Ejection state prediction for a pneumatic micro droplet ...

Bulletin of the JSME

Journal of Advanced Mechanical Design, Systems, and ManufacturingVol.14, No.1, 2020

Paper No.19-00268© 2020 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2020jamdsm0001]

Ejection state prediction for a pneumatic micro-droplet

generator by BP neural networks

Fei WANG*, Weijie BAO*，**, Yiwei WANG*，**, Xiaoyi WANG*，***, Keyan REN*, Zhihai WANG*，**

and Jiangeng LI* * Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China

E-mail: [email protected] ** Key Laboratory of Optoelectronics Technology, Beijing University of Technology, Beijing 100124, China

*** Beijing Engineering Research Center for IoT software and Systems, Beijing University of Technology, Beijing 100124, China

Received: 23 May 2019; Revised: 23 October 2019; Accepted: 6 December 2019

1. Introduction

Micro-droplet ejection technology, beside of being used in inkjet printing, is also widely used in many fields such as printed electronics (Raut, et al., 2018), and 3D additive manufacturing (Hoath, 2018). Micro-droplet ejection is related to micro-sample dispensing technique and is used in the field of combinatorial chemistry and biomedicine (Basaran, et al, 2013). In recent years, biological cell printing technology, also based on micro-droplet ejection, shows potentials to solve problems that are difficult in traditional tissue engineering. People have achieved a variety of cell printing by modifying commercially available printers (thermal, piezoelectric, and electrostatic types, etc.) (Gudupati, et al., 2016), but still suffered from cell precipitation, clogging of nozzle, reservoir cleaning difficulties etc. Some companies (Ex. Microfab) have developed piezoelectric micro-droplet generator that are specifically designed for cell printing (Christensen, et al., 2015) Micro-droplet generators based on micro-valves are also widely used for cell printing (Ng, et al., 2017). However, at the nozzle, the bio-ink is impacted repeatedly by a tiny plunger (driven by a solenoid actuator) at high speed, which may cause potential damage to the cells. In our previous experiment, a home-build pneumatic micro-droplet generator (shown in Fig. 1(a)) was tested. Unlike the micro-valve systems, here, the high-speed solenoid valve stays outside of the reservoir, so there is no moving part in contact with the liquid. The high-speed solenoid valve is briefly turned on, and the high-pressure gas enters the reservoir. A pressure pulse P(t) is generated in the reservoir, forcing the liquid out through a nozzle to form a micro-droplet. The pneumatic micro-droplet generator is simple to operate, good for liquids of wide ranges of viscosity (Goghari, et al., 2008) and temperature (Luo, et al., 2012). Initially used for cell printing, it achieved nearly 100% cell viability (Wang, et al., 2018a), making it a potential choice for dispensing cell laden biomedical samples.

1

Abstract

Micro-droplet generation is related to liquid dispensing technology that has potential applications in many fields.

Specifically, pneumatic micro-droplet generation is controlled by a solenoid valve being briefly turned on, so

that high pressure gas enters the liquid reservoir, forming a gas pressure pulse waveform , forcing the liquid

out through a tiny nozzle to form a micro-droplet. For each ejection, is acquired by a high speed pressure

sensor, and the ejection state is obtained by machine vision methods. A prediction model based on BP neural

network is established, with as input and the droplet ejection state as output. Experiments show that the BP

neural network can predict the number of droplets with an accuracy higher than 99%. It is also shown that the

BP neural network can improve the prediction accuracy for the position of droplets relative to the nozzle, at a

given moment. Under typical working conditions, is not consistent. As a result, the ejection state is not

consistent either. These prediction models may be used for real time monitoring and control of the pneumatic

micro-droplet generator.

Keywords : Micro-droplet, Pneumatic, BP neural network, Ejection state, Machine vision

2© 2020 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2020jamdsm0001]

Fei Wang, Bao, Yiwei Wang, Xiaoyi Wang, Ren, Zhihai Wang and Li, Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.14, No.1 (2020)

For commercial printers, inks are uniform and stable. Therefore, the printing parameters can be fixed; and the ejection

state is highly consistent over a long period of time. But for the pneumatic micro-droplet generator, as will be described

later, the pressure pulse waveform is far from being consistent. Therefore, for each pressure pulse, the state the

droplet ejection (including number of droplets, break time and position of the liquid flow, initial speed of the droplet,

etc.) is not consistent either. In addition, for many situations, the ink is non-standard and its flow properties may even

change over time, making the situation more complex (For example, biological cells contained in the bio-ink tends to

precipitate, leading to changes of ink composition and its flow properties. As another example, sodium alginate, a popular

bio-ink material, may slowly react with calcium ions in the ink, resulting in changes of flow properties over time.).

