtained using the SDOF response based on AMUSE and SOBI are listed in Table 1 and are compared with true analytical modes of the system and also with the results obtained using OMA-EMIF algorithm [36]. Though the frequency estimates using AMUSE and SOBI is close to the true modes in comparison to the OMA-EMIF algorithm, damping is overestimated for all the modes. However, overall results are satisfactory. Further, Figures 6-9 show, the modal assurance criterion (MAC) plots for comparing the modal vectors obtained using various methods. The modal vectors obtained using AMUSE and SOBI are in good agreement with each other. However the MAC values are not that high when modal vectors obtained using AMUSE are compared with true modes or OMA-EMIF results. The high MAC values for true and OMA-EMIF modal vectors indicate that the OMA-EMIF method is able to extract the modal vectors of the system better in comparison to the ICA techniques. Note that using AMUSE or SOBI, the modes are obtained in a random order. Also, the repeated modes around 53.3 Hz have interchanged when estimated using OMA-EMIF algorithm.
Figure 1: Analytical 15 Degree of Freedom System
Figure 2: Power Spectrum of Modal Coordinate Responses obtained using AMUSE
Figure 3: Power Spectrum of Modal Coordinate Responses obtained using SOBI
Figure 4: Power Spectrum of Modal Coordinate Responses obtained using FOBI
Figure 5: Power Spectrum of Modal Coordinate Responses obtained using JADE
Table 1: Comparison of Modal Parameters True Modes Damp 1.0042 1.9372 2.7347 2.9122 3.3375 3.3454 3.7145 3.858 4.2978 4.5925 2.6093 2.4548 2.3288 2.221 2.122
Freq 15.985 30.858 43.6 46.444 53.317 53.391 59.413 61.624 68.811 73.63 128.84 136.55 143.86 150.83 157.47
3.3289 2.8564 3.2718 3.6481 4.0763 4.7860 3.6833 3.6157 4.1523 4.4249 2.6146 2.6030 2.4513 2.3207 2.0669
15.9857 30.8619 43.6932 46.5883 53.7487 53.7683 59.1164 61.3713 68.2375 73.1519 128.5604 136.4652 143.8957 150.8782 157.7820
ICA - AMUSE Damp 2.1133 2.4042 3.1196 3.4458 3.7103 3.5785 4.1244 4.3618 4.5887 4.8149 2.710 2.5743 2.4323 2.3162 2.2087
Freq 15.9774 30.8709 43.6511 46.4035 53.3869 53.4237 59.4877 61.6476 68.9075 73.7923 128.9026 136.6159 143.9370 150.9051 157.54
ICA - SOBI Damp 2.2314 2.4123 3.1441 3.4787 3.8181 3.6199 4.2735 4.4495 4.7218 4.9619 2.7803 2.6264 2.4734 2.3589 2.2391
Figure 6: MAC Comparison Plot - AMUSE / SOBI
Freq 15.9806 30.8725 43.6543 46.4059 53.4067 53.4271 59.5196 61.6577 68.9299 73.8233 128.9105 136.6253 143.9487 150.9175 157.5533
Figure 7: MAC Comparison Plot - AMUSE / OMA-EMIF
Figure 8: MAC Comparison Plot - AMUSE / True Modes
Figure 9: MAC Comparison Plot - True Modes / OMA-EMIF
6. Conclusions The paper discusses four popular ICA / BSS techniques along with the general concept of independent component analysis (ICA) and blind source separation (BSS). It is shown how these techniques can be utilized for output-only modal parameter estimation purposes by relating them to the concepts of modal filtering and modal expansion theorem. The studies conducted on an analytical system reveal that second order statistics based ICA / BSS algorithms give better results in comparison to the higher order statistics based algorithms. Though ICA / BSS based results are not as good as general OMA algorithms based results, it is still an interesting area to explore considering the simplicity of the method and its ability to extract all modal parameters (modal frequencies and mode shapes) in one step. These algorithms are comparatively less time consuming and does not require use of such tools as consistency diagrams. One of the issues with these algorithms is the fact that one should have at least as many sensors to measure the system output as the number of system modes one is interested in. The future research in this area needs to concentrate on better understanding of the various ICA algorithms for better application to modal analysis. Application to more experimental and real-life structures will also aid in throwing more light on advantages and limitations of these methods. Frequency domain based ICA / BSS is yet another area whose development might result in better implementation of these techniques to OMA.
