ﻲﺑﺎﻳﺎﺟ ﻭ ﻱﺯﺎﺳﺭﺎﻜﺷﺁﺐﻴﻋ ﻪﺑ ﻡﻭﺎﻘﻣﻡﺪﻋ ﺖﻴﻌﻄﻗ ﻢﺘﺴﻴﺳ ﻱﺍﺮﺑﻱﺎﻫ ﻢﻛﺍﺮﺗﺮﻳﺬﭘ ﻪﺑﺪﻧﺎﺑ ﺵﻭﺭﮔﻑﺍﺮ

ﺪﻠﺟ 7 ﻩﺭﺎﻤﺷ ، 3 ﺰﻴﻳﺎﭘ ، 1392 ﻪﺤﻔﺻ ، 52 - 41

ﻲﺑﺎﻳﺎﺟ ﻭ ﻱﺯﺎﺳﺭﺎﻜﺷﺁ ﺐﻴﻋ

ﻪﺑ ﻡﻭﺎﻘﻣ ﻡﺪﻋ

ﺖﻴﻌﻄﻗ ﻢﺘﺴﻴﺳ ﻱﺍﺮﺑ

ﻱﺎﻫ ﻢﻛﺍﺮﺗ ﺮﻳﺬﭘ

ﻪﺑ ﺪﻧﺎﺑ ﺵﻭﺭ ﮔ

ﻑﺍﺮ

ﻲﻌﻧﺎﺻ ﺪﻤﺣﺍ ،

1

ﻩﺩﺍﺯ ﻦﻳﻮﻧ ﺖﺒﺤﺻﺎﺑ ﺎﺿﺮﻴﻠﻋ

2

ﻱﺍﺮﺘﻛﺩ ﻱﻮﺠﺸﻧﺍﺩ1

ﻲﺳﺪﻨﻬﻣ ﺎﻀﻓﺍﻮﻫ ﻩﻭﺮﮔ ، ﺯﺍﻭﺮﭘ ﻚﻴﻣﺎﻨﻳﺩ ﻩﺎﮕﺸﻧﺍﺩ ،

ﻲﺳﻮﻃ ﻦﻳﺪﻟﺍﺮﻴﺼﻧ ﻪﺟﺍﻮﺧ ﻲﺘﻌﻨﺻ

، asanei@mail.kntu.ac.ir

ﻳﺩﺎﺘﺳﺍ2

ﺭﺎ ﺓﺪﻜﺸﻧﺍﺩ ، ﻲﺳﺪﻨﻬﻣ ﺎﻀﻓﺍﻮﻫ ﻭﺮﮔ ، ﺯﺍﻭﺮﭘ ﻚﻴﻣﺎﻨﻳﺩ ﻩ ﻩﺎﮕﺸﻧﺍﺩ ،

ﻲﺳﻮﻃ ﻦﻳﺪﻟﺍﺮﻴﺼﻧ ﻪﺟﺍﻮﺧ ﻲﺘﻌﻨﺻ

، novinzadeh@kntu.ac.ir

ﻪﻟﺎﻘﻣ ﺖﻓﺎﻳﺭﺩ ﺦﻳﺭﺎﺗ) 14

/6 / 1392 ﻪﻟﺎﻘﻣ ﺵﺮﻳﺬﭘ ﺦﻳﺭﺎﺗ ، 25

/8 / 1392 (

ﻩﺪﻴﻜﭼ : ﻪﺑ ﻢﺘﺴﻴﺳ ﻥﺩﻮﺑ ﻲﻄﺧﺮﻴﻏ ﻞﻴﻟﺩ ﻢﻛﺍﺮﺗ ﻱﺎﻫ

ﻪﺑ ﻡﻭﺎﻘﻣ ﺐﻴﻋ ﻲﻳﺎﺳﺎﻨﺷ ،ﺮﻳﺬﭘ ﻡﺪﻋ

ﺖﻴﻌﻄﻗ ﻦﻳﺍ ﻱﺍﺮﺑ ﻉﻮﻧ ﻢﺘﺴﻴﺳ ﺩﺭﻮﻣ ﺮﺘﻤﻛ ﺎﻫ

ﻪﺟﻮﺗ ﻪﺘﻓﺮﮔﺭﺍﺮﻗ ﺖﺳﺍ ﻝﺪﻣ ﻪﻟﺎﻘﻣ ﻦﻳﺍ ﺭﺩ . ﺪﻧﺎﺑ

ﻑﺍﺮﮔ ﻪﺑ ﻡﺮﻓ ﻱﺍﺮﺑ ،LFT ﻩﺎﮕﺘﺳﺩ ﻱﺎﻫ ﻢﻛﺍﺮﺗ ﻩﺩﺍﺩ ﻪﻌﺳﻮﺗ ﺮﻳﺬﭘ ﻲﻣ

ﻥﺎﺸﻧ ﻪﻟﺎﻘﻣ ﻦﻳﺍ ﺞﻳﺎﺘﻧ .ﺩﻮﺷ

ﻲﻣ ﻲﻣ ﻑﺍﺮﮔﺪﻧﺎﺑ ﻲﻠﻋ ﺹﺍﻮﺧ ﻪﻛ ﺪﻫﺩ ﻱﺍﺮﺑ ﺪﻧﺍﻮﺗ

ﻪﺑ ﺖﺳﺩ ،ﻲﻠﻴﻠﺤﺗ ﻲﮕﻧﻭﺰﻓﺍ ﻂﺑﺍﻭﺭ ﻥﺩﺭﻭﺁ ﺭﻮﻀﺣ ﺭﺩ

ﻡﺪﻋ ﺖﻴﻌﻄﻗ ﺎﻫ ﺍﺮﻗ ﻩﺩﺎﻔﺘﺳﺍ ﺩﺭﻮﻣ ﺭ

.ﺩﺮﻴﮔ ﻪﺑ ﻑﺍﺮﮔﺪﻧﺎﺑ ﺯﺍ ﻩﺩﺎﻔﺘﺳﺍ ﺖﻳﺰﻣ ﻡﺮﻓ

ﻲﮕﻧﻭﺰﻓﺍ ﻂﺑﺍﻭﺭ .ﺖﺳﺍ ﻦﻴﻌﻣﺎﻧ ﻲﮕﻧﻭﺰﻓﺍ ﻂﺑﺍﻭﺭ ﺯﺍ ﻦﻴﻌﻣ ﻲﻠﻴﻠﺤﺗ ﻲﮕﻧﻭﺰﻓﺍ ﻂﺑﺍﻭﺭ ﻥﺩﺮﻛ ﺍﺪﺟ ،LFT

ﻩﺪﻧﺎﻤﻴﻗﺎﺑ ﻪﺒﺳﺎﺤﻣ ﻱﺍﺮﺑ ﻦﻴﻌﻣ ﻲﻠﻴﻠﺤﺗ ﻲﻘﻴﺒﻄﺗ ﻪﻧﺎﺘﺳﺁ ﻪﺒﺳﺎﺤﻣ ﻱﺍﺮﺑ ﻦﻴﻌﻣﺎﻧ ﻲﻠﻴﻠﺤﺗ ﻲﮕﻧﻭﺰﻓﺍ ﻂﺑﺍﻭﺭ ﻭ ،ﺎﻫ

ﻩﺪﻧﺎﻤﻴﻗﺎﺑ ﺖﻴﺳﺎﺴﺣ ﺰﻴﻟﺎﻧﺁ ﻭ ﺎﻫ

ﺩﺭﻮﻣ

ﻔﺘﺳﺍ ﻲﻣ ﺭﺍﺮﻗ ﻩﺩﺎ ﻝﺪﻣ ،ﻥﺎﻳﺎﭘ ﺭﺩ .ﺩﺮﻴﮔ ﻱﺎﻫ

ﻪﻌﺳﻮﺗ ﻩﺩﺍﺩ ﻩﺪﺷ ﻲﻣ ﻲﺠﻨﺳ ﺭﺎﺒﺘﻋﺍ ﻲﺷﺯﻮﻣﺁ ﻝﺎﺜﻣ ﻚﻳ ﻖﻳﺮﻃ ﺯﺍ ، ﻮﺷ

ﻧ .ﺪ

:ﻱﺪﻴﻠﻛ ﺕﺎﻤﻠﻛ ،ﻑﺍﺮﮔﺪﻧﺎﺑ

ﻱﺯﺎﺳﺭﺎﻜﺷﺁ

،ﻲﻠﻴﻠﺤﺗ ﻲﮕﻧﻭﺰﻓﺍ ﻂﺑﺍﻭﺭ ،ﺐﻴﻋ ﻲﺑﺎﻳﺎﺟ ﻭ ﻡﺪﻋ

ﺖﻴﻌﻄﻗ

، ﻝﺎﻴﺳ ﻢﻛﺍﺮﺗ ﺮﻳﺬﭘ .

Robust Fault Detection and Isolation to Compressible Systems Using Bond Graph Approach

Ahmad Sanei, Alireza Basohbat Novinzadeh

Abstract: In the papers published on Fault Detection and Isolation(FDI) using Bond Graph approach, robust FDI in the compressible flow systems has less been developed in the literature, due to the strong nonlinearities in this systems. In this paper, Bond Graph model in LFT form is developed for compressible systems. The results of this research are shown the causal properties of bond graph can be used to obtain the Analytical Redundancy Relations (ARRs) in presence of parameter uncertainties. The advantage of the bond graph model in LFT form is generation of ARRs and decoupling of the nominal part from the uncertain part. The nominal part can be used to calculate of the residual and the uncertain part can be used to obtain of adaptive thresholds and sensitivity analysis. In the following, the developed model is validated by pedagogical example.

Keywords: Bond Graph, Fault Detection and Isolation (FDI), Analytically Redundancy Relations (ARRs)

,

Uncertainties, Compressible fluid.

1 -

0B

ﻪﻣﺪﻘﻣ

ﺵﻭﺭ ﻩﺯﻭﺮﻣﺍ ﺭﺎﻜﺷﺁ ﻱﺎﻫ

ﺐﻴﻋ ﻲﺑﺎﻳﺎﺟ ﻭ ﻱﺯﺎﺳ (FDI)^P0F

1

Pﻪﺑ

ﺭﻮﻃ

ﻩﺩﺮﺘﺴﮔ ﻱﺍ ﻲﻣ ﺭﺍﺮﻗ ﻩﺩﺎﻔﺘﺳﺍ ﺩﺭﻮﻣ ﻝﺮﺘﻨﻛ ﻢﺘﺴﻴﺳ ﺭﺩ ﺮﻴﮔ

ﻧ ﺵﻭﺭ .ﺪ ﻱﺎﻫ

1. Fault Detection & Isolation (FDI)

ﺭﺎﻜﺷﺁ ﻱﺍﺮﺑ ﻲﻔﻠﺘﺨﻣ ﻩﺪﺷ ﺩﺎﻬﻨﺸﻴﭘ ﺐﻴﻋ ﻲﺑﺎﻳﺎﺟ ﻭ ﻱﺯﺎﺳ

ﻲﻣ ﻪﻛ ﺖﺳﺍ -

ﻝﺪﻣ ﻱﺎﻨﺒﻣ ﺮﺑ ﻪﺘﺳﺩ ﻭﺩ ﻪﺑ ﺍﺭ ﺎﻬﻧﺁ ﻥﺍﻮﺗ

P1F

2

Pﻝﺪﻣ ﻱﺎﻨﺒﻣ ﻥﻭﺪﺑ ﻭ

P2F

3

Pﻢﻴﺴﻘﺗ -

ﺩﻮﻤﻧ ﻱﺪﻨﺑ 1]

- 3 . [ 2. Model based

3. Non-Model based

ﻲﻔﻴﻛ ﺵﻭﺭ ﻭﺩ ﻪﺑ ،ﻕﻮﻓ ﺵﻭﺭ ﻭﺩ ﺯﺍ ﻚﻳ ﺮﻫ

P3F

1

Pﻲﻤﻛ ﻭ

P4F

2

Pﻢﻴﺴﻘﺗ ﻱﺪﻨﺑ

ﻲﻣ .ﺪﻧﻮﺷ ﺎﻳ ﻭ ﻡﻮﻠﻌﻣﺎﻧ ﻝﺪﻣ ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﺎﻣﺍ ﻡﻮﻠﻌﻣ ﻝﺪﻣ ﻲﻠﻛ ﺭﺎﺘﺧﺎﺳ ﺮﮔﺍ

