Continuous Monitoring of Industrial Processes through Cross-Correlation Techniques

Proceedings of the 18th World Congress The International Federation of Automatic Control Milano (Italy) August 28 - September 2, 2011

Continuous Monitoring of Industrial Processes through Cross-Correlation Techniques Tomi Roinila ∗ Mikko Huovinen ∗ Matti Vilkko ∗ Tomi Helin ∗ Department of Automation Science and Engineering, Tampere University of Technology, Finland, P.O. Box 692, FIN-33101, e-mail: [email protected]. ∗

Abstract: The systems in process industries are typically very large and complex. There are hundreds or thousands of I/O variables and the subprocesses are typically linked with strong interactions. Therefore, monitoring such processes, and ensuring their desired operation may become difficult and challenging. Even more challenging is continuous monitoring where a system is kept normally operating while measuring and evaluating its dynamics. This paper proposes techniques for continuous monitoring of industrial processes using non parametric identification methods. Maximum-length-based binary sequences are applied as excitation signals, and the system-characterizing models are estimated through cross-correlation technique. The proposed methods are verified by experimental data from a physical process emulating the traditional headbox of a paper machine. Keywords: Industry automation, Industrial control, Frequency-response characteristics, Frequency-response methods, System identification, Fault detection, Fault identification. 1. INTRODUCTION System-identification experiments in the process industries are often expensive and time-consuming due to slow process dynamics. Furthermore, during typical plant tests, production is disrupted which often causes off-specification production. However identification tests are often needed to evoke the underlying process characteristics. Therefore, developing new identification methods that do not disturb normal operation is of great interest for process industry. An astonishing fact is that most of the developed identification techniques are not used by industrial control engineers, although there is an urgent need for efficient and effective identification methods in process control industry. It has been claimed that one reason for this failure of technology transfer is that too many people concentrate on parameter estimation and convergence analysis, while too few people study test design and model validation, the part that is close to model applications (Zhu, 1998). The identification practice is still very much based on single-variable type of thinking although industrial processes are typically very complex and highly disturbed. The basic identification experiments are called step tests, in which each manipulating variable (MV) is stepped separately and some clear step responses are expected for modelling each transfer function. In many cases, this approach may provide sufficient information on the dynamics of a system but not necessarily. Very often, the external noise masks the step response data. In order to avoid this problem, the size of the step may have to be increased to an unacceptably large level, thus evoking nonlinear process characteristics. In addition, such tests produce information 978-3-902661-93-7/11/$20.00 © 2011 IFAC

only on limited frequency bandwidth. Thus, in the end the models derived from this approach may not be accurate for complex and highly disturbed processes (Liu et al., 2006). An alternative to the above-described time-domain analysis is to analyze the processes in the frequency domain. In practical measurements, the system-characterizing models can be found either by parametric or non parametric system identification methods (Pintelon and Schoukens, 2001). Parametric methods require a selection of an input stimulus (Godfrey et al., 2005), a priori selection of a parameterized model structure including system order and number of zeros, construction of a suitable prediction error equation and loss function, and methods to minimize the loss function. These methods return the parameters of the system model such as the coefficients of the system difference or differential equations, transfer function, or state-space model and are useful e.g. for complex controller design. Non parametric methods do not assume a system model and require only a selection of a stimulus. Non parametric methods return frequency-response-function (FRF) data directly and are useful e.g. for quality assessment procedures. Cross-correlation techniques (Ljung, 1999) with carefully selected excitation sequences provide efficient means to measure the system-characterizing frequency responses. Very often, an excitation signal with a broadband spectrum is applied. The excitation signal with a broadband spectrum has energy at several frequencies thus allowing to measure a frequency response at those frequencies simultaneously. The signals having a broadband spectrum are generally divided into binary, near-binary, and non binary sequences,

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18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011

each having many attractive properties. For continuous monitoring of the industrial processes it is important that the system is not disturbed too much in order to guarantee the normal operation. Thus, the excitation has to be selected such that its amplitude in the time domain is kept small but the energy, i.e. the amplitude in the frequency domain, is maximized. One method to analyze this quality of an excitation is to measure the signal peak factor, also known as crest factor (Wulich, 2000). The smaller the peak factor is, the greater the energy is in relation to the signal amplitude. It can be shown, that the binary signals have the lowest possible peak factor (Godfrey, 1991b). Thus, the binary sequences can be considered as one of the most well-suited excitations for continuous FRF-measurements of industrial processes. Another advantage of the binary sequences over the near- or non binary signals is that they can be generated with low-cost applications whose outputs can only cope with a small number of signal levels. One of the most popular binary signals used in FRF measurements is the periodic pseudorandom binary sequence (PRBS) (Davies, 1970). One special class of these signals is the maximum-length binary sequence (MLBS) (Godfrey et al., 1999). The sequence is very popular in the applications of system identification due to its straightforward implementation, low peak factor, attractive frequency content, and other useful properties. The MLBSbased measurement techniques have been used as a general method to measure the frequency responses of various linear systems and have been applied e.g. in the fields of acoustics (Vanderkooy, 1994), impedance spectroscopy of single living cells (Hirvonen et al., 2008), sensors for gas and odor or aroma analysis (Amrani et al., 1998), sonar systems for zooplankton survey (Xiang and Chu, 2004), and electrical circuits (Miao et al., 2006; Roinila et al., 2009) . The research question is to find out whether it is possible to extract meaningful information for monitoring purposes of industrial processes using frequency-domain methods and how to design appropriate stimulus signals. This question is approached by providing techniques to measure continuously the appropriate models of a process while allowing its normal operation at the same time. The models are then used for process monitoring purposes in order to obtain a cheap and effective monitoring practice that does not disturb the process too much. The rest of the paper is organized as follows. The characteristics of a typical industrial process are discussed in Section 2. Section 3 reviews the basic theory applied in this paper; cross-correlation technique in system identification, and the MLBS excitation and its design procedure are briefly introduced. Experimental evidence based on a physical process emulating the traditional headbox of a paper machine is presented in Section 4 supporting the theoretical findings. Finally, the conclusions are drawn in Section 5. 2. CHARACTERISTICS OF PROCESS INDUSTRY The processes in process industries are typically very large and complex. There are hundreds or thousands of I/O variables and the subprocesses are typically linked with strong interactions. The dynamics can also be difficult. Very slow

dynamics are typical, non-minimum phase behavior, oscillating behavior and varying time delays are often present. The slow dynamics alone dictates relative long time for identification test. Furthermore, the processes are typically highly nonlinear depending on the operation point and therefore linear approaches are valid only locally. The operating points may vary frequently which is typical for today’s multiproduct processes, i.e. different paper grades are typically produced using the same machinery. The disturbances are typically many in numbers and their influence is strong. They also often have slow and irregular variations. Typical source of such unmeasured disturbances are feed composition variations and weather changes. The disturbances make the identification task more difficult as too large test signal amplitudes are not permitted and thus unknown disturbances can mask the response of interest. Too large test signals may cause offspecification end products and/or may evoke nonlinear process characteristics. Although the processes can be considered continuous (i.e. they are operated continuously for long periods of time) there are events that change the operating point to areas where the process dynamics change. Also the transient phases may take some time where the data does not represent normal operating conditions (e.g. grade change in a paper machine). Furthermore, there are gaps in the production where the whole process or parts of it is not operating at all. Paper machine web breaks are a good example of this. One of the main reasons for process identification needs in the process industries arise from the increased utilization of Model Predictive Control (MPC). Other uses for process models include process monitoring and simulation/training practices. The current MPC practice is to use manual single variable step tests for model identification. The advantage is that control engineer can watch many step responses during the tests and can learn about the process behaviour in an intuitive manner. The biggest problem of single variable step test is its high cost in time and in manpower. Another problem is that the data from such tests may not contain good information about the multivariable characteristics of the process and that step signals may not excite enough dynamic information of the process (Zhu, 1998; Li and Georgakis, 2008; Zhu, 1998). Therefore, it is important to find the most expedient means to reliably identify the process in limited time and resources while minimizing disruption to production. Reidentification might be necessary if the process or operating conditions change significantly (Conner and Seborg, 2004). A problem with separate single variable tests is their high cost in time and manpower. This problem can be solved by using automatic multivariable test approach, but when several input test signals are applied at the same time, there are some cross-effect between the test signals. For the sake of identifying different impacts on the same output from different inputs in such experiment, these inputs need to be uncorrelated with each others. Various methods have been developed in designing uncorrelated test signals for multivariable processes (Liu et al., 2006). However, to gain

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a simple reference case, this paper focuses on the single variable case. 3. CROSS-CORRELATION TECHNIQUE In steady state, for small-signal disturbances, a typical industrial process can be considered as a linear timeinvariant system. The sampled system can be described as y(m) =

m X

k=1

g(k)u(m − k) + v(m)

(1)

where y(m) is the sampled output signal, u(m) the input signal (excitation), g(m) the system impulse response and v(m) represents disturbances, such as measurement and quantization noises. The cross-correlation between the input and output signal can be given by

Ruy (m) = =

M X

k=1 M X

k=1

u(k)y(k + m) h(k)Ruu (m − k) + Ruv (m)

(2)

is that the system is perturbed with a signal resembling white noise. This requirement can be approximately met by applying the pseudo-ramdom binary sequence (PRBS) (Godfrey, 1993). 3.1 Maximum-Length Binary Sequence There exist several classes of PRBS signals but one class, called maximum-length binary sequences (MLBS), is very popular because the signal is easy to generate by using shift register circuitry with feedback (Godfrey, 1991a), shown in Fig.1. The MLBS-based signals exhibit a number of fascinating and useful properties for non parametric system-identification measurements such as low peak factor, periodicity and adequate energy content (Godfrey, 1993). One of the most important properties is that the periodic ACF of the MLBS is approximately a periodic unit impulse sequence (Rife and Vanderkooy, 1989). The shape of the ACF is shown in Fig.2 where a denotes the signal amplitude, N the signal length and ∆t the signal pulse width. Using a sufficiently long signal period, the bias can be considered to be negligible and thus (5) holds. Another important property of the MLBS is its deterministic nature. Therefore, the signal can be repeated precisely and it is possible to increase the signal-to-noise ratio (SNR) by synchronous averaging of the response periods. XOR

x

ci

cm

where M denotes the total length of collected data, Ruu (m) is the auto correlation of the input signal, and Ruv (m) the cross correlation between the input and disturbance signals. In the case of white noise as an input signal the following characteristics hold. 

Ruu (m) = αδ(m) Ruv (m) = 0

(4)

Hence, the cross correlation between the measured input and output signals yields the system impulse response. Using finite-length signals an estimate is obtained for Ruy (m) yielding an estimated impulse response. The response can be converted to the frequency domain and presented as FRF by applying discrete Fourier transform (DFT) (James, 2004) M −1 X ˆ uy (m)e−jkωTs ˆ jωTs ) = 1 R G(e α

(5)

k=0

where M denotes the total length of collected data, ˆ jωTs ) the estimated FRF, Ts sampling interval, and G(e ˆ xy (m) the estimated cross correlation between the meaR sured input and output signals. The requirement in (5)

2

MLBS ...

i

...

n

SHIFT REGISTER

Fig. 1. n-bit shift register with XOR feedback for MLBS generation. fMLBS (t )

(3)

where α denotes the variance of u(m), and δ(m) the Kronecker delta function. Thus, the auto correlation of the input signal is a delta function and the cross-correlation of the input and disturbance signal is zero. Under the assumption of (3), the cross correlation in (2) can be represented as Ruy (m) = αg(m)

1

...

+a2

-a 2 / N

-Dt

Dt

t N Dt

Fig. 2. Shape of auto-correlation function of MLBS. The power spectrum of the MLBS is defined as the Fourier transform of the sequence ACF and describes how the signal energy is divided. The spectrum follows the sinc 2 function and is given by Godfrey (1991a)

ΦMLBS (q) =

a2 (N + 1) sin2 (πq/N ) , q = ±1, ±2, . . . (6) N2 (πq/N )2

where q denotes the sequence number of the spectral line. The power spectrum has an envelope and drops to zero at the sequence generation frequency, as shown in Fig.3. The frequencies where the signal energy lie are known as harmonics. The harmonics occur at frequencies q/Tp where Tp is the time length of one signal period. In the FRF measurements, the excitation signal should usually have approximately equal amount of energy at the frequencies where the system is to be identified. According

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enough to provide approximately uniform power to the whole frequency band.

F MLBS ( f ) F MLBS ( f1 ) / 2

Effective frequency band

1/ Dt

2 / Dt

3 / Dt

The number of MLBS periods R can be decided by evaluating the power of external noise which defines the variance of the FRF. Using √ multiple excitation periods the noise is reduced by 1/ R. f

Fig. 3. Shape of power spectrum of MLBS. to Fig.3 the energy in the MLBS is clearly non uniformly spread over the harmonics. However, the mentioned requirement can be approximately met by generating the sequence with a sufficiently high frequency. Typically, the spectrum is considered √ to be flat until the power has dropped to |ΦMLBS (f1 )|/ 2 (i.e. 3 dB), where |ΦMLBS (f1 )| denotes the power at the first harmonic. This part of the excitation signal is known as an effective frequency band. Thus, the signal generation frequency has to be selected such that the effective frequency band equals with the frequency band where the system is to be identified. 3.2 Excitation Signal Design The design procedure of the MLBS excitation can be formulated by defining first the specification variables as fBW required bandwidth, fres required frequency resolution and fvar maximum allowable variance of the FRF. The excitation signal is then generated using the design variables as P fgn R a

length of one MLBS period, MLBS generation frequency, number of MLBS periods and MLBS amplitude.

The amplitude of the excitation needs to be chosen carefully. It has to be low enough to avoid major disturbances in the output of the process and too great effects of nonlinear dynamical phenomena, but high enough to provide good SNR. The nonlinearities and noise characteristics depend both on the system under test and specified operational conditions. Thus, it is difficult to give specific advice for amplitude selection. Therefore, selection of the amplitude should be based on good understanding of the system and its operational requirements. The amount of nonlinearity and general characteristics of the measurement environment are the key issues. 4. EXPERIMENTAL VERIFICATION The applied part of the research was done in a physical process emulating the traditional headbox of a paper machine, shown in Fig.4. The headbox is a paper machine subprocess designed to ensure an even flow of pulp from the headbox to the wire by dampening disturbances. An essential part in this is ensuring a constant feed pressure by using pressurized and controlled volume of air above the volume of pulp. The pulp escapes the headbox from the bottom through the outflow nozzles called the slice opening, and the constant overall pressure in the headbox provides a constant flow. The second tank in Fig.4 is only needed in the laboratory equipment for recycling the liquid in the process, i.e. it is not present or needed in an actual headbox process.

The selection of MLBS period P has to fulfill two requirements. The authors in Rife and Vanderkooy (1989) showed that the measurement results will be corrupted by timealiasing unless the length of one excitation period is at least as large as the length of the settling time T of system impulse response. Another point of view in selecting P is that it defines the frequency resolution. Hence, P should be selected such that P = 2n − 1 ≥ fgn · T

(7)

The power spectrum Φuu (n) of the MLBS excitation u(n) is defined by the Fourier transform of its autocorrelation function φuu (n). The spectrum follows the envelope of sin2 (f )/f 2 function with a zero power at the MLBS generation frequency and its harmonics. The power has its maximum value at first harmonic and falls 3 dB by the frequency given by sin2 (πk/P )/(πk/P )2 = 0.707

(8)

i.e. approximately k = P/3. Hence, the generation frequency fgn of the MLBS has to be chosen to be high

Fig. 4. The process. The headbox has two main actuators, an air compressor providing air flow and a pump providing pulp flow to the

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headbox. The compressor is used to control the surface level and the pump is used to control the pressure level inside the headbox. The process variables are strongly interconnected (e.g. if one wants to change the pressure it surely affects the surface level). Thus, a MIMO controller is used to minimize the effects of these interactions. Besides the measurements needed for the controllers, there is also the measurement of pulp flow from the headbox which is also the output of main interest. As the slice opening is kept at constant level, the outflow is a function of only the overall pressure inside the headbox. However the function is nonlinear. The system is controlled by a basic PC using Matlab/simulink environment. The data is collected directly in the Matlab environment. In the experiments an additional excitation signal is added to the output of the pressure controller. The signal characteristics are determined from the process characteristics such as process gains, dominant time constants and measurement characteristics. The process characteristics are inherently nonlinear and dependant on the operating point (i.e. pressure and surface levels). Therefore the used signal should be adjusted for different operating points or designed so that it is applicable in all the used operating points. It should also be remembered that any results obtained are sufficiently accurate only locally. All the experiments were performed with a 9-bit-length MLBS with a generation frequency of 0.1 Hz. The sequence was designed as shown in section 3. At this point the stimulus signal was designed to be executed as a singleinput-variable experiment, i.e. only one stimulus signal is applied in a test. The amplitude of the excitation was experimentally adjusted in a way that assures sufficient process excitation even in the operating points where the process gain is at its lowest. This will result in unnecessarily large amplitude for other operating points but the approach was chosen for its simplicity. Also this is sufficient approach as the output is not disturbed too much and the nonlinear characteristics caused by the stimulus are not significant in any of the operating points. Fig.5a shows a sample of the applied MLBS, and Fig.5b shows its frequency content. The excitation was added into the pressure control signal which was measured together with the outflow. All the experiments were performed with four excitation periods, and the results were averaged in order to improve the SNR.

a)

b)

As the figure indicates, the outflow with perturbation is close to its desired value and hence, the system is not disturbed too much, even though the amplitude of the applied excitation signal was unnecessarily large.

a)

b)

Fig. 6. a) Frequency response from pressure control to outflow, and b) sample of perturbed and non perturbed outflow signals. Fig.7a shows how the frequency response from the pressure control signal to the outflow varies when the pressure set point (SP) is changed. The difference can be explained by the nonlinear characteristics of the process and shows that operating point wise reference values may be needed for monitoring purposes. Fig.7b show samples of the perturbed control signal levels with different pressure set points. These features can be used e.g. for detecting a bias component in the pressure measurement which drives the process to a new operating point as the controller sees the biased measurement results and tries to correct the situation.

a)

b)

Fig. 7. a) Frequency response from pressure control to outflow, and b) sample of perturbed control signals. Finally a test was conducted to emulate machinery wear. Fig.8 shows the frequency response from the pressure control signal to the outflow when the original set up was modified by manipulating the pump control signal with a backlash operator. The figure clearly shows the difference between fully functioning and worn equipment, especially at low frequencies. The differences in the frequency responses can be explained by studying further how the signal is modified by the backlash operator. Applying simple Fourier analysis it can be seen that the backlash operator reduces the excitation amplitude, especially at low frequencies, thus modifying correspondingly the measured frequency response.

Fig. 5. Sample of applied MLBS excitation a) in time domain, and b) corresponding power spectrum.

5. CONCLUSION

Fig.6a shows the frequency response from the pressure control signal to the outflow when (5) was applied. Fig.6b shows a sample of outflow, with and without perturbation.

Continuous monitoring and evaluation of processes while allowing normal system operation is of great interest in various fields of industry. Typically the experiments in

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Normal Operation Fault Mode

5

Gain (dB)

0 −5 −10 −15 −20

−3

−2

10

10 Frequency (Hz)

Fig. 8. Frequency response from pressure control to outflow with normal operation and fault mode the process industry are expensive and time consuming. In addition, usually the experiments cannot be performed on-line thus slowing down the production. This paper presented methods to measure and evaluate an industry process through non parametric identification methods. Maximum-length binary sequence (MLBS) was applied as an excitation and a system model was computed through cross-correlation technique. MLBS excitation has very low peak factor thus making it as a wellsuited excitation for sensitive systems. In addition, due to the deterministic nature of the MLBS and its adequate frequency content, the measurements can be performed accurately in a wide range of frequencies. The key point of the paper was to present a technique which can be applied on-line, i.e. not disturbing too much the normal operation of a process. The proposed method was verified by experimental measurement from a physical process emulating the traditional headbox of a paper machine. The results confirmed that frequency-domain analysis is a valid method for monitoring purposes. It is emphasized that the presented experiments were all performed as a single-input-variable experiments. It may be obvious, however, that for a more sufficient monitoring of a typical industrial process, multi-input-variable experiments are required. This, in turn, requires methods to identify multiple-input multiple-output (MIMO) systems, and will be one of the future work of the authors. The presented methods can be used in various frequencyresponse-based applications in process industry. Possible applications could be system validation, controller design, and system monitoring. REFERENCES Amrani, M., Dowdeswell, R., Payne, P., and Persaud, K. (1998). Pseudo-random binary sequence interrogation technique for gas sensors. Sensors and Actuators B: Chemical, 47, 118–124. Conner, J. and Seborg, D. (2004). An evaluation of MIMO input designs for process identification. Industrial and Engineering Chemistry Research, 43, 38473854.

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