The University of Sheffield
Automatic Control and Systems Engineering

Professor Zi-Qiang Lang
Professor of Complex Systems Analysis and Design

Photo of Dr Z Q LangAddress:
Professor Z Q Lang, BSc, MSc, PhD
Department of Automatic Control and Systems Engineering
University of Sheffield
Sheffield
S1 3JD
Tel: (+44) (0)114 222 5623
Fax: (+44) (0)114 222 5683
Email: z.lang @ sheffield.ac.uk
Room: C01, Amy Johnson Building

Research interests
Grants as PI
Professional activities and recognition
Key publications

Research interests

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Principal Investigator for the Research Grants:

UK Northern Wind Innovation Program (NWIP) Grant, `Novel Integrated Condition Monitoring System for Wind Turbine Components´, 2010-2011, £8,0664
Royal Society, `Experimental study of beneficial effect of nonlinear damper on vibration control´, 2010-2012, £1,1190
EPSRC, `New Generation Damping Technologies´ 21/03/08-20/03/11, £378519
EPSRC, `Nonlinear Output Frequency Response Functions: A New Concept in the Frequency Domain Analysis of Nonlinear Systems´, 01/04/04 to 30/11/06, £122980
Royal Society, The application of advanced optimization approaches to analytical engineering designs, 01/05/06 to 31/12/06, £6900
Royal Society, Application of advanced optimization approaches to the design of engineering systems and structures, 01/08/04 to 31/08/04, £1800
University Research Fund, Development of a Symbolic Computing Software Package for Nonlinear System Analysis and Design, 01/01/04 to 31/06/04, £3000

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Professional activities and recognition

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Key publications

  Details of Publication Brief description of contribution
1 Lang, Z Q and Billings, S A, 2005, Energy transfer properties of nonlinear systems in the frequency domain. International Journal of Control, Vol. 78, pp345-362 In this paper, I propose a novel concept called Nonlinear Output Frequency Response Function (NOFRF), and show that the new NOFRF concept and associated techniques have great potential to be used for fault diagnosis of a wide range of engineering systems and structures. Experts in this field think `this paper brings significant new results to the subject area, and the NOFRF concept may solve decade old problems in representation of the multidimensional frequency domain characteristics of nonlinear systems´.
2 Peng Z K, Lang, Z Q, and Billings, S A, 2007, Crack detection using nonlinear output frequency response functions. Journal of Sound and Vibration , Vol. 301, pp777-788 This paper reports a successful application of the novel NOFRF concept proposed in Paper 1 to the detection of cracks in a real engineering structure.
3 Lang, Z Q, Billings, S A, Tomlinson, G R, and Yue R, 2006. Analytical description of the effects of system nonlinearities on output frequency responses: A case study.Journal of Sound and Vibration, Vol.295, pp584-601. In this paper I derive, for the first time, an analytical relationship between the output frequency response and characteristic parameters of a class of nonlinear mechanical systems, and demonstrate the potential of using this new relationship to analytically perform the system analysis and design. The results provide an important basis for the analytical study and design of nonlinear engineering systems and structures in the frequency domain.
4 Lang Z Q, Billings S A, Yue R, and Li J, 2007, Output frequency response functions of nonlinear Volterra systems. Automatica, Vol. 43, pp805-816. In this paper, I propose the novel concept of Output Frequency Response Function (OFRF), and show that the output spectra of a wide class of nonlinear systems can be described by the OFRF concept that is a polynomial function of the system parameters which define the system nonlinearities. The results provide a considerably significant foundation for the development of a general methodology for the analysis and design of nonlinear systems in the frequency domain and have been considered to be `an extremely interesting development´ in this area.
5 Jing X J, Lang Z Q, Billings S A, and Tomlinson G R, 2006, The parametric characteristics of frequency response functions for nonlinear systems, International Journal of Control, Vol.79, pp1552-1564. The paper is concerned with the study of the parametric characteristics of the frequency response functions of a wide class of nonlinear systems. The results can be used to effectively determine the structure of the Output Frequency Response Function (OFRF), a new concept I proposed in Paper 4, which defines a very significant polynomial relationship between the system output spectrum and time domain model parameters.
6 Wu Xiaofeng, Lang Z Q, and Billings S A, 2007. Analysis of output frequencies of nonlinear systems. IEEE Trans on Signal Processing, Vol.55, No.7, pp.3239-3246. On the basis of a series of work I have done on output frequencies of nonlinear systems which published in IJC and IEEE Trans on Circuit and Systems several years ago, this paper extends the previous work to a much more general case. The new results are considered to `have provided a rather nice way for treating the often onerous task in nonlinear system frequency analysis´. Together with my previous results, this paper comprehensively answers a very basic question in the frequency domain analysis of nonlinear systems that is `what are exactly the output frequencies of a nonlinear system´.

