CN101446828A - Nonlinear process quality prediction method - Google Patents

Abstract

The invention relates to a nonlinear process quality prediction method, which comprises the steps as follows: in step one, data is acquired, and acquired data comprises correlative variable data during the process; and each fault generates two groups of data that is training data and real-time working condition data; in step two, independent elements are extracted through analyzing ICA by utilizing the independent elements; and an input matrix X and an output matrix Y are broken down into a linear relation indicated by a independent component matrix and a residual error matrix; in step three, a relation model built up between the input matrix X and the output matrix Y is processed through RMSE valuation; and in step four, observed data Y and data Y obtained by a regressive model are compared, and a quality prediction result is obtained. The nonlinear process quality prediction method has the advantages as follows: the capacity and the accuracy for the quality prediction are increased, the dependency relationship of high price statistics is reduced, the independent information can be removed effectively, nonlinear optimization process is not needed, and the amount of calculation is simple.

Description

A kind of nonlinear process quality prediction method

Technical field

The invention belongs to quality forecasting technique field, particularly a kind of nonlinear process quality prediction method.

Background technology

The information that is comprised at the leaching process variable is set up the performance that the experimental forecast model is used to monitor industrial process very big profit.Partial least square method has been widely used in many industrial processes, comprising independent variable collinearity, noisy, the variable dimension height of measurement data, and the situation that observed reading is lacked than independent variable when describing potential data structure.The complexity expansion of partial least square method is suggested and uses.For example, several recurrence offset minimum binaries (RPLS) algorithm is suggested: online process model building changes with the procedure of adaptation, and off-line modeling is to handle the lot of data sample.The piecemeal RPLS algorithm that has moving window and forgetting factor adaptation scheme is suggested.Yet partial least square method can not show tangible nonlinear characteristic, because its supposition process data is linear.The use of polynomial expression Nonlinear Mapping is based on such hypothesis: the relation between independent variable and the response latent variable can be by the method modeling of polynomial expansion.The KPLS non-linear PLS algorithm of mentioning different from the past is: original input data non-linearly is converted to the feature space of any dimension by Nonlinear Mapping, then, sets up the Linear PLS model on feature space.By finding out latent variable, KPLS provides good forecasting model, shows the intelligibility that a kind of good nonlinear relationship has been improved model simultaneously between these latent variables and the response variable.Kernel method is applied on the chemical industry more and more.

In PLS and KPLS method, in input or feature space, use the PCA method that two scalar matrixs are resolved into score vector and load vector.PCA is data projection to a lower dimensional space, wherein comprised the maximum variation direction of raw data and correlativity between variable has been described.PCA only extracts irrelevant composition but not independent component, therefore those non-Gaussian data performances that appear in the industrial data is short of.Recently, several multivariate statistics process monitorings (MSPM) method based on ICA is suggested.The target of ICA is the linear combination of observation data being resolved into statistics independent component (independent entry).People such as Kano have also proposed a kind of new MPSM method based on ICA and external analysis, to improve the monitoring performance and identify quality from the service condition normal variation.People such as Lee have proposed the statistic processes monitoring method based on ICA.They extract independent component with the ICA method, again they are divided into main independent component and less important independent component, and this method is applicable to non-Gaussian data.This monitoring method based on ICA is generalized to the monitoring and the batch production process monitoring of dynamic process respectively.

Multivariate statistics process control as pivot analysis PCA and offset minimum binary PLS has been effectively applied to improve the product quality of industrial process.Yet PCA and PLS are linear method in essence, so on most chemistry and bioprocess non-linear, the practical application of PCA and PLS still is a significant problem.Kernel method is a kind of potential very effective method, and it can be by projecting to the original input space the crucial quality variable that high-dimensional feature space forecasts non-linear process.And compare with other nonlinear method, the sharpest edges of kernel method are exactly that it does not comprise the nonlinear optimization process.What kernel method only needed in itself is linear algorithm, makes them simple as linear multivariate sciagraphy.Because it can use different kernel functions, so they can handle most of non-linear process.

As everyone knows, many systematic procedure variablees that are observed all are dependent.Measurable process variable may be the combination of independent variable, and these independent variables can not directly be measured.Independent component analysis (ICA) can extract latent factor or composition (being also referred to as blind source) effectively from the multivariate statistics data.

Summary of the invention

Deficiency at the prior art existence, the invention provides a kind of nonlinear process quality prediction method, particularly a kind of based on independent component analysis ICA modified partial least square method PLS or based on the quality prediction method of independent component analysis ICA modified core partial least square method KPLS.

