CN104989503A - Observation method and observation system for NOx output concentration of diesel SCR system - Google Patents

Abstract

The invention discloses an observation method and an observation system for a NOx output concentration of a diesel SCR (Selective Catalyst Reduction) system. The observation system comprises an SCR system, a sensor positioned at an air inlet end of the SCR system and used for detecting the NOx concentration, a sensor positioned at the air inlet end of the SCR system and used for detecting a NH3 concentration, a sensor positioned at an exhaust end of the SCR system and used for detecting the NOx concentration, a sensor positioned at the exhaust end of the SCR system and used for detecting the NH3 concentration, an UKF (Unscented Kalman Filter) observation algorithm module, and a concentration display module, wherein detection data of the sensors positioned at the air inlet end of the SCR system and used for detecting the NOx concentration and the NH3 concentration respectively, and the sensors positioned at the exhaust end of the SCR system and used for detecting the NOx concentration and the NH3 concentration respectively are input to the UKF observation algorithm module; and through performing the UKF operation on the detection data, the NOx output concentration is output to the concentration display module. With the adoption of the method performing output state observation through UKF, the precision of the estimated concentration is ensured, and the problem of cross sensitivity of the NOx sensors is solved excellently.

Description

A kind of SCR system of diesel engine NOx exports observation procedure and the observation system of concentration

Technical field

The invention belongs to diesel engine vent gas reprocessing SCR system control field, relate to a kind of control method of estimation, specifically, relate to observation procedure and observation system that a kind of SCR system of diesel engine NOx exports concentration, be specially adapted to the estimation observation in diesel engine vent gas after-treatment system-SCR system, NOx being exported to concentration.

Background technique

Nearly ten years, in automobile industry, the market share of diesel engine is increasing always, mainly because it has no small advantage in fuel efficiency, durability with in application area compared with petrol engine.But in recent years along with the deterioration of earth environment and the raising of people's environmental consciousness, exhaust pollution of diesel engines problem especially nitrogen oxides pollution more and more caused the concern of people.The technology such as in order to solve exhaust pollution of diesel engines problem, people have researched and developed in-cylinder combustion control, NOx capture technique, selective catalytic reduction system operating (SCR).And along with the increasingly stringent of Abgasgesetz, deeply, SCR system is considered to a kind of exhaust aftertreatment technology of most promising removal nitrogen oxide in the research of technology.

SCR system is widely used in the discharge reducing NOx in diesel engine.SCR (SelectiveCatalytic Reduction) is exactly mainly a kind of Selective catalytic reduction technology, it sprays into urea at system entry end, utilizes the ammonia of its hydrolysis to be reduced to by NOx the free of contamination nitrogen of air and water under the effect of catalyzer.

As shown in Figure 1, conventional SCR system comprises: SCR system; Be positioned at the detection NO of SCR system inlet end _xthe sensor 1 of concentration, is positioned at the detection NH of SCR system inlet end ₃the sensor 2 of concentration, is positioned at the detection NO of SCR system exhaust end _xthe sensor 3 of concentration, is positioned at the detection NH of SCR system exhaust end ₃the sensor 4 of concentration.

In SCR system, the injection of urea is the unique input control of system, and the concentration of NOx and ammonia be considered to SCR control in important parameter, so the design of output concentration to control algorithm of NOx and ammonia is most important.Traditional output concentration observation is generally all by means of sensor, but when NOx sensor measures NOx concentration, the ammonia mixed in NOx has sub-fraction and is oxidized to NOx, causes the measurement of sensor to there is certain error; In addition also have some state observers to be suggested to address this problem, but their accuracy of observation can not meet actual demand well.These problems all can affect economic benefit and the working efficiency of SCR system.

Therefore, a kind of novel NOx output state visualizer of development and Design is most important.

Summary of the invention

The object of the invention is to export NOx sensor and affect by ammonia in order to solve in SCR system and measure inaccurate problem, and provide a kind of method of agreeing with SCR system to improve the precision of measurement as much as possible.

In order to achieve the above object, the invention provides the observation system that a kind of SCR system of diesel engine NOx exports concentration, this observation system comprises:

SCR system;

Be positioned at the sensor of the detection NOX concentration of SCR system inlet end,

Be positioned at the sensor of the detection NH3 concentration of SCR system inlet end,

Be positioned at the sensor of the detection NOX concentration of SCR system exhaust end,

Be positioned at the sensor of the detection NH3 concentration of SCR system exhaust end,

UKF observation algorithm module,

Concentration display modular;

The detection NO of SCR system inlet end _xthe sensor of concentration, detection NH ₃the sensor of concentration, the detection NO of SCR system exhaust end _xthe sensor of concentration and detection NH ₃the detection data of the sensor of concentration are all input to UKF observation algorithm module; This UKF observation algorithm module is by carrying out computing to described detection data, and the NOx concentration of output-scr system exhaust end is to concentration display modular.

Above-mentioned observation system, wherein, described UKF observation algorithm module refers to Unscented kalman filtering algoritic module, and it comprises following steps:

Step 1, sets up state-space model according to chemical reaction in SCR system;

Step 2, applies among UKF computation model by the mathematical state spatial model of foundation, forms UKF algorithm;

Step 3, uses the above-mentioned UKF algorithm of Software Coding, carries out computer sim-ulation, thus draw the output concentration of NOx.

Above-mentioned observation system, wherein, described UKF algorithm is divided into two steps:

Step 2.1, forecasting process;

Step 2.2, renewal process.

