CN105759605A - Nonlinear system defect detection and positioning algorithm based on adaptive parameter model particle filter (PF) - Google Patents

Abstract

The invention provides a PF (particle filter)-based novel intelligent defect detection algorithm without priori knowledge. A visual defect detection problem is made, the PF is used for estimating a hidden state, happening of the defect or the position of the defect in a 2-D image is judged through chi-square test. In the method, the brightness of a two-dimensional image in each row or column is an assumed time sequence or a random process as shown in the specifications. In order to detect fault/defects in the image (system), a reasonable state and a measurement model are firstly brought forward for the particle filter; then according to the model, the particle filter estimates the state and measure information (residual error) along rows and columns; and finally, through the chi-square test, mutant measurement information is used for positioning the position of the defect in the detection image. Effectiveness of the algorithm is proved through a test on a real database.

Description

Nonlinear system defects detection and location algorithm based on the filtering of auto-adaptive parameter model particle

Technical field

A kind of method that the present invention relates to technical field of image processing, specifically a kind of nonlinear system defects detection based on the filtering of auto-adaptive parameter model particle and localization method.

Background technology

Fault detect, is the branch controlling engineering, its one stochastic system of monitoring and identifying when fault occurs, the information such as the type of fault and position.Fault detection method improves in production process and application process in various industries and plays basic effect, as at process monitoring, quality control, product manufacturing, medium recovery and facility maintenance etc..In recent years, defect detecting technique low cost, high automatization and high-quality advantage bring increasing income.The metrical information that the inspection of quality is included using camera, eddy current, ultrasound wave, x-ray sensor and other sensors to provide by fault/defects detection is to analyze extraction fault message.Along with camera is in the high demand of Industrial quality control, vision detection system has attracted more concern in recent years.No matter linearly or nonlinearly the fault detect of system, the defects detection of view-based access control model detection system monitors the change of measured value such as through camera.

Existing defect inspection method can be roughly divided into two classes, it may be assumed that based on signal processing with based on the method for model.Signal processing algorithm is by using mathematical statistics method analytical tool to extract defect to measuring.In nonlinear system, the method such as ripe method such as Gabor filtering and wavelet transformation has proved to be the effective defect inspection method when a small amount of prior information.In recent years, based on Gabor filtering and wavelet transformation defects detection to find grid surface and stably repetition texture there is good effect because being easier to find defect at frequency domain.Signal processing technology is directed to substantial amounts of computational intelligence method such as fuzzy logic and neutral net, and it provides some effective solutions for various industry fault detection problem.But, data-driven method is subject to the restriction of computational load and memory space.

In the past few decades, scholars propose various defect/fault detection method based on model.Essence based on the algorithm of model is to estimate system mode from sensor measurement.Bayes method is wherein most popular a kind of algorithm based on model, and it produces the posteriori system distributions comprising hidden state, such as the generation of defect and type etc..Bayesian filter and deformation algorithm thereof are the effective vision solutions of the fault detect of test material surface defect and the Process Control System with reliability requirement, for instance: Monitoring of Chemical.For linear Gaussian Systems, Kalman filter has been used in surface defect vision detection system.Particle filter (Particlefilter, PF), namely the nonlinear and non-Gaussian of Bayesian filter realizes algorithm, has been used to the fault detect of chemical process.But, under actual vision-based detection scene, remain a challenge owing to lacking suitable visual system, state estimation and fault detect.When background pixel presents the gray probability distribution of complexity, linear Gauss model cannot meet the requirement of defects detection and location at actual vision detection system.

Summary of the invention

The present invention is directed to prior art above shortcomings, it is proposed to a kind of new method automatically detected based on the fault of nonlinear system/defect of PF.The present invention can alleviate checked object gradation of image skewness and the problem causing the interference such as intensity profile rule change due to the geometry of checked object itself effectively；Additionally, the particle filter algorithm of the present invention does not need prior information, there is stronger robustness.

The present invention is achieved by the following technical solutions, and the present invention comprises the following steps:

The first step, sets up state model and the measurement model of visual system.

Described state model, specifically:

x_k=F_kx_k-1+v_k(1)

Wherein x_kIt is at seasonal effect in time series state, F_kIt is this state transition model, v_kIt it is zero-mean white Gauss noise variance sequenceFor the problem of this paper defects detection, this dynamic model adopts F_kRandom walk model when=1.In gaussian sequence, each state also can be written as

WhereinRepresent the expectation A and variance B of a Gauss distribution.

