In haze governance, there involves all sorts of conflicted factors. But everyone expects a green China, and different roles also need to undertake the responsibility to governance haze together. Apparently, among all roles, the government should bear the most important responsibility because of its dominant role of social manager and regulatory maker for the industrial production and social life. Next, enterprises, especially large enterprises in China can also not be absent in haze governance because they the main emitters of air pollutions, and have to do some good things without doubt. Additionally every citizen is not only a victim in China haze, but also a responsible person to reduce haze, because each citizen is not only the recipient of the environment, but also the resource consumer and polluter.

Then, according to the characteristics of China haze [1] - [6] , a six dimensional evaluation index system of haze control is proposed here, including air quality, haze days, pollution source, greening, public health, GDP, and so on. Obviously, the evaluation performance of China haze governance is a multi-input multi-output (MIMO) data-driven model, including government, enterprise, citizen, and six performance indexes.

It is assumed that k is time variable, input vector is μ(k) (), output vector is y(k) (), and transfer function is φ(k) (), then the transfer function of China haze control can be written as a vector

where

where is called as quasi gradient matrix.

Hence the evaluation of China haze is a multi-objective evaluation problem, involving all kinds of nonlinear input and output data. There are many practical systems, which are multi-input multi-output, where some systems, such as China haze control system, their input or output variables are strongly coupled and decoupled. This kind of model can not be easily solved by traditional algorithm, so it is necessary to seek a non-decoupling algorithm for haze model of multi-input multi-output nonlinear system.

As China haze control system is a multi-output, the gradient vector can be presented as a gradient matrix with several single output vectors. Similar to the case of single-output, all haze control data generated by the gradient matrix will form control law of the data-driven model. Then the input-output relationship of China haze can be given as the equation of these vectors, greatly reducing the solving difficulty of control law.

Assuming

where. Let be a full rank sub phalanx with rank, , where N is the number of full rank matrices with rank, and is defined as the norm of, so there are s sub phalanxes with full rank. That is

There is

where is often called an advantage sub-square of with rank. Correspondingly, are intended advantage control variables of the system, and it is obvious that, at different times, intended advantage control variables of the system are different.

Assuming, the sub-order advantage phalanx of and can all be determined.

Thus the advantaged controlled variables, and output variables in accord with row can also be gotten.

After the removal of from vector, the rest component is noted as. Similarly the rest component of the vector is named as after the removal of. After the rearrangement of the order of components and, there is

Since every vector in the vector group can be expressed as a linear independent vectors, for the expected output at time k + 1, only component can be given independently. Assuming it is set as

The Equation (1) can be further simplified as follows

In the formula (11), making, the formula (11) can be simplified as

So, , the estimated value of can be gotten easily

where denotes the adjoined matrix of, and represents the determinant of.

In summary, the required control law of data-driven model can be described as follows

In which, represents the desired value of an available separated component of at time k + 1, and

where is the appropriate parameters, and is the control parameter matrix.

To verify the proposed model, a prototype is built. The initial simulation data comes from the following sources.

1) According to Bulletin China Environment in World Environment Day (June 5, 2014) and the latest version of China Ambient Air Quality Standard, among 74 main cities in China, there are only three cities of Haikou, Zhoushan, and Lhasa whose air qualities reach the national standard, so the compliance rate is only 4.1%. In the whole of 2014, the average haze days is 35.9 days, exceeding previous year by 18.3 days, and is the worst since 1961.

2) According to China Index of Air Quality Monitoring City Rankings in April 2014, the initial simulated values are selected from 100 China cities before rank 100 in air quality ranking, with higher than SO₂ = 38 μg/m³, NO₂ = 56 μg/m³, PM2.5 = 63 μg/m³, and PM10 = 100 μg/m³, respectively.

3) According to 2013 Chinese Greening State Gazette, up to March 12 in 2014, the national green area is 1.812 million hectares, 93,000 hectares more than in 2012; urban green is 12.26 square meters per capita, 0.46 square meters more than in 2012; national urban green coverage and greening levels are 39.59% and 35.72% respectively.

4) GDP is 568,845 trillion at the end of 2013, with an increasing of 7.7% over the previous year.

Based on the actual data above, basic simulation parameters are generated. To facilitate the analysis, all kinds of data are normalized in the interval [0,1], and it does not affect the strategy simulation and decision-making.

The simulation environment includes hardware configuration, such as Core i3 M 350@2.27GHz dual-core processor, and 2GB Memory, and software as Matlab7.11.0.584 (R2010b), 32-bit. Each simulation takes about six minutes.

According to the referred data above, the initial values of simulation parameters are set as follows. Government profit = 0.8, regulatory cost = 0.2, regulatory probability = 0.8; enterprise profit = 0.3, penalty cost = 0.5, treatment cost = 0.2; citizen profit = 0.6, participation cost = 0.3, not-participated loss = 0.5. The initial simulation stage of China haze control is shown in Figure 1.

As we can see, in Figure 1, at early stage of simulation, the SO₂ is 0.42, NO₂ is 0.51, PM = 0.45; industrial emission is 0.41, traffic emission = 0.32, coal combustion is 0.33; haze days is 0.443, civic health equals to 0.086, GDP was 0.564. The average haze days in the map is 44.38 days, and there are many red circles in the China map meaning bad haze situation. The radar chart in the lower right area can present the six-dimensional evaluation indexes for decision support. In the whole simulation process, all kinds of parameters will change according to the variation of multi input of data-driven model.

When simulation is finished, the results are shown in Figure 2.

From Figure 2, as can be seen, air quality is apparently improved, such as SO₂ is decreased to 0.15, NO₂ is down to 0.15, PM is lower than 0.02, and air quality in radar chart is lessened from 0.347 in Figure 1 to 0.144 in Figure 2. At the same time, several pollutant sources are also diminished, for example, industrial emissions = 0.45, traffic exhaust = 0.21, coal combustion = 0.03, and haze source in radar chart is decreased from 0.232 in Figure 1 to 0.095 in Figure 2. In haze distribution map the average haze days is lessened to 4.473 days, and red area is decreased evidently. Additionally radar chart verifies that the haze control strategy seems to be effective, for example, number of haze days is cut down to 0.044, civic health rises to 0.231, GDP grows to 0.642.

Therefore, it is apparent that to strengthen government governance is effective way to diminish China haze. To comparison, two strategies to strengthen government governance are employed to simulation, where the one is to strengthen legislation and lay enforce, the other is to promote the green energy, as shown in Figure 3 and Figure 4, respectively.

As we can see from Figure 3, legislation strategy may be helpful to haze control, and may produce a certain difference. The average haze source is 0.107, and haze days is 0.017, air quality is 0.149, GDP = 0.670, health = 0.350, and greening = 0.165. From Figure 3, legislation strategy does not affect the industrial production and is helpful to get higher GDP and better greening, though air quality is relative stable with higher GDP according to Figure 2. Whereas green energy strategy in Figure 4 may be different from legislation strategy in Figure 3. The average haze source is 0.100, and haze days is 0.058, air quality is 0.139, GDP = 0.641, health = 0.273, and

greening = 0.161. From Figure 4, green energy strategy may be different in different areas and different industrial distribution, and is helpful to get higher health, but is not helpful to higher GDP.

In practice, because China is vast, and industrial development in China is deeply uneven, environmental department and district government in China can select different strategies according to the local characteristics and the difference between different areas and industries. Based on this simulation system, different districts can input different data by its owner and try different governance strategies before its practice to avoid risk and optimize cost.