Above-mentioned observation system, wherein, the forecasting process of described step 2.1 comprises:

Step 2.1.1, structure sigma point: in k-1 step, according to the statistic of stochastic regime variable x with covariance P _k-1structure sigma point set, formula is:

$X_{k-1}^{\left(i\right)}=\left\{\begin{array}{c}{\hat{x}}_{k-1},i=0\\ {\hat{x}}_{k-1}+{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k-1}\right)}_i,i=1,...n_x\\ {\hat{x}}_{k-1}-{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k-1}\right)}_i,i=n_x+1,...2n_x\end{array}\right.,$

Wherein λ represents first scale parameter, λ=α ²(n _x+ q)-n _x, n _xrepresent state space dimension, n _xget 3; Q represents second scale parameter, and q gets 0 or 3-n _x; α is set as 0.001;

Step 2.1.2, carries out propagation to sigma point and calculates:

$X_{k|k-1}^{\left(i\right)}=f(X_{k-1}^{\left(i\right)},u_{k-1}),$

Wherein u represents the detection data inputted by sensor;

Step 2.1.3, calculates and exports prior state (i.e. priori average X _k|k-1, this prior state is X _k-1with X _ka middle step) and error covariance

Wherein, the priori mean value computation formula of output is:

${\hat{x}}_{k|k-1}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_m^{\left(i\right)}{X}_{k|k-1}^{\left(i\right)},$

Error covariance P _k|k-1formula is:

$P_{k|k-1}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_c^{\left(i\right)}(X_{k|k-1}^{\left(i\right)}-{\hat{x}}_{k|k-1}){(X_{k|k-1}^{\left(i\right)}-{\hat{x}}_{k|k-1})}^T+Q,$

Wherein Q is noise covariance, with for the weighting of computation of mean values and covariance, be defined as follows:

$W_m^{\left(i\right)}=\{\begin{array}{c}\frac{\mathrm{\λ}}{\mathrm{\λ}+n_x},i=0\\ \frac{\mathrm{\λ}}{2(\mathrm{\λ}+n_x)},i=1,...2n_x\end{array},$

$W_c^{\left(i\right)}=\left\{\begin{array}{c}\frac{\mathrm{\λ}}{\mathrm{\λ}+n_x}+(1-{\mathrm{\α}}^2+\mathrm{\β}),i=0\\ \frac{\mathrm{\λ}}{2(\mathrm{\λ}+n_x)},i=1,\mathrm{...2}{n}_x\end{array}\right.,$

Wherein β is constant, gets 2.

Above-mentioned observation system, wherein, the renewal process of described step 2.2 comprises:

Step 2.2.1, structure sigma point: estimate X according to the prior state that step 2.1.3 calculates _k|k-1, again construct sigma point, formula is:

$X_{k|k-1=}^{\left(i\right)}\left\{\begin{array}{c}{\hat{x}}_{k|k},i=0\\ {\hat{x}}_{k|k-1}+{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k|k-1}\right)}_i,i=1,\mathrm{...}{n}_x\\ {\hat{x}}_{k|k-1}-{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k|k-1}\right)}_i,i=n_x+1,\mathrm{...2}{n}_x\end{array}\right.,$

Step 2.2.2, computational prediction exports: propagate and calculate each sigma point, formula is:

$Y_{k|k-1}^{\left(i\right)}=g(X_{k|k-1}^{\left(i\right)},u_k),$

The formula that prediction exports is as follows:

${\hat{Y}}_{k|k-1}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_m^{\left(i\right)}{Y}_{k|k-1}^{\left(i\right)},$

Step 2.2.3, calculates kalman gain K _k, formula is:

$P_{y_k{y}_k}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_c^{\left(i\right)}(Y_{k|k-1}^{\left(i\right)}-{\hat{Y}}_{k|k-1}){(Y_{k|k-1}^{\left(i\right)}-{\hat{Y}}_{k|k-1})}^T+R,$

$P_{x_k{y}_k}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_c^{\left(i\right)}(X_{k|k-1}^{\left(i\right)}-{\hat{x}}_{k|k-1}){(Y_{k|k-1}^{\left(i\right)}-{\hat{Y}}_{k|k-1})}^T,$

$K_k=P_{x_k{y}_k}{P}_{y_k{y}_k}^{-1},$

Wherein the output error covariance doped, be average and prediction output cross covariance, R is noise covariance;

Step 2.2.4, calculates posteriority state estimation and posteriority covariance: in kth step, according to the measured value exported, can calculate posteriority state x _kwith covariance P _k, formula is:

${\hat{x}}_k={\hat{x}}_{k|k-1}+K_k(Y_k-{\hat{Y}}_{k|k-1}),$

$P_k=P_{k|k-1}-K_k{P}_{y_k{y}_k}{K}_k^T,$

Wherein Y _krepresent the actual measured value of kth step.

Above-mentioned observation system, wherein, the state-space model described in step 1 is:

$\left[\begin{array}{c}{\stackrel{\·}{C}}_{NO}\\ {\stackrel{\·}{\mathrm{\θ}}}_{{\mathrm{NH}}_3}\\ {\stackrel{\·}{C}}_{{\mathrm{NH}}_3}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{C}}_{No}=-C_{NO}({\mathrm{\Θr}}_{re}{\mathrm{\θ}}_{{\mathrm{NH}}_3}+\frac{F}{V})+r_{ox}{\mathrm{\Θ\θ}}_{{\mathrm{NH}}_3}\\ {\stackrel{\·}{\mathrm{\θ}}}_{{\mathrm{NH}}_3}=-{\mathrm{\θ}}_{{\mathrm{NH}}_3}(r_{ad}{C}_{{\mathrm{NH}}_3}+r_{de}+r_{re}{C}_{No}+r_{ox})+r_{ad}{C}_{{\mathrm{NH}}_3}\\ {\stackrel{\·}{C}}_{{\mathrm{NH}}_3}=-C_{{\mathrm{NH}}_3}\[{\mathrm{\Θr}}_{ad}(1-{\mathrm{\θ}}_{{\mathrm{NH}}_3})+\frac{F}{V}\]+{\mathrm{\Θr}}_{de}{\mathrm{\θ}}_{{\mathrm{NH}}_3}\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ \frac{F}{V}\end{array}\right]C_{{\mathrm{NH}}_3,in}+\left[\begin{array}{c}\frac{F}{V}\\ 0\\ 0\end{array}\right]C_{NO,in};$

Wherein, x=ad, de, ox, re; Ad represents forward adsorption reaction, and de represents the reaction of reverse desorption, and ox represents oxidation reaction, and re represents reduction reaction; C _nOrepresent the concentration of NOx, represent the concentration of ammonia; represent the concentration of ammonia entrance, C _{nO, in}represent that the concentration of NOx in tail gas discharged by diesel engine; F is tail gas flow velocity; V is the volume of SCR system; T represents temperature, and E, K and R are constants, C _xrepresent the concentration of x, represent the ammonia coverage scale on catalyzer; Θ represents the ammonia coverage scale ability that catalyzer is total.

