From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Jan 2 10:37:16 2002 Received: (from root@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.2) id g02GbF322283 for reliable_computing-outgoing; Wed, 2 Jan 2002 10:37:15 -0600 (CST) Received: from patan.sun.com (patan.Sun.COM [192.18.98.43]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.2) with ESMTP id g02Gb3V22278 for ; Wed, 2 Jan 2002 10:37:09 -0600 (CST) Received: from engmail4.Eng.Sun.COM ([129.144.134.6]) by patan.sun.com (8.9.3+Sun/8.9.3) with ESMTP id JAA18727; Wed, 2 Jan 2002 09:36:26 -0700 (MST) Received: from phys-mpkmaila (phys-mpkmaila.Eng.Sun.COM [129.146.18.131]) by engmail4.Eng.Sun.COM (8.9.3+Sun/8.9.3/ENSMAIL,v2.1p1) with ESMTP id IAA15975; Wed, 2 Jan 2002 08:36:43 -0800 (PST) Received: from gww (gww.Eng.Sun.COM [129.146.78.116]) by mpkmail.eng.sun.com (iPlanet Messaging Server 5.2 (built Nov 13 2001)) with SMTP id <0GPB00CYVKTZZ3 [at] mpkmail [dot] eng.sun.com>; Wed, 02 Jan 2002 08:37:11 -0800 (PST) Date: Wed, 02 Jan 2002 08:36:43 -0800 (PST) From: William Walster Subject: Re: Two additional early Moore papers: full text now available To: reliable_computing [at] interval [dot] louisiana.edu, rbk [at] louisiana [dot] edu Reply-to: William Walster Message-id: <0GPB00CYWKTZZ3 [at] mpkmail [dot] eng.sun.com> MIME-version: 1.0 X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4.2 SunOS 5.8 sun4u sparc Content-type: TEXT/plain; charset=us-ascii Content-transfer-encoding: 7BIT Content-MD5: hdeGBK3Sc8IFjgWBS4CHrw== Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Baker, Is the web site OK? I cannot view any of the papers, either from my Sun workstation or my PC laptop. Bill >Date: Fri, 28 Dec 2001 15:24:54 -0600 >From: "R. Baker Kearfott" >Subject: Two additional early Moore papers: full text now available >X-Sender: rbk5287 [at] pop [dot] louisiana.edu >To: reliable_computing [at] interval [dot] louisiana.edu >MIME-version: 1.0 > >Colleagues, > >Sun Microsystems has bought the copyrights to two additional early >papers by Moore, and I have made them available from the URL: > >http://interval.louisiana.edu/Moores_early_papers/bibliography.html > >The citations to these papers in that short bibliography are as >follows: > >[6] R. E. Moore. The automatic analysis and control of error in digital > computing based on the use of interval numbers. In L. B. Rall, editor, > Error in Digital Computation, Vol. I, chapter 2, pages 61-130. John > Wiley and Sons, Inc., New York, 1965. John Wiley and Sons, Inc. has > given permission for this paper to be posted indefinitely on the > non-password protected website > http://interval.louisiana.edu/Moores_early_papers/Moore_in_Rall_V1.pdf > for use by the interval research community. > >[7] R. E. Moore. Automatic local coordinate transformations to reduce the > growth of error bounds in interval computation of solutions of ordinary > differential equations. volume II of Error in Digital Computation, pages > 103-140. John Wiley and Sons, Inc., New York, New York, 1965. John > Wiley and Sons, Inc. has given permission for this paper to be posted > indefinitely on the non-password protected website > http://interval.louisiana.edu/Moores_early_papers/Moore_in_Rall_V2.pdf > for use by the interval research community. > >Best regards, > >Baker > >--------------------------------------------------------------- >R. Baker Kearfott, rbk [at] louisiana [dot] edu (337) 482-5346 (fax) >(337) 482-5270 (work) (337) 981-9744 (home) >URL: http://interval.louisiana.edu/kearfott.html >Department of Mathematics, University of Louisiana at Lafayette >Box 4-1010, Lafayette, LA 70504-1010, USA >--------------------------------------------------------------- > > From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Jan 2 12:09:05 2002 Received: (from root@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.2) id g02I95122579 for reliable_computing-outgoing; Wed, 2 Jan 2002 12:09:05 -0600 (CST) Received: from imf05bis.bellsouth.net (mail305.mail.bellsouth.net [205.152.58.165]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.2) with ESMTP id g02I8tV22574 for ; Wed, 2 Jan 2002 12:09:00 -0600 (CST) Received: from u8174 ([65.81.242.148]) by imf05bis.bellsouth.net (InterMail vM.5.01.04.00 201-253-122-122-20010827) with SMTP id <20020102180934.OVGG17507.imf05bis.bellsouth.net@u8174> for ; Wed, 2 Jan 2002 13:09:34 -0500 Message-Id: <2.2.32.20020102180737.0075c96c [at] pop [dot] louisiana.edu> X-Sender: rbk5287 [at] pop [dot] louisiana.edu X-Mailer: Windows Eudora Pro Version 2.2 (32) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Wed, 02 Jan 2002 12:07:37 -0600 To: reliable_computing [at] interval [dot] louisiana.edu From: "R. Baker Kearfott" Subject: Moore's dissertation now available Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Colleagues, I have added a link to Ramon Moore's dissertation on the bibliography page available at http://interval.louisiana.edu/Moores_early_papers/bibliography.html (The actual link is http://interval.louisiana.edu/Moores_early_papers/disert.pdf Except for Moore's 1966 book and Moore's 1999 historical writeup in "Reliable Computing," all of the references in this bibliography of early papers now have links to full-text. Enjoy. Best regards, Baker --------------------------------------------------------------- R. Baker Kearfott, rbk [at] louisiana [dot] edu (337) 482-5346 (fax) (337) 482-5270 (work) (337) 981-9744 (home) URL: http://interval.louisiana.edu/kearfott.html Department of Mathematics, University of Louisiana at Lafayette Box 4-1010, Lafayette, LA 70504-1010, USA --------------------------------------------------------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Jan 2 17:19:10 2002 Received: (from root@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.2) id g02NJAm23238 for reliable_computing-outgoing; Wed, 2 Jan 2002 17:19:10 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.2) with ESMTP id g02NJ0V23232 for ; Wed, 2 Jan 2002 17:19:06 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.3/8.11.3) with SMTP id g02NIe925317 for ; Wed, 2 Jan 2002 16:18:40 -0700 (MST) Message-Id: <200201022318.g02NIe925317 [at] cs [dot] utep.edu> Date: Wed, 2 Jan 2002 16:18:40 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: interval webpage To: reliable_computing [at] interval [dot] louisiana.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: 1u+ZwFyFOWe0e7F1CJmXLA== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Friends, Our system adminsitrator has just moved the web files to a new server. The connection will now be faster (hopefully), but there may be glitches (e.g., I may have erroneously updated some files in the old server; as a result, what you see is not updated). Please let me know if there are any problems. Thanks Vladik From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Jan 2 21:48:07 2002 Received: (from root@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.2) id g033m6m23806 for reliable_computing-outgoing; Wed, 2 Jan 2002 21:48:06 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.2) with ESMTP id g033lvV23801 for ; Wed, 2 Jan 2002 21:48:02 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.3/8.11.3) with SMTP id g033ljv26030; Wed, 2 Jan 2002 20:47:46 -0700 (MST) Message-Id: <200201030347.g033ljv26030 [at] cs [dot] utep.edu> Date: Wed, 2 Jan 2002 20:47:44 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: fuzzy PDE workshop To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: OmJNrk+2WlKXcRehLHqhZA== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Since a fuzzy set can be viewed as a nested interval, interval methods will probably be of great use for fuzzy PDE applications. With this is mind, some of us may be interested in the following workshop: Date: Wed, 02 Jan 2002 16:39:21 -0600 From: Masoud Nikravesh X-Accept-Language: en MIME-Version: 1.0 To: BISC CC: Masoud NikRavesh , "Lotfi A. Zadeh" Subject: BISC: BISC PROGRAM-FPDES WORKSHOP/ MARCH 2002 Content-Transfer-Encoding: 7bit ********************************************************************* Berkeley Initiative in Soft Computing (BISC) ********************************************************************* F I R S T C A L L F O R W O R K S H O P M A R C H 2002 BISC Program University of California Berkeley Fuzzy Partial Differential Equation Solver (FPDES) WORKSHOP Alternative Areas: Fuzzy Difference Equations and Fuzzy-Relational Equations ================================================================ IMPORTANT DATES Jan 25, 2002: Receipt of extended abstracts (<1000 words) Feb 1, 2002: Notification of acceptance Feb 5, 2002: Receipt of Authors' Confirmation, including Arrival and Departure dates. Feb 15, 2002: Receipt of camera ready PAPER Feb 25, 2002: Receipt of PAPER presentation March 2002: WORKSHOP-BISC Program (All Speaker's and BISC invited