Acknowledgements The authors would like to extend their thanks to Dr. Pando Georgiev for his guidance and Dr. Cichocki, Dr. Amari and others for the ICALAB package [37] that is used in this study.
References [1]
Ewins, D.J.; "Modal testing: Theory, practice and applications", 2nd edition, Research Studies Press Limited, Hertfordshire, England, 2000.
[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]
Maia, J.M., Silva, J.M.; "Theoretical and experimental modal analysis", Research Studies Press Limited, Hertfordshire, England, 1997. Allemang, R.J.; "Vibrations: Experimental modal analysis", Structural Dynamics Research Laboratory, Department of Mechanical, Industrial and Nuclear Engineering, University of Cincinnati, 1999, http://www.sdrl.uc.edu/sdrl_jscript_homepage.html Heylen, W., Lammens, S., Sas, P.; "Modal analysis testing and theory", PMA-K.U. Leuven, Belgium, 1995. Chauhan, S., Allemang, R.J., Brown, D.L.; "Unified Matrix Polynomial Approach for Operational Modal Analysis", Proceedings of the 25th IMAC, Orlando (FL), USA, 2007. Cichocki, A., Amari, S.; "Adaptive blind signal and image processing", John Wiley and Sons, New York, 2002. Hyvarinen, A., Karhunen, J., Oja, E.; "Independent Component Analysis", John Wiley and Sons, New York, 2001. Hyvarinen, A., Oja, E.; "Independent component analysis: Algorithms and applications", Neural Networks, Vol. 13, p. 411-430, 2000. Cardoso, J.F.; "Blind signal separation: statistical principles", Proceedings of the IEEE, Vol. 86, Number 10, pp. 2009-2025, October, 1998. Lathauwer, L.D., Bart De Moor, Vandewalle, J.; "An introduction to independent component analysis", Journal of Chemometrics, Vol. 14, pp. 123-149, 2000. Zang, C., Friswell, M.I., Imregun, M.; "Structural damage detection using independent component analysis"; Structural Health Monitoring, Vol. 3, Number 1, pp 69-83, 2004. Poyhonen, S., Jover, S., Hyotyniemi, H.; "Independent component Analysis of vibrations for fault diagnosis of an induction motor", Proceedings of the IASTED International conference on Circuits, Signals and Systems, Cancun, Mexico, May, 2003, Vol. 1, pp. 203-208. Ypma, A., Pajunen, P.; "Rotating machine vibration analysis with second-order independent component analysis", Proceedings of the workshop on ICA and Signal Separation, Aussois, France, 1999, pp. 37-42. Kerschen, G., Poncelet, F., Golinval, J.C.; "Physical interpretation of independent component analysis in structural dynamics", Mechanical Systems and Signal Processing (2006), doi: 10.1016/j.ymssp.2006.07.009. Poncelet, F., Kerschen, G., Golinval, J.C.; "Experimental modal analysis using blind source separation techniques"; Proceedings of ISMA International Conference on Noise and Vibration Engineering, Katholieke Universiteit Leuven, Belgium, 2006. Tong, L., Soon, V.C., Huang, Y., Liu, R.; "AMUSE: a new blind identification algorithm", Proceedings of IEEE ISCAS, pp. 1784-1787, Vol. 3, New Orleans, LA, 1990. Belouchrani, A., Abed-Meraim, K.K., Cardoso, J.F., Moulines, E.; "Second order blind separation of correlated sources", Proceedings of International Conference on Digital Signal Processing, pp. 346-351, 1993. Cardoso, J.F., Souloumiac, A.; "Jacobi angles for simultaneous diagonalization", SIAM Journal of Matrix Analysis and Applications, Vol. 17, Number 1, pp. 161-164, January, 1996. Cardoso, J.F.; "Super-symmetric decomposition of the fourth order cumulant tensor. Blind identification of more sources than sensors", Proceedings of IEEE ISCAS, pp. 3109-3112, Vol. 5, Toronto, 1991. Nandi, A.K., Zarzoso, A.; "Fourth-order cumulant based blind source separation", IEEE Signal Processing Letters, Vol. 3 Number 12, pp. 312-314, December, 1996. ICA Central, http://www.tsi.enst.fr/icacentral/ Tony Bell's ICA Webpage, http://www.cnl.salk.edu/~tony/ica.html "Special Issue: Blind source separation", Mechanical Systems and Signal Processing, Vol. 19 (6), pp. 11631380, November, 2005. Hori, G.; "A new approach to joint diagonalization", Proceedings of 2nd International Workshop on ICA and BSS, ICA' 2000, pp. 151-155, Helsinki, Finland, June 2000. Cardoso, J.F., Souloumiac, A.; "Blind beamforming for non Gaussian signals", Proceedings of IEE Radar and Signal Processing, Vol. 140 (6), pp. 362-370, December 1993. Antoni, J.; "Blind separation of vibration components: principles and demonstrations", Mechanical Systems and Signal Processing, Vol. 19 (6), pp. 1166-1180, November 2005. Smaragdis, P.; "Blind separation of convolved mixtures in the frequency domain", Neurocomputing, Vol. 22, pp. 21-34, 1998. Dapena, A., Servière, C.; "A simplified frequency domain approach for blind separation of convolutive mixtures", Proceedings of ICA, San Diego, USA, pp. 569–574, 2001.