ﻱﺍﺭﺍﺩ ﻡﺪﻋ ﺖﻴﻌﻄﻗ ﻲﻔﻴﻛ ﺵﻭﺭ ﺪﺷﺎﺑ ﻱﺩﺎﻳﺯ

، ﻭ ﺭﺩ ﻦﻳﺍﺮﻴﻏ ﺕﺭﻮﺻ ﺵﻭﺭ

ﻲﻣ ﺩﺎﻬﻨﺸﻴﭘ ﻲﻤﻛ .ﺩﺩﺮﮔ

ﺮﮕﻳﺩ ﻑﺮﻃ ﺯﺍ ﺩ

ﻢﺘﺴﻴﺳ ﺭ

،ﻲﻌﻗﺍﻭ ﻱﺎﻫ

ﻪﺑ ﻞﻴﻟﺩ ﻩﺯﺍﺪﻧﺍ ﻱﺎﻫﺰﻳﻮﻧ ﺩﻮﺟﻭ -

ﻦﻴﻤﺨﺗ ﺭﺩ ﻩﺎﺒﺘﺷﺍ ﺎﻳ ﻭ ﻲﺘﺧﺎﺳ ﻱﺎﻬﺴﻧﺍﺮﻠﺗ ،ﻢﺘﺴﻴﺳ ﺕﺎﺷﺎﺸﺘﻏﺍ ،ﻱﺮﻴﮔ ،ﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻡﺪﻋ ﺖﻴﻌﻄﻗ ﻱﺍﺮﺑ ﻦﻳﺍﺮﺑﺎﻨﺑ .ﺩﺭﺍﺪﻧ ﺩﻮﺟﻭ ﺮﻔﺻ ﺭﺩ

ﺮﻈﻧ ﻦﺘﻓﺮﮔ

ﻡﺪﻋ ﺖﻴﻌﻄﻗ ﻢﺘﺴﻴﺳ ﺯﺍ ﻲﻘﻴﻗﺩ ﻝﺪﻣ ﺖﺳﺍ ﻡﺯﻻ ﺍﺪﺘﺑﺍ ،ﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﺎﺑ ﺍﺭ

ﻦﺘﻓﺮﮔﺮﻈﻧﺭﺩ ﻡﺪﻋ

ﺖﻴﻌﻄﻗ ﻪﺑ ﺖﺳﺩ ﺱﺎﺳﺍ ﻦﻳﺍ ﺮﺑ .ﺩﺭﻭﺁ

، ﻦﻴﻳﺎﭘ ﻭ ﻻﺎﺑ ﺩﻭﺪﺣ

ﺯﺍ ﻲﺷﺎﻧ ﻡﺪﻋ ﺖﻴﻌﻄﻗ ﻱﺎﻫ ﺐﻴﻋ ﻥﻼﻋﺍ ﻪﻧﺎﺘﺳﺁ ﺩﻭﺪﺣ ﺭﺩ ﻱﺮﺘﻣﺍﺭﺎﭘ

ﻩﺪﺷﺮﺸﺘﻨﻣ ﻭ ﻪﻧﺎﺘﺳﺁ ﺎﻫ ﻲﻣ ﻞﻜﺷ ﻩﺪﻧﺎﻤﻴﻗﺎﺑ ﻪﻛ ﻲﻧﺎﻣﺯ ،ﻂﻳﺍﺮﺷ ﻦﻳﺍ ﺭﺩ .ﺪﻧﺮﻴﮔ -

ﺝﺭﺎﺧ ﺎﻫ ﺯﺍ ﺭﺍﺮﻗ ﻪﻧﺎﺘﺳﺁ ﺪﻧﺮﻴﮔ ﻢﺘﺴﻴﺳ ، ﺭﺍﺪﺸﻫ ﻱﺎﻫ ﻩﺪﻨﻫﺩ ﻥﻼﻋﺍ ﺐﻴﻋ

، ﻝﺎﻌﻓ

ﻲﻣ .ﺪﻧﻮﺷ ﺮﻃ ﺭﺩ ﻝﻭﺍ ﻡﺎﮔ ﻢﺘﺴﻴﺳ ﻲﺣﺍ

ﺶﻳﺎﭘ ﺮﺑ ﻱﺎﻨﺒﻣ ،ﻝﺪﻣ ﻪﺑ ﺖﺳﺩ ﻝﺪﻣ ﻥﺩﺭﻭﺁ

ﻢﺘﺴﻴﺳ ﻲﺿﺎﻳﺭ

، ﻡﺪﻋ ﺖﻴﻌﻄﻗ ﺎﻫ ﺵﻭﺭ .ﺖﺳﺍ ﻝﺪﻣ ﻱﺍﺮﺑ ﻱﺩﺎﻳﺯ ﻱﺎﻫ

ﻱﺯﺎﺳ

ﻢﺘﺴﻴﺳ ﻩﺪﺷ ﺩﺎﻬﻨﺸﻴﭘ ﻲﻜﻴﻣﺎﻨﻳﺩ ﻱﺎﻫ ﻪﻛ ﻑﺍﺮﮔﺪﻧﺎﺑ ﺵﻭﺭ ﻥﺎﻴﻣ ﻦﻳﺍ ﺭﺩ ﺎﻣﺍ ،ﺪﻧﺍ

ﺮﺑ ﺱﺎﺳﺍ ﻲﻣ ﺭﺎﻛ ﻱژﺮﻧﺍ ﻥﺯﺍﻮﺗ ﺭﺎﻛ ﺯﺍ ﻲﻜﻳ ،ﺪﻨﻛ

ﺪﻣﺁ ﺵﻭﺭ ﻦﻳﺮﺗ ﺎﻫ ﻪﺑ ﺭﺎﻤﺷ

ﻲﻣ ﻦﻳﺍ ﻪﭼﺮﮔﺍ .ﺩﻭﺭ ﻝﺎﺳ ﺭﺩ ﺭﺎﺑ ﻦﻴﻟﻭﺍ ﺵﻭﺭ

1966 ﺮﺘﻨﻳﺎﭘ ﻂﺳﻮﺗ 4]

[ ﻪﺑ ﻭ -

ﻝﺪﻣ ﺭﻮﻈﻨﻣ ﻢﺘﺴﻴﺳ ﺖﻟﺎﺣ ﺕﻻﺩﺎﻌﻣ ﺝﺍﺮﺨﺘﺳﺍ ﻭ ﻱﺯﺎﺳ ﻲﻓﺮﻌﻣ ﻲﻜﻴﻣﺎﻨﻳﺩ ﻱﺎﻫ

ﺎﻣﺍ ،ﺪﺷ

ًﺍﺪﻌﺑ ) ﺶﻧﺍﺩﺮﮔﺎﺷ ﻂﺳﻮﺗ ﻮﻧﺭﺎﻛ

ﻱﺍﺮﺑ ( ﻢﺘﺴﻴﺳ ﻲﻳﺎﻫ ﻩﺯﻮﺣ ﺎﺑ ﻪﻛ ﻱﺎﻫ

ﻭ ﺮﺳ(... ﻭ ﻲﻜﻴﻣﺎﻨﻳﺩﻮﻣﺮﺗ ،ﻲﻳﺎﻴﻤﻴﺷ ،ﻲﻜﻳﺮﺘﻜﻟﺍ ،ﻲﻜﻴﻧﺎﻜﻣ) ﻱژﺮﻧﺍ ﻒﻠﺘﺨﻣ ﺪﻧﺭﺍﺩ ﺭﺎﻛ

، ﺗ ﻪﻌﺳﻮ ﻩﺩﺍﺩ ﺪﺷ 5] ﻝﺎﺳ ﺭﺩ .[ 1999 ﻱﺎﻗﺁ ﻦﻴﻔﻟﺩ - ﻦﻳﺍ ﺯﺍ ﻱﻮﮕﻧﺎﺗ

ﻝﺮﺘﻨﻛ ﻦﻴﻴﻌﺗ ﻱﺍﺮﺑ ﺵﻭﺭ ﻩﺪﻫﺎﺸﻣ ﻭ ﺮﻳﺬﭘ

ﻩﺩﺎﻔﺘﺳﺍ ﻢﺘﺴﻴﺳ ﻚﻳ ﻥﺩﻮﺑ ﺮﻳﺬﭘ

]ﺩﻮﻤﻧ 6 ﻝﺎﺳ ﺭﺩ ﻥﺁ ﺯﺍ ﺪﻌﺑ .[

2001 ﻭ ﺺﻴﺨﺸﺗ ﻱﺍﺮﺑ ﻑﺍﺮﮔﺪﻧﺎﺑ ﺵﻭﺭ

ﺐﻴﻋ ﻲﺑﺎﻳﺎﺟ ﺖﻓﺎﻳ ﻪﻌﺳﻮﺗ

]7 8, ﺩ ﺍﺮﻴﺧﺍ .[

ﺟ ﺷﻭﺭ ﺶﻧﺍﺭﺎﻜﻤﻫ ﻭ ﻱﺭﺰ ﻲ

ﺍﺭ

ﻭ ﺺﻴﺨﺸﺗ ﻱﺍﺮﺑ ﻴﻋ ﻲﺑﺎﻳﺎﺟ

ﺐ ﻡﺪﻋ ﺭﻮﻀﺣ ﺭﺩ ﺖﻴﻌﻄﻗ

ﻩﺩﻮﻤﻧ ﻪﺋﺍﺭﺍ ﺎﻫ ﺪﻧﺍ

، ﻪﻛ

ﻪﺑ ﻡﺮﻓ ﻥﺍﻮﻨﻋ LFT^P5F

3

Pﻩﺪﺷ ﻪﺘﺧﺎﻨﺷ ﺖﺳﺍ

9،10] ﻡﺮﻓ ﻪﺑ ﻑﺍﺮﮔﺪﻧﺎﺑ ﺖﻳﺰﻣ . [

ﻲﻠﻴﻠﺤﺗ ﻲﮕﻧﻭﺰﻓﺍ ﻂﺑﺍﻭﺭ ﻪﻛ ﺖﺳﺍ ﻦﻳﺍLFT ARRs)^P6F

4

P(

ﻪﺑ ﻦﻴﻌﻣﺎﻧ ﻭ ﻦﻴﻌﻣ -

ﻲﻣ ﺝﺍﺮﺨﺘﺳﺍ ﻑﺍﺮﮔﺪﻧﺎﺑ ﻝﺪﻣ ﺯﺍ ﻚﻴﺗﺎﻤﺘﺴﻴﺳ ﺭﻮﻃ ﻦﻴﻌﻣ ﺖﻤﺴﻗ .ﺩﻮﺷ

ﻥﺎﻤﻫ ،

ﻦﺘﻓﺮﮔﺮﻈﻧﺭﺩ ﻥﻭﺪﺑARRs ﻡﺪﻋ

ﻗ ﺖﻴﻌﻄ ﺖﺳﺍ

، ﻩﺪﻧﺎﻤﻴﻗﺎﺑ ﻪﺒﺳﺎﺤﻣ ﻱﺍﺮﺑ ﻪﻛ ﺎﻫ

ﻲﻣ ﺭﺍﺮﻗ ﻩﺩﺎﻔﺘﺳﺍ ﺩﺭﻮﻣ ﺖﻤﺴﻗ .ﺪﻧﺮﻴﮔ

ﻞﻣﺎﺷ ﻪﻛ ﺰﻴﻧ ﻦﻴﻌﻣﺎﻧ ﻡﺪﻋ

ﺖﻴﻌﻄﻗ ﺎﻫ

ﻪﻧﺎﺘﺳﺁ ﻪﺒﺳﺎﺤﻣ ﻱﺍﺮﺑ ،ﺖﺳﺍ ﻲﻣ ﺭﺍﺮﻗ ﻩﺩﺎﻔﺘﺳﺍ ﺩﺭﻮﻣ ﺎﻫ

.ﺩﺮﻴﮔ

ﺭﺩ ﻥﻮﻨﻛﺎﺗ ﻪﻛ ﻲﺗﻻﺎﻘﻣ ﺭﺩ ﺹﻮﺼﺧ

ﻪـﺑFDI ﻑﺍﺮﮔﺪـﻧﺎﺑ ﺵﻭﺭ

ﺮـﺸﺘﻨﻣ

ﻩﺪﺷ

، ﻪﺑ ﻌﻄﻗ ﻡﺪﻋ ﻴ ﺖ ﻢﺘﺴﻴﺳ ﺭﺩ ﻱﺎﻫ ﺬﭘ ﻢﻛﺍﺮﺗ ﻳﺮ ﺖﺳﺍ ﻩﺪﺸﻧ ﻪﺘﺧﺍﺩﺮﭘ .