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A list of selected publications

Lang Z Q, Park G, Farrar C R, Todd M D, Mao Z, Zhao L, Worden K, 2011,Transmissibility of Nonlinear Output Frequency Response Functions with Application in Detection and Location of Damage in MDOF Structural Systems, International Journal of Nonlinear Mechanics, in press.

Peng Z K, Lang Z Q, Wolters C, Billings S A, Worden K, 2011, Feasibility study of structural damage detection using NARMAX modelling and Nonlinear Output Frequency Response Function based analysis, Mechanical Systems and Signal Processing, Vol. 25, pp1045-1061

Laalej, H. Lang Z Q, 2010, Numerical Investigation of the Effects of MR Damper Characteristic Parameters on Vibration Isolation of SDOF Systems Under Harmonic Excitations, Journal of Intelligent Material Systems and Structures, Vol. 21, pp 483-501.

Peng Z K, Lang Z Q, Chu F L, and Meng G, 2010, Locating nonlinear components in periodic structures using nonlinear effects, Structural Health Monitoring, doi:10.1177/1475921710361327.

Jing XJ, Lang Z Q , 2009, Frequency domain analysis of a dimensionless cubic nonlinear damping system subject to harmonic input, NONLINEAR DYNAMICS , pp 469-485

Lang Z Q, Jing X J, Billings, S A, and Tomlinson G R, Peng, Z K, 2009, Theoretical Study of the Effects of Nonlinear Viscous Damping on Vibration Isolation of sdof Systems, Journal of Sound and Vibration, Vol. 323, pp352-365.

Lang Z Q, Peng Z K, 2008, A novel approach for nonlinearity detection in vibrating systems. Journal of Sound and Vibration, Vol.314, pp603-615.

Peng, Z K, Lang Z Q, Billings, S A, and Tomlinson G R, 2008, Comparisons between harmonic balance and nonlinear output frequency response function in nonlinear system analysis. Journal of Sound and Vibration, Vol.311, pp. 56-73.

Jing X J, Lang Z Q, Billings, S A, 2008, Magnitude bounds of generalized frequency response functions for nonlinear Volterra systems described by NARX model, Automatica, Vol.144, pp838-845.

Jing X J, Lang Z Q, Billings, S A, 2008, Mapping from parametric characteristics to generalized frequency response functions of nonlinear systems, International Journal of Control, Vol. 81, pp1071–1088

Jing X J, Lang Z Q, Billings, S A, Tomlinson, G R, 2008, Frequency domain analysis for suppression of output vibration from periodic disturbance using nonlinearities, Journal of Sound and Vibration, Vol. 314, pp536-557.

H Wei, Lang Z Q, Billings S A, 2008, Constructing an Overall Dynamical model for a system with changing design parameter properties, International Journal of Modelling, Identification, and Control, Vol.5, pp93-104

Jing X J, Lang, Z Q, Billings, S A, 2008, Frequency domain analysis for nonlinear Volterra systems with a general nonlinear output function. International Journal of Control, Vol.81, No.2, pp235 –251.

Jing X J, Lang, Z Q, Billings, S A, 2008, Output Frequency Response Function based Analysis for Nonlinear Volterra Systems. Mechanical Systems and Signal Processing, Vol.22, pp 102–120.

Lang, Z Q, Agurto, A, Tian, G Y, and Sophian A, 2007, A system identification based approach for pulsed eddy current non-destructive evaluation. Measurement Science and Technology, Vol.18, No.7, pp.2083-2091.

Lang, Z Q, Billings S A, Yue R, and Li J, 2007, Output frequency response function of nonlinear Volterra systems. Automatica, Vol. 143, No.5, pp805-816.

Peng, Z K, Lang, Z Q, 2007, Detecting the position of non-linear component in periodic
structures from the system responses to dual sinusoidal excitations. International Journal of Non-Linear Mechanics, Vol.42, No.9, pp1074-1083.