[29] Rahbar, K., Reilly, J.; "Blind source separation algorithm for MIMO convolutive mixtures", Proceedings of International Workshop on Independent Component Analysis and Signal Separation, pp. 242-247, Dec 2001.
[30] Joho, M., Rahbar, K.; "Joint diagonalization of correlation matrices by using Newton methods with application to blind signal separation", Proceedings Of IEEE Sensor Array and Multichannel Signal Processing Workshop SAM, 2002.
[31] Randall, R.B., Holley, L.; "Blind source separation and system identification for convolutive mixtures with well separated modes", Proceedings of ISMA International Conference on Noise and Vibration Engineering, Katholieke Universiteit Leuven, Belgium, 2006. [32] Meirovitch, L.; "Analytical methods in vibrations", The Macmillan Company, New York, 1967. [33] Shelly, S.J.; "Investigation of discrete modal filters for structural dynamic applications", PhD Dissertation, Department of Mechanical, Industrial and Nuclear Engineering, University of Cincinnati, 1991. [34] Shelley, S.J., Allemang, R.J., "Calculation of Discrete Modal Filters Using the Modified Reciprocal Modal Vector Method", Proceedings of the 10th IMAC, San Diego, CA, February, 1992. [35] Shelley, S.J., Allemang, R.J., Slater, G.L., Schultze, J.F., "Active Vibration Control Utilizing an Adaptive Modal Filter Based Modal Control Method", Proceedings of the 11th IMAC, Kissimmee, FL, February, 1993. [36] Chauhan, S., Martell, R., Allemang, R.J., Brown, D.L.; "Considerations in the application of spatial domain algorithms in operational modal analysis", Proceedings of ISMA International Conference on Noise and Vibration Engineering, Katholieke Universiteit Leuven, Belgium, 2006. [37] Cichocki, A., Amari, S., Siwek, K., Tanaka, T.; ICALAB Toolboxes, http://www.bsp.brain.riken.jp/ICALAB.
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The Last Continent Page 22
Rincewind had learned that hauling on the reins only had the effect of making his arms ache. The only way to stop the little horse when he didn't want to be stopped was probably to get off, run ahead, and dig a trench in front of him. Once again the riders came up behind Rincewind and thudded past, foam streaming from the horses' mouths. 'Excuse me. Am I on the right road for—?' And they were gone. He caught up with them ten minutes later in a thicket of mountain ash, milling around uncertainly while their leader shouted at them. 'I say, can anyone tell me—' he ventured. Then he saw why they had stopped. They'd run out of forwards. The ground fell away into a canyon, a few patches of grass and a handful of bushes clinging to the very nearly sheer drop. Snowy's nostrils flared and, without even pausing, he continued down the slope. He should have skidded, Rincewind saw. In fact he should have dropped. The slope was almost vertical. Even mountain goats would only try it roped together. Stones bounced around him and a few of the larger ones managed to hit him on the back of the neck, but Snowy trotted downwards at the same deceptive speed that he used on the flat. Rincewind settled for hanging on and screaming. Halfway down, he saw the wild herd gallop along the canyon, skid around a rock and disappear between the cliffs. Snowy reached the bottom in a shower of pebbles and paused for a moment. Rincewind risked opening an eye. The little horse's nostrils flared again as it looked down the narrow canyon. It stamped a hoof uncertainly. Then it looked at the vertiginous far wall, only a few metres away. 'Oh, no,' moaned Rincewind. 'Please, no . . .' He tried to untangle his legs but they had met right under the horse's stomach and twisted their ankles together. He must be able to do something to gravity, he told himself, as Snowy trotted up the cliff as though it wasn't a wall but merely a sort of vertical floor. The corks on his hat brim banged against his nose. And ahead . . . above . . . was an overhang . . . 'No, please, no, please don't . . .' He shut his eyes. He felt Snowy draw to a halt. and breathed a sigh of relief. He risked a look down, and the huge hooves were indeed standing on solid, flat rock.
