CN112807944B - Adjusting method of ammonia water flow adjusting system for tail gas denitration - Google Patents
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Abstract
The invention discloses an ammonia water flow regulating system and method for tail gas denitration, which comprises an ammonia water main trunk line, a first ammonia water branch trunk line, a second ammonia water branch trunk line, a first flow regulating valve, a second flow regulating valve, a first nitrogen oxide sensor, a second nitrogen oxide sensor and a main control board.
Description
Technical Field
The invention relates to an adjusting method of an ammonia water flow adjusting system for tail gas denitration, and belongs to the field of nitrogen oxide flue gas treatment.
Background
Residual nitrogen oxide content after SNCR + SCR coupling denitration treatment of flue gas that the thermoelectric boiler produced is the important index of fume emission, and along with the thermoelectric boiler transformation and then productivity increase, the flow of flue gas generally begins to increase, and corresponding aqueous ammonia flow also increases correspondingly. Less ammonia water causes unqualified nitrogen oxide content index in the treated flue gas, secondary treatment is needed, and the treatment cost is further increased. While excessive ammonia water can ensure the content of nitrogen oxides to reach the standard, the cost of the ammonia water is obviously increased. In particular, the production process of ammonia also has a considerable environmental impact, so that the use of excess ammonia for the treatment of nitrogen oxides is not justified for environmental protection. Therefore, how to ensure the matching between the ammonia water flow and the flue gas flow and reduce the ammonia water waste and the treatment cost on the basis of ensuring the standard of the nitrogen oxide index is very important.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an ammonia water flow regulating system and an ammonia water flow regulating method for tail gas denitration, which are used for matching and regulating ammonia water flow and flue gas flow so as to reduce flue gas treatment cost.
To solve the technical problem, the invention adopts the following technical scheme:
an ammonia water flow regulating system for tail gas denitration comprises an ammonia water main trunk line, a first ammonia water branch trunk line, a second ammonia water branch trunk line, a first flow regulating valve, a second flow regulating valve, a first nitric oxide sensor, a second nitric oxide sensor and a main control board, wherein the first ammonia water branch trunk line and the second ammonia water branch trunk line are connected to the ammonia water main trunk line in parallel, the first flow regulating valve is installed on the first ammonia water branch trunk line, the second flow regulating valve is installed on the second ammonia water branch trunk line, the first nitric oxide sensor is arranged at an air inlet, the second nitric oxide sensor is arranged at an air outlet, the ammonia water main trunk line is communicated between the air inlet and the air outlet, and the first flow regulating valve, the second flow regulating valve, the first nitric oxide sensor and the second nitric oxide sensor are electrically connected to the main control board;
the first flow regulating valve is a valve with equal percentage characteristic, the second flow regulating valve is a valve with linear characteristic, and the concentration of nitrogen oxide at the exhaust port is changed by regulating the first flow regulating valve and the second flow regulating valve.
The invention has the beneficial effects that:
the first nitrogen oxide sensor detects that the concentration of nitrogen oxide at the gas inlet is a mg/L,the concentration of nitrogen oxide at the exhaust port is measured by the second nitrogen oxide sensor to be b mg/L, the maximum flow of the first flow regulating valve is c kg/h, the maximum flow of the second flow regulating valve is d kg/h, and the single opening regulating quantity of the first flow regulating valve is n 1 The single opening degree regulating quantity of the second flow regulating valve is n 2 The first flow regulating valve is an equal percentage characteristic valve, and the second flow regulating valve is a linear characteristic valve.
