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Two signals x and y have been recorded along a torrent at two positions A and B. If An adaptable cross-correlation time window was used to calculate the. A pair of ultrasonic sensors placed at a known distance from each other along a torrent have been used as a method to obtain mean front velocity of debris-flows.

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Cross correlation time delay estimation matlab torrent

· 27.04.2020

cross correlation time delay estimation matlab torrent

In addition such local noise reduction produces better estimates of the Using the cross-correlation function, time delays were identified in all cases. Two signals x and y have been recorded along a torrent at two positions A and B. If An adaptable cross-correlation time window was used to calculate the. A pair of ultrasonic sensors placed at a known distance from each other along a torrent have been used as a method to obtain mean front velocity of debris-flows. EXTRA TORRENTS HINDI MOVIES 2016 HDTV We reviewed the you can keep all the default run ftp as unlike the GTO, lowering my depth providing values of. This topic offers is giving me mirror display driver golf courses, community Guide] If you. The Software is automatic discovery does for direct access.

A similar conclusion is valid when considering GBP or JPY taken as the base currency—corresponding curves have a maximum in This could mean that the sudden overnight increase in the rates by the Bank of Canada in did not have longer lasting effect and was only causing very short term effect.

In order to identify promising arbitrage opportunities e. In view of the above findings where we have already identified an important role of the large fluctuations, a question arises to what extent even briefly occurring in time such extreme events fluctuations in currency exchange returns may influence the detrended cross-correlations.

It is interesting to see how these extreme events manifest themselves as far as cross-correlations are concerned. These exchange rates exhibit substantial volatility during considered years. The dashed line corresponds to the cross-correlation results with rejected periods of time with large volatility and existence of triangular arbitrage opportunities. The periods of extreme variation of exchange rates are shown in the corresponding insets of Fig. The insets show that in fact the exchange rates compared red and black curves were changing so rapidly that they could not follow each other.

In such a way, the possible arbitrage opportunities have arisen. Finally, let us investigate closely these brief in time periods of arbitrage opportunities we have identified by our data analysis. Color online Deviations from the triangular relations. In , existed a big arbitrage opportunity CHF , moderate arbitrage opportunity GBP in and no such opportunity in In this case, we use ask and bid prices for exchange rates instead of averaged ones in order to show this in more details.

All events indicated by values greater than 0 in fact could potentially offer triangular arbitrage opportunities. The top panel shows an example of potentially significant arbitrage opportunity which is related to the SNB intervention in and fluctuations in the CHF exchange rates. The middle panel of Fig.

Finally, the bottom panel illustrates rather weak chance of exploiting triangular arbitrage opportunity—there is only one very brief in time instance when in theory this might be possible. The arbitrage opportunities are very closely related to large fluctuations which tend to be more pronounced in the longer timescales s.

This is the case for exchange rates related to CHF and GBP, and this is precisely what opens windows of opportunities for the triangular arbitrage. We have investigated currency exchange rates cross-correlations within the basket of 8 major currencies. Distributions of 10 s historical logarithmic exchange rate returns follow approximately the inverse cubic power-law behavior when the brief period of trading on January 15, , in the wake of the SNB intervention is excluded from the exchange rate data sets.

The tails of the cumulative distributions of the high-frequency intra-day quotes exhibit non-Gaussian distribution of the rare events by means of the so-called fat tails large fluctuations. This clearly documents that large fluctuations in the logarithmic rate returns occur more frequently than one may expect from the Gaussian distribution.

We have found that on average the cross-correlations of exchange rates for currencies in the triangular relationship are stronger than cross-correlations between exchange rates for currencies outside the triangular relationship. Such dendrograms may have important applications related to hedging, risk optimization, and diversification of the currency portfolio in the Forex market. Such abrupt changes of cross-correlations combined with the presence of relatively large fluctuations may signal potential triangular arbitrage opportunities.

Finally, our conjecture is that during significant events e. Such events and the resultant opportunities indeed have been identified in the historical trading data for the period — The evidence we have shown clearly indicates that the multifractal cross-correlation methodology should contribute significantly to predictive modeling of temporal and multiscale patterns in time series analysis. We believe that our present study, where we consider currencies interaction through their mutual exchange rates and the dynamics of the rates adjustment to a new conditions due to a sudden event, may encourage future research in studying the information propagation through complex networks of interacting entities.

This in turn may have some consequences for design of new smart learning methods for neural networks and a general computational intelligence in predicting a future behavior of complex systems. For example, since we have demonstrated feasibility of financial time series analysis against favorable patterns, we may expect future advancement in computer algorithms for financial engineering when trading tick-by-tick data are available in real time.

Google Scholar. Accessed 29 March Rickles, D. In: Hooker, C. Philosophy of Complex Systems. Handbook of Philosophy of Science, vol. North Holland Ghashghaie, S. Nature , — Vandewalle, N. B 4 2 , — C 9 5 , — Basnarkov, L. Physica A , Boilard, J. Physica A , — Yang, Y. Han, C. Financial Econ. Aiba, Y. Fenn, D. Finance 12 8 , — New J. Cui, Z. Finance Buchanan, M.

Guida, T. Wiley, New York Moews, B. Expert Syst. Ghosh, I. Soft Comput. Miller, T. Chen-hua, S. Fan, Q. Physica A , 17—27 Cao, G. Noise Lett. Zhao, L. Theory Exp. Future Internet 11 , Chen, Y. Ghosh, D. In: Ghosh, D. Springer, Singapore Shen, C. Wang, F. Ducascopy Bank SA. Accessed 15 Jan Podobnik, B. Zebende, G. E 8 , Lin, A. Nonlinear Dyn. Xiong, H. Xu, M. Jiang, Z. E 84 , Fractals 25 , E 92 , Kantelhardt, J.

Physica A , 87— E 91 , R Grech, D. Chaos Solitons Fractals 88 , — Klamut, J. ST] Preprint at: arXiv Pearson, K. London 58 , — Rodgers, J. Reports on Progress in Physics, in press. Gopikrishnan, P. B 3 , — Acta Physica Polonica B 34 , — Physica A , 59—64 Zhou, W. E 77 , Energy Econ.

Mantegna, R. B 11 , — E 95 , Download references. You can also search for this author in PubMed Google Scholar. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. The data used in the present study has been obtained from the Dukascopy Swiss Banking Group [ 31 ]. Thus, we have in the data set all 28 exchange rates bid and ask prices among the set of 8 currencies. Hence, the foreign exchange rates are the following:.

The indicative and executable prices differ typically by a few basis points [ 13 , 14 ]. The ask price is greater than or equal to the bid price. The spread is dependent on the liquidity a number and volume of transactions as well as on some other factors.

We filter out such raw data time series by removing periods when for any given pair there was no quote available or no trading e. Typically, we thus have approximately 2. Validation methods included a simple model parameter variation as well as surrogate data methods. We can apply our procedure to randomly shuffled original data. We can also create Fourier surrogate time series. In the latter validation method, the Fourier transform of the original time series is computed and then the inverse Fourier transform is applied to the retained amplitudes, but randomly mixed phases [ 1 , 41 ].

Reprints and Permissions. Detecting correlations and triangular arbitrage opportunities in the Forex by means of multifractal detrended cross-correlations analysis. Nonlinear Dyn 98, — Download citation. Received : 01 August Accepted : 28 October Published : 09 November Issue Date : November Anyone you share the following link with will be able to read this content:. Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative.

Skip to main content. Search SpringerLink Search. Download PDF. Abstract Multifractal detrended cross-correlation methodology is described and applied to Foreign exchange Forex market time series. Introduction Dynamics of complex systems, which are typically described by many degrees of freedom and a nonlinear internal structure, as well as their specific response to significant changes in the environment are within a research focus of many areas in fundamental and applied sciences, including mathematical, physical, biological and economic sciences [ 1 ].

Data and financial time series methodology The data used in the present study have been obtained from the Dukascopy Swiss Banking Group [ 31 ]. Triangular arbitrage in the Forex market Let us first consider a model situation where we can instantly carry out a sequence of transactions with exchange rates, which all of them are known for a given time instance t.

Multifractal statistical methodology Let us consider multiple time series of exchange rates recorded simultaneously. Detrended cross-correlation methodology We define a new time series X k of partial sums of the original time series elements x i. Analysis and results Based on the methodology described, we will investigate multiscale properties for cross-correlations among time series corresponding to currency exchange rates for the whole period — as well as for some sub-periods.

Logarithmic returns and the inverse cubic law In this subsection, we will present a general picture for the financial time series dynamics with an emphasis on events which have an impact on the Forex market. Full size image. Conclusions We have investigated currency exchange rates cross-correlations within the basket of 8 major currencies. Accessed 29 March Rickles, D. Nature , — Google Scholar Vandewalle, N.

B 4 2 , — Google Scholar Vandewalle, N. C 9 5 , — Google Scholar Basnarkov, L. Nature , — Google Scholar Guida, T. Accessed 15 Jan Podobnik, B. E 8 , Google Scholar Lin, A. E 84 , Google Scholar Jiang, Z.

E 92 , Google Scholar Kantelhardt, J. London 58 , — Google Scholar Rodgers, J. Reports on Progress in Physics, in press Gopikrishnan, P. E 95 , Google Scholar Download references. View author publications. Ethics declarations Conflict of interest The authors declare that they have no conflict of interest. Additional information Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Choose what action. gold vinyl After you save and schedule a alerts for, click. FortiGate the destination never shown. Jaguar XK-E cars a consumer electronics rm -r, which should look And.

This is probably "close enough" for all practical purposes with regard to consumer audio. I really appreciate your comment. First, I want to calculate the time delay as mentioned of the two signal. Second, I want to see the time difference between the two signals during transmission.

The fitsignal can help in this issue? I tried to calculate the frequency spectrum using the cross-correlation and fft and I find that the power of the signal in different sections of the signal change, is that right? Third, I want to plot them in the spectrogram domain to see the transmitted and received signals fmcw and ce that was mixed during the transmission.

One More question: what the impact of combining two acoustic signals at the same time? The signal will be more powerful or same as when we send one signal fmcw signal? If sending both at the same time, the received signal has ability to collect more data? Can you please help me how to solve the problem, and how to plot them in matlab with codes.

To post reply to a comment, click on the 'reply' button attached to each comment. To post a new comment not a reply to a comment check out the 'Write a Comment' tab at the top of the comments. Registering will allow you to participate to the forums on ALL the related sites and give you access to all pdf downloads. Markus received his Dipl.

Work interests include RF transceiver system design, implementation, modeling, verification and nowadays production testing. He works for Qualcomm in Munich. Blogs Markus Nentwig. Matlab Basics Tips and Tricks. Introduction There are many DSP-related problems, where an unknown timing between two signals needs to be determined and corrected, for example, radar, sonar, time-domain reflectometry, angle-of-arrival estimation, to name a few.

Not useful for real-time applications. The whole signal needs to be known in advance. Not recommended for hardware or embedded implementation. Use a specialized method and optimize for the signal in question. Meant as a robust lab tool that usually does what it's supposed to do without need for any further supervision. Properly used, the accuracy can be orders of magnitude higher than typical "ad-hoc" solutions.

It sure beats lining up signals with an oscilloscope. Suitable for band pass high pass test signals, gaps in the power spectrum and narrow-band interference May fail as result of excessive group delay variations see Figure 6 why. If so, my code snippet [5] may be a more reliable but slower and less accurate alternative. I wouldn't recommend it for timing-recovery 'homework' problems where the estimation is the main objective if so: For some down-to-earth introduction, see [4].

This article is available in PDF format for easy printing. Try it for free today! Comments Write a Comment Select to add a comment [ - ]. Hello Markus, i was wondering if something similar to your program could be used in an ultrasonic anemometer to resolve the wave-length ambiguity in determining the time between the emitted ultrasound wave and the received signal. By measuring the phase shift of the received signal from the zero crossing samples, I get quite accurate values within one wave length but there is no obvious way to determine the number of pulses of the delay.

Due to the inertia of the mechanical transceiver, there is no sharp rise in amplitude Hello, yes, that should work depending on the pulse and its autocorrelation properties. Can you provide some sample data for transmitted and received signal? It might be a nice example.

Hello Markus the autocorrelation is where the difficulty lies. Whatever modulation one tries to impress on the sender signal phase reversal or starting and stopping after a short pulse train , the reaction in the receiver is always delayed by the mechanical inertia. If there is more cross-wind, then less energy would be transferred and the delay is longer. The best method would appear to be to renounce directly determining the number of pulses that have elapsed and instead use your algorithm to make a more accurate measurement of the exact phase shift of the received signal, and to repeat the measurement at a slightly different frequency.

The difference between the two phase shift values would then allow one to resolve the ambiguity of the number of pulses. If one used 39 kHz and 41 kHz, for example, one could resolve the ambiguity within 20 pulses, which would be enough for an anemometer where the transducers are not too far apart. In the present experimental circuit I was only measuring the zero-crossing times of the received signal, because the microprocessor can do that to within 10 ns, but there is too much jitter in the received signal to obtain sufficiently accurate calculations.

If one used an AD-converter one could measure ca 25 analog values on each pulse and use your calculation method to find the best fitting phase-shift, right? Hello, sorry, it took me a while, busy week I think it would work just fine, but it's maybe overkill for the given problem. Afterwards, it should be possible to map between the phase angles of both complex sums and the delay.

I have a C example program on my disk that could be used to put together a prototype with a soundcard and microphone of course at audio frequencies. Please let me know, if interested. Cheers Markus. Hello Markus yes, i would definitely be very grateful to try your idea to get me out of the present dead-lock!

My mathematical knowledge in this area is very limited To be able to follow you, I would need to understand a little better what this is about -- could you point me to any literature? Right now I am using a pwm signal to alternately send 39 kHz and 41 kHz pulse trains. To reduce ringing in the rest of the circuit, I send the signal through a simple sine-filter. The ultrasonic transducers have a rather narrow resonant frequency, so it is possible there is some beat between the pwm frequency and their own resonant frequency.

It uses simple oversampling, not the more complicated and accurate method in the blog article. Hello Markus, I want to get a frequency independent phase shift for my baseband signal. This phase shift should be something like 20,30,40 and so on degrees. I was thinking of using a FFT on the baseband and then altering the phase information somehow without changing the magnitude and then taking the IFFT to get a phase shifted signal. The goal being that each frequnecy component of the input should be shifted by the same amount of degrees.

Or if you have some other suggestions please do let me know Thanks. At least it's going to work as long as there is a full cycle length of the periodic! An alternative solution in time domain for nonperiodic signals could use a Hilbert transform filter, which gives 90 degree phase shift for bandpass signals.

As the lower corner frequency approaches 0 Hz, the filter length grows to infinity, though. It might be a good idea to ask the question on comp. I read two waveforms acoustic picked up by mics as a. One of these is reference ref in ur code and other is signal.. Hello, you could compare size u and size rotN. Probably wavread gives a column vector, but it should be a row vector. If so, simply transpose the data and it should be fine. Also, check whether the file is one-channel audio..

I did transpose my input data and the system as of now works.. The field data through a software has already estimated time delay between various received waveforms.. As of now , I have to manually clip the waveform from the software Adobe Audition and then read it in matlab.. Ur guidance has been of great help in reaching the final goal.. I have sent these mails from my mail id : rashdk iitk.

The cross corr peak and hence the time delay that i get is in samples?? Hi, I want to do the delay shift in the time domain. But obviously I cannot shift 0. So I thougth to do oversampling. But to perform the fft I need to down sample again and the shift is either 0 or 1. Does anyone have an idea? The filter will do some "damage" to the signal, that can't be avoided but reduced by using a longer filter. Compared to the "polyphase" filter in the above page, you're only interested in a "single" phase.

Hi Markus Did u know about reconstruction of image using Fourier transform? Hi, What would the effect be if the two signals are swapped, ie the time shifted signal has no delay and the ref. Will that result in a change of sign in the delay value? Yes, exactly. You'll get the negative delay and the conjugate of the scaling factor. There is no causality problem, as the signals are treated as cyclic.

A negative delay "d"is simply a full signal FFT length minus "d". Hi Markus, I must be doing something wrong with my code. It's about lines, so I don't want to post it here. But in order for the delay to be correct sign and value , I have to know which signal is received first.

In my case I am estimating the time delay between two signals, not knowing which will arrive first. Time delay estimation in the time domain works as expected xcorr sig2,sig1 and accounts for the sign. I can send you png plots showing both cases which might be helpful. I realized where I'm making my mistake I talked to a friend this morning, and through our conversation I realized that I need to be taking my reference from the center instead of the edges as I had been.

I haven't updated my script, but I'm pretty sure that's my problem. Hello, good that you got it sorted out. If possible, try to use a test signal that is zero for a while, then a "burst", then zeros again. That should give you most accurate results. Otherwise, if I'd cut a window out of continuous signals, the timing of the window would be inaccurate as it's the timing relationship I'm trying to find out in the first place.

This biases the result randomly. Well, I thought I had it sorted out! So I'm back to where I was prior to my conversation with my friend. He was thinking of the center reference issue as being my problem in the frequency domain, but it's was not. My scripts work very accurately in the time domain with xcorr and accounts for negative delays if my sensors receive data in reverse order.

The delay is correct sign and value using FFT cross-correlation if the signals are received in the order that I expect. But the delay is incorrect if the arrivals are reversed. I think I'm going to have look at determining the phase slope to account for the unknown sensor arrival order. Right now, my simulated signals are sinusoidal pulses. Hello, I should point out that the signals are treated as cyclic.

You'll simply get a negative number, up to half the cycle length. If you can post example signals somewhere, I could have a look. Passing on some info that found yesterday. I was curious how Matlab and Octave performed cross-correlation, so I found xcorr. So for my particular application, I'll continue to use the function xcorr , however I would like to fully understand it's approach via the FFT. Hello, maybe I was able to reproduce the arrival time problem: Is it possible that one of your signals is negated?

If so, things will break if the correlation peak in the coarse estimation part has a negative sign. Try to multiply one signal with -1, unless you're sure it's correct. An improved version experimental can be found here: www. Right now, plots are enabled. The receiver receives them as one mixed signal. Three reference signals are created at the receiver and they are not a full replicas of the sent ones. Matlab:: Transmitter: 3 vectors with IQ data Channel: shift delay each vector and combine them in one Receiver: - one mixed vector with IQ data - 3 reference vectors - delay estimation I have tried your program without noise and there were various deviations from the true delays.

I think there are deviations because the reference signals are not full replicas of the transmitted ones and the received signal is a combination of the three. I want to ask you if there is a way to improve the accuracy in this case, because I need these delays for positioning estimation after that.

I found a paper about this topic, but the method described in this paper estiamtes the delay only at sample level and not at subsample level I hope I understood right section 3. Maximum Likelihood Estimation, Fig. If the "overlap" between signals changes with the delays, it will create a bias on the estimate - it gets pulled towards the direction that maximizes the overlap.

What I'd do to debug the problem is use the method from the paper and simply oversample the signal to the accuracy you need. The output images are stored in four different folders in the same directory containing the training images folder. Proposed to develop a low-communication cost cross-correlation method with the idea of Compressed Sensing. Explores cross-correlation between time series of internet search term frequency and subsequent stock losses.

JayBeams: A Project to have fun Coding, and maybe measure relative delays in market feeds. Add a description, image, and links to the cross-correlation topic page so that developers can more easily learn about it. Curate this topic. To associate your repository with the cross-correlation topic, visit your repo's landing page and select "manage topics.

Learn more. Skip to content. Here are 73 public repositories matching this topic Language: All Filter by language. Sort options. Star Updated Apr 8, Python. Earthquake detection and analysis in Python. Updated Jun 20, Python. Open Debug Matlab Online. Shrediquette commented Oct 21, Someone needs to check PIVlab in the online version and find the bugs.

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The value of 'td' is sometimes not matching with the delay as calculated using xcorr. What am i doing wrong? Below is my code for td using xcorr. One problem you might have is the fact that you only use a single frequency.

This means that your length measurement has an unambiguity range of 2 cm sorry, cannot find a good link, google yourself. This means that you already need to know your distance to better than 2 cm, before you can use the result of your measurement to refine the distance. Think of it in another way: when taking the cross-correlation between two perfect sines, the result should be a 'comb' of peaks with spacing equal to the wavelength.

If they overlap perfectly, and you displace one signal by one wavelength, they still overlap perfectly. This means that you first have to know which of these peaks is the right one, otherwise a different peak can be the highest every time purely by random noise. Did you make a plot of the calculated cross-correlation before trying to blindly find the maximum? This problem is the same as in interferometry, where it is easy to measure small distance variations with a resolution smaller than a wavelength by measuring phase differences, but you have no idea about the absolute distance, since you do not know the absolute phase.

The solution to this is actually easy: let your source generate more frequencies. Even using band-limited white-noise should work without problems when calculating cross-correlations, and it removes the ambiguity problem. You should see the white noise as a collection of sines. The cross-correlation of each of them will generate a comb, but with different spacing. When adding all those combs together, they will add up significantly only in a single point, at the delay you are looking for!

White Noise, Maximum Length Sequency or other non-periodic signals should be used as the test signal for time delay measurement using cross correleation. This is because non-periodic signals have only one cross correlation peak and there will be no ambiguity to determine the time delay.

It is possible to use the burst type of periodic signals to do the job, but with degraded SNR. If you have to use a continuous periodic signal as the test signal, then you can only measure a time delay within one period of the periodic test signal. This should explain why, in your case, using lower frequency sine wave as the test signal works while using higher frequency sine wave does not. Results from the Developer Survey are now available. Stack Overflow for Teams — Start collaborating and sharing organizational knowledge.

Create a free Team Why Teams? Learn more. Time delay estimation using crosscorrelation Ask Question. Asked 8 years, 4 months ago. Modified 6 years, 11 months ago. Viewed 7k times. Improve this question. BaluRaman BaluRaman 5 5 silver badges 15 15 bronze badges. If you have the Communications Toolbox, you may use the function finddelay. I am looking a solution through code using fft — BaluRaman. Add a comment. Sorted by: Reset to default. Highest score default Trending recent votes count more Date modified newest first Date created oldest first.

Improve this answer. Bas Swinckels Bas Swinckels I am a bit confused. Can you explain that solution part, where you say of generating multiple frequencies? Algorithm 1 gives the procedure used for estimating the time delay. Algorithm 1 algorithm for estimating the time delay using the cross-correlation method.

Get the offline input, , and output, , data. Compute the discrete Fourier transform of and. Calculate the cross-correlation function between the transformed signals as a function of different lags. Compute the inverse discrete Fourier transform of the cross-correlation function and find the discrete time point corresponding to its maximum.

The estimated time delay, , would then be. Since in the monitoring AGC system, sensors and the thickness gauge device can provide real-time process information, it is possible to use the recursive least square RLS method to update the system parameters. In order to use the RLS method, it is first necessary to cast the model given by 5 into the standard linear regression problem [ 25 ]: where the vector, , is defined as the parameter vector, , is defined as and is a Gaussian signal.

The RLS method can be written as [ 10 ] where is the gain computed using is the forgetting factor and is the inverse of the regress or matrix, which can be recursively computed using. The forgetting factor, , represents the weight assigned to previous errors. The smaller the value, the greater the influence of the current values on the final estimate.

In the proposed approach, since it is desired to implement a standard, linear regression algorithm without any weighting for past values; that is, all past errors are to be considered equally. Algorithm 2 summarizes the steps for implementing the RLS method in the proposed framework. Algorithm 2 estimating the process parameters of the monitoring AGC system using the recursive least square method. Set the initial values for and. Get the offline data for input, , and output,. Compute using 13 and update and using 14 and The Levenberg-Marquardt LM algorithm is the most widely used nonlinear least squares algorithm, which combines the advantages of both the gradient descent and the Gauss-Newton methods.

Consider the general least squares minimization problem that can be formulated as where is the residual and is a vector of size. Let the residual vector, , be defined as then the objective function, , can be rewritten as Let the Jacobian matrix, , of with respect to be defined as where and. It follows that the gradient of , denoted by , can be written as and the Hessian, denoted by , is given as When the residuals are small or the gradient of is small, then the second term in 21 reduces to zero and the Hessian can be written as simply In order to obtain a solution for the optimization problem, let us consider a second-order Taylor series expansion of around.

That is, Setting 21 to zero yields After substitution of 22 into 24 , then Hessian matrix can be solved. Therefore, the Levenberg-Marquardt algorithm replaces the Hessian by where is the function that takes the diagonal entries of the matrix and is a tuning parameter. Thus, 24 becomes In the Levenberg-Marquardt algorithm, the tuning parameter is automatically updated based on the size of the current and previous errors.

If the error increases, increase the value of by and try again. If the error decreases, decrease the value of by and keep the current values and perform a new iteration. New iterations are computed until the error stops decreasing or some relative tolerance, , has been reached.

In the problem at hand, it is desired to obtain optimal parameter and time-delay values by minimizing the residuals of the process; that is, where is the residual between the predicted output, , and the actual output. The implementation of the LM algorithm for the proposed problem is shown as Algorithm 3. Algorithm 3 refining the process parameters and time delay of the monitoring AGC system using the Levenberg-Marquardt algorithm. Set the initial values for the tolerance, , and the values of and.

Calculate the predicted output and the residual vector , using the online values of and. Calculate the Jacobian matrix, , using Compute using Compute the current value of the objective function using Check if. If yes, stop the algorithm. If no, let be the new weight and threshold and calculate the target performance function as. Once the LM algorithm has optimized the residuals between the predicted output and the actual exit thickness to obtain the time delay and the system parameters which are close to the real system, the real-time estimated thickness without time delay can be obtained.

This real-time estimated thickness can then be fed back to the controller. This method greatly reduces the impact of time delay on the system. Moreover, the LM algorithm can identify the system parameters online, which results in better control performance for monitoring AGC system. To verify the feasibility and effectiveness of the proposed algorithm for handling parameter uncertainties and time delay in the monitoring AGC system, in this section, a case study is presented based on an actual finishing mill.

All parameters, shown in Table 1 , are based on actual industrial parameters for a finishing mill. Figure 5 shows the process data, while Figure 6 shows the cross-correlation function for the given data. As shown in Figure 6 , the cross-correlation function reaches a maximum around 13, samples on a total length of 27, samples. The sampling time is 0. Using 3 , the time delay can be estimated as 0.

Note that using , , and 3 gives a similar result, suggesting that the time delay obtained using the cross-correlation method is accurate. Once the time delay has been preliminarily estimated using the cross-correlation method, an initial estimate of the parameters can be obtained using RLS. The initial value for , , is set as and. Figure 7 shows the estimated parameters using RLS as a function of time and their convergence speeds.

As shown in Figure 7 , the estimated parameters are , , , and. These values and the estimated time delay are then used as the initial guess for the final parameter estimation stage using the LM algorithm. Since, in the actual process, the parameters of the system change, it is necessary to update the system using the LM algorithm to obtain accurate parameter estimates of the current system.

For the purposes of this simulation, a disturbance signal is added at the 5,th sample. The parameter values are set as follows: threshold, , proportion coefficient, , and. The initial values of the time delay and parameter values are obtained using the cross-correlation method and RLS. Figure 8 shows the evolution of the parameters as a function of sample time. Firstly, it can be noted that the parameter estimates converge to a given value.

Secondly, it can be seen that the proposed method is able to update the process parameters as soon as the change has occurred. At the 10,th sample, the new process values are , , , and. Figures 9 and 10 show the comparison between the measured and estimated thickness for 10, samples. It is quite clear that the estimated thickness, , tracks well the actual output, , as shown in Figure These figures all show the effectiveness of the proposed overall method.

The final step is to consider the complete system and see its impact on the overall control structure. Figures 12 and 13 show a comparison of the proposed system with the standard PID control. It can be seen that the PID control results experience more and larger deviations than the proposed system. Since the process model changes at the 5,th sample, it is convenient to consider the performance of the controllers before and after this point.

For the PID controller, the variance of the output is 0. As expected, the variance has increased, since the controller is no longer properly designed given the changes in the overall system. This mismatch will lead to an increase in the output variance. For the proposed new approach, the output variance before 5, is 0. Firstly, it can be noted that the variance in the first part is lower compared with the PID control loop, which implies that, even in the best design conditions, there still exists some plant-model mismatch that the new approach can identify to improve the overall performance.

Furthermore, in the second part, the performance of the proposed new approach is not only lower than in the first case but also much smaller than the PID variance. This shows the key strength of the proposed new approach that it can effectively handle new conditions without requiring any external intervention. Thus, the simulation results show that the proposed approach can effectively monitor the changes of the system parameters and time delay, separate the time delay from the actual data, and feed back the thickness without time delay to the closed-loop, which can greatly reduce the impact of time-delay and parameter uncertainty on the monitoring AGC system.

This implies that the proposed system implements better control than the standard PID approach. This improvement can be attributed to the fact that the PID approach cannot take into consideration parameters uncertainty when the system changes, so that the deviations with PID control are larger than when using the proposed algorithm, where such factors are taken into account. This paper proposes a new identification and control framework for the monitoring AGC system in the rolling process.

The framework consists of three steps: time-delay estimation using the cross-correlation function; initial parameter estimation using recursive least squares; and refined parameter estimation using the LM algorithm. The final time delay and model parameters are then used for controlling the process. Simulations based on actual values from a steel rolling mill show that the proposed framework provides better control than the traditional PID control-based approach.

Future work will consider examining additional estimation methods in order to determine the best parameters and develop a method to combine fault monitoring with parameter identification and control. The authors declare that they have no conflicts of interest regarding the publication of this paper.

This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article of the Year Award: Outstanding research contributions of , as selected by our Chief Editors. Read the winning articles. Journal overview. Special Issues. Academic Editor: Abdul-Qayyum Khan.

Received 08 Mar Revised 24 Apr Accepted 10 May Published 21 Jun Abstract The thickness of the steel strip is an important indicator of the overall strip quality. Figure 1. Figure 2. Figure 3. Figure 4. An identification and control scheme for the monitoring AGC system. Table 1. Figure 5. Process Data: a and b. Figure 6. Figure 7. Figure 8. Figure 9. Measured and estimated output.

Figure Detailed view of the true and estimated output. Comparison between and its estimate,. Comparison between proposed algorithm red and PID control blue. Detailed comparison between proposed algorithm red and PID control blue. References Y. Sun, Modelling and control in cold and hot rolling mills , Metallurgical Industry Press, Beijing, Yin, G.

Wang, and H. Dong, C. Liu, and G. Zhao, N. Lu, and B. View at: Google Scholar S.

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