Peng, Z K, Lang, Z Q, Billings, S A, 2007, Linear parameter estimation for multi-degree-of-freedom nonlinear systems using nonlinear output frequency response functions. Mechanical Systems and Signal Processing, Vol.21, No.8, pp.3108-3122.

Peng, Z.K., Lang, Z.Q., Billings, S.A. and Lu, Y, 2007, Analysis of bilinear oscillators under harmonic loading using nonlinear output frequency response functions. International Journal of Mechanical Sciences, Vol.49, No.11, pp1213-1225.

Peng, Z K, Lang, Z Q, 2007, Relationship between harmonic balance method and non-linear output frequency response function approach. Journal of Mechanical Engineering Science. Vol.211, No.2,pp1533-1543.

Peng, Z K, Lang, Z Q, 2007, On the Convergence of the Volterra Series Representation of the Duffing´s Oscillators subjected to Harmonic Excitations. Journal of Sound and Vibration, Vol.305, pp322-332.

Peng, Z K, Lang, Z Q, Billings, S A, 2007, Crack detection using nonlinear output frequency response functions. Journal of Sound and Vibration, Vol.301, pp777-788.

Peng, Z K, Lang, Z Q, Billings, S A, 2007, Resonances and resonant frequencies for a class of nonlinear systems. Journal of Sound and Vibration, Vol.300, pp993-1014.

Peng, Z K, Lang, Z Q, Billings, S A, 2007, Nonlinear Output Frequency Response Functions of MDOF Systems with Multiple Nonlinear Components. International Journal of Non-Linear Mechanics, Vol.42, No.7,pp941-958.

Peng, Z K, Lang, Z Q, Billings, S A, 2007, Nonlinear output frequency response functions for multi-input nonlinear Volterra systems. International Journal of Control, Vol.80, No.6, pp843-855.

Jing X J, Lang, Z Q, Billings, S A, 2007, New bounded characteristics of NARX model in the frequency domain. International Journal of Control, Vol.80, No.1, pp140-149.

Wu X, F, Lang, Z Q, and Billings, S A, 2007, Analysis of the output frequencies of nonlinear systems. IEEE Trans on Signal Processing, Vol.55, NO.7, pp.3239-3246.

Wei H, Lang, Z Q, Billings S A, 2007, An algorithm for determining the output frequency range of Volterra models with multiple inputs. IEEE Transactions on Circuits and Systems II-Express Briefs, Vol. 54, No.6, pp.532-536.

Lang, Z Q, Billings S A, Tomlinson G R, Yue R, 2006, Analytical description of the effects of system nonlinearities on output frequency responses: A case study. Journal of Sound and Vibration, Vol 295, pp584-601.

Tomlinson, G R, Lang, Z Q, Billings, S A, Xie, F, 2006, Suppressing resonant vibrations via energy transfer concepts. Structural Control and Health Monitoring. Vol. 13, pp 523-535.

Wu X, F, Lang, Z Q, Billings, S A, 2006, A new method for the design of energy transfer filters. International Journal of Control, Vol.79, pp968-981.

Jing X J, Lang, Z Q, Billings, S A, Tomlinson, G R, 2006, The parametric characteristics of frequency response functions for nonlinear systems. International Journal of Control, Vol 79, pp1552-1564.

Lang, Z Q, Billings, S A, 2005, Energy transfer properties of nonlinear systems in the frequency domain. International Journal of Control, Vol.78, pp345—362.

Wu X F, Lang, Z Q, Billings S A, 2005, An orthogonal least squares based approach to FIR designs. International Journal of Automation and Computing. Vol.2, pp163-170.

Yue, R, Billings, S.A., Lang, Z Q, 2005, An investigation into the characteristics of nonlinear frequency response functions, Part 1: Understanding the higher dimensional frequency spaces. International Journal of Control, Vol.78, pp1031-1044.

Yue, R, Billings, S.A., Lang, Z Q, 2005, An investigation into the characteristics of nonlinear frequency response functions, Part 2: New analysis methods based on symbolic expansions and graphical techniques. International Journal of Control, Vol.78, pp1130-1149.

Billings, S.A., Lang, Z Q, 2002 Nonlinear systems in the frequency domain: Energy transfer filters. International Journal of Control, Vol.75, pp1066-1081.

Lang, Z Q, Billings, S.A, 2000, Evaluation of output frequency responses of nonlinear systems under multiple inputs. IEEE Transactions on Circuits and Systems II, Vol.47, pp28-38.