There were no corks hanging in front of Rincewind's hat. In dread and slowly mounting terror, he turned his eyes to what they'd always thought of as upwards. There was solid rock above him, as well. Only it was a long way up, or down. And the corks were all hanging upwards, or downwards. Snowy was standing on the underside of the overhang, apparently enjoying the view. He flared his nostrils again, and shook his mane. He'll fall off, Rincewind thought. Any minute now he'll realize he's upside down and he'll fall off and from this height a horse'll splat. On top of me. Snowy appeared to reach a decision, and set off again, around the curve of the overhang. The corks swung back and hit Rincewind in the face but, hey, all the trees had the green bits pointing up, except that they were the grey bits. Rincewind looked across the chasm at the horsemen. 'G'day!' he said, waving his hat in the air as Snowy set off again. 'I think I'm about to have a technicolour snake!' he added, and threw up. '
'ere, mistah?' someone shouted back. 'Yes?'
'That was a chunder!'
'Right! No worries!' It turned out that this piece of land was only a narrow spur between canyons. Another sheer drop loomed up, or down. But to Rincewind's relief the horse turned aside at the brink and trotted along the edge. 'Oh, no, please . . .' A tree had fallen down and bridged the gulf. It was very narrow, but Snowy wheeled on to it without slowing. Both ends of the tree drummed up and down on the lip of the cliff. Pebbles began to fall away. Snowy bounced across the gap like a small ball and stepped off on the far side just before the treetrunk teetered and dropped on to the rocks. 'Please, no . . .' There wasn't a cliff here, just a long slope of loose rocks. Snowy landed among them, and flared his nostrils as the entire slope of scree began to move.
Rincewind saw the herd gallop past in the narrow canyon bottom, far below. Large rocks bounded alongside him as the horse continued down in his own personal landslide. One or two jumped and bounced ahead, smashing on to the canyon floor just behind the last of the herd. Numb with fear and the shaking, Rincewind looked further along the canyon. It was blind. The end was another cliff . . . Stone piled into stone, building a rough wall across the canyon floor. As the last boulder slammed into place Snowy landed on top of it, almost daintily. He looked down at the penned herd, milling in confusion, and flared his nostrils. Rincewind was pretty sure horses couldn't snigger, but this one radiated an air of sniggerruity. It was ten minutes later that the horsemen rode up. By then the herd was almost docile. They looked at the horses. They looked at Rincewind, who grinned horribly and said, 'No worries.' Very slowly, he didn't fall off Snowy. He simply swivelled sideways, with his feet still twisted together, until his head banged gently on the ground. That was bloody great riding, mate!'
'Could someone separate my ankles, please? I fear they may have fused together.' A couple of the riders dismounted and, after some effort, pulled him free. The leader looked down at him. 'Name your price for that little battler, mate!' said Remorse. 'Er . . . three . . . er . . . squids?' said Rincewind, muzzily. 'What? For a wiry little devil like that? He's got to be worth a coupla hundred at least!'
'Three squids is all I've got . . .'
'I reckon a few of them rocks hit him on the head,' said one of the stockmen who were holding Rincewind up. 'I mean I'll buy him off'f you, mister,' said Remorse, patiently. 'Tell you what – two hundred squids, a bag of tucker and we'll set you right on the road to . . . Where was it he wanted to go, Clancy?'
'Bugarup,' murmured Rincewind. 'Oh, you don't wanna go to Bugarup,' said Remorse. 'Nothing in Bugarup but a bunch of wowsers and pooftahs.'
's okay, I like parrots,' mumbled Rincewind, who was just hoping that they would let him go so that he could hold on to the ground again. 'Er . . . what's Ecksian for going mad with terrified fatigue and collapsing in a boneless heap?' The men looked at one another. 'Isn't that "snagged as a wombat's tonker"?'
'No, no, no, that's when you chuck a twister, isn't it?' said Clancy. 'What? Strewth, no. Chucking a twister's when . . . when you . . . yeah, it's when you . . . yeah, it's when your nose . . . Hang on, that's "bend a smartie" . . .'