researcher's travel expenses including Hotel and Airfare will be paid by BISC Program) Contact and Question: PAPER STRUCTURE =============== 1. Title 2. Abstract 3. Introduction 4. General background 5. Methodology 6. Summary and Conclusions 7. Key references 8. Appendix To receive more information or if you have any question, please contact Dr. Masoud Nikravesh (nikravesh [at] cs [dot] berkeley.edu) and cc to Prof. Lotfi Zadeh (zadeh [at] cs [dot] berkeley.edu). -- Dr. Masoud Nikravesh BISC Associate Director and Program Administrator BTExact Technologies (British Telecom-BT) Senior Research Fellow Chairs: BISC-SIG-FLINT,ES, RT Berkeley Initiative in Soft Computing (BISC) Computer Science Division- Department of EECS University of California, Berkeley, CA 94720 Phone: (510) 643-4522; Fax: (510) 642-5775 Email: Nikravesh [at] cs [dot] berkeley.edu URL: http://www-bisc.cs.berkeley.edu/ Staff Scientist Lawrence Berkeley National Lab, Imaging and Collaborative Computing Group Email: Masoud [at] media [dot] lbl URL: http://vision.lbl.gov/ -------------------------------------------------------------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Jan 3 04:11:35 2002 Received: (from root@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.2) id g03ABY024574 for reliable_computing-outgoing; Thu, 3 Jan 2002 04:11:34 -0600 (CST) Received: from web10301.mail.yahoo.com (web10301.mail.yahoo.com [216.136.130.79]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.2) with SMTP id g03ABJV24569 for ; Thu, 3 Jan 2002 04:11:30 -0600 (CST) Message-ID: <20020103100420.95908.qmail [at] web10301 [dot] mail.yahoo.com> Received: from [202.54.67.204] by web10301.mail.yahoo.com via HTTP; Thu, 03 Jan 2002 02:04:20 PST Date: Thu, 3 Jan 2002 02:04:20 -0800 (PST) From: "Rama Rao M.V." Subject: can u help me To: reliable_computing [at] interval [dot] louisiana.edu MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Date 03 Jan,2002 Hyderabad, India Sir I am M.V.Rama Rao from Hyderabad in South India. I teach Structural Engineering to Under-graduate students at a local engineering college. I am currently pursuing my Ph.D. work entitled " Dyanmic Analysis of Cable-Stayed Bridge by Fuzzy-Finite Element Modelling" since June,2000 at Osmania University,Hyderabad,India. I hold a master's degree in Structural Engineering from Indian Institute of Technology,Kanpur which is one of the premier institutions of engineering education in India. My work involves 1. introducing uncertainity in finite element analysis of cable-stayed bridges by replacing the floating point variables with fuzzy interval numbers. 2.Computing the static and dynamic response of such structures to uncertain interval loading I developed a fuzzy-finite element static analysis of structures and was able to obtain satisfactory results Now I have to solve dynamic analysis problem by suitably adapting the eigen-value problem to include fuzzy interval numbers. So i took the jacobi method and converted to fuzzy interval method. I am able to obtain fuzzy eigen values and modeshape vectors. But I have a lingering doubt as to whether whatever I am doing makes sense or not. Anyhow, intutively I feel that a vibrating body will have fuzzy natural frequeny and modeshapes. as per results, i am getting a wide variation in the eigen values even for a small variation in the stiffness matrix Sitting here in India, I do not have access to literature and am proceeding by instinct. Can you kindly help me in this regard.Can you kindly send me any software or literature i can use for the purpose of comparision? I will be very greatful to you Kidly reply to me Yours truly, M.V.Rama Rao __________________________________________________ Do You Yahoo!? Send your FREE holiday greetings online! http://greetings.yahoo.com From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Jan 3 06:01:57 2002 Received: (from root@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.2) id g03C1vv25195 for reliable_computing-outgoing; Thu, 3 Jan 2002 06:01:57 -0600 (CST) Received: from mail8.wi.rr.com ([24.94.162.176]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.2) with ESMTP id g03C1jV25190 for ; Thu, 3 Jan 2002 06:01:51 -0600 (CST) Received: from Marquette.edu ([65.29.171.35]) by mail8.wi.rr.com with Microsoft SMTPSVC(5.5.1877.537.53); Thu, 3 Jan 2002 06:01:48 -0600 Message-ID: <3C34481D.9050800 [at] Marquette [dot] edu> Date: Thu, 03 Jan 