Abstract
The urban rail transit power supply system is an important part of the urban power distribution network and the power source of the rail transit system. It is responsible for providing safe and reliable electrical energy to urban rail trains and power lighting equipment. This paper processes the obtained long-period rail transit power load learning sample data matrix, according to the principle of normalization processing, effectively eliminates irregular data in the sample set and fills in possible missing data, thereby eliminating bad data or fake data for model learning. Moreover, this avoids the generation of huge errors that cause exponential growth in the model due to the increase in the learning sample size and the irregularity of the data. According to the characteristics of power load, this paper comprehensively considers the influence of temperature and date type on the maximum daily load, applies the fuzzy neural network model to the long-period load forecasting of long-period rail transit, and introduces the whole process of establishing the forecasting model in detail. Through detailed analysis of the actual data provided by the EUNITE network, the relevant factors affecting the daily maximum load were determined, and then the appropriate fuzzy input was selected to establish the corresponding fuzzy neural network prediction model, and a relatively ideal prediction result was obtained. The experimental results fully proved the great potential of fuzzy neural network in long-term power load forecasting.
Introduction
At present, the speed of social and economic development is getting faster and faster [1]. As a major part of the transportation industry, urban rail transit has also ushered in a period of rapid development and has received more and more attention [2]. A number of urban rail transit projects in my country have been completed and put into operation, and more cities are under planning, application and construction [3]. The next period of time will become the golden period of urban rail transit development. Urban rail transit has many advantages, such as fast operation, large transportation volume, low noise, and environmental protection [4]. It provides a good choice for the increasingly serious urban traffic problems of all countries in the world. Urban rail transit has a history of more than 100 years. Many cities in the world have built rail transit lines, which are tens of thousands of kilometers long. Since London built the world’s first subway, great changes have taken place in all aspects of urban rail transit, and related technologies have also been greatly improved [5, 6].
The regression analysis method is to find the model of the correlation relationship and predict the future load by fitting the historical data of the impact factor value and the electricity consumption [7]. This method relies on the accuracy of the predictive value of the impact factor itself, the diversity and unpredictability of the impact factor, which makes this method limited in some cases [8]. The grey forecasting method is a method of forecasting some systems with uncertain factors. It can find out the laws that work in a certain period and establish a load forecasting model without much data [9]. Grey forecasting has the characteristics of few original data and simple methods. The grey forecasting model can be applied to almost all non-linear changing load index forecasts [10]. The exponential solution of the differential equation of this method is more suitable for load indicators with an exponential growth trend. For indicators with other trends, the degree of data dispersion is large, the fitting gray level is large, and the accuracy is difficult to improve [11]. It is not suitable for the long-term postponement forecast of long-term rail transit for several years. Researchers use a fuzzy neural network algorithm when predicting the load of the Greek power grid [12]. The self-learning ability of the neural network is used to train the original load data. After the training is completed, fuzzy control rules are generated and applied to long-term load forecasting [13]. Relevant scholars use the priority vector method to establish a load forecasting model, which selects the type day and season as the influencing factors [14]. According to the adaptability of the priority vector method, the relationship between the variables is automatically generated in the system. At the same time, historical load data and various influencing factors will be constantly updated over time, and the linear method produced by this method can solve such problems well [15]. Therefore, this method can well solve the problem of various influencing factors on load changes. Relevant scholars have proposed long-period load forecasting methods based on fuzzy time series and seasonality [16]. Because of the different seasonal changes in different regions, time variables are particularly important in load forecasting models [17]. This paper proposes to combine the fuzzy time series with the seasonal differential autoregressive moving average model to establish a forecasting model, considering the necessary parameters. It has been verified that the forecasting effect of this method is very good and it is a kind of effective solution to the load forecasting problem. Some scholars have proposed the application of support vector machines to load forecasting [18]. The support vector machine method can process a large amount of historical load data, which is better than autoregressive models and other neural networks. It compares the support vector machine method with the autoregressive model, and finally it can be seen that this method can achieve better results when the training data is consistent. Relevant scholars have proposed an improved prediction model for the Elman network [19]. The Elman network is used because it has the ability to analyze dynamic problems, so it can model the load problem as a dynamic model. In load forecasting, it is also important to consider influencing factors. Therefore, comprehensive meteorological factors are used as the input of the network model to improve the problem of excessive input [20].
