CN111612226B - Group daily average arrival number prediction method and device based on hybrid model - Google Patents

Group daily average arrival number prediction method and device based on hybrid model Download PDF

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CN111612226B
CN111612226B CN202010395764.0A CN202010395764A CN111612226B CN 111612226 B CN111612226 B CN 111612226B CN 202010395764 A CN202010395764 A CN 202010395764A CN 111612226 B CN111612226 B CN 111612226B
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朱小伶
王亚珅
张熙
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Beijing University of Posts and Telecommunications
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Abstract

The invention provides a group daily average arrival number prediction method and device based on a mixed model, wherein the method comprises the following steps: constructing a mixed model based on historical data of the average population daily number; predicting the average daily arrival number of the population based on a mixed model; the hybrid model comprises a linear model constructed based on a linear data part in the historical data and a nonlinear model constructed based on a nonlinear data part in the historical data. According to the group daily average arrival number prediction method based on the mixed model, the linear model and the nonlinear model are respectively constructed according to the linear data part and the nonlinear data part in the historical data of the group daily average arrival number, the linear model and the nonlinear model are combined to form the mixed model, the mixed model fully integrates the respective specific advantages of the linear model and the nonlinear model to predict the group daily average arrival number, and the accuracy and the reliability of the group daily average arrival number are effectively improved.

Description

Group daily average arrival number prediction method and device based on hybrid model
Technical Field
The invention relates to the technical field of machine learning, in particular to a method and a device for predicting the average number of people arriving at a group day based on a mixed model.
Background
A population-specific daily arrival prediction study predicts the number of future daily arrivals for a given area. The study was mainly directed to predictive analysis of time series data. In the related art, an AutoRegressive Integrated Moving Average (ARIMA) model and a Back Propagation (Back) neural network are mainly used for predictive analysis of time series data.
The ARIMA model has a good effect on predicting time sequence data in a linear field, but the ARIMA model has a poor effect on a complex nonlinear problem; the BP neural network is effectively applied to nonlinear data analysis. However, when modeling the linearity problem with the BP neural network, the results are unstable.
Disclosure of Invention
The invention provides a method and a device for predicting the average daily arrival number of a group based on a mixed model, and aims to solve the technical problem of reliably predicting the daily arrival number of a specific group.
The method for predicting the average daily arrival number of the population based on the mixed model comprises the following steps:
constructing a mixed model based on historical data of the average population daily number;
predicting the average number of arriving people of the population on a daily basis based on the mixture model;
wherein the hybrid model comprises a linear model constructed based on a linear data portion in the historical data and a non-linear model constructed based on a non-linear data portion in the historical data.
According to the group daily average arrival number prediction method based on the mixed model, the linear model and the nonlinear model are respectively constructed according to the linear data part and the nonlinear data part in the historical data of the group daily average arrival number, the linear model and the nonlinear model are combined to form the mixed model, the mixed model is fully fused with the respective specific advantages of the linear model and the nonlinear model to predict the group daily average arrival number, and the accuracy and the reliability of the group daily average arrival number are effectively improved.
According to some embodiments of the invention, the building a mixture model based on historical data of the population average daily number comprises:
constructing the linear model based on historical data of the average population day;
training the non-linear model based on the historical data and a residual of the linear model;
and combining the linear model and the nonlinear model according to a preset rule to form the mixed model.
In some embodiments of the invention, the constructing the linear model based on historical data of population average daily population includes:
identifying and grading a model based on the historical data;
performing parameter estimation on the model to construct the linear model;
and carrying out diagnostic test on the constructed linear model.
According to some embodiments of the invention, an autocorrelation function or a partial autocorrelation function is used to perform regularity and non-regularity judgment on the historical data so as to identify and rank the model;
and determining parameters of the linear model by adopting a least square method.
In some embodiments of the invention, the linear model is an ARIMA model and the non-linear model is a BP neural network model.