ﻦﻤﻬﺑ

ﻝﺪــﻣ ،ﻪــﻟﺎﻘﻣ ﻦــﻳﺍ ﺭﺩ ﻞــﻴﻟﺩ ﻌﻄﻗ ﻡﺪــﻋ

ــﻴ ﺖ ﻡﺮــﻓ ﻪــﺑ ﻝﺯﺎــﻧ ﻥﺍﺪــﻴﻣ ﻱﺍﺮــﺑLFT

ﺕﻻﺎﻴﺳ ﻲﺘﻴﻓﺮﻇ ﻥﺍﺪﻴﻣ ﻭ ﻚﻴﭘﻭﺮﺘﻧﺰﻳﺁ ﺬﭘ ﻢﻛﺍﺮﺗ

ﻳﺮ ﻩﺩﺍﺩ ﻥﺎـﺸﻧ ﻭ ﻪﻌﺳﻮﺗ ﻲـﻣ

-

ﺩﻮﺷ ﻪﻛ ﻲﻣ ﻑﺍﺮﮔﺪﻧﺎﺑ ﻲﻠﻋ ﺹﺍﻮﺧ ﻲـﻠﻴﻠﺤﺗ ﻲـﮕﻧﻭﺰﻓﺍ ﻂﺑﺍﻭﺭ ﺪﻧﺍﻮﺗ

ARRs

ﻪﺑ ﺍﺭ ﻪﻧﻮﮔ ﻡﺮﻓ ﺯﺍ ﻱﺍ ﺍ ﻂﺑﺍﻭﺭ ﻪﻛ ﺪﻨﻛ ﺝﺍﺮﺨﺘﺳﺍLFT

ﻞﻣﺎـﺷ ﻲـﻠﻴﻠﺤﺗ ﻲﮕﻧﻭﺰﻓ

ﺖﻬﺟ ﻦﻴﻌﻣ ﺖﻤﺴﻗ ﺯﺍ .ﺪﻨﺷﺎﺑ ﻦﻴﻌﻣﺎﻧ ﺖﻤﺴﻗ ﻭ ﻦﻴﻌﻣ ﺖﻤﺴﻗ ﺖﺳﺩ ﻪﺑ

ﻥﺩﺭﻭﺁ

1. Qualitative 2. Quantitative

3. Linear fractional transformation 4. Analytically Redundancy Relations(ARRs)

ﻩﺪﻧﺎﻤﻴﻗﺎﺑ ﺖﻬﺟ ﻦﻴﻌﻣﺎﻧ ﺖﻤﺴﻗ ﺯﺍ ﻭ ﺎﻫ ﺖﺳﺩ ﻪﺑ

ﻪﻧﺎﺘـﺳﺁ ﻥﺩﺭﻭﺁ ﻲـﻘﻴﺒﻄﺗ ﻱﺎـﻫ

ﻩﺩﺎﻔﺘﺳﺍ ﻲﻣ ﺩﻮﺷ . ﺵﻭﺭ ﻚــﻳ ﻑﺍﺮﮔﺪــﻧﺎﺑ ﺵﻭﺭ ﻪــﻛ ﻲﻳﺎــﺠﻧﺁ ﺯﺍ ﺮــﮕﻳﺩ ﻑﺮــﻃ ﺯﺍ

ﻪـﺑ ﺍﺭ ﺖـﻟﺎﺣ ﺕﻻﺩﺎﻌﻣ ﻪﻛ ﺖﺳﺍ ﻲﻜﻴﻓﺍﺮﮔ ﻴﺗﺎﻤﺘـﺴﻴﺳ ﺕﺭﻮـﺻ

ﺝﺍﺮﺨﺘـﺳﺍ ﻚ

ﻲـــﻣ ﻡﺮـــﻧ ﻭ ﺪـــﻨﻛ ﻩﺪـــﺷ ﻪـــﺋﺍﺭﺍ ﺹﻮـــﺼﺧ ﻦـــﻳﺍ ﺭﺩ ﻱﺩﺎـــﻳﺯ ﻱﺎـــﻫﺭﺍﺰﻓﺍ

-

ﺪﻧﺍ ) Symbols2000 11]

،[ 20-Sim 12] ﻭ ،[ ]Ms1 13 ([ ﻩﺩﺍﺩ ﻪﻌﺳﻮﺗ ﻝﺪﻣ ،

ﻥﺎـﻳﺎﭘ ﺭﺩ .ﺩﻮﺑﺪـﻫﺍﻮﺧ ﺰﻴﻧ ﻕﻮﻓ ﻱﺎﻫﺭﺍﺰﻓﺍ ﻡﺮﻧ ﺭﺩ ﺍﺮﺟﺍ ﻞﺑﺎﻗ ﻪﻟﺎﻘﻣ ﻦﻳﺍ ﺭﺩ ﻩﺪﺷ ﺭﺍﺰـﻓﺍ ﻡﺮـﻧ ﻂـﺳﻮﺗ ﻭ ﻩﺩﺎـﺳ ﻝﺎـﺜﻣ ﻚـﻳ ﺐـﻟﺎﻗ ﺭﺩ ﻩﺪﺷ ﻩﺩﺍﺩ ﻪﻌﺳﻮﺗ ﻝﺪﻣ ﺰﻴﻧ 20Sim ﻲﺠﻨﺳ ﺭﺎﺒﺘﻋﺍ ﻲﻣ

ﺩﻮﺷ .

2 -

1B

ﻲﻠﻴﻠﺤﺗ ﻲﮕﻧﻭﺰﻓﺍ ﻂﺑﺍﻭﺭ (ARRs)

ﺐﻴﻋ ﻲﺑﺎﻳﺎﺟ ﻭ ﻲﻳﺎﺳﺎﻨﺷ ﺭﺩ (FDI)

ﺭﺩ .ﺩﺭﺍﺩ ﺩﻮﺟﻭ ﻩﺎﮔﺪﻳﺩ ﻭﺩ ،

ﻪﻧﻮﻤﻧ ﺭﺎﺑ ﺮﻫ ﺭﺩ ﻝﻭﺍ ﻩﺎﮔﺪﻳﺩ ﻝﺪﻣ ﻲﺟﻭﺮﺧ ﻭ ﻩﺩﺍﺩ ﻝﺪﻣ ﻪﺑ ﻱﺩﻭﺭﻭ ،ﻱﺭﺍﺩﺮﺑ

ﻲﻣ ﻪﺒﺳﺎﺤﻣ ﻪﺑ ،ﻲﻌﻗﺍﻭ ﻢﺘﺴﻴﺳ ﻭ ﻝﺪﻣ ﻲﺟﻭﺮﺧ ﻑﻼﺘﺧﺍ .ﺩﺩﺮﮔ

ﻥﺍﻮﻨﻋ

ﻪﺑ ﻩﺪﻧﺎﻤﻴﻗﺎﺑ ﻲﻣ ﺖﺳﺩ ) ﺪﻳﺁ ﻞﻜﺷ 1 ﺩﺎﻌﺑﺍ ﻪﺑ ﻪﺘﺴﺑ ﻪﺒﺳﺎﺤﻣ ﻦﻳﺍ ﻥﺎﻣﺯ .((ﻒﻟﺍ)

ﻪﺑ ﺖﺳﺍ ﻦﻜﻤﻣ ﻝﺪﻣ ﻲﮔﺪﻴﭽﻴﭘ ﻭ ﻥﺩﻮﺑ ﻲﻄﺧﺮﻴﻏ ،ﻢﺘﺴﻴﺳ ﺪﺷﺎﺑ ﺩﺎﻳﺯ ﻱﺭﺪﻗ

ﻡﺎﮕﻨﻫ ﻪﺑ ﻪﺒﺳﺎﺤﻣ ﻥﺎﻜﻣﺍ ﻪﻛ

P7F

5

Pﻪﺘﺷﺍﺪﻧ ﺩﻮﺟﻭ ﺪﺷﺎﺑ

ﻩﺎﮔﺪﻳﺩ ﺯﺍ ﻪﻛ ﺖﺳﺎﺠﻨﻳﺍ

.

ﻪﺑ ﻡﻮﺳﻮﻣ ﻲﻠﻴﻠﺤﺗ ﻲﮕﻧﻭﺰﻓﺍ ﻂﺑﺍﻭﺭ ﺯﺍ ﻩﺩﺎﻔﺘﺳﺍ ﺎﻳ ﻡﻭﺩ ARRs

ﻲﻣ ﻩﺩﺎﻔﺘﺳﺍ

ﻱﺎﻫﺪﻴﻗ ﺵﻭﺭ ﻦﻳﺍ ﺭﺩ .ﺩﻮﺷ ﻪﺑ ﻲﻤﺘﺴﻴﺳ

ﻪﻧﻮﮔ ﻲﻣ ﻪﺘﺷﻮﻧ ﻱﺍ ﻂﻘﻓ ﻪﻛ ﺪﻧﻮﺷ

ﻪﺑ .ﺪﻨﺷﺎﺑ ﻡﻮﻠﻌﻣ ﻱﺎﻫﺮﻴﻐﺘﻣ ﻞﻣﺎﺷ ﺮﮕﻳﺩ ﺕﺭﺎﺒﻋ

ARRs ﻭ ﻲﻜﻴﺗﺎﺘﺳﺍ ﻱﺎﻫﺪﻴﻗ

ﻱﺩﻭﺭﻭ ،ﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻞﻣﺎﺷ) ﻡﻮﻠﻌﻣ ﺮﻳﺩﺎﻘﻣ ﻪﻛ ﺪﻨﺘﺴﻫ ﻲﻜﻴﻣﺎﻨﻳﺩ ﻭ ﻱﺎﻫ

ﻲﺟﻭﺮﺧ ﻩﺯﺍﺪﻧﺍ ﻱﺎﻫ ﻪﺑ ﺍﺭ (ﻩﺪﺷ ﻱﺮﻴﮔ ﻂﺒﺗﺮﻣ ﺮﮕﻳﺪﻤﻫ

ﻲﻣ ﻞﻜﺷ)ﺪﻨﻛ 1

.((ﺏ)

ﻞﻜﺷ 1 ﻱﺍﺮﺑ ﻒﻠﺘﺨﻣ ﻩﺎﮔﺪﻳﺩ ﻭﺩ : ﻩﺪﻧﺎﻤﻴﻗﺎﺑ ﺪﻴﻟﻮﺗ

ﻩﺪﺷ ﻩﺩﺎﻔﺘﺳﺍ ﻡﻭﺩ ﻩﺎﮔﺪﻳﺩ ﺯﺍ ﺐﻴﻋ ﻲﻳﺎﺳﺎﻨﺷ ﻱﺍﺮﺑ ﻪﻟﺎﻘﻣ ﻦﻳﺍ ﺭﺩ ﻪﻛ ،ﺖﺳﺍ

ﻲﻠﻴﻠﺤﺗ ﻲﮕﻧﻭﺰﻓﺍ ﻂﺑﺍﻭﺭ ﻦﺘﺷﺍﺩ ﻥﺁ ﻪﻣﺯﻻ (ARRs)

ﻱﺍﺮﺑ ﻦﻴﻨﭽﻤﻫ .ﺖﺳﺍ

ﺝﺍﺮﺨﺘﺳﺍ ﻡﺪﻋ ﻦﺘﻓﺮﮔﺮﻈﻧﺭﺩﺎﺑARRs

ﻩﺩﺎﻔﺘﺳﺍ ﻑﺍﺮﮔﺪﻧﺎﺑ ﺵﻭﺭ ﺯﺍ ،ﺖﻴﻌﻄﻗ

ﻲﻣ ﺩﻮﺷ

.

