CN106097285A - A kind of ECT image rebuilding method based on adaptive extended kalman filtering - Google Patents

Abstract

The invention discloses a kind of ECT image rebuilding method based on adaptive extended kalman filtering, comprise the following steps: set up system equation and measure equation, spreading kalman iterative filtering, until it reaches default stopping criterion for iteration.The present invention uses noiseproof feature preferable EKF method that capacitance chromatography imaging is carried out image reconstruction, system noise is added when setting up system equation, and the covariance matrix of on-line amending system noise, make state-space model more can reflect real multi-phase fluid movement, improve image reconstruction accuracy.

Description

A kind of ECT image rebuilding method based on adaptive extended kalman filtering

Technical field

The present invention relates to a kind of ECT image rebuilding method, a kind of ECT based on adaptive extended kalman filtering Image rebuilding method, belongs to the Visual retrieval technical field of two phase flow/multi-phase fluid movement.

Background technology

Capacitance chromatography imaging (Electrical Capacitance Tomography, ECT) is the development eighties in 20th century A kind of detection technique got up, this technology has Noninvasive, radiationless, response is fast, low cost and other advantages, is used for industry two Mutually in the detection of stream/multi-phase fluid movement.Two phase flow/multi-phase fluid movement common in industry includes: gas/liquid two phase flow, gas/solid biphase Stream, liquid/solid two phase flow, liquid liquid two phase flow, gas liquid solid three-phase flow and oil/gas/water three-phase flow.In two phase flow/multiphase flow detection The major parameter needing detection includes: flow pattern, void fraction, flow, flow velocity, density, temperature and pressure etc., flows the most accurately Type identification is significant to the detection of other parameters such as void fraction.The flow pattern of two phase flow/multiphase flow is by observing fluid The geometric shape of flowing is identified, and recognition methods currently mainly has three kinds: by visual observation identification flow pattern, by measuring The change identification flow pattern of some parameter in fluid, by chromatography imaging technique identification flow pattern, capacitance chromatography imaging is i.e. a kind of layer Analysis imaging technique.Electrical capacitance tomography carries out being broadly divided into two steps during multiphase flow detection: direct problem and inverse problem.Its In, direct problem determines interelectrode capacitance value by dielectric constant distribution；By measuring capacitance, inverse problem determines that dielectric constant divides Cloth, in order to identify the flow pattern of two phase flow/multiphase flow.

Due to less qualitative, the pathosis during reverse temperature intensity and " soft field " effect, many image reconstruction algorithms are carried Go out, such as Landweber iterative algorithm, Tikhonov regularization algorithm etc..Though these algorithms obtain quality not in emulation experiment Wrong reconstruction image, but because noise immunity is the best in applying at the scene, rebuild effect and have a greatly reduced quality.Kalman filter method profit By the statistical property of noise, image intensity value being estimated has preferable noise immunity, but Kalman filter can obtain The precondition of excellent estimated value is to set up state-space model accurately.The ECT state-space model set up at present is broadly divided into Two kinds of situations:

1, system noise is not considered.

2 although it is contemplated that system noise, but the covariance matrix of system noise is set to constant.

But when multi-phase fluid movement, flow pattern can change in time, and both state-space models all cannot be accurately Multi-phase fluid movement situation is described.Therefore, this problem to be solved, need add-on system noise in system model, and in real time The covariance matrix of on-line amending system noise, so that state-space model is more nearly with real multi-phase fluid movement.

Summary of the invention

The technical problem to be solved in the present invention is to provide a kind of ECT image reconstruction based on adaptive extended kalman filtering Method.

For solving above-mentioned technical problem, the technical solution used in the present invention is:

A kind of ECT image rebuilding method based on adaptive extended kalman filtering, comprises the following steps:

Step 1: set up system equation and measure equation, being made up of step in detail below:

Step 1-1: set up system equation:

g_k=g_k-1+ω_k-1 (1)

In formula, g_kAnd g_k-1Represent k moment and the image intensity value in k-1 moment respectively；ω_k-1System noise for the k-1 moment Sound, described system noise is white noise, and its average is 0, and covariance matrix is Q_k；

Step 1-2: set up nonlinear equation:

V_k=U_k(g_k)+v_k (2)

In formula, V_kMeasurement capacitance for the k moment；U_k(g_k) represent gradation of image measurement capacitance and between non-linear Relation；v_kFor the measurement noise in k moment, described measurement noise is white noise, and its average is 0, and covariance matrix is R；

Step 1-3: the nonlinear equation setting up described step 1-2 carries out Taylor series expansion:

V_k=U_k(g₀)+J_k(g₀)·(g_k-g₀)+H.O.Ts+v_k (3)

In formula, H.O.Ts represents higher order term, for white Gaussian noise；J_k(g₀) it is Jacobian matrix, it is defined as:

$J_k\left(g_0\right)=\frac{\∂U_k\left(g_k\right)}{\∂g_k}{|}_{g_k=g_0}---\left(4\right)$

Step 1-4: set up and measure equation:

$z_k={\mathrm{Sg}}_k+{\stackrel{\‾}{v}}_k---\left(5\right)$

In formula, z_kFor AVHRR NDVI value；S is normalization sensitivity matrix；g_kFor normalized image gray value；For linear measurement noise, its average is 0, and variance is

Step 2: spreading kalman iterative filtering, is made up of step in detail below:

Step 2-1: filtering initial value is set: gradation of image initial value g₀It is 0 vector, error co-variance matrix initial value P₀For α I, I is unit matrix, and α is proportionality coefficient.

Step 2-2: calculate the covariance matrix Q of system noise_kRenewal equation:

$Q_k=K_k\·{\hat{P}}_{vk}\·K_k^T+P_k-P_{k-1}---\left(6\right)$

In formula,Represent innovation sequenceVariance matrix, z_kRepresent the AVHRR NDVI value in k moment；Represent the step measurement predictor from moment k-1 to moment k；K_kFor filtering gain matrix；P_kAnd P_k-1Represent moment k respectively Filtering error covariance matrix with moment k-1；

Step 2-3: EKF:

$\left\{\begin{array}{c}{\hat{g}}_{k/k-1}={\hat{g}}_{k-1}\\ {\hat{g}}_k={\hat{g}}_{k/k-1}+K_k\[z_k-S{\hat{g}}_{k/k-1}\]\\ K_k=P_{k/k-1}{S}^T{\[{\mathrm{SP}}_{k/k-1}{S}^T+\stackrel{\‾}{R}\]}^{-1}\\ P_{k/k-1}=P_{k-1}+Q_{k-1}\\ P_k=\[I-K_{k}S\]P_{k/k-1}\end{array}\right.---\left(7\right)$

In formula,WithRepresent the estimated value of the gradation of image of moment k and moment k-1 respectively；Represent from moment k One-step prediction value to moment k-1 gradation of image；P_k/k-1Represent the one-step prediction covariance from the k-1 moment to k moment；Q_k-1Table Show k-1 moment system noise covariance matrix；

Step 3: judge whether to reach default stopping criterion for iterationε is for terminating threshold value, if it is, turn To step 4；Otherwise turn to step 2；

Step 4: the optimal estimation value of output gradation of image.

Sequence innovation sequence in described step 2-2Variance matrix be:

${\hat{P}}_{vk}={\mathrm{SP}}_{k/k-1}{S}^T+R---\left(8\right)$

Sequence innovation sequence in described step 2-2The computational methods of variance matrix be:

${\hat{P}}_{vk}=E\[(z_k-{\hat{z}}_{k/k-1}){(z_k-{\hat{z}}_{k/k-1})}^T\]---\left(9\right)$

In formula, measurement capacitance z_kIt is expressed as:

z_k=H_kx_k+v_k (10)

One step surveying predictive valueIt is expressed as:

${\hat{z}}_{k/k-1}=H_k{\hat{x}}_{k/k-1}---\left(11\right)$

In formula, H_kRepresent the state-transition matrix in k moment,Represent the status predication value in k-1 moment to k moment.

Use and have the beneficial effects that produced by technique scheme:

The present invention uses noiseproof feature preferable EKF method that capacitance chromatography imaging is carried out image reconstruction, Add system noise, and the covariance matrix of on-line amending system noise when setting up system equation, make state-space model more Real multi-phase fluid movement can be reflected, improve image reconstruction accuracy.

Accompanying drawing explanation

Fig. 1 is the flow chart of the present invention.

Detailed description of the invention

The present invention is further detailed explanation with detailed description of the invention below in conjunction with the accompanying drawings.