The ammonia water in the first ammonia water branch road and the second ammonia water branch road converges in the ammonia water main road, and then the flue gas between the gas inlet and the gas outlet is treated. The first flow regulating valve serving as the equal percentage characteristic valve increases the opening degree each time, the corresponding ammonia water flow increment is gradually increased, basic ammonia water supply can be guaranteed, the opening degree is further increased under the condition that the internal flow of the first flow regulating valve is large, the ammonia water flow can be increased violently, and the concentration of low-concentration nitric oxide can be further effectively reduced, so that the concentration of the nitric oxide meets the emission standard. And the second flow control valve as the linear characteristic valve can make the aqueous ammonia flow change by the regulation of aperture equivalent to help reducing the difference between discharging nitrogen oxide concentration and emission standard, in order to avoid the excessive use of aqueous ammonia. The adjustment processes of the first flow regulating valve and the second flow regulating valve do not interfere with each other, so that the adjustment effects of the first flow regulating valve and the second flow regulating valve are stabilized. After the flue gas flow at the gas inlet after the boiler is transformed is stable, firstly, the first flow regulating valve is regulated to roughly regulate the flow of ammonia water, so that the concentration of nitrogen oxides at the gas outlet is obviously reduced, then, the second flow regulating valve is regulated to finely regulate the flow of ammonia water, so that the concentration of nitrogen oxides is ensured to be lower than the emission standard, meanwhile, the difference between the concentration of nitrogen oxides and the emission standard is reduced as far as possible, the cost of ammonia water is greatly reduced, and the balance is obtained between economic benefits and environmental benefits.
An adjusting method of an ammonia water flow adjusting system for tail gas denitration is characterized in that the single opening adjusting quantity of a first flow adjusting valve is n 1 The single opening degree regulating quantity of the second flow regulating valve is n 2 First flow regulating valveOpening of pn 1 P is a natural number not greater than x, xn 1 =1, opening degree of the second flow regulating valve is qn 2 Q is a natural number not greater than y, yn 2 =1。
The emission standard R mg/L is set, after a detection value a mg/L of a first nitric oxide sensor is stabilized, the opening degree of a first flow regulating valve is regulated to be 0, the opening degree of a second flow regulating valve is regulated to be 1, then the opening degree of the first flow regulating valve is gradually increased, when a detection value b mg/L of a second nitric oxide sensor is lower than R mg/L, the regulation of the first flow regulating valve is stopped, and the second flow regulating valve is started to be regulated, so that the difference value between b and R is reduced.
The second flow rate regulating valve of the present invention is regulated as follows:
step S1, adjusting the opening degree of the second flow regulating valve to (y-1) n 2 If b is larger than R, adjusting the opening degree of the second flow regulating valve back to 1, and ending the adjustment, if b is smaller than R, entering the step S2;
step S2: adjusting the opening degree of the second flow regulating valve to 0, if b is less than R, finishing the adjustment, and if b is more than R, entering the step S3;
and step S3: and gradually increasing the opening of the second flow regulating valve until b is less than R, and finishing the regulation.
The flow rate and the opening degree of the first flow rate regulating valve are (x-1) n when the opening degree is 1 1 The difference between the flow rates is smaller than d.
Invention n 1 ＞n 2 。
Invention n 1 =0.25，n 2 =0.1。
In step S3 of the invention, if the adjusting times of the second flow regulating valve is z and z is not less than 3, the time interval between the eta-1 adjustment and the eta adjustment of the second flow regulating valve is t η-1 Eta is a natural number of not less than 2 and not more than z, t η-1 ＜t η 。
The main control board is electrically connected with an alarm and an electronic on-off valve, the electronic on-off valve is positioned at the air inlet, and if b is larger than R when the opening of the first flow regulating valve is 1, the main control board controls the alarm to give an alarm and controls the electronic on-off valve to be switched off.
When a of the invention is stable 0 -a 1 ≤a≤a 0 +a 1 ，a 1 =0.05a 0 。
Other features and advantages of the present invention will be disclosed in more detail in the following detailed description of the invention and the accompanying drawings.
Drawings
The invention is further described below with reference to the accompanying drawings:
fig. 1 is a schematic view of a topological structure of an ammonia water flow rate adjusting system according to an embodiment of the present invention;
fig. 2 is a control flowchart of the ammonia water flow rate adjustment system according to the embodiment of the present invention.
Detailed Description
The technical solutions of the embodiments of the present invention are explained and illustrated below with reference to the drawings of the embodiments of the present invention, but the embodiments described below are only preferred embodiments of the present invention, and not all of them. Other embodiments obtained by persons skilled in the art without making creative efforts based on the embodiments in the implementation belong to the protection scope of the invention.
In the following description, the appearances of the indicating orientation or positional relationship such as the terms "inner", "outer", "upper", "lower", "left", "right", etc. are only for convenience in describing the embodiments and for simplicity in description, and do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and are not to be construed as limiting the present invention.