ﺳﺩ ﺪﻨﭼ ﻪﺑ ﻩﺪﺷ ﻪﺘﺧﺎﻨﺷ ﻱﺎﻫﺮﻴﻐﺘﻣ ﻑﺍﺮﮔﺪﻧﺎﺑ ﺵﻭﺭ ﺭﺩ ﻲﻣ ﻢﻴﺴﻘﺗ ﻪﺘ

-

) ﻊﺑﺎﻨﻣ .ﺪﻧﻮﺷ Se

f ﻭ )ﻩﺪﺷ ﻞﻳﺪﻌﺗ ﻊﺑﺎﻨﻣ ،(S

MSe f ﻭ ﺮﻳﺩﺎﻘﻣ ،(MS

ﻩﺯﺍﺪﻧﺍ ) ﺎﻫﺭﻮﺴﻨﺳ ﺯﺍ ﻩﺪﺷ ﻱﺮﻴﮔ De

f ﻭ ﻱﺩﻭﺭﻭ ﻭ ﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻭ ( D ﻱﺎﻫ

) ﻢﺘﺴﻴﺳ ﻭθ (u ﻦﻳﺍﺮﺑﺎﻨﺑ . :

5. On-line

0 ) , , , , , , , (

:f D D S S MS MS uθ =

ARR _{e f e f e f} ( )1

ﻥﺎﻤﻫ ﺖﻴﻠﻋ ﺺﺧﺎﺷ ﺹﺍﻮﺧ ﺯﺍ ﻩﺩﺎﻔﺘﺳﺍ ﻱﺭﺎﺘﻓﺭ ﻑﺍﺮﮔﺪﻧﺎﺑ ﺭﺩ ﻪﻛ ﺭﻮﻃ

P8F

1

P

ﻪﺑ ﺭﺩ ﻲﻤﻬﻣ ﺶﻘﻧ ﺝﺍﺮﺨﺘﺳﺍ ﺭﺩ ،ﺪﻨﺘﺷﺍﺩ ﺖﻟﺎﺣ ﺕﻻﺩﺎﻌﻣ ﻥﺩﺭﻭﺁ ﺖﺳﺩ

ﺎﺑ ﺎﻣﺍ .ﺪﺷﺪﻫﺍﻮﺧ ﻩﺩﺎﻔﺘﺳﺍ ﺹﺍﻮﺧ ﻦﻳﺍ ﺯﺍ ﺰﻴﻧ ﺎﻫARRs ﺖﺷﺍﺩ ﻪﺟﻮﺗ ﻲﺘﺴﻳ

ﻩﺩﺎﻔﺘﺳﺍ ﺖﻟﺎﺣ ﺕﻻﺩﺎﻌﻣ ﺝﺍﺮﺨﺘﺳﺍ ﺖﻬﺟ ﻱﺭﺎﺘﻓﺭ ﻑﺍﺮﮔﺪﻧﺎﺑ ﺯﺍ ﻪﻛ ﻲﻣﺎﮕﻨﻫ ﻲﻣ ﺩﻮﺷ ﻩﺯﺍﺪﻧﺍ ﺮﻳﺩﺎﻘﻣ ، ﻪﺑ ،ﺎﻫﺭﻮﺴﻨﺳ ﻂﺳﻮﺗ ﻩﺪﺷ ﻱﺮﻴﮔ

ﻲﺟﻭﺮﺧ ﻥﺍﻮﻨﻋ

ﻲﻣ ﻞﻤﻋ ﻢﺘﺴﻴﺳ ﺺﺧﺎﺷ ،ﺖﻟﺎﺣ ﻦﻳﺍ ﺭﺩ ﻦﻳﺍﺮﺑﺎﻨﺑ .ﺪﻨﻨﻛ

ﻱﺍﺮﺑ ﺖﻴﻠﻋ ﻱﺎﻫ

ﻩﺯﺍﺪﻧﺍ ﻱﺎﻫﺭﻮﺴﻨﺳ ﻲﻌﺳ ﻱﺮﻴﮔ

، ﻪﺑ ﻞﻜﺷ ﺕﺭﻮﺻ 2

(ﻒﻟﺍ) ﻩﺩﺍﺩ ﻥﺎﺸﻧ ﻲﻣ -

ﺷ ﺩﻮ ] 14 ، 15 ﻲﻟﺎﺣﺭﺩ .[

ﻱﺍﺮﺑ ﻑﺍﺮﮔﺪﻧﺎﺑ ﺯﺍ ﻲﺘﻗﻭ ﻪﻛ ﺐﻴﻋ ﻲﺑﺎﻳﺎﺟ

ﻩﺩﺎﻔﺘﺳﺍ

ﻲﻣ ﺩﻮﺷ ﻩﺯﺍﺪﻧﺍ ﺮﻳﺩﺎﻘﻣ ، ﻪﺑ ،ﺎﻫﺭﻮﺴﻨﺳ ﻂﺳﻮﺗ ﻩﺪﺷ ﻱﺮﻴﮔ

ﻱﺩﻭﺭﻭ ﻥﺍﻮﻨﻋ

ﺺﺧﺎﺷ ﻥﺎﻜﻣ ،ﻥﺁ ﺎﺑ ﺐﺳﺎﻨﺘﻣ ﻭ ﻩﺩﺮﻛ ﻞﻤﻋ ﻢﺘﺴﻴﺳ ﺮﻴﻴﻐﺗ ﺰﻴﻧ ﺖﻴﻠﻋ ﻱﺎﻫ

ﻞﻜﺷ) ﺖﻓﺎﻳﺪﻫﺍﻮﺧ 2

ﻱژﺮﻧﺍ ﻑﺮﺼﻣ ﺎﻫﺭﻮﺴﻨﺳ ﺭﺩ ﻥﻮﭼ ﻲﻓﺮﻃ ﺯﺍ .((ﺏ)

ﺮﺑﺎﻨﺑ ،ﺩﺭﺍﺪﻧ ﺩﻮﺟﻭ ﻞﻜﺷ ﺭﺩ ﻦﻳﺍ

2 (ﺏ) ﺪﻧﺎﺑ ﺭﺩ ﻱﻭﺮﺸﻴﭘ ﺭﺍﺪﻘﻣ 4

ﺮﻔﺻ

:ﻲﻨﻌﻳ ﺖﺳﺍ 0

0

3

1

4= ⇒

∑

=

= i

fi

. f

ﻞﻜﺷ 2:

(ﺝ) ﻩﺪﺷ ﺱﻮﻜﻌﻣ ﺖﻟﺎﺣ ﺭﺩ ﻲﻌﺳ ﺭﻮﺴﻨﺳ (ﺏ) ﻲﻌﺳ ﺭﻮﺴﻨﺳ (ﻒﻟﺍ) ﻩﺪﻧﺎﻤﻴﻗﺎﺑ ﻦﻴﻴﻌﺗ ﻱﺍﺮﺑ ﻱﺯﺎﺠﻣ ﺭﻮﺴﻨﺳ

ﻪﺒﺳﺎﺤﻣ ﺍﺭ ﻩﺪﻧﺎﻤﻴﻗﺎﺑ ﺭﺍﺪﻘﻣ ﻪﻛ ﻱﺯﺎﺠﻣ ﺭﻮﺴﻨﺳ ﻒﻳﺮﻌﺗ ﻱﺍﺮﺑ ﻡﻮﻬﻔﻣ ﻦﻳﺍ ﺯﺍ ﻲﻣ ﻲﻣ ﻩﺩﺎﻔﺘﺳﺍ ﺪﻨﻛ ﻪﻛ ﺪﻨﺘﺴﻫ ﻲﻳﺎﻫﺭﻮﺴﻨﺳ ،ﻱﺯﺎﺠﻣ ﻱﺎﻫﺭﻮﺴﻨﺳ .ﺩﻮﺷ

ﺖﻣﻼﻋ ﺎﺑ ﺍﺭ ﺎﻬﻧﺁ ﻭ ﻪﺘﺷﺍﺩ ﻲﺗﺎﺒﺳﺎﺤﻣ ﺖﻴﻫﺎﻣ ﻲﻣ ﻥﺎﺸﻧ ‘*’

ﻫﺩ ﺪﻨ ﻞﻜﺷ) 2

ﻩﺪﻳﺍ ﺖﻟﺎﺣ ﺭﺩ .((ﺝ) ﻲﻣ ﺭﺎﻛ ﻲﻤﺳﺍ ﻂﻳﺍﺮﺷ ﺭﺩ ﻢﺘﺴﻴﺳ ﻪﻛ ﻝﺁ

ﺭﺍﺪﻘﻣ ،ﺪﻨﻛ

ﻩﺯﺍﺪﻧﺍ ﻱﺮﻴﮔ ﻲﺘﻟﺎﺣﺭﺩ ﻲﻟﻭ .ﺖﺳﺍ ﺮﻔﺻ ﺮﺑﺍﺮﺑ ،ﻱﺯﺎﺠﻣ ﺭﻮﺴﻨﺳ ﻂﺳﻮﺗ ﻩﺪﺷ -

ﺭﺎﻛ ﺏﻮﻴﻌﻣ ﺖﻟﺎﺣ ﺭﺩ ﻢﺘﺴﻴﺳ ﻪﻛ ﻲﻣ

ﻩﺪﻧﺎﻤﻴﻗﺎﺑ ﻚﻳ ﺎﻬﻧﺁ ﻲﺟﻭﺮﺧ ،ﺪﻨﻛ

ﻞﻜﺷ ﺭﺩ ﻦﻳﺍﺮﺑﺎﻨﺑ .ﺖﺷﺍﺩﺪﻫﺍﻮﺧ 2

(ﺝ) ﻞﺑﺎﻗ ﺮﻳﺯ ﻪﻄﺑﺍﺭ ﺯﺍ ﻲﮕﻧﻭﺰﻓﺍ ﻂﺑﺍﻭﺭ

ﺩﻮﺑﺪﻫﺍﻮﺧ ﻪﺒﺳﺎﺤﻣ :

0 0

3

1 4

5= = ⇒ = =

=

∑

= i

fi

ARR f

f

ARR ( )2

،ﻩﺪﺷ ﺱﻮﻜﻌﻣ ﻥﺁ ﺖﻴﻠﻋ ﺺﺧﺎﺷ ﻪﻛ ﻱﺭﻮﺴﻨﺳ ﺩﺭﻮﻣ ﺭﺩ ﻝﻻﺪﺘﺳﺍ ﻦﻴﻤﻫ ﻩﺯﺍﺪﻧﺍ ﺍﺭ ﻱﻭﺮﺸﻴﭘ ﺭﺍﺪﻘﻣ ﻲﻟﻭ ﻱﺮﻴﮔ

ﻲﻣ .ﺖﺳﺍ ﻕﺩﺎﺻ ﺪﻨﻛ

ﻲﺣﺍﺮﻃ ﺭﺩ

،ﺐﻴﻋ ﻲﺑﺎﻳﺎﺟ ﻭ ﺶﻳﺎﭘ ﻢﺘﺴﻴﺳ ﻪﺑ ﺯﺍ ﺪﻌﺑ

ﻂﺑﺍﻭﺭ ﻥﺩﺭﻭﺁ ﺖﺳﺩ

ﺟ ﻭ ﻱﺯﺎﺳﺭﺎﻜﺷﺁ ﻲﻳﺎﻧﺍﻮﺗ ﻪﻌﻟﺎﻄﻣ ﻱﺍﺮﺑ ،ﻲﻠﻴﻠﺤﺗ ﻲﮕﻧﻭﺰﻓﺍ ﻲﺑﺎﻳﺎ

ﺯﺎﻴﻧ ﺐﻴﻋ

ﺲﻳﺮﺗﺎﻣ ﻞﻴﻜﺸﺗ ﻪﺑ ﺐﻴﻋ ﺖﻣﻼﻋ

FSM^P

9F

2

Pﺖﺳﺍ

ﺲﻳﺮﺗﺎﻣ ﺯﺍ ﻪﻧﻮﻤﻧ ﻚﻳ .