The device for predicting the average arrival number of the population in the day based on the mixed model comprises the following components:
the model building module is used for building a mixed model based on historical data of the average daily population;
a calculation module for predicting the average daily arrival number of the population based on the mixture model;
wherein the hybrid model comprises a linear model constructed based on a linear data portion in the historical data and a nonlinear model constructed based on a nonlinear data portion in the historical data.
According to the prediction device for the average number of people arriving at the group based on the mixed model, the model construction module respectively constructs the linear model and the nonlinear model according to the linear data part and the nonlinear data part in the historical data of the average number of people arriving at the group, the linear model and the nonlinear model are combined to form the mixed model, the mixed model fully integrates the respective specific advantages of the linear model and the nonlinear model, and the calculation module is used for predicting the average number of people arriving at the group by using the mixed model, so that the accuracy and the reliability of the average number of people arriving at the group are effectively improved.
According to some embodiments of the invention, the model building module comprises:
the linear model building module is used for building the linear model based on historical data of the daily average population;
a nonlinear model construction module for training the nonlinear model based on the historical data and a residual of the linear model;
and the mixed model building module is used for combining the linear model and the nonlinear model according to a preset rule to form the mixed model.
In some embodiments of the invention, the linear model building module comprises:
the identification and order fixing module is used for identifying and fixing the order of the model based on the historical data;
the parameter estimation module is used for carrying out parameter estimation on the model and constructing the linear model;
and the diagnostic test module is used for carrying out diagnostic test on the constructed linear model.
According to some embodiments of the present invention, the identification and order-fixing module is configured to perform regularity and irregularity determination on the historical data by using an autocorrelation function or a partial autocorrelation function, so as to perform model identification and order fixing;
the parameter estimation module determines parameters of the linear model by a least square method.
In some embodiments of the invention, the linear model is an ARIMA model and the non-linear model is a BP neural network model.
Drawings
FIG. 1 is a flow chart of a method for predicting the average daily arrival number of a population based on a mixture model according to an embodiment of the invention;
FIG. 2 is a schematic diagram of a method for predicting the average daily arrival number of people in a population based on a mixture model according to an embodiment of the invention;
FIG. 3 is a flow chart of a method for constructing a hybrid model according to an embodiment of the invention;
FIG. 4 is a flow chart of a method of constructing an ARIMA model according to an embodiment of the invention;
FIG. 5 is a schematic diagram of a device for predicting the average daily arrival number of people in a population based on a mixture model according to an embodiment of the invention;
FIG. 6 is a schematic structural diagram of a model building module according to an embodiment of the invention;
FIG. 7 is a block diagram of a linear model building block according to an embodiment of the invention.
Detailed Description
To further illustrate the technical means and effects of the present invention adopted to achieve the predetermined purposes, the present invention is described in detail below with reference to the accompanying drawings and preferred embodiments.
In order to complete the prediction analysis of the number of the daily arriving people of a certain specific group, the invention adopts a mixed model method combining a linear model and a nonlinear model for specific analysis.
As shown in fig. 1, a method for predicting the average daily arrival number of a population based on a mixture model according to an embodiment of the present invention includes:
s100: constructing a mixed model based on historical data of the average population daily number;
s200: predicting the average daily arrival number of the population based on a mixed model;
the hybrid model comprises a linear model constructed based on a linear data part in the historical data and a nonlinear model constructed based on a nonlinear data part in the historical data.
According to the group daily average arrival number prediction method based on the mixed model, the linear model and the nonlinear model are respectively constructed according to the linear data part and the nonlinear data part in the historical data of the group daily average arrival number, the linear model and the nonlinear model are combined to form the mixed model, the mixed model is fully fused with the respective specific advantages of the linear model and the nonlinear model to predict the group daily average arrival number, and the accuracy and the reliability of the group daily average arrival number are effectively improved.
As shown in FIG. 3, according to some embodiments of the invention, constructing a mixture model based on historical data of the population's daily average population includes:
s110: constructing a linear model based on historical data of the daily average population;
s120: training a non-linear model based on historical data and a residual error of the linear model;
s130: and combining the linear model and the nonlinear model according to a preset rule to form a mixed model.
