The computer simulation of the membrane bioreactor MBR has become the research focus of the MBR simulation. In order to compensate for the defects, for example, long test period, high cost, invisible equipment seal, and so forth, on the basis of conducting indepth study of the mathematical model of the MBR, combining with neural network theory, this paper proposed a threedimensional simulation system for MBR wastewater treatment, with fast speed, high efficiency, and good visualization. The system is researched and developed with the hybrid programming of VC++ programming language and OpenGL, with a multifactor linear regression model of affecting MBR membrane fluxes based on neural network, applying modeling method of integer instead of float and quad tree recursion. The experiments show that the threedimensional simulation system, using the above models and methods, has the inspiration and reference for the future research and application of the MBR simulation technology.
The MBR simulation is a simulation of the MBR water treatment process and is a system used for special engineering and researchers. It belongs to the visual simulation, is also a dynamic simulation, and uses visualization techniques to simulate the MBR water treatment process. Because of using the visual model designed by OpenGL technology to replace physical prototype, it greatly reduces the cost, improves the efficiency of research, makes security get a good guarantee, and improves the ability of facing customers and the market.
The building of visual simulation system of MBR emulator uses the OpenGL graphics standards that are designed in accordance with the computer graphic technology and graphics principle. OpenGL technology system complies with the visual and optical principles necessary for system development. OpenGL technology has many advantages and is very suitable for the visual design of the MBR simulation system. OpenGL also has light processing technology, puts the parameters, the distance of light source and vertex, the light to the vertex and the direction vector of the vertex to the viewpoint, and so forth, into optical model, and calculates the color of each vertex, and can express the 3D optical properties of the objects through the whole lighting model. So the color of the visual simulation graphics shows the spatial relationship between the object and the viewpoint and light sources and demonstrates a strong sense of three dimensions in the visual features.
This paper conducts the research of MBR water treatment process by combining numerical simulative computing and the method of visualization in scientific computing. It realized the onepiece conversion from simulative computing to computer visual graphics, eliminated the lengthy middle of the data processing, and observed the distribution, variation, and objective laws of the device fastly and intuitively. At the same time, it helps to understand the specific details of the water treatment, improve processing efficiency, and thus provide a reference and basis for the design, improvement, and optimization of the MBR. This paper will discuss it by two aspects, the data modeling and visualization realized.
The test of this paper mainly inspects pollution load, pollutant removal, the performance of sludge sedimentation, organics removal, and so forth, all of which impact membrane fouling of the reactor. Thus, its feedback pollution situation through threedimensional simulation of the MBR and measures through the membrane fouling index
Known by the membrane fouling of the filter model, the initial states
The set of the final membrane fluxes is determined by many factors, so we will discuss and research it later in this paper.
Collecting actual operating data is the basis of establishing the mathematical model of the MBR. To collect relevant data, it is necessary to clear the quantitative relationship between the various elements, also observe and analyse systematically for the research problems, and summarize the goal of the decision and the restrictions of all the aspects of decision making.
For the collection of field data, this paper extracts the required data sources by using the field test data based on the MBR system, as Table
Data table of the collected fluxes, pressure, and so forth.
Time  Temperature  Pressure  MLSS of inflow  MLSS of outflow  Total resistance  Fluxes 