A kind of ECT image rebuilding method based on adaptive extended kalman filtering, comprises the following steps:

Step 1: set up system equation and measure equation, being made up of step in detail below:

Step 1-1: set up system equation:

g_k=g_k-1+ω_k-1 (1)

In formula, g_kAnd g_k-1Represent k moment and the image intensity value in k-1 moment respectively；ω_k-1System noise for the k-1 moment Sound, described system noise is white noise, and its average is 0, and covariance matrix is Q_k；

Described system equation utilizes system noise reflection multiphase flow pattern change, when setting up system equation, adds system Noise, with reflection when liquid flow pattern changes, the change of system model, its noise variance matrix is unknown, needs to estimate；

Step 1-2: set up nonlinear equation:

V_k=U_k(g_k)+v_k (2)

In formula, V_kMeasurement capacitance for the k moment；U_k(g_k) represent gradation of image measurement capacitance and between non-linear Relation；v_kFor the measurement noise in k moment, described measurement noise is white noise, and its average is 0, and covariance matrix is R；

Described nonlinear equation is used for describing measurement capacitance and gradation of image relation；Measurement capacitance and image intensity value Between be non-linear relation, utilize and measure noise and represent the noise produced during measurement, it is believed that measure the variance matrix R of noise Measure during constant；

Step 1-3: the nonlinear equation setting up described step 1-2 carries out Taylor series expansion:

V_k=U_k(g₀)+J_k(g₀)·(g_k-g₀)+H.O.Ts+v_k (3)

In formula, H.O.Ts represents higher order term, for white Gaussian noise；J_k(g₀) it is Jacobian matrix, it is defined as:

$J_k\left(g_0\right)=\frac{\∂U_k\left(g_k\right)}{\∂g_k}{|}_{g_k=g_0}---\left(4\right)$

Step 1-4: set up and measure equation:

$z_k={\mathrm{Sg}}_k+{\stackrel{\‾}{v}}_k---\left(5\right)$

In formula, z_kFor AVHRR NDVI value；S is normalization sensitivity matrix；g_kFor normalized image gray value；For linear measurement noise, its average is 0, and variance is

Step 2: spreading kalman iterative filtering, is made up of step in detail below:

Step 2-1: filtering initial value is set: gradation of image initial value g₀It is 0 vector, error co-variance matrix initial value P₀For α I, I is unit matrix, and α is proportionality coefficient.

Step 2-2: calculate the covariance matrix Q of system noise_kRenewal equation:

$Q_k=K_k\·{\hat{P}}_k\·K_k^T+P_k-P_{k-1}---\left(6\right)$

In formula,Represent innovation sequenceVariance matrix, z_kRepresent the AVHRR NDVI value in k moment；Represent the step measurement predictor from moment k-1 to moment k；K_kFor filtering gain matrix；P_kAnd P_k-1Represent moment k respectively Filtering error covariance matrix with moment k-1；

Step 2-3: EKF:

$\left\{\begin{array}{c}{\hat{g}}_{k/k-1}={\hat{g}}_{k-1}\\ {\hat{g}}_k={\hat{g}}_{k/k-1}+K_k\[z_k-S{\hat{g}}_{k/k-1}\]\\ K_k=P_{k/k-1}{S}^T{\[{\mathrm{SP}}_{k/k-1}{S}^T+\stackrel{\‾}{R}\]}^{-1}\\ P_{k/k-1}=P_{k-1}+Q_{k-1}\\ P_k=\[I-K_{k}S\]P_{k/k-1}\end{array}\right.---\left(7\right)$

In formula,WithRepresent the estimated value of the gradation of image of moment k and moment k-1 respectively；Represent from moment k One-step prediction value to moment k-1 gradation of image；P_k/k-1Represent the one-step prediction covariance from the k-1 moment to k moment；Q_k-1Table Show k-1 moment system noise covariance matrix；

The present invention is based on maximum likelihood criterion, the covariance matrix Q to system noise_kRevise in real time；

Step 3: judge whether to reach default stopping criterion for iterationε=0.001 in the present embodiment, If it is, turn to step 4；Otherwise turn to step 2；

Step 4: the optimal estimation value of output gradation of image.

Sequence innovation sequence in described step 2-2Variance matrix be:

${\hat{P}}_{vk}={\mathrm{SP}}_{k/k-1}{S}^T+R---\left(8\right)$

Sequence innovation sequence in described step 2-2The computational methods of variance matrix be:

${\hat{P}}_{vk}=E\[(z_k-{\hat{z}}_{k/k-1}){(z_k-{\hat{z}}_{k/k-1})}^T\]---\left(9\right)$

In formula, measurement capacitance z_kIt is expressed as:

z_k=H_kx_k+v_k (10)

One step surveying predictive valueIt is expressed as:

${\hat{z}}_{k/k-1}=H_k{\hat{x}}_{k/k-1}---\left(11\right)$

In formula, H_kRepresent the state-transition matrix in k moment,Represent the status predication value in k-1 moment to k moment.

