the following discussion of the embodiments of the invention directed to a system and method for preventing anode starvation by detecting changes in membrane permeation of the membranes in a fuel cell stack is merely exemplary in nature , and is in no way intended to limit the invention or its applications or uses . fig1 is a cross - sectional view of a fuel cell 10 that is part of a fuel cell stack of the type discussed below . the fuel cell 10 includes a cathode side 12 and an anode side 14 separated by a perfluorosulfonic acid membrane 16 . a cathode side diffusion media layer 20 is provided on the cathode side 12 , and a cathode side catalyst layer 22 is provided between the membrane 16 and the diffusion media layer 20 . likewise , an anode side diffusion media layer 24 is provided on the anode side 14 , and an anode side catalyst layer 26 is provided between the membrane 16 and the diffusion media layer 24 . the catalyst layers 22 and 26 and the membrane 16 define an mea . the diffusion media layers 20 and 24 are porous layers that provide for input gas transport to and water transport from the mea . a cathode side flow field plate or bipolar plate 28 is provided on the cathode side 12 , and an anode side flow field plate or bipolar plate 30 is provided on the anode side 14 . fig2 is a simplified block diagram of a fuel cell system 40 including a fuel cell stack 42 . the fuel cell system 40 is intended to generally represent any type of fuel cell system that requires an anode exhaust gas bleed to remove nitrogen from the anode side of the stack 42 . examples of such fuel cell systems include fuel cell systems that re - circulate the anode exhaust gas back to the anode inlet and fuel cell systems that employ a split stack design with anode flow - shifting , both of which are referred to herein as an “ anode sub - system .” hydrogen gas from a hydrogen source 44 is provided to the anode side of the fuel cell stack 42 on line 48 . an anode exhaust gas is output from the fuel cell stack 42 on line 50 and is sent to a bleed valve 56 . as discussed above , nitrogen cross - over from the cathode side of the fuel cell stack 42 dilutes the hydrogen in the anode side of the stack 42 , thereby affecting fuel cell stack performance . therefore , it is necessary to periodically bleed the anode exhaust gas from the anode sub - system using the bleed valve 56 to reduce the amount of nitrogen in the anode sub - system , i . e ., in the anode side of the fuel cell stack 42 . when the bleed valve 56 is open , the bled anode exhaust gas flows through a bleed line 48 . a pressure sensor 60 is also provided in the line 50 to measure the pressure of the anode sub - system of the fuel cell system 40 . air from a compressor 62 is provided to the cathode side of the fuel cell stack 42 on line 64 . a cathode exhaust gas is output from the fuel cell stack 42 on a cathode exhaust gas line 66 . a mixing device 68 is provided in the line 66 for mixing the cathode exhaust gas and the bled anode exhaust gas on the line 48 . a controller 54 monitors the pressure of the anode sub - system of the fuel cell system 40 , as measured by the pressure sensor 60 , controls the speed of the compressor 62 , controls the injection of hydrogen from the hydrogen source 44 to the anode side of the stack 42 , and controls the position of the anode bleed valve 56 , as is discussed in more detail below . the controller 54 also utilizes a model to estimate the permeation flow rate of nitrogen from the cathode side to the anode side and the concentration of nitrogen in the anode side of the stack 42 , and to determine when to bleed nitrogen from the anode side of the stack 42 . in addition , the controller 54 measures the length of time required for the anode sub - system to reach atmospheric pressure after the fuel cell system 40 has been shutdown . the controller 54 may adjust the cathode to anode nitrogen permeation estimation through the stack 42 based on the time necessary for the anode side to reach atmospheric pressure , as discussed in more detail below . during normal operation of the fuel cell system 40 , nitrogen from the cathode side of the stack 42 permeates through the membranes in the fuel cells to the anode side of the stack 42 , which dilutes the fuel concentration in the anode side of the stack 42 . thus , to achieve stable operation of the fuel cells , the nitrogen concentration in the anode side of the fuel cell stack 42 needs to be estimated and controlled . over time , the permeation rate of the membrane 16 changes due to thinning and other physical changes of the membrane 16 , causing the rate of permeation of nitrogen through the membrane 16 to change . therefore , the change in the rate of permeation of nitrogen through the membrane 16 needs to be periodically determined and accounted for in the estimation of nitrogen concentration in the anode side of the stack 42 to avoid estimating an incorrect level of anode concentration , as is described in more detail below . to determine changes in the rate of permeation of the membrane 16 , the pressure profile of the anode side of the stack 42 after shutdown of the fuel cell system 40 can be used . during a normal shutdown , the cathode side of the stack 42 is depleted of oxygen , causing high levels of nitrogen and low levels of hydrogen at atmospheric pressure . the cathode side is at atmospheric pressure because the cathode side of the stack 42 is not sealed , as is known to those