After analyzing the advantages of neural network and fuzzy control theory, in order to obtain more accurate load forecasting data, the neural network and fuzzy control theory are combined to construct a fuzzy neural network hybrid load forecasting model. This not only inherits the advantages of neural network intelligence “learning and training”, but also introduces fuzzy control theory to optimize the internal structure of the neural network, thereby ensuring the efficient and stable operation of the load forecasting system. Combining fuzzy control theory, a fuzzy neural network structure with three layers and four functional units including input layer, hidden layer and output layer is established, and the membership function of the error correction connection weight and threshold value among the neurons in the fuzzy neural network is analyzed with Matlab software. Taking EUNITE’s data as an example, the whole process of establishing a power load forecasting model is introduced in detail. The results are compared with the results of EUNITE, which shows the advantages of fuzzy neural network for power load forecasting.
The rest of this article is organized as follows. Section 2 discusses related theories and key technologies. Section 3 builds a long-period power load forecasting model based on fuzzy neural network. In Section 4, a simulation experiment is carried out and the experimental results are analyzed. Section 5 summarizes the full text.
Related theories and key technologies
Long-period rail transit load forecast
The size of the long-period rail transit load is related to many factors. Among these factors are uncertain factors (such as weather, temperature, etc.) as well as deterministic factors.
Since the load forecasting is based on the past and present of the electric load to infer its future value, the object of this work is the uncertainty event, which has the following characteristics:
1) Inaccuracy of prediction results
The size of the power load is affected by various complex factors, which are developing and changing, such as social and economic development, climate change, new technology development, political policies, etc. People can predict some factors in advance, while others cannot or are difficult to predict accurately. In addition, the continuous updating of prediction methods and theories will also affect the accuracy of prediction.
2) Conditionality of prediction
Various power load forecasts are made under certain conditions. These conditions have inevitable conditions and assumptions. Load forecasts made under certain conditions are often reliable. The accuracy of forecasts made under assumptions is obviously conditional. For example, when the prediction model is trained, the initial values of some parameters are set differently, and the prediction results will be different. Obviously, the load prediction made from this has specific conditions.
3) Multi-scheme of prediction results
Due to the different requirements of load forecasting accuracy and the constraints of forecasting conditions, coupled with the diversity of forecasting methods and theoretical mathematical models, the forecasting results are not unique.
Because load forecasting has the characteristics of uncertainty, conditionality, and multiple schemes. The establishment of load forecasting models and the implementation of forecasting methods are generally based on the following basic principles.
1) Similarity principle
The principle of similarity means that the development process and development status of things may be similar to the development process and development status of a certain stage in the past, and the same prediction model can be established based on this similarity. For example: during special holidays (such as the Spring Festival, National Day and other long public holidays), due to the similar social power demand, the power load shows a certain similarity.
2) Principle of continuity
The principle of continuity refers to the development of the forecast object from the past to the present, and then from the present to the future, some of its characteristics can be maintained and continued. This process is continuously changing. For example, electricity consumption in various regions has continuity, and these continuities provide a basic basis for electricity forecasting.
3) Correlation principle
That is to say, the future load development and changes have a strong correlation with many other factors, which directly affect the forecast results. For example, the load forecast of a certain place is related to the economic factors, meteorological factors and historical load of the area. If there is no influence of other factors, the shape of the daily power load curve should be similar.
Data preprocessing in long-period load forecasting of long-period rail transit
Load forecasting is based on historical data, but the collection of historical data comes from actual load data, which is sometimes affected by human factors, special events, random and unexpected factors, etc., and has randomness, making it possible at a certain moment. If the data in the historical load has abnormal values, it will have two effects: one, when used as modeling data, interferes with the correct understanding of the law of load changes; second, when used as the predicted value of the test result, it may cause Misjudgment of the results of load forecasting. Therefore, it is necessary to analyze and process the data.