Described seasonal effect in time series state x_k, a specifically white Gaussian noise status switch.When checked target zero defect, the brightness along every pixel scanning line presents little change.Therefore, in a flawless image, gray level can be defined as a white Gaussian noise status switch along scanning lineOr

Described measurement model, specifically:

z_k=g_k(x_k)+w_k(3)

Wherein g_k() represents from state estimation x_kTo measured value z_kTransfer function, w_kIt it is zero-mean white Gauss noise variance sequence

Described measured value z_kIt is digital picture is gray value or the brightness of pixel.Assuming that in the image of a width M × N, the gray scale of any a line or string pixel can as a time series or stochastic processOrWherein k is the one-dimensional coordinate of the scanning line about pixel.

Second step, for each pixel, Bayesian filter can be produced along the scanning line of image by following recurrence formulaState estimation.

p_k|k-1(x_k|z_1:k-1)=∫ f_k|k-1(x_k|x)p_k-1(x|z_1:k-1)dx(4)

$p_k\left(x_k\right|z_{1:k})=\frac{g_k\left(z_k\right|x_k)p_{k|k-1}\left(x_k\right|z_{1:k-1})}{\∫g_k\left(z_k\right|x)p_{k|k-1}\left(x_k\right|z_{1:k-1})dx}---\left(5\right)$

Wherein, f_k|k-1(|) is the transfering density defined by (1) or (2), g_k(|) is the likelihood function defined by (3).Posterior density p_k(x_k|z_1:k) include all status informations at moment k and obtained the state estimation of kth pixel on scanning line by maximum a posteriori criterion

3rd step, once obtain the state estimation in the k-1 moment(that is, along the brightness of-1 pixel of kth of scanning line), discreet value z_k|k-1With actual measured value z_kBetween difference can by newly ceasingRepresenting, it can be obtained by calculated below,

${\mathrm{\ν}}_k^{*}=z_k-z_{k|k-1}---\left(6\right)$

Here, z_k|k-1Can be derived by (1) and (3),

$z_{k|k-1}=g_k\left(x_{k|k-1}\right)=g_k(F_k*{\hat{x}}_{k-1})---\left(7\right)$

x_k|k-1It it is the state estimated with (1).From (6) and (7) it can be seen that newly ceaseShowing the difference between true measurement and the defect-free pixel of a pixel, this can be used to judge defect.

4th step, as measured value z_kIt is gaussian variable, it is possible to set up chi-square test statistic

5th step, detects defect by X 2 test and positions, if

$\left|\right|{\mathrm{\ν}}_k^{*}|{|}_{{\mathrm{\Σ}}^{-1}}^2>\mathrm{\λ}={\mathrm{\χ}}_n^2\left(\mathrm{\α}\right)---\left(8\right)$

Then represent and defect detected.Wherein 1-α is confidence level, the degree of freedom that n represents, λ is detection threshold value.

Compared with prior art, the invention has the beneficial effects as follows: effectively alleviate checked object gradation of image skewness and the problem causing the interference such as intensity profile rule change due to the geometry of checked object itself；Additionally, the particle filter algorithm of the present invention does not need prior information, there is stronger robustness.

Detailed description of the invention

Below embodiments of the invention are elaborated: the present embodiment is carried out under premised on technical solution of the present invention, give detailed embodiment and process, but protection scope of the present invention is not limited to following embodiment.

Embodiment

The first step, sets up state model and the measurement model of visual system.

Described state model, specifically:

x_k=F_kx_k-1+v_k(1)

Wherein x_kIt is at seasonal effect in time series state, F_kIt is this state transition model, and v_kIt it is zero-mean white Gauss noise variance sequenceFor the problem of this paper defects detection, this dynamic model adopts F_kRandom walk model when=1.In gaussian sequence, each state also can be written as

WhereinRepresent the expectation A and variance B of a Gauss distribution.

Described seasonal effect in time series state x_k, a specifically white Gaussian noise status switch.When checked target zero defect, the brightness along every pixel scanning line presents little change.Therefore, in a flawless image, gray level can be defined as a white Gaussian noise status switch along scanning lineOr

Described measurement model, specifically:

z_k=g_k(x_k)+w_k(3)

Wherein g_k() represents from state estimation x_kTo measured value z_kTransfer function, w_kIt it is zero-mean white Gauss noise variance sequence

Described measured value z_kIt is digital picture is gray value or the brightness of pixel.Assuming that in the image of a width M × N, the gray scale of any a line or string pixel can as a time series or stochastic processOrWherein k is the one-dimensional coordinate of the scanning line about pixel.

