Monitorowanie obciążeń i stanu technicznego konstrukcji mostowych

Holnicki-Szulc, J.; Świercz, A.

Artykuł - szczegóły

Tytuł artykułu

Monitorowanie obciążeń i stanu technicznego konstrukcji mostowych

Autorzy

Holnicki-Szulc J. , Świercz A.

Treść / Zawartość

Pełne teksty:

IPPT_Reports_2014_1_J_Holnicki-Szulc_A_Swiercz_online_14_November_2014.pdf

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Identyfikatory

Warianty tytułu

Load and Structural Health Monitoring of truss bridges

Języki publikacji

Abstrakty

Podstawowym celem pracy jest przedstawienie wyników prac badawczych przeprowadzonych w ramach projektu MONIT realizowanego w latach 2009-2012. Tematyka tych prac była związana zarówno z rozważaniami teoretycznymi jak i implementacją systemów ukierunkowanych na praktyczne zastosowania. Część teoretyczna poświęcona jest głównie metodom rozpoznawania obciążeń występujących w transporcie szynowym i drogowym oraz modelowaniu i identyfikacji istotnych (ze względu na bezpieczeństwo) parametrów konstrukcji. Identyfikację przeprowadzano z zastosowaniem gradientowych metod optymalizacyjnych, które - podobnie jak inne podejścia - mogą być wykorzystane do lokalnego monitorowania konstrukcji za pomocą opracowanej wirtualnej izolacji podstruktur. W odniesieniu do opracowanych rozwiązań praktycznych należy wymienić dynamiczną wagę drogową, dynamiczną wagę kolejową oraz system Moni-Most. Zainstalowana w jezdni dynamiczna waga drogowa umożliwia pomiar nacisków osiowych pojazdów w ruchu. System ten pozwala wyselekcjonować te pojazdy, które mogą być przeciążone i przyczyniać się do dewastacji dróg. Podobną funkcję spełnia dynamiczna waga kolejowa, która może dostarczać informacji właścicielowi infrastruktury o przekroczeniu przez składy należące do przewoźników dopuszczalnych nacisków osiowych lub/i prędkości. System Moni-Most jest przeznaczony do monitorowania drgań konstrukcji mostowych wywołanych przez przejeżdżające pojazdy. Jego wdrożenie wykonano jako system zintegrowany z dynamiczną wagą kolejową, która dostarcza danych o obciążeniu konstrukcji. Przedstawione w monografii rozwiązania mają na celu monitorowanie stanu technicznego infrastruktury transportowej, służą poprawie bezpieczeństwa i zmniejszenia ich awaryjności. Niniejsze opracowanie zawiera również wybrane aspekty związane z zagadnieniem monitorowania i oceny stanu technicznego konstrukcji.

The main goal of this monograph is to present the results of the research project MONIT accomplished between 2009-2012. The subject of this work was associated with theoretical considerations and with implementation of systems aimed at practical applications. The theoretical part is mainly devoted to methods for load identification in rail and road transport, and to parametric modeling and identification of structural modifications. The identification has been performed using gradient-based optimization methods, which - like the other approaches - can be used for local substructural monitoring by means of the developed virtual substructure isolation method. Among the most important developed practical solutions, one should mention the dynamic rail and road weigh-in-motion systems and the Moni-Most system. The first solution, installed in a roadway, measures online vehicle axial loads during their passages. The system enables preliminary selection of potentially overloaded vehicles, which contribute to the devastation of roads. A similar function is provided by the rail weigh-in-motion system, which can provide information to the owner of the rail infrastructure about passage of trains that exceed the admissible axial loads (and/or speed). The Moni-Most system is designed for monitoring of bridge structures based on vibrations caused by passing vehicles. Its implementation was integrated with the rail weigh-in-motion system, which provides information about the current load of the structure. The presented solutions are designed for technical condition monitoring of transport infrastructure, and they can be used to improve transport safety and reduce the failure rates. This study includes also selected problems related to structural health monitoring.

Słowa kluczowe

most konstrukcja mostu obciążenia infrastruktura transportu projekt MONIT

bridge load rail infrastructure transport infrastructure MONIT project

Wydawca

Instytut Podstawowych Problemów Techniki PAN

Czasopismo

IPPT Reports on Fundamental Technological Research

Rocznik

2014

Tom

nr 1

Strony

1--244

Opis fizyczny

Bibliogr. 113 poz., rys., tab.