In some embodiments of the present invention, as shown in FIG. 4, constructing a linear model based on historical data of the population's average daily population includes:
s111: identifying and grading the model based on historical data;
s112: performing parameter estimation on the model to construct a linear model;
s113: and carrying out diagnostic test on the constructed linear model.
According to some embodiments of the invention, an autocorrelation function or a partial autocorrelation function is used for judging regularity and non-regularity of historical data so as to identify and rank a model;
the parameters of the linear model are determined using a least squares method.
In some embodiments of the invention, the linear model may employ an ARIMA model and the non-linear model may employ a BP neural network model.
As shown in fig. 5, the apparatus for predicting the average daily arrival number of the population based on the mixture model according to the embodiment of the present invention includes: the device comprises a model building module and a calculating module.
The model building module is used for building a mixed model based on historical data of the average daily population;
the calculation module is used for predicting the average daily arrival number of the population based on the mixed model;
the hybrid model comprises a linear model constructed based on a linear data part in the historical data and a nonlinear model constructed based on a nonlinear data part in the historical data.
According to the prediction device for the average number of people arriving at the group based on the mixed model, the model construction module respectively constructs the linear model and the nonlinear model according to the linear data part and the nonlinear data part in the historical data of the average number of people arriving at the group, the linear model and the nonlinear model are combined to form the mixed model, the mixed model fully integrates the respective specific advantages of the linear model and the nonlinear model, and the calculation module is used for predicting the average number of people arriving at the group by using the mixed model, so that the accuracy and the reliability of the average number of people arriving at the group are effectively improved.
According to some embodiments of the invention, as shown in FIG. 6, the model building module comprises: the device comprises a linear model building module, a nonlinear model building module and a mixed model building module.
The linear model building module is used for building a linear model based on historical data of the daily average population, the nonlinear model building module is used for training a nonlinear model based on the historical data and residual errors of the linear model, and the mixed model building module is used for combining the linear model and the nonlinear model according to a preset rule to form a mixed model.
In some embodiments of the present invention, as shown in FIG. 7, the linear model building block comprises: an identification and staging module, a parameter estimation module, and a diagnostic test module.
The identification and order-fixing module is used for identifying and fixing the model based on historical data. The parameter estimation module is used for carrying out parameter estimation on the model and constructing a linear model. And the diagnostic test module is used for carrying out diagnostic test on the constructed linear model.
According to some embodiments of the invention, the identification and order-fixing module is configured to perform regularity and irregularity determination on the historical data by using an autocorrelation function or a partial autocorrelation function to identify and order the model. The parameter estimation module determines parameters of the linear model by a least square method.
In some embodiments of the invention, the linear model is an ARIMA model and the non-linear model is a BP neural network model.
The method for predicting the average daily arrival number of the population based on the hybrid model is described in detail below by taking an ARIMA model as a linear model and a BP neural network model as a non-linear model in combination with the accompanying drawings. It is to be understood that the following description is only exemplary in nature and is not to be taken as a specific limitation of the invention.
The invention provides a mixed model with linear modeling capability and non-linear modeling capability aiming at the actual problem of predicting the number of people arriving at the average population day. Researches show that by combining different models, the average daily arrival number of people in a group can be accurately and reliably predicted.
It should be noted that, since the ARIMA model cannot capture the nonlinear structure of the data, the residual error of the linear model will contain information about the nonlinearity, and therefore, the result of the BP neural network can be used as a prediction of the ARIMA model error term. Relevant studies have demonstrated that neural networks can significantly outperform linear regression models when data contains outliers or multiple collinearity; meanwhile, the performance of the neural network on the effect of the linear regression problem depends on the sample size and the noise level.
The hybrid model constructed by the invention comprises three steps:
first, an ARIMA model was introduced to analyze the linear part of the study; secondly, modeling and estimating a residual error of the ARIMA model by the BP neural network model; and finally, combining the ARIMA model (linear model) with the BP neural network model (nonlinear model) and outputting a final result.