'Er—' said Rincewind, clutching his head. 'What? "Bend a smartie" is when your ears get blocked underwater.' Clancy looked uncertain, and then seemed to reach a decision. 'Yeah, that's right!'
'Nah, that's "gonging like a possum's armpit", mate.'
'Excuse me—' said Rincewind. 'That ain't right. "Gonging like a possum's armpit" is when you crack a crusty. When your ears are stuffed like a Mudjee's kettle after a week of Fridays, that's "stuck up like Morgan's mule".'
'No, you're referrin' to "happier than Morgan's mule in a choccy patch"—'
'You mean "as fast as Morgan's mule after it ate Ma's crow pie".'
'How fast was that? Exactly?' said Rincewind. They all stared at him. Taster'n an eel in a snakepit, mate!' said Clancy. 'Don't you understand plain language?'
'Yeah,' said one of the men, 'he might be a fancy rider but I reckon he's dumber than a—'
'Don't anyone say anything!' shouted Rincewind. 'I'm feeling a lot better, all right? Just . . . all right, all right?' He straightened his ragged robe and adjusted his hat. 'Now, if you could just set me on the right road to Bugarup, I will not trespass further on your time. You may keep Snowy. He can bed down on a ceiling somewhere.'
'Oh, no, mister,' said Remorse. He reached into a shirt pocket, pulled out a bundle of notes and licked his thumb to count off twenty. 'I always pays me debts. You want to stay with us a while first? We could use another rider and it's tough going on the road by yourself. There's bush rangers about.' Rincewind rubbed his head again. Now that his various bodily organs had wobbled their way back into their approximate positions he could get back to general low-key generalized dread.
They won't have to worry about me,' he mumbled. 'I promise not to light fires or feed the animals. Well, I say promise - most of the time they're trying to feed off me.' Remorse shrugged. 'Just so long as there's no more of those damn dropping bears,' said Rincewind. The men laughed. 'Drop-bears? Who's been feedin' you a line about drop-bears?'
'What do you mean?'
'There's no such thing as drop-bears! Someone must've seen you coming, mate!'
'Huh? They've got . . . they went,' Rincewind waved his arm, 'boing . . . all over the place . . . great big teeth . . .'
'I reckon he madder'n Morgan's mule, mate!' said Clancy. The group went silent. 'How mad is that, then?' said Rincewind. Clancy leaned on his saddle and looked nervously at the other men. He licked his lips. 'Well, it's . . .'
'Well, it's . . . it's . . .' His face twisted up. 'It's . . .'
'Ver'. . .?' Rincewind hinted. 'Ver' . . .' Clancy mumbled, clutching the syllable like a lifeline. 'Hmm?'
'Ver . . . ry . . .'
--- Read books free online at novel68.com ---
'Keep going, keep going . . .'
'Ver . . . ry . . . mad?' said Clancy. 'Well done! See? So much easier,' said Rincewind. 'Someone mentioned something about food?' Remorse nodded to one of the men, who handed Rincewind a sack. 'There's beer and veggies and stuff and, 'cos you're a good sport, we're giving you a tin of jam, too.'
'And I'm wondering about your hat,' said Remorse. 'Why's there all corks round it?'
'Knocks the flies out,' said Rincewind. 'That works, does it?'
'Course not,' said Clancy. 'If'n it does, some-one'd have thought of it by now.'
'Yes. Me,' said Rincewind. 'No worries.'
'Makes you look a bit of a drongo, mate,' said Clancy. 'Oh, good,' said Rincewind. 'Which way's Bugarup?'
'Just turn left at the bottom of the canyon, mate.'
'That's all?'
'You can ask again when you meet the bush rangers.'
'They've got some sort of cabin or station, have they?'
'They've . . . Well, just remember they'll find you if you get lost.'
'Really? Oh, well, I suppose that's part of their job. Good day to you.'
'No worries.' The men watched Rincewind until he was out of sight. 'Didn't seem very bothered, did he?'
'He's a bit gujeroo, if you ask me.'
'Yes, boss?'
'You made that one up, didn't you . . .?'
'Well . . .'
'You bloody did, Clancy.'
Clancy looked embarrassed, but then rallied. 'All right, then,' he said hotly. 'What about that one you used yesterday, "as busy as a one- armed carpenter in Smackaroo"?'
'What about it?'
'I looked it up in the atlas and there's no such place, boss.'
'There damn well is!' There isn't. Anyway, no one'd employ a one-armed carpenter, would they? So he wouldn't be busy, would he?'