Twórcy

autor

Holnicki-Szulc J.

Instytut Podstawowych Problemów Techniki, Polskiej Akademii Nauk

autor

Świercz A.

Instytut Podstawowych Problemów Techniki, Polskiej Akademii Nauk

Bibliografia

1. M. Krawczuk, P. Kudela, K. Majewska, P. Malinowski, M. Mieloszyk, L. Murawski, S. Opoka, W. Ostachowicz, M. Radzieński, T. Wandowski, A. Żak. Monitorowanie stanu technicznego konstrukcji i ocena jej żywotności. Wydawnictwo Naukowe Instytutu Technologii Eksploatacji - PIB, 2012.
2. E. Wu, C. Tsai, L. Tseng. A deconvolution method for force reconstruction in rods under axial impact. Journal of Acoustical Society of America, 104:1418-1426, 1998.
3. H. Y. Kim. Diagnostic system for monitoring structural health condition. US Patent 7246521 B2, 2007.
4. F. K. Chang, M. Lin. Diagnostic layer and methods for detecting structural integrity of composite and metallic materials. US Patent 6370964 B1, 2002.
5. M. Lin, F. K. Chang. The manufacture of composite structures with a built-in network of piezoceramics. Composites Science and Technology, 62:919-939, 2002.
6. C. Caneva, F. Domenichini, F. Sarasini. Structural integrity monitoring of composite laminates using embedded acoustic emission polymeric transducers. Proceedings ofthe Second European Workshop on Structural Health Monitoring, pages 1219-1226, July 7-9, 2004.
7. V. Giurgiutiu, A. N. Zagrai, J. Bao. Piezoelectric wafer embedded active sensors for aging aircraft structural health monitoring. Structural Health Monitoring: An International Journal, 1(1):41-61, 2002.
8. E. S. Blazic, R. A. Bueker, L. O. Waters, W. D. Farwell, J. P. Smalanskas. Confor-mal circuit for structural health monitoring and assessment. US Patent 5184516, 1993.
9. P. Martin, Y. Feng, X. Wang. Detector technology evaluation. Raport instytutowy, Department of Civil and Environmental Engineering University of Utah Traffic Lab, 2003.
10. J. Gajda, R. Sroka. Wielo czujnikowa fuzja danych w systemach ważenia pojazdów w ruchu. Pomiary Akustyka Kontrola, 9:550-553, 2007.
11. J. Gajda, R. Sroka, M. Stencel, A. Wajda, T. Żegleń. Systemy ważenia pojazdów samochodowych w ruchu. Drogownictwo, 3/2001:78-81, 2001.
12. A. Regan, M. Park, S. Nandiraju, C. H. Yang. Strategies for successful implementation of virtual weigh and compliance systems in California. Raport instytutowy UCB-ITS-PRR-2006-19, University of California, Irvine, October 2006.
13. J. Heidemann, F. Silva, X. Wang, G. Giuliano, M. Hu. Sensors for unplanned roadway events-simulation and evaluation. Raport instytutowy Metrans Project 04-08, METRANS, May 2005.
14. R. Calderara. Long-term stable quartz wim sensors. National Traffic Data Acquisition Conference Albuquerque, New Mexico, pages 613-626. Kistler Instrumente AG Winterthur CH-8408 Winterthur, Switzerland, 5-9 May 1996.
15. A. Rosochowski. Technical feasibility of a three-axis force transducer for measuring pressure and friction on the model die surface - prototype development. Journal of Materials Processing Technology, 115:192-204, 2001.
16. O. Mack. Investigations of piezoelectric force measuring devices for use in legal weighing metrology. Measurement, 40:778-785, 2007.
17. G. Gautschi. Piezoelectric Sensorics. Spriger-Verlag Berlin Heidelberg, 2002.
18. T. Ikeda. Fundamentals of Piezoelectricity. Oxford University Press, 1990.
19. Theory and Modeling Guide Volume I: ADINA, 2006.
20. A. Preumont, V. Piefort. Finite element modeling of smart piezoelectric shell structures. 5th National Congress on Theoretical and Applied Mechanics-Louvain-la-Neuve, May 2000.
21. F. Wang, R. Machemehl. Predicting truck tire pressure effects upon pavement performance. Raport instytutowy SWUTC/06/167864-1, Center for Transportation Research University of Texas, April 2006.
22. W. Siłka. Teoria ruchu samochodu. Wydawnictwa Naukowo-Techniczne, 2002.