Specifically, step 1, ARIMA-based population arrival prediction:
the autoregressive moving average model (ARIMA model) is one of the most widely used models in time series models. Generally speaking, ARIMA is applicable to modeling of time series data. The ARIMA model is constructed according to the arrival number of the specific group in the specified time period. Generally, the ARIMA (p, d, q) model includes three types of parameters: an autoregressive parameter p, a fraction d, and a moving average parameter q.
The invention introduces a Box-Jenkins method to construct a model. As shown in fig. 4, the construction of ARIMA model mainly includes three steps: (1) identifying; (2) estimating; and (3) diagnosis and inspection. Furthermore, before fitting the ARIMA model, the stationarity of the sequence order needs to be ensured.
Specifically, the method comprises the following steps: the "identification" process refers to using Auto-Correlation Functions (ACFs) and Partial Auto-Correlation Functions (PACFs) to study and judge regular and irregular data; in the estimation process, a backward least square method is applied to determine parameters of the ARIMA model; in the diagnosis and examination stage, whether the residuals are independent and normally distributed is checked through white noise test, and whether the modeling of the established model on the sequence is sufficient is verified.
In the ARIMA model, the future values of variables can be expressed as a linear function of several past values and random errors. That is, the basic process of generating a time series has the following form:
y t ＝θ 0 +φ 1 y t-1 +φ 2 y t-2 +…+φ p y t-p +ε t -θ 1 ε t-1 -θ 2 ε t-2 -…-
θ q ε t-q (1)
wherein, y t And ε t Respectively representing the error of the true value and the random over the time period t, { phi i |i∈[1,p]And { theta } j |j∈[1,q]Denotes the model parameters. Q is an integer as described above, often referred to as the order of the model. Assuming random error (i.e.. Epsilon.) t ) Are independent and identically distributed, and have a mean of 0 and a variance of σ 2 。
It should be noted that formula (1) encompasses the special case of the ARIMA model. In particular, if q =0, equation (1) becomes an AR model of order P; when p =0, the model becomes an MA model of order q. The core of ARIMA model construction is the determination of the appropriate model order (p, q). Finally, the fitted ARIMA model is used for predicting the number of people arriving at the population day in a specific time period.
Step 2: population arrival prediction based on BP neural network
The role of BP neural networks in establishing appropriate weights in distributed adaptive networks has been demonstrated many times. The learning process is accomplished by iteratively adjusting the weights based on a set of input patterns and a corresponding set of desired output patterns. In this iterative process, the input pattern is presented to the network and propagated forward to determine the signal produced at the output unit. The difference between the actually generated output signal and the predetermined desired output signal in each output cell represents an error that propagates back through the network to adjust the weights. Training continues until the network responds with an output signal, and at the same time, the sum of Root Mean Square Errors (RMSE) of the desired output signal is less than a preset threshold.
When input pattern x is applied to the network, each cell is dynamically determined to be activated using the following logic activation function:
Figure BDA0002487496900000081
wherein, y x,j Indicates that the cell j, w is activated in response to the application pattern x j,i Represents the weight from cell i to cell j, and e j Is the deviation of cell j. Then, the back propagation is invoked to update all the weights in the network according to the following rules:
Δw j,i (n+1)＝η·δ x,j ·y x,i +α·Δw j,i (n) (3)
where n represents the number of iterations, i.e., the number of times the system is iteratively trained, η represents the learning rate, and α is considered to be a momentum factor. Delta x,j The error signal representing cell j is discussed in the following cases:
(1) Error signal delta of output layer unit x,j According to the base line value (denoted as y) * x,j ) The difference from the actual value is calculated as follows:
Figure BDA0002487496900000082
(2) Concealing the error signal delta of a layer unit x,j Is a function of the error signals of the cells in the layer above the cell j and the weights of the connections:
Figure BDA0002487496900000091
in general, in practical application, the invention adopts the BP neural network to predict the daily arrival of the population in a specific time period: after each input pattern is presented to the network, an error vector between the output units is determined and propagated back through the network to update the weights. The next input pattern is then processed and the process is repeated. The two parameters η and α (in equation (3)) refer to the adjustment of the step size and the weight of the "memory" of the previous step, respectively. Assuming that the appropriate η and α are chosen, the back propagation process will generally converge to a minimum that meets the user-required criteria, the sum of the squared errors of the output signals for all inputs x, i.e., the sum of the squared errors
Figure BDA0002487496900000092
Will typically be less than a preset threshold.
