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CN102520049A - Three-electrode solid electrolyte hydrogen sensor and hydrogen concentration measuring method using such sensor - Google Patents

Three-electrode solid electrolyte hydrogen sensor and hydrogen concentration measuring method using such sensor Download PDF

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Publication number
CN102520049A
CN102520049A CN2011103359703A CN201110335970A CN102520049A CN 102520049 A CN102520049 A CN 102520049A CN 2011103359703 A CN2011103359703 A CN 2011103359703A CN 201110335970 A CN201110335970 A CN 201110335970A CN 102520049 A CN102520049 A CN 102520049A
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solid electrolyte
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potential electrode
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杨春玲
郑月顺
张岩
郑应荣
刘永慧
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Harbin Institute of Technology
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Harbin Institute of Technology
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Abstract

The invention discloses a three-electrode solid electrolyte hydrogen sensor and a hydrogen concentration measuring method using such sensor, and relates to a solid electrolyte hydrogen sensor and a hydrogen concentration measuring method using such sensor, which solve the problem of low detection accuracy of hydrogen concentration existing in the conventional solid electrolyte hydrogen sensor. The device comprises a first measuring electrode, a second measuring electrode and a reference electrode, which are parallel to one another, are adjacently arranged at equal distance and are all vertically fixed on the upper end face of an electrolyte substrate. The method comprises the following step of: calculating an electromotive force ratio factor R by measuring electromotive force E1 between the first measuring electrode and the reference electrode and electromotive force E2 between the second measuring electrode and the reference electrode so as to calculate the hydrogen concentration. The sensor and the method are applicable to detecting the hydrogen concentration.

Description

Three electrode solid electrolyte hydrogen gas sensors and adopt the density of hydrogen measuring method of this sensor
Technical field
The present invention relates to a kind of solid electrolyte hydrogen gas sensor and adopt the density of hydrogen measuring method of this sensor.
Background technology
Hydrogen is widely used in fields such as petrochemical process, industrial or agricultural, electronics industry, like the petrochemical complex hydrogen preparation field, and ammonia, methyl alcohol and other chemicals synthetic, semiconductor fabrication, the reduction of chemicals and metallurgy, bioenergy etc.Hydrogen is flammable explosive gas, very easily blasts with air mixed.Hydrogen leak is the fire explosion major hazard source; Blast like the Fukushima nuclear power station is just directly relevant with hydrogen leak; In order to ensure the security of the petrochemical production process that has hydrogen, must study the discrimination method of hydrogen, measure the concentration of hydrogen rapidly and accurately; Detect the leakage of fire explosion source hydrogen effectively, and send control information.In addition, the development of hydrogen fuel cell automobile and market-oriented problem relate to the problem of aspects such as metering of transportation, the amounts of hydrogen of storage, the hydrogen of hydrogen, and these all be unable to do without the accurate measurement of density of hydrogen.Militarily, hydrogen fuel has become ideal, eco-friendly power source efficient, cleaning is widely used on the propellant and space shuttle of nuclear submarine, guided missile, rocket, and China's 921 manned astro-engineerings are classified the continuous 0-2% density of hydrogen that shows as research topic.
Also there are many technical matterss in the hydrogen gas sensor of application market, as the semi-conductor type hydrogen gas sensor need under hot conditions, heat, power consumption is big, sets off an explosion easily, and can only qualitative detection, can't realize the accurate measurement of concentration; The catalytic combustion-type hydrogen gas sensor also is a kind of hot type element of hot operation, and its shortcoming is to be prone to poison, and power consumption is big, and stability is bad; Galvanochemistry type hydrogen gas sensor does not need heating work, but operating temperature range is narrower, and electrolytic solution is prone to dry, and the life-span is short; The optical type hydrogen gas sensor is that the quick material of hydrogen is coated onto on the optical device, and this sensor is prone to delamination, foaming phenomenon after repeatedly circulating, thereby uses limited.