23. C. Helg, L. Pfohl. Signal processing requirements for wim lineas type 9195. Raport instytutowy, Kistler Instrumente AG, Winterthur, Switzerland, 2000.
24. F. Moses. Weigh-in-motion system using instrumented bridges transportation. Engineering Journal, 105:233-249, 1979.
25. P. Chatterjee, E. O'Brien, Y. Li, A. Gonzalez. Wavelet domain analysis for identification of vehicle axles from bridge measurements. Computers and Structures, 84:1792-1801, 2006.
26. W. Schulz, J. Seim, E. Udd, M. Morrell, H. Marty Laylor, G. McGill, R. Edgar. Traffic monitoring/control and road condition monitoring using fiber optic based systems. Smart systems for bridges, structures, and highways. Conference, Newport Beach CA, 1999.
27. R. Karoumi, J. Wiberg, A. Liljencrantz. Monitoring traffic loads and dynamic effects using an instrumented railway bridge. Engineering Structures, 27:1813-1819, 2005.
28. M. Niedzwiecki, A. Wasilewski. New algorithms for the dynamic weighing of freight trains. Control Engineering Practice, 5:603-618, 1997.
29. Systemy ważenia DGW-B SHENK, http://www.schenckprocess.pl.
30. D. Senyanskiy. Problem of increasing the accuracy of railway carriages weighing in motion. XVII IMEKO World Congress Metrology in the 3rd Millennium, June 22-27 2003.
31. A. Laudati, G. Lanza, A. Cusano, A. Cutolo, M. Giordano, G. Breglio, A. Antonelli. Railway monitoring and train tracking by fiber brag grating sensors: a case study in Italy. Proc. of the 4th European Workshop on Structural Health Monitoring, Krakow, Poland, 2-4 July 2008.
32. Gotcha company. Wheel flat detection and axle load measurement system. Raport instytutowy, TagMaster, 2005.
33. T. Roeleveld. Measurement of wheel-rail contact forces. Symposium of Advances in Contact Mechanics: a tribute to Prof. J.J. Kalker, Delft, Netherlands, 22-24 October 2008.
34. G. James. Analysis of Traffic Load Effects on Railway Bridges. Praca doktorska, Structural Engineering Division Royal Institute of Technology, Stockholm, Sweden, 2003.
35. A. Bracciali, P. Folgarait. New sensor for lateral and vertical wheel-rail forces measurements. Conference on Railway Engineering, London, 6-7 July 2004.
36. P. Kolakowski, A. Orlowska, K. Sekula, A. Swiercz, D. Sala. Two-year monitoring campaign of a railway truss bridge. 3rd International Conference on Experimental Vibration Analysis for Civil Engineering Structures - EVACES'09, Wroclaw, Poland, 14-16 October 2009.
37. T. Uhl. The inverse identification problem and its technical application. Archive Applied Mechanics, 77:325-337, 2007.
38. H. Inoue, J. Harrigan, S. Reid. Review of inverse analysis for indirect measurement of impact force. Appl. Mech. Rev, 54:503-524, 2001.
39. J. Nielsen, J. Oscarsson. Simulation of dynamic train-track interaction with state-dependent track properties. Journal ofSound and Vibration, 275:515-532, 2004.
40. K. Sekuła, P. Kołakowski. Piezo-based weigh-in-motion system for the railway transport. Structural Control and Health Monitoring, doi: 10.1002/stc.416, 2010.
41. D. Sala, P. Pawlowski, J. Motylewski, P. Kolakowski. Wireless transmission system for a bridge application. 3rd International Conference on Experimental Vibration Analysis for Civil Engineering Structures - EVACES'09, Wroclaw, Poland, 14-16 October 2009.
42. D. Sala, P. Pawlowski, P. Kolakowski. Wireless transmission system dedicated to shm of railway infrastructure. European Workshop on Structural Health Monitoring - EWSHM'10, Sorrento, Italy, 29 June - 2 July 2010.
43. P. Kołakowski, J. Szelążek, K. Sekuła, A. Świercz, K. Mizerski, P. Gutkiewicz. Structural health monitoring of a railway truss bridge using vibration-based and ultrasonic methods. Smart Materials and Structures, 20(3):(10pp), 2011.
44. J. Holnicki-Szulc i inni. Smart Technologies for Safety Engineering. Wiley, 2008.
45. P. Kołakowski. Damage identification by the static virtual distortion method. Engineering Transactions, 52(4), 2004.