،FSM

ﻪﻛ ﻲﺘﻟﺎﺣ ﻱﺍﺮﺑ ﻭ ﺭﻮﺴﻨﺳ m

ﺭﺩ ﺏﻮﻴﻌﻣ ﻲﻟﺎﻤﺘﺣﺍ ﺮﺘﻣﺍﺭﺎﭘ n

ﻴﺳ ﺍﺩ ﺩﻮﺟﻭ ﻢﺘﺴ ﺩﺭ

ﻝﻭﺪﺟ ﺭﺩ ، 1

ﻩﺪﺷ ﻩﺩﺍﺩ ﻥﺎﺸﻧ :ﺖﺳﺍ

1. Causal stroke

2. Fault Signature Matrix(FSM)

ﻱﺮﻨﻳﺎﺑ ﺲﻳﺮﺗﺎﻣ ﻚﻳ ﻕﻮﻓ ﺲﻳﺮﺗﺎﻣ n×(m+2)

ﻥﺁ ﺎﻀﻋﺍ ﻪﻛ ﻩﺩﻮﺑ '0'

ﻭ '1'

ﻪﻳﺍﺭﺩ ﻥﺩﺮﻛﺮﭘ ﺭﺩ .ﺪﻨﺘﺴﻫ ﺲﻳﺮﺗﺎﻣ ﻡﺍij

)FSM

i=1,...n; j=1,…,m ﺭﺩ (

ﻲﮕﺘﺴﺑﺍﻭ ﺕﺭﻮﺻ ARR^Rj^R

i ﻪﺑ ﻪﻄﺑﺍﺭ ﺭﺩ ﺮﮔﺍ ﻲﻨﻌﻳ)θ ﺮﺘﻣﺍﺭﺎﭘARRs

θi

ﻩﺪﺷ ﺮﻫﺎﻇ ﺩﺪﻋ ( ﺪﺷﺎﺑ ﺩﺪﻋ ﺕﺭﻮﺻ ﻦﻳﺍ ﺮﻴﻏ ﺭﺩ ﻭ'1'

ﻲﻣ ﺝﺭﺩ'0' .ﺩﺩﺮﮔ

ﻒﻳﺮﻌﺗ 1 : ﻪﺘﻔﮔ ﻲﻣ ﺮﺘﻣﺍﺭﺎﭘ ﺭﺩ ﺐﻴﻋ ﺩﻮﺷ θi

ﻥﺪﺷ ﺭﺎﻜﺷﺁ ﺖﻴﻠﺑﺎﻗ

ﺩﺭﺍﺩ

، ﺮﻄﺳ ﺉﺎﻀﻋﺍ ﺯﺍ ﻲﻜﻳ ﻞﻗﺍﺪﺣ ﺮﮔﺍ ﺎﻬﻨﺗ ﻭ ﺮﮔﺍ .ﺪﺷﺎﺑ ﺮﻔﺻ ﻒﻟﺎﺨﻣ ﻡﺍi

ﺮﺘﻣﺍﺭﺎﭘ ﺭﺩ ﺐﻴﻋ ﻱﺯﺎﺳﺭﺎﻜﺷﺁ ﻲﻳﺎﻧﺍﻮﺗ θi

ﺮﻄﺳ ﺭﺩ ، ﻥﻮﺘﺳ ﻭ ﻡﺍi

ﻡﺍm+1

،

ﺎﺑ M^R_b^R=1

، ﺎﺑ ﺐﻴﻋ ﻱﺯﺎﺳﺭﺎﻜﺷﺁ ﻲﻳﺎﻧﺍﻮﺗ ﻡﺪﻋ ﻭ M^R_b^R=0

ﻧ ﻥﺎﺸ ﻲﻣ ﻩﺩﺍﺩ -

.ﺩﻮﺷ





= otherwisw

component j

in faults to sensitive is ARRs i S if

th th

ji 0, ,

1 (3⁾

ﻒﻳﺮﻌﺗ 2 : ﻪﺘﻔﮔ ﻲﻣ ﺮﺘﻣﺍﺭﺎﭘ ﺭﺩ ﺐﻴﻋ ﺩﻮﺷ θi

ﻚﻴﻜﻔﺗ ﺖﻴﻠﺑﺎﻗ ﻱﺮﻳﺬﭘ

ﺮﮔﺍ ﺎﻬﻨﺗ ﻭ ﺮﮔﺍ ﺩﺭﺍﺩ ﻪﺑ ﻁﻮﺑﺮﻣ ﺮﻄﺳ ﺭﺩ ﺐﻴﻋ ﺖﻣﻼﻋ

θi

ﺩﺮﻓ ﻪﺑ ﺮﺼﺤﻨﻣ

ﺮﺘﻣﺍﺭﺎﭘ ﺭﺩ ﺐﻴﻋ ﻱﺮﻳﺬﭘ ﻚﻴﻜﻔﺗ ﻲﻳﺎﻧﺍﻮﺗ .ﺪﺷﺎﺑ θi

ﺮﻄﺳ ﺭﺩ ، ﻥﻮﺘﺳ ﻭ ﻡﺍi

ﻡﺍm+2

، ﺎﺑ I^R_b^R=1 ﺎﺑ ﺐﻴﻋ ﻲﺑﺎﻳﺎﺟ ﻲﻳﺎﻧﺍﻮﺗ ﻡﺪﻋ ﻭ ، I^R_b^R=0

ﻩﺩﺍﺩ ﺶﻳﺎﻤﻧ

ﻲﻣ .ﺩﻮﺷ ﻝﻭﺪﺟ

1:

ﺎﻄﺧ ﻚﻴﻜﻔﺗ ﺲﻳﺮﺗﺎﻣ (FSM)

RIb

RMb

RARRm

R…

RARRj

R…

RARR1

R1

θ

Rij

Ri

θ

Rn

θ

ﻪﺑ ﺯﺍ ﺪﻌﺑ ﺖﻣﻼﻋ ﺭﺍﺩﺮﺑ ﺖﺳﺍ ﻡﺯﻻ ،ﺐﻴﻋ ﺖﻣﻼﻋ ﺲﻳﺮﺗﺎﻣ ﻥﺩﺭﻭﺁ ﺖﺳﺩ

ﺖﺳﺍ ﻱﺮﻨﻳﺎﺑ ﺭﺍﺩﺮﺑ ﻚﻳ ﺐﻴﻋ ﺖﻣﻼﻋ ﺭﺍﺩﺮﺑ .ﺩﻮﺷ ﻒﻳﺮﻌﺗ ﺐﻴﻋ ﻪﻛ

ﻪﺑ -

ﺕﺭﻮﺻ ) ,..., , (c₁c₂ c_m C=

ﻲﻣ ﻒﻳﺮﻌﺗ ﺩﻮﺷ ﺭﺍﺩﺮﺑ ﺯﺍ ﺰﺟ ﺮﻫ ﻥﺁ ﺭﺩ ﻪﻛ C

ﻲﻣ ﺖﻴﻌﺒﺗ ﺮﻳﺯ ﻥﻮﻧﺎﻗ ﺯﺍ :ﺪﻨﻛ



 >

= otherwisw

c_i c^{i i}

, 0

|

| ,

1 ε ( )4

ﻥﺁ ﺭﺩ ﻪﻛ εi

ﻪﺑ ﻁﻮﺑﺮﻣ ﻲﻘﻴﺒﻄﺗ ﻪﻧﺎﺘﺳﺁ ARR^R_i^R

ﺮﮔﺍ ﻦﻳﺍﺮﺑﺎﻨﺑ .ﺖﺳﺍ

ﺪﺷﺎﺑ ﺐﻴﻋ ﻥﻭﺪﺑ ﻢﺘﺴﻴﺳ

، ﻩﺪﻧﺎﻤﻴﻗﺎﺑ ﻱﺩﺪﻋ ﺭﺍﺪﻘﻣ ﻥﻮﭼ ﺯﺍ ﺮﺘﻤﻛ ﺎﻫ

ﻪﻧﺎﺘﺳﺁ ﻫ ﻪﻃﻮﺑﺮﻣ ﻱﺎﻫ ﻱﺮﻨﻳﺎﺑ ﺭﺍﺩﺮﺑ ﺪﻨﺘﺴ

C

ﺮﻴﻏﺭﺩ ﺩﻮﺑﺪﻫﺍﻮﺧ ﺮﻔﺻ ﺮﺑﺍﺮﺑ

ﻦﻳﺍ ﺕﺭﻮﺻ

، ﺭﺍﺩﺮﺑ

C

ﻦﻳﺍ ﻪﺴﻳﺎﻘﻣ ﺯﺍ ﻪﻛ ﺖﺳﺍ ﺮﻔﺻﺮﻴﻏ ﻱﺮﻨﻳﺎﺑ ﺭﺍﺩﺮﺑ ﻚﻳ

ﺲﻳﺮﺗﺎﻣ ﻱﺎﻫﺮﻄﺳ ﺎﺑ ﺭﺍﺩﺮﺑ ﻲﻣ ﻲﺑﺎﻳﺎﺟ ﺎﻄﺧFSM

ﺩﻮﺷ .

3 -

2B

ﻡﻭﺎﻘﻣ ﻝﺮﺘﻨﻛ

ﻡﻭﺎﻘﻣ ﻝﺮﺘﻨﻛ ﺰﻴﻟﺎﻧﺁ ﻭ ﻪﻌﻟﺎﻄﻣ ﻪﺑ

ﻡﺪﻋ ﻉﻮﺿﻮﻣ ،ﺖﻴﻌﻄﻗ ﺯﺍ ﻱﺭﺎﻴﺴﺑ

ﻩﺩﻮﺑ ﻱﺯﻭﺮﻣﺍ ﺕﺎﻘﻴﻘﺤﺗ ﻪﻌﻟﺎﻄﻣ ﻱﺍﺮﺑ ﻝﺪﻣ ﻭﺩ .ﺖﺳﺍ

ﺭﺩ ﻡﻭﺎﻘﻣ ﻝﺮﺘﻨﻛ ﻢﺘﺴﻴﺳ

-

ﻲﻣ ﺭﺍﺮﻗ ﻩﺩﺎﻔﺘﺳﺍ ﺩﺭﻮﻣ ﻲﻄﺧ ﻱﺎﻫ ﻚﻴﻧﻮﻧﺎﻛ ﻡﺮﻓ ﻡﺎﻧ ﻪﺑ ﻝﺪﻣ ﻦﻴﻟﻭﺍ .ﺩﺮﻴﮔ

10F

3

ﻩﺪﺷ ﻪﺘﺧﺎﻨﺷ ﺖﻟﺎﺣ ﺕﻻﺩﺎﻌﻣ ،ﻡﺮﻓ ﻦﻳﺍ ﺭﺩ .ﺖﺳﺍ

ﻱﺍﺮﺑ ﻱﺍﺭﺍﺩ ﻪﻛ ﻲﻤﺘﺴﻴﺳ

ﻡﺪﻋ ﺖﺳﺍ ﺖﻴﻌﻄﻗ

، ﻪﺑ ﺕﺭﻮﺻ ) ﻂﺑﺍﻭﺭ 2(

ﻩﺩﺍﺩ ﻥﺎﺸﻧ ﻲﻣ ﻮﺷ :ﺩ

3. Cononical form





∆ + +

∆ +

=

∆ + +

∆ +

=

u D D x C C y

u B B x A A x

n n

n n

] [

] [

] [ ]

 [

(5 ) ﻥﺁ ﺭﺩ ﻪﻛ x

u y, , ﻪﺑ ﻭ ﻢﺘﺴﻴﺳ ﻲﺟﻭﺮﺧ ﻭ ﻱﺩﻭﺭﻭ ،ﺖﻟﺎﺣ ﺐﻴﺗﺮﺗ

n n n

n B C D

A, , ,

ﺲﻳﺮﺗﺎﻣ ﻪﻳﺍﺭﺩ ﻪﻛ ﺪﻨﺘﺴﻫ ﺖﻟﺎﺣ ﻱﺎﻀﻓ ﻱﺎﻫ ﻥﺁ ﻱﺎﻫ

ﻪﺑ ﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻲﻤﺳﺍ ﺮﻳﺩﺎﻘﻣ ﺯﺍ ﻲﻣ ﺖﺳﺩ

.ﺪﻳﺁ

D C B

A ∆ ∆ ∆

∆ , , ,

ﺰﻴﻧ

ﻣ ﺲﻳﺮﺗﺎ ﻪﺑ ﻪﻛ ﺪﻨﺘﺴﻫ ﻑﺍﺮﺤﻧﺍ ﻱﺎﻫ ﻡﺪﻋ ﺩﻮﺟﻭ ﺖﻠﻋ

ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﺭﺩ ﺖﻴﻌﻄﻗ

ﻩﺪﻣﺁ ﺩﻮﺟﻮﺑ ﻢﺘﺴﻴﺳ ﺪﻧﺍ

.