Second step, for each pixel, Bayesian filter can be produced along the scanning line of image by following recursive BayesianState estimation.

p_k|k-1(x_k|z_1:k-1)=∫ f_k|k-1(x_k|x)p_k-1(x|z_1:k-1)dx(4)

$p_k\left(x_k\right|z_{1:k})=\frac{g_k\left(z_k\right|x_k)p_{k|k-1}\left(x_k\right|z_{1:k-1})}{\∫g_k\left(z_k\right|x)p_{k|k-1}\left(x_k\right|z_{1:k-1})dx}---\left(5\right)$

Wherein, f_k|k-1(|) is the transfering density defined by (1) or (2), g_k(|) is the likelihood function defined by (3).Posterior density p_k(x_k|z_1:k) include all status informations at moment k and obtained the state estimation of kth pixel on scanning line by maximum a posteriori criterion

The present embodiment pairState estimation be divided into following four step:

Step 1. initializes

From prior state density p (x₀) in take N number of particle, it is assumed that the weights omega=1/N of N number of particle.

Step 2. is sampled

First, p (x in (4)_k-1|z_1:k-1) particleBy state modelPropagating, it by below equation, can use (1) or (2) to obtain.

Secondly, for a new observed value z_k, each by the sampling particle taken out in (11)By below equation by self adaptation likelihood function weighting proposed in (10).

$w_k^{\left(i\right)}\∝p\left(z_k\right|x_k^{\left(i\right)})---\left(12\right)$

Finally, weight normalization

${\mathrm{\ω}}_t^{\left(j\right)}={\mathrm{\ω}}_t^{\left(j\right)}/\underset{j=1}{\overset{N}{\Σ}}{\mathrm{\ω}}_t^{\left(j\right)}---\left(13\right)$

The described self adaptation likelihood function in (10), specifically:

All parameters at the Gaussian term of (10)(9) pdf model in the k-1 moment can be passed through, use K average to approach and automatically update.Then likelihood function (10) can be used to replace g_k() realizes PF or Bayes's recurrence.Owing to complex distributions well adapting to ability, proposed adaptive measuring model can help to represent the system of reality.

Pdf model in described (9), specifically:

Wherein π_{K-1, m}BeThe weight of the m-th gauss component in mixing, μ_{K-1, m}It is meansigma methods, σ_{K-1, m}Being variance, G is the Gaussian component number of wherein G=3～5.

Step 3. resampling

Method according to wheel disc, in the particle of step 1In resample new particle, select the probability of a particle to be proportional to its weight.After particle resampling, the particle resampledWeight is identical, such that it is able to the Posterior distrbutionp p in time k approximate (5)_k(x_k|z_1:k)。

Step 4. state is extracted

State estimationBoth minimum mean square error criterion can have been used to extract,

${\hat{x}}_k\≈\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}{\tilde{x}}_k^{\left(i\right)}---\left(14\right)$

Can be extracted by maximum a posteriori (MAP) criterion again,

${\hat{x}}_k=\arg \underset{x_k}{max}p\left(x_k\right|z_{1:k})\≈\arg \underset{x_k}{max}{\mathrm{\ω}}_k^{\left(i\right)}---\left(15\right)$

3rd step, once obtain the state estimation in the k-1 moment(that is, along the brightness of-1 pixel of kth of scanning line), discreet value z_k|k-1With actual measured value z_kBetween difference can by newly ceasingRepresenting, it can be obtained by calculated below,

${\mathrm{\ν}}_k^{*}=z_k-z_{k|k-1}---\left(6\right)$

Here, z_k|k-1Can be derived by (1) and (3),

$z_{k|k-1}=g_k\left(x_{k|k-1}\right)=g_k(F_k*{\hat{x}}_{k-1})---\left(7\right)$

x_k|k-1It it is the state estimated with (1).From (6) and (7) it can be seen that newly ceaseShowing the difference between true measurement and the defect-free pixel of a pixel, this can be used to judge defect.

4th step, as measured value z_kIt is gaussian variable, it is possible to set up chi-square test statistic

First the present embodiment should use (6) to calculate the new breath of each pixelUnder gaussian assumptions, residual sequenceWithIt is Gauss distribution, squared statistic (NRSS) ε that normalization newly ceases_kApproximate card side distribution form

${\mathrm{\ϵ}}_k={\mathrm{\ν}}_k^{*\′}{S}_k^{-1}{\mathrm{\ν}}_k^{*}---\left(16\right)$

Wherein,RepresentCovariance.Inspection principle for the goodness of fit, ε_kBeing used as statistics, mistake/defect can be obtained along scanning line by X 2 test,

${\mathrm{\ϵ}}_k>\mathrm{\λ}={\mathrm{\χ}}_n^2\left(\mathrm{\α}\right)---\left(17\right)$

Wherein, 1-α represents confidence level, and n is n=dim (z_k) degree of freedom, λ be detection threshold value.λ can be referred to by α and n in chi-square distribution table.If the statistic ε of a pixel_kMeeting (17), the signal of an instruction defect point provides.