Present invention also offers a kind of observation procedure adopting above-mentioned SCR system of diesel engine NOx to export the observation system of concentration, this observation procedure comprises the following steps:

Step S1, by the detection NO being positioned at SCR system inlet end _xthe sensor of concentration detects NO _xinput concentration, by the detection NH being positioned at SCR system inlet end ₃the sensor of concentration detects NH ₃input concentration, by the detection NO being positioned at SCR system exhaust end _xthe sensor of concentration detects NO _xoutput concentration, by the detection NH being positioned at SCR system exhaust end ₃the sensor of concentration detects NH ₃output concentration;

Step S2, the NO that step 1 is detected _xinput concentration, NH ₃input concentration, NO _xoutput concentration and NH ₃output concentration be input to UKF observation algorithm module and carry out simulation calculating;

The NO that step S3, step S2 calculate _xoutput concentration output display on concentration display modular.

Above-mentioned observation procedure, wherein, the UKF observation algorithm modular simulation operation method in step S2 comprises:

Step S2.1, sets up state-space model according to chemical reaction in SCR system;

Step S2.2, applies among UKF computation model by the mathematical state spatial model of foundation, forms UKF algorithm;

Step S2.3, uses the UKF algorithm described in Software Coding, carries out computer sim-ulation, thus draw the output concentration of NOx.

Above-mentioned observation procedure, wherein, described UKF algorithm is divided into two steps:

Step S2.2.1, forecasting process;

Step S2.2.2, renewal process.

Above-mentioned observation procedure, wherein, described forecasting process comprises:

Step S2.2.1.1, structure sigma point: in k-1 step, according to the statistic of stochastic regime variable x with covariance P _k-1structure sigma point set

$X_{k-1}^{\left(i\right)}=\left\{\begin{array}{c}{\hat{x}}_{k-1},i=0\\ {\hat{x}}_{k-1}+{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k-1}\right)}_i,i=1,...n_x\\ {\hat{x}}_{k-1}-{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k-1}\right)}_i,i=n_x+1,...2n_x\end{array}\right.,$

Wherein λ represents first scale parameter, λ=α ²(n _x+ q)-n _x, n _xrepresent state space dimension, n _xget 3; Q represents second scale parameter, and q gets 0 or 3-n _x; α is set as 0.001;

Step S2.2.1.2, carries out propagation to sigma point and calculates:

$X_{k|k-1}^{\left(i\right)}=f(X_{k-1}^{\left(i\right)},u_{k-1}),$

Wherein u representative input;

Step S2.2.1.3, calculates and exports average and error covariance:

Wherein, the priori mean value computation formula of output is:

${\hat{x}}_{k|k-1}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_m^{\left(i\right)}{X}_{k|k-1}^{\left(i\right)},$

Error covariance formula is:

$P_{k|k-1}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_c^{\left(i\right)}(X_{k|k-1}^{\left(i\right)}-{\hat{x}}_{k|k-1}){(X_{k|k-1}^{\left(i\right)}-{\hat{x}}_{k|k-1})}^T+Q,$

Wherein Q is noise covariance, with for the weighting of computation of mean values and covariance, be defined as follows:

$W_m^{\left(i\right)}=\left\{\begin{array}{c}\frac{\mathrm{\λ}}{\mathrm{\λ}+n_x},i=0\\ \frac{\mathrm{\λ}}{2(\mathrm{\λ}+n_x)},i=1,...2n_x\end{array}\right.,$

$W_c^{\left(i\right)}=\left\{\begin{array}{c}\frac{\mathrm{\λ}}{\mathrm{\λ}+n_x}+(1-{\mathrm{\α}}^2+\mathrm{\β}),i=0\\ \frac{\mathrm{\λ}}{2(\mathrm{\λ}+n_x)},i=1,...2n_x\end{array}\right.,$

Wherein β is constant, gets 2;

Described renewal process comprises:

Step S2.2.2.1, structure sigma point: estimate according to the prior state that step S2.2.1.3 calculates, again construct sigma point, formula is:

$X_{k|k-1=}^{\left(i\right)}\left\{\begin{array}{c}{\hat{x}}_{k|k},i=0\\ {\hat{x}}_{k|k-1}+{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k|k-1}\right)}_i,i=1,\mathrm{...}{n}_x\\ {\hat{x}}_{k|k-1}-{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k|k-1}\right)}_i,i=n_x+1,\mathrm{...2}{n}_x\end{array}\right.,$

Step S2.2.2.2, computational prediction exports: propagate and calculate each sigma point, formula is:

$Y_{k|k-1}^{\left(i\right)}=g(X_{k|k-1}^{\left(i\right)},u_k),$

It is as follows that prediction exports formula:

${\hat{Y}}_{k|k-1}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_m^{\left(i\right)}{Y}_{k|K-1}^{\left(i\right)},$

Step S2.2.2.3, calculate kalman gain K (k), formula is:

$P_{y_k{y}_k}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_c^{\left(i\right)}(Y_{k|k-1}^{\left(i\right)}-{\hat{Y}}_{k|k-1}){(Y_{k|k-1}^{\left(i\right)}-{\hat{Y}}_{k|k-1})}^T+R,$