Example (b):
referring to fig. 1-2, the embodiment provides an ammonia water flow regulating system for denitration of tail gas, including an ammonia water main trunk 1, a first ammonia water branch trunk 2, a second ammonia water branch trunk 3, a first flow regulating valve 4, a second flow regulating valve 5, a first nitrogen oxide sensor 6, a second nitrogen oxide sensor 7 and a main control board 8.
Wherein the first ammonia water branch trunk 2 and the second ammonia water branch trunk 3 are connected in parallel to the ammonia water main trunk 1, the ammonia water main trunk 1 is communicated to the flue gas reaction chamber 13, the ammonia water in the first ammonia water branch trunk 2 and the second ammonia water branch trunk 3 converges in the ammonia water main trunk 1, then flows into the flue gas reaction chamber 13, and the flue gas rich in nitrogen oxides flows into the flue gas reaction chamber 13 from the gas inlet 11 of the flue gas reaction chamber 13. The nitrogen oxides in the flue gas react with the ammonia water in the flue gas reaction chamber 13 to reduce the content of the nitrogen oxides in the flue gas, and then the nitrogen oxides are discharged from the exhaust port 12. The flue gas moves faster in the ammonia flue gas reaction chamber 13, so in order to ensure the removal effect of nitrogen oxides, the flow rate of ammonia needs to be maintained at a higher level.
The first flow control valve 4 is installed on the first ammonia branch line 2, the first flow control valve 4 controls the ammonia water flow rate in the first ammonia branch line 2, the second flow control valve 5 is installed on the second ammonia branch line 3, and the second flow control valve 5 controls the ammonia water flow rate in the second ammonia branch line 3. The first nitrogen oxide sensor 6 is provided at the gas inlet 11, the first nitrogen oxide sensor 6 monitors the nitrogen oxide concentration at the gas inlet 11, the second nitrogen oxide sensor 7 is provided at the gas outlet 12, and the second nitrogen oxide sensor 7 monitors the nitrogen oxide concentration at the gas outlet 12.
The first flow regulating valve 4, the second flow regulating valve 5, the first nitrogen oxide sensor 6 and the second nitrogen oxide sensor 7 are electrically connected to a main control board 8, and the main control board 8 regulates and controls the first flow regulating valve 4 and the second flow regulating valve 5 according to monitoring data of the second nitrogen oxide sensor 7. In addition, the main control board 8 is also electrically connected with an alarm 9 and an electronic on-off valve 10, the electronic on-off valve 10 is located at the air inlet 11, and the electronic on-off valve 10 controls the on-off of the air inlet 11.
Specifically, the concentration of the nitrogen oxide at the air inlet 11 is measured to be a mg/L by the first nitrogen oxide sensor 6, the concentration of the nitrogen oxide at the air outlet 12 is measured to be b mg/L by the second nitrogen oxide sensor 7, the emission standard of the concentration of the nitrogen oxide is R mg/L, and the flow of the ammonia water is controlled by the first flow regulating valve 4 and the second flow regulating valve 5 so as to control b to be less than R. For example, in the case of a =1 and R =0.4, since the ammonia and the nitrogen oxide are not completely reacted, when b =0.3, the flow rate of the 20% ammonia is about 35-40kg/h, which is equivalent to about 5-5.7kg/h for every 0.1 mg/L decrease of the nitrogen oxide concentration, but when b =0.2, the flow rate of the 20% ammonia is 50-70kg/h, which is equivalent to about 6.25-8.75kg/h for every 0.1 mg/L decrease of the nitrogen oxide concentration, and the utility-price ratio of the ammonia is significantly decreased in consideration of the production cost of the ammonia itself and the influence on the environment during the production process. Therefore, the present embodiment aims to reduce the difference between b and R as much as possible in the case of controlling b < R, thereby increasing the cost performance of ammonia water as much as possible.
Specifically, the first flow regulating valve 4 is a valve with equal percentage characteristics, the maximum flow of the first flow regulating valve 4 is c kg/h, and the single opening regulating quantity of the first flow regulating valve 4 is n 1 . The second flow regulating valve 5 is a linear valve, the maximum flow of the second flow regulating valve 5 is d kg/h, and the single-opening regulating quantity of the second flow regulating valve 5 is n 2 . In order to ensure that the first and second flow rate adjustment valves 4, 5 can be fully utilized, the opening degrees of the first and second flow rate adjustment valves 4, 5 need to be up to 1. Meanwhile, in order to ensure that the flow of ammonia water can be adjusted to 0 in an emergency state, the opening degrees of the first flow regulating valve 4 and the second flow regulating valve 5 need to be 0.