5th step, detects defect by X 2 test and positions, if

$\left|\right|{\mathrm{\ν}}_k^{*}|{|}_{{\mathrm{\Σ}}^{-1}}^2>\mathrm{\λ}={\mathrm{\χ}}_n^2\left(\mathrm{\α}\right)---\left(8\right)$

Then representing and defect detected, wherein 1-α is confidence level, the degree of freedom that n represents, λ is detection threshold value.

In the present embodiment, completing along line chi square test when all, latent defect point is stored in detection mask Θ (M × N), and it is the matrix of a M × N, and value 1 is a marginal point, and value 0 is intact trapping spot.It is likewise possible to obtain mask Θ ' (M × N) along row.Consider the two test different sensitivity along row and column direction, final maskCan be obtained by calculating

$\widehat{\mathrm{\Θ}}(i,j)=\mathrm{\Θ}(i,j)|{\mathrm{\Θ}}^{\′}(i,j)---\left(18\right)$

Wherein (i, j) represents the testing result of the i-th row jth row pixel in image to A, and " | " represents logic or operator.It addition, the generation of the defect in order to position less false alarm exactly, add up ε_kSummation calculated, for from image distinguish defect.

Implementation result

Proposed detector is detected by defect image data base, wherein comprises the defect of multiple type on harddisk surface.In our experiment, proposed defects detection algorithm is performed by the personal computer of the CPU of Intel 2.2GHz.When code does not optimize, the image detection of 1024 × 768 resolution completes with the speed of on average 20 frames per second.

The sample result using proposed defect detector is shown in Fig. 1 and Fig. 2.Draw the cusum of the scanning line of the row and column of NSSRs such as Fig. 1, and with red circle marking of defects position, it calculates centrally through the NSSRs response curve suddenlyd change.When Fig. 2 represents the NSSR directly using each pixel, another defective locations result of the same detection part of mask images in (18).Fig. 1 shows, NSSRs and cusum both approaches thereof are had the drawback that effectively in the picture for finding.In experiment below, the method for the location of each is optional.

Fig. 3-Fig. 6 illustrates various types of defect, for instance, burn into hard bubbles, bubble, crackle etc., and this is to show, this detector can use the erroneous judgement of much less, accurately and automatically identifies and location complex background defect area.As it is well known, uneven illumination and geometry cause the discontinuity at flawless regions scatter, this makes defects detection more difficult.In order to alleviate its impact, it is proposed that PF this measure adaptive model more accurately, it can suppress the discontinuity of defect-free pixel to affect.

Accompanying drawing explanation

Fig. 1 uses the cusum of NSSRs to carry out defect location；

Fig. 2 uses NSSR to carry out defect location；

The method proposed for Fig. 3-Fig. 6 application in checking various defects.

Claims (7)

1. the nonlinear system defects detection based on the filtering of auto-adaptive parameter model particle and localization method, it is characterised in that comprise the following steps:

The first step, sets up state model and the measurement model of visual system.

Second step, for each pixel, Bayesian filter can be produced along the scanning line of image by recursive BayesianState estimation.

3rd step, by newly ceasingRepresent discreet value z_k|k-1With actual measured value z_kBetween difference.

4th step, as measured value z_kIt is gaussian variable, it is possible to set up chi-square test statistic.

5th step, detects defect by X 2 test and positions.

2. the nonlinear system defects detection based on the filtering of auto-adaptive parameter model particle according to claim 1 and localization method, is characterized in that, described state model, specifically

x_k=F_kx_k-1+v_k

Wherein x_kIt is at seasonal effect in time series state, F_kIt is this state transition model, and v_kIt it is zero-mean white Gauss noise variance sequenceFor the problem of this paper defects detection, this dynamic model adopts F_kRandom walk model when=1.In gaussian sequence, each state also can be written as

WhereinRepresent the expectation A and variance B of a Gauss distribution.

