Adaptive-filter technology for detecting steel-strip surface roughness

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1)Cold Rolling Mill,Baoshan Iron & Steel Co.,Ltd.,Shanghai 201900,China;2)Research Institute,Baoshan Iron & Steel Co.,Ltd.,Shanghai 201999,China

Abstract: To address the shortcomings of traditional filtering methods that utilize the scattering method for the online detection of strip surface roughness and to improve the accuracy of the identification of strip surface roughness,in this paper,a regression-smoothing adaptive-filtering method was investigated for use in the online detection of surface roughness in the cold-rolled strip.The results show that by the use of robust locally weighted regression to perform noise-reduction preprocessing of the initial parameters in the online detection of surface roughness,followed by the establishment of a kernel function,the regression-smoothing adaptive-filtering method can update the weight based on the relative positions of historical and current data.When the changes in neighboring data exceed the established threshold value of 0.75 μm,the width of the smoothing window is automatically reduced,thereby realizing adaptive variable-step regression-smoothing filtering of online roughness detection data.By the use of this regression-smoothing adaptive-filtering method,the accuracy of detecting the surface roughness of a cold-rolled strip can be improved and the requirements of downstream users better satisfied.

Key words: surface roughness; online inspection; adaptive-filtering method

1 Introduction

The exterior panels of high-end automobiles must have high degrees of freshness,glossiness,and image definition after painting.In addition to the painting process itself,the material surface morphology is an important factor influencing the painting quality of the exterior panels of automobiles[1].As such,surface morphology is an important surface-quality index of the cold-rolled strip.In general,important indexes for assessing surface profiles include the shape error,waviness,and surface roughness,which characterize the macro,intermediate,and micro geometric errors,respectively[2-3].Of these three indexes,surface roughness,which can directly affect the stamping and steel flow characteristics of the steel sheet,is a critical index of the quality of the cold-rolled product[4-5].Therefore,it is necessary to monitor the surface roughness of the cold-rolled strip during the production process.

The detection method used currently in the produc-tion of cold-rolled strips involves the inspection of sample strips at the exit of the cold-rolled post-processing unit (such as the continuous hot-dip galvanizing unit or the flattening unit),then offline testing of the sample in the laboratory to obtain the surface-roughness parameter values,and then comparing these obtained values with the technical requirements of the downstream users.If the surface roughness of the strip does not meet the require-ments of the downstream users,the production-process parameters of similar strips must be adjusted in the subsequent production plan.The sample inspection,offline analysis test,and online-process parameter adjustment are implemented successively until the strip surface roughness values meet the requirements of downstream users in every respect.This method is characterized by hysteresis and discontinuity,and its results do not represent the roughness characteristics of the entire strip because the sampling locations are generally at the head and tail ends of the strip.

With the continuous advances in technology,surface detection technology has developed rapidly and can be mainly categorized as either contact-detection technology,which is represented by the pin contact method,or non-contact-detection technology[6-8].Non-contact-detection technology can be further divided into optical and atomic-force methods[9-10].Optical methods include the inter-ference method,scattering method,speckle method,stylus method,diffraction method,and fiber-sensing method[11].The results obtained by contact-detection methods are reliable,but the test sample surface is easily damaged and the probe is liable to wear[12],which limits the application of contact-detection instruments in surface inspection.Although its accuracy is high,the atomic-force method is not suitable for detecting the surface roughness of the cold-rolled strip due to the small distance between the probe and the measured surface.In contrast,the light-scattering method is characterized by a fast detection speed,wide detection range,good anti-interference,small size,and easy integration,and has attracted a great deal of attention and wide practical application in theoretical research and engineering applications in the online measurement of surface roughness.The SORM 3plus system,developed by EMG Auto-mation GmbH of Germany,uses the light-scattering method to measure the surface roughness of cold-rolled strips in motion without making contact with the strip.More than 50 units of the SORM 3plus system have been installed in China and around the world,thereby partially replacing the use of offline sampling detection[13].

One of the key technological aspects of the non-destructive online detection of strip surface roughness by the scattering method is the filtering algorithm.Fig.1 shows the original surface-contour signal detected by the sensor,in which the original signal can be seen to include the shape error,waviness,and surface-roughness information,along with noise and many other interfering signals[14].Therefore,the original signal is filtered to quickly and accurately identify the parameter values of the strip surface roughness from the initial detection signal obtained by the measurement.Existing filtering algorithms mainly use high-pass filters[15-16].Although these are fast,the accuracy and precision of their parameter detection are difficult to improve due to the limitation of the single-filtering condition of the high-pass filter.As such,the filtering algorithm has become a bottleneck in the effort to expand the application of the light-scattering method for the online detection of strip surface roughness.As a result,high-precision adaptive-filtering technology has attracted increasing attention[17-18].