46. P. Kołakowski, T. G. Zieliński, J. Holnicki-Szulc. Damage identification by dynamic virtual distortion method. Journal of Intelligent Material Systems and Structures, 15(6):479-494, 2004.
47. A. Świercz, P. Kołakowski, J. Holnicki-Szulc. Damage identification in skeletal structures using the virtual distortion method in frequency domain. Mechanical Systems and Signal Processing, 22(8):1826-1839, 2008.
48. M. Kokot, J. Holnicki-Szulc. Defect identification in electrical circuits via the virtual distortion method. Part 1: Steady-state case. Journal of Intelligent Material Systems and Structures, 20(12):1465-1473, 2009.
49. A. Orlowska, P. Kolakowski, J. Holnicki-Szulc. Modelling and identification of delamination in double-layer beams by the virtual distortion method. Computers and Structures, 86(23-24):2203-2214, 2008.
50. J. Holnicki-Szulc, P. Kolakowski, N. Nasher. Leakage detection in water networks. Journal of Intelligent Material Systems and Structures, 16(3):207-219, 2005.
51. Ł. Jankowski. Dynamic load identification for structural health monitoring. IPPT Reports on Fundamental Technological Research, 2/2013.
52. J. Hou, Ł. Jankowski, J. Ou. Experimental study of the substructure isolation method for local health monitoring. Journal of Structural Control & Health Monitoring, 19(4):491-510, 2012.
53. J. Hou, Ł. Jankowski, J. Ou. A substructure isolation method for local structural health monitoring. Journal of Structural Control & Health Monitoring, 18(6):601-618, 2011.
54. J. Hou, J. Ou, Ł. Jankowski. The experiment of substructure isolation and identification using local time series (in Chinese). Engineering Mechanics, 30(4):129-135, 2013.
55. J. Hou, J. Ou, Ł. Jankowski. The study and experiment of substructure damage identification based on local primary frequency (in Chinese). Engineering Mechanics, 29(9):99-105, 2012.
56. J. Hou, Ł. Jankowski, J. Ou. Substructure isolation method for online local damage identification using time series. Proc. of the 6th European Workshop on Structural Health Monitoring (EWSHM 2012), Dresden, Germany, 3-6 July 2012.
57. J. Hou, Ł. Jankowski, J. Ou. Large substructure identification using substructure isolation method. Proc. SPIE 8345, page 83453V, 2012.
58. J. Hou, Ł. Jankowski, J. Ou. Local damage identification in frequency domain based on substructure isolation method. Proc. of the 6th Int’l Workshop on Advanced Smart Materials and Smart Structures Technology (ANCRiSST 2011), Dalian, China, 25-26 July 2011.
59. J. Hou, Ł. Jankowski, J. Ou. Substructural damage identification using local primary frequency. Proc. of the 11th International Symposium on Structural Engineering (ISSE 11th), Guangzhou, China, 18-20 December 2010.
60. J. Hou, Ł. Jankowski, J. Ou. Substructural damage identification using time series of local measured response. Proc. of the 5th World Conference on Structural Control and Monitoring (5WCSCM 2010), Tokyo, Japan, 12-14 July 2010.
61. J. Hou, Ł. Jankowski, J. Ou. Substructure isolation and identification using FFT of measured local responses. Proc. of the 5th European Workshop on Structural Health Monitoring (EWSHM 2010), pages 913-918, Sorrento, Italy, 29 June – 2 July 2010.
62. J. Hou, Ł. Jankowski, J. Ou. Online local structural health monitoring using the substructure isolation method. 38th Solid Mechanics Conf. (SolMech ‘2012), pages 307-308, Warsaw, Poland, 27-31 August 2012.
63. J. Hou, Ł. Jankowski, J. Ou. Substructure isolation for local structural health monitoring. ECCOMAS Thematic Conference: Int'l Symposium on Inverse Problems in Mechanics of Structures and Materials (IPM'09), Rzeszów-Łańcut, Poland, 23-25 April 2009.
64. P. C. Hansen. Deconvolution and regularization with toeplitz matrices. Numerical Algorithms, 29:323-378, 2002.