1) Identification of abnormal data
There are many reasons for abnormal data, but the following analysis can be used to identify and analyze abnormal data.
Missing data is data that needs to be repaired, mainly including some signal transmission errors in a short period of time or the data collection system does not reflect the load data caused by accident changes in a timely manner. This type of data collection is interrupted and a large amount of original data is lost.
Unreal data that cannot be repaired is data that needs to be replaced, which is mainly caused by a long-term system failure or database failure, which manifests as abnormal changes in load data over a long period of time or even throughout the day, completely deviating from the normal trend of load changes.
The real bad historical data is the data that needs to be smoothed. It mainly includes the abnormal fluctuation of load data caused by shock load and external interference. Although the collected data is real, it cannot be directly applied to the forecasting program. The original data must be pre-processed before forecasting, trying to smooth the volatility of the load curve.
2) Handling of abnormal data
Because the causes of abnormal data are complex and diverse, the processing methods for abnormal data should also be handled separately according to specific reasons.
The load at a certain moment is compared with the load at the previous moment. If the difference is greater than a certain threshold, it is considered a load glitch. When analyzing the data, you use the load data of the previous two times as the benchmark and set the maximum variation range of the data to be processed. When the data to be processed exceeds this range, it is regarded as abnormal data, and the average value method is used to stabilize its changes. The formula is as follows:
Among them, L(d,t) represents the load value at time t on day d, and α(t) and β(t) are the thresholds.
If the difference is greater than a certain threshold, you use the average value method instead. To correct the bad data out of the range, the correction formula is:
Among them, L(t) is the average load of the data to be processed at time t in the last few days, namely:
In the formula, θ(t) represents the threshold.
Since load forecasting is an estimation of future load, errors will inevitably occur. You can compare the accuracy of the prediction result, and also compare the situation of different algorithms and different models in specific load forecasting requirements. Forecast error also has important reference value for making decisions using forecast data.
There are many reasons for the error, mainly in the following aspects:
First, when models with different structures predict, there will be differences in the prediction results, which will inevitably bring errors.
Second, the influence factors of the load in each area are different, and the forecasting methods will be very different. Therefore, there is a problem of how to correctly choose a suitable forecasting method from the numerous forecasting methods. If you choose improperly, errors will follow.
Third, a large amount of data is needed to perform load forecasting, and various data cannot be guaranteed to be completely accurate and reliable, which will also bring forecast errors.
Fourth, the staff will bring random errors when forecasting.
After understanding the causes of forecast errors, the forecasting model or forecasting technology can be improved. At the same time, the prediction error must be calculated and analyzed, and then the selected prediction model can be tested. There are many methods and indicators for calculating and analyzing forecast errors. The main methods for calculating forecast errors are as follows:
The absolute error is the average value of the relative forecast errors at each point in a certain forecast period (usually a day or a week), which reflects the overall situation of the forecast errors in the forecast period. The absolute error is expressed as:
The mean square error is the average of the sum of squares of errors in a certain forecast period, namely:
It reflects the degree of dispersion of errors. The mean square error is the average of the sum of squares of absolute errors. It avoids the problem that positive and negative errors cannot be added together. This article uses the mean square error to describe the performance of the network. The root mean square error of training is the square root of the mean square error. In fact, the root mean square error can better express the degree of dispersion. The root mean square error is expressed as:
Fuzzy logic control system
Controllers based on fuzzy control theory only need less logical operation information to build a powerful functional system. Often, from the beginning, some membership sets and operation rules that the functional model should have are used to form a function through intelligent optimization of the network system. The fuzzy reasoning criterion in the fuzzy controller is usually constructed by the specific parameter characteristics required by the model. That is to say, the fuzzy operation logic of the system can be realized by simply modifying some of the fuzzy inference characteristic values of the system, which is very beneficial for later development and utilization. The control system of a single BP neural network model requires more historical sample data for repeated training, and is very dependent on the experience of the programmer and other external constraint information. If in the process of model construction, a certain parameter is not considered carefully, it is difficult to obtain a model structure that can meet the demand for load forecasting, and the entire control logic may enter an infinite lag or premature cycle. The fuzzy control logic uses independent units with a large number of functional characteristics to mutually constrain to form corresponding functional criteria. It is a calculation criterion formed by the fusion of multiple internal basic rules. Even if one of the basic rules has problems, other rules can still be adjusted internally. For compensation, the effect of its operation is very small. Fuzzy control system can effectively solve the problem of poor robustness and sensitivity of neural network system. It can adjust the internal fuzzy function unit to adapt to the changes of external constraint parameters, thereby greatly improving the accuracy and real-time performance of load forecasting.
