# Fault diagnosis and prognosis of a hydro-motor drive system using priority valve

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## Abstract

In this article, an improved fault isolation in the model-based fault detection and isolation (FDI) method is presented using parallely computed bond graph models. All component faults in a system may not be uniquely isolable. However, some faulty parameters’ subspaces may be identified. One of the possible solutions as proposed in this article is to estimate parameters from the actual performance of the plant assuming a single fault hypothesis. Then incorporating the estimated values, all the parallel models are run on a single-core processor and their responses are compared with the healthy plant to identify the actual fault. In this respect, a typical hydro-motor drive system is considered for the FDI analysis, where a stable source of flow is supplied through a priority flow divider valve to two hydro-motors. A methodology for parametric fault isolation under single fault assumption with minimum measurements is discussed. Such method is capable to estimate the remaining useful life (RUL) of the faulty components of a system. The proposed methodology used for identifying the fault and estimating the RUL is simple enough to adopt it in industrial practices.

## Keywords

Priority valve Bond graph Hydro-motor Priority flow Bypass flow Fault detection and isolation (FDI) Analytical redundancy relation (ARR) Diagnostic bond graph (DBG) Fault signature matrix (FSM) Remaining useful life (RUL)## List of symbols

*A*_{sp}Area of the valve spindle toward the main port

*A*_{bp}Area of the valve spindle toward the bypass port

*A*_{pr}Area of the valve spindle toward the priority port

*β*_{f}Generalized bulk modulus of the fluid

*D*_{m1}Motor displacement rate of hydro-motor HM

_{1}*D*_{m2}Motor displacement rate of hydro-motor HM

_{2}*D*_{p}Volume displacement rate of loading pump

*C*Single-port energy storage capacitive elements

*d*_{bp}Diameter of the bypass port

*d*_{pr}Diameter of the priority port

*F*_{sp}Stopper reaction force on the valve spindle

*F*_{ff}Flow force on the valve spindle

*I*Single-port energy storage inertial element

*J*_{ld1}Load inertia connected with hydro-motor HM

_{1}*J*_{ld2}Load inertia connected with hydro-motor HM

_{2}*K*_{stf}Stiffness of the fluid at the respective plenum

*K*_{sp}Valve spring stiffness

*K*_{s}Bulk stiffness of the fluid at the pump plenum

*K*_{vp}Bulk stiffness of the fluid at the valve plenum

*K*_{bp}Bulk stiffness of the fluid at the plenum of the bypass port

*K*_{pr}Bulk stiffness of the fluid at the plenum of the priority port

*K*_{m1}Bulk stiffness of the fluid at the plenum of the hydro-motor HM1

*K*_{m2}Bulk stiffness of the fluid at the plenum of the hydro-motor HM2

*K*_{a}Generalized bulk stiffness of the fluid

*M*_{ld1}Angular momentum of the load connected with hydro-motor HM

_{1}*M*_{ld2}Angular momentum of the load connected with hydro-motor HM

_{2}*P*_{s}Supply pressure

*P*_{vp}Pressure at the valve inlet port

*P*_{pr}Priority pressure

*P*_{bp}Bypass pressure

*F*_{isp}Force due to inertia of valve spindle

*P*_{vp}Pressure on the valve spindle

- \(\Delta P_{\text{ct}}\)
Critical pressure difference across the valve port

*P*_{m1}Inlet pressure of hydro-motor HM

_{1}*P*_{m2}Inlet pressure of hydro-motor HM

_{2}*R*_{pr}Resistance of the priority port of the valve

*R*_{bp}Resistance of the bypass port of the valve

*R*_{lp}Pump leakage resistance

- \(R_{\text{ld1}}\)
Load resistance of hydro-motor HM

_{1}- \(R_{\text{ld2}}\)
Load resistance of hydro-motor HM

_{2}*R*_{lm1}Leakage resistance of the hydro-motor HM

_{1}*R*_{lm2}Leakage resistance of the hydro-motor HM

_{2}*R*_{sp}Valve spindle damping coefficient

*R*Single-port energy storage resistive elements

- SF
Single-port element that indicates source of flow

- SE
Single-port element that indicates source of effort

- TF
Two-port element that converts rotational speed into volume displacement rate and vice versa

- \(\dot{V}_{\text{cvp}}\)
Compressibility flow loss at the valve plenum

- \(\dot{V}_{\text{cpr}}\)
Compressibility flow loss at the priority port plenum

- \(\dot{V}_{\text{cbp}}\)
Compressibility flow loss at the bypass port plenum

- \(\dot{V}_{\text{lm}}\)
Leakage flow of the hydro-motor

- \(\dot{V}_{\text{lp}}\)
Pump leakage

- \(\dot{V}_{\text{cs}}\)
Compressibility flow loss at supply plenum

- \(\dot{V}_{\text{s}}\)
Pump supply

- \(\dot{V}_{\text{pr}}\)
Priority flow

- \(\dot{V}_{\text{pb}}\)
Bypass flow

- \(\dot{V}_{\ln 1}\)
Flow through the line connecting the priority port with plenum of the hydro-motor HM