$P_{x_k{y}_k}=\underset{i\·=0}{\overset{2n_x}{\Σ}}{W}_c^{\left(i\right)}(X_{k|k-1}^{\left(i\right)}-{\hat{x}}_{k|k-1}){(Y_{k|k-1}^{\left(i\right)}-{\hat{Y}}_{k|k-1})}^T,$

$K_k=P_{x_k{y}_k}{P}_{y_k{y}_k}^{-1},$

Wherein dope output error covariance, be average and prediction output cross covariance, R is noise covariance;

Step 2.2.2.4, calculates posteriority state estimation and posteriority covariance: in kth step, according to the measured value exported, can calculate posteriority state and covariance, formula is:

${\hat{x}}_k={\hat{x}}_{k|k-1}+K_k(Y_k-{\hat{Y}}_{k|k-1}),$

$P_k=P_{k|k-1}-K_k{P}_{y_k{y}_k}{K}_k^T,$

Wherein Y _krepresent the actual measured value of kth step.

The present invention proposes observation procedure and the observation system of the estimation of a kind of SCR output state, the method of output state observation is carried out by Unscented kalman filtering, demonstrate the validity of designed visualizer in simulations, and ensure that the precision of estimated concentration, reach the purpose of design of expection, solve the cross sensitivity problem that NOx sensor exists with flying colors.

Accompanying drawing explanation

Fig. 1 is conventional SCR system structural drawing.

Fig. 2 is SCR layout chart of the present invention.

Fig. 3 is the SCR output terminal NOx concentration data estimator curve that adopts observation procedure of the present invention to calculate and sensing data (actual value) curve comparison figure.

Fig. 4 is that during SCR output terminal NOx concentration adopts observation procedure of the present invention to calculate, cross sensitivity factor of influence contrasts with hypothesis cross sensitivity factor of influence.

Embodiment

Below in conjunction with accompanying drawing, by describing a preferably specific embodiment in detail, the present invention is further elaborated.

As shown in Figure 2, be SCR observation system of the present invention, it comprises:

SCR system;

Be positioned at the sensor 1 of the detection NOX concentration of SCR system inlet end,

Be positioned at the sensor 2 of the detection NH3 concentration of SCR system inlet end,

Be positioned at the sensor 3 of the detection NOX concentration of SCR system exhaust end,

Be positioned at the sensor 4 of the detection NH3 concentration of SCR system exhaust end,

UKF observation algorithm module,

Concentration display modular;

The detection NO of SCR system inlet end _xthe sensor 1 of concentration and detection NH ₃the sensor 2 of concentration, the detection NO of SCR system exhaust end _xthe sensor 3 of concentration and detection NH ₃the detection data of the sensor 4 of concentration are all input to UKF observation algorithm module; This UKF observation algorithm module is by carrying out computing to described detection data, and the NOx concentration of output-scr system exhaust end is to concentration display modular.

The specific algorithm of UKF observation algorithm module of the present invention is:

The first step, sets up state-space model according to chemical reaction in SCR system.In SCR system, main chemical reactions has following.

1) NH ₃adsorption and de-adsorption on a catalyst

Wherein θ _freerepresent catalytic reaction point in SCR system, represent the activation NH be adsorbed on catalyzer ₃.(ad represents forward adsorption reaction to the positive reverse reaction speed of reaction; De represents the reaction of reverse desorption) be:

$R_{ad}=K_{ad}{e}^{-(E_{ad}/RT)}{C}_{{\mathrm{NH}}_3}(1-{\mathrm{\θ}}_{{\mathrm{NH}}_3}),---\left(2\right)$

$R_{de}=K_{de}{e}^{-(E_{de}/RT)}{\mathrm{\θ}}_{{\mathrm{NH}}_3},---\left(3\right)$

Wherein R _xrepresent chemical reaction rate (x refers to ad or de), T represents temperature, and E, K and R are constants, C _nH3represent NH ₃concentration, represent the ammonia coverage scale on catalyzer, it can be expressed as:

${\mathrm{\θ}}_{{\mathrm{NH}}_3}=\frac{M_{{\mathrm{NH}}_3}^{*}}{\mathrm{\Θ}}---\left(4\right)$

Wherein represent the molecular weight of adsorbing ammonia on a catalyst, Θ represents the ammonia coverage scale ability that catalyzer is total.

2) NH ₃oxidation (ox represents oxidation reaction)

${\mathrm{NH}}_3^{*}+1.25O_2\→NO+1.5H_{2}O---\left(5\right)$

$R_{ox}=K_{ox}{e}^{-(E_{ox}/RT)}{\mathrm{\θ}}_{{\mathrm{NH}}_3},---\left(6\right)$

3) reduction of NOx

There is a lot of complicated chemical reaction in the reduction of NOx, comprise the reduction of NO, NO ₂reduction, and NO and NO ₂be reduced together.Show after deliberation, the reduction reaction of NO is reaction main in NOx reduction, so we only consider the reduction reaction of NO at this, and reaction following (re represents reduction reaction):

$4{\mathrm{NH}}_3^{*}+4NO+O_2\→4N_2+6H_{2}O,---\left(7\right)$

$R_{re}=K_{re}{e}^{-(E_{re}/RT)}{C}_{NO}{\mathrm{\θ}}_{{\mathrm{NH}}_3}---\left(8\right)$

According to mole conservation and the conservation of mass, we can set up state space by above-mentioned four chemical rate equation, as follows:

$\left[\begin{array}{c}{\stackrel{\·}{C}}_{NO}\\ {\stackrel{\·}{\mathrm{\θ}}}_{{\mathrm{NH}}_3}\\ {\stackrel{\·}{C}}_{{\mathrm{NH}}_3}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{C}}_{No}=-C_{NO}({\mathrm{\Θr}}_{re}{\mathrm{\θ}}_{{\mathrm{NH}}_3}+\frac{F}{V})+r_{ox}{\mathrm{\Θ\θ}}_{{\mathrm{NH}}_3}\\ {\stackrel{\·}{\mathrm{\θ}}}_{{\mathrm{NH}}_3}=-{\mathrm{\θ}}_{{\mathrm{NH}}_3}(r_{ad}{C}_{{\mathrm{NH}}_3}+r_{de}+r_{re}{C}_{No}+r_{ox})+r_{ad}{C}_{{\mathrm{NH}}_3}\\ {\stackrel{\·}{C}}_{{\mathrm{NH}}_3}=-C_{{\mathrm{NH}}_3}\[{\mathrm{\Θr}}_{ad}(1-{\mathrm{\θ}}_{{\mathrm{NH}}_3})+\frac{F}{V}\]+{\mathrm{\Θr}}_{de}{\mathrm{\θ}}_{{\mathrm{NH}}_3}\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ \frac{F}{V}\end{array}\right]C_{{\mathrm{NH}}_3,in}+\left[\begin{array}{c}\frac{F}{V}\\ 0\\ 0\end{array}\right]C_{NO,in},---\left(9\right)$

Wherein x=ad, de, ox, re; C _nOwith represent the concentration of NOx and ammonia respectively; represent the concentration of ammonia entrance, C _{nO, in}represent that the concentration of NOx in tail gas discharged by diesel engine; F is tail gas flow velocity; V is the volume of SCR system.

NOx sensor affects by ammonia and there is cross sensitivity problem, and according to research, we learn sensor measurement concentration C _{nO, sen}with the actual concentration of NOx with the concentration of ammonia there is following relation:

$C_{NO,sen}=C_{NO}^{*}+K_{cs}{C}_{{\mathrm{NH}}_3},---\left(10\right)$

Wherein K _csrepresent cross sensitivity factor of influence.Sensitive problem is intersected, so we think that the measurement concentration of ammonia is relatively accurate because ammonia gas sensor does not exist.

In order to arrange the initial conditions that UKF calculates, first, in our calculating below, first suppose K _cs=0.5.In order to the rationality of verify hypothesis, we also can estimate K in estimation NOx concentration process simultaneously _csvalue, and provide the contrast of estimated value and default later, as shown in Figure 4, the Kcs estimated value calculated can be infinitely close to default 0.5 very soon, and the correctness of algorithm is described.Second step writes out UKF Computing Principle, applied among UKF computation model by the mathematical state spatial model of foundation.UKF estimated state is generally divided into two steps, comprises prediction and upgrades.The UKF equation of nonlinear system is generally expressed as follows:

(1), forecasting process

A), sigma point is constructed:

In k-1 step, according to the statistic of stochastic regime variable x with covariance P _k-1structure sigma point set:

$X_{k-1}^{\left(i\right)}=\left\{\begin{array}{c}{\hat{x}}_{k-1},i=0\\ {\hat{x}}_{k-1}+{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k-1}\right)}_i,i=1,...n_x\\ {\hat{x}}_{k-1}-{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k-1}\right)}_i,i=n_x+1,...2n_x\end{array}\right.,---\left(11\right)$

Wherein λ is scale parameter, λ=α ²(n _x+ q)-n _x.N _xfor state space dimension, be 3 in the present invention.Q is second scale parameter, generally gets 0 or 3-n _x.α is set as a very little constant, gets 0.001 in the present invention.

B), carry out propagation to sigma point to calculate

Conversion formula is as follows, and wherein u represents the detection data inputted by sensor:

$X_{k|k-1}^{\left(i\right)}=f(X_{k-1}^{\left(i\right)},u_{k-1}),---\left(12\right)$

C), output average and error covariance is calculated

The priori average exported and error covariance formula are calculated as follows:

${\hat{x}}_{k|k-1}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_m^{\left(i\right)}{X}_{k|k-1}^{\left(i\right)},\left(13\right)$

$P_{k|k-1}=\underset{i=0}{\overset{2n}{\Σ}}{W}_c^{\left(i\right)}(X_{k|k-1}^{\left(i\right)}-{\hat{x}}_{k|k-1}){(X_{k|k-1}^{\left(i\right)}-{\hat{x}}_{k|k-1})}^T+Q,---\left(14\right)$

Wherein Q is noise covariance, with for the weighting of computation of mean values and covariance, be defined as follows:

$W_m^{\left(i\right)}=\left\{\begin{array}{c}\frac{\mathrm{\λ}}{\mathrm{\λ}+n_x},i=0\\ \frac{\mathrm{\λ}}{2(\mathrm{\λ}+n_x)},i=1,...2n_x\end{array}\right.,---\left(15\right)$

$W_c^{\left(i\right)}=\left\{\begin{array}{c}\frac{\mathrm{\λ}}{\mathrm{\λ}+n_x}(1-{\mathrm{\α}}^2+\mathrm{\β}),i=0\\ \frac{\mathrm{\λ}}{2(\mathrm{\λ}+n_x)},i=1,...2n_x\end{array}\right.,---\left(16\right)$

Wherein β is constant, in Gaussian distribution, generally gets 2 for obtaining best estimate.

(2), renewal process

A), sigma point is constructed

Estimate (i.e. priori average) according to the prior state calculated above, again construct sigma point.

