Wavelet Technology in Vehicle Power Management

  • Xi Zhang
  • Chris MiEmail author
Part of the Power Systems book series (POWSYS)


The wavelet technology is introduced in this book for to the vehicle power management system by the authors for the first time. It can identify the high-frequency transients and real time power demand of the drive line. By using the wavelet transform, a proper power demand combination can be achieved for power sources in all types of hybrid vehicles. The objective of the wavelet-based power management strategy is to improve system efficiency and life expectancy of power sources (i.e., the fuel cell and battery), usually in the presence of various constraints due to drivability requirements and component characteristics. This chapter depicts the fundamental concepts of wavelets and filter banks for the design of the vehicle power management system. The feasibility analysis and detailed process of the wavelet-based vehicle power management strategy are given for various types of vehicle configurations. Additionally, the application of the wavelets for vehicle real-time environment is demonstrated.


Fuel Cell Continuous Wavelet Transform Power Demand Haar Wavelet Riesz Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Goupillaud P, Grossman A, Morlet J (1984) Cycle-octave and related transforms in seismic signal analysis. Geoexploration 23:85–102CrossRefGoogle Scholar
  2. 2.
    Stark HG (2005) Wavelets and signal processing-an application-based introduction. Springer, Berlin HeidelbergGoogle Scholar
  3. 3.
    Dym H, McKean H (1985) Fourier series and integrals. Academic Press, Orlando, FLzbMATHGoogle Scholar
  4. 4.
    Bracewell RN (2000) The fourier transform and its applications, 3rd edn. McGraw-Hill, BostonGoogle Scholar
  5. 5.
    Gramatikov B, Georgiev I (1995) Wavelets as alternative to short-time fourier transform in signal-averaged electrocardiography. Med Biol Eng Comput 33:482–487CrossRefGoogle Scholar
  6. 6.
    Rioul O, Vetterli M (1991) Wavelets and signal processing. IEEE Signal Process Mag 8:11–38CrossRefGoogle Scholar
  7. 7.
    Antoine JP, Carrette P, Murenzi R et al (1993) Image analysis with two-dimensional continuous wavelet transform. Signal Process 31:241–272zbMATHCrossRefGoogle Scholar
  8. 8.
    Zheng WM (1992) Admissibility conditions for symbolic sequences of the Lozi map. Chaos, Solitons and Fractals 2:461–470MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Fukuda S, Hirosawa H (1999) Smoothing effect of wavelet-based speckle filtering: the Haar basis case. IEEE Trans Geosci Remote Sens 37:1168–1172CrossRefGoogle Scholar
  10. 10.
    Oppenheim AV, Schafer RW, Buck JR et al (1999) Discrete-time signal processing. Rrentice Hall, Upper Saddle River, NJGoogle Scholar
  11. 11.
    Shannon CE (1949) Communication in the presence of noise. Proc Inst Radio Eng 37:10–21MathSciNetGoogle Scholar
  12. 12.
    Honda L (1998) Abstraction of Shannon’s sampling theorem.ICICE Trans Fundam Electron, Commun Comput Sci E81-A:1187–1193Google Scholar
  13. 13.
    Vrhel MJ, Lee C, Unser M (1997) Fast continuous wavelet transform: a least-squares formulation. Signal Process 57:103–119zbMATHCrossRefGoogle Scholar
  14. 14.
    Gosz J, Liu WK (1996) Admissible approximations for essential boundary conditions in the reproducing kernel particle method. Comput Mech 19:120–135zbMATHCrossRefGoogle Scholar
  15. 15.
    Louis AK, Maass P, Rieder A (1997) Wavelets, theory and applications. Wiley, New YorkzbMATHGoogle Scholar
  16. 16.
    Christensen O (1996) Frames containing a riesz basis and approximation of the frame coefficients using finite-dimensional methods. J Math Anal App 199:256zbMATHCrossRefGoogle Scholar
  17. 17.
    Arfken G (1985) Mathematical methods for physicists, 3rd edn. Academic Press, Orlando, FLGoogle Scholar
  18. 18.
    Mallat SG (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell 11:674–693zbMATHCrossRefGoogle Scholar
  19. 19.
    Meyer Y (1992) Wavelets and operators, volume 37 of cambridge studies in advanced mathematics. Cambridge University Press, Cambridge, MAGoogle Scholar
  20. 20.
    Jansen M, Oonincx P (2005) Second generation wavelets and applications. Springer, LondonGoogle Scholar
  21. 21.
    Vetterli M, Herley C (1992) Wavelets and filter banks: theory and design. IEEE Trans Signal Process 40:2207–2232zbMATHCrossRefGoogle Scholar
  22. 22.
    Jin Q, Luo ZQ, Wong KM (1994) Optimum complete orthonormal basis for signal analysis and design. IEEE Trans Inf Theory 40:732–742zbMATHCrossRefGoogle Scholar
  23. 23.
    Soman AK, Vaidyanathan PP (1993) On orthonormal wavelets and paraunitary filter banks. IEEE Trans Signal Process 41:1170–1183zbMATHCrossRefGoogle Scholar
  24. 24.
    Rajqopal K, Babu JD, Venkataraman S (2007) Generalized adaptive IFIR filter bank structures. Signal Process 87:1575–1596CrossRefGoogle Scholar