In a word, based on the existing problems of the hydrogen gas sensor in the present practical application, exploitation solid electrolyte hydrogen gas sensor still all will have and important meaning in the commercial application field in the scientific research field.But existing solid electrolyte sensor is that it is bigger that this method is influenced by thermal perturbation through output electromotive force inverting density of hydrogen, and the accuracy of detection of hydrogen gas sensor is lower.
Summary of the invention
The present invention is for the low problem of the accuracy of detection of the density of hydrogen that solves existing solid electrolyte hydrogen gas sensor, thereby a kind of three electrode solid electrolyte hydrogen gas sensors is provided and adopts the density of hydrogen measuring method of this sensor.
Three electrode solid electrolyte hydrogen gas sensors; It comprises solid electrolyte substrate; It also comprises potential electrode, No. two potential electrode and contrast electrode; One end of one end of a said potential electrode, an end of No. two potential electrode and contrast electrode all is fixed on the upper surface of solid electrolyte substrate, and a said potential electrode, No. two potential electrode are all vertical with the upper surface of solid electrolyte substrate with contrast electrode; Potential electrode, No. two potential electrode and contrast electrode are parallel to each other, and in potential electrode, No. two potential electrode and the contrast electrode arbitrarily between the two distance equate.
A potential electrode is a platinum electrode; No. two potential electrode are nickel electrode; Contrast electrode is a tungsten electrode; Solid electrolyte substrate is a phosphotungstic acid.
Adopt the density of hydrogen measuring method of above-mentioned three electrode solid electrolyte hydrogen gas sensors, it is realized by following steps:
Step 1, three electrode solid electrolyte hydrogen gas sensors are placed the environment that has hydrogen to be measured;
Electromotive force E between step 2, employing electrodynamic type potential electrode of detector measurement and the contrast electrode 1, adopt the electromotive force E between No. two potential electrode of electrodynamic type detector measurement and the contrast electrode 2, said two electromotive force can adopt following formulate:
E 1 = - T F ( ϵ H + Pt - ϵ H + W + k log n H + Pt n H + W )
E 2 = - T F ( ϵ H + Ni - ϵ H + W + k log n H + Ni n H + W )
In the formula, F is a Faraday constant, i.e. the electric weight of 1mol electron institute band, F=96485.3415C; T is an absolute temperature, and unit is K;
Figure BDA0000103851080000023
Be H +, three of potential electrode, solid electrolyte substrate and an air composition adsorbs molar heat capacity on practising physiognomy,
Figure BDA0000103851080000024
Be H +, three of contrast electrode, solid electrolyte substrate and air composition adsorb molar heat capacity on practising physiognomy,
Figure BDA0000103851080000025
Be H +, three of No. two potential electrode, solid electrolyte substrate and air compositions adsorb molar heat capacity on practising physiognomy; K is a Boltzmann constant, k=1.38065 * 10 -23J/K;
Figure BDA0000103851080000026
Be to adsorb H on the three phase boundary at potential electrode and contrast electrode two ends +The ratio of molal quantity,
Figure BDA0000103851080000027
Be to adsorb H on the three phase boundary at No. two potential electrode and contrast electrode two ends +The ratio of molal quantity;
Step 3, the electrodynamic type detector that step 2 is obtained are measured the electromotive force E between potential electrode and the contrast electrode 1, and the electromotive force E between No. two potential electrode and the contrast electrode 2, through formula:
R = E 1 E 2 = ϵ H + Pt - ϵ H + W + k log n H + Pt n H + W ( ϵ H + Ni - ϵ H + W + k log n H + Ni n H + W ) = ζ ( n )