skilled in the art . the anode side of the stack 42 , however , is sealed and is left sealed at system shutdown , thus the anode side of the fuel cell stack 42 has a pressurized mixture of a known amount of hydrogen and nitrogen . when the fuel cell system 40 enters the off state , or is shutdown , hydrogen in the anode side of the stack 42 will rapidly diffuse through the membrane 16 into the cathode side of the stack 42 until the hydrogen partial pressure has equilibrated across the membrane 16 . this will cause a decrease in pressure in the anode side of the fuel cell stack 42 , as measured by the pressure sensor 60 . the decrease in pressure in the anode side of the stack 42 will typically create a vacuum as hydrogen rapidly permeates to the cathode side of the stack 42 . nitrogen has a lower permeation rate than hydrogen through the membrane 16 due to the larger size of the nitrogen molecules compared to the hydrogen molecules . thus , nitrogen will permeate through the membrane 16 at a slower rate than the hydrogen , causing the pressure in the anode side of the fuel cell stack 42 to increase until the nitrogen partial pressures equilibrate across the membrane 16 . because of the difference in permeation rate between hydrogen and nitrogen , the resulting pressure trajectory of the anode side of the stack 42 after each shutdown , as measured by the pressure sensor 60 , can be correlated to changes in the permeation rate of the membranes of the fuel cells in the stack 42 . the faster the hydrogen pressure and the nitrogen pressure in the anode side of the stack 42 equilibrate , as measured by the pressure sensor 60 , the higher the rate of permeation of the membranes . fig3 is a graph with shutdown time in minutes on the x - axis and anode pressure in kpa on the y - axis , which illustrates the impact of membrane thickness on anode pressure at shutdown of the fuel cell system 40 . as shown in fig3 , line 70 illustrates the change in pressure over time of a membrane that is 6 μm thick , line 72 illustrates the change in pressure over time of a membrane that is 12 μm thick , and line 74 illustrates the change in pressure over time of a membrane that is 18 μm thick . fig3 illustrates that the pressure equilibrium over time after shutdown , i . e ., how long the anode side takes of the stack 42 takes to reach atmospheric pressure , is directly related to the thickness of the membrane 16 , indicating that membrane permeation can be estimated using the anode pressure trajectory of a fuel cell system 40 after a typical shutdown of the system 40 . the correlation between the thickness of the membrane 16 and the pressure changes in the anode sub - system may be used by an adaptive controller , such as the controller 54 , to adapt the estimation of nitrogen concentration in the anode side to changes in membrane permeation , allowing for the anode fuel concentration to be accurately estimated over the life of the fuel cell stack 42 . a better estimation of fuel concentration allows for improved efficiency , performance and durability . fig4 is a flow chart diagram 80 for an algorithm for detecting changes in the permeation rate of the membranes 16 in the stack 42 . at box 82 , the fuel cell system 40 transitions from run mode to off mode , i . e ., is shutdown . after the fuel cell system 40 transitions to off mode at the box 82 , the algorithm records the amount of time it takes for the pressure in the anode sub - system to equilibrate with atmospheric pressure , or the pressure of the cathode sub - system , at box 84 . next , the algorithm determines if the amount of time necessary for the pressure in the anode sub - system to equilibrate has changed since the last shutdown , or has changed from a calibrated value , at decision diamond 86 . if no change in time has occurred , then the algorithm does not take any action at box 88 . the fuel cell system 40 will operate without a permeation correction at box 90 and will return to the box 82 when the fuel cell system 40 transitions from run mode to off mode . if a change in the amount of time it takes for the pressure in the anode sub - system to equilibrate with atmospheric pressure is detected at the decision diamond 86 , then the algorithm will modify the estimation of anode fuel concentration and / or modify the nitrogen bleed schedule in proportion to the change in the permeation rate of the membrane 16 , as determined by the change in time , at box 92 , and the fuel cell system 40 will run with the new permeation correction to the fuel estimation and / or nitrogen bleed schedule at box 94 . for example , the frequency of performing anode bleeds to remove nitrogen from the anode side using the bleed valve 56 may be increased , the duration of the anode bleeds using the bleed valve 56 may be increased , and / or the flow of anode fuel to the stack may be increased . after making the appropriate modification at the box 92 and operating with the new modification at the box 94 , the algorithm will return to the box 82 when the fuel cell system 40 transitions from run mode to off mode . the foregoing discussion discloses and describes merely exemplary embodiments of the present invention . one skilled in the art will readily recognize from such discussion and from the accompanying drawings and claims that various changes , modifications and variations can be made therein without departing from the spirit and scope of the invention as defined in the following claims .