$X_{k|k-1=}^{\left(i\right)}\left\{\begin{array}{c}{\hat{x}}_{k|k},i=0\\ {\hat{x}}_{k|k-1}+{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k|k-1}\right)}_i,i=1,\mathrm{...}{n}_x\\ {\hat{x}}_{k|k-1}-{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k|k-1}\right)}_i,i=n_x+1,\mathrm{...2}{n}_x\end{array}\right.,---\left(17\right)$

B), computational prediction exports

Propagate and calculate each sigma point

$Y_{k|k-1}^{\left(i\right)}=g\left(X_{k|k-1}^{\left(i\right)}{u}_k\right),---\left(18\right)$

Then prediction output formula is as follows:

${\hat{Y}}_{k|k-1}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_m^{\left(i\right)}{Y}_{k|k-1}^{\left(i\right)},---\left(19\right)$

C), kalman gain is calculated

Need the kalman gain K that best in this process simultaneously _k.Accounting equation is as follows:

$P_{y_k{y}_k}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_c^{\left(i\right)}(Y_{k|k-1}^{\left(i\right)}-{\hat{Y}}_{k|k-1}){(Y_{k|k-1}^{\left(i\right)}-{\hat{Y}}_{k|k-1})}^T+R,---\left(20\right)$

$P_{x_k{y}_k}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_c^{\left(i\right)}(X_{k|k-1}^{\left(i\right)}-{\hat{x}}_{k|k-1}){(Y_{k|k-1}^{\left(i\right)}-{\hat{Y}}_{k|k-1})}^T,---\left(21\right)$

$K_k=P_{x_k{y}_k}{P}_{y_k{y}_k}^{-1},---\left(22\right)$

Wherein the output error covariance doped, be average and prediction output cross covariance, R is noise covariance.

D), posteriority state estimation (i.e. Posterior Mean) and posteriority covariance is calculated

In kth step, according to the measured value exported, posterior state x can be calculated _kwith covariance P _k.

${\hat{x}}_k={\hat{x}}_{k|k-1}+K_k(Y_k-{\hat{Y}}_{k|k-1}),---\left(23\right)$

$P_k=P_{k|k-1}-K_k{P}_{y_k{y}_k}{K}_k^T,---\left(24\right)$

Wherein Y _krepresent the actual measured value of kth step.

3rd step, uses the above-mentioned UKF algorithm of Software Coding, carries out computer sim-ulation, thus draw our output estimation.The NOx data estimator curve drawn and True Data curve comparison, as Fig. 3, demonstrate the correctness that UKF estimates, the precision of measurement is reliable, solves the cross sensitivity problem that NOx sensor exists.

In sum, the present invention sets up state-space model according to chemical reaction in SCR system, use Unscented kalman filtering (UKF) method, according to sensor actual concentration and the constrained input concentration measuring concentration relationship formula and measurement, calculate the true output concentration of NOx, solve the cross sensitivity problem that NOx sensor exists with flying colors.

Although content of the present invention has done detailed introduction by above preferred embodiment, will be appreciated that above-mentioned description should not be considered to limitation of the present invention.After those skilled in the art have read foregoing, for multiple amendment of the present invention and substitute will be all apparent.Therefore, protection scope of the present invention should be limited to the appended claims.

Claims (10)

1. SCR system of diesel engine NOx exports an observation system for concentration, and it is characterized in that, this observation system comprises:

SCR system;

Be positioned at the detection NO of SCR system inlet end _xthe sensor (1) of concentration,

Be positioned at the detection NH of SCR system inlet end ₃the sensor (2) of concentration,

Be positioned at the detection NO of SCR system exhaust end _xthe sensor (3) of concentration,

Be positioned at the detection NH of SCR system exhaust end ₃the sensor (4) of concentration,

UKF observation algorithm module,

Concentration display modular;

Wherein, by the detection NO of described SCR system inlet end _xthe sensor (1) of concentration and detection NH ₃the sensor (2) of concentration, the detection NO of SCR system exhaust end _xthe sensor (3) of concentration and detection NH ₃the detection data of the sensor (4) of concentration are all input to UKF observation algorithm module; This UKF observation algorithm module, by carrying out computing to described detection data, exports the output concentration of NOx to concentration display modular.

2. observation system as claimed in claim 1, it is characterized in that, described UKF observation algorithm module refers to Unscented kalman filtering algoritic module, and it comprises following steps:

Step 1, sets up state-space model according to chemical reaction in SCR system;

Step 2, applies among UKF computation model by the mathematical state spatial model of foundation, forms UKF algorithm;

Step 3, uses the UKF algorithm described in Software Coding, carries out computer sim-ulation, thus draw the output concentration of NOx.

3. observation system as claimed in claim 1, it is characterized in that, described UKF algorithm is divided into two steps:

Step 2.1, forecasting process;

Step 2.2, renewal process.

4. observation system as claimed in claim 1, it is characterized in that, the forecasting process of described step 2.1 comprises:

Step 2.1.1, structure sigma point: in k-1 step, according to the statistic of stochastic regime variable x with covariance P _k-1structure sigma point set

$X_{k-1}^{\left(i\right)}=\left\{\begin{array}{c}{\hat{x}}_{k-1},i=0\\ {\hat{x}}_{k-1}+{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k-1}\right)}_i,i=1,\mathrm{...},n_x\\ {\hat{x}}_{k-1}-{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k-1}\right)}_i,i=n_x+1,\mathrm{...2}{n}_x\end{array}\right.,$

Wherein λ represents first scale parameter, λ=α ²(n _x+ q)-n _x, n _xrepresent state space dimension, n _xget 3; Q represents second scale parameter, and q gets 0 or 3-n _x; α is set as 0.001;

Step 2.1.2, carries out propagation to sigma point and calculates:

$X_{k|k-1}^{\left(i\right)}=f(X_{k-1}^{\left(i\right)},u_{k-1}),$

Wherein u represents the detection data inputted by sensor;

Step 2.1.3, calculates and exports priori average and error covariance:

Wherein, the priori mean value computation formula of output is:

${\hat{x}}_{k|k-1}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_m^{\left(i\right)}{X}_{k|k-1}^{\left(i\right)},$

Error covariance formula is:

$p_{k|k-1}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_c^{\left(i\right)}\left(X_{k|k-1}^{\left(i\right)}\right){(X_{k|k-1}^{\left(i\right)}-{\hat{x}}_{k|k-1})}^T+Q,$

Wherein Q is noise covariance, with for the weighting of computation of mean values and covariance, be defined as follows:

$W_m^{\left(i\right)}=\{\begin{array}{c}\frac{\mathrm{\λ}}{\mathrm{\λ}+n_x},i=0\\ \frac{\mathrm{\λ}}{2(\mathrm{\λ}+n_x)},i=1,\mathrm{...2}{n}_x\end{array},$

$W_c^{\left(i\right)}=\left\{\begin{array}{c}\frac{\mathrm{\λ}}{\mathrm{\λ}+n_x}+(1-{\mathrm{\α}}^2+\mathrm{\β}),i=0\\ \frac{\mathrm{\λ}}{2(\mathrm{\λ}+n_x)},i=1,...,2n_x\end{array}\right.,$

Wherein β is constant, gets 2.