ﻞﻜﺷ 3:

ﻡﺮﻓ LFT

ﺩﺭﺍﺪﻧﺎﺘﺳﺍ ﻲﻠﺧﺍﺩ ﻝﺪﻣ ﻡﺎﻧ ﺎﺑ ﻝﺪﻣ ﻦﻴﻣﻭﺩ

P11F

1

PP

Pﻲﻠﺧﺍﺩ ﺭﻮﺨﺴﭘ ﻪﻘﻠﺣ ﻝﺪﻣ ﺎﻳ

P12F

2

PP Pﻩﺪﺷ ﻪﺘﺧﺎﻨﺷﻡﺪﻋ ،ﻡﺮﻓ ﻦﻳﺍ ﺭﺩ .ﺖﺳﺍ

ﺍﺪﺟ ﻝﺪﻣ ﻲﻤﺳﺍ ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﺯﺍ ﺖﻴﻌﻄﻗ

ﻡﺪﻋ ﺮﺛﺍ ﻭ ﻩﺪﺷ ﻪﺑ ﺖﻴﻌﻄﻗ

ﻮﺻ ﻲﻣ ﻝﺪﻣ ﺩﺭﺍﻭ ﺭﻮﺨﺴﭘ ﻚﻳ ﺕﺭ ﻞﻜﺷ)ﺩﻮﺷ

3 .(

ﻪﺑ ﻡﺮﻓ ﻦﻳﺍ ﺭﺩ ﺖﻟﺎﺣ ﺕﻻﺩﺎﻌﻣ ﺩﻮﺑﺪﻨﻫﺍﻮﺧ ﺮﻳﺯ ﺕﺭﻮﺻ

.











∆

=

+ +

=

+ +

=

+ +

=

z w

u D w D x C z

u D w D x C z

B w B x A x

n n

n

n n n

.

22 21 2

12 11

 2

)6 ( ﻥﺁ ﺭﺩ ﻪﻛ

n n n n n

n B C C D D

B₂ = , ₂ = , ₂₂ =

ﻭ ، ﻭw ﻪﺑ z ﺐﻴﺗﺮﺗ

ﻭ ﻢﺘﺴﻴﺳ ﻲﻜﻤﻛ ﻲﺟﻭﺮﺧ ﻭ ﻱﺩﻭﺭﻭ ﻞﻣﺎﺷ ﻪﻛ ﺖﺳﺍ ﻱﺮﻄﻗ ﺲﻳﺮﺗﺎﻣ ﺰﻴﻧ ∆

ﻡﺪﻋ ﺖﻴﻌﻄﻗ ﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻲﺒﺴﻧ ﻱﺎﻫ ﺖﺳﺍ

.

ﻪﺑ ﻪﭼ ﺮﮔﺍ ﻪﺑ ﺖﻟﺎﺣ ﺕﻻﺩﺎﻌﻣ ﻥﺩﺭﻭﺁ ﺖﺳﺩ ﺯﺍ ﺩﺭﺍﺪﻧﺎﺘﺳﺍ ﻭ ﻚﻴﻧﻮﻧﺎﻛ ﻡﺮﻓ

،ﻡﻭﺎﻘﻣ ﻝﺮﺘﻨﻛ ﻪﻌﻟﺎﻄﻣ ﺖﻬﺟ ﻥﺁ ﻩﺩﺎﻔﺘﺳﺍ ﻭ ﻱﺭﺎﺘﻓﺭ ﻝﺪﻣ ﻑﺍﺮﮔﺪﻧﺎﺑ ﻱﻭﺭ ﻩﺩﻮﺑ ﺮﻴﺧﺍ ﺕﺎﻘﻴﻘﺤﺗ ﻉﻮﺿﻮﻣ ] ﺖﺳﺍ