2002 06:01:33 -0600 From: "Dr. George Corliss" Reply-To: George.Corliss [at] Marquette [dot] edu Organization: Marquette University, EECE User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:0.9.4) Gecko/20011128 Netscape6/6.2.1 X-Accept-Language: en-us MIME-Version: 1.0 To: "Rama Rao M.V." CC: reliable_computing [at] interval [dot] louisiana.edu Subject: Re: can u help me References: <20020103100420.95908.qmail [at] web10301 [dot] mail.yahoo.com> Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk M.V.Rama Rao, I cannot be specifically helpful in the way you request, but let me offer a suggestion: Try going back to first principles. The PDE approximates the physics, Finite elements approximate the PDE, We usually solve the FE equations approximately. The result we conventionally compute is an approximation to an approximation to an approximation. If we introduce intervals or fuzzy sets at the last step, we have an enclosure of an approximation to an approximation. The PDEs were probably derived by constructing a model and then taking a limit as delta something approaches zero. Try going back to the physical model from which the PDEs were derived and see if you can solve that. You are then two or three steps closer to the physics. One advantage is that you may be able to formulate the original problem as a fixed point operator, as an integral operator, as a linear or nonlinear system, or as an optimization problem, all of which are FAR more suitable for fuzzy or interval techniques than derivative operators. One disadvantage: few people have done this, so you will probably have a difficult time convincing your advisor, your thesis committee, and journal editors that you can solve structural problems without finite elements or even PDEs. This is a MAJOR paradymn shift, so if you attempt it, be prepared to do battle with the establishment. Contributors to this group can offer some encouragement in your battle. Bill Walster reads this group regularly. Bill, please send a copy of your paper from the SCAN 2000 proceedings I just received yesterday. That paper does not tell you how to do what I describe, but it gives strong encouragement to look for ways to make it work. Another suggestion: Look at the sensitivity in your model. Even for the floating point model, consider using automatic differentiation to compute partial output variables of interest ------------------------------------ partial input variables If you have Fortran, C, or C++ code, it is probably not terribly hard to derive code that computes these sensitivities. There are good software tools freely available. See a recent book by Andreas Griewank published by SIAM. It sounds as though the sensitivities of the eigenvalues with respect to the stiffness matrix is probably high. If so, the results you observe are the fault of the design, not the fault of your computations. That suggests you either take engineering steps to mitigate the effects of unstability in the design or else revise the design to be less sensitive (more stable) with respect to stiffness. In that case, your computations have been EXTREMELY valuable, because they have uncovered a potentially dangerous design, since I would expect the natural stiffness of materials to change slightly over time as the bridge ages. You have demonstrated the need for a redesign. Good luck. Keep us posted on your work. Dr. George F. Corliss Electrical and Computer Engineering Haggerty Engineering 296 Marquette University P.O. Box 1881 Milwaukee, WI 53201-1881 USA George.Corliss [at] Marquette [dot] edu Office: 414-288-6599; Dept: 288-6820; Fax: 288-5579 Rama Rao M.V. wrote: > I am M.V.Rama Rao from Hyderabad in South India. > I teach Structural Engineering to Under-graduate > students at a local engineering college. > I am currently pursuing my Ph.D. work entitled " > Dyanmic Analysis of Cable-Stayed Bridge by > Fuzzy-Finite Element Modelling" since June,2000 at > Osmania University,Hyderabad,India. > I hold a master's degree in Structural Engineering > from Indian Institute of Technology,Kanpur which is > one of the premier institutions of engineering > education in India. > My work involves > 1. introducing uncertainity in finite element analysis > of cable-stayed bridges by replacing the floating > point variables with fuzzy interval numbers. > 2.Computing the static and dynamic response of such > structures to uncertain interval loading > I