Nonlinear process quality prediction method of the present invention may further comprise the steps:

The step 1 data acquisition

The data of gathering comprise variable data relevant in the process, for each process, all produce two groups of data, i.e. training data and real-time working condition data;

Step 2 utilizes independent component analysis ICA to extract independent entry; Be about to input matrix X and output matrix Y and resolve into the linear relationship that independent component matrix and residual matrix are represented;

Step 3 is carried out the RMSE assessment to the relational model of setting up between input matrix X and the output matrix Y; Promptly utilize modified PLS method or modified KPLS method to set up regression model between input matrix X and the output matrix Y;

The data Y of step 4 comparative observation and the data of utilizing regression model to draw

Draw the quality value of forecasting, when $Y=\hat{Y}$ Be that the expression process does not exist quality problems, Y gets over convergence

The forecast precision of value representation procedure quality is high more.

Modified PLS method of the present invention is upgraded and is used for realizing two main targets: be accurately approximate X in basis and Y with the independent component and set up relational model between X and Y in the input space.Scalar matrix X and Y are expressed as m (≤d) individual independent component s in new PLS method ₁, s ₂..., s _mLinear combination.Therefore, improved PLS method resolves into following form to input quantity X and output quantity Y with zero-mean:

$X=\mathrm{AS}+E,A={\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="A200810246926E00101.png,A200810246926E00102.png"\; state="\{\{state\}\}">U</figure-callout>}}_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1---\left(1\right)$

$Y=\mathrm{GV}+F,G={\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="A200810246926E00122.png,A200810246926E00131.png"\; state="\{\{state\}\}">U</figure-callout>}}_2{\mathrm{\&Lambda;}}_2^{\frac{1}{2}}{B}_2---\left(2\right)$

In the formula, S and V represent the independent component matrix, and E and F represent residual matrix, and G is non-quadratic function, and A is matrix and A=[a ₁..., a _m] ∈ R ^{D * m}, represent the A matrix to belong to the real number space of d * m dimension, wherein a is the d dimensional vector; U is the orthogonal matrix of proper vector; Λ is the diagonal matrix of eigenwert, B ₁, B ₂Represent vectorial zm after the albefaction ²And the linear relationship between the independent component S.

Improved PLS regression model can be expressed as follows with regression coefficient matrix H and residual error battle array L:

Y＝XH+L (3)

H=Ξ (Π wherein ^TΞ) ^-1Γ ^T,

$\mathrm{\&Xi;}=X^T\left({\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="A200810246926E00122.png,A200810246926E00131.png"\; state="\{\{state\}\}">U</figure-callout>}}_2{\mathrm{\&Lambda;}}_2^{\frac{1}{2}}{B}_2\right)---\left(4\right)$

$\mathrm{\&Pi;}=X^T\left({\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="A200810246926E00101.png,A200810246926E00102.png"\; state="\{\{state\}\}">U</figure-callout>}}_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1\right){\left(\left({\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="A200810246926E00101.png,A200810246926E00102.png"\; state="\{\{state\}\}">U</figure-callout>}}_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1\right)\right)}^T{\left({\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="A200810246926E00101.png,A200810246926E00102.png"\; state="\{\{state\}\}">U</figure-callout>}}_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1\right)}^{-1}---\left(5\right)$

$\mathrm{\&Gamma;}=Y^T\left({\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="A200810246926E00101.png,A200810246926E00102.png"\; state="\{\{state\}\}">U</figure-callout>}}_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1\right){\left(\left({\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="A200810246926E00101.png,A200810246926E00102.png"\; state="\{\{state\}\}">U</figure-callout>}}_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1\right)\right)}^T{\left({\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="A200810246926E00101.png,A200810246926E00102.png"\; state="\{\{state\}\}">U</figure-callout>}}_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1\right)}^{-1}---\left(6\right)$

In the formula, Ξ, Π ^TAnd Γ ^TBe self-defining variable.

Modified KPLS method of the present invention is upgraded and is used to realize two main targets: be accurately approximate X in basis and Y with the independent component and set up relational model between X and Y at feature space.When the test data number is n _tThe time, the training data of forecast and test data can obtain as follows, are respectively:

$\hat{Y}=\mathrm{\&Phi;H}=\mathrm{K\&Xi;}{\left({\left({\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="A200810246926E00101.png,A200810246926E00102.png"\; state="\{\{state\}\}">U</figure-callout>}}_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1\right)}^T\mathrm{K\&Xi;}\right)}^{-1}{\mathrm{\&Gamma;}}^{T}Y---\left(7\right)$