16 ، 17 ﻦﻳﺍ ﺎﻣﺍ ،.[

ﻪﺒﻨﺟ ﻱﻭﺭ ﺵﺭﺍﺰﮔ -

ﻲﻣ ﺰﻛﺮﻤﺘﻣ ﻑﺍﺮﮔﺪﻧﺎﺑ ﺯﺍ ﻲﻳﺎﻫ ﻮﺷ

ﺩ ﻥﺍﻮﺘﺑ ﻥﺁ ﻱﻭﺭ ﺯﺍ ﻪﻛ ﺍﺭ ARRs

ﻡﺪﻋ ﻦﺘﻓﺮﮔﺮﻈﻧﺭﺩﺎﺑ ﺖﻴﻌﻄﻗ

ﻡﺮﻓ ﻂﻘﻓ ﻲﻨﻌﻳ .ﺩﻮﻤﻧ ﺝﺍﺮﺨﺘﺳﺍ ﺎﻫ ﺩﺭﻮﻣLFT

ﺭﺍﺮﻗ ﻲﺳﺭﺮﺑ ﺖﻓﺮﮔﺪﻫﺍﻮﺧ

ﻪﺑ ﻑﺍﺮﮔﺪﻧﺎﺑ ﻝﺪﻣ . ﻡﺮﻓ

ﺩﺎﺠﻳﺍ ﻥﺎﻜﻣﺍ LFT

ﻩﺪﻧﺎﻤﻴﻗﺎﺑ ﺭﺎﻛﺩﻮﺧ ﻪﻧﺎﺘﺳﺁ ﻭ ﺎﻫ

ﻲﻣ ﺍﺭ ﻲﻘﻴﺒﻄﺗ ﻱﺎﻫ ﺪﻫﺩ

ﻪﻛ ﻪﻧﺎﺘﺳﺁ ﻫ ﻲﻘﻴﺒﻄﺗ ﻱﺎ

ﺵﻭﺭ ﻥﺩﻮﺑ ﻡﻭﺎﻘﻣ ﻡﺪﻋ ﻪﺑ ﺍﺭFDI

ﺖﻴﻌﻄﻗ ﻲﻣ ﻦﻴﻤﻀﺗ ﺎﻫ .ﺪﻨﻛ

ﻑﺍﺮﮔﺪﻧﺎﺑ ﻪﭼﺮﮔﺍ ﻪﺑ

ﻡﺮﻓ ﻝﺎﻘﺘﻧﺍ ،ﻲﺘﻣﻭﺎﻘﻣ ،ﻩﺮﻴﺧﺫ ﻱﺎﻬﻧﺎﻤﻟﺍ ﻱﺍﺮﺑ LFT

ﻩﺪﻨﻫﺩ ﻩﺪﻨﺧﺮﭼ ﻭ ﺎﻫ ﻊﺟﺮﻣ ﺭﺩ ﺎﻫ

18] ﻩﺪﻣﺁ[ ﻡﺮﻓ ﺎﻣﺍ ﺖﺳﺍ ﺕﻻﺎﻴﺳ ﻱﺍﺮﺑLFT

ﻢﻛﺍﺮﺗ ﻩﺪﺸﻧ ﻩﺩﺍﺩ ﻪﻌﺳﻮﺗ ﺮﻳﺬﭘ ﻪﻟﺎﻘﻣ ﻦﻳﺍ ﺭﺩ ﺍﺬﻟ .ﺖﺳﺍ

ﻡﺮﻓ ﺎﻧ ﻱﺍﺮﺑLFT ﻝﺯ

ﻢﻛﺍﺮﺗ ﻝﺎﻴﺳ ﻲﺘﻴﻓﺮﻇ ﻥﺍﺪﻴﻣ ﻭ ﻚﻴﭘﻭﺮﺘﻧﺰﻳﺁ ﻩﺩﺍﺩ ﻪﻌﺳﻮﺗ ﺮﻳﺬﭘ

ﻪﻣﺍﺩﺍ ﺭﺩ ﻭ ﻩﺪﺷ

ﻪﺑ ﻲﮕﻧﻮﮕﭼ ﻪﻧﺎﺘﺳﺁ ﻭ ﻲﻠﻴﻠﺤﺗ ﻲﮕﻧﻭﺰﻓﺍ ﻂﺑﺍﻭﺭ ﻥﺩﺭﻭﺁ ﺖﺳﺩ

ﺭﺩ ﻲﻘﻴﺒﻄﺗ ﻱﺎﻫ

.ﺪﺷﺪﻫﺍﻮﺧ ﻩﺩﺍﺩ ﺢﻴﺿﻮﺗ ﻝﺎﺜﻣ ﻚﻳ ﺐﻟﺎﻗ

1. Standard interconnection model 2. Internal feedback loop

4 -

3B

ﻢﻛﺍﺮﺗ ﻝﺎﻴﺳ ﺮﻳﺬﭘ

ﻢﻛﺍﺮﺗ ﻝﺎﻴﺳ ﻪﻛ ﺪﻳﺮﻴﮕﺑ ﺮﻈﻧﺭﺩ ﺍﺭ ﻲﻟﺮﺘﻨﻛ ﻢﺠﺣ ﻲﻣ ﺮﻳﺬﭘ

ﺯﺍ ﺪﻧﺍﻮﺗ

ﻢﺠﺣ ﻱﺎﻫﺯﺮﻣ .ﺪﻨﻛ ﺭﻮﺒﻋ ﻝﺮﺘﻨﻛ

ﻩﺪﺷ ﻞﻘﺘﻨﻣ ﻱژﺮﻧﺍ ،ﻝﺮﺘﻨﻛ ﻢﺠﺣ ﻦﻳﺍ ﺭﺩ

ﻪﺑ ﻪﺟﻮﺗ ﻲﺘﺴﻳﺎﺑ ﺎﻣﺍ .ﺖﺳﺍ ﻲﻣﺮﺟ ﻥﺎﻳﺮﺟ ﺥﺮﻧ ﺯﺍ ﻲﻌﺑﺎﺗ ،ﻡﺮﺟ ﻝﺎﻘﺘﻧﺍ ﻪﻄﺳﺍﻭ

ﻞﻘﺘﻨﻣ ﻲﻣﺮﺟ ﻥﺎﻳﺮﺟ ﺥﺮﻧ ،ﻑﺮﻃ ﻚﻳ ﺯﺍ ﻪﻛ ﺖﺷﺍﺩ ﻱﺎﻫﺯﺮﻣ ﻖﻳﺮﻃ ﺯﺍ ﻩﺪﺷ

ﻝﺮﺘﻨﻛ ﻢﺠﺣ

، ﻥﺎﻳﺮﺟ ﻲﻜﻴﻣﺎﻨﻳﺩﻮﻣﺮﺗ ﺹﺍﻮﺧ ﻭ ﺭﺎﺸﻓ ﺖﺒﺴﻧ ﺯﺍ ﻲﻌﺑﺎﺗ

ﺮﮕﻳﺩ ﻑﺮﻃ ﺯﺍ .ﺖﺳﺍ ﺖﺳﺩﻻﺎﺑ

، ﺯﺍ ﻲﻌﺑﺎﺗ ﺰﻴﻧ ﻲﻜﻴﻣﺎﻨﻳﺩﻮﻣﺮﺗ ﺹﺍﻮﺧ ﺩﻮﺧ

ﻞﻘﺘﻨﻣ ﻱژﺮﻧﺍ ﺺﻟﺎﺧ ﺥﺮﻧ ﺮﺘﻨﻛ ﻢﺠﺣ ﻪﺑ ﻩﺪﺷ

ﻝ ﺕﻻﺎﻴﺳ ﺭﺩ ﻦﻳﺍﺮﺑﺎﻨﺑ .ﺖﺳﺍ

ﻢﻛﺍﺮﺗ ﻝﺮﺘﻨﻛ ﻢﺠﺣ ﻥﻭﺭﺩ ﻱژﺮﻧﺍ ﺕﺍﺮﻴﻴﻐﺗ ﺥﺮﻧ ﻭ ﻲﻣﺮﺟ ﻥﺎﻳﺮﺟ ،ﺮﻳﺬﭘ

، ﻪﺑ

ﻪﺘﺴﺑﺍﻭ ﺮﮕﻳﺪﻤﻫ ﻚﻴﭘﻭﺮﺘﻧﺰﻳﺁ ﻥﺎﻳﺮﺟ ﺽﺮﻓﺎﺑ ﺶﻧﺍﺭﺎﻜﻤﻫ ﻭ پﻮﻧﺭﺎﻛ .ﺪﻧﺍ

، ﻭ

ﻪﺑ ﻪﻛ ﻲﻣﺮﺟ ﻥﺎﻳﺮﺟ ﺥﺮﻧ ﻪﺒﺳﺎﺤﻣ ﺭﻮﻈﻨﻣ (ﺝﺭﺎﺧ ﺎﻳ) ﺩﺭﺍﻭ ﻝﺮﺘﻨﻛ ﻢﺠﺣ ﻪﺑ

ﻲﻣ ﻚﻴﭘﻭﺮﺘﻧﺰﻳﺁ ﻝﺯﺎﻧ ﻥﺍﺪﻴﻣ ،ﺩﻮﺷ .ﺪﻧﺩﻮﻤﻧ ﻲﻓﺮﻌﻣ ﻑﺍﺮﮔﺪﻧﺎﺑ ﺭﺩ ﺍﺭ R

ﻝﺮﺘﻨﻛ ﻢﺠﺣ ﻥﻭﺭﺩ ﻱژﺮﻧﺍ ﻭ ﻡﺮﺟ ﺉﺎﻘﺑ ﻦﻴﻧﺍﻮﻗ ﺉﺎﺿﺭﺍ ﺭﻮﻈﻨﻣ ﻪﺑ ﻦﻴﻨﭽﻤﻫ

،

ﻲﺘﻴﻓﺮﻇ ﻥﺍﺪﻴﻣ .ﺪﻧﺩﻮﻤﻧ ﻲﻓﺮﻌﻣ ﻑﺍﺮﮔﺪﻧﺎﺑ ﺭﺩ ﺍﺭC

ﻥﺍﺪﻴﻣ ﻩﺪﺷ ﻲﻓﺮﻌﻣ ﻱﺎﻫ

ﻪﻛ ﺖﺳﺍ ﻲﻬﻳﺪﺑ ﻭ ﺪﻨﺘﺴﻫ ﻲﻤﺳﺍ ﻱﺎﻫﺮﺘﻣﺭﺎﭘ ﻞﻣﺎﺷ ﻝﺪﻣ ﺭﺩ

ﻩﺪﺷ ﻲﻓﺮﻌﻣ ﻱﺎﻫ

ﻩﺪﺸﻧ ﺭﻮﻈﻨﻣ ﻱﺮﺘﻣﺍﺭﺎﭘ ﺖﻴﻌﻄﻗ ﻡﺪﻋ ﺶﺨﺑ ﺭﺩ .ﺖﺳﺍ

ﻦﻳﺍ ﻢﺸﺷ ﻭ ﻢﺠﻨﭘ ﻱﺎﻫ

ﻪﺑ ﻭ ،ﻪﻟﺎﻘﻣ ﻦﻳﺍ ﻡﺪﻋ ﻦﺘﻓﺮﮔﺮﻈﻧﺭﺩ ﺭﻮﻈﻨﻣ

ﺖﻴﻌﻄﻗ ﻪﺑ ﻑﺍﺮﮔﺪﻧﺎﺑ ﻝﺪﻣ ،ﺎﻫ ﻡﺮﻓ

ﻱﺎﻫ ﻥﺍﺪﻴﻣ ﻱﺍﺮﺑLFT ﻭR

ﻩﺩﺍﺩ ﻪﻌﺳﻮﺗ C ﻲﻣ ﺲﭙﺳ ﻭ ﺩﻮﺷ ﺩﺮﺑﺭﺎﻛ ﻩﻮﺤﻧ

ﻝﺪﻣ ﻪﻌﺳﻮﺗ ﻱﺎﻫ ﻴﻋ ﻲﺑﺎﻳﺎﺟ ﻭ ﻱﺯﺎﺳﺭﺎﻜﺷﺁ ﺖﻬﺟ ﻪﺘﻓﺎﻳ ﻚﻳ ﻖﻳﺮﻃ ﺯﺍ ،ﺐ

ﺢﻴﺿﻮﺗ ﻲﺷﺯﻮﻣﺁ ﻝﺎﺜﻣ ﻩﺩﺍﺩ

ﻲﻣ .ﺩﻮﺷ

5 -

4B

ﻡﺮﻓ

ﻚﻴﭘﻭﺮﺘﻧﺰﻳﺁ ﻝﺯﺎﻧ ﻱﺍﺮﺑ

LFT

ﻡﺮﻓ ﻪﻌﺳﻮﺗ ﺯﺍ ﻞﺒﻗ ﻢﻛﺍﺮﺗ ﻢﺘﺴﻴﺳ ﻱﺍﺮﺑLFT

ﻲﻣ ﻱﺭﻭﺁﺩﺎﻳ ﺮﻳﺬﭘ ،ﺩﺩﺮﮔ

ﻡﺪﻋ ﺮﺘﻣﺍﺭﺎﭘ ﻱﻭﺭ ﺖﻴﻌﻄﻗ ﻲﻣ ﺍﺭθ

ﻪﺑ ﻥﺍﻮﺗ ﺕﺭﻮﺻ θn+∆θ = .ﺩﺍﺩ ﻥﺎﺸﻧ θ

ﻲﺗﺭﻮﺻﺭﺩ ﻪﻛ ﺶﻳﺎﻤﻧ ﻑﺪﻫ ﻡﺪﻋ

ﻪﺑ ﺖﻴﻌﻄﻗ ﻡﺮﻓ LFT

،ﺪﺷﺎﺑ ﺖﺳﺍ ﺮﺘﻬﺑ

ﻪﺑ ﺍﺭ ﺮﺘﻣﺍﺭﺎﭘ ﻡﺪﻋ ﺕﺭﺎﺒﻋ ﺭﺩ ﻲﻤﺳﺍ ﺮﺘﻣﺍﺭﺎﭘ ﺏﺮﻀﻠﺻﺎﺣ ﺕﺭﻮﺻ ﻥﺎﺸﻧ ﺖﻴﻌﻄﻗ

ﺩ ﺩﺍ :ﻲﻨﻌﻳ .

n n

n n

n where

θ δ θ δ

θ θ θ θ θ θ

θ= +∆ = (1+∆ )= (1+ _θ) _θ =^∆ ( )7 ﻻﺎﺑ ﻪﻄﺑﺍﺭ ﺭﺩ θ

∆ δθ, ﻪﺑ ﺮﻳﺩﺎﻘﻣ ﺯﺍ ﺮﺘﻣﺍﺭﺎﭘ ﻲﺒﺴﻧ ﻭ ﻖﻠﻄﻣ ﻑﺍﺮﺤﻧﺍ ﺐﻴﺗﺮﺗ

ﻲﻣ ﺮﺘﻣﺍﺭﺎﭘ ﻲﻤﺳﺍ .ﺪﺷﺎﺑ

ﻲﺘﻟﺎﺣﺭﺩ ﻪﺑ ﺮﺘﻣﺍﺭﺎﭘ ﻪﻛ ﺕﺭﻮﺻ

ﺮﻫﺎﻇ1/θ ﻡﺪﻋ ،ﺩﻮﺷ ﻪﺑ ﺖﻴﻌﻄﻗ ﻡﺮﻓ ﺍﺭLFT

ﻲﻣ ﺰﻴﻧ ﻪﺑ ﻥﺍﻮﺗ :ﺩﺍﺩ ﻥﺎﺸﻧ ﺮﻳﺯ ﻞﻜﺷ

θ θ δ θ θ δ

θ θ

θ θ

θ θ θ

θ θ θ θ θ θ

θ θ θ θ

θ

θ +∆

− ∆

= +

∆ = +

− ∆

=

∆ +

∆

−

∆

= +

∆

= +

∆

= +

n n

n n

n n n n

n n n

where ₁

1 ) 1 1( ) 1

1(

) (

) ( ) ( 1 1

)8 ( ﻚﻴﭘﻭﺮﺘﻧﺰﻳﺁ ﻝﺯﺎﻧ ﻥﺍﺪﻴﻣ ،ﺕﺎﺤﻴﺿﻮﺗ ﻦﻳﺍ ﺎﺑ ﻩﺩﺍﺩ ﻥﺎﺸﻧ

ﻜﺷ ﺭﺩ ﻩﺪﺷ ﻞ

4 -

(ﻒﻟﺍ) ﻲﻣ ﺮﻈﻧﺭﺩ ﺍﺭ ﻡﺮﺟ ﻥﺎﻳﺮﺟ .ﻢﻳﺮﻴﮔ

mn

ﻱژﺮﻧﺍ ﻥﺎﻳﺮﺟ ﻭ

En

ﻝﺯﺎﻧ ﺯﺍ ﻪﻛ

ﻲﻣ ﺭﻮﺒﻋ ﻚﻴﭘﻭﺮﺘﻧﺰﻳﺁ ﺎﺑ ﺖﺳﺍ ﺮﺑﺍﺮﺑ ﺪﻨﻛ

5] :[































 −



 





= −

=

















 −



 





= −

+ +

γ γ γ γ γ γ

γ γ γ

γ

1 2 1 2

1 2 1

2

r r u

u en Pn u p n n

r r u

u n dn n

P R P

P T A C T C m E

P P RT

P C A m

 n





)9 (

ﻻﺎﺑ ﻪﻄﺑﺍﺭ ﺭﺩ

Aen

ﺐﻳﺮﺿ ﺏﺮﻀﻠﺻﺎﺣ ﺮﺑﺍﺮﺑ ﻭ ﻩﺩﻮﺑ ﻝﺯﺎﻧ ﻝﺩﺎﻌﻣ ﻊﻄﻘﻣ ﺢﻄﺳ

ﻪﻴﻠﺨﺗ Cdn

ﻲﻤﺳﺍ ﻊﻄﻘﻣ ﺢﻄﺳ ﺭﺩ An

.ﺖﺳﺍ ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻦﻴﻨﭽﻤﻫ

P T R C_p, , , γ,

ﻪﺑ ﻥﺎﺸﻧ ﺐﻴﺗﺮﺗ ﺐﻳﺮﺿ ،ﺯﺎﮔ ﺖﺑﺎﺛ ،ﺎﻣﺩ ،ﺭﺎﺸﻓ ﻩﺪﻨﻫﺩ

ﻝﺎﻴﺳ ﻩﮋﻳﻭ ﻱﺎﻣﺮﮔ ﺖﺒﺴﻧ ﻭ ﺖﺑﺎﺛ ﺭﺎﺸﻓ ﻩﮋﻳﻭ ﻱﺎﻣﺮﮔ

، ﺲﻳﻮﻧﺮﻳﺯ ﻭ ﻱﺎﻫ ﻭu

ﻪﺑd ﻦﻴﻳﺎﭘ ﻭ ﺖﺳﺩﻻﺎﺑ ﻥﺎﻳﺮﺟ ﻪﺑ ﺐﻴﺗﺮﺗ .ﺩﺭﺍﺩ ﻩﺭﺎﺷﺍ ﺖﺳﺩ

Pr

ﻧ ﺰﻴﻧ ﺭﺎﺸﻓ ﺖﺒﺴ

ﻪﺑ ﻭ ﺖﺳﺍ ﻝﺯﺎﻧ ﻑﺮﻃﻭﺩ ﻲﻣ ﻒﻳﺮﻌﺗ ﺮﻳﺯ ﺕﺭﻮﺻ

:ﺩﻮﺷ









〈

=

〉

=

=

crit u crit d

r

crit u d u

d r r

P P if P P P

P P if P p P P

P (10)