5. observation system as claimed in claim 1, it is characterized in that, the renewal process of described step 2.2 comprises:

Step 2.2.1, structure sigma point: the priori average calculated according to step 2.1.3, again construct sigma point, formula is:

$X_{k|k-1}^{\left(i\right)}=\{\begin{array}{c}{\hat{x}}_{k|k-1},i=0\\ {\hat{x}}_{k|k-1}+{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k|k-1}\right)}_i,i=1,\mathrm{...}{n}_x\\ {\hat{x}}_{k|k-1}-{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k|k-1}\right)}_i,i=n_x+1,\mathrm{...2}{n}_x\end{array},$

Step 2.2.2, computational prediction exports: propagate and calculate each sigma point, formula is:

$Y_{k|k-1}^{\left(i\right)}=g(X_{k|k-1}^{\left(i\right)},u_k),$

It is as follows that prediction exports formula:

${\hat{Y}}_{k|k-1}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_m^{\left(i\right)}{Y}_{k|k-1}^{\left(i\right)},$

Step 2.2.3, calculates kalman gain K _k, formula is:

$P_{y_k{y}_k}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_c^{\left(i\right)}(Y_{k|k-1}^{\left(i\right)}-{\hat{Y}}_{k|k-1}){(Y_{k|k-1}^{\left(i\right)}-{\hat{Y}}_{k|k-1})}^T+R,$

$P_{x_k{y}_k}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_c^{\left(i\right)}(X_{k|k-1}^{\left(i\right)}-{\hat{x}}_{k|k-1}){(Y_{k|k-1}^{\left(i\right)}-{\hat{Y}}_{k|k-1})}^T,$

$K_k=P_{x_k{y}_k}{P}_{y_k{y}_k}^{-1},$

Wherein dope output error covariance, be average and prediction output cross covariance, R is noise covariance;

Step 2.2.4, calculates Posterior Mean and posteriority covariance: in kth step, according to the measured value exported, can calculate Posterior Mean and covariance, formula is:

${\hat{x}}_k={\hat{x}}_{k|k-1}+K_k(Y_k-{\hat{Y}}_{k|k-1}),$

$P_k=P_{k|k-1}-K_k{P}_{y_k{y}_k}{K}_k^T,$

Wherein Y _krepresent the actual measured value of kth step.

6. observation system as claimed in claim 1, it is characterized in that, the state-space model described in step 1 is:

$\left[\begin{array}{c}{\stackrel{\·}{C}}_{NO}\\ {\stackrel{\·}{\mathrm{\θ}}}_{{\mathrm{NH}}_3}\\ {\stackrel{\·}{C}}_{{\mathrm{NH}}_3}\end{array}\right]=\left[\begin{array}{c}{\stackrel{\·}{C}}_{NO}=-C_{NO}({\mathrm{\Θr}}_{re}{\mathrm{\θ}}_{{\mathrm{NH}}_3}+\frac{F}{V})+r_{ox}{\mathrm{\Θ\θ}}_{{\mathrm{NH}}_3}\\ {\stackrel{\·}{\mathrm{\θ}}}_{N{H}_3}=-{\mathrm{\θ}}_{{\mathrm{NH}}_3}(r_{ad}{C}_{{\mathrm{NH}}_3}+r_{de}+r_{re}{C}_{NO}+r_{ox})+r_{ad}{C}_{{\mathrm{NH}}_3}\\ {\stackrel{\·}{C}}_{{\mathrm{NH}}_3}=-C_{{\mathrm{NH}}_3}\[{\mathrm{\Θr}}_{ad}(1-{\mathrm{\θ}}_{{\mathrm{NH}}_3})+\frac{F}{V}\]+{\mathrm{\Θr}}_{de}{\mathrm{\θ}}_{{\mathrm{NH}}_3}\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ \frac{F}{V}\end{array}\right]C_{{\mathrm{NH}}_3,in}+\left[\begin{array}{c}\frac{F}{V}\\ 0\\ 0\end{array}\right]C_{NO,in};$

Wherein, x=ad, de, ox, re; Ad represents forward adsorption reaction, and de represents the reaction of reverse desorption, and ox represents oxidation reaction, and re represents reduction reaction; C _nOrepresent NO _xconcentration, represent the concentration of ammonia; represent the concentration of ammonia entrance, C _{nO, in}represent that the concentration of NOx in tail gas discharged by diesel engine; F is tail gas flow velocity; V is the volume of SCR system; T represents temperature, and E, K and R are constants, C _xrepresent the concentration of x, represent the ammonia coverage scale on catalyzer; Θ represents the ammonia coverage scale ability that catalyzer is total.