  25. 25.
    Daubechies I (1988) Orthonormal bases of compactly supported wavelets. Commun Pure Appl Math XLI:909–996MathSciNetCrossRefGoogle Scholar
  26. 26.
    Cariolaro G, Kraniauskas P, Vangelista L (2005) A novel general formulation of up/downsampling commutativity. IEEE Trans Signal Process 53:2124–2134MathSciNetCrossRefGoogle Scholar
  27. 27.
    Muthuvel A, Makur A (2001) Eigenstructure approach for characterization of FIR PR filterbanks with order one polyphase. IEEE Trans Signal Process 49:2283–2291CrossRefGoogle Scholar
  28. 28.
    Vaidyanathan PP, Nquyen TQ, Doqanata Z et al (1989) Improved technique for design of perfect reconstruction FIR QMF banks with lossless polyphase matrices. IEEE Trans Acoust Speech Signal Process 37:1042–1058CrossRefGoogle Scholar
  29. 29.
    Vetterli M, Le Gall D (1989) Perfect reconstruction FIR filter banks: some properties and factorizations. IEEE Trans Acoust Speech Signal Process 37:1057–1071CrossRefGoogle Scholar
  30. 30.
    Lu HC, Tzeng ST (2001) Adaptive lifting schemes with perfect reconstruction. Int J Syst Sci 32:25–32MathSciNetzbMATHGoogle Scholar
  31. 31.
    Sinap A, van Assche W (1996) Orthogonal matrix polynomials and applications. J Comput Appl Math 66:27–52MathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    Vaidyanathan PP, Hoang PQ (1988) Lattice structures for optimal design and robust implementation of two-band perfect reconstruction QMF banks. IEEE Trans Acoust Speech Signal Process 36:81–94CrossRefGoogle Scholar
  33. 33.
    Nagai T, Fuchie T, Ikehara M (1997) Design of linear phase M-channel perfect reconstruction FIR filter banks. IEEE Trans Signal Process 45:2380–2387CrossRefGoogle Scholar
  34. 34.
    Vandiyanathan PP (1987) Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary m, having the perfect-reconstruction property. IEEE Trans Acoust Speech Signal Process 35:476–492CrossRefGoogle Scholar
  35. 35.
    Nguyen TQ, Vaidyananthan PP (1990) Structures for M-Channel perfect- reconstruction FIR QMF banks which yield linear-phase analysis filters. IEEE Trans Acoust Speech Signal Process 38:433–446zbMATHCrossRefGoogle Scholar
  36. 36.
    Yan X, Hou M, Sun L et al (2007) The study on transient characteristic of proton exchange membrane fuel cell stack during dynamic loading. J Power Sources 163:966–970CrossRefGoogle Scholar
  37. 37.
    Liu X, Hui SYR (2005) An analysis of a double-layer electromagnetic shield for a universal contactless battery charging platform. 36th IEEE Power Electron Specialists Conference 2005, pp 1767–1772Google Scholar
  38. 38.
    Jossen A (2006) Fundamentals of battery dynamics. J Power Sources 154:530–538CrossRefGoogle Scholar
  39. 39.
    Ribeiro PF (1994) Wavelet transform: an advanced tool for analyzing non-stationary harmonic distortion in power systems. Proc IEEE ICHPS VI:21–23Google Scholar
  40. 40.
    Robertson D, Camps Q, Mayer J et al (1996) Wavelets and electromagnetic power system transients. IEEE Trans Power Delivery 11:1050–1058CrossRefGoogle Scholar
  41. 41.
    Galli AW (1997) Analysis of electrical transients in power systems via a novel wavelet recursive method. PhD Dissertation, Purdue University, PurdueGoogle Scholar
  42. 42.
    Heydt GT, Galli AW (1997) Transient power quality problems analyzed using wavelets. IEEE Trans Power Delivery 12:908–915CrossRefGoogle Scholar
  43. 43.
    Meliopoulos APS, Lee CH (1997) Wavelet-based transient analysis, Proceedings of North American power symposium, pp 339–346Google Scholar
  44. 44.
    Strzelecki RM, Benysek G (2008) Energy storage systems. Springer, LondonGoogle Scholar
  45. 45. Accessed 1 Feb 2009
  46. 46.
    Zhang X, Mi CC, Masrur A, Daniszewski D et al (2008) Wavelet based power management of hybrid electric vehicles with multiple onboard power sources. J Power Sources 185:1533–1543CrossRefGoogle Scholar
  47. 47.
    Walter GG, Shen XP (2001) Wavelets and other orthogonal systems. CRC Press, Boca Raton, FLzbMATHGoogle Scholar
  48. 48.
    Ben-Aris J, Rao KR (1993) A novel approach for template matching by nonorthogonal image expansion. IEEE Trans Circuits Syst Video Technol 3:71–84CrossRefGoogle Scholar
  49. 49.
    Wang X (2006) Moving window-based double Haar wavelet transform for image processing. IEEE Trans Image Process 15:2771–2779CrossRefGoogle Scholar
  50. 50.
    Zhang X, Mi CC, Masrur A et al (2008) Wavelet-transform-based power management of hybrid vehicles with multiple on-board energy sources including fuel cell, battery and ultracapacitor. J Power Sources 185:1533–1543CrossRefGoogle Scholar
  51. 51.
    Suter BW (1998) Multirate and wavelet signal processing. Academic Press, New YorkzbMATHGoogle Scholar

Copyright information

© Springer-Verlag London Limited  2011

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringUniversity of Michigan-DearbornDearbornUSA

Personalised recommendations