$\widehat{Y_t}={\mathrm{\&Phi;}}_{t}H=K_t\mathrm{\&Xi;}{\left({\left({\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="A200810246926E00101.png,A200810246926E00102.png"\; state="\{\{state\}\}">U</figure-callout>}}_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1\right)}^T\mathrm{K\&Xi;}\right)}^{-1}{\mathrm{\&Gamma;}}^{T}Y---\left(8\right)$

Φ wherein _tBe mapping test point matrix, $K_t\&Element;R^{n_r\&times;n}$ Be the nuclear matrix that is used to test, its formation element is K _Ij=k (x _i, x _j), wherein k (x, y)=＜Φ (x), Φ (y) 〉, x wherein _i, x _jThe sampled value of representing the i time and the j time.Some most popular kernel functions are as radially basic kernel function: $k(x,y)=\exp (-\frac{{\left|\right|x-y\left|\right|}^2}{\mathrm{\&sigma;}}),$ Polynomial kernel function: k (x, y)=＜x, y 〉 ^r, sigmoid kernel function: k (x, y)=tanh (β ₀＜x, y 〉+β ₁), σ wherein, r, β ₀And β ₁Be constant.Before using modified KPLS, should carry out the average centralization at higher dimensional space.

The performance of partial least square method modeling method can be assessed by their forecast precision and execution characteristics.Under the standard of root square error (RMSE), the performance of each model is all assessed.The definition of RMSE performance index is:

$\mathrm{RMSE}={(\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{({\hat{y}}_i-y_i)}^2/n)}^{\frac{1}{2}}---\left(9\right)$

Y wherein _iBe reference value,

Be predicted value, n is a total sample number.

The invention has the advantages that: adopt based on the KPLS method of ICA method improvement and carry out ability and the degree of accuracy that the quality forecast has improved the quality forecast, reduced the dependence of statistics at high price simultaneously, can effectively remove non-dependence information, this method does not need the nonlinear optimization process, and the calculated amount of this method is simple.The innovative point of this paper be to utilize ICA but not PCA as effective processing means of PLS and KPLS, extracted independent component but not major component, carried the important information of more original system, make the product quality forecasting procedure of ICA-PLS and ICA-KPLS more can mate observation data accurately, improved quality forecast precision and ability.Its performance is: ICA has been arranged as the processing means, make this method can be applied to nongausian process (much all is nongausian process because the industrial circle process has), ICA merges PLS can handle similar linear process, and ICA merging KPLS can handle most non-linear process.Can see that from embodiment the quality forecast that this method process that is applied to detects has very big prospect.

Description of drawings

The test data response variable Y that Fig. 1 uses modified PLS method analog simulation to obtain ₁Graph of a relation between predicted value and the observed reading;

The test data response variable Y that Fig. 2 uses the emulation of modified KPLS method to obtain ₁Graph of a relation between predicted value and the observed reading;

The test data response variable Y that Fig. 3 uses modified PLS method to obtain ₂Graph of a relation between predicted value and the observed reading;

The test data response variable Y that Fig. 4 uses modified KPLS method to obtain ₂Graph of a relation between predicted value and the observed reading;

Fig. 5 Tennessee Yi Siman process layout;

Use improvement PLS method to obtain test data response variable Y in Fig. 6 Tennessee process ₃Predicted value and observed reading between graph of a relation;

Use improvement KPLS method obtains the graph of a relation between test data response variable predicted value and observed reading in Fig. 7 Tennessee process;

Embodiment

Embodiment 1 is used for the analog simulation process with nonlinear process quality prediction method of the present invention

The operation steps of this method in analogue means comprises:

The step 1 image data

This analogue means has three input X, two output Y and B matrix B=[12; 51; 37], input X is the white noise with zero-mean and unit variance, for example X*=randn (100,3) * C0, wherein C0=[136; 217; 384].

Step 2 utilizes independent component analysis ICA to extract independent entry; Be about to input matrix X and output matrix Y and resolve into the linear relationship that independent component matrix and residual matrix are represented; Linear relationship between input X and output Y variable is from Y ^*=BX ^*In calculate, the variable that has write down is Y=Y ^*+ e and X=X ^*, the average of e is that zero variance is 0.1, i.e. e ∈ N{0,0.1I}.