1) Basic principles of fuzzy logic control
The basic principle of the fuzzy control system is to construct the corresponding computer control language with expert knowledge. It is an arithmetic analysis method that transforms traditional empirical control into electronic soft control. It effectively solves the traditional complex system that cannot be described by precise mathematical and physical models. In terms of the basic principles of fuzzy control system construction, the fuzzy logic control system is a nonlinear intelligent control system based on expert fuzzy set theory, fuzzy control language variables, and basic fuzzy inference operations. It is an excellent product of the combination of fuzzy mathematical reasoning and process control logic. The basic method of fuzzy control is to establish a knowledge database, that is, in the daily operation process, the operator’s experience is summarized into several fuzzy control rules, which are directly stored in the computer memory after the data information is fuzzified, as the basic reference database. When in operation, it will be directly compared with the knowledge base, thus forming the corresponding fuzzy decision, and controlling the corresponding actuator to complete the command control. Combining fuzzy control with improved BP neural network can obtain a load forecasting model with the advantages of high control accuracy, strong adaptive ability, strong convergence performance, good convergence, and vibration resistance.
2) Working principle of fuzzy neural network control system
Fuzzy neural network control is based on the neural network algorithm, through the computer’s internal fuzzy operation controller, the error between the actual output and the ideal output of the current neural network system learning sample is calculated, and the fuzzy knowledge base rules that have been formed are used for fuzzy inference. The basic design idea of fuzzy neural network control is to organically combine fuzzy decision-making theory with the reverse iterative correction process of each functional neuron error, give full play to the advantages of fuzzy control and neural network control, so as to obtain a more satisfactory logic operation effect. The network logic operation control block diagram is shown in Fig. 1.

Block diagram of fuzzy neural network control system.
As shown in Fig. 1, the fuzzy neural network control system is mainly composed of fuzzy inference controller and neural network controller. In the operation process, the fuzzy inference controller takes the deviation e and the deviation rate ec as the input of the fuzzy inference controller. The fuzzy inference decision table is used to obtain the error correction values of the input layer neuron constraint parameter (ki), hidden layer neuron constraint parameter (kh) and output layer neuron constraint parameter (ko) of the neural network controller, which can be expressed as:
Kio, koh, koo are the modified parameter values formed after fuzzy inference; ki, kh, ko are the newly tuned connection weights and thresholds within each neuron formed after fuzzy inference of the fuzzy inference controller.
Through real-time online modification of the neural network controller’s input layer, hidden layer, output layer neuron connection weights and thresholds by the fuzzy inference controller, it can meet the different errors e and error rate ec of learning samples to control the neural network, the neurons of each layer of the device are connected to the time-varying characteristics of the channel constraints, and the entire long-period load forecasting calculation process has a good analysis and calculation performance that combines dynamic and static.
The fuzzy neural network model established in this paper is a neural network structure with three layers and four functional units. The division of functional units is shown in Fig. 2.

Fuzzy neural network structure with three layers and four functional units.
It can be seen from Fig. 2 that the structure of the fuzzy neural network includes the input layer, the fuzzification layer, the fuzzy inference layer, and the defuzzification layer. Each deterministic input neuron in the structure is only connected to its own fuzzy neuron; the neurons in the other layers are “fully connected” with the neurons in the adjacent layer. The functions and roles of each layer of the network are described in detail below.
The first layer is the input layer, which is used to receive deterministic input information. The number of neurons is equal to the number of sample input variables; each input variable is connected to a group of fuzzy operation neurons, and the received input information is directly transmitted to one layer as input.