Calculate electromotive force ratio factor R; In the formula: n is a density of hydrogen to be measured, and ζ (.) is a funtcional relationship to be separated;
Step 4, the electromotive force ratio factor R that step 3 is obtained are passed through formula:
n = g ( ( Σ m = 1 K V m f ( W m R + b 1 m ) ) + b 2 )
Obtain the concentration n of hydrogen to be measured;
In the formula: f (.) is latent layer activation function, and said latent layer activation function selected the logarithmic activation function for use:
Figure BDA0000103851080000032
Realize; G (.) is the output layer activation function, and said output layer activation function is selected linear function for use: y=ax+b realizes; W mWeight coefficient for the input layer activation function; V mWeight coefficient for latent layer activation function; b 1mBe latent layer deviation; b 2Be the output layer deviation;
Wherein: output layer deviation b 2Value be according to formula:
b 2 l + 1 = b 2 l - η ▿ R ( b 2 l ) + α ( b 2 l - b 2 l - 1 )
Training is obtained; In the following formula,
Figure BDA0000103851080000034
For error function to output layer deviation b 2Partial derivative, that is:
▿ Rb 2 = 2 N Σ i = 1 k [ ( n ( e i ) - n i ′ ) n ( e i ) ′ b 2 ]
In the following formula:
Figure BDA0000103851080000036
Be training output result, and
Figure BDA0000103851080000037
n i' be the sample point output valve, e iBe the sample point input value, N is a sample number; K is a neuron number, and i is an integer;
The weight coefficient W of input layer activation function mBe according to formula:
W m l + 1 = W m l - η ▿ R ( W m l ) + α ( W m l - W m l - 1 )
Training is obtained, in the formula,
Figure BDA0000103851080000039
For error function to W mPartial derivative, that is:
▿ EWm = 2 N Σ i = 1 k [ ( n ( e i ) - n i ′ ) n ( e i ) ′ Wm ]
In the following formula; N (e i) ' Wm=a * V m* f 1' * e i,
F in the following formula 1' be that logarithmic function is to input layer Q (i)=W me i+ b 1mThe local derviation value, that is:
f 1 ′ = - e Q ( i ) ( 1 + e Q ( i ) ) 2 ;
Latent layer activation function V mWeight coefficient be according to formula:
V m l + 1 = V m l - η ▿ R ( V m l ) + α ( V m l - V m l - 1 )
Training obtains, in the following formula:
▿ RVm = 2 N Σ i = 1 k [ ( n ( e i ) - n i ′ ) n ( e i ) ′ Vm ]
In the following formula, n (e i) ' Vm=a * f (Wm * e i+ b 1m);
Latent layer deviation b 1mFor being according to formula:
b 1 m l + 1 = b 1 m l - η ▿ R ( b 1 m l ) + α ( b 1 m l - b 1 m l - 1 )
Training obtains, in the following formula: For error function to b 1mPartial derivative, that is:
▿ Rb 1 m = 2 N Σ i = 1 k [ ( n ( e i ) - n i ′ ) n ( e i ) ′ b 1 m ]
In the following formula, n ( e i ) ′ b 1 m = a × V m × f 1 ′ .
At weight coefficient W to the input layer activation function mThe weight coefficient V of latent layer activation function mLatent layer deviation b 1mWith output layer deviation b 2Training result, be by the decision of the value of error e, be specially:
According to formula:
e = 1 N Σ i = 1 N ( n ( e i ′ ) - n i ′ ) 2
Obtain the value of error e;
Value and error threshold T with the error e that obtains compares then, when the value of error e during more than or equal to error threshold T, continues to train; When the value of error e during less than error threshold T, end training, obtain the weight coefficient W of input layer activation function mThe weight coefficient V of latent layer activation function mLatent layer deviation b 1mWith output layer deviation b 2Training result; Said error threshold T=0.01~0.03.
Beneficial effect: three electrode solid electrolyte hydrogen gas sensors of the present invention and adopt the density of hydrogen measuring method of this sensor not receiving under the Influence of Temperature to separate electromotive force and density of hydrogen; The density of hydrogen accuracy of detection is high, and the sensing range of density of hydrogen can reach 0-5%.
Description of drawings
Fig. 1 is a structural representation of the present invention.