_{1}- \(\dot{V}_{\ln 2}\)
Flow through the line connecting the bypass port with plenum of the hydro-motor HM

_{2}- \(\dot{V}_{\text{cm1}}\)
Compressibility flow loss at the plenum of the hydro-motor HM

_{1}- \(\dot{V}_{\text{cm2}}\)
Compressibility flow loss at the plenum of the hydro-motor HM

_{2}- \(\dot{V}_{\text{m1}}\)
Inlet flow of the hydro-motor HM

_{1}- \(\dot{V}_{\text{m2}}\)
Inlet flow of the hydro-motor HM

_{2}- \(\dot{V}_{\text{lm1}}\)
Leakage flow from the plenum of hydro-motor HM

_{1}- \(\dot{V}_{\text{lm2}}\)
Leakage flow from the plenum of hydro-motor HM

_{2}- \(\dot{V}_{\text{mo1}}\)
Outlet flow of the hydro-motor HM

_{1}- \(\dot{V}_{\text{mo2}}\)
Outlet flow of the hydro-motor HM

_{2}*V*_{a}Generalized specific volume

*ω*_{m}Generalized speed of the hydro-motor

*ω*_{m1}Speed of hydro-motor HM

_{1}*ω*_{m2}Speed of hydro-motor HM

_{2}- 0
Common effort junctions in bond graph model

- 1
Common flow junction in bond graph model

- ·
It indicates the time derivative of the variable

## Notes

## References

- 1.Wong T (2001) Hydraulic power steering system design and optimisation simulation. In: SAE 2001 World Congress. https://doi.org/10.4271/2001-01-0479
- 2.Feng G, Jiang F (2003) The principle development and applied research of the load sensing hydraulic system. Coal Mine Mach 9:27–29Google Scholar
- 3.Coskum G, Kolcuoglu T, Dogramacr T et al (2016) Analysis of priority flow control valve with hydraulic system simulation model. Braz Soc Mech Sci Eng. https://doi.org/10.1007/s40430-016-0691-7 CrossRefGoogle Scholar
- 4.Ould Bouamama B, Medjaher K, Samantaray AK et al (2006) Supervision of an industrial steam generator, Part I: bond graph modelling. Control Eng Pract 14(1):71–83CrossRefGoogle Scholar
- 5.Samantaray AK, Medjaher K, Ould-Bouamama B, Staroswiecki M, Dauphin-Tanguy G (2006) Diagnostic bond graphs for online fault detection and isolation. Simul Model Pract Theory 14(3):237–262CrossRefGoogle Scholar
- 6.Athanasatos P, Costopoulos T (2012) Proactive fault finding in a 4/3-way direction control valve of a high pressure hydraulic system using the bond graph method with digital simulation. Mech Mach Theory 50:64–89CrossRefGoogle Scholar
- 7.Isermann R (2005) Model-based fault-detection and diagnosis-status and applications. Annu Rev Control 29:71–85CrossRefGoogle Scholar
- 8.Medjaher K, Zerhouni N (2009) Residual-based failure prognostic in dynamic systems. IFAC Proc Vol 42(8):716–721CrossRefGoogle Scholar
- 9.Khorasgani H, Biswas G, Sankararaman S (2016) Methodologies for system-level remaining useful life prediction. Reliab Eng Syst Saf 154:8–18CrossRefGoogle Scholar
- 10.Zhao Z, Chang L (2011) Dynamic analysis of load sense steering hydraulic system priority valve. In: 2nd international conference on mechanic automation and control engineering. IEEE, Hohhot, China. ISBN: 978-1-4244-9436-1Google Scholar
- 11.Sueur C, Dauphin-Tanguy G (1989) Structural controllability/observability of linear systems represented by bond graphs. J Frankl Inst 326(6):869–883MathSciNetCrossRefGoogle Scholar
- 12.Prakash O, Samantaray AK (2017) Model-based diagnosis and prognosis of hybrid dynamical systems with dynamically updated parameters. Bond graphs for modelling. Control and fault diagnosis of engineering systems. Springer, Berlin, pp 195–232Google Scholar
- 13.Mukherjee A, Karmakar R, Samantaray AK (2006) Bond graph in modeling, simulation and fault identification. I.K. International Pvt. Ltd, New DelhiGoogle Scholar
- 14.Symbols 6.0, High Tech Consultants, Step, IIT, Kharagpur, IndiaGoogle Scholar
- 15.Hasan E, Dasgupta E, Ghoshal SK (2015) Comparison of the efficiency of the high speed low torque hydrostatic drives using bent axis motor: an experimental study. Proc Inst Mech Eng Part E J Process Mech Eng 231(4):650–666CrossRefGoogle Scholar
- 16.Cacho R, Felez J, Vera C (2000) Deriving simulation models from bond graphs with algebraic loops: the extension to multibond graph systems. J Frankl Inst 337(5):579–600CrossRefGoogle Scholar