The second layer is the fuzzification layer, which is used to convert each deterministic input into a fuzzy amount. Each fuzzy neuron represents a membership function, and each input variable corresponds to a group of neurons arranged in space. These neurons can be assigned different membership functions as needed. The number of neurons can also be dynamically adjusted, generally based on the following principles: if the input-output relationship has obvious nonlinear characteristics, you choose a larger value; if the input-output relationship has obvious linear characteristics, you choose a smaller value.
The third layer is the fuzzy inference layer, which realizes the mapping from fuzzy input to fuzzy output (that is, mapping from the input vector space to the solution space). The fuzzy input vector obtained by the fuzzification layer is stored in the input weight of each neuron, and the fuzzy output vector (ie solution vector) calculated by the fuzzy inference layer is stored in the output weight.
The fourth layer is the defuzzification layer, which is used to convert the fuzzy output obtained by network inference into actual values.
The model established in this article is a model of normal days, including working days and two days off. Special holidays require additional models. There are many factors that affect load characteristics, such as the current date type, load conditions, weather factors, temperature, major political, economic activities, and other random factors that will affect the future load conditions. Some unpredictable factors such as politics and economic activities are generally not considered in the forecasting model. This article still considers some deterministic factors when selecting the input variables of the forecasting model.
In order to more reflect the regularity of historical data, you can choose more inputs, but too much input of the model will increase the burden on the network and affect the training ability of the model network.
The process of load forecasting experiment
In order to obtain more accurate long-period rail transit long-period load forecasting data and improve the overall efficiency of system scheduling and operation, it is an efficient and stable measure to perform intelligent analysis and calculation of traditional historical sample data information through a computer. The basic flow chart of long-period load forecasting is shown in Fig. 3.

Block diagram of the long-period load forecasting process of fuzzy neural network.
It can be seen from Fig. 3 that in order to ensure more accuracy of the load forecast data of the fuzzy neural network model, external constraint parameters such as date type, meteorological data, and intervention items that affect load fluctuations are introduced. The computer automatically analyzes and summarizes the historical load fluctuation data set for learning and training the model, and establishes the corresponding historical load fluctuation database of the corresponding reference day, which is used as the reference constraint equivalent for the generation of the fuzzy neural network forecasting daily load data information curve. The fuzzy neural network system is the core of the intelligent learning, training and forecasting of the entire load data information. The model intelligently analyzes the forecast daily load data obtained, and through the corresponding “24-hour load error correction at each point of the forecast day” functional module, it can meet the error demand. The load fluctuation data and curves are convenient for electric power dispatching and electric energy marketing planning staff to formulate efficient and stable dispatching operation plan strategies.
Figure 4 is the daily maximum load data for a certain two years, and Fig. 5 is the daily average temperature data for a certain two years. It can be seen from the figure that the influence of seasons on power load is very obvious. It can be seen from the comparison of the two figures. For winter, the temperature is very low and the load level is obviously higher. In summer, the temperature is high and the load level is obviously low. From the overall level, the overall load level in winter tends to be higher than in summer.

Maximum daily load in a certain two years.

Daily average temperature in a certain two years.
Figure 6 shows the daily maximum load in a certain month. It can be seen from the figure that the electric load has obvious volatility. For example, 196, 314, 465, and 600 all have troughs, and these four days are all Sundays. It is not difficult to see the pattern in the figure, the electrical load on weekdays is obviously greater than that on weekends. The minimum load of a week usually occurs on Sunday.

Maximum daily load in a certain month.
From the above analysis, it is not difficult for us to see that there is an inevitable connection between the power load and the temperature. And this connection is obviously ambiguity and nonlinear.
Through the above analysis, we choose temperature, date type and holiday factors as the input of the fuzzy network, and the output is the load data of the forecast day.
Taking into account the uncertainty of the weather forecast, we will use the daily average temperature as the network input. Because the forecast of the average temperature in the weather forecast is quite accurate. First, the temperature data value is blurred. Taking into account the possibility of exceeding the historical minimum and maximum temperature, we have appropriately enlarged the range and determined that the universe of temperature T is -10 degrees. Regarding the choice of the membership function form, the triangular membership function has attracted more and more attention due to its easy calculation and excellent performance, so here we choose the triangular membership function form.