(h)  ( 
(MPa)  (mg/L)  (mg/L)  ( 
( 
1  24  0.016  343.38  70.48  0.185  46.4 
2  24  0.0168  378.15  83.87  0.2403  45.5 
3  24  0.0175  392.42  87.06  0.2989  45.3 
4  24  0.0243  472.43  85.63  0.3796  42.2 
5  24  0.0268  483.73  59.62  0.3957  45.1 
6  24  0.0291  583.16  95.05  0.441  42.2 
7  24  0.0325  556.43  85.46  0.5119  39.7 
8  24  0.0362  503.56  71.91  0.6075  37.3 
9  24  0.0351  591.41  105.46  0.7143  31.4 
10  24  0.0385  561.85  107.63  0.8421  28.9 
11  24  0.0269  612.42  107.95  0.7623  21.7 
12  24  0.0226  655.47  81.61  0.9737  14.5 
13  24  0.0198  712.43  103.98  1.1659  11.2 
14  24  0.0193  615.12  91.01  1.2911  10.5 
15  24  0.0187  715.89  95.52  1.254  9.4 
It can be seen from the data of Table
The data contrast diagram of total resistance and membrane fluxes.
The data contrast diagram of pressure and membrane fluxes.
The data contrast diagram of MLSS of inflow and membrane fluxes.
For MBR simulation system, the establishment of an appropriate mathematically experimental model can evaluate and simulate the existing system. Through the simulation system, we can find problems in time, adjust the system’s parameters, and get a more stable and reasonable treatment effect. We can also guide the design of the new system, so that researchers can design the reactor more reasonably and scientifically.
Mathematical modeling is a complex process. For the relationship between the total drag and membrane fluxes, we can see the inverse relationship in Figure
There are many other factors affecting the membrane fluxes, in addition to including the resistance. In the previous research, we have established the mathematical model between COD and MLSS. In order to be closer to the actual simulation environment, on the basis of that, this paper studies the mathematical model between multiple factors, such as pressure difference, and MLSS and membrane resistance. Through the mathematical model between the many factors and the membrane resistance, we finally establish the mathematically experimental model between multifactor and membrane fouling indexes.
The relationship between the important parameters such as pressure difference, time, and MLSS and the total resistance of the membrane is complex and not a simple linear relationship. At the beginning of establishing mathematical model, we try to use only a single multiple linear regression to establish a simple relationship between the parameters and use it to analyze the relationship between the factors. Through discussing, researching, and testing the model established, we found that a single multiple linear regression is the sensitivity of the parameters, and the model of parameters is easy to deform for the abnormality of a parameter, and the model also has small tolerance for the new parameters. So a single multiple linear regression model is only applicable in the test conditions of the stable parameters and the small environmental changes, that is, lacking close to actual simulation environment research. So after reading a large portion of literature and researching the actual MBR processing environment, this paper proposes a multiple linear regression experimental model based on neural network, suited for MBR sewage treatment environment.
According to the charts in Section
Neural network (NN) [
The structure of neural network.
As shown in Figure
According to the neural network theory, combined with the characteristics of impacting membrane factors, this paper presents a kind of neural network system suitable for MBR, and the factor affecting the membrane is called neural factors unit, as shown in Figure
The structure of neural network of impacting MBR factors.
As Figure
For the structure diagram of MBR neural network, the output layer, namely, the final membrane flux, is the combined effect of the various flux of the hidden layer. Setting the total membrane fluxes, it can be shown specifically by the following formula:
The membrane flux
Viscosity values
According to the experimental studies, after excepting the known effect of the factors for membrane flux, the effect of the unknown relationships of the factors for membrane flux is small but cannot been ignored. So for the small part, we try to establish mathematical model with simple methods, and this paper uses the multiple linear to establish the relationship between them. This paper uses the knowledge based on neural network to solve the multiple factors. It is not only to ensure the independent effects of the various factors for membrane fluxes, but also not to neglect the common effects of the factors for membrane fluxes. So this model will be more close to realistic simulation environment.
The uncertainty of the effect of various factors for membrane fluxes increases the difficulty of building model. Since the regression equation based on multiply linear is easy to fluctuate with changing the single factor, it is very suitable for the processing environment to change very little like the MBR reactor in a short time. To establish multiple linear regression equation is a process to estimate multifactor linear model and seek the estimator. Similar to a linear regression analysis, the basic idea of that is also based on the principle of the least square, solving the multicoefficient to make the residual sum of squares observations
The normal equations of (
If coefficient matrix of (
The structure matrix of the multiple linear regression model of the data of that formula is
So, (
If the determinant of
These are regression coefficients of the multiple linear regression equations. As (
Among this,
Putting (
Among this,
Equations (
Therefore, the coefficient of the multiple linear regression equation can first solve
We put the regression equation of membrane fluxes between the multiple factors that is solved into the index equation of the membrane fouling. Then,
Here, the mathematically experimental model of the MBR membrane fouling index has been built.
This subject is based on VC++ 6.0 and OpenGL, combines the realtime processing of the data of the MBR simulation system with the threedimensional graphics processing module, and conducts the realtime threedimensional solid model and data generated.
It is a good support for OpenGL in the Windows operating system, which makes developing OpenGL applications become more simple and fast by using the VC++ 6.0 or the Visual C++ of other versions, such as VS2005 and others in Windows system [
It needs to establish the interface application [