Step 3 is carried out the RMSE assessment to the relational model of setting up between input matrix X and the output matrix Y; Promptly utilize modified PLS method or modified KPLS method to set up regression model between input matrix X and the output matrix Y; Promptly

$\hat{Y}=\mathrm{\&Phi;H}=\mathrm{K\&Xi;}{\left({\left({\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="A200810246926E00101.png,A200810246926E00102.png"\; state="\{\{state\}\}">U</figure-callout>}}_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1\right)}^T\mathrm{K\&Xi;}\right)}^{-1}{\mathrm{\&Gamma;}}^{T}Y---\left(7\right)$

$\widehat{Y_t}={\mathrm{\&Phi;}}_{t}H=K_t\mathrm{\&Xi;}{\left({\left({\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="A200810246926E00101.png,A200810246926E00102.png"\; state="\{\{state\}\}">U</figure-callout>}}_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1\right)}^T\mathrm{K\&Xi;}\right)}^{-1}{\mathrm{\&Gamma;}}^{T}Y---\left(8\right)$

Used two groups of data, one is that training set has 100 records, and another is that the real-time working condition data have 30 records.

The data Y of step 4 comparative observation and the data of utilizing regression model to draw

Draw the quality value of forecasting.For comparing the quality of forecast (ICA-PLS and ICA-KPLS) of two kinds of methods, drawn out the figure of predicted value comparative observation data.Based on the forecast characteristic of two kinds of homing methods of all response variables as depicted in figs. 1 and 2.Performance comparison is as shown in table 1:

Table 1: modeling in the simple case and test data summary

Model	RMSE Training	RMSE Test
			PLS(30)	0.1962	0.2251
KPLS(30)	0.0719	0.1045
			PLS(50)	0.2869	0.4563
KPLS(50)	0.1058	0.1072

Show in the table that the RMSE value that obtains with PLS is 0.2251, the RMSE value that KPLS obtains is 0.1045, and at this moment the model of setting up with the KPLS method mates training data almost ideally, represents the good product quality that this process is produced.Obviously, use KPLS to substitute PLS and greatly improved forecast precision.

When training set has 100 records, the real-time working condition data have 40 records.Forecast characteristic based on two homing methods of all response variables is shown in Fig. 3 and Fig. 4.By table 1, the RMSE value that obtains with PLS is 0.4563, the RMSE value that obtains with KPLS is 0.1072, at this moment the regression model of setting up with KPLS also is close to and ideally mates training data, illustrate that the ratio of precision of using the model prediction quality that the KPLS method sets up uses the precision height of the regression model quality of forecast that the PLS method sets up, and calculated amount is little.As shown in figures 1 and 3, the PLS model is not a matched data fully, because DATA DISTRIBUTION is almost perpendicular to transverse axis, whether forecast precision of this explanation PLS regression model is low, can not the accurate forecast process change.On the other hand, the KPLS data float to more approaching cornerwise distribution (Fig. 2 and Fig. 4), obviously use the KPLS regression model to improve prediction ability.

Embodiment 2 is used for Tennessee Yi Siman process with nonlinear process quality prediction method of the present invention

Tennessee Yi Shiman process is the non-linear process of a complexity, and it is that an industrial process that gears to actual circumstances being provided by Eastman Chemical is with evaluation procedure control and monitoring method.Test process is based on the simulation actual industrial process, and wherein composition, dynamics, operating conditions are modified to be fit to proprietary reason.This control structure synoptic diagram is presented at Fig. 5.

The step 1 image data

In this process 5 formant processes are arranged: a reactor, a condenser, a recycle compressor, a separation vessel and a stripping tower; It has comprised 8 composition: A, B, C, D, E, F, G and H.Four kinds of reactant As, C, D and E and inert material B are added in the reactor together, form product G and H, go back by-product F.The Tennessee process comprises 22 continuous process measurements, 12 control variable and 19 composition measurements that must frequently not sample.People such as Chiang have well described the details of this process.Totally 52 variablees are used for the monitoring of this research.We have got rid of all composition measurements, because they are difficult to on-line measurement in practice.The emulated data of using three minutes sampling interval to collect the training and testing collection.For each quality, all can generate two groups of data.Training data is used for setting up model, and verification msg is used for verification model.The training dataset of each quality is made up of 480 observed readings.The test data set of each quality is made up of 960 observed readings.Test data concentrates all quality all to obtain from the 160th sampling.

Step 2 utilizes independent component analysis ICA to extract independent entry; Be about to input matrix X and output matrix Y and resolve into the linear relationship that independent component matrix and residual matrix are represented; Linear relationship between input X and output Y variable is from Y ^*=BX ^*In calculate, the variable that has write down is Y=Y ^*+ e and X=X ^*, the average of e is that zero variance is 0.1, i.e. e ∈ N{0,0.1I}.

Step 3 forecast characteristic of two kinds of homing methods in the Tennessee process has been considered all input and output values.Response variable is shown among Fig. 6-7.Performance parameter is summarized in the table 2.