There are 11 input nodes, node 1 to node 7 represent the 7 fuzzy membership degrees of the actual temperature of the forecast day, node 8 to node 10 represent the date type of the forecast day, and the 11th node represents the holiday indication degree of the forecast day. There is one output node, which represents the normalized load data of the forecast day.
The hidden layer and training parameters of the network are determined through multiple experiments. According to the experimental situation, we finally choose the number of hidden layers as 1, and the number of hidden layer nodes as 15. The excitation function from the input layer to the hidden layer uses the tan sig function, and the excitation function from the hidden layer to the output layer uses the purelin function. With trainlm, the training effect of this function is better than other algorithms, but this function requires more memory.
In order to ensure that the network does not appear over-fitting. We introduced test samples. First, we organize historical data into arrays, including input arrays and target output arrays. Then we divide it into training data and test data. For example, if we want to predict the data of a certain day, we will use the data from January to November of a certain year as the training data. Since the December data is closest in time to the forecast date, we will use it as the test data. When predicting the load on January 2nd, the known information on the 1st day is added to the test set, and the data on December 1st is classified as the training set. That is, the total guarantee test set is the amount of data in the month before the prediction, until the total daily maximum load in January is predicted.
We use the neural network software package in Matlab software to train the network until it reaches a stable output. The trained network can be used for prediction. We input the input data of the forecast day into the network for simulation, and the simulation result is denormalized to obtain the predicted value.
Forecast results
In order to clearly show the prediction effect of this network, we compare our prediction results with actual data, as shown in Fig. 7. Figure 8 shows the absolute error between the forecast results and actual data in a certain year.

Comparison of forecast results and actual data in January of a certain year.

The absolute error between the forecast results and actual data in a certain year in January.
It can be seen from the figure that the predicted value and the actual value have the same changing trend. The predicted value has a good grasp of the periodicity of actual load changes, and well reflects the influence of holidays on the actual load. In order to evaluate our prediction effect more clearly, we will compare our results with the results of the EUNITE competition through a series of indicators.
The fuzzy neural network accomplishes the prediction task well, and the absolute error is smaller than the EUNITE competition result. To further clarify the effectiveness of this method, we also used this method to forecast the power load in August of a certain year. That is, we use the data before July as the training sample, and use the July data as the test sample. The result is shown in Fig. 9. The absolute error between the forecast results in August and the actual data is shown in Fig. 10.

Comparison of forecast results and actual data in August of a certain year.

The absolute error between the forecast results and actual data in August of a certain year.
It can be seen that the model is also very effective in forecasting in August. The absolute forecast error is kept below 6 and the effect is good. It can be seen that the model we have established is suitable for long-term load forecasting in various seasons throughout the year, and the effect meets the requirements.
This paper establishes a multi-input and three-output fuzzy neural network inference controller, analyzes and studies the membership functions of language variables including error e and error rate ec, and establishes corresponding fuzzy inference based on actual experience in the load forecasting process. A fuzzy neural network structure with three layers and four functional units including input layer, hidden layer and output layer is established, and input and output data are selected. By analyzing EUNITE’s original data and analyzing the limited data, a suitable fuzzy neural network is established for short-term maximum load forecasting, and good results have been achieved. It proves the great potential of fuzzy neural network and its feasibility in power load forecasting. Fuzzy neural network overcomes the shortcomings of a single neural network and can fuzzify the information of factors that affect the load. The fuzzified temperature and other information are used as network input to predict the daily maximum load, which makes it easier for the network to capture the nonlinear relationship between input and output, and improves the prediction accuracy. The date type and holiday indication are converted into binary numbers as part of the fuzzy neural network input, which speeds up the convergence of the network to a certain extent, thereby shortening the training time and meeting the real-time requirements of power forecasting. There are many factors that affect the power load, such as the humidity of the forecast day, special social events, and the increase in electricity bills. These factors are bound to affect the changing law of the power load trend. Therefore, further research on these factors is needed.