developed a fuzzy-finite element static analysis of > structures and was able to obtain satisfactory results > Now I have to solve dynamic analysis problem by > suitably adapting the eigen-value problem to include > fuzzy interval numbers. > So i took the jacobi method and converted to fuzzy > interval method. I am able to obtain fuzzy eigen > values and modeshape vectors. > But I have a lingering doubt as to whether whatever I > am doing makes sense or not. Anyhow, intutively I feel > that a vibrating body will have fuzzy natural frequeny > and modeshapes. > as per results, i am getting a wide variation in the > eigen values even for a small variation in the > stiffness matrix > > Sitting here in India, I do not have access to > literature and am proceeding by instinct. > Can you kindly help me in this regard.Can you kindly > send me any software or literature i can use for the > purpose of comparision? From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Jan 3 06:28:23 2002 Received: (from root@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.2) id g03CSNT25355 for reliable_computing-outgoing; Thu, 3 Jan 2002 06:28:23 -0600 (CST) Received: from zeus.polsl.gliwice.pl (root [at] zeus [dot] polsl.gliwice.pl [157.158.1.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.2) with ESMTP id g03CS4V25348 for ; Thu, 3 Jan 2002 06:28:11 -0600 (CST) Received: from andrzej1 (a18.asystent.polsl.gliwice.pl [157.158.187.18]) by zeus.polsl.gliwice.pl (8.9.3 (PHNE_22672)/8.9.3) with SMTP id NAA13073; Thu, 3 Jan 2002 13:26:51 +0100 (MET) Message-ID: <001f01c19451$ded1ae70$0200a8c0@andrzej1> From: "Andrzej Pownuk" To: "Rama Rao M.V." , Cc: "Andrzej Pownuk" References: <20020103100420.95908.qmail [at] web10301 [dot] mail.yahoo.com> Subject: Re: can u help me Date: Thu, 3 Jan 2002 13:26:19 +0100 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2600.0000 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk > Date 03 Jan,2002 > Hyderabad, > India > > Sir > > I am M.V.Rama Rao from Hyderabad in South India. > I teach Structural Engineering to Under-graduate > students at a local engineering college. > I am currently pursuing my Ph.D. work entitled " > Dyanmic Analysis of Cable-Stayed Bridge by > Fuzzy-Finite Element Modelling" since June,2000 at > Osmania University,Hyderabad,India. > I hold a master's degree in Structural Engineering > from Indian Institute of Technology,Kanpur which is > one of the premier institutions of engineering > education in India. > My work involves > 1. introducing uncertainity in finite element analysis > of cable-stayed bridges by replacing the floating > point variables with fuzzy interval numbers. > 2.Computing the static and dynamic response of such > structures to uncertain interval loading > I developed a fuzzy-finite element static analysis of > structures and was able to obtain satisfactory results > Now I have to solve dynamic analysis problem by > suitably adapting the eigen-value problem to include > fuzzy interval numbers. > So i took the jacobi method and converted to fuzzy > interval method. I am able to obtain fuzzy eigen > values and modeshape vectors. > But I have a lingering doubt as to whether whatever I > am doing makes sense or not. Anyhow, intutively I feel > that a vibrating body will have fuzzy natural frequeny > and modeshapes. > as per results, i am getting a wide variation in the > eigen values even for a small variation in the > stiffness matrix > > Sitting here in India, I do not have access to > literature and am proceeding by instinct. > Can you kindly help me in this regard.Can you kindly > send me any software or literature i can use for the > purpose of comparision? > I will be very greatful to you > > Kidly reply to me > > Yours truly, > M.V.Rama Rao > > I am not sure, but you probably use the following algorithm: 1) Data: K(h) - stiffness matrix M(h) - mass matrix h - vector of uncertain parameters which belong to the interval vector [h]. Eigen-value problem det(K(h)-w^2*M(h))=0, h belong to [h]. 2) Formulate an interval eigen-value problem det(IK([h])-w^2*IM([h]))=0 where IK([h]) is an interval extension of the stiffness matrix, IM([h]) is an interval extension of the mass matrix. 