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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

In this study, a hybridized neuro-genetic optimization methodology realized by embedding numerical simulations trained artificial neural networks (ANN) into a genetic algorithm (GA) is used to optimize the flow rectification efficiency of the diffuser element for a valveless diaphragm micropump application. A higher efficiency ratio of the diffuser element consequently yields a higher flow rate for the micropump. For that purpose, optimization of the diffuser element is essential to determine the maximum pumping rate that the micropump is able to generate. Numerical simulations are initially carried out using CoventorWare® to analyze the effects of varying parameters such as diffuser angle, Reynolds number and aspect ratio on the volumetric flow rate of the micropump. A limited range of simulation results will then be used to train the neural network via back-propagation algorithm and optimization process commence subsequently by embedding the trained ANN results as a fitness function into GA. The objective of the optimization is to maximize the efficiency ratio of the diffuser element for the range of parameters investigated. The optimized efficiency ratio obtained from the neuro-genetic optimization is 1.38, which is higher than any of the maximum efficiency ratio attained from the overall parametric studies, establishing the superiority of the optimization method.

In recent developments, micropumps utilizing piezoelectric actuation have been commonly employed for directing the fluid purposes especially in BioMEMS and microfluidic systems [

On the other hand, the earliest concept of valveless micropumps incorporating diffuser elements have been developed [

Generally, valveless diffuser micropumps are driven by a piezoelectric element bonded to a flexible diaphragm with no additional moving parts. Application of voltage on the piezoelectric element induces deformation on the diaphragm which creates displacement in the vertical direction (

The working principle of the diffuser elements in a valveless micropump is schematically shown in

Investigation on the effects of the diffuser element on the performance of valveless micropumps have been analyzed previously by simulating the diffuser model either by using commercially available numerical simulation software [

The purpose of this paper will be to present a neuro-genetic methodology to simulate and optimize the performance of the diffuser elements for applications in valveless diaphragm micropumps. The optimization methodology begins by simulating the diffuser model using commercially available numerical simulation software package, CoventorWare® to study the performance of the diffuser element under different working conditions and geometrical parameters. The simulation results obtained will be utilized for training the artificial neural networks (ANN) model.

An artificial neural network (ANN) is based on the working process of human brain in decision making. It is categorized as an artificial intelligence method and has been applied in many different fields such as control [

In order to perform optimization, direct associations between ANN and the optimization tool is required. Genetic algorithm (GA), which is also categorized as an artificial intelligence method, offers compatibility with ANN since GA would be able to find the global optimum in the local parametric search space provided by ANN. In view of that, the trained ANN is embedded as a fitness function into GA where the combined artificial neural network-genetic algorithm; hence the term “neuro-genetic”; will be used in sequence as a tool for search and optimization purposes. GA was the desired optimization techniques as both ANN and GA can be easily modeled and integrated in Matlab® since toolbox for both of these techniques is available as standard. Generally, GA is a robust adaptive search method based on Darwinian principles of natural selection, survival of the fittest and natural genetics. It combines survival of the fittest among string structures with a structured yet randomized information exchange to form a search algorithm with some of the innovative flair of human search [

In this work, the purpose of the neuro-genetic optimization was to find the maximum efficiency ratio of diffuser element based on the diffuser angle, Reynolds number and aspect ratio under the specified working conditions and geometrical parameters of the micropump.

A schematic of the typical diffuser element is shown in

Generally the effectiveness of the diffuser element for applications in valveless micropump is gauged through the flow rectification efficiency. The flow rectification efficiency is the measure of the ability of the pump to direct the flow in one preferential direction and can be defined as the ratio of the micropump net flow rate, _{net}

The pressure loss for the diffuser element at both the diffuser and nozzle direction can be represented in terms of the pressure loss coefficient,

Based on the geometrical relationship and continuity equation of fluid flow, the rate of displaced volume satisfy:

For the same opening angle

Utilizing expression from

The dimensional analysis for the diffuser element using Buckingham ∏ theorem presented by Ahmadian and Mehrabian [

In this work, a simplified model of the valveless micropump has been proposed to evaluate the performance of the diffuser element. The numerical model consists of a supply chamber, an output chamber and a diffuser element as shown in

In order to ease computational demands, only a 2-D simulation of the micropump was carried out. This could be achieved in CoventorWare® by creating only a single element through the thickness of the micropump with mesh refinement at the edges. Tetrahedrons mesh type will be used and mesh sensitivity analysis will be conducted for preliminary simulation to determine the minimum element size required to ensure that the simulation results obtained will be independent of the meshing densities. This could be achieved by refining the mesh until the change in the simulation results is within 1% as shown in

All the simulations use water as the working liquid, thereby limiting the problem to incompressible flow. Actuation pressures ranging from 1 kPa to 20 kPa applied on the supply chamber and fluid flow through the diffuser element will be considered as laminar since the Reynolds numbers is expected at below 500 based on previous studies of the diffuser element [

Simulation results obtained from CoventorWare® simulations will be used to train the ANN model so that the diffuser element efficiency ratio can be predicted for different diffuser angle, Reynolds number and aspect ratio. The artificial neural network used in the present study is shown in

It should be noted that from the range of parameters simulated in CoventorWare®, there will be five sets of data for each category of parameters that will not be used as training inputs to the ANN. This is because simulation data that were not trained will be used instead to verify the accuracy of the ANN results. This is performed by comparing the predicted ANN results to the CoventorWare® simulation results. Once the ANN results are validated, a well trained ANN will be established. At this stage any new sets of values for parameters such as diffuser angle, Reynolds number and aspect ratio that are fed into the ANN model will, upon simulation, generate prediction for the efficiency ratio with high level of accuracy.

After completing the training process, the trained ANN will then be embedded into genetic algorithms (GA) for the search and optimization purpose. Simulation for the GA has been performed using a self-developed code in Matlab® through modification to the Genetic Algorithm Toolbox (GAOT) [

Numerical simulations for both the positive and negative direction of flow for the diffuser element have been conducted using the range of parameters given earlier in

The net flow rate shows the effective fluid volume flowing through the diffuser element in the desired direction (positive direction). From

Similar characteristics can be observed for variations in Reynolds number where there exists an optimized maximum efficiency ratio for a given diffuser angle as shown in

The effect of the diffuser element aspect ratio on the efficiency ratio is given in _{d}

Following results obtained, it can be ascertained that there are distinctive features for the influence of each parameters (diffuser angle, Reynolds number and aspect ratio) on the efficiency ratio of the diffuser element. Since mathematical modeling relating the efficiency ratio to

In order to assess the accuracy of the ANN predictions, validation has been made by comparing results for the efficiency ratio of the untrained numerical simulations with the ANN predictions.

Once a well-trained ANN is found, it is then embedded as a fitness function into genetic algorithms (GA) for optimization purposes. The optimization analysis has been performed to find the maximum efficiency ratio from the range of parameters available for selection in the trained ANN.

For the range of parameters indicated earlier in

The efficiency ratio of the diffuser element has been successfully optimized for valveless diaphragm micropump applications. The optimization process has been realized using a hybridized neuro-genetic optimization methodology by embedding numerical simulations trained artificial neural networks (ANN) into genetic algorithms (GA). The fluid flow behavior through the diffuser element has been initially simulated using CoventorWare® software for different diffuser angles, Reynolds numbers and aspect ratios where results obtained have been used for training the ANN model via the back-propagation method. The trained ANN is a superior tool when utilized to conduct parametric studies where it has been shown that predictions with errors of less than 2% were generated. The trained ANN, combined with GA to form the neuro-genetic tool, predicted that the maximum efficiency ratio is 1.38 for the range of parameters investigated. The predicted efficiency ratio is higher than the maximum efficiency ratio attained from the overall parametric studies, establishing the optimization method superiority.

Working principle of a typical valveless micropump utilizing diffuser element during (a) suction mode (b) supply mode.

Fluid flow in a diffuser element.

Simplified model of the valveless micropump.

Meshed model of the valveless micropump with applied boundary conditions.

Illustration of the artificial neural network model.

Net flow rate at the throat of diffuser element for variation in diffuser angle at different actuation pressure (

Efficiency ratio of the diffuser element for variation in Reynolds number at different diffuser angle (

Efficiency ratio of the diffuser element for variation in aspect ratio at different diffuser angle (Re = 200) at a constant actuation pressure of 10 kPa.

Comparison of efficiency ratio obtained from CoventorWare® simulations with ANN predictions for variations in diffuser angle at different Re numbers.

Maximum efficiency ratio obtained using GA for variations in

Mesh sensitivity analysis for flow at diffuser direction (Diffuser angle = 5°;

^{3}μl/s) |
||||
---|---|---|---|---|

500 | 3921 | 9.9328 | - | 12 |

200 | 6371 | 9.7247 | 2.139912 | 23 |

100 | 7757 | 9.4892 | 2.481769 | 41 |

50 | 13523 | 9.3241 | 1.77068 | 52 |

30 | 55720 | 9.2309 | 1.009652 | 97 |

20 | 85237 | 9.2309 | 0 | 138 |

Range of parameters simulated in CoventorWare®.

Throat width, |
50–100 | 100 |

Diffuser length, |
*Depends upon aspect ratio | 2000 |

Thickness (μm) | – | 150 |

Aspect ratio, |
5–40 | 20 |

Chamber width, |
– | 5000 |

Diffuser angle, |
2–25 | 2, 5, 7, 9, 10 |

Actuation pressure, |
1–20 | 1, 5, 10, 15, 20 |

Architecture of the ANN.

Architecture | Feed-forward |

Training algorithm | Back-propagation |

Transfer function | All logsig |

Hidden layer and neurons | 2 hidden layer with 3 neurons each |

Maximum epoch | 1000 |

Learning rate | 0.000001 |

Sum Square Error (SSE) | 1e–5 |

Crossovers parameters.

Arithmetic | 4 |

Heuristic | [2 3] |

Simple | 4 |

Mutations parameters.

Boundary | 3 |

Multi Non-Uniform | [3 10 1] |

Non-Uniform | [3 10 1] |

Uniform | 3 |

Comparison of efficiency ratio results obtained from CoventorWare® simulations with ANN prediction for different parameters (Basic design values:

θ = 4° | 1.2153 | 1.2197 | 0.358 |

θ = 8° | 1.3236 | 1.3241 | 0.042 |

θ = 12° | 1.2776 | 1.2711 | −0.504 |

θ = 16° | 1.1432 | 1.1345 | −0.766 |

θ = 20° | 1.0172 | 1.0093 | −0.771 |

Re = 100 | 1.1904 | 1.1986 | 0.684 |

Re = 150 | 1.2075 | 1.2096 | 0.174 |

Re = 250 | 1.2553 | 1.2620 | 0.534 |

Re = 300 | 1.2750 | 1.2643 | −0.840 |

Re = 350 | 1.2844 | 1.3016 | 1.340 |

AR = 10 | 1.2135 | 1.2364 | 1.887 |

AR = 15 | 1.2240 | 1.2266 | 0.213 |

AR = 25 | 1.2397 | 1.2512 | 0.928 |

AR = 30 | 1.2390 | 1.2260 | −1.050 |

AR = 35 | 1.2430 | 1.2440 | 0.081 |

Maximum efficiency ratio obtained using GA for different diffuser angle.

100 | 1.290 | 17 |

200 | 1.326 | 9 |

400 | 1.307 | 6 |

Parameters associated with the diffuser element to obtain the highest efficiency ratio.

Diffuser angle, |
8 |

Reynolds number, Re | 240 |

Aspect ratio, |
40 |

| |

Maximum efficiency ratio, |
1.38 |

Five highest efficiency ratios obtained along with the corresponding parameters generated using neuro-genetic optimization.

8 | 220 | 40 | 1.38 |

9 | 220 | 40 | 1.36 |

7 | 220 | 40 | 1.35 |

9 | 200 | 40 | 1.35 |

8 | 210 | 40 | 1.34 |