Described EKF equation obtains based on the criterion that error variance is minimum.

Claims (1)

1. an ECT image rebuilding method based on adaptive extended kalman filtering, it is characterised in that:

Comprise the following steps:

Step 1: set up system equation and measure equation, being made up of step in detail below:

Step 1-1: set up system equation:

g_k=g_k-1+ω_k-1 (1)

In formula, g_kAnd g_k-1Represent k moment and the image intensity value in k-1 moment respectively；ω_k-1For the system noise in k-1 moment, institute Stating system noise is white noise, and its average is 0, and covariance matrix is Q_k；

Step 1-2: set up nonlinear equation:

V_k=U_k(g_k)+v_k (2)

In formula, V_kMeasurement capacitance for the k moment；U_k(g_k) represent gradation of image measurement capacitance and between non-linear relation； v_kFor the measurement noise in k moment, described measurement noise is white noise, and its average is 0, and covariance matrix is R；

Step 1-3: the nonlinear equation setting up described step 1-2 carries out Taylor series expansion:

V_k=U_k(g₀)+J_k(g₀)·(g_k-g₀)+H.O.Ts+v_k (3)

In formula, H.O.Ts represents higher order term, for white Gaussian noise；J_k(g₀) it is Jacobian matrix, it is defined as:

$J_k\left(g_0\right)=\frac{\∂U_k\left(g_k\right)}{\∂g_k}{|}_{g_k=g_0}---\left(4\right)$

Step 1-4: set up and measure equation:

$z_k={\mathrm{Sg}}_k+{\stackrel{\‾}{v}}_k---\left(5\right)$

In formula, z_kFor AVHRR NDVI value；S is normalization sensitivity matrix；g_kFor normalized image gray value；For linear measurement noise, its average is 0, and variance is

Step 2: spreading kalman iterative filtering: be made up of step in detail below:

Step 2-1: filtering initial value is set: gradation of image initial value g₀It is 0 vector, error co-variance matrix initial value P₀For α I, I it is Unit matrix, α is proportionality coefficient.

Step 2-2: calculate the covariance matrix Q of system noise_kRenewal equation:

$Q_k=K_k\·{\hat{P}}_{vk}\·K_k^T+P_k-P_{k-1}---\left(6\right)$

In formula,Represent innovation sequenceVariance matrix, z_kRepresent the AVHRR NDVI value in k moment；Table Show the step measurement predictor from moment k-1 to moment k；K_kFor filtering gain matrix；P_kAnd P_k-1Represent moment k and moment respectively The filtering error covariance matrix of k-1；

Step 2-3: EKF:

$\left\{\begin{array}{c}{\hat{g}}_{k/k-1}={\hat{g}}_{k-1}\\ {\hat{g}}_k={\hat{g}}_{k/k-1}+K_k\[z_k-S{\hat{g}}_{k/k-1}\]\\ K_k=P_{k/k-1}{S}^T{\[{\mathrm{SP}}_{k/k-1}{S}^T+\stackrel{\‾}{R}\]}^{-1}\\ P_{k/k-1}=P_{k-1}+Q_{k-1}\\ P_k=\[I-K_{k}S\]P_{k/k-1}\end{array}\right.---\left(7\right)$

In formula,WithRepresent the estimated value of the gradation of image of moment k and moment k-1 respectively；Represent from moment k then Carve the one-step prediction value of k-1 gradation of image；P_k/k-1Represent the one-step prediction covariance from the k-1 moment to k moment；Q_k-1Represent k-1 Moment system noise covariance matrix；

Step 3: judge whether to reach default stopping criterion for iterationε is for terminating threshold value, if it is, turn to step Rapid 4；Otherwise turn to step 2；

Step 4: the optimal estimation value of output gradation of image.

Sequence innovation sequence in described step 2-2Variance matrix be:

${\hat{P}}_{vk}={\mathrm{SP}}_{k/k-1}{S}^T+R---\left(8\right)$

Sequence innovation sequence in described step 2-2The computational methods of variance matrix be:

${\hat{P}}_{vk}=E\[(z_k-{\hat{z}}_{k/k-1}){(z_k-{\hat{z}}_{k/k-1})}^T\]---\left(9\right)$

In formula, measurement capacitance z_kIt is expressed as:

z_k=H_kx_k+v_k (10)

One step surveying predictive valueIt is expressed as:

${\hat{z}}_{k/k-1}=H_k{\hat{x}}_{k/k-1}---\left(11\right)$

In formula, H_kRepresent the state-transition matrix in k moment,Represent the status predication value in k-1 moment to k moment.