3) Solve the following interval eigen-value problem Iw([h])={w: det(K-w^2*M)=0, K belong to IK([h]), M belong to IM(h)} Unfortunately the exact solution is the following: w([h])={w: det(K(h)-w^2*M(h))=0, h belong to [h]} and Iw([h]) <> w([h]) It can be shown that inf(Iw([h])) <= inf(w([h])) <= sup(w([h])) <= sup(Iw([h])) I know a person who has similar problems. He solved many examples and he got strange results using presented algorithm. If the interval vector [h] is sufficiently narrow, then the exact solution of your problem can be found using only endpoints of [h], but this method is not perfect. The exact solution has clear physical interpretation. Andrzej Pownuk ------------------------------------------------ Andrzej Pownuk Ph.D., research associate (adjunct) at: Chair of Theoretical Mechanics Faculty of Civil Engineering Silesian University of Technology E-mail: pownuk [at] zeus [dot] polsl.gliwice.pl URL: http://zeus.polsl.gliwice.pl/~pownuk/ ------------------------------------------------ From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Jan 3 09:42:51 2002 Received: (from root@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.2) id g03Fgnm25821 for reliable_computing-outgoing; Thu, 3 Jan 2002 09:42:49 -0600 (CST) Received: from mercury.Sun.COM (mercury.Sun.COM [192.9.25.1]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.2) with ESMTP id g03FgaV25815 for ; Thu, 3 Jan 2002 09:42:37 -0600 (CST) Received: from engmail4.Eng.Sun.COM ([129.144.134.6]) by mercury.Sun.COM (8.9.3+Sun/8.9.3) with ESMTP id HAA15919; Thu, 3 Jan 2002 07:42:12 -0800 (PST) Received: from phys-mpkmaila (phys-mpkmaila.Eng.Sun.COM [129.146.18.131]) by engmail4.Eng.Sun.COM (8.9.3+Sun/8.9.3/ENSMAIL,v2.1p1) with ESMTP id HAA15758; Thu, 3 Jan 2002 07:42:10 -0800 (PST) Received: from gww (gww.Eng.Sun.COM [129.146.78.116]) by mpkmail.eng.sun.com (iPlanet Messaging Server 5.2 (built Nov 13 2001)) with SMTP id <0GPD00FZICZ1B2 [at] mpkmail [dot] eng.sun.com>; Thu, 03 Jan 2002 07:42:39 -0800 (PST) Date: Thu, 03 Jan 2002 07:42:08 -0800 (PST) From: William Walster Subject: Re: can u help me To: ramu_mallela [at] yahoo [dot] com, George.Corliss [at] Marquette [dot] edu Cc: reliable_computing [at] interval [dot] louisiana.edu Reply-to: William Walster Message-id: <0GPD00FZJCZ1B2 [at] mpkmail [dot] eng.sun.com> MIME-version: 1.0 X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4.2 SunOS 5.8 sun4u sparc Content-type: multipart/mixed; boundary="Boundary_(ID_YaGgR+faU8zUjjTjONW19A)" Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk --Boundary_(ID_YaGgR+faU8zUjjTjONW19A) Content-type: TEXT/plain; charset=us-ascii Content-transfer-encoding: 7BIT Content-MD5: Oy+99o84RkfljlaYjgGHPg== Thanks, George. The paper you mention is attached. I might add that John Gustafson has a nice paper in which he outlines the idea of starting underlying conservation laws rather than PDEs when solving dynamical problems. Good luck, Rama, Bill G. William (Bill) Walster, Ph.D. Interval Technology Engineering Manager Sun Microsystems, Inc. 16 Network Circle, MS UMPK16-304 Menlo Park, CA 94025 (650) 786-9004 Direct (650) 786-9551 Fax bill.walster [at] eng [dot] sun.com >Date: Thu, 03 Jan 2002 06:01:33 -0600 >From: "Dr. George Corliss" >Subject: Re: can u help me >To: "Rama Rao M.V." >Cc: reliable_computing [at] interval [dot] louisiana.edu >MIME-version: 1.0 >Content-transfer-encoding: 7bit >X-Accept-Language: en-us >User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:0.9.4) Gecko/20011128 Netscape6/6.2.1 > >M.V.Rama Rao, > >I cannot be specifically helpful in the way you request, >but let me offer a suggestion: > >Try going back to first principles. > >The PDE approximates the physics, >Finite elements approximate the PDE, >We usually solve the FE equations approximately. > >The result we conventionally compute is an approximation >to an approximation to an approximation. If we introduce >intervals or fuzzy sets at the last step, we have an >enclosure of an approximation to an approximation. > >The PDEs were probably derived by constructing a model >and then taking a limit as delta something approaches >zero. Try going back to the physical model from which >the PDEs were derived and see if you can solve that. >You are then two or three steps closer to the physics. > >One advantage is that you may be able to formulate >the original problem as a fixed point operator, as >an integral operator, as a linear or nonlinear system, >or as an optimization problem, all of which are FAR more >suitable for fuzzy or interval techniques than derivative >operators. > >One disadvantage: few people have done this, so