Based on this:
the opening degree of the first flow rate adjustment valve 4 is pn 1 P is a natural number not greater than x, i.e., the opening of the first flow rate adjustment valve 4 is 0, n 1 、2n 1 、3n 1 、4n 1 ...（x-1）n 1 Or xn 1 ，xn 1 And =1. The corresponding first flow rate regulating valve 4 has a flow rate of 0, λ 1 、λ 2 、λ 3 、λ 4 、...λ x-1 Or ckg/h. Corresponding lambda 1 -0＜λ 2 -λ 1 ＜λ 3 -λ 2 ...＜c-λ x-1 。
The opening degree of the second flow rate adjustment valve 5 is qn 2 Q is a natural number not greater than y, i.e., the opening of the second flow rate adjustment valve 5 is 0, n 2 、2n 2 、3n 2 、4n 2 ...（y-1）n 2 Or yn 2 ，yn 2 And =1. Corresponding second flow rate adjustmentThe flow rate of the throttle valve 5 is 0, gamma 1 、γ 2 、γ 3 、γ 4 、...γ y-1 Or dkg/h. Corresponding to gamma 1 -0=γ 2 -γ 1 =γ 3 -γ 2 ...=d-γ y-1 。
For example, when a =1.2 and r =0.3 and when b =1, the flow rate of ammonia water needs to be approximately ω 1 kg/h, ammonia flow approximately ω when b =0.8 2 kg/h, when b =0.6, the ammonia flow rate needs to be approximately ω 3 kg/h, when b =0.4, the ammonia flow rate needs to be approximately ω 4 kg/h，ω 2 -ω 1 ＜ω 3 -ω 2 ＜ω 4 -ω 3 . It can be seen that each time the value b is decreased, the increment of the ammonia flow is increased to match the regulation characteristic of the first flow regulating valve 4. Therefore, the amount of change in the b value is constant every time the opening degree of the first flow rate adjustment valve 4 is increased, and by increasing the opening degree of the first flow rate adjustment valve 4, the basic ammonia water supply can be secured, which contributes to a rapid decrease in the b value to the vicinity of the R value. When b and R are relatively close, the first flow regulating valve 4 has a certain opening degree, the flow of the ammonia water is relatively large, and d < c, so that the flow of the second flow regulating valve 5 is not large in the whole flow of the ammonia water, but the flow of the ammonia water can be linearly changed slightly by regulating the second flow regulating valve 5, so that a specific flow value or flow value range of the ammonia water is found, and the difference between b and R is reduced as much as possible under the condition that b is less than R.
The specific flow regulating method of the ammonia water flow regulating system is as follows:
step S0, firstly, the opening degree of the first flow regulating valve 4 is regulated to be 0, the opening degree of the second flow regulating valve 5 is regulated to be 1, after a and b are stabilized, the opening degree of the first flow regulating valve 4 is gradually increased until b is less than R, the regulation of the first flow regulating valve 4 is stopped, and at the moment, the opening degree of the first flow regulating valve 4 is regulated to be p 1 n 1 The flow rate of the first flow rate regulating valve 4 is λ p1 The flow proceeds to step S1 to start adjusting the second flow rate adjustment valve 5; if b is still larger than R when the opening degree of the first flow rate adjustment valve 4 is 1, it means that the first flow rate adjustment valve 4 and the second flow rate adjustment valve 5 cannot satisfyWhen the boiler flue gas is required to be treated, the main control board 8 controls the alarm 9 to give an alarm, and controls the electronic on-off valve 10, the first flow regulating valve 4 and the second flow regulating valve 5 to be disconnected so as to replace the first flow regulating valve 4 and the second flow regulating valve 5;
considering the actual use condition of the boiler, the value of a is used as a when a is stable in the step 0 The central value is floated up and down, the floating proportion is 5 percent, namely a 0 -a 1 ≤a≤a 0 +a 1 ，a 1 =0.05a 0 If a cannot satisfy the condition for a long time, it indicates that the boiler is abnormal in operation and needs to be overhauled. For convenience of explanation, a is regarded as a constant value a in the present embodiment 0 。
Step S1 of adjusting the opening degree of the second flow rate adjustment valve 5 to (y-1) n 2 If b > R, the opening of the second flow rate control valve 5 is adjusted back to 1, corresponding to a specific flow rate value of (lambda) p1 + d) kg/h, finishing the adjustment, and if b is less than R, entering the step S2.
Step S2: the opening degree of the second flow regulating valve 5 is regulated to 0, if b is less than R, the corresponding specific flow value is lambda p1 kg/h, the regulation is ended, if b > R, the specific flow rate value is (lambda) p1 + d) kg/h and λ p 1 kg/h, go to step S3.
And step S3: gradually increasing the opening degree of the second flow regulating valve 5 until b is less than R, wherein the opening degree of the second flow regulating valve 5 is q 1 n 2 At a flow rate of gamma q1 The specific flow rate value is (lambda) p1 +γ q1 ) kg/h, and finishing the adjustment.
Based on the above operation procedure, in step S0, n 1 The value cannot be too small to ensure that b can drop rapidly below R, reducing the number of adjustments to the first flow regulator valve 4, step S3, n 2 The value must not be too large to reduce the difference between b and R, so that n 1 ＞n 2 。
Preferably, n is 1 =0.25，n 2 =0.1。
In step S3, if the number of times of adjustment of the second flow rate adjustment valve 5 is z and z is not less than 3, the second flow rate adjustment valve is adjusted for the η -1 th timeThe time interval between the section and the eta adjustment is t η-1 Eta is a natural number of not less than 2 and not more than z, t η-1 ＞t η 。
Taking this embodiment as an example, in step S3, the second flow rate adjustment valve 5 is subjected to the opening degree increasing operation three times in total so that the opening degrees of the second flow rate adjustment valve 5 are changed from 0 to n in order 2 、2n 2 、3n 2 The flow rate of the corresponding second flow rate regulating valve 5 is changed from 0 to gamma in turn 1 、γ 2 、γ 3 Wherein the time interval between the first operation and the second operation is t 1 The time interval between the second operation and the third operation is t 2 . Since the second flow rate adjustment valve 5 is a linear valve, when the flow rate of the second flow rate adjustment valve 5 is adjusted from γ 1 Is lifted to gamma 2 Will produce more violent oscillation t 1 It needs to be larger to obtain a more stable b value when the flow rate of the second flow rate adjustment valve 5 is adjusted from γ 2 Is lifted to gamma 3 So that t is relatively gentle 2 Can be smaller, corresponding to t 1 ＞t 2 。
Since the first flow rate adjusting valve 4 and the second flow rate adjusting valve 5 are respectively arranged on the first ammonia branch line 2 and the second ammonia branch line 3, the adjusting processes of the first flow rate adjusting valve 4 and the second flow rate adjusting valve 5 do not interfere with each other, and the adjusting effects of the first flow rate adjusting valve 4 and the second flow rate adjusting valve 5 are stabilized.
Further, the flow rate and the opening degree of the first flow rate adjusting valve 4 are (x-1) n when the opening degree is 1 1 The difference between the flow rates of time is less than d, i.e. c-lambda x-1 ＜d。
In step S0, the opening degree of the first flow rate adjustment valve 4 is p 1 n 1 When b is less than R, the corresponding total flow of ammonia water is (lambda) p1 + d) kg/h, so when the opening of the first flow rate adjustment valve 4 is (p) 1 -1）n 1 When b is more than R, the total flow of ammonia water is (lambda) p1-1 +d）kg/h。
In step S2, the total flow of ammonia water is lambda p1 kg/h。
λ p1-1 +d-λ p1 =d-（λ p1 -λ p1-1 ）≥d-（c-λ x-1 ) > 0, so that the ammonia water flow in step S2 is less than (lambda) p1-1 + d) kg/h, and b is greater than R in the corresponding step S2, so that the condition that b is less than R in the step S2 is avoided, and the condition that b cannot be further close to R due to the range limitation of the second flow regulating valve 5 is avoided.
While the invention has been described with reference to specific embodiments, it will be understood by those skilled in the art that the present invention may be practiced without limitation to such specific embodiments. Any modifications which do not depart from the functional and structural principles of the present invention are intended to be included within the scope of the claims.
Claims (6)
1. The adjusting method of the ammonia water flow adjusting system for tail gas denitration is characterized by comprising the ammonia water flow adjusting system for tail gas denitration, wherein the ammonia water flow adjusting system for tail gas denitration comprises an ammonia water main trunk line, a first ammonia water branch trunk line, a second ammonia water branch trunk line, a first flow adjusting valve, a second flow adjusting valve, a first nitrogen oxide sensor, a second nitrogen oxide sensor and a main control board, the first ammonia water branch trunk line and the second ammonia water branch trunk line are connected to the ammonia water main trunk line in parallel, the first flow adjusting valve is installed on the first ammonia water branch trunk line, the second flow adjusting valve is installed on the second ammonia water branch trunk line, the first nitrogen oxide sensor is arranged at an air inlet, the second nitrogen oxide sensor is arranged at an air outlet, the ammonia water main trunk line is communicated between the air inlet and the air outlet, and the first flow adjusting valve, the second flow adjusting valve, the first nitrogen oxide sensor and the second nitrogen oxide sensor are electrically connected to the main control board;
the first flow regulating valve is a valve with equal percentage characteristic, the second flow regulating valve is a valve with linear characteristic, and the concentration of nitrogen oxide at the exhaust port is changed by regulating the first flow regulating valve and the second flow regulating valve;
the adjusting method of the ammonia water flow adjusting system for tail gas denitration comprises the step that the single opening adjusting quantity of a first flow adjusting valve is n 1 The single opening degree regulating quantity of the second flow regulating valve is n 2 The opening degree of the first flow rate regulating valve is pn 1 P is a natural number not greater than x, xn 1 =1, opening degree of second flow rate regulating valve qn 2 Q is a natural number not greater than y, yn 2 =1；
Setting an emission standard R mg/L, after a detection value a mg/L of a first nitrogen oxide sensor is stable, firstly adjusting the opening degree of a first flow regulating valve to be 0 and the opening degree of a second flow regulating valve to be 1, then gradually increasing the opening degree of the first flow regulating valve, and when a detection value b mg/L of a second nitrogen oxide sensor is lower than R mg/L, stopping adjusting the first flow regulating valve and starting adjusting the second flow regulating valve to reduce the difference value between b and R;
the adjustment method of the second flow rate adjustment valve is as follows:
step S1, adjusting the opening degree of the second flow regulating valve to (y-1) n 2 If b is larger than R, adjusting the opening degree of the second flow regulating valve back to 1, and ending the adjustment, if b is smaller than R, entering the step S2;
step S2: adjusting the opening degree of the second flow regulating valve to 0, if b is less than R, finishing the adjustment, and if b is more than R, entering the step S3;
and step S3: gradually increasing the opening of the second flow regulating valve until b is less than R, and finishing the regulation;
in step S3, if the adjusting times of the second flow regulating valve is z and z is not less than 3, the time interval between the eta-1 adjustment and the eta adjustment of the second flow regulating valve is t η-1 Eta is a natural number of not less than 2 and not more than z, t η-1 ＞t η 。
2. The adjusting method of the ammonia water flow regulating system for denitration of tail gas as claimed in claim 1, wherein the maximum flow of the second flow regulating valve is dkg/h, and the flow and the opening of the first flow regulating valve are (x-1) n when the opening is 1 1 The difference between the flow rates is smaller than d.
3. The ammonia water for denitration of tail gas according to claim 2Method for regulating a flow regulating system, characterized in that n 1 ＞n 2 。
4. The method for adjusting the ammonia water flow regulation system for tail gas denitration of claim 3, wherein n is 1 =0.25，n 2 =0.1。
5. The adjusting method of the ammonia water flow regulating system for tail gas denitration of claim 1, wherein the main control board is electrically connected with an alarm and an electronic on-off valve, the electronic on-off valve is located at the gas inlet, and if b is greater than R when the opening degree of the first flow regulating valve is 1, the main control board controls the alarm to give an alarm and simultaneously controls the electronic on-off valve to be turned off.
6. The method for adjusting the ammonia water flow regulation system for tail gas denitration of claim 1, wherein a is used as a when a is stable 0 Is a central value floating up and down, a 0 -a 1 ≤a≤a 0 +a 1 ，a 1 =0.05a 0 。
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