7. adopt SCR system of diesel engine NOx according to claim 1 to export an observation procedure for the observation system of concentration, it is characterized in that, this observation procedure comprises the following steps:

Step S1, by the detection NO being positioned at SCR system inlet end _xthe sensor (1) of concentration detects NO _xinput concentration, by the detection NH being positioned at SCR system inlet end ₃the sensor (2) of concentration detects NH ₃input concentration, by the detection NO being positioned at SCR system exhaust end _xthe sensor (3) of concentration detects NO _xoutput concentration, by the detection NH being positioned at SCR system exhaust end ₃the sensor (4) of concentration detects NH ₃output concentration;

Step S2, the NO that step 1 is detected _xinput concentration, NH ₃input concentration, NO _xoutput concentration and NH ₃output concentration be input to UKF observation algorithm module and carry out simulation calculating;

The NO that step S3, step S2 calculate _xoutput concentration output display on concentration display modular.

8. observation procedure as claimed in claim 7, it is characterized in that, the UKF observation algorithm modular simulation operation method in step S2 comprises:

Step S2.1, sets up state-space model according to chemical reaction in SCR system;

Step S2.2, applies among UKF computation model by the mathematical state spatial model of foundation, forms UKF algorithm;

Step S2.3, uses the UKF algorithm described in Software Coding, carries out computer sim-ulation, thus draw the output concentration of NOx.

9. observation procedure as claimed in claim 8, it is characterized in that, described UKF algorithm is divided into two steps:

Step S2.2.1, forecasting process;

Step S2.2.2, renewal process.

10. observation procedure as claimed in claim 9, it is characterized in that, described forecasting process comprises:

Step S2.2.1.1, structure sigma point: in k-1 step, according to the statistic of stochastic regime variable x with covariance P _k-1structure sigma point set

$X_{k-1}^{\left(i\right)}=\left\{\begin{array}{c}{\hat{x}}_{k-1},i=0\\ {\hat{x}}_{k-1}+{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k-1}\right)}_i,i=1,...n_x\\ {\hat{x}}_{k-1}-{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k-1}\right)}_i,i=n_x+1,...2n_x\end{array}\right.,$

Wherein λ represents first scale parameter, λ=α ²(n _x+ q)-n _x, n _xrepresent state space dimension, n _xget 3; Q represents second scale parameter, and q gets 0 or 3-n _x; α is set as 0.001;

Step S2.2.1.2, carries out propagation to sigma point and calculates:

$X_{k|k-1}^{\left(i\right)}=f(X_{k-1}^{\left(i\right)},u_{k-1}),$

Wherein u representative input;

Step S2.2.1.3, calculates and exports average and error covariance:

Wherein, the priori mean value computation formula of output is:

${\hat{x}}_{k|k-1}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_m^{\left(i\right)}{X}_{k|k-1}^{\left(i\right)},$

Error covariance formula is:

$P_{k|k-1}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_c^{\left(i\right)}\left(X_{k|k-1}^{\left(i\right)}{\hat{x}}_{k|k-1}\right){(X_{k|k-1}^{\left(i\right)}-{\hat{x}}_{k|k-1})}^T+Q,$

Wherein Q is noise covariance, with for the weighting of computation of mean values and covariance, be defined as follows:

$W_m^{\left(i\right)}=\{\begin{array}{c}\frac{\mathrm{\λ}}{\mathrm{\λ}+n_x},i=0\\ \frac{\mathrm{\λ}}{2(\mathrm{\λ}+n_x)},i=1,\mathrm{...2}{n}_x\end{array},$

$W_c^{\left(i\right)}=\{\begin{array}{c}\frac{\mathrm{\λ}}{\mathrm{\λ}+n_x}+(1-{\mathrm{\α}}^2+\mathrm{\β}),i=0\\ \frac{\mathrm{\λ}}{2(\mathrm{\λ}+n_x)},i=1,\mathrm{...2}{n}_x\end{array},$

Wherein β is constant, gets 2;

Described renewal process comprises:

Step S2.2.2.1, structure sigma point: estimate according to the prior state that step S2.2.1.3 calculates, again construct sigma point, formula is:

$X_{k|k-1}^{\left(i\right)}=\left\{\begin{array}{c}{\hat{x}}_{k|k-1},i=0\\ {\hat{x}}_{k|k-1}+{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k|k-1}\right)}_i,i=1,...n_x\\ {\hat{x}}_{k|k-1}-{\left(\sqrt{(n_x+\mathrm{\λ})}{P}_{k|k-1}\right)}_i,i=n_x+1,...2n_x\end{array}\right.,$

Step S2.2.2.2, computational prediction exports: propagate and calculate each sigma point, formula is:

$Y_{k|k-1}^{\left(i\right)}=g(X_{k|k-1}^{\left(i\right)},u_k),$

It is as follows that prediction exports formula:

${\hat{Y}}_{k|k-1}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_m^{\left(i\right)}{Y}_{k|k-1}^{\left(i\right)},$

Step S2.2.2.3, calculate kalman gain K (k), formula is:

$P_{y_k{y}_k}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_c^{\left(i\right)}(Y_{k|k-1}^{\left(i\right)}-{\hat{Y}}_{k|k-1}){\left(Y_{k|k-1}^{\left(i\right)}{\hat{Y}}_{k|k-1}\right)}^T+R,$

$P_{x_k{y}_k}=\underset{i=0}{\overset{2n_x}{\Σ}}{W}_c^{\left(i\right)}(X_{k|k-1}^{\left(i\right)}-{\hat{x}}_{k|k-1}){(Y_{k|k-1}^{\left(i\right)}-{\hat{Y}}_{k|k-1})}^T,$

$K_k=P_{x_k{y}_k}{P}_{y{k}_{}{y}_k}^{-1},$

Wherein dope output error covariance, be average and prediction output cross covariance, R is noise covariance;

Step 2.2.2.4, calculates Posterior Mean and posteriority covariance: in kth step, according to the measured value exported, can calculate Posterior Mean and covariance, formula is:

${\hat{x}}_k={\hat{x}}_{k|k-1}+K_k(Y_k-{\hat{Y}}_{k|k-1}),$

$P_k=P_{k|k-1}-K_k{P}_{y_k{y}_k}{K}_k^T,$

Wherein Y _krepresent the actual measured value of kth step.