Embodiment one, combination Fig. 1 explain this embodiment; Three electrode solid electrolyte hydrogen gas sensors; It comprises solid electrolyte substrate 4; It also comprises potential electrode 1, No. two potential electrode 2 and contrast electrodes 3; One end of one end of a said potential electrode 1, an end of No. two potential electrode 2 and contrast electrode 3 all is fixed on the upper surface of solid electrolyte substrate 4, and a said potential electrode 1, No. two potential electrode 2 are all vertical with the upper surface of solid electrolyte substrate 4 with contrast electrode 3; Potential electrode 1, No. two potential electrode 2 and contrast electrode 3 are parallel to each other, and in potential electrode 1, No. two potential electrode 2 and the contrast electrode 3 arbitrarily between the two distance equate.
Principle of work: the electrochemical reaction of three electrode solid electrolyte type hydrogen gas sensors mainly is to occur in three places of practising physiognomy.So-called three to practise physiognomy be the intersection of electrolyte plate, electrode and ambient gas environment, and behind contacted with hydrogen to an electrode in the surrounding environment or No. two electrodes, hydrogen molecule can be H by catalytic decomposition +With electronics, electronics can pass through electrolyte and be sent on the contrast electrode 3, will cause the variation of electromotive force between two potential electrode and the contrast electrode like this.The present invention separates with density of hydrogen electromotive force through under the state that does not receive Influence of Temperature, thereby obtains high-precision density of hydrogen testing result.
The three electrode solid electrolyte type hydrogen gas sensors of this embodiment; When being operated under the environment with thermal perturbation; Has advantage highly sensitive, that the response time short, the life-span is long; Main performance index is: (1) need not heating, effectively reduces power consumption, increases explosion-proof security, effectively reduces failure mode, the long service life that material causes under hot conditions; (2) sensitivity is less than 100PPm; (3) response time is less than 10s; (4) life-span was greater than 5 years; (5) the novel three electrode solid electrolyte hydrogen gas sensors based on the adaptive algorithm model that designed can not receive to separate electromotive force and density of hydrogen, measurement range 0-5% under the Influence of Temperature.
The difference of embodiment two, this embodiment and embodiment one described three electrode solid electrolyte hydrogen gas sensors is that No. one potential electrode 1 is a platinum electrode.
The difference of embodiment three, this embodiment and embodiment one described three electrode solid electrolyte hydrogen gas sensors is that No. two potential electrode 2 is a nickel electrode.
The difference of embodiment four, this embodiment and embodiment one described three electrode solid electrolyte hydrogen gas sensors is that contrast electrode 3 is a tungsten electrode.
The difference of embodiment five, this embodiment and embodiment one, two, three or four described three electrode solid electrolyte hydrogen gas sensors is that solid electrolyte substrate 4 is a phosphotungstic acid.
The density of hydrogen measuring method of embodiment six, employing embodiment one described three electrode solid electrolyte hydrogen gas sensors, it is realized by following steps:
Step 1, three electrode solid electrolyte hydrogen gas sensors are placed the environment that has hydrogen to be measured;
Electromotive force E between step 2, employing electrodynamic type potential electrode 1 of detector measurement and the contrast electrode 3 1, adopt the electromotive force E between No. two potential electrode 2 of electrodynamic type detector measurement and the contrast electrode 3 2, said two electromotive force can adopt following formulate:
E 1 = - T F ( ϵ H + Pt - ϵ H + W + k log n H + Pt n H + W )
E 2 = - T F ( ϵ H + Ni - ϵ H + W + k log n H + Ni n H + W )
In the formula, F is a Faraday constant, i.e. the electric weight of 1mol electron institute band, F=96485.3415C; T is an absolute temperature, and unit is K;
Figure BDA0000103851080000061
Be H +, three of potential electrode 1, solid electrolyte substrate 4 and an air composition adsorbs molar heat capacity on practising physiognomy,
Figure BDA0000103851080000062
Be H +, three of contrast electrode 3, solid electrolyte substrate 4 and air composition adsorb molar heat capacity on practising physiognomy,
Figure BDA0000103851080000063
Be H +, three of No. two potential electrode 2, solid electrolyte substrate 4 and air compositions adsorb molar heat capacity on practising physiognomy; K is a Boltzmann constant, k=1.38065 * 10 -23J/K;
Figure BDA0000103851080000064
Be to adsorb H on the three phase boundary at potential electrode 1 and contrast electrode 3 two ends +The ratio of molal quantity,
Figure BDA0000103851080000065
Be to adsorb H on the three phase boundary at No. two potential electrode 2 and contrast electrode two ends +The ratio of molal quantity;
Step 3, the electrodynamic type detector that step 2 is obtained are measured the electromotive force E between potential electrode 1 and the contrast electrode 3 1, and the electromotive force E between No. two potential electrode 2 and the contrast electrode 3 2, through formula:
R = E 1 E 2 = ϵ H + Pt - ϵ H + W + k log n H + Pt n H + W ( ϵ H + Ni - ϵ H + W + k log n H + Ni n H + W ) = ζ ( n )
Calculate electromotive force ratio factor R; In the formula: n is a density of hydrogen to be measured, and ζ (.) is a funtcional relationship to be separated,
Step 4, the electromotive force ratio factor R that step 3 is obtained are passed through formula:
n = g ( ( Σ m = 1 K V m f ( W m R + b 1 m ) ) + b 2 )
Obtain the concentration n of hydrogen to be measured;
In the formula: f (.) is latent layer activation function, and said latent layer activation function selected the logarithmic activation function for use:
Figure BDA0000103851080000068
Realize; G (.) is the output layer activation function, and said output layer activation function is selected linear function for use: y=ax+b realizes; W mWeight coefficient for the input layer activation function; V mWeight coefficient for latent layer activation function; b 1mBe latent layer deviation; b 2Be the output layer deviation;
Wherein: output layer deviation b 2Value be according to formula:
b 2 l + 1 = b 2 l - η ▿ R ( b 2 l ) + α ( b 2 l - b 2 l - 1 )
Training is obtained; In the following formula,
Figure BDA00001038510800000610
For error function to output layer deviation b 2Partial derivative, that is:
▿ Rb 2 = 2 N Σ i = 1 k [ ( n ( e i ) - n i ′ ) n ( e i ) ′ b 2 ]
In the following formula:
Figure BDA0000103851080000072
Be training output result, and
Figure BDA0000103851080000073
n i' be the sample point output valve, e iBe the sample point input value, N is a sample number; K is a neuron number, and i is an integer;
The weight coefficient W of input layer activation function mBe according to formula:
W m l + 1 = W m l - η ▿ R ( W m l ) + α ( W m l - W m l - 1 )
Training is obtained, in the formula,
Figure BDA0000103851080000075
For error function to W mPartial derivative, that is:
▿ EWm = 2 N Σ i = 1 k [ ( n ( e i ) - n i ′ ) n ( e i ) ′ Wm ]
In the following formula: n (e i) ' Wm=a * V m* f 1' * e i,
F in the following formula 1' be that logarithmic function is to input layer Q (i)=W me i+ b 1mThe local derviation value, that is:
f 1 ′ = - e Q ( i ) ( 1 + e Q ( i ) ) 2 ;
Latent layer activation function V mWeight coefficient be according to formula:
V m l + 1 = V m l - η ▿ R ( V m l ) + α ( V m l - V m l - 1 )
Training obtains, in the following formula:
▿ RVm = 2 N Σ i = 1 k [ ( n ( e i ) - n i ′ ) n ( e i ) ′ Vm ]
In the following formula, n (e i) ' Vm=a * f (Wm * e i+ b 1m);
Latent layer deviation b 1mFor being according to formula:
b 1 m l + 1 = b 1 m l - η ▿ R ( b 1 m l ) + α ( b 1 m l - b 1 m l - 1 )
Training obtains, in the following formula:
Figure BDA00001038510800000711
For error function to b 1mPartial derivative, that is:
▿ Rb 1 m = 2 N Σ i = 1 k [ ( n ( e i ) - n i ′ ) n ( e i ) ′ b 1 m ]
In the following formula, n ( e i ) ′ b 1 m = a × V m × f 1 ′ .
At weight coefficient W to the input layer activation function mThe weight coefficient V of latent layer activation function mLatent layer deviation b 1mWith output layer deviation b 2Training result, be by the decision of the value of error e, be specially:
According to formula:
e = 1 N Σ i = 1 N ( n ( e i ′ ) - n i ′ ) 2
Obtain the value of error e;
Value and error threshold T with the error e that obtains compares then, when the value of error e during more than or equal to error threshold T, continues to train; When the value of error e during less than error threshold T, end training, obtain the weight coefficient W of input layer activation function mThe weight coefficient V of latent layer activation function mLatent layer deviation b 1mWith output layer deviation b 2Training result; Said error threshold T=0.01~0.03.

Claims (7)

1. three electrode solid electrolyte hydrogen gas sensors; It comprises solid electrolyte substrate (4); It is characterized in that: further comprising a potential electrode (1), No. two potential electrode (2) and contrast electrode (3); One end of one end of one end of a said potential electrode (1), No. two potential electrode (2) and contrast electrode (3) all is fixed on the upper surface of solid electrolyte substrate (4), and a said potential electrode (1), No. two potential electrode (2) and contrast electrode (3) are all vertical with the upper surface of solid electrolyte substrate (4); A potential electrode (1), No. two potential electrode (2) and contrast electrode (3) are parallel to each other, and any distance between the two equates in a potential electrode (1), No. two potential electrode (2) and the contrast electrode (3).
2. three electrode solid electrolyte hydrogen gas sensors according to claim 1 is characterized in that a potential electrode (1) is platinum electrode.
3. three electrode solid electrolyte hydrogen gas sensors according to claim 1 is characterized in that No. two potential electrode (2) are nickel electrode.
4. three electrode solid electrolyte hydrogen gas sensors according to claim 1 is characterized in that contrast electrode (3) is a tungsten electrode.
5. according to claim 1,2,3 or 4 described three electrode solid electrolyte hydrogen gas sensors, it is characterized in that solid electrolyte substrate (4) is a phosphotungstic acid.
6. adopt the density of hydrogen measuring method of the described three electrode solid electrolyte hydrogen gas sensors of claim 1, it is characterized in that: it is realized by following steps:
Step 1, three electrode solid electrolyte hydrogen gas sensors are placed the environment that has hydrogen to be measured;
Step 2, employing electrodynamic type detector are measured the electromotive force E between a potential electrode (1) and the contrast electrode (3) 1, adopt the electrodynamic type detector to measure the electromotive force E between No. two potential electrode (2) and the contrast electrode (3) 2, said two electromotive force can adopt following formulate:
E 1 = - T F ( ϵ H + Pt - ϵ H + W + k log n H + Pt n H + W )
E 2 = - T F ( ϵ H + Ni - ϵ H + W + k log n H + Ni n H + W )
In the formula, F is a Faraday constant, i.e. the electric weight of 1mol electron institute band, F=96485.3415C; T is an absolute temperature, and unit is K; Be H +Absorption molar heat capacity on three of a potential electrode (1), solid electrolyte substrate (4) and air composition practised physiognomy,
Figure FDA0000103851070000014
Be H +Absorption molar heat capacity on three of contrast electrode (3), solid electrolyte substrate (4) and air composition practised physiognomy,
Figure FDA0000103851070000015
Be H +Absorption molar heat capacity on three of No. two potential electrode (2), solid electrolyte substrate (4) and air composition practised physiognomy; K is a Boltzmann constant, k=1.38065 * 10 -23J/K;
Figure FDA0000103851070000021
Be to adsorb H on the three phase boundary at a potential electrode (1) and contrast electrode (3) two ends +The ratio of molal quantity,
Figure FDA0000103851070000022
Be to adsorb H on the three phase boundary at No. two potential electrode (2) and contrast electrode two ends +The ratio of molal quantity;
