Railway marshalling station operation situation evaluation system based on machine learning
By applying machine learning technology in railway marshalling stations, combining entropy weight-CRITIC and K-Means methods, a railway marshalling station transportation production operation situation evaluation model is constructed, and the problems of long evaluation cycles and insufficient effectiveness in the existing technology are solved, and the problem of long evaluation cycles and insufficient efficiency is realized. The timely and accurate assessment of the transportation production operation trend of railway marshalling stations has been made, and the efficiency and safety of transportation production management has been improved.
Patent Information
- Application Number
- CN202411208543.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-08-30
- Publication Date
- 2024-12-17
AI Technical Summary
In the evaluation of the transportation production operation trend of railway marshalling stations, the methods are relatively traditional and the application of modern data analysis technology is lacking, resulting in long evaluation cycles and insufficient efficiency, making it difficult to achieve timely and macro-level short-term operation of railway marshalling stations. Comprehensive monitoring and evaluation.
Using a machine learning-based railway marshalling station operation situation evaluation system, through the entropy weight-CRITIC combination empowerment method and the K-Means clustering method, a railway marshalling station transportation production operation situation evaluation model is constructed, and a situation level evaluation is carried out in combination with the BP neural network. Form a visual interface to achieve timely and accurate situation evaluation.
It has achieved timely, macro and comprehensive monitoring and evaluation of the transportation production operation trends of railway marshalling stations, improved operational efficiency and safety, and provided more scientific and reasonable decision-making support for transportation production management.
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Figure CN119151138A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of railway dispatching, and in particular to a railway marshalling yard operation situation assessment system based on machine learning. Background Art
[0002] Railway marshaling yards, as the core component of the railway transportation system, undertake a series of key operational tasks such as train arrival, departure, disassembly, and marshaling. Their operating efficiency and safety are directly related to the smoothness and stability of the entire railway transportation network. In recent years, with the rapid development of the country's economy and society and the continuous improvement of people's living standards, the demand for railway freight has shown an increasingly strong trend. This growth trend not only highlights the important position of railway transportation in the national economy, but also puts forward higher requirements for the transportation production operations of railway marshaling yards.
[0003] However, in the transportation production operation process of the railway marshalling yard, various bottlenecks and problems often occur due to factors such as complex operation processes, changeable operating environments, and numerous operating equipment, such as low operating efficiency, high operating costs, and hidden safety hazards in operations. These problems not only restrict the improvement of the transportation production capacity of the railway marshalling yard, but also affect the overall efficiency and competitiveness of railway transportation. Therefore, evaluating the transportation production operation status of the railway marshalling yard has become an important issue that needs to be urgently solved in the current railway transportation field. Through in-depth analysis and evaluation of the transportation production operation status of the railway marshalling yard, bottlenecks and problems in the operation process can be discovered in a timely manner, providing strong support for optimizing the operation process, improving operation efficiency, and ensuring operation safety.
[0004] In recent years, with the rapid progress of information technology and the widespread application of technologies such as machine learning and artificial intelligence, new means and methods have been provided for the assessment of the transportation production operation situation of railway marshalling yards. By collecting and analyzing massive data in the transportation production operation process of railway marshalling yards, an accurate situation assessment model is constructed based on machine learning algorithms and artificial intelligence technology, so that dispatching and commanding personnel can timely grasp the current transportation production operation situation of railway marshalling yards.
[0005] The concept of situation assessment first appeared in the military field. It was proposed by the Joint Directors of Laboratory (JDL) in the United States in 1986. After Endsley's continuous in-depth research, the basic theoretical system of situation assessment was gradually formed. Since the relevant research was proposed, the situation theory at home and abroad has been continuously deepened and widely used in many industries such as military stations, production control, information security, and transportation.
[0006] The military field mainly studies battlefield situations so that commanders can make reasonable strategic decisions. Azarewicz et al. studied template-based multi-factor plan identification and tactical situation assessment. Template refers to a set of rules for various variables in a combat entity. When reasoning about the battlefield situation, the immediate factors are compared with the factors in the template. Through comparative analysis of the similarity of the factors, the template is flexibly adjusted, and the battlefield situation reasoning results are updated to assist strategic decision makers in controlling the battlefield situation and making strategic deployments.
[0007] In the field of production control, situation research has been specifically applied to power monitoring, industrial control and other aspects. Miao et al. proposed a situation assessment calculation model and a nuclear power plant situation assessment measurement method based on this model, and simulated and demonstrated the application of the model in the automation-assisted assessment decision-making of nuclear power plants. Based on the basic theoretical analysis of situation awareness, Panteli et al. emphasized the importance of situation awareness theory in maintaining the overall good operation of the power system, and proposed a general process for achieving situation awareness, aiming to provide guidance for technical and user-oriented information systems.
[0008] In terms of information security, situational research started early. In 1999, Bass introduced the concept of situational awareness into the field of network security research and proposed the use of multi-sensor data fusion technology to study cyberspace situational awareness. Subsequently, other scholars cited a variety of methods or theories to continue to study network security situation in depth. Ambrosio et al. proposed a hybrid startup computer software system for security situation assessment and response measures evaluation in the face of large-scale network attacks, which is used to assess the risks and uncertainties brought by network attacks and provide timely responses and strategy adjustment measures.
[0009] The research objects of situation research in the field of transportation are different. There are many related studies on road traffic. Scholars have conducted in-depth research on it by combining different theoretical methods. Schubert et al. proposed a system that can perceive the surrounding environment of the vehicle, evaluate the current traffic conditions and provide lane change suggestions to the driver. It systematically integrates vehicle and road image detection and processing technology, vehicle identification and tracking technology, and vehicle lane change decision technology under uncertainty based on Bayesian networks, and proposed a highly automated driving assistance decision system that can be further improved.
[0010] There are relatively few situation studies on other modes of transportation. In terms of urban rail transit, Yu Xinming conducted research on disaster chains in urban rail transit systems based on the relevant theories of disaster chains and multi-layer networks, constructed a disaster chain network model for multi-layer urban rail transit systems, and conducted safety situation assessments on urban rail transit systems based on this model. There are also related studies combining situation assessments in airway transportation. Zhao Yifei and others studied airway traffic situation assessment based on situation awareness, and proposed an airway traffic situation assessment method at three levels: situation element extraction, situation understanding, and situation prediction, combining fuzzy comprehensive evaluation methods, and verified the effectiveness and feasibility of this method through examples.
[0011] In the field of railway transportation, Yan Xu and others took the multi-attribute analysis of accidents as the starting point, constructed and quantified the regional railway transportation safety situation characterization index system, and constructed an improved ideal point method-cosine similarity evaluation model based on combined weights based on relative distance and relative trend.
[0012] The evaluation of railway marshalling yards at home and abroad mainly focuses on three aspects: safety, reliability and operational efficiency.
[0013] In terms of safety, scholars such as Li Yinghong, Zhao Xiaohui and Mu Mingxin have constructed a safety evaluation index system for marshalling yards based on management, equipment, environment and personnel, and used matter-element analysis and fuzzy network analysis to build safety evaluation models. Based on the basic concepts, methods and processes of safety evaluation, Muttram conducted safety analysis using railway driving safety as an evaluation example.
[0014] At the reliability level, Chen Liang and others conducted a quantitative analysis of the working reliability of the dismantling and marshalling subsystem through queuing theory and random process theory, constructed calculation formulas under different queuing models, and took Zhengzhou North Station as an example to collect actual data and verify it using mathematical statistics methods, calculated the working reliability of the dismantling and marshalling subsystem, and discussed measures to improve its reliability.
[0015] In terms of operational efficiency, Wang Yang and others took Fengtai West Station as a specific case to explore the main factors for the low operational efficiency of the current marshalling yard, and then proposