3.3.1. Measurement Model of Development Level and Self-Organizing Evolution Level
Assuming that the system consists of subsystems, which are expressed as separately, the whole system is represented as , is composite function.
Step 1: Standardize the original data
The range standard method is used to standardize the original data of
subsystem:
where,
is the original value of the
th index in the
year of the subsystem
,
and
are the minimum and maximum value of the
th index in the
year of the subsystem
,
represent the standardized data of the subsystem
in the
year.
Step 2: Entropy weight method is used to calculate index weight
The proportion of the
th index in all indexes in the
year is as follows:
The information entropy of the
th index is:
The utility value of the
th index is:
The weight of the
th index is:
Step 3: Calculate the development level of computing systems
The development level of the system
is:
3.3.2. Synergy Level Measurement Model
(1) Basic Model
Step 1: Set the complex system composed of m subsystems, which are expressed as separately. The whole system is recorded as , is a composite function. The driving force for the system to change from disordered state to ordered state is the cooperation and competition between order parameters within the system.
The order parameters of each subsystem in the development process are:
If plays a positive role in the ordering of the system, the larger its value, the higher the ordering degree of the system, and the smaller its value, the lower the ordering degree of the system. If plays a negative role in the ordering of the system, the larger its value, the lower the ordering degree of the system, and the smaller its value, the higher the ordering degree of the system.
Step 2: Calculate the order degree of
on
Step 3: The geometric average method is used to calculate the “total contribution” of the variables
of the
th subsystem to the order degree of the
th subsystem.
The larger the value of , the higher contribution of to the system order, the higher the system order, and vice versa.
Step 4: Set the initial time
, and the order degree of each subsystem is
. When the whole composite system evolves to time
, the order degree of each subsystem is
. The synergy level of the composite system is:
where,
satisfy the following conditions:
In Equation (13),
is the magnitude of the change in the system order degree of the variables in the subsystem from
to
, which describes the degree to which the whole system becomes more orderly from
to
. Moreover, it is indicated that the system has a positive degree of synergy if and only if the following formula is established:
Equation (14) indicates that the system is developing in a coordinated way in the time region , while on the contrary, it indicates that at least one subsystem in the system has not developed in an orderly direction. In particular, if , it means that at least one subsystem is developing in the direction of disorder, it can be determined that the system is in the stage of non-cooperative development from to .
(2) Extended Model
Existing models can calculate the degree of cooperation between several parallel subsystems in one-dimensional space. However, if you extend the system to two dimensions, considering the radiation effects between different hierarchical systems, we need to expand the original model. The system is extended to two dimensions, and each subsystem in the system is divided into two categories: the main chain subsystem and the auxiliary chain subsystem, which are, respectively, in two levels in the system, and interweave and influence each other to form a complex system (assuming that the main chain subsystem consists of several subsystems and the auxiliary chain subsystem is a single subsystem). Each subsystem of the main chain is independent of each other. The auxiliary chain subsystem has radiant influence on each subsystem of the main chain, the more ordered the auxiliary chain subsystem is with other subsystems, the more orderliness of the whole system can be improved, and the greater the contribution to the orderliness of the whole system. Therefore, the synergy degree of the auxiliary chain subsystem to each subsystem of the main chain can be taken as the weight of each subsystem of the main chain. The order degree of the main chain affected by the radiation of the auxiliary chain is calculated, and then the synergy degree between the main chain order degree and the auxiliary chain order degree is calculated, according to the basic model. This not only reflects the hierarchical relationship of different subsystems in the complex system, but also reflects the radiation influence degree of the auxiliary chain subsystem on the main chain subsystem, i.e., the weight.
Set the main chain of a complex system be composed of m subsystems, which are expressed as respectively, and the auxiliary chain subsystem is expressed as . The whole system is recorded as and is a composite function.
The synergy degree between the auxiliary chain subsystem and the main chain subsystem is set as
, and the weight of the main chain subsystem
is calculated by the synergy degree; thus, the order degree
of the main chain affected by the radiation of the auxiliary chain is calculated, and then the synergy degree
between the main chain and the auxiliary chain is calculated according to the order degree of the main chain and the auxiliary chain.
where,
.
The higher the value of , the higher the synergy level between systems, and vice versa. If the order degree of one subsystem is large, but the order degree of the other subsystem is small or reduced, the synergy level between systems will be affected.
3.3.3. Renewal GM (1, 1) Grey Prediction Model
According to the grey system theory, although the indications presented by the elements of the objective system are complex and changeable, its development and change have their own objective laws. The theory takes small samples with known and unknown information and uncertain systems with poor information as research objects. Through the generations, development and extraction of valuable information for some known information, the correct description of system operation behavior, and evolution law is realized, and then the quantitative prediction of its future changes can be made [
39]. The dynamic prediction model based on grey system theory is called grey prediction, of which GM (1, 1) model, a special case of GM (1, N) proposed by Deng, is the most widely used. The model has strong applicability for data processing and prediction with the characteristics of “small samples and poor information”. Due to the late start of China’s PV industry and the limited number of years that can obtain the original data, it is not suitable for the prediction method that requires a large amount of data. Therefore, the grey prediction model provides an effective method for predicting the self-organizing evolution level of PV industry chain system. Because the traditional GM (1, 1) model usually ignores the disturbance factors in the process of system evolution; thus, affecting the prediction accuracy, especially leading to poor prediction accuracy in the medium and long term [
40,
41,
42], we used the renewal GM (1, 1) model to predict the evolution level.
The specific steps are as follows:
Step 1: generate a first-order buffer sequence.
Grey sequence can weaken the randomness of the original sequence by introducing buffer operator; thus, showing its regularity. Therefore, the first-order weakening operator D is introduced to obtain the first-order buffer sequence.
Set the original data sequence:
D is an average weakening buffer operator (AWBO) and D
2 is second-order weakening operator. The first-order buffer sequence is:
where,
The second-order buffer sequence is:
where,
Step 2: generate an accumulation sequence.
Sequence is generated by accumulating the second-order buffer sequence
where,
Step 3: establish differential equations
where,
are the parameters to be estimated.
Rewrite it in the form of a matrix:
where,
,
,
Step 4: calculate the estimated value using the least square method
The GM (1, 1) differential equation can be obtained by substituting the estimated value
into the equation:
Step 5: the above results to obtain the predicted value
Step 6: iterative prediction.
The latest data
predicted by the GM (1, 1) model are added to the original buffer sequence
, and the earliest data are eliminated at the same time to make the sequence equal to dimensions. Then the GM (1, 1) model is established, so that the renewal prediction grey number is used to roll the prediction one by one; thus, replacing the prediction until the prediction target is completed, and the following sequence is obtained:
where,
are the original data and
are the forecast data.