Therefore, real-time monitoring and control of the micro-droplet ejection is necessary.

Pneumatic micro-droplet ejection is a complex multi-phase flow process driven by the pressure pulse . And the

formation of the droplet needs considering instability caused by the surface tension effects (Eggers, et al., 2008).

Theoretically, it is necessary to solve the Navier-Stokes equation and the level set (or phase field) equation in

combination. Although the finite element method can give a result, the simulation process is time-consuming, and its

reliability still need to be verified. High speed photography is the most direct and effective method to study the process

of micro-droplet ejection (Pongrác, et al., 2014). But the experimental equipment is expensive, and real-time processing

of a large amount of images is not so realistic. Optical measurements, such as light scattering, can achieve high-speed

measurement of some geometrical parameters (such as the droplet diameter) (Gao, et al.,2016) , but the system needs to

work in the dark, which limits its practicability. A predictive model through some readily available experimental data

may be helpful in solving the problem. With the development of machine learning, some scholars have begun to apply it

to the studies of complex fluids. A machine learning algorithm is used to construct a complex relationship between flow

/ energy distributions and driving / boundary conditions, for the flow field monitoring around the boundary layer (Debien,

et al., 2016). In the field of micro-droplet generation, a neural network was used to predict the droplet sizes in a

microfluidic system (Mahdi, et al., 2016). Recently, machine learning was applied to drop-on-demand systems for

optimizing their operation parameters (Wang, et al. 2018b; Shi, et al., 2018). In both works, neural networks are used to

established corresponding relation among main operation parameters (including voltage amplitude and pulse width),

liquid parameters (viscosity and surface tension) and ejection parameters (number of droplet etc.). For the pneumatic

ejection, as will be described later, the opening and closing of the high speed solenoid valve shows large inconsistency,

especially for ejection at higher rate. Therefore, even with operation parameters fixed, the ejection may still be quite

different. As the pressure pulse waveform in the reservoir is more directly related to the droplet ejection state, it is

proposed in this paper to use deep neural network training to obtain a nonlinear prediction model with as the input

and the characteristics of the ejection state as the output (Bengio, et al. ,2016).

Fig. 1 (a) photo of the home-build pneumatic micro-droplet generator, (b) Schematic representation of a pneumatic micro-

droplet generator. It consist of a reservoir (1), a nozzle (2), a high speed solenoid valve (3), a pressure regulator (4),

a T-joint (5), a venting tube (6). The micro-droplet ejection is monitored by a camera (7) with LED illumination (8).

The gas pressure in the reservoir is monitored by a high speed pressure sensor (9). The micro-droplet ejection and

monitoring are automatically operated by a controller (10).

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The pressure pulse waveform can be collected in real time and can be analyzed quickly. The establishment of

such prediction model may have two potential applications. Firstly, by direct predicting the ejection state through the

pressure waveform, it can replace the machine vision based monitoring method to some extent. Secondly, failure of the

prediction model may be a more sensitive indication that the flow properties of the ink have changed.

2. Pneumatic micro-droplet generator and its working principles

Referring to the previous literature (Cheng, et al., 2003), the home-build pneumatic micro-droplet generator is shown

schematically in Fig. 1(b). The setup includes a micro-droplet ejection system and an attached monitoring module. The

ejection system includes a liquid reservoir, a nozzle, a high-speed solenoid valve, a pressure regulator, and air path

(mainly, a venting tube and a T-joint); the monitoring module includes an industrial CCD Camera with LED illumination

for machine vision monitoring, and a high-speed pressure sensor for monitoring the gas pressure in the reservoir. Both

the ejection system and the monitoring module are operated automatically by a controller.

2.1 The Generation of Pressure Pulse P(t) in the Reservoir

The generation of the pressure pulse in the reservoir may be understood by making an electro-acoustic analogy

(Kinsler, et al., 1999). Specifically, the pressure in the reservoir in Fig. 2(a) and the voltage across the capacitor in the

RLC circuit shown in Fig. 2(b) satisfy the same differential equation, where capacitance, inductance, and electric

resistance are the electric counterparts for compliance, inertance, and acoustic resistance. The ideal switch in series of a

resistance is equivalent to the solenoid valve, the constant voltage source corresponds to the constant pressure at the

front end of the solenoid valve. The values in Fig. 2(b) are estimated compliance, inertance, and acoustic resistance in SI

units. In the equivalent electric circuit, when the switch is turned on, the voltage source charges the capacitor that is

shunted by the inductor and the resistor. After the switch is turned off, the capacitor is discharged through the inductor

and the resistor. Through a simulation (via Multisim) of the charging and discharging process, the voltage across the

capacitance, or equivalently the pressure inside the reservoir is calculated.

Fig. 2 (a) the micro-droplet generator comprising mainly the solenoid valve, the reservoir, and the venting tube, where “V”

is the volume of gas (volume above the liquid). (b): acoustic-electric analogy, in which compliance corresponds to

capacitance, inertance corresponds to inductance, acoustic resistance corresponds to electric resistance. The ideal

switch in series with an electric resistance is equivalent to the solenoid valve, the constant voltage source corresponds

to the constant pressure at the front end of the solenoid valve. (c) and (d) are measured and simulated , where

the solenoid valve is kept “ON” for 10 ms.

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By comparing the actual pressure waveform with the simulation result, as shown respectively in Fig. 2(c) and (d),

the effectiveness of the electro-acoustic analogy model is verified. Based on the above analysis, ∆t, as marked in Fig.

2(c) and (d), is roughly the period of time that the solenoid valve is “ON”. The amplitude of the waveform is largely

determined by . The pressure oscillation is associated with the well-known Helmholtz cavity, with its frequency

determined by the volume of gas in the reservoir (“V” in Fig. 2(a)), and the geometry of the venting tube, and has been

discussed in many literatures. Fluctuation of the and is very obvious in practical experiments. Meanwhile, the

geometry of the Helmholtz cavity changes versus shift of liquid level in the reservoir.

2.2. Measuring Pressure Pulse Waveform P(t) in the Reservoir

A high-speed pressure sensor (acquisition frequency 1MHz, measuring range -20kPa~+20kPa) is used to collect the

gas pressure waveform in the reservoir. A virtual oscilloscope (sampling frequency 25kHz) simultaneously

acquires the analog output signal of the pressure sensor and a synchronization signal generated by the controller. The

rising edge of the synchronization signal is used as trigger for the high speed solenoid valve. Fig. 3(a) shows the GUI of

the virtual oscilloscope, where both the pressure waveform (upper curve) and the synchronization signal (lower

curve) are displayed.

Starting from the rising edge of the synchronization signal, corresponding pressure waveform is recorded as ,

at 256 discrete moments (i = 0 - 255, or 0 - 10.2 ms). After that, the pressure is negligibly small. By smoothing, high

quality pressure waveform data are obtained. Figure 3(b) shows the pressure waveforms of two measurements for the

same operation parameters. Although they look similar, the distance between the generated droplet and the nozzle at

certain delay (defined as in Fig. 4) is not consistent. The vertical solid line in the graph will be described latter.

2.3. Machine-vision Based Ejection State Monitoring

The machine vision monitoring uses a monochromatic industrial CCD camera (Daheng Optoelectronics, Model

MER-125-30UM) with a resolution of . For the imaging optics, a Navitar 6.5× zoom lenses (magnification of

0.7 - 4.5×) is used. As the information obtained from the machine vision method is sensitive to the magnification, the

imaging system is always calibrated based on the fact that the outer diameter of the nozzle is 600 μm. In the rest of this

paper, one pixel corresponds to 20 μm. The camera is triggered relative to the synchronization signal, via a delay function.

Therefore, the acquired pressure waveforms are in one-to-one correspondence with the captured droplet images.

The image processing is shown in Fig. 4. Usually, the nozzle and droplet only occupy a small region of the whole

image. Therefore, the region of interest (ROI) of the original image is specified first to improve image processing

efficiency (as in Fig. 4(a)). In the second step, binarization of the ROI is performed by ultilizing an automatic threshold

segmentation method (Otsu algorithm) for grayscale images (as in Fig. 4(b)). Due to refraction effect, there is tiny dark

Fig. 3 (a) the pressure waveform, together with the synchronization signal, acquired by a virtual oscilloscope (b) two

truncated pressure waveforms (after smoothing). The generated droplets shows different (displacement of

droplet relative to the nozzle at certain delay, see Fig.4), 133 pixels (red) and 196 pixels (black) respectively.

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region within the droplet. For not to affect the subsequent extraction of the droplet information, in the 3rd step, an image

filling algorithm may be used to have the dark region removed, as shown in Fig. 4(c). The complete droplet area is then

labeled by a connected region analysis. On this basis, the number 𝑁𝑑 of droplets, and the geometrical parameters of

each droplet, including the centroid coordinates ( ), the size of the droplet, are obtained, shown in Fig. 4(d).

Typical size of the droplet is 40 pixel (800 μm ) in diameter. With the coordinate of the droplet, 𝐻𝑑 is defined as its

displacement relative to the nozzle, also shown in the figure.

3. Prediction of ejection state from pressure waveform P(t) via BP neural networks

3.1. Micro-droplet Experiment and the Taking of the “Big Data”

The ejection experiment is performed with DI water, using a 300 μm internal diameter nozzle, with ejection frequency

set to 20 Hz. A rather diverse set of ejection parameters are used. Specifically, varies in the range of 1.5 - 3 ms;

solenoid valve front end pressure 𝑃0 is tuned in the range of 40 - 60 kPa. The liquid level changes during the experiment,

so the oscillation period, as seen in Fig. 2(c) and (d), varies from 3 to 4 ms. This produces rich varieties of pressure pulse

waveforms and the corresponding ejection states, serving as the “Big Data” for training of the neural networks.

Each sample of database consists of a waveform, as well as parameters for characterizing the ejection state.

In this paper, two parameters are taken, the number of the droplets ejected, referred as ; the location of the droplet

relative to the nozzle at a given moment, referred as 𝐻𝑑 . It is found that the droplets appear 3 - 4 ms after the

synchronization signal. After detached from the nozzle, the droplet should not be affected much by . Based on this

prior knowledge, valid portion of can be reduced to < 4.7 ms (or < 119), the region on the left side of the

solid line in Fig. 3(b).

The data should be normalized in favor of numerically stable training for the neural networks. Traditionally, the

samples of pressure are normalized independently, as shown by Eq. (1), where s is the sample number, and is the

infinity norm operator.

(1)

However, since the magnitude of the press plays a key role in the generation of the droplets, we should preserve this

information by normalizing the samples globally, which is shown by Eq. (2).

(2)

For data such as droplet number 𝑁𝑑 and location 𝐻𝑑, the normalization is done via the following Eq. (3)

(3)

Fig. 4 Machine vision processing steps for acquiring the micro-droplet ejection states, including positions, sizes, and

numbers of the micro-droplets.

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It should be mentioned that, the output of the neural network need to be de-normalized to produce the final prediction.

3.2. Principle of BP Neural Network

Neurons, the basic units of human brain, form network, where each neuron takes combined signals from some

neurons, and produces an output for some other neurons. An artificial neural network replicates this by having layers of

nodes, with each connected to nodes in the preceding and subsequent layers. The first layer of nodes is the input layer,

simply for taking input signals. For each node in the hidden layers and output layer, as shown in Fig. 5(b), the combined

input is from the nodes in the preceding layer, moderated by link weights that represent possible damping effects

associated with signal transmission between neurons. Then a node bias and an activation function, which mimic threshold

behavior of the neuron, are applied to generate the final output of that node. A neural network with only one hidden layer

is shown in Fig. 5(a). Typically, it is the link weights and node biases that are iteratively refined to give a better and better

neural network.

The BP neural network is a multi-layer feed-forward network trained by the error back propagation algorithm. Its

learning rule is to use the gradient descent method to continuously adjust the link weights and node biases by back

propagation so that the squared error sum between the actual output and the expected output of the neural network is the

smallest. BP neural network has self-learning, self-organization, self-adaptive ability and strong nonlinear mapping

ability, and is often applied to the study of non-deterministic problems with complex causality. Therefore, we use BP

neural network to construct the relationship between the pressure waveform and the droplet ejection state.

3.3. Predicting the Number of Droplets from P(t) Via BP Neural Networks

The number of droplets generated by each ejection is an important parameter. For predicting from , BP

neural networks with one hidden layer are used. There are 120 nodes in the input layer, and one node in the output layer.

The activation functions of the hidden layer and output layer nodes are the “tansig” function.

Fig. 5 (a) A neural network with one hidden layer. The output layer has only one node. The input layer nodes are only for

taking input signals. (b) For the nodes in the hidden layer and the output layer, the combined input is from the nodes

in the preceding layer, moderated by link weights. The combined input is biased, and then a “tansig” activation

function is applied.

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Our database consists of 10000 samples, with either none, one droplet, or two droplets per ejection. 80% of the

samples were randomly selected as the training set, and the remaining 20% of the samples are left for testing. Fig. 6(a)

shows the predicted droplet number for a neural network with only one node in the hidden layer ( ). To get the

number of droplets, the predicted values need to be rounded off to integers. The prediction is 97.8% correct. For the

network that has two nodes in the hidden layer , the prediction is 99.9% correct, even without performing a

round-off, quite different from the case. Similar prediction accuracy is also realized for larger than two,

as shown in Table 1.

Further studies are conducted on the neural network with . As shown in Table 2, for the three ejection states

(with 0, 1, or 2 droplets), the outputs of the two hidden layer nodes are displayed. For the node in the output layer, its

link weights with the two hidden layer nodes are 1.93 and -4.01 respectively, and its node bias is 2.08. Therefore, the

combined input and hence the output of this node can be calculated. Finally, the predicted number of droplets is obtained

by so-called de-normalization.

Although with “tansig” activation function, the outputs of these hidden layer nodes have only two options, 1 and -1.

Therefore, for the output layer node, there are options of input, hence options of output. In this experiment,

there are only 3 categories of ejection states (0 droplet, 1 droplet, and 2 droplets), which can be well represented by those

options as long as It makes sense that (under the condition of ) the prediction can be accurate even

before round-off to integers.

0 500 1000 1500 2000

0

1

2

(a)

num

ber

of

dro

ple

ts

test set0 500 1000 1500 2000

0

1

2

num

ber

of

dro

ple

ts

test set

(b)

Fig. 6 Prediction of droplet number for a test set (with 2000 samples). (a) neural network with only one hidden layer node,

and (b) neural network with two hidden layer nodes. The blue circle represents the actual number of the droplets,

and the red dot represents the predicted value of the neural network (before round-off to integers). The neural

networks are trained with a training set of 8000 samples.

Table 1 Statistics of prediction for the droplet number per ejection, by neural networks of

different .

Number of Nodes in

the Hidden Layer

(𝒏𝑯)

Statistics of Prediction Results

Correct Prediction Total number of

samples tested Accuracy

1 1956 2000 97.8%

2 1999 2000 99.95%

3 1999 2000 99.95%

4 1998 2000 99.9%

5 1999 2000 99.95%

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3.4. Predicting the droplet location from P(t) via BP neural networks

As described earlier, the pressure waveforms are inconsistent. Therefore, at a given moment (delayed relative to the

synchronization signal, see Fig. 3), the distance 𝐻𝑑 between the generated droplet and the nozzle distributes in a wide

range. In this paper, we focus on the situation of single droplet per ejection. It should be pointed out that 𝐻𝑑 is not the

most suitable parameter to characterize an ejection state, because it is collectively determined by break time and position

of the liquid flow, as well as initial velocity of the droplet. However, measurement of those physical quantities needs

ultrahigh-speed photography and image processing, so is prohibitively expensive. The parameter 𝐻𝑑 becomes the easily

available alternative.

Our database consists of 3000 samples, all with one droplet per ejection. The training set takes 70% of the total

samples (the rest of samples are left for testing). A straightforward and reasonable prediction of 𝐻𝑑 for the test set is the

statistical average of 𝐻𝑑 data for the training set, referred as 𝐻𝑑̅̅ ̅̅ . The prediction errors are shown as blue circles in Fig.

7. And the standard error of predictions reaches 30 pixels.

0 200 400 600-70

-35

0

35

70

Err

or

(pix

el)

test set

Table 2 For the three ejection states (with 0, 1, or 2 droplets), the outputs of the two hidden

layer nodes, the input and output of the output layer node, and the predicted droplet numbers

(before round-off), are displayed.

Target Number of Droplets per Ejection

0 droplet 1 droplet 2 droplets

Outputs of the

Hidden Layer Nodes

Node 1 -1 1 1

Node 2 1 1 -1

Input to the Output Layer Node -3.851 0 8.0128

Output of the Output Layer Node -1 0 1

Predicted Droplet Number (After De-

normalization) 0 1 2

Fig. 7 Prediction errors of droplet positions (relative to the nozzle), by two methods, which are taking statistical average

of droplet positions (blue circles), and using BP neural networks (red stars). The prediction errors are measured in

pixel.

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For predicting from , BP neural networks with one hidden layer are used. There are 120 nodes in the input

layer. There is one node in the output layer because 𝐻𝑑 is the only output. The activation functions of the hidden layer

and output layer nodes are the “tansig” function. As shown in Fig. 7, the red dots indicate the prediction errors based on

waveforms via a neural network with 5 nodes in the hidden layer ( ). It can be seen from the Figure, and

also from Table 3 (see next paragraph) that the neural network improves the prediction accuracy by nearly 3 times

compared with the prediction based on statistical average. Typical neural network performance is shown in Fig. 8.

For networks with different 𝑛𝐻, two groups of training and testing are conducted. In the first group, training set

accounts for 70% of the total samples, and is used to roughly determine the optimal . The standard error of prediction

decreases with 𝑛𝐻, and tends to be stable for 𝑛𝐻 larger than 5. For the second group, the training set accounts for 30%

of the total samples. The comparison of the two groups indicates the neural network prediction model possesses good

generalization ability.

The time domain waveform can be reasonably converted into its spectrum , in the frequency domain.

It is instructive to establish a prediction model for 𝐻𝑑, but with as inputs. A similar BP neural network with one

hidden layer is used. for a typical pressure waveform is shown in Fig. 9. is negligibly small with 𝑖 > 19.

Fig. 8 Typical neural network performance. Specifically in this figure, the best validation performance is 0.028791 at

epoch 17.

Fig. 9 Discrete Fourier transformation (DFT) of a typical , where = , = 0 - 119. The transformation is

performed using FFT technique. Only the amplitude of the DFT is shown in the Figure. The inset shows

the same data of low frequency region.

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So for the first trial, to be safe, the input layer takes the lowest 20 frequency components of . Significantly

improved prediction accuracy, similar to that shown in Fig. 7 is obtained.

Then, as shown in Table 4, BP neural networks with different are examined in two groups of training and testing.

Similar to what we have done earlier, in the first group, the training set accounts for 70% of the total samples, which is

used to roughly determine the optimal . The standard error of the prediction decreases on increasing , reaches the

minimum at = 5. Keep increasing leads to gradual and minor deterioration of prediction accuracy. In the second

group, the training set accounts for 30% of the total samples. Comparison of results from these two groups indicates the

prediction model has good generalization ability.

The neural networks with a hidden layer of 5 nodes will be used for the rest of the paper. Our next goal is to determine

which frequency components are decisive for the prediction of . As shown in Table 5, selected are taken as

inputs to the neural network. Two sets of experiments are carried out, all with the training set accounting for 70% of the

total samples. In the first set, shown in the left part of Table 5, the high frequency components are gradually deleted from

the inputs of the neural network. It is shown that the prediction error is rather small as long as the lowest four frequency

components ( ) are kept as inputs. Drop-off of more low frequency components leads to abrupt increasing

of prediction error.

Table 3 Standard errors of predictions based on neural networks, with as inputs.

Networks with different numbers of hidden layer nodes are examined in two groups of

experiments, with the training sets take 70% and 30% of total samples, respectively.

Number of Hidden Layer

Nodes ( )

Standard Error (in pixel) of the Prediction

70% training set 30% training set

1 12.71 12.78

2 11.75 12.44

3 11.45 12.02

4 11.13 11.49

5 10.79 11.49

6 10.99 11.48

7 10.91 11.65

8 10.61 11.40

9 10.91 11.40

10 10.90 11.57

Table 4 Standard errors of predictions based on neural networks, with as inputs.

Networks with different numbers of hidden layer nodes are examined in two groups of

experiments.

Number of Hidden Layer

Nodes ( )

Standard Error (in pixel) of the Prediction

70% training set 30% training set

1 11.86 12.84

2 11.56 11.71

3 11.07 11.65

4 10.89 11.43

5 10.57 11.35

6 10.84 11.27

7 10.76 11.25

8 10.71 11.48

9 11.00 11.41

10 11.15 11.23

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For the second set of experiments, shown in the right side of Table 5, the prediction accuracy gets worse rapidly as

the lowest frequency components are gradually removed from the neural network. The results of these two sets of

experiments are mutually corroborated. That the lower frequency components are more relevant to is also consistent

with our common knowledge of spectra for acoustic signals. In particular, represents the DC component of the

pressure waveform, which is relevant to the speed at which the liquid is extruded. Therefore, it is not surprised that

should be included for good prediction of . Although not shown here, simulation based on finite element

method (COMSOL 5.3) also shows that the impact of high frequency components (higher than ) on 𝐻𝑑 can be

ignored. In addition, for completeness, standard errors for prediction models based on 1-3 and 2-3 frequency components

are also presented in Table 5.

The pressure waveforms corresponding to different number of droplets are usually quite different in shape. Therefore,

predicting the number of droplets by the pressure waveforms is more like to demonstrate that the BP neural network can

be applied to such nonlinear ejection process. In contrast, the technique of predicting by pressure waveform may

have more practical applications. As described earlier, in biomedical applications, detection of fluid property change is

highly expecting. Taking the viscosity change as an example, as a demonstration of this scheme, glycerin water mixture

is used for different viscosity. Under the same operation parameters ( and ), a data set is collected using 8% glycerin

concentration solution. The BP neural network prediction model and the vision based model are established and

tested (80% of this data set is for training and 20% for testing). The left side of Fig. 10 shows the prediction errors, and

a standard error is obtained, similar to those shown in figure 7 and table 3. Then, glycerin concentration is reduced to

6%, 4% and 2%, the ejection states are collected and used as test data sets. With the operation parameters fixed, it is

found that 𝐻𝑑 increases with the decrease of viscosity (glycerin concentration). The prediction error will get larger for

Table 5 Standard errors of for the neural network prediction, where different frequency

components of spectrum are taken as inputs.

components

(taken as inputs)

Standard

Error

components

(taken as inputs)

Standard

Error

components

(taken as inputs)

Standard

Error

0~19 10.57 0~19 10.57 1~3 13.58

0~9 10.78 1~19 13.65 2~3 15.72

0~4 10.89 2~19 15.68

0~3 10.86 3~19 16.10

0~2 11.65 4~19 17.27

0~1 13.32 9~19 20.58

0 25.42

Fig. 10 Prediction errors of vision based method ( ) in blue and BP neural network model in red, measured for several

glycerin water solutions (with glycerin concentration marked). Both prediction models are obtained, based on the

training data set taken with 8% glycerin solution. The dashed line for each figure defines the region of ,

where σ is standard error, derived from the test data set, also taken with 8% glycerin solution.

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both prediction models, shown in Fig. 10. Once the prediction error (after 10-point moving average) is greater than ,

it is determined that the viscosity of the liquid has changed. Compared with the vision based prediction model, the

standard error σ of the BP neural network prediction model is much smaller. Therefore, based on the above criterion,

failure of the BP neural network model is a more sensitive indication of viscosity change.

4. Conclusions

In summary, prediction of ejection states for a pneumatic micro-droplet generator based on measured pressure

waveform in the reservoir is realized through BP neural networks. The number of droplets , and the position

of droplet (at a certain delay time relative to the synchronization signal) 𝐻𝑑 are important parameters for evaluating the

ejection states. In the first study, a model with two or more nodes in the hidden layer can predict with an accuracy

as high as 99%. In the second study, compared with the prediction solely from statistical average, a neural network

with 5 nodes in the hidden layer, reduces the standard error of the prediction by a factor of 3. The inputs of the neural

network can be the pressure waveform (in the time domain), or this spectrum (in the frequency domain). These prediction

methods based on BP neural networks may be in the future used for monitoring and controlling of the pneumatic micro-

droplet generator.

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