'Listen, Clancy—'
'He'd go fishing or something, wouldn't he?'
'Clancy, we're supposed to be carving a new language out of the wilderness here—'
'Probably'd need someone to help him bait the line, but—'
'Clancy, will you shut up and go and get the horses?' It took twenty minutes to roll enough of the rocks away, and five minutes after that Clancy reported back. 'Can't find the little bastard, boss. And we looked underneath all the others.'
'It couldn't have got past us!'
'Yes it could, boss. You saw it goin' up those cliffs. Probably miles away by now. You want I should go after that bloke?' Remorse thought about it, and spat. 'No, we got the colt back. That's worth the money.' He stared reflectively down the canyon. 'You all right, boss?'


text:
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State Rep. Chris Rabb announced that he will host a Holiday Open House on Wednesday, Dec. 19 from noon to 3 p.m. at his district office located at 7216 Germantown Ave.
"I'm always excited for the chance to hear from my constituents and to celebrate the holidays together," Rabb said. "But it's also important to keep in touch and to make sure that fellow community members know how to apply for and access programs like LIHEAP that can be crucial for keeping the heat on during these cold winter months."
District office staff will be available to assist constituents with applications and information on LIHEAP, SEPTA Key and Property Tax Rent Rebate assistance programs, or other state-related issues.
Refreshments such as hot chocolate, coffee, tea and dessert will be available.
Contact the district office at (215) 242-7300 for more information.


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County View
John Healy
In a few months' time, celebrations will mark the 100th anniversary of the arrival of the Benedictine order of nuns to Kylemore. The order were there to found their famous girls' international boarding school. Their arrival to the peace and tranquillity of Connemara marked the end of an arduous journey that had seen them flee their home in Ypres, Belgium, after several hundred years.
As German bombs rained down on their convent, the sisters fled on foot, guarded by the 8th Battalion of the Royal Munster Fusiliers, and given Red Cross freedom of passage via England to arrive in the west of Ireland.
Two years later, they had purchased the imposing mansion of Kylemore Castle from the Duke and Duchess of Manchester, after crippling gambling debts had driven the titled couple to bankruptcy.
Kylemore had been originally built in 1868 as the private home of Mitchell Henry and his wife. Henry had qualified as a doctor, but on the death of his wealthy cotton-merchant father, had returned to Manchester to take over the family business. On a holiday in Connemara, he fell in love with the region and determined to build his home in Kylemore. He acquired an estate of 13,000 acres and construction began on the castle. It took four years to complete, employed over a hundred men, and brought prosperity and employment to the region. The elegant structure included 70 rooms in all, and a replica Gothic cathedral and a mausoleum were added.
Mitchell Henry became an MP for Galway, an ardent advocate of Irish nationalism, and he and his wife – Margaret Vaughan from Co Down – raised a family of nine children. But Henry was left bereft following the death of Margaret at age 45, from a fever contracted in Egypt, and he returned to England. She was laid to rest in the mausoleum, where he himself was buried on his death in 1910.
The new owner, the profligate Lord Manchester, lived in Kylemore for a number of years, but then came his financial collapse. With its takeover in 1920 by the Benedictines, Kylemore Abbey was famed as a secondary boarding school for the next century, attracting the privileged and wealthy from all over the world to avail of its much-lauded and comprehensive curriculum.
The Benedictines won huge moral and financial support from Church and State to fund its work at Kylemore. Among its strongest benefactors was Count John McCormack and, a measure of the school's prestige, a banquet in his honour was held in the Shelbourne Hotel in 1923 at which the Governor General of the new Irish Free State was the main speaker.
However, in a Europe in turmoil, there were times when the future of Kylemore Abbey school must have been in doubt. A tentative plan to sell the property in 1930 came to the ears of the National Bank, which had advanced the original loan of £40,000 to buy the property. Taking fright at the idea that it might be sold without its knowledge, the bank went to the High Court to secure an injunction restraining any sale without providing for the indemnity of the original guarantors.
But the crisis was overcome, and Kylemore Abbey went from strength to strength. Today, the abbey and restored walled gardens attract 250,000 visitors a year, making it the most-visited tourist attraction in the west. And although no longer a secondary school, the educational links continue with the University of Notre Dame, thanks in no small part to the influence of the philanthropist, Martin Naughton, who sits on the trustee boards of both the Irish and American institutions.
Kylemore jewel celebrates century
County View


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