Table 2: modeling in the Tennessee Yi Siman process and test data summary

Model	RMSE Training	RMSE Test
			PLS(variable 44)	0.2549	0.4983
KPLS(variable 44)	0.1945	0.3034
			PLS(variable 47)	0.2879	0.5997
KPLS(variable 47)	0.2058	0.3194

The data Y of step 4 comparative observation and the data of utilizing regression model to draw

Draw the quality value of forecasting.

For variable 44, be 0.4983 with the RMSE value of PLS method, the RMSE value that obtains with the KPLS method is 0.3034, uses KPLS to improve prediction ability.As shown in Figure 6, the PLS model does not have matched data fully, because DATA DISTRIBUTION almost is vertical.As shown in Figure 7, the KPLS model mates training data fully.

For variable 47, be 0.5997 with the RMSE value of PLS, the RMSE value that obtains with KPLS is 0.3194, this means that also using KPLS to substitute PLS has greatly improved prediction ability.Obviously, use to show that the method that proposes has above captured linearity between process variable and nonlinear relationship effectively and improved prediction ability with KPLS.

Claims (4)

1. nonlinear process quality prediction method is characterized in that this forecasting procedure may further comprise the steps:

The step 1 data acquisition

The variable data of being correlated with in the gatherer process for each process, all produces two groups of data, i.e. training data and real-time working condition data;

Step 2 utilizes independent component analysis method ICA to extract independent entry, and input matrix X and output matrix Y are resolved into the linear relationship that independent component matrix and residual matrix are represented;

Step 3 is carried out the RMSE assessment to the relational model of setting up between input matrix X and the output matrix Y; Promptly to utilizing input variable X that modified PLS method or modified KPLS method set up and the regression model between the output variable Y to assess;

The step 4 comparative observation to data Y and the data that draw of regression model

Draw the quality value of forecasting.

2. a kind of nonlinear process quality prediction method according to claim 1 is characterized in that described input matrix X of step 2 and output matrix Y are decomposed into:

$X=\mathrm{AS}+E,A=U_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1$

$Y=\mathrm{GV}+F,G=U_2{\mathrm{\&Lambda;}}_2^{\frac{1}{2}}{B}_2$

Wherein, S and V represent the independent component matrix, and E and F represent residual matrix, and G is non-quadratic function, and A is matrix and A=[a ₁..., a _m] ∈ R ^{D * m}, representative be the real number space that the A matrix belongs to d * m dimension, wherein a is the d dimensional vector; U is the orthogonal matrix of proper vector; Λ is the diagonal matrix of eigenwert, B ₁, B ₂Represent vectorial z after the albefaction and the linear relationship between the independent component S.

3. a kind of nonlinear process quality prediction method according to claim 1 is characterized in that the regression relation model that the described modified PLS of step 3 method is set up is expressed as with regression coefficient matrix H and residual error battle array L:

Y＝XH+L

In the formula, H=Ξ (П ^TΞ) ^-1Г ^T,

$\mathrm{\&Xi;}=X^T\left(U_2{\mathrm{\&Lambda;}}_2^{\frac{1}{2}}{B}_2\right)$

$\mathrm{\&Pi;}=X^T\left(U_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1\right){\left(\left(U_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1\right)\right)}^T{\left(U_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1\right)}^{-1}$

$\mathrm{\&Gamma;}=Y^T\left(U_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1\right){\left(\left(U_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1\right)\right)}^T{\left(U_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1\right)}^{-1}$

In the formula, Ξ, П ^TAnd Г ^TBe self-defining variable.

4. a kind of nonlinear process quality prediction method according to claim 1 is characterized in that the regression model that the described modified KPLS of step 3 method is set up is:

$\hat{Y}=\mathrm{\&Phi;H}=\mathrm{K\&Xi;}{\left({\left(U_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1\right)}^T\mathrm{K\&Xi;}\right)}^{-1}{\mathrm{\&Gamma;}}^{T}Y$

$\widehat{Y_t}={\mathrm{\&Phi;}}_{t}H=K_t\mathrm{\&Xi;}{\left({\left(U_1{\mathrm{\&Lambda;}}_1^{\frac{1}{2}}{B}_1\right)}^T\mathrm{K\&Xi;}\right)}^{-1}{\mathrm{\&Gamma;}}^{T}Y$

In the formula, Φ _tBe mapping test point matrix, $K_t\&Element;R^{n_t\&times;n}$ Be the nuclear matrix that is used to test, K _Ij=k (x _i, x _j) be its formation element, wherein k (x, y)=＜Φ (x), Φ (y) 〉, and before using modified KPLS method, earlier carry out average centralization, wherein x at higher dimensional space _i, x _jThe sampled value of representing the i time and the j time.

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