Step 3, the electrodynamic type detector that step 2 is obtained are measured the electromotive force E between a potential electrode (1) and the contrast electrode (3) 1, and the electromotive force E between No. two potential electrode (2) and the contrast electrode (3) 2, through formula:
R = E 1 E 2 = ϵ H + Pt - ϵ H + W + k log n H + Pt n H + W ( ϵ H + Ni - ϵ H + W + k log n H + Ni n H + W ) = ζ ( n )
Calculate electromotive force ratio factor R; In the formula: n is a density of hydrogen to be measured, and ζ (.) is a funtcional relationship to be separated;
Step 4, the electromotive force ratio factor R that step 3 is obtained are passed through formula:
n = g ( ( Σ m = 1 K V m f ( W m R + b 1 m ) ) + b 2 )
Obtain the concentration n of hydrogen to be measured;
In the formula: f (.) is latent layer activation function, and said latent layer activation function selected the logarithmic activation function for use:
Figure FDA0000103851070000025
Realize; G (.) is the output layer activation function, and said output layer activation function is selected linear function for use: y=ax+b realizes; W mWeight coefficient for the input layer activation function; V mWeight coefficient for latent layer activation function; b 1mBe latent layer deviation; b 2Be the output layer deviation;
Wherein: output layer deviation b 2Value be according to formula:
b 2 l + 1 = b 2 l - η ▿ R ( b 2 l ) + α ( b 2 l - b 2 l - 1 )
Training is obtained; In the following formula,
Figure FDA0000103851070000027
For error function to output layer deviation b 2Partial derivative, that is:
▿ Rb 2 = 2 N Σ i = 1 k [ ( n ( e i ) - n i ′ ) n ( e i ) ′ b 2 ]
In the following formula:
Figure FDA0000103851070000029
Be training output result, and
Figure FDA00001038510700000210
n i' be the sample point output valve, e iBe the sample point input value, N is a sample number; K is a neuron number, and i is an integer;
The weight coefficient W of input layer activation function mBe according to formula:
W m l + 1 = W m l - η ▿ R ( W m l ) + α ( W m l - W m l - 1 )
Training is obtained, in the formula, For error function to W mPartial derivative, that is:
▿ EWm = 2 N Σ i = 1 k [ ( n ( e i ) - n i ′ ) n ( e i ) ′ Wm ]
In the following formula: n (e i) ' Wm=a * V m* f 1' * e i,
F in the following formula 1' be that logarithmic function is to input layer Q (i)=W me i+ b 1mThe local derviation value, that is:
f 1 ′ = - e Q ( i ) ( 1 + e Q ( i ) ) 2 ;
Latent layer activation function V mWeight coefficient be according to formula:
V m l + 1 = V m l - η ▿ R ( V m l ) + α ( V m l - V m l - 1 )
Training obtains, in the following formula:
▿ RVm = 2 N Σ i = 1 k [ ( n ( e i ) - n i ′ ) n ( e i ) ′ Vm ]
In the following formula, n (e i) ' Vm=a * f (Wm * e i+ b 1m);
Latent layer deviation b 1mFor being according to formula:
b 1 m l + 1 = b 1 m l - η ▿ R ( b 1 m l ) + α ( b 1 m l - b 1 m l - 1 )
Training obtains, in the following formula:
Figure FDA0000103851070000038
For error function to b 1mPartial derivative, that is:
▿ Rb 1 m = 2 N Σ i = 1 k [ ( n ( e i ) - n i ′ ) n ( e i ) ′ b 1 m ]
In the following formula, n ( e i ) ′ b 1 m = a × V m × f 1 ′ .
7. according to the said density of hydrogen measuring method of claim 6, it is characterized in that at weight coefficient W to the input layer activation function mThe weight coefficient V of latent layer activation function mLatent layer deviation b 1mWith output layer deviation b 2Training result, be by the decision of the value of error e, be specially:
According to formula:
e = 1 N Σ i = 1 N ( n ( e i ′ ) - n i ′ ) 2
Obtain the value of error e;
Value and error threshold T with the error e that obtains compares then, when the value of error e during more than or equal to error threshold T, continues to train; When the value of error e during less than error threshold T, end training, obtain the weight coefficient W of input layer activation function mThe weight coefficient V of latent layer activation function mLatent layer deviation b 1mWith output layer deviation b 2Training result; Said error threshold T=0.01~0.03.
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Application publication date: 20120627