To solve the shortcomings of traditional filtering methods by the online detection of strip surface rough-ness via the light-scattering method,this paper examines the performance of a regression-smoothing adaptive-filtering method suitable for the online detection of cold-rolled-strip surface roughness to improve the accuracy of the identification of the strip-surface-roughness parameter values.

2 Principle and composition of the detec-tion system

2.1 Detection principle

The high-precision filtering method uses a filter designed according to a certain structure and an accompanying algorithm.

As technology has continued to develop,filters are now divided into two categories:classic and modern.The classic filter contains the preformed frequency band information of different signals,and then effectively removes unnecessary information,which means it is impossible to remove noise signals that overlap with the spectrum of a useful signal.Modern filters contain no preformed infor-mation,so all original information is regarded as random signals,the statistical characteristics of which are used to derive the best estimation algorithm for useful signals,which are implemented using either hardware or software[19].

In this study,a modern filter was used and the matching adaptive-filtering method was investi-gated.The filtering frequency of this filtering method changes automatically to adapt to the input signal,that is,the strip-surface parameter information obtained in the previous moment is used to automatically adjust the current filtering parameters to obtain the statistical characteristics of the random changes in useful signals and noise,thereby achieving optimal filtering.This adaptive-filtering method is more suitable for the real-time online measurement of the surface roughness of the cold-rolled strip.

When the strip surface roughness is detected online,the statistical characteristics of original detected signal are unknown.The adaptive-filtering method can automatically adjust its parameters to meet optimal criteria requirements.According to different criteria,different adaptive algorithms are generated.Two basic algorithms are the least mean squares error algorithm and the recursive least squares algorithm[20].

The recursive least squares algorithm was used in this study.The basic principle of adaptive-filtering is as follows:the input signalx(n) passes through a digital filter with adjustable parameters to generate an output signaly(n).The output signaly(n) is compared with the standard signald(n) to obtain the error signale(n).Via an adaptive algorithm,e(n) andx(n) are used to adjust the parameters of the filter,which are iteratively calculated until the error signale(n) is minimized.

2.2 Testing process and equipment

Fig.2 shows the design of the surface-roughness online-detection regression-smoothing adaptive-filtering method.A light beam travels to the modulator through the optical fiber,then part of the parallel beam is projected onto the rough strip surface to be tested and is scattered using a certain angular setting.The light entering the modulator interacts with the scattered light collected from the strip surface,thereby changing the optical properties of the light,including its intensity,phase,wave-length,frequency,and polarization states.This transforms the light into a modulated signal light,which is then sent to a photosensitive element through the optical fiber.There,it is demodulated by the demodulator to obtain the initial parameters of the surface roughness of the strip.The filtered output parameters of the strip surface roughness are thus obtained after filtering.

The equipment used for the online detection of cold-rolled-strip surface roughness is installed at the exit section of the flattening unit.The surface-roughness parameters of the strip after flattening,including the surface profile arithmetic mean deviationRa,the micro-roughness ten-point heightRz,and the peak densityPc,are detected in real time.As the strip moves continuously forward at a certain speed,the surface-roughness parameters and their variations along the length of the strip are detected in real time.

2.3 Design of regression-smoothing adaptive-filtering algorithm

2.3.1 Preprocessing of locally weighted regression noise reduction

The initial strip-surface-roughness output values from the demodulator are defined as (xi,yi),i=1,2,…,n,where:xiis the number of sampling points andyirepresents the initial parameters of the strip surface roughness (such asRa,Rz,andPc).For a randomkgroup of initial strip-surface-roughness values(xk,yk),k=1,2,…,n,a weighted least squares method is used to fit the followingd-order polynomial:

(1)

where,βjis the estimated coefficient,j=0,1,…,d.

To obtain the polynomial with the best fit,the estimated coefficients of the polynomial are optimized,and the error betweenngroups of initial strip-surface-roughness values and the polynomial calculation results is weighted,summed,and minimized as shown in the following equation:

(2)

where,Qis the weighted residual square sum;wk(xi) is linear weight function,the expression for which is as follows:

(3)

where,hiis the width of the smoothing window;andW(x) is linear weight function coefficient.

2.3.2 Secondary smoothing

(4)

where,sis the median absolute value of the residuals;andB(x) is quadratic weight function coefficient.

The weighted error obtained in the noise-reduction process can be rewritten as follows:

(5)

2.3.3 Iterative optimization

In addition,during noise-reduction preprocessing,when the changes (yk+1-yk) in the initial strip-surface-roughness values (xk,yk) and the neigh-boring data (xk+1,yk+1) considerably exceed the preset adjustable thresholdε,the width of the smoothing window of the filtering algorithmhiis reduced.If the changes (yk+1-yk) in the initial strip-surface-roughness values (xk,yk) and the neighboring data (xk+1,yk+1) do not exceedε,hiremains unchanged,the principle for which is as follows:

(6)

3 Experimental results and analysis

The regression-smoothing adaptive-filtering method was used to filter the initial strip-surface-roughness values,an operational flow chart of which is shown in Fig.3.First,noise-reduction preprocessing was performed on the initial strip-surface-roughness values obtained from the demodulator,which were then output.The primary weight was defined as a functionwof the width of the smoothing window,and the weighted least squares method was used to fit thed-order polynomial.Next,the coefficientβjwas estimated,the weighted residual square sumQwas minimized,and the noise was reduced to obtain the initial smoothed values.Then,based on the residualeof the smoothed and actual values,a quadratic weight functionδwas established.A weighting error was added to the function and the weighting function was updated toδw.Lastly,the weighted least squares method was used to perform multiple iterations of the secondary smoothing process.

During this process,if the difference between adjacent data points of the initial roughness values exceeded the threshold,the width of the smoothing window was reduced.After repeating the noise-reduction preprocess,it was finally determined that whenε=0.75 μm,a satisfactory smooth waveform could be obtained.

Fig.4 shows the waveform diagram of the arithmetic mean deviations from the initial parameters in the cold-rolled-strip-surface profile obtained by the demodulator.Figs.5 and 6 show the waveform diag-rams of the surface mean arithmetic deviations of the cold-rolled strip obtained by applying the regression-smoothing adaptive-filtering and high-pass filtering methods,respectively.A comparison of these figures clearly indicates that low-frequency components are present in the waveform diagram of the initial para-meters without filtering,and these low-frequency components have been eliminated in the waveform diagrams processed by the regression-smoothing adaptive-filtering and high-pass filtering methods.

Fig.4Thewaveformdiagramofthearithmeticmeandeviationsfromtheprofileobtainedusingtheinitialparametersofthecold-rolled-stripsurface

Fig.5Thewaveformdiagramofthesurfacemeanarithmeticdeviationsobtainedbyapplyingtheregression-smoothingadaptive-filteringmethod

Fig.6Thewaveformdiagramofthesurfacemeanarithmeticdeviationsobtainedbyapplyingthehigh-passfilteringmethod

A comparison of the results obtained by applying the regression-smoothing adaptive-filtering method with those obtained by the standard method reveals that the deviation between the two was 1.86%.A comparison of the results obtained by applying high-pass filtering method with those obtained by the standard method reveals that the deviation between the two was 5.89%.Therefore,it can be inferred that the accuracy of the regression-smoothing adaptive-filtering method in extracting the surface roughness signal of the cold-rolled strip was higher than that of the high-pass filtering method.

4 Conclusions

In this paper,the performance of the strip-surface-roughness adaptive-filtering detection technology was investigated regarding its ability to improve the accuracy of the online detection of the surface rough-ness of the cold-rolled strip.The main conclusions are as follows:

(1) The adaptive-filtering method automatically adjusts the current filtering parameters based on the strip-surface parameter information obtained in the previous moment to identify the random and changeable statistical characteristics of the useful signals and noise,based on which it achieves optimal filtering.Therefore,it is more suitable for the real-time online measurement of the cold-rolled-strip surface roughness.

(2) The regression-smoothing adaptive-filtering calculation method was applied to perform noise-reduction preprocessing by the use of robust locally weighted regression on the initially online-detected parameters of surface roughness.It then established a kernel function and updated the weight based on the relative positions of historical and current data.When the change in neighboring data exceeded the established threshold ofε=0.75 μm,the width of the smoothing window was automatically reduced to real-ize adaptive variable-step-size regression-smoothing filtering of online-detected surface-roughness data.

(3) A comparison of the results obtained by the application of the regression-smoothing adaptive-filtering method with those obtained by the standard method revealed a deviation between the two of 1.86%.A comparison of the results obtained by the application of the high-pass filtering method with those obtained by the standard method revealed that the deviation between the two was 5.89%.There-fore,it can be inferred that the accuracy of the regression-smoothing adaptive-filtering method in extracting the surface-roughness signal of the cold-rolled strip was higher than that of the high-pass filtering method.