you >will probably have a difficult time convincing your advisor, >your thesis committee, and journal editors that you can >solve structural problems without finite elements or even >PDEs. This is a MAJOR paradymn shift, so if you attempt it, >be prepared to do battle with the establishment. Contributors >to this group can offer some encouragement in your battle. > >Bill Walster reads this group regularly. Bill, please >send a copy of your paper from the SCAN 2000 proceedings >I just received yesterday. That paper does not tell >you how to do what I describe, but it gives strong >encouragement to look for ways to make it work. > >Another suggestion: Look at the sensitivity in your model. >Even for the floating point model, consider using automatic >differentiation to compute > > partial output variables of interest > ------------------------------------ > partial input variables > >If you have Fortran, C, or C++ code, it is probably not >terribly hard to derive code that computes these >sensitivities. There are good software tools freely >available. See a recent book by Andreas Griewank >published by SIAM. > >It sounds as though the sensitivities of the eigenvalues >with respect to the stiffness matrix is probably high. If >so, the results you observe are the fault of the design, >not the fault of your computations. That suggests you >either take engineering steps to mitigate the effects of >unstability in the design or else revise the design to be >less sensitive (more stable) with respect to stiffness. > >In that case, your computations have been EXTREMELY valuable, >because they have uncovered a potentially dangerous design, >since I would expect the natural stiffness of materials to >change slightly over time as the bridge ages. You have >demonstrated the need for a redesign. > >Good luck. Keep us posted on your work. > >Dr. George F. Corliss >Electrical and Computer Engineering >Haggerty Engineering 296 >Marquette University >P.O. Box 1881 >Milwaukee, WI 53201-1881 USA >George.Corliss [at] Marquette [dot] edu >Office: 414-288-6599; Dept: 288-6820; Fax: 288-5579 > >Rama Rao M.V. wrote: > >> I am M.V.Rama Rao from Hyderabad in South India. >> I teach Structural Engineering to Under-graduate >> students at a local engineering college. >> I am currently pursuing my Ph.D. work entitled " >> Dyanmic Analysis of Cable-Stayed Bridge by >> Fuzzy-Finite Element Modelling" since June,2000 at >> Osmania University,Hyderabad,India. >> I hold a master's degree in Structural Engineering >> from Indian Institute of Technology,Kanpur which is >> one of the premier institutions of engineering >> education in India. >> My work involves >> 1. introducing uncertainity in finite element analysis >> of cable-stayed bridges by replacing the floating >> point variables with fuzzy interval numbers. >> 2.Computing the static and dynamic response of such >> structures to uncertain interval loading >> I developed a fuzzy-finite element static analysis of >> structures and was able to obtain satisfactory results >> Now I have to solve dynamic analysis problem by >> suitably adapting the eigen-value problem to include >> fuzzy interval numbers. >> So i took the jacobi method and converted to fuzzy >> interval method. I am able to obtain fuzzy eigen >> values and modeshape vectors. >> But I have a lingering doubt as to whether whatever I >> am doing makes sense or not. Anyhow, intutively I feel >> that a vibrating body will have fuzzy natural frequeny >> and modeshapes. >> as per results, i am getting a wide variation in the >> eigen values even for a small variation in the >> stiffness matrix >> >> Sitting here in India, I do not have access to >> literature and am proceeding by instinct. >> Can you kindly help me in this regard.Can you kindly >> send me any software or literature i can use for the >> purpose of comparision? > > --Boundary_(ID_YaGgR+faU8zUjjTjONW19A) Content-type: APPLICATION/pdf; name=output.pdf; x-unix-mode=0755 Content-transfer-encoding: BASE64 Content-disposition: attachment; filename=output.pdf Content-description: output.pdf Content-MD5: 9eR6tbJ0JA5otecJh1yIhQ== JVBERi0xLjENCiXi48/TDQoyIDAgb2JqDQo8PA0KL0xlbmd0aCAzNTM0DQov RmlsdGVyIC9MWldEZWNvZGUNCj4+DQpzdHJlYW0NCoAMRBAoEcjODQUQiwIB eRynAjOcxARSxCBiMxALYuIBsMRkIBuOY+cjLCDNCCEVIQLyMNIGICpJwUMR qLhgNhAMJzA5rN4GNBmLhwIBqNxjNpcVDbCJ1TRBBoQLRhNhhGCoY4QWxQVi 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