65. P.C. Hansen. Discrete inverse problems: insight and algorithms. SIAM, Philadelphia, 2010.
66. Ä. Björck. Numerical Methods in Scientific Computing, wolumin 2. SIAM, Philadelphia, 2009.
67. E. Jacquelin, A. Bennani, P. Hamelin. Force reconstruction: analysis and regularization of a deconvolution problem. Journal of Sound and Vibration, 265(1):81-107, July 2003.
68. P. C. Hansen. The L-curve and its use in the numerical treatment of inverse problems. P. R. Johnston, redaktor, Computational Inverse Problems in Electro-cardiology, rozdział: 4, pages 119-142. WIT Press, Southampton, 2001.
69. J. N. Juang, R. S. Pappa. An eigensystem realization algorithm for modal parameter identification and model reduction. Journal of Guidance, Control, and Dynamics, 8(5):620-627, 1985.
70. R. J. Allemang. The modal assurance criterion - twenty years of use and abuse. Sound and Vibration, pages 14-21, 2003.
71. F. Claeyssen, N. Lhermet, R. Le Letty, F. Barillot, M. Debarnot, M. F. Six, G. Thomin, M. Privat, P. Bouchilloux. Piezoelectric actuators and motors based on shell structures. Proceedings of SPIE, wolumin 3991, pages 202-209, 2000.
72. Ch. Boller, F.-K. Chang, Y. Fujino. Encyclopedia of Structural Health Monitoring. Wiley, 2009.
73. D. Balageas, C.-P. Fritzen, A. Guemes. Structural Health Monitoring. ISTE Ltd, 2006.
74. A. Morassi, F. Vestroni F. Dynamic Methods for Damage Detection in Structures. Springer, 2008.
75. F. N. Najm. Circuit Simulation. John Wiley & Sons, 2010.
76. J. Vlah, K. Singhal. Computer Methods for Circuit Analysis and Design. Van Nostrand Reinhold Company, 1994.
77. C. W. Ho, A. Ruehli, P. Brennan. The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems, 22(6):504-509, 1975.
78. L. M. Wedepohl, L. Jackson. Modified nodal analysis: an essential addition to electrical circuit theory and analysis. Engineering Science and Educational Journal, 11(3):84-92, 2002.
79. J. W. Bandler, A. E. Salama. Fault diagnosis of analog circuits. Proceedings of the IEEE, 73(8), 1985.
80. R. W. Liu. Testing and Diagnosis ofAnalog Circuits and Systems. Van Nostrand Reinhold, New York, 1991.
81. P. Kabisatpathy, A. Barua, S. Sinha. Fault Diagnosis of Analog Integrated Circuit. Springer, 2005.
82. J. Holnicki-Szulc, redaktor. Smart technologies for safety engineering. Wiley, 2008.
83. P. Kolakowski, M. Wiklo, J. Holnicki-Szulc. The virtual distortion method - a versatile reanalysis tool for structures and systems. Structural and Multidisciplinary Optimizatio, 36(3):217-234, 2008.
84. A. Bloch. Electromechanical analogies and their use for the analysis of mechanical and electromechanical systems. Journal of the Institution of Electrical Engineer, 92:157-169, 1945.
85. H. E. Koenig, W. A. Blackwell. Electromechanical System Theory. McGraw-Hill, New York, 1961.
86. M. Kokot. Damage Identification in Electrical Network for Structural Health Monitoring. rozprawa doktorska, IPPT PAN, 2011.
87. M. Skłodowski. Współczesny monitoring obiektów budowlanych. Przegląd Budowlany, 3:37-46, 2009.
88. B. Gliśić, D. Inaudi. Fibre Optic Methods for Structural Health Monitoring. John Wiley & Sons, England, 2007.
89. B. Glisic, D. Inaudi, L. J. Ming, Y. T. Yew, N. C. Tat. Large scale lifespan monitoring of high-rise buildings using long-gage fiber optic sensors. The 3rd International Conference on Structural Health Monitoring of Intelligent Infrastructure - SHMII-3, 13-16 November 2007.
90. T. Graver, D. Inaudi, J. Doornink. Growing market acceptance for fiber-optic solutions in civil structures. Proceedings of SPIE - the International Society for Optical Engineering, wolumin 5589, pages 44-55, 2004.
91. A. Świercz, G. Mikułowski, C. Graczykowski, R. Wiszowaty, J. Holnicki-Szulc, P. Kołakowski. Zastrzeżenie patentowe (P.397312): Sposób generowania wstępnie zaprojektowanego udarowego obciążenia konstrukcji oraz urządzenia do generowania wstępnie zaprojektowanego udarowego obciążenia konstrukcji, 2011.