Described seasonal effect in time series state x_k, a specifically white Gaussian noise status switch.When checked target zero defect, the brightness along every pixel scanning line presents little change.Therefore, in a flawless image, gray level can be defined as a white Gaussian noise status switch along scanning lineOr

3. the nonlinear system defects detection based on the filtering of auto-adaptive parameter model particle according to claim 1 and localization method, is characterized in that, described measurement model, specifically

z_k=g_k(x_k)+w_k

Wherein g_k() represents from state estimation x_kTo measured value z_kTransfer function, w_kIt it is zero-mean white Gauss noise variance sequence

Described measured value z_kIt is digital picture is gray value or the brightness of pixel.Assuming that in the image of a width M × N, the gray scale of any a line or string pixel can as a time series or stochastic processOrWherein k is the one-dimensional coordinate of the scanning line about pixel.

4. the nonlinear system defects detection based on the filtering of auto-adaptive parameter model particle according to claim 1 and localization method, is characterized in that, describedState estimation adopt recursive Bayesian method produce, specifically

p_k|k-1(x_k|z_1.k-1)=∫ f_k|k-1(x_k|x)p_k-1(x|z_1:k-1)dx

$p_k\left(x_k|z_{1:k}\right)=\frac{g_k\left(z_k\right|x_k)p_{k|k-1}\left(x_k\right|z_{1:k-1})}{\∫g_k\left(z_k\right|x)p_{k|k-1}\left(x_k\right|z_{1:k-1})dx}$

Wherein, f_k|k-1(|) is by the transfering density of the state model definition in claim 2, g_k(|) is the likelihood function defined by the measurement model in claim 2.Posterior density p_k(x_k|z_1k) include all status informations at moment k and obtained the state estimation of kth pixel on scanning line by maximum a posteriori criterion

5. the nonlinear system defects detection based on the filtering of auto-adaptive parameter model particle according to claim 1 and localization method, is characterized in that, described new breathBy discreet value z_k|k-1With actual measured value z_kBetween difference represent, specifically

${\mathrm{\ν}}_k^{*}=z_k-z_{k|k-1}$

Here, z_k|k-1Can be derived by the state model in claim 2 and the measurement model in claim 2,

$z_{k|k-1}=g_k\left(x_{k|k-1}\right)=g_k(F_k*{\hat{x}}_{k-1})$

x_k|k-1It it is the state estimated with the state model in claim 2.It can be seen that newly ceaseShowing the difference between true measurement and the defect-free pixel of a pixel, this can be used to judge defect.

6. the nonlinear system defects detection based on the filtering of auto-adaptive parameter model particle according to claim 1 and localization method, it is characterized in that, the approximate card side distribution form of the squared statistic (NRSS) that described chi-square test statistic is newly ceased by normalization represents, specifically

${\mathrm{\ϵ}}_k={\mathrm{\ν}}_k^{{*}^{\′}}{S}_k^{-1}{\mathrm{\ν}}_k^{*}$

Wherein,RepresentCovariance.At the inspection principle of the goodness of fit, ε_kBeing used as statistics, mistake/defect can be obtained along scanning line by X 2 test,

${\mathrm{\ϵ}}_k>\mathrm{\λ}={\mathrm{\χ}}_n^2\left(\mathrm{\α}\right)$

Wherein, 1-α represents confidence level, and n is n=dim (z_k) degree of freedom, λ be detection threshold value.λ can be referred to by α and n in chi-square distribution table.If the statistic ε of a pixel_kMeeting X 2 test, the signal of an instruction defect point provides.

7. the nonlinear system defects detection based on the filtering of auto-adaptive parameter model particle according to claim 1 and localization method, is characterized in that, described X 2 test detection defect also positions, specifically

$\left|\right|{\mathrm{\ν}}_k^{*}|{|}_{{\mathrm{\Σ}}^{-1}}^2>\mathrm{\λ}={\mathrm{\χ}}_n^2\left(\mathrm{\α}\right)$

Then represent and defect detected.The confidence level that wherein 1-α is, the degree of freedom that n represents, λ is detection threshold value.

In the present embodiment, completing along row chi square test when all, latent defect point is stored in detection mask Θ (M × N), and it is the matrix of a M × N, and value 1 is a marginal point, and value 0 is intact trapping spot.It is likewise possible to obtain mask Θ ' (M × N) along row.Consider the two test different sensitivity along row and column direction, final maskCan be obtained by calculating

$\widehat{\mathrm{\Θ}}(i,j)=\mathrm{\Θ}(i,j)|{\mathrm{\Θ}}^{\′}(i,j)$

Wherein (i, j) represents the testing result of the i-th row jth row pixel in image to A, and " | " represents logic or operator.It addition, the generation of the defect in order to position less false alarm exactly, add up ε_kSummation calculated, for from image distinguish defect.