Applications of interval computations to earthquake-resistant engineering: How to compute derivatives of interval functions fast. (English) Zbl 0844.65010
The authors propose a method for fast computation of derivatives of interval functions. The method is applied to an earthquake-resistant engineering problem, which requires the computations of derivatives of interval functions in real time.
Reviewer: S.Markov (Sofia)
MSC:
| 65D25 | Numerical differentiation |
| 65G30 | Interval and finite arithmetic |
| 86A17 | Global dynamics, earthquake problems (MSC2010) |
Keywords:
numerical differentiation; earthquake-resistant engineering problem; derivatives of interval functionsReferences:
| [1] | Aberth, O.Precise numerical analysis Wm. C. Brown. Publ., Dubuque, Iowa, 1988. · Zbl 0665.65001 |
| [2] | Bellman, R.Introduction to matrix analysis. McGraw Hill, N.Y., 1970. · Zbl 0216.06101 |
| [3] | Bohlender, G., Ulrich, C., Wolff von Gudenberg, J., and Rall, L. B.Pascal-SC. A computer language for scientific computations. Academic Press, N.Y., 1987. |
| [4] | Burden, R. L. and Faires, J. D.Numerical analysis. Prindle, Weber & Schmidt, Boston, MA, 1985. |
| [5] | Chung, L. L., Lin, R. C., Soong T. T., and Reinhorn, A. M.,Experimental study of active control for MDOF seismic structures. Journal of Engineering Mechanics115 (8) (1989), pp. 1609–1627. · doi:10.1061/(ASCE)0733-9399(1989)115:8(1609) |
| [6] | Corliss, G. F.Applications of differentiation arithmetic. In: Moore, R. E., (ed.) ”Reliability in computing”, Academic Press, N.Y., 1988. pp. 127–148. |
| [7] | Dehghanyar, T. J., Masri, S. F., Miller, R. K., and Caughey, T. K.On-line parameter control of nonlinear flexible structures. In: ”Proceedings of the 2nd International Symposium on Structural Control, Martinus-Nijhoff, Boston, MA, 1987”, pp. 141–159. |
| [8] | Jaja, J.An introduction to parallel algorithms. Addison-Wesley, Reading, MA, 1992. |
| [9] | Karmarkar, N.A new polynomial-time algorithm for linear programming. Combinatorica4 (1984), pp. 373–396. · Zbl 0557.90065 · doi:10.1007/BF02579150 |
| [10] | Kobori, T.State-of-the-art of structural control research in Japan. In: ”Proceedings of the US National Workshop on Structural Control, October 25–26, 1990”, pp. p1–p21. |
| [11] | Kobori, T. et al.U.S. Patent No. 5,036,633. |
| [12] | Kobori, T., Kanayama, H., and Kamagata, S.A proposal of new anti-seismic structure with active seismic response control system–dynamic intelligent building. In: ”Proceedings of the 9th World Conference on Earthquake Engineering, Tokyo–Kyoto, Japan,VIII”, pp. 465–470. |
| [13] | Kobori T., Kanayama, H., and Kamagata, S.Active seismic response control systems for nuclear power plant equipment facilities. Nuclear Engineering and Design111 (1989), pp. 351–356. · doi:10.1016/0029-5493(89)90245-8 |
| [14] | Kobori, T., Yamada, S., and Kamagata, S.U.S. Patent No. 4,922,667. |
| [15] | Kreinovich, V., Lakeyev, A., and Noskov, S.Optimal solution of interval linear systems is intractable (NP-hard). Interval Computations (1) (1993). · Zbl 0829.65032 |
| [16] | Markov, S.Interval differential equations. In: Nickel, K. E. (ed.) ”Interval Mathematics 1980”, Academic Press, N.Y., 1980, pp. 145–164. |
| [17] | Meirovitch, L., Baruch, H., and Oz, H.A comparison of control techniques for large flexible structures. Journal of Guidance,6 (4) (1983), pp. 302–310. · Zbl 0512.93012 · doi:10.2514/3.19833 |
| [18] | Moore, R. E.Automatic local coordinate transformations to reduce the growth of error bounds in interval computation of solution of ordinary differential equations. In: Rall, L. B. (ed.) ”Errors in Digital Computations, Proceedings of a Symposium”, John Wiley & Sons, N.Y., 1965, pp. 103–140. |
| [19] | Moore, R. E.Interval analysis. Prentice Hall, Englewood Cliffs, N.J., 1966. · Zbl 0176.13301 |
| [20] | Moore, R. E.Mathematical elements of scientific computing. Holt, Rinehart and Winston, N.Y., 1975. · Zbl 0376.65001 |
| [21] | Moore, R. E.Methods and applications of interval analysis. SIAM, Philadelphia, 1979. · Zbl 0417.65022 |
| [22] | Nemir, D. C., Koivo, A. J., and Kashyap, R. L.Pseudolinks and the self-tuning control of a non-rigid link mechanism, IEEE Transactions on Systems, Man and Cybernetics18 (1) (1988), pp. 40–48. · doi:10.1109/21.87053 |
| [23] | Osegueda, R. A., Nemir, D. C., and Lin, Y. J.On-line adaptive stiffness control to tailor modal energy contents in structures. In: ”ADPA/AIAA/ASME/SPIE Conference on Active Materials and Adaptive Structures, Alexandria, VA, November 5–8, 1991”. |
| [24] | Rall, L. B.Applications of software for automatic differentiation in numerical computation. In: Alefeld, G. and Grigorieff, R. D. (eds) ”Fundamentals of Numerical Computations (Computer-Oriented Numerical Analysis)”, Springer-Verlag, Wien, N.Y., 1980, pp. 141–156. |
| [25] | Rall, L. B.Automatic differentiation: techniques and applications. Lecture Notes in Computer Science 120, Springer-Verlag, Berlin-Heidelberg-N.Y., 1981. · Zbl 0473.68025 |
| [26] | Rall, L. B.Differentiation and generation of Taylor coefficients in Pascal-SC. In: Kulisch, U. W. and Miranker, W. L. (eds) ”A New Approach to Scientific Computation”, Academic Press, N.Y., 1983, pp. 291–309. |
| [27] | Ratschek, H. and Schröder, G.Über die Abteitung von intervallwertigen Funktionen. Computing7 (1971), pp. 172–187. · Zbl 0221.65032 · doi:10.1007/BF02242344 |
| [28] | Sendov, B.Some topics of segment analysis. In: Nickel, K. E. (ed.) ”Interval Mathematics, 1980”, Academic Press, N.Y., 1980, pp. 203–222. · Zbl 0539.65030 |
| [29] | Shary, S. P.Solution of ”outer” and ”inner” problems for an interval system of linear algebraic equations. Ph.D Dissertation Kransoyarsk–Ekaterinburg, 1991 (in Russian). · Zbl 0829.65038 |
| [30] | Shary, S. P.A new class of algorithms for optimal solution of interval linear systems. Interval Computations (2) (1992), pp. 18–29. · Zbl 0829.65039 |
| [31] | Soong, T. T.Active structural control: theory and practice. Longman Scientific, Essex, 1990. |
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