92. R. S. Phelan, W. P. Vann, J. Bice. FRP Reinforcing Bars in Bridge Decks Field Instrumentation and Short-Term Monitoring. Texas Tech University, Research Report 9-1520-04, 2003.
93. T. A. Hoffard, L. J. Malvar. Fiber-reinforced polymer composites in bridges: a state-of-the-art report. Raport instytutowy, Naval Facilities Engineering Command, 2005.
94. P. W. R. Beaumont. Fracture and Damage Mechanics of Composite Materials, wolumin 2, rozdział: The Mechanics of Damage in Structural Composite Materials. Technomic Publishing AG, 1992.
95. G. S. Springer, S. W. Tsai. Thermal conductivity of unidirectional materials. Journal of Composite Materials, 1:166-173, 1967.
96. U.S. Geological Survey. Mineral commodity summaries: 2013. Raport instytutowy, U.S. Department of the Interior, 2013.
97. F. A. Oluokun, E. G. Burdette, J. H. Deatheridge. Early-age concrete strength prediction by maturity - another look. Materials Journal, 87(6):565-572, 1990.
98. V. Lozär. A computer-controlled apparatus for thermal conductivity measurement by the transient hot wire method. Journal of Thermal Analysis and Calorimetry, 46(2):495-505, 1996.
99. D. Mikulić, B. Milovanović, I. Gabriel. Analysis of thermal properties of cement paste during setting and hardening. Proceedings of International Symposium on Nondestructive Testingof Mateirals and Structures, pages 465-471, Istambul, 2011.
100. J. F. Lamond, J. H. Pielert. Significance of tests and properties of concrete and concrete making materials. ASTM International, 169, 2006.
101. B. Klemczak. Modelowanie efektów termiczno-wilgotnościowych i mechanicznych w betonowych konstrukcjach masywnych. Wydawnictwo Politechniki Śląskiej, 2008.
102. W. Kiernożycki. Betonowe konstrukcje masywne. Teoria, wymiarowanie, realizacja. Polski Cement, Kraków, 2003.
103. S. Hamadi, W. E. Schiesser, G. W. Griffiths. Metod of lines. Scholarpedia, 2((7):2859), 2007.
104. S. Brenner, R. L. Scott. The Mathematical Theory of Finite Element Methods. Springer, wydanie 2nd edition, 2005.
105 Y. X. Wang, J. M. Wen. Gear method for solving differential equations of gear systems. J. Phys.: Conf. Ser., 48:143-148, 2006.
106. C. Cesariccio, D. Spano, P. Duce, R. L. Snyder. An imporved model for determining degree-day values from daily temperature data. Int. J. Biometeorol.,45(4):161-169, 2001.
107. J. Kurzawa, W. Kiernożycki. Uwarunkowania technologiczne w procesie realizacji elementów i konstrukcji masywnych z betonu. Number 441. Prace Naukowe Politechniki Szczecińskiej, Wydawnictwo Uczelniane Politechniki Szczecińskiej, 1991.
108. G. Knor, M. A. Glinicki, J. Holnicki-Szulc, A. Ossowski, Z. Ranachowski. Influence of calcareous fly ash on the temperature of concrete in massive elements during the first 72 hours of hardening. Roads and Bridge, 13(12):113-126, 2013.
109. G. De Schutter, L. Taerwe. General hydration model for portland cement and blast furnace slag cement. Cement and Concrete Research, 25(3):593-604, 1995.
110. G. Knor, M. A. Glinicki, J. Holnicki-Szulc. Determination of thermal properties of hardening concrete by means of inverse problem solution. Roads and Bridges - Drogi i Mosty, 4(11), 2012.
111. G. Knor, J. Holnicki-Szulc, M. A. Glinicki. Determination of thermal properties of hardening concrete containing high calcium fly ash. Structural Faults + Repair-2012, University of Edinburgh, 2012. ISBN No: 0-947664-71-7.
112. R. Hooke, T. A. Jeeves. „Direct search" solution of numerical and statistical problems. Journal of the Association for Computing Machinery (ACM), 8(2):212-229, 1961.
113 Ch. Audet, J. E. Dennis Jr. Analysis of generalized pattern searches. SIAM Journal on Optimization, 13(3):889-903, 2003.

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Bibliografia

Identyfikator YADDA

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