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Ultrasonic characterization of aqueous mixture comprising insoluble and soluble substances with temperature compensation
Chemometrics and Intelligent Laboratory Systems 159 (2016) 12–19
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Chemometrics and Intelligent Laboratory Systems journal homepage: www.elsevier.com/locate/chemolab
Ultrasonic characterization of aqueous mixture comprising insoluble and soluble substances with temperature compensation
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Xiaobin Zhana, Shulan Jiangb, Yili Yanga, Jian Lianga, Tielin Shia, Xiwen Lia, a b
State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China Tribology Research Institute, Southwest Jiaotong University, Chengdu 610031, China
A R T I C L E I N F O
A BS T RAC T
Keywords: Ultrasonic spectrum Substance concentration Multicomponent mixture Temperature compensation Process control
This paper presents an ultrasonic technique for simultaneously determining the concentrations of insoluble and soluble substances in aqueous mixtures at different temperatures. First of all, the phase velocity spectra and the attenuation spectra of aqueous mixtures which are sensitive to the concentrations of substances are analyzed. Then, a synergy interval partial least squares (Si-PLS) model is applied to build the sub-models for the concentrations of substances at different temperature points. Finally, the overall model is constructed to build the relations among the sub-models by linear interpolation, in which the temperature effects are taken into account. The experimental and analytical results show that the overall model has the potential to simultaneously determine the concentrations of substances in aqueous mixtures at different temperatures. The proposed technique is time-saving in analyzing online signals, and thus will find wide applications in laboratory and industry for investigating aqueous mixtures and monitoring online processes.
1. Introduction In food, chemical and pharmaceutical industries, aqueous mixtures comprising insoluble and soluble substances have been widely used in such processes as mixing, suspension, crystallization, etc. It is of great industrial interest to develop a rapid and reliable analytical method for quantifying the concentrations of substances in aqueous mixtures [1]. To this end, many techniques have been proposed. Conventional methods, e.g., manual timed sampling and titration analysis, are time-consuming and difficult to be implemented online [2]. Optical and electrical techniques require the presence of specific properties of media, like transparency or electrical conductivity [3]. In comparison with the aforementioned techniques, the ultrasonic technique is quite applicable to the optically opaque, conductive and non-conductive, highly-concentrated dispersed systems [4]. Since the ultrasonic spectra are affected by the concentrations of insoluble and soluble substances in aqueous mixtures, the ultrasonic technique has been widely used for the measurement of substance concentrations [5–8]. Krause et al. [5] combined the multivariate regression method and the ultrasonic spectra to simultaneously detect the concentrations of sugar and ethanol in aqueous solutions. Rodriguez-Molares et al. [6] proposed an empirical model based on ultrasonic attenuation, temperature, and frequency to estimate the biomass concentration of a biological suspension. Zhan et al. [7]
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developed an ultrasonic measurement system based on least squares support vector machines and ultrasonic spectrum for online measurement of particle concentrations in multi-component suspensions. These studies suggest that the ultrasonic technique can be successfully applied to analyze the concentrations of substances in some solutions or suspensions, but the measurement of the concentrations of substances in aqueous mixtures comprising insoluble and soluble substances using the ultrasonic technique has been scarcely reported. Geier et al. [8] combined the measurements of ultrasonic velocity and attenuation coefficient to simultaneously determine the concentrations of yeast (insoluble substance) and maltose (soluble substance). Goodenough et al. [2] measured the concentration of particulate matter in a fluctuating high-temperature liquid system which included soluble substance through the attenuation coefficient. In their studies, the attenuation coefficient was proportional to the concentration of insoluble particles, but independent to that of soluble substance because the concentration of soluble substance was small. However, the concentrations of soluble substances in many mixtures are high so that the attenuation cannot be ignored, and those methods will result in the measurement inaccuracy. The use of ultrasonic technique may be limited by the complexity of mixtures, which may give rise to unmanageable or inaccurate physical models for describing the relation between ultrasonic features and substance concentrations [9]. Being fast and easy to perform, the
Corresponding author. E-mail address: [email protected] (X. Li).
http://dx.doi.org/10.1016/j.chemolab.2016.09.008 Received 10 April 2016; Received in revised form 22 July 2016; Accepted 24 September 2016 Available online 24 September 2016 0169-7439/ © 2016 Elsevier B.V. All rights reserved.
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multivariate methods are alternatives to traditional ones and used to correlate target variables (Y) with descriptor variables (X) [10]. The partial least squares (PLS) model is capable of modeling the complex system in high-dimensional feature spaces and with fewer training data [11]. Although the entire PLS modeling process including sample preparation, signal processing, feature extraction, parameter optimization and model evaluation is time-consuming, the analysis can be completed in a short time once the PLS model is established [12]. Therefore, the PLS model is a promising technique for online measurement of the concentrations of substances in aqueous mixtures. The full spectrum often contains hundreds or thousands of variables, but some variables may contain useless or irrelevant information like noise and background [13]. Thus, the selection of specific spectral interval is of great importance to simplify model, reduce the computational efforts and improve the accuracy and robustness of model [14]. In industrial processes, it is crucial to take the temperature effects into consideration. Temperature affects the physical parameters of substances and further the ultrasonic signals. Some researchers [15,16] have detected the concentrations of ternary mixtures at constant temperature. The accurate temperature control is needed to get a good estimation of concentration. Krause et al. [17] combined the submodels for different temperature points by linear approximation of each coefficient over temperature to build a unified model which was used to detect the concentrations of substances in ternary solutions at different temperatures. However, the method required the sub-models to have the same framework about regression coefficients and predictor variables. Huang et al. [18] designed an ultrasonic device to measure solid suspension concentrations at different temperatures using the linear functions of attenuation and temperature for concentration, but this method was suitable for the binary mixture only. This paper is aimed to establish a reliable method for simultaneous measurement of the concentrations of insoluble and soluble substances in aqueous mixture at different temperatures. Titanium dioxide (TiO2) and glucose are taken as insoluble and soluble substances in the experiments respectively. At first, the phase velocity spectra and the attenuation spectra of aqueous mixtures are analyzed. Then, the submodels for predicting the concentrations of substances at different temperature points are built. Finally, the overall model is built to establish the relations among sub-models by linear interpolation, and the temperature effects are taken into consideration. The proposed method is less time-consuming in analyzing online signals and thus will find wide applications in laboratory and industry for investigating aqueous mixture and monitoring online processes.
Fig. 1. The distributions of samples at each temperature point. (The solid up triangles represent the calibration subset, and the hollow down triangles stand for the prediction subset.).
respectively. 600 g pure water is added into the possible combinations of TiO2 and glucose to obtain 35 samples. These samples (the sample of pure water is excluded) constitute the prediction subset which is used to evaluate the model performance only. The temperature points for prediction are selected in the range from 16 to 40 °C and with an interval of 1 °C. 2.2. Experimental setup The measurement cell as well as the measuring principles are explained schematically in Fig. 2 The wave is transmitted into the samples by an ultrasonic sensor (Olympus V306-SU, with the center frequency of 2.25 MHz), which is excited via an ultrasonic pulser/ receiver (Olympus Models 5072 PR) at 100 Hz. The ultrasonic sensor has direct contact with the samples in order to reduce the arbitrary influences of coupling agent and so on, enhance the signal strength of reflected echoes and improve the stability and repeatability of system. The incident wave which traverses the samples is reverberated from the front face of reflector. The reflected echoes are received by the same ultrasonic sensor (pulse-echo method) and detected with an oscilloscope (Tektronix DPO7254) at the sampling rate of 500 MHz. The samples and the measurement cell are contained in a transparent flat-bottomed cylindrical tank, while the tank is immersed in a circulating thermostatic water bath to control the sample temperature with the accuracy of ± 0.1 °C. The temperatures of the samples are measured by Pt 100 temperature sensors. To ensure the homogeneity of samples, the samples are constantly stirred with a four-bladed pitched blade turbine impeller. The experiments are carried out for each sample at all temperature
2. Materials and methods 2.1. Sample preparation The samples are aqueous mixtures composed of pure water, TiO2 (as the insoluble substance) and glucose (as the soluble substance). The substance concentration refers to the fraction of the mass of one substance to that of the mixture. The samples are prepared as shown in Fig. 1. At every temperature point, TiO2 is prepared in 8 groups from 0 g to 210 g, with an interval of 30 g, and glucose is prepared in 13 groups from 0 g to 180 g, with an interval of 15 g, respectively. 600 g pure water is added into the possible combinations of TiO2 and glucose to obtain 104 samples (including the sample of pure water). These samples make up the calibration subset which is used to build the calibration model. The temperature points for calibration are selected in the range from 16 to 40 °C and with an interval of 2 °C. Similarly, at every temperature point, TiO2 is prepared in 5 groups from 0 g to 210 g, with an interval of 27 g between the first and second groups and 54 g from the second to fifth groups, and glucose is prepared in 7 groups from 0 g to 180 g, with an interval of 28 g,
Fig. 2. The measurement cell.
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Fig. 3. (a) The typical time domain signal; (b) The windowed, averaged and zero-padded time domain signals of (a); (c) The amplitude spectrum of (b).
The ultrasonic amplitude spectrum of sample depends on the ultrasonic sensor, sample and reflector plate, etc. A normalized calibration enables the ultrasonic sensor to respond to the differences of sample properties rather than the measurement instruments. Hence, the ultrasonic attenuation spectrum of sample, as an alternative preprocess of the amplitude spectrum, is calibrated by measuring the amplitude spectrum of pure water at the same temperature and calculated with the equation below:
points separately. The ultrasonic signals and temperatures of samples are real-time acquired with an interval of 1 s after the samples become homogeneous and the temperatures become stable. For each sample, 300 ultrasonic signals and 300 temperature data are collected over a 5 min period. 2.3. Signal processing The ultrasonic signals of samples in the time domain are windowed over 5 μs in the same way. The windowed ultrasonic signals and temperatures of each sample are averaged, and then the averaged ultrasonic signals are zero-padded and mapped to the frequency domain using the fast Fourier transform (FFT) algorithm. The amplitude and phase of ultrasonic spectrum are denoted as X(k) and θ (k ) respectively. The process is shown in Fig. 3. The ultrasonic spectrum in the bandwidth of 1.76–3.28 MHz is chosen for further analysis because the signal-to-noise ratio is sufficiently high in the range. In this paper, the phase velocity of sample is derived from the ultrasonic velocity of water and the difference of the phase spectra between the sample and the water via the following formula [19,20]:
vs (k )=
vw vw 1− 4πfd (θs (k ) − θw (k ))
α ( f )=
1 ⎛ Xw (k ) ⎞ ln ⎜ ⎟ 2d ⎝ Xs (k ) ⎠
(2)
where Xw (k ) and Xs (k ) are the amplitude spectra of pure water and sample, respectively. 2.4. Analysis method The ultrasonic signals transmitted through the samples vary with the concentrations of substances and temperatures. In industrial processes, it is very difficult to keep the temperatures of samples constant. Hence, it is necessary to take the temperature effects into consideration. A two-stage architecture is proposed for modeling, which compensates the temperature effects and improves the model predictability. The two-stage architecture is presented in Fig. 4. In the first stage, the sub-models for the concentrations of substances at different temperature points of calibration subsets are built. The partial least squares (PLS) regression is a popular multivariate calibration method for quantitative analysis of spectral data [22]. However, the full spectrum may contain useless or irrelevant information like noise and background which can worsen the predictability of model [23]. The synergy interval PLS (Si-PLS) model is a commonly-used method and helpful to search for all possible sub-
(1)
where θs (k ) and θw (k ) are the phase spectra of sample and water at the same temperature respectively,d is the ultrasonic path length, vw is the ultrasonic velocity of water. The absolute phase spectrum is calculated by unwrapping the phase derived from FFT of echo signal and then compensating for time offsets brought by the oscilloscope trigger delay according to the Fourier shift theory [19]. The ultrasonic velocity of water vw is assumed to be dispersionless and dependent on the temperature of water [21]. 14
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Fig. 4. The flow chart for the whole process of modeling.
interval combinations and find out the optimal spectral intervals that contribute to the maximal precision of model [24]. Therefore, in this study, the selection of spectral subintervals is conducted with synergy interval PLS (Si-PLS) to effectively improve the performance of model. In the second stage, the overall model is constructed to build the relations among sub-models. The output results of independent submodels are taken as the inputs of the overall model. In this way, submodels and an overall model with simple structures take the place of a complex higher dimensional dynamic model. For each sub-model, the parameters can be trained separately so that the sick matrix and divergence problems in a higher dimensional model can be avoided. There is a need to take some steps prior to the establishment of the regression model. The target variables are the concentrations of substances (by weight), which are stored in the target matrix Y. The predictor variables are the ultrasonic spectra of samples including the phase velocity spectra and the attenuation spectra, which are stored in the rows of the predictor matrix X (vs ( f ), α( f )). In the end, the columns of X are scaled to the unit variance and subtracted the respective mean values, which is called data normalization. In this way, no column is of greater significance than the other ones. In this paper, the root mean square error of 10-fold cross-validation (RMSECV) is used to decide the model parameters. The coefficient of determination of the prediction subset (Rp2 ) as well as the RMSE of the prediction subset (RMSEP) are used to assess the predictability of models and reveal whether there is an over-fitting problem with models.
Fig. 5. The dependence of the ultrasonic attenuation coefficient (f=2.25 MHz) on the concentrations of glucose and TiO2 at 26 °C. (The concentration is a fraction of total substances in the suspension.)
A sets of experiments are conducted by adding glucose in TiO2 suspensions of different initial concentrations, in order to observe the sensitivity of the concentration of glucose to the attenuation coefficient and test the additional effects on the attenuation coefficient along with increasing concentration of glucose. As can be seen in Fig. 5, the concentration of glucose has less effects on the attenuation coefficient when the concentration of TiO2 is small or zero, but the influences of the glucose concentration on the attenuation coefficient gradually become remarkable along with the increase of the concentration of TiO2. The cause might be that the soluble substance changes the physical properties of the continuous phase and further the attenuation coefficient of insoluble substance. Thus, it can be inferred that it is impossible to simultaneously determine the concentrations of glucose and TiO2 solely based on the attenuation coefficient. Fig. 6 shows changes in phase velocities (f=2.25 MHz) with increasing glucose in TiO2 suspensions of different initial concentrations at 26 °C. There exist significant differences in the phase velocities at different concentrations of glucose and/or TiO2, which suggests that both glucose and TiO2 affect the ultrasonic velocity. It is noteworthy that the phase velocity of soluble substance or ternary mixture that includes little insoluble substance is almost independent of frequency
3. Results and discussion 3.1. Velocity spectrum and attenuation spectrum A comparison is made between the influences of the concentrations of TiO2 and glucose on the attenuation coefficient (f=2.25 MHz) with glucose solution and TiO2 suspension at 26 °C, as is illustrated in Fig. 5. The increase of the concentration of TiO2 leads to the conversion of acoustic energy into the energy of other forms and thus significantly affects the attenuation coefficient. The concentration of TiO2 is linearly correlated to the attenuation coefficient (R2=0.996). Nevertheless, the attenuation coefficient of glucose is rather smaller than that of TiO2. It can be seen from Fig. 5 that the attenuation coefficient of glucose keeps nearly constant and is free from the influences of the concentration of glucose. 15
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Fig. 6. The dependence of the phase velocity (f=2.25 MHz) on the concentrations of TiO2 and glucose. (The concentration is a fraction of total substances in the suspension.)
Fig. 7. The optimal spectral subintervals (blue areas) and the minimum RMSECV values of the nine Si-PLS models. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
and even can be assumed to be dispersionless. Although some researchers simultaneously have determined the concentrations of substances by measuring the ultrasonic velocities at two different temperatures [25], it is very tedious to change the temperature of mixture according to the measurement requirements in some industrial processes. Therefore, it is rather difficult to simultaneously measure the concentrations of glucose and TiO2 via the phase velocity spectrum. According to the analysis above, to simultaneously measure the concentrations of aqueous mixture that comprises soluble and insoluble substances, the combination of the phase velocity spectrum and the attenuation spectrum is a good choice. However, for a given mixture system, the velocity spectrum and the attenuation spectrum of the mixture are affected not only by the concentrations of substances but also temperature. Thus, the temperature effects must be compensated in the measurement of mixture when the temperature is inconstant.
The performance of the optimal Si-PLS models at 26 °C is shown in Table 1. The optimal Si-PLS model for glucose is achieved when the ultrasonic spectrum is split into 18 subintervals and the 5th, 8th, 11th and 17th subintervals make up the combination of optimal spectral subintervals, while the optimal Si-PLS model for TiO2 is achieved when the ultrasonic spectrum is split into 20 subintervals and the 4th, 11th, 12th and 20th subintervals constitute the combination of optimal spectral subintervals. The maximum optimal number of subintervals is 20 as shown in Table 1 and the model performance cannot be improved if the number of subintervals exceeds 20. The results show that the combination of phase velocity spectrum and attenuation spectrum is very suitable for the measurement of concentrations of soluble and insoluble substances and superior to the phase velocity spectrum or the attenuation spectrum. It can be found in Table 1 that the phase velocity spectrum and the attenuation spectrum result in the lower measurement accuracy for TiO2 and glucose respectively. Fig. 8 is the scatter plot of the reference concentrations and the predicted concentrations obtained with the Si-PLS models at 26 °C using the calibration and prediction subsets. It can be seen that the low glucose concentrations have relatively large errors, which may be attributable to the less influences of glucose on the ultrasonic spectrum at low concentrations, as is shown in Fig. 5. In spite of slight differences, it is clear that there is no systematic error in the predictions, as the points are randomly distributed around the bisectrix line along the entire range of y-values. In the same way, the model parameters and the optimal subinterval(s) for other temperature points can be found. The performance of the optimal models at some temperature points is shown in Fig. 9. There is an increasing trend of measurement errors along with the rise of temperature. This may be cause by the temperature characteristics of the ultrasonic sensor. In short, the results indicate the sub-models feature a relatively high prediction accuracy.
3.2. Sub-models based on Si-PLS The sub-models based on Si-PLS for the concentrations of substances at different temperature points of calibration subsets are built. To further study the relations between the concentrations of substances and the ultrasonic spectrum, the phase velocity spectrum in the bandwidth of 1.76–3.28 MHz (200 data points), the attenuation spectrum in the bandwidth of 1.76–3.28 MHz (200 data points) and the combination of both (400 data points) are used as the predictor variables of the Si-PLS models, respectively. At the same time, the concentrations of glucose, TiO2 and the combination of both are used as the target variables of the Si-PLS models, respectively. In the course of calibration, the predictability of Si-PLS model may be severely influenced by the number of subintervals, the combination of subintervals and the number of PLS factors, so these parameters should be optimized simultaneously to build the optimal model. At first, the predictor variables are divided into 2–25 subintervals, respectively. Then, the Si-PLS models are developed using the subintervals and the combination of subintervals, and the performance of models is evaluated for each case. Finally, the optimal model parameters are determined according to RMSECV. The nine Si-PLS models which are built at 26 °C with different target variables and predictor variables are shown in Fig. 7. In each row, the strip and the blue areas in the strip represent the range of predictor variables and the optimal spectral subintervals of Si-PLS model, respectively. The first and latter halves of predictor variables are the phase velocity spectrum and the attenuation spectrum, respectively. For each Si-PLS model, the minimum RMSECV value is listed on the left side of each row.
3.3. Overall model based on linear interpolation To calculate the concentrations of substances at any temperature in the range from 16 to 40 °C, the overall model is constructed to build the relations among sub-models. As the model parameters and the spectral intervals of sub-models are different, it is very difficult to build the overall model through fitting the model parameters of sub-models. Hence, it is an alternative method to build the overall model using the output results of independent sub-models. In this way, the parameters of sub-models can be trained separately to maximize the performance of the overall model. At the temperature T0 , Th and Tl are the two temperature points 16
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Table 1 The results of Si-PLS models with the optimal spectral subintervals at 26 °C. Case
Target variables
Predictor variables
Subintervals/ All subintervals
RMSECV∑ (wt.%)
RMSECVG (wt.%)
RMSECVT (wt.%)
RMSEPG (wt.%)
RMSEPT (wt.%)
1 2 3 4 5 6 7 8 9
φG φT φG φT φG φT φT φT φT φG φG φG
Velocity + Attenuation Velocity Attenuation Velocity + Attenuation Velocity Attenuation Velocity + Attenuation Velocity Attenuation
(5 8 11 17)/18 (7 10 12 20)/20 (7 15 18)/18 (4 11 12 20)/20 (5 9 11)/13 (1 4 5 18)/18 (5 8 11 17)/18 (2 3 4 5)/20 (3 11 17)/18
0.35 0.65 0.49 0.26 0.62 0.29 0.31 0.43 0.47
0.28 0.61 0.39 0.26 0.62 0.29 / / /
0.34 0.48 0.52 / / / 0.31 0.43 0.47
0.42 0.68 0.57 0.38 0.68 0.40 / / /
0.43 0.50 0.58 / / / 0.42 0.52 0.54
*The subscripts ∑, G and T refer to all substances, glucose and TiO2 in the mixture, respectively.
closest to T0 and the sub-models are built at the two temperature points. Th and Tl can be defined as:
⎧T0+2>Th≥T0 ⎨ ⎩ T0≥Tl≥T0−2
(3)
l T0 ) at the temperature T0 can be The concentrations of substances Y( calculated by linear interpolation: l l l T0 )=Y( l Tl )+ Y(Th ) − Y(Tl ) ∙(T0−Tl ) Y( Th − Tl
(4)
l Tl ) and Y( l Th ) are the output results of the sub-models at the where Y( temperatures Tl and Th , respectively. The two sub-models take the ultrasonic spectrum at the temperature T0 as the input. The RMSEPT and RMSEPG of the over-all model are 0.53 wt.% and 0.58 wt.% respectively when the predicted concentrations are calculated using linear interpolation (see Eq. (4)) between the results of two neighboring sub-models with the prediction subset at all temperature points. Fig. 10 shows the scatter plot of the reference concentrations and the predicted concentrations using the prediction subset at different temperature points. Although the reported error is still quite high, the measurement of concentrations at varying temperatures is
Fig. 9. The performance of Si-PLS models at some temperature points.
made possible. Nevertheless, the large interval of the temperature points in which the sub-models are built and the nonlinear relations between the temperature and the outputs of sub-models may be the
Fig. 8. The predicted concentrations vs. the reference concentrations of (a) TiO2 and (b) glucose at 26 °C.
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temperature measurements and the fluctuation of temperatures. Compared with the offline predicted results in Fig. 8, the errors of online measured concentrations are larger, where the dynamic measurement along with the fluctuation of echo signals may be concerned. The noise disturbances arising from the fluctuation of temperatures and echo signals cannot be eliminated without the mean method in consideration of real-time measurement. In the event that low realtime requirements are put forward, the measurement accuracy can be further improved through increasing the length of time-moving window to average the ultrasonic signals and temperatures or slip averaging the measurement results. The measurement performance indicates that the overall model is appropriate for the online measurement of concentrations and capable of modeling dynamic systems. Although it takes long to optimize the model parameters and select the optimal spectral subinterval(s), the detection of the concentrations of substances using the proposed method needs just some simple vector multiplications. Therefore, the online implementation is possible owing to the advantage of short processing time. 4. Conclusion Fig. 10. The predicted concentrations vs. the reference concentrations with the prediction subset at different temperatures.
In this paper, the combination of ultrasonic spectrum and multivariate methods is proposed to simultaneously detect the concentrations of soluble and insoluble substances in an aqueous mixture in the range from 16 to 40 °C. A two-stage architecture is applied for modeling, which compensates the temperature effects and improves the model predictability. The Si-PLS model is proposed to build the sub-models for the concentrations of substances at different temperature points. Then the overall model is constructed to build the relations among the sub-models by linear interpolation, in which the temperature effects are taken into account. The experimental and analytical results show that the overall model has the potential to simultaneously determine the concentrations of substances in aqueous mixtures at different temperatures. The high measurement rates can be achieved and the real-time monitoring of industrial processes can be realized. The proposed method will find wide applications in laboratory and industry for investigation of aqueous mixtures and online process monitoring. Nevertheless, further work is needed to achieve a higher accuracy and realize the online implementation. What’s more, the influences of bubbles may need to be taken into consideration in some industrial applications.
Fig. 11. The results of real-time concentration measurements at different temperatures.
main reasons for the high overall RMSEP value. Hence, the performance of the overall model will be effectively improved by decreasing the interval of the temperature points.
Conflict of interests The authors declare that there is no conflict of interests.
3.4. Online measurement Acknowledgments The online measurement ability of the overall model is evaluated using the prediction subset. In the evaluation process, the ultrasonic signals and temperatures of the samples are real-time acquired with an interval of 1 s after the samples become homogeneous. A time-moving window with a length of 10 s is used to average the ultrasonic signals and temperatures. The phase velocity spectra and the attenuation spectra are calculated and the optimal spectral intervals are selected according to the sub-models dependent on temperature. Afterwards, the concentrations of substances can be calculated through the results of sub-models and Eq. (4). The measurement errors of concentrations of TiO2 and glucose using the prediction subset are less than ± 0.66 wt. % and ± 0.69 wt.% respectively, which meet the general industrial requirements. The online measured concentrations of the mixture composed of 20.18 wt.% TiO2 and 12.56 wt.% glucose in the range from 25 to 30 °C are shown in Fig. 11. The straight solid lines represent the reference concentrations. Fig. 11 shows that more errors are found during the rise of temperature. This may be caused by the time delay of
This research work is supported by Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT13017), and the National Natural Science Foundation of China (Grant No. 51605179). We are grateful to the website http://www. models.kvl.dk/, where we downloaded Si-PLS Matlab codes free of charge. References [1] D. Krause, T. Schöck, M.A. Hussein, T. Becker, Ultrasonic characterization of aqueous solutions with varying sugar and ethanol content using multivariate regression methods, J. Chemom. 25 (2011) 216–223. [2] T.I.J. Goodenough, V.S. Rajendram, S. Meyer, D. Pretre, Detection and quantification of insoluble particles by ultrasound spectroscopy, Ultrasonics 43 (2005) 231–235. [3] G. Locher, B. Sonnleitner, A. Fiechter, On-line measurement in biotechnology: techniques, J. Biotechnol. 25 (1992) 23–53. [4] L. Liu, Application of ultrasound spectroscopy for nanoparticle sizing in high concentration suspensions: a factor analysis on the effects of concentration and
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Ultrasonic characterization of aqueous mixture comprising insoluble and soluble substances with temperature compensation
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Xiaobin Zhana, Shulan Jiangb, Yili Yanga, Jian Lianga, Tielin Shia, Xiwen Lia, a b
State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China Tribology Research Institute, Southwest Jiaotong University, Chengdu 610031, China
A R T I C L E I N F O
A BS T RAC T
Keywords: Ultrasonic spectrum Substance concentration Multicomponent mixture Temperature compensation Process control
This paper presents an ultrasonic technique for simultaneously determining the concentrations of insoluble and soluble substances in aqueous mixtures at different temperatures. First of all, the phase velocity spectra and the attenuation spectra of aqueous mixtures which are sensitive to the concentrations of substances are analyzed. Then, a synergy interval partial least squares (Si-PLS) model is applied to build the sub-models for the concentrations of substances at different temperature points. Finally, the overall model is constructed to build the relations among the sub-models by linear interpolation, in which the temperature effects are taken into account. The experimental and analytical results show that the overall model has the potential to simultaneously determine the concentrations of substances in aqueous mixtures at different temperatures. The proposed technique is time-saving in analyzing online signals, and thus will find wide applications in laboratory and industry for investigating aqueous mixtures and monitoring online processes.
1. Introduction In food, chemical and pharmaceutical industries, aqueous mixtures comprising insoluble and soluble substances have been widely used in such processes as mixing, suspension, crystallization, etc. It is of great industrial interest to develop a rapid and reliable analytical method for quantifying the concentrations of substances in aqueous mixtures [1]. To this end, many techniques have been proposed. Conventional methods, e.g., manual timed sampling and titration analysis, are time-consuming and difficult to be implemented online [2]. Optical and electrical techniques require the presence of specific properties of media, like transparency or electrical conductivity [3]. In comparison with the aforementioned techniques, the ultrasonic technique is quite applicable to the optically opaque, conductive and non-conductive, highly-concentrated dispersed systems [4]. Since the ultrasonic spectra are affected by the concentrations of insoluble and soluble substances in aqueous mixtures, the ultrasonic technique has been widely used for the measurement of substance concentrations [5–8]. Krause et al. [5] combined the multivariate regression method and the ultrasonic spectra to simultaneously detect the concentrations of sugar and ethanol in aqueous solutions. Rodriguez-Molares et al. [6] proposed an empirical model based on ultrasonic attenuation, temperature, and frequency to estimate the biomass concentration of a biological suspension. Zhan et al. [7]
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developed an ultrasonic measurement system based on least squares support vector machines and ultrasonic spectrum for online measurement of particle concentrations in multi-component suspensions. These studies suggest that the ultrasonic technique can be successfully applied to analyze the concentrations of substances in some solutions or suspensions, but the measurement of the concentrations of substances in aqueous mixtures comprising insoluble and soluble substances using the ultrasonic technique has been scarcely reported. Geier et al. [8] combined the measurements of ultrasonic velocity and attenuation coefficient to simultaneously determine the concentrations of yeast (insoluble substance) and maltose (soluble substance). Goodenough et al. [2] measured the concentration of particulate matter in a fluctuating high-temperature liquid system which included soluble substance through the attenuation coefficient. In their studies, the attenuation coefficient was proportional to the concentration of insoluble particles, but independent to that of soluble substance because the concentration of soluble substance was small. However, the concentrations of soluble substances in many mixtures are high so that the attenuation cannot be ignored, and those methods will result in the measurement inaccuracy. The use of ultrasonic technique may be limited by the complexity of mixtures, which may give rise to unmanageable or inaccurate physical models for describing the relation between ultrasonic features and substance concentrations [9]. Being fast and easy to perform, the
Corresponding author. E-mail address: [email protected] (X. Li).
http://dx.doi.org/10.1016/j.chemolab.2016.09.008 Received 10 April 2016; Received in revised form 22 July 2016; Accepted 24 September 2016 Available online 24 September 2016 0169-7439/ © 2016 Elsevier B.V. All rights reserved.
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multivariate methods are alternatives to traditional ones and used to correlate target variables (Y) with descriptor variables (X) [10]. The partial least squares (PLS) model is capable of modeling the complex system in high-dimensional feature spaces and with fewer training data [11]. Although the entire PLS modeling process including sample preparation, signal processing, feature extraction, parameter optimization and model evaluation is time-consuming, the analysis can be completed in a short time once the PLS model is established [12]. Therefore, the PLS model is a promising technique for online measurement of the concentrations of substances in aqueous mixtures. The full spectrum often contains hundreds or thousands of variables, but some variables may contain useless or irrelevant information like noise and background [13]. Thus, the selection of specific spectral interval is of great importance to simplify model, reduce the computational efforts and improve the accuracy and robustness of model [14]. In industrial processes, it is crucial to take the temperature effects into consideration. Temperature affects the physical parameters of substances and further the ultrasonic signals. Some researchers [15,16] have detected the concentrations of ternary mixtures at constant temperature. The accurate temperature control is needed to get a good estimation of concentration. Krause et al. [17] combined the submodels for different temperature points by linear approximation of each coefficient over temperature to build a unified model which was used to detect the concentrations of substances in ternary solutions at different temperatures. However, the method required the sub-models to have the same framework about regression coefficients and predictor variables. Huang et al. [18] designed an ultrasonic device to measure solid suspension concentrations at different temperatures using the linear functions of attenuation and temperature for concentration, but this method was suitable for the binary mixture only. This paper is aimed to establish a reliable method for simultaneous measurement of the concentrations of insoluble and soluble substances in aqueous mixture at different temperatures. Titanium dioxide (TiO2) and glucose are taken as insoluble and soluble substances in the experiments respectively. At first, the phase velocity spectra and the attenuation spectra of aqueous mixtures are analyzed. Then, the submodels for predicting the concentrations of substances at different temperature points are built. Finally, the overall model is built to establish the relations among sub-models by linear interpolation, and the temperature effects are taken into consideration. The proposed method is less time-consuming in analyzing online signals and thus will find wide applications in laboratory and industry for investigating aqueous mixture and monitoring online processes.
Fig. 1. The distributions of samples at each temperature point. (The solid up triangles represent the calibration subset, and the hollow down triangles stand for the prediction subset.).
respectively. 600 g pure water is added into the possible combinations of TiO2 and glucose to obtain 35 samples. These samples (the sample of pure water is excluded) constitute the prediction subset which is used to evaluate the model performance only. The temperature points for prediction are selected in the range from 16 to 40 °C and with an interval of 1 °C. 2.2. Experimental setup The measurement cell as well as the measuring principles are explained schematically in Fig. 2 The wave is transmitted into the samples by an ultrasonic sensor (Olympus V306-SU, with the center frequency of 2.25 MHz), which is excited via an ultrasonic pulser/ receiver (Olympus Models 5072 PR) at 100 Hz. The ultrasonic sensor has direct contact with the samples in order to reduce the arbitrary influences of coupling agent and so on, enhance the signal strength of reflected echoes and improve the stability and repeatability of system. The incident wave which traverses the samples is reverberated from the front face of reflector. The reflected echoes are received by the same ultrasonic sensor (pulse-echo method) and detected with an oscilloscope (Tektronix DPO7254) at the sampling rate of 500 MHz. The samples and the measurement cell are contained in a transparent flat-bottomed cylindrical tank, while the tank is immersed in a circulating thermostatic water bath to control the sample temperature with the accuracy of ± 0.1 °C. The temperatures of the samples are measured by Pt 100 temperature sensors. To ensure the homogeneity of samples, the samples are constantly stirred with a four-bladed pitched blade turbine impeller. The experiments are carried out for each sample at all temperature
2. Materials and methods 2.1. Sample preparation The samples are aqueous mixtures composed of pure water, TiO2 (as the insoluble substance) and glucose (as the soluble substance). The substance concentration refers to the fraction of the mass of one substance to that of the mixture. The samples are prepared as shown in Fig. 1. At every temperature point, TiO2 is prepared in 8 groups from 0 g to 210 g, with an interval of 30 g, and glucose is prepared in 13 groups from 0 g to 180 g, with an interval of 15 g, respectively. 600 g pure water is added into the possible combinations of TiO2 and glucose to obtain 104 samples (including the sample of pure water). These samples make up the calibration subset which is used to build the calibration model. The temperature points for calibration are selected in the range from 16 to 40 °C and with an interval of 2 °C. Similarly, at every temperature point, TiO2 is prepared in 5 groups from 0 g to 210 g, with an interval of 27 g between the first and second groups and 54 g from the second to fifth groups, and glucose is prepared in 7 groups from 0 g to 180 g, with an interval of 28 g,
Fig. 2. The measurement cell.
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Fig. 3. (a) The typical time domain signal; (b) The windowed, averaged and zero-padded time domain signals of (a); (c) The amplitude spectrum of (b).
The ultrasonic amplitude spectrum of sample depends on the ultrasonic sensor, sample and reflector plate, etc. A normalized calibration enables the ultrasonic sensor to respond to the differences of sample properties rather than the measurement instruments. Hence, the ultrasonic attenuation spectrum of sample, as an alternative preprocess of the amplitude spectrum, is calibrated by measuring the amplitude spectrum of pure water at the same temperature and calculated with the equation below:
points separately. The ultrasonic signals and temperatures of samples are real-time acquired with an interval of 1 s after the samples become homogeneous and the temperatures become stable. For each sample, 300 ultrasonic signals and 300 temperature data are collected over a 5 min period. 2.3. Signal processing The ultrasonic signals of samples in the time domain are windowed over 5 μs in the same way. The windowed ultrasonic signals and temperatures of each sample are averaged, and then the averaged ultrasonic signals are zero-padded and mapped to the frequency domain using the fast Fourier transform (FFT) algorithm. The amplitude and phase of ultrasonic spectrum are denoted as X(k) and θ (k ) respectively. The process is shown in Fig. 3. The ultrasonic spectrum in the bandwidth of 1.76–3.28 MHz is chosen for further analysis because the signal-to-noise ratio is sufficiently high in the range. In this paper, the phase velocity of sample is derived from the ultrasonic velocity of water and the difference of the phase spectra between the sample and the water via the following formula [19,20]:
vs (k )=
vw vw 1− 4πfd (θs (k ) − θw (k ))
α ( f )=
1 ⎛ Xw (k ) ⎞ ln ⎜ ⎟ 2d ⎝ Xs (k ) ⎠
(2)
where Xw (k ) and Xs (k ) are the amplitude spectra of pure water and sample, respectively. 2.4. Analysis method The ultrasonic signals transmitted through the samples vary with the concentrations of substances and temperatures. In industrial processes, it is very difficult to keep the temperatures of samples constant. Hence, it is necessary to take the temperature effects into consideration. A two-stage architecture is proposed for modeling, which compensates the temperature effects and improves the model predictability. The two-stage architecture is presented in Fig. 4. In the first stage, the sub-models for the concentrations of substances at different temperature points of calibration subsets are built. The partial least squares (PLS) regression is a popular multivariate calibration method for quantitative analysis of spectral data [22]. However, the full spectrum may contain useless or irrelevant information like noise and background which can worsen the predictability of model [23]. The synergy interval PLS (Si-PLS) model is a commonly-used method and helpful to search for all possible sub-
(1)
where θs (k ) and θw (k ) are the phase spectra of sample and water at the same temperature respectively,d is the ultrasonic path length, vw is the ultrasonic velocity of water. The absolute phase spectrum is calculated by unwrapping the phase derived from FFT of echo signal and then compensating for time offsets brought by the oscilloscope trigger delay according to the Fourier shift theory [19]. The ultrasonic velocity of water vw is assumed to be dispersionless and dependent on the temperature of water [21]. 14
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Fig. 4. The flow chart for the whole process of modeling.
interval combinations and find out the optimal spectral intervals that contribute to the maximal precision of model [24]. Therefore, in this study, the selection of spectral subintervals is conducted with synergy interval PLS (Si-PLS) to effectively improve the performance of model. In the second stage, the overall model is constructed to build the relations among sub-models. The output results of independent submodels are taken as the inputs of the overall model. In this way, submodels and an overall model with simple structures take the place of a complex higher dimensional dynamic model. For each sub-model, the parameters can be trained separately so that the sick matrix and divergence problems in a higher dimensional model can be avoided. There is a need to take some steps prior to the establishment of the regression model. The target variables are the concentrations of substances (by weight), which are stored in the target matrix Y. The predictor variables are the ultrasonic spectra of samples including the phase velocity spectra and the attenuation spectra, which are stored in the rows of the predictor matrix X (vs ( f ), α( f )). In the end, the columns of X are scaled to the unit variance and subtracted the respective mean values, which is called data normalization. In this way, no column is of greater significance than the other ones. In this paper, the root mean square error of 10-fold cross-validation (RMSECV) is used to decide the model parameters. The coefficient of determination of the prediction subset (Rp2 ) as well as the RMSE of the prediction subset (RMSEP) are used to assess the predictability of models and reveal whether there is an over-fitting problem with models.
Fig. 5. The dependence of the ultrasonic attenuation coefficient (f=2.25 MHz) on the concentrations of glucose and TiO2 at 26 °C. (The concentration is a fraction of total substances in the suspension.)
A sets of experiments are conducted by adding glucose in TiO2 suspensions of different initial concentrations, in order to observe the sensitivity of the concentration of glucose to the attenuation coefficient and test the additional effects on the attenuation coefficient along with increasing concentration of glucose. As can be seen in Fig. 5, the concentration of glucose has less effects on the attenuation coefficient when the concentration of TiO2 is small or zero, but the influences of the glucose concentration on the attenuation coefficient gradually become remarkable along with the increase of the concentration of TiO2. The cause might be that the soluble substance changes the physical properties of the continuous phase and further the attenuation coefficient of insoluble substance. Thus, it can be inferred that it is impossible to simultaneously determine the concentrations of glucose and TiO2 solely based on the attenuation coefficient. Fig. 6 shows changes in phase velocities (f=2.25 MHz) with increasing glucose in TiO2 suspensions of different initial concentrations at 26 °C. There exist significant differences in the phase velocities at different concentrations of glucose and/or TiO2, which suggests that both glucose and TiO2 affect the ultrasonic velocity. It is noteworthy that the phase velocity of soluble substance or ternary mixture that includes little insoluble substance is almost independent of frequency
3. Results and discussion 3.1. Velocity spectrum and attenuation spectrum A comparison is made between the influences of the concentrations of TiO2 and glucose on the attenuation coefficient (f=2.25 MHz) with glucose solution and TiO2 suspension at 26 °C, as is illustrated in Fig. 5. The increase of the concentration of TiO2 leads to the conversion of acoustic energy into the energy of other forms and thus significantly affects the attenuation coefficient. The concentration of TiO2 is linearly correlated to the attenuation coefficient (R2=0.996). Nevertheless, the attenuation coefficient of glucose is rather smaller than that of TiO2. It can be seen from Fig. 5 that the attenuation coefficient of glucose keeps nearly constant and is free from the influences of the concentration of glucose. 15
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Fig. 6. The dependence of the phase velocity (f=2.25 MHz) on the concentrations of TiO2 and glucose. (The concentration is a fraction of total substances in the suspension.)
Fig. 7. The optimal spectral subintervals (blue areas) and the minimum RMSECV values of the nine Si-PLS models. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
and even can be assumed to be dispersionless. Although some researchers simultaneously have determined the concentrations of substances by measuring the ultrasonic velocities at two different temperatures [25], it is very tedious to change the temperature of mixture according to the measurement requirements in some industrial processes. Therefore, it is rather difficult to simultaneously measure the concentrations of glucose and TiO2 via the phase velocity spectrum. According to the analysis above, to simultaneously measure the concentrations of aqueous mixture that comprises soluble and insoluble substances, the combination of the phase velocity spectrum and the attenuation spectrum is a good choice. However, for a given mixture system, the velocity spectrum and the attenuation spectrum of the mixture are affected not only by the concentrations of substances but also temperature. Thus, the temperature effects must be compensated in the measurement of mixture when the temperature is inconstant.
The performance of the optimal Si-PLS models at 26 °C is shown in Table 1. The optimal Si-PLS model for glucose is achieved when the ultrasonic spectrum is split into 18 subintervals and the 5th, 8th, 11th and 17th subintervals make up the combination of optimal spectral subintervals, while the optimal Si-PLS model for TiO2 is achieved when the ultrasonic spectrum is split into 20 subintervals and the 4th, 11th, 12th and 20th subintervals constitute the combination of optimal spectral subintervals. The maximum optimal number of subintervals is 20 as shown in Table 1 and the model performance cannot be improved if the number of subintervals exceeds 20. The results show that the combination of phase velocity spectrum and attenuation spectrum is very suitable for the measurement of concentrations of soluble and insoluble substances and superior to the phase velocity spectrum or the attenuation spectrum. It can be found in Table 1 that the phase velocity spectrum and the attenuation spectrum result in the lower measurement accuracy for TiO2 and glucose respectively. Fig. 8 is the scatter plot of the reference concentrations and the predicted concentrations obtained with the Si-PLS models at 26 °C using the calibration and prediction subsets. It can be seen that the low glucose concentrations have relatively large errors, which may be attributable to the less influences of glucose on the ultrasonic spectrum at low concentrations, as is shown in Fig. 5. In spite of slight differences, it is clear that there is no systematic error in the predictions, as the points are randomly distributed around the bisectrix line along the entire range of y-values. In the same way, the model parameters and the optimal subinterval(s) for other temperature points can be found. The performance of the optimal models at some temperature points is shown in Fig. 9. There is an increasing trend of measurement errors along with the rise of temperature. This may be cause by the temperature characteristics of the ultrasonic sensor. In short, the results indicate the sub-models feature a relatively high prediction accuracy.
3.2. Sub-models based on Si-PLS The sub-models based on Si-PLS for the concentrations of substances at different temperature points of calibration subsets are built. To further study the relations between the concentrations of substances and the ultrasonic spectrum, the phase velocity spectrum in the bandwidth of 1.76–3.28 MHz (200 data points), the attenuation spectrum in the bandwidth of 1.76–3.28 MHz (200 data points) and the combination of both (400 data points) are used as the predictor variables of the Si-PLS models, respectively. At the same time, the concentrations of glucose, TiO2 and the combination of both are used as the target variables of the Si-PLS models, respectively. In the course of calibration, the predictability of Si-PLS model may be severely influenced by the number of subintervals, the combination of subintervals and the number of PLS factors, so these parameters should be optimized simultaneously to build the optimal model. At first, the predictor variables are divided into 2–25 subintervals, respectively. Then, the Si-PLS models are developed using the subintervals and the combination of subintervals, and the performance of models is evaluated for each case. Finally, the optimal model parameters are determined according to RMSECV. The nine Si-PLS models which are built at 26 °C with different target variables and predictor variables are shown in Fig. 7. In each row, the strip and the blue areas in the strip represent the range of predictor variables and the optimal spectral subintervals of Si-PLS model, respectively. The first and latter halves of predictor variables are the phase velocity spectrum and the attenuation spectrum, respectively. For each Si-PLS model, the minimum RMSECV value is listed on the left side of each row.
3.3. Overall model based on linear interpolation To calculate the concentrations of substances at any temperature in the range from 16 to 40 °C, the overall model is constructed to build the relations among sub-models. As the model parameters and the spectral intervals of sub-models are different, it is very difficult to build the overall model through fitting the model parameters of sub-models. Hence, it is an alternative method to build the overall model using the output results of independent sub-models. In this way, the parameters of sub-models can be trained separately to maximize the performance of the overall model. At the temperature T0 , Th and Tl are the two temperature points 16
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Table 1 The results of Si-PLS models with the optimal spectral subintervals at 26 °C. Case
Target variables
Predictor variables
Subintervals/ All subintervals
RMSECV∑ (wt.%)
RMSECVG (wt.%)
RMSECVT (wt.%)
RMSEPG (wt.%)
RMSEPT (wt.%)
1 2 3 4 5 6 7 8 9
φG φT φG φT φG φT φT φT φT φG φG φG
Velocity + Attenuation Velocity Attenuation Velocity + Attenuation Velocity Attenuation Velocity + Attenuation Velocity Attenuation
(5 8 11 17)/18 (7 10 12 20)/20 (7 15 18)/18 (4 11 12 20)/20 (5 9 11)/13 (1 4 5 18)/18 (5 8 11 17)/18 (2 3 4 5)/20 (3 11 17)/18
0.35 0.65 0.49 0.26 0.62 0.29 0.31 0.43 0.47
0.28 0.61 0.39 0.26 0.62 0.29 / / /
0.34 0.48 0.52 / / / 0.31 0.43 0.47
0.42 0.68 0.57 0.38 0.68 0.40 / / /
0.43 0.50 0.58 / / / 0.42 0.52 0.54
*The subscripts ∑, G and T refer to all substances, glucose and TiO2 in the mixture, respectively.
closest to T0 and the sub-models are built at the two temperature points. Th and Tl can be defined as:
⎧T0+2>Th≥T0 ⎨ ⎩ T0≥Tl≥T0−2
(3)
l T0 ) at the temperature T0 can be The concentrations of substances Y( calculated by linear interpolation: l l l T0 )=Y( l Tl )+ Y(Th ) − Y(Tl ) ∙(T0−Tl ) Y( Th − Tl
(4)
l Tl ) and Y( l Th ) are the output results of the sub-models at the where Y( temperatures Tl and Th , respectively. The two sub-models take the ultrasonic spectrum at the temperature T0 as the input. The RMSEPT and RMSEPG of the over-all model are 0.53 wt.% and 0.58 wt.% respectively when the predicted concentrations are calculated using linear interpolation (see Eq. (4)) between the results of two neighboring sub-models with the prediction subset at all temperature points. Fig. 10 shows the scatter plot of the reference concentrations and the predicted concentrations using the prediction subset at different temperature points. Although the reported error is still quite high, the measurement of concentrations at varying temperatures is
Fig. 9. The performance of Si-PLS models at some temperature points.
made possible. Nevertheless, the large interval of the temperature points in which the sub-models are built and the nonlinear relations between the temperature and the outputs of sub-models may be the
Fig. 8. The predicted concentrations vs. the reference concentrations of (a) TiO2 and (b) glucose at 26 °C.
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temperature measurements and the fluctuation of temperatures. Compared with the offline predicted results in Fig. 8, the errors of online measured concentrations are larger, where the dynamic measurement along with the fluctuation of echo signals may be concerned. The noise disturbances arising from the fluctuation of temperatures and echo signals cannot be eliminated without the mean method in consideration of real-time measurement. In the event that low realtime requirements are put forward, the measurement accuracy can be further improved through increasing the length of time-moving window to average the ultrasonic signals and temperatures or slip averaging the measurement results. The measurement performance indicates that the overall model is appropriate for the online measurement of concentrations and capable of modeling dynamic systems. Although it takes long to optimize the model parameters and select the optimal spectral subinterval(s), the detection of the concentrations of substances using the proposed method needs just some simple vector multiplications. Therefore, the online implementation is possible owing to the advantage of short processing time. 4. Conclusion Fig. 10. The predicted concentrations vs. the reference concentrations with the prediction subset at different temperatures.
In this paper, the combination of ultrasonic spectrum and multivariate methods is proposed to simultaneously detect the concentrations of soluble and insoluble substances in an aqueous mixture in the range from 16 to 40 °C. A two-stage architecture is applied for modeling, which compensates the temperature effects and improves the model predictability. The Si-PLS model is proposed to build the sub-models for the concentrations of substances at different temperature points. Then the overall model is constructed to build the relations among the sub-models by linear interpolation, in which the temperature effects are taken into account. The experimental and analytical results show that the overall model has the potential to simultaneously determine the concentrations of substances in aqueous mixtures at different temperatures. The high measurement rates can be achieved and the real-time monitoring of industrial processes can be realized. The proposed method will find wide applications in laboratory and industry for investigation of aqueous mixtures and online process monitoring. Nevertheless, further work is needed to achieve a higher accuracy and realize the online implementation. What’s more, the influences of bubbles may need to be taken into consideration in some industrial applications.
Fig. 11. The results of real-time concentration measurements at different temperatures.
main reasons for the high overall RMSEP value. Hence, the performance of the overall model will be effectively improved by decreasing the interval of the temperature points.
Conflict of interests The authors declare that there is no conflict of interests.
3.4. Online measurement Acknowledgments The online measurement ability of the overall model is evaluated using the prediction subset. In the evaluation process, the ultrasonic signals and temperatures of the samples are real-time acquired with an interval of 1 s after the samples become homogeneous. A time-moving window with a length of 10 s is used to average the ultrasonic signals and temperatures. The phase velocity spectra and the attenuation spectra are calculated and the optimal spectral intervals are selected according to the sub-models dependent on temperature. Afterwards, the concentrations of substances can be calculated through the results of sub-models and Eq. (4). The measurement errors of concentrations of TiO2 and glucose using the prediction subset are less than ± 0.66 wt. % and ± 0.69 wt.% respectively, which meet the general industrial requirements. The online measured concentrations of the mixture composed of 20.18 wt.% TiO2 and 12.56 wt.% glucose in the range from 25 to 30 °C are shown in Fig. 11. The straight solid lines represent the reference concentrations. Fig. 11 shows that more errors are found during the rise of temperature. This may be caused by the time delay of
This research work is supported by Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT13017), and the National Natural Science Foundation of China (Grant No. 51605179). We are grateful to the website http://www. models.kvl.dk/, where we downloaded Si-PLS Matlab codes free of charge. References [1] D. Krause, T. Schöck, M.A. Hussein, T. Becker, Ultrasonic characterization of aqueous solutions with varying sugar and ethanol content using multivariate regression methods, J. Chemom. 25 (2011) 216–223. [2] T.I.J. Goodenough, V.S. Rajendram, S. Meyer, D. Pretre, Detection and quantification of insoluble particles by ultrasound spectroscopy, Ultrasonics 43 (2005) 231–235. [3] G. Locher, B. Sonnleitner, A. Fiechter, On-line measurement in biotechnology: techniques, J. Biotechnol. 25 (1992) 23–53. [4] L. Liu, Application of ultrasound spectroscopy for nanoparticle sizing in high concentration suspensions: a factor analysis on the effects of concentration and
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