ﻞﻜﺷ 4 : (ﻒﻟﺍ) - (ﺏ) ﻚﻴﭘﻭﺮﺘﻧﺰﻳﺁ ﻝﺯﺎﻧ -

ﻡﺮﻓ ﻚﻴﭘﻭﺮﺘﻧﺰﻳﺁ ﻝﺯﺎﻧLFT

ﻡﺪﻋ ﻦﺘﻓﺮﮔﺮﻈﻧﺭﺩﺎﺑ ﻝﺩﺎﻌﻣ ﻊﻄﻘﻣ ﺢﻄﺳ ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻱﻭﺭ ﺖﻴﻌﻄﻗ

Ae

ﻭ

ﺎﻣﺮﮔ ﺐﻳﺮﺿ ﻩﮋﻳﻭ ﻱ

ﻪﺑ ،ﻚﻴﭘﻭﺮﺘﻧﺰﻳﺁ ﻝﺯﺎﻧ ﻥﺍﺪﻴﻣ ﺮﺑ ﻢﻛﺎﺣ ﻂﺑﺍﻭﺭ ،Cp -

ﺗﺭﻮﺻ ) ﻂﺑﺍﻭﺮ 11 ( :ﺩﻮﺑﺪﻨﻫﺍﻮﺧ































 −



 





∆ − +

∆ +

=

















 −



 





−

∆

= +

+ +

γ γ γ γ γ γ

γ γ γ

γ

1 2 1 2

1 2 ) ) ( )(

(

1 ) 2 (

r r u

u e en P p

r r u

u e e

P R P

t P T A A C C E

P RT P

P A A m

n n





) 11 ( ﻪﺑ ﺍﺭ ﻻﺎﺑ ﻂﺑﺍﻭﺭ ﻢﻴﻫﺍﻮﺨﺑ ﻪﭽﻧﺎﻨﭼ ﻡﺮﻓ

،ﻢﻴﻫﺩ ﺶﻳﺎﻤﻧLFT ﻪﺑ ﻪﺟﻮﺗﺎﺑ

) ﻂﺑﺍﻭﺭ 7 :(

P P C e

e Ae n A C

n A

C C A

A E

E

m m

P e

P

e =∆ =∆







+ +

= +

= δ δ

δ δ δ

, ,

) 1 )(

1 (

) 1 (







 (12)

ﺮﻳﺩﺎﻘﻣ ﻻﺎﺑ ﻂﺑﺍﻭﺭ ﺭﺩ ﻪﻛ

n n E m ,

ﻲﺷﺎﻧ ﻱژﺮﻧﺍ ﻥﺎﻳﺮﺟ ﻭ ﻲﻤﺳﺍ ﻲﻣﺮﺟ ﻲﺑﺩ

ﻪﻄﺑﺍﺭ ﺯﺍ ﺎﻬﻧﺁ ﺮﻳﺩﺎﻘﻣ ﻭ ﺖﺳﺍ ﻲﻤﺳﺍ ﺖﻟﺎﺣ ﺭﺩ ﻝﺎﻴﺳ ﻲﭙﻟﺎﺘﻧﺍ ﺯﺍ )9

ﻞﺑﺎﻗ ( -

ﻪﻄﺑﺍﺭ ﻪﺑ ﻪﺟﻮﺗﺎﺑ ﻦﻳﺍﺮﺑﺎﻨﺑ .ﺖﺳﺍ ﻪﺒﺳﺎﺤﻣ )

12 ( ﻡﺮﻓ ، ﻚﻴﭘﻭﺮﺘﻧﺰﻳﺁ ﻝﺯﺎﻧLFT

ﻪﺑ ﻩﺩﺍﺩ ﻥﺎﺸﻧ ﺕﺭﻮﺻ ﻞﻜﺷﺭﺩ ﻩﺪﺷ

4 ﻮﺧ (ﺏ) :ﺭﻮﻛﺬﻣ ﻞﻜﺷ ﺭﺩ .ﺩﻮﺑﺪﻫﺍ















=∆

=∆

+ +

=

=

=

=

=

P P C e

e A A

C A C E n E E E E

n m m A m

C C A

A E Z Z

m Z Z

P e

e

P e P e

δ δ

δ

δ δ δ δ δ

ω δ ω

;

; .

;

; .

;

; .





) 13 ( ﻻﺎﺑ ﻪﻄﺑﺍﺭ ﺭﺩ

e

P A

C ∆

∆ , ﻡﺪﻋ ﻭ ﻖﻠﻄﻣ ﺖﻴﻌﻄﻗ

e

P A

C δ

δ , ﻡﺪﻋ ﺖﻴﻌﻄﻗ

ﺖﺑﺎﺛ ﺭﺎﺸﻓ ﻩﮋﻳﻭ ﻱﺎﻣﺮﮔ ﺐﻳﺮﺿ ﻭ ﻝﺯﺎﻧ ﻩﺎﮔﻮﻠﮔ ﻊﻄﻘﻣ ﺢﻄﺳ ﻪﺑ ﻁﻮﺑﺮﻣ ﻲﺒﺴﻧ ﺖﺳﺍ .

6 -

5B

ﻡﺮﻓ

ﻥﺍﺪﻴﻣ ﻱﺍﺮﺑ

LFT C

ﺭﺩ ﻲﺘﻴﻓﺮﻇ ﻥﺍﺪﻴﻣ ﺮﻳﺩﺎﻘﻣ ﻲﻟﺍﺮﮕﺘﻧﺍ ﺖﻟﺎﺣ ﺭﺩ ،C

V m E, , ﻪﺑ ﻥﺍﻮﻨﻋ

ﻱﺩﻭﺭﻭ ﻲﻣ ﻪﺘﻓﺮﮔﺮﻈﻧﺭﺩ ﻥﺍﺪﻴﻣ ﻪﻄﺑﺍﺭ ﺯﺍ ﻪﻈﺤﻟ ﺮﻫ ﺭﺩ ﺭﺎﺸﻓ ﻭ ﺎﻣﺩ ﻭ ﺪﻧﻮﺷ

ﻲﻣ ﻪﺒﺳﺎﺤﻣ ﺮﻳﺯ ﻞﻜﺷ) ﺪﻧﻮﺷ

5 .((ﻒﻟﺍ)

∫ ∫

∫ ∫

₌

=

dt V C

dt m ZR P dt m

dt E T C

v v 







1 , (14)

ﻞﻜﺷ 5 ﺣ ﺭﺩ (ﻒﻟﺍ) ﻲﺘﻴﻓﺮﻇ ﻥﺍﺪﻴﻣ: ﻲﻘﺘﺸﻣ ﺖﻟﺎﺣ ﺭﺩ (ﺏ) ﻲﻟﺍﺮﮕﺘﻧﺍ ﺖﻟﺎ

DBG

ﻩﺩﺎﻔﺘﺳﺍ ﺐﻴﻋ ﺺﻴﺨﺸﺗ ﻱﺍﺮﺑ ﺭﻮﻛﺬﻣ ﻝﺪﻣ ﺯﺍ ﻪﻛ ﻲﺘﻟﺎﺣﺭﺩ ﺎﻣﺍ ﻭ ﺎﻣﺩ ،ﺩﻮﺷ

ﻩﺯﺍﺪﻧﺍ ﻱﺭﺎﺸﻓ ﻩﺪﺷ ﻱﺮﻴﮔ

ﻪﺑ ،ﺎﻫﺭﻮﺴﻨﺳ ﻂﺳﻮﺗ ﺩﺭﺍﻭ ﻡﻮﻠﻌﻣ ﺮﻳﺩﺎﻘﻣ ﻥﺍﻮﻨﻋ

،ﺖﺑﺎﺛ ﻢﺠﺣ ﻩﮋﻳﻭ ﻱﺎﻣﺮﮔ ﺐﻳﺮﺿ ﻥﺩﻮﺑ ﺖﺑﺎﺛ ﺽﺮﻓ ﺎﺑ ﻭ ﻩﺪﺷ ﻥﺍﺪﻴﻣ ﺮﻳﺩﺎﻘﻣ E m, ﻦﻴﻌﻣ ﺖﻟﺎﺣﺭﺩ ﻪﻄﺑﺍﺭ ﺯﺍ

) 15 ( ﻲﻣ ﻪﺒﺳﺎﺤﻣ ﻞﻜﺷ) ﺪﻧﻮﺷ

6 .((ﻒﻟﺍ)









=

=

) (

) (

R Z

C PV dt E d

RT Z

PV dt m d

n v n n

n n n





) 15 ( ﻻﺎﺑ ﻪﻄﺑﺍﺭ ﺭﺩ ﻢﻛﺍﺮﺗ ﺐﻳﺮﺿZ

ﺮﻫ ﺭﺩ ﻥﺁ ﻖﺘﺸﻣ ﻭ ﺭﺍﺪﻘﻣ ﻭ ﻩﺩﻮﺑ ﻱﺮﻳﺬﭘ

ﻪﺑ ﻪﻈﺤﻟ .ﺖﺳﺍ ﻪﺒﺳﺎﺤﻣ ﻞﺑﺎﻗ ﻝﺎﻴﺳ ﺭﺎﺸﻓ ﻭ ﺎﻣﺩ ﺯﺍ ﻲﻌﺑﺎﺗ ﺕﺭﻮﺻ V

C_v, ﺰﻴﻧ

ﻪﺑ ﻢﺠﺣ ﺐﻴﺗﺮﺗ ﻲﻣ ﻪﻈﺣﻼﻣ . ﺖﺳﺍ ﺖﺑﺎﺛ ﻢﺠﺣ ﺭﺩ ﺯﺎﮔ ﻩﮋﻳﻭ ﻱﺎﻣﺮﮔ ﻭ

ﺩﻮﺷ

ﻥﺍﺪﻴﻣ ﺮﺑ ﻢﻛﺎﺣ ﻂﺑﺍﻭﺭ ﺖﻟﺎﺣ ﻦﻳﺍ ﺭﺩ ﻪﺑC

ﻩﺪﺷ ﺮﻫﺎﻇ ﻲﻘﺘﺸﻣ ﺕﺭﻮﺻ ﻪﺑ .ﺪﻧﺍ

ﻑﺍﺮﮔﺪﻧﺎﺑ ﻑﺍﺮﮔﺪﻧﺎﺑ ﺎﺣﻼﻄﺻﺍ ،ﺪﺷﺎﺑ ﻲﻘﺘﺸﻣ ﻡﺮﻓ ﻪﺑ ﺎﻬﻧﺁ ﺖﻴﻠﻋ ﻪﻛ ﻲﻳﺎﻫ

ﺺﻴﺨﺸﺗ ﻝﺪﻣ DBG^P13F

1

Pﻪﺘﻔﮔ

ﻲﻣ ﻞﻜﺷ)ﺩﻮﺷ 5 .((ﺏ)

ﻡﺪﻋ ﺩﻮﺟﻭ ﺽﺮﻓﺎﺑ ﻢﺘﺴﻴﺳ ﻢﺠﺣ ﻱﻭﺭ ﺖﻴﻌﻄﻗ

) ﻢﻛﺍﺮﺗ ﺐﻳﺮﺿ ،(V -

ﻱﺮﻳﺬﭘ

)

ﻩﮋﻳﻭ ﻱﺎﻣﺮﮔ ﺐﻳﺮﺿ ﻭ(Z )

(C_P

ﻲﺘﻴﻓﺮﻇ ﻥﺍﺪﻴﻣ ﺮﺑ ﻢﻛﺎﺣ ﻂﺑﺍﻭﺭ ، C

ﻪﺑ .ﺩﺮﻛﺪﻨﻫﺍﻮﺧ ﺮﻴﻴﻐﺗ ﻡﺪﻋ ﻦﺘﻓﺮﮔﺮﻈﻧﺭﺩ ﺭﻮﻈﻨﻣ

ﺖﻴﻌﻄﻗ ﺭﺩ ﺖﺳﺍ ﻲﻓﺎﻛ ،ﺎﻫ

ﻪﺑ ﻻﺎﺑ ﻪﻄﺑﺍﺭ ﻲﻤﺳﺍ ﺮﻳﺎﻘﻣ ﻱﺎﺟ

Pn n

n Z C

V , ,

ﻪﺑ ﺮﻳﺩﺎﻘﻣ ﺐﻴﺗﺮﺗ

P Pn P n

n V Z Z Z C C C

V

V= +∆ , = +∆ , = +∆

:ﺩﺍﺩ ﺭﺍﺮﻗ ﺍﺭ

1.Diagnosis Bond Graph (DBG)