And step 3: hybrid model combining ARIMA model and BP neural network
The invention assumes that the time series consists of a linear autocorrelation structure and a non-linear component. Let Y t Representing the original time sequence, L t Is a linear component, N t Is a non-linear component. Therefore, the invention provides a hybrid model, which combines the prediction result (i.e. linear component) of ARIMA with the prediction result (i.e. non-linear component) of BP to generate the overall prediction result of the daily arrival prediction study.
In particular, the original time series can be regarded as a combination of linear components and linear components, as follows:
Y t ＝L t +N t (6)
the invention firstly utilizes an ARIMA model (see step 1 for details) to process the linear component L t Modeling is carried out to obtain a prediction result
Figure BDA0002487496900000093
Furthermore, we will refer to the original time series Y in step t t And a linear component->
Figure BDA0002487496900000094
The residual error between is denoted as e t I.e. by
Figure BDA0002487496900000095
Obviously, the residual of the linear model contains only the non-linear relation and is implicitly embedded in the original time series Y t The non-linear relationship of (a). Note that the residual is important in diagnosing the adequacy of the linear model, which is not sufficient if there is still a linearly dependent structure in the residual.
However, any significant non-linear mode in the residual will expose the limitations of ARIMA. The non-linear relationship can be discovered by modeling the residual error with a neural network. Therefore, the invention introduces a BP neural network model to residual errors e t Estimating, and expressing the prediction result of the BP neural network model as
Figure BDA0002487496900000096
(see step 2 for details). Through the above work, the hybrid model generates an overall prediction result as follows:
Figure BDA0002487496900000097
in summary, the invention is directed to a hybrid model method combining a linear model (ARIMA model) and a nonlinear model (BP neural network) for time series prediction, the hybrid model sufficiently integrates the respective unique advantages of the ARIMA model and the BP neural network, realizes the behavior law of a specific group automatically captured and predicted from historical data, and realizes the prediction of the position of the specific group at a certain time in the future and the prediction of the number of people arriving at a specified area and a surrounding area. The method has wide applicable range and can be applied to various tasks such as group abnormal behavior detection, group behavior rule modeling and the like.
While the invention has been described in connection with specific embodiments thereof, it is to be understood that it is intended by the appended drawings and description that the invention may be embodied in other specific forms without departing from the spirit or scope of the invention.

Claims (8)

1. A method for predicting the average daily arrival number of people in a group based on a mixed model is characterized by comprising the following steps:
constructing a mixed model based on historical data of the average population daily number;
predicting the average number of arriving people of the population on a daily basis based on the mixture model;
wherein the hybrid model comprises a linear model constructed based on a linear data portion in the historical data and a nonlinear model constructed based on a nonlinear data portion in the historical data;
the historical data of the population average daily population is time sequence data, the linear model is an ARIMA model, the nonlinear model adopts a BP neural network, and when an input mode x is applied to the network, the following logic activation functions are used for dynamically determining whether each unit in the BP neural network is activated or not:
Figure FDA0004040601350000011
wherein, y x,j Indicates that the unit j, w is activated in response to the application pattern x j,i Represents the weight from cell i to cell j, and e j Is the deviation of cell j and then calls back propagation to update all weights in the network according to the following rule:
Δw j,i (n+1)＝η·δ x,j ·y x,i +α·Δw j,i (n)；
where n represents the number of iterations, i.e. the number of times the system is iteratively trained, η represents the learning rate, and α is considered as a momentum factor, δ x,j The error signals of the cell j, the output layer and the hidden layer are respectively discussed as follows:
error signal delta of output layer unit x,j According to the base line value y * x,j The difference from the actual value is calculated as follows:
Figure FDA0004040601350000012
concealing the error signal delta of a layer unit x,j Is a function of the error signals of the cells in the layer above the cell j and the weights of the connections:
δ x,j ＝y x,j ·(1-y x,j )·∑ k δ x,k ω k,j 。
2. the method for predicting the average daily population arriving people based on the mixture model as claimed in claim 1, wherein the constructing the mixture model based on the historical data of the average daily population includes:
constructing the linear model based on historical data of the population daily average number;
training the non-linear model based on the historical data and a residual of the linear model;
and combining the linear model and the nonlinear model according to a preset rule to form the mixed model.
3. The method for predicting the average daily population arriving people based on the hybrid model as claimed in claim 2, wherein the constructing the linear model based on the historical data of the average daily population includes:
identifying and scaling a model based on the historical data;
performing parameter estimation on the model to construct the linear model;
and carrying out diagnostic test on the constructed linear model.
4. The mixed model based population average arrival population prediction method of claim 3,
judging regularity and non-regularity of the historical data by adopting an autocorrelation function or a partial autocorrelation function so as to identify and order the model;
and determining parameters of the linear model by adopting a least square method.
5. A device for predicting the average arrival number of people in a group based on a hybrid model is characterized by comprising:
the model building module is used for building a mixed model based on historical data of the average daily population;
the calculation module is used for predicting the average daily arrival number of the group based on the mixed model;
wherein the hybrid model comprises a linear model constructed based on a linear data portion in the historical data and a nonlinear model constructed based on a nonlinear data portion in the historical data;
the historical data of the population average daily population is time sequence data, the linear model is an ARIMA model, the nonlinear model adopts a BP neural network, and when an input mode x is applied to the network, the following logic activation functions are used for dynamically determining whether each unit in the BP neural network is activated or not:
Figure FDA0004040601350000021
wherein, y x,j Indicates that the unit j, w is activated in response to the application pattern x j,i Represents the weight from cell i to cell j, and e j Is the deviation of cell j and then calls back propagation to update all weights in the network according to the following rule:
Δw j,i (n+1)＝η·δ x,j ·y x,i +α·Δw j,i (n)；
where n represents the number of iterations, i.e. the number of times the system is iteratively trained, η represents the learning rate, and α is considered as a momentum factor, δ x,j The error signals of the output layer and the hidden layer are respectively discussed as follows:
error signal delta of output layer unit x,j According to the base line value y * x,j With the actual valueThe difference between them is calculated as follows:
Figure FDA0004040601350000031
concealing the error signal delta of a layer unit x,j Is a function of the error signals of the cells in the layer above the cell j and the weights of the connections:
Figure FDA0004040601350000032
6. the mixed model based population daily average arriving people prediction device of claim 5, wherein the model building module comprises:
the linear model building module is used for building the linear model based on historical data of the average daily population;
a nonlinear model construction module for training the nonlinear model based on the historical data and a residual of the linear model;
and the mixed model building module is used for combining the linear model and the nonlinear model according to a preset rule to form the mixed model.
7. The mixed model based population averaged daily arrival population prediction device of claim 6, wherein the linear model construction module comprises:
the identification and order fixing module is used for identifying and fixing the order of the model based on the historical data;
the parameter estimation module is used for carrying out parameter estimation on the model and constructing the linear model;
and the diagnostic test module is used for carrying out diagnostic test on the constructed linear model.
8. The mixed model based population average arrival population prediction apparatus of claim 7,
the identification and order-fixing module is used for judging regularity and non-regularity of the historical data by adopting an autocorrelation function or a partial autocorrelation function so as to identify and fix the order of the model;
the parameter estimation module determines parameters of the linear model by a least square method.
CN202010395764.0A 2020-05-12 2020-05-12 Group daily average arrival number prediction method and device based on hybrid model Active CN111612226B (en)

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