After related parameters are set, in order to meet the special needs of the OpenGL pixel format, we need to reset the pixel format of the drawing window. Here, we declare a structure variable Pixelformatdescriptor and make the structure variable support OpenGL and the color mode of it, but we also need to set appropriately some structural members. Then, we use the structure variable as parameter to call function ChoosePixelFormat(), so as to allocate a number pixel formats. Then we call SetPixelFormat() to set the number of pixel formats allocated to the current pixel format. After reseting the pixel format, the next step is to establish the coloring scene for OpenGL. The role of the coloring scene is equivalent to the scene of the device in Windows and is similar to the equipment scene. Only after setting the coloring scene, OpenGL can call the drawing statement by itself to draw graphics in Windows.
Win32API provides several scene functions operating coloring with the prefix wgl, including wglCreateContext(), wglDeleteContext(), wglGetCurrentContent(), wglGetCurrentDC(), and wglDeleteContent(). What we need to know is that the coloring scene has set thread for unit. Namely, in order to execute statements of the drawing function of the coloring scene in OpenGL, each drawing thread must use a coloring scene as the scene coloring scene. In these functions of the coloring scene, wglCreateContext() is the function established by the coloring scene, with a handle of the device scene as its parameter and returning a handle of the coloring scene linking with the handle of the equipment scene. Then we call the function wglMakeCurrent() with these two handle as parameters, which makes the coloring scene as the coloring scene used by the current thread. Then, it is built the application programming interface of the VC++ 6.0 and OpenGL in Windows.
In the virtual system of the MBR simulation, the MBR water treatment is the most important part of the simulation and also the researching focus of this subject. Through providing these advanced features of the OpenGL for the MBR mathematical model that has been established, including modeling, coordinate transformation, coloring, light, and smooth of the twodimensional and threedimensional graphics functions and texture mapping and NURBS curve, the virtual model of the MBR simulation can generate the threedimensional simulation scene of the MBR and draw threedimensional objects [
The synthesis method is the basic method of building a virtual model in OpenGL. Using OpenGL to draw the threedimensional entity model is the same with other entity models, and they all are synthesized through the simple rule and have three cases as follows.
The synthesis of the rule entity, such as the design of the rule entity of shape model of the MBR reactor, can simply use the spatial geometry provided by the OpenGL, such as the combination of cylinder, the cone, and the sphere. Then changing the size and location of these spatial geometries, through adjusting some parameters of OpenGL functions, makes them combine into the entity rule that meets the demand.
The synthesis of the surfacely complex entity, such as the design of the sludge layer of the MBR reactor, can use the backup provided by NURBS functions in OpenGL Glu library. Through the evaluating program, OpenGL can draw the number of the NURBSs and can also calculate the number of the curves and surfaces of the Bezier. When we need to draw the curved surface, we must first determine the most similar polygon to the maximum plane of this surface or use directly the polygon of the physical interface to ensure that the vertexes of the polygon locate in the edge of the surface basically. After the polygon is established, we construct the surface based on that again, and the degree of the bump of the surface can be determined by controlling the position of the point. For the construction of the closed surface, we need to ensure the smoothness of the junctions by arranging the same control points in the junction.
The synthesis of irregular complex entities: the triangle can join into any polygon, and its function is outstanding in the OpenGL programming design. So it is preferred in the design of OpenGL physical synthetic, and in the hardware level, the drawing of the triangle is highly optimized by most of the threedimensional accelerated hardware and the accelerated card of the graphics. For some irregular entities, we can first synthesize some simple geometry through the triangle or polygon and then combine them. And for those like the membrane module of the MBR, they need to show the detail feature of the local one, while the surface of the membrane module changes with membrane fouling. For the kind of the object with changable, complex graphics or needing to express the detail feature of the local, it is especially suitable to join with the triangle.
The virtual object of this paper is mainly the virtual device class including the simulation of the MBR water treatment. In order to simulate all kinds of virtual objects in the process of the MBR water treatment, we need to build the behavior model of various objects, and they have the essential difference of this simple geometric model. The objectoriented technology is the ideal choice in the design and realization of the virtual object. Through the objectoriented technology, it is easy to make the object of the virtual entity show consistency with the behavior of the physical object that it corresponds to, and then the kind of virtual system can show authenticity. For the kind of virtual device of the MBR membrane module having the capacity of the conduct, the object of objectoriented technology corresponds to the virtual device, object’s properties show the properties of the virtual device, and the method of the object shows the behavior of the device. The encapsulation of the object makes them maintain the excellent interface between objects and the independence at the same time, and the polymorphism of the object makes the class library have a good extensibility, and the inheritance of the object reflects the classifiable level of the device.
After the mathematic test model and the virtual model built, it still needs to research the state of the MBR reactor by combining the method of numerical simulation and scientific visualization. It abandons the original output of the tedium digital form and realizes the conversion from mathematical simulation to visual graphics. It can also observe the state, change, and related rules of the MBR water treatment fastly and intuitively, so as to offer the reference and basis for the design, improvement and optimization of the MBR.
The equipments need for research include sewage pumps, air pump, flow meter, vacuum gauge, and MBR. The component of the membrane that this subject adopts is hollow fiber membrane microporous filter (MF) components of polyvinylidene fluoride (PVDF) from the research center of Tianjin Motimo, and fiber aperture is 0.2
PVDF has the characteristics of good antipollution performance, high flux, the smoothness in the surface of inside and outside, relatively high strength, good recovery in cleaning flux, and so on. The parameters of the main performance are as in Table
The membrane parameter of PVDF.
Physical parameters  Index 

