##
**The inverse identification problem and its technical application.**
*(English)*
Zbl 1190.74021

Summary: This paper presents an overview of a loading force identification technique. Load identification methods are based on the solution of the inverse identification problem. Many different approaches for linear systems have been developed in this area. For both linear and nonlinear systems, methods based on the minimization of assumed objective functions are formulated. The least square error between the simulated and measured system responses is mainly used as the objective function. The dynamic programming optimization method formulated by Bellman is commonly used for the minimization of the objective function to estimate the excitation forces. The inverse identification problem in most practical cases is ill-posed because not all the state variables or initial conditions are known. Ill-posed inverse identification problems can be solved using several techniques, the most useful of which are: the generalized cross-validation method, the dynamic programming technique and Tikhonov’s method. This article presents the theoretical background and main limits to the application of inverse identification methods. Numerical and experimental tests on a laboratory rig were made to verify the formulated procedures. The method is applied to the identification of wheel-rail contact forces during rail vehicle operation. The method can be applied for indirect measurements of contact forces in railway equipment testing.

Full Text:
DOI

### References:

[1] | Allemang, R.J., Brown, D.L., Fludang, W.: Modal parameter estimation: unified matrix polynomial approach, Proceedings of the 12th IMAC, pp. 501–514 (1994) |

[2] | Anger G. (1990) Inverse problems in differential equations. Plenum, New York · Zbl 0707.35157 |

[3] | Bracciali A., Cascini G. (2000) Rolling contact force energy reconstruction, J. Sound Vib. 236(2): 185–192 |

[4] | Busby H.R., Trujillo D.M. (1986) Solution of an inverse dynamics problem using an eigenvalue reduction technique, Comput. Struct. 25(1):123–136 · Zbl 0616.73118 |

[5] | Cannon J.R., Hornung U. (1986) Inverse Problems. Birkhauser Verlag, Vauser · Zbl 0593.00010 |

[6] | Chudzikiewicz A. (1991) Selected elements of the contact problems necessary for investigating the rail vehicle system. In: Kisilowski J., Knothe K. (eds) Advanced railway vehicle system dynamics. WNT, Warszawa |

[7] | Chudzikiewicz, A.: Elements of vehicle diagnostics, (in Polish) ITE, Radom (2002) |

[8] | Czop, P., Uhl, T.: Load identification methods based on parametric models for mechanical structures, In: 8th IEEE international conference on methods and models in automation and robotics, Szczecin, pp. 203–209 (2002) |

[9] | Dobson B.J., Rider E. (1990) A review of the indirect calculation of excitation forces from measured structural response data. J. Mech. Eng. Sci. 204, 69–75 |

[10] | Giergiel J., Uhl T. (1989) Identification of impact forces in mechanical systems. Arch. Mach. Des. 36(2–3): 321–336 |

[11] | Giergiel J., Uhl T. (1989) Identification of the input excitation forces in mechanical structures. Arch. Transp. 1(1): 8–24 |

[12] | Golub G.H., van Loan C.F. (1996) Matrix Computations. John Hopkins University Press, Baltimore · Zbl 0865.65009 |

[13] | Góral, G., Zbydoń, K., Uhl, T.: Intelligent transducers of in-operational loads in construction fatigue monitoring. Mach. Dyn. Probl. 2–3, 73–88 (2002) |

[14] | Hadamard J. (1923) Lectures on Coughy’s Problem in Linear Partial Differential Equations. Yale University Press, New Haven · JFM 49.0725.04 |

[15] | Hansel E. (1991) Inverse Theory and Applications for Engineers. Prentice Hall, Englewood Cliffs · Zbl 0804.68096 |

[16] | Inoue H., Ishida K., Kishimoto T. Shibuya (1991) Measurements of impact load by using an inverse analysis technique. JSME Int. J. series I 34(4): 453–458 |

[17] | Kanehara, H., et al.: Study on online measurement of longitudinal creep force of railway vehicles, In: Proceedings of the conference J-Rail’98, November, Tokyo, pp. 457–469 (1998) |

[18] | Kanehara H., Fujioka T. (2002) Measuring rail/wheel contact points of running railway vehicles. Wear 253, 275–283 |

[19] | Lechowicz, S., Hunt, C.: Monitoring and managing wheel condition and loading. In: Proceeding of International Symposium for transportation recorders, Arlington, pp. 205–239 (1999) |

[20] | Li, J.: Application of mutual energy theorem for determining unknown force sources, Proceeding Of Internoise 88, Avignion, pp. 245–263 (1988) |

[21] | Liu G.R., Han X. (2003) Computational Inverse techniques in nondestructive evaluation. CRC Press, Boca Raton · Zbl 1067.74002 |

[22] | Meirovitch L., Baruch H. (1982) Control of self-adjoint distributed-parameter systems. J. Guid. Control Dyn. 5, 60–66 · Zbl 0516.93029 |

[23] | Mendrok, K.: Identification of loads in mechanical systems, Ph.D. Thesis, University of Science and Technology, Krakow (2003) |

[24] | Nielsen, J., Johansson, A.: Out of round railway wheels–literature survey, In: Proceedings Of the Institute of Mechanical Engineers – part F, vol. 214, pp. 79–91 (2002) |

[25] | Philips D.L. (1962) A technique for the numerical solution of certain equations of the first kind. J. ACM 9: 84–97 · Zbl 0108.29902 |

[26] | Simonian S.S. (1981) Inverse problems in structural dynamics. Int. J. Numer. Methods Eng. 17, 357–365 · Zbl 0498.73087 |

[27] | Tikhonov A.N., Arsenin V.Y. (1977) Solution of Ill-Possed Problems. Winston and Sons, Washington, DC · Zbl 0354.65028 |

[28] | Trujillo D.M. (1987) Application of dynamic programming to the general inverse problem. Int. J. Numer. Methods Eng. 23, 613–624 · Zbl 0378.49019 |

[29] | Trujillo D.M., Busby H.R. (1997) Practical Inverse Engineering. CRC Press, London · Zbl 0898.73002 |

[30] | Uhl T. (1998) Computer Assisted Identification of Mechanical Structures (in Polish). WNT, Warszawa |

[31] | Uhl T. (2002) Identification of loads in mechanical structures – helicopter case study Comput. Assist. Mech. Eng. Sci. 9, 151–160 · Zbl 1002.74524 |

[32] | Uhl T., Pieczara J. (2003) Identification of operational loading forces for mechanical structures, Arch. Transp. 16(2): 109–126 |

[33] | Uhl T., Mendrok K. (2005) Inverse Identification Problems: Theory and Practical Applications (in Polish). ITE Press, Kraków |

[34] | Zhang, Q., Allemang, R.J., Brown, D.L.: Modal filter: concept and applications. In: Proceeding of 8th IMAC, pp. 487–496 (1990) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.