Inner diameter (mm) 

Wall thickness (mm)  0.6 
Fiber aperture (m)  0.2 
External diameter (mm) 

Area ( 
20 
Tolerance range of PH value 

Tolerance range of temperature ( 

Effluent turbidity (NTU)  <0.2 
Pressure load (MPa) 

In this paper, we use water processor composed of 15 pieces of membrane biological reactor fixed volume, and the specific parameters of the equipment are shown in Table
Equipment specifications of the MBR.
Physical parameters  Index 

Number of membranes (slice)  15 
Area of membrane ( 
300 
Design flux of membrane (T/D) 

Size of membrane reactor (mm)  1450 * 780 * 2000 
The visualization of the MBR is mainly divided into two parts of the visualization of the shape space and the internal component and is shown in Figure
Process of the MBR visualization.
The shape and components of the MBR reactor are using all types of primitives and more complex threedimensional graphics in basic libraries and auxiliary libraries of OpenGL. In the establishment of the MBR simulation system, this paper adopts integer instead of float and uses integer to establish the model as far as possible. The benefits of doing that can improve the speed of system modeling and postprocessing of the graphic by reducing operations of the floating point, so as to improve the speed and efficiency of the processing of the MBR threedimensional simulation system.
(1)
It has the initial coordinate system and the coordinate system of the current drawing in simulation system, and their length is from
(2)
The establishment of the MBR reactor model requires the extraction, expression, and quantization of the data. The extraction of data is according to the parameters of the MBR equipment provided. And after extracting the parameter, we need the parameter to abstract, analyse and correct. Then we can quantify the data and model it.
(a)
The construction of the graphics is composed of point, line, and surface in the MBR threedimensional system. After the establishment of the coordinate system, we extract the parameter of the above physical model, such as length, width, high, thickness, and the number, scale it in proportion in the coordinate system, and get the coordinate of each point in the simulated environment of the specific model. Then, we get the virtual model of the MBR reactor by using the line. According to four vertexes, we draw a rectangle as follows:
glBegin(m_nPattern); // Begin to draw in the method of m_ nPattern
glVertex3fv(v1); // Vertex 1
glVertex3fv(v2); // Vertex 2
glVertex3fv(v3); // Vertex 3
glVertex3fv(v4); // Vertex 4
glEnd(); // End of drawing.
Six faces of this cube are drown according to the four vertexes of each surface and shown in Figure
Framework model of the MBR reactor.
After establishing the framework model, we draw the outline of the model. Then, we quantify the point of the framework spaced, so as to obtain the extension of the model in space. The specific method is as follows:
// Standardization of vector, and standardized by the length, width, and height
After quantification, we refine the structure texture of the model for the framework model by using the method of the recursion of the fourbinary tree. Because a rectangle of the model composes of four small, if we adopt the method of the single recursion, the processing efficiency of program modeling will be very low. In fact, using the method of the recursion of the fourbinary tree is a way, which uses the space for the time and uses a certain memory space for the considerable speed of the modeling. The experimental results show that it is feasible. The result is shown in Figure
The texture structure of the reactor.
(b)
After building the framework of the MBR reactor, it needs to add the modules, and these modules are variable. For example, membrane modules can be simulated by using the mathematical model established according to the input data and can adjust the color of the membrane module according to the results of the simulation. Then according to color, we can distinguish the state and the level of the contamination of the current membrane module.
Adding the module has the sewage model, pipe model, and so on. This paper used the method of adding surface to the framework for this kind of model, such as some common plane and curve surfaces:
// Set some parameters
glPushMatrix();
glEnable(GL_COLOR_MATERIAL);
glDepthMask(GL_FALSE);
glEnable(GL_BLEND);
glBlendFunc(GL_SRC_ALPHAGL_ONE_MINUS_SRC_ALPHA);
glBegin(GL_QUADS); //Begin to draw plan figure
glVertex3fv(&vertex_list [index_list [i]
glVertex3fv(&vertex_list [index_list [i]
glVertex3fv(&vertex_list [index_list [i]
glVertex3fv(&vertex_list [index_list [i]
glEnd();
glDepthMask(GL_TRUE);
glPopMatrix().
The modeling diagram adding modules is shown in Figure
Modules diagram of the MBR reactor.
This paper proposed multiple linear regression models based on neural network. Though to collect and analyse the real data, we draw the relationship chart of membrane flux, pressure difference, MLSS, and total resistance and establish the threedimensional simulation model of the MBR reactor. After analyzing data relationship chart between the parameters, we know the influence of various parameters for the membrane resistance using multiple linear regression equation, and then we establish the mathematical model between each parameter and membrane fouling by the relationship of the membrane resistance and flux. The membrane pollution index can be intuitive shown in the graphics of the MBR threedimensional simulation model, which is obtained by the relationship of this experimental model. The flexible application of the computer visualization technology in the MBR threedimensional simulation system effectively shortened the researching cycle of the MBR sewage treatment and improved the efficiency of the work. The researching and designing idea has the inspiring and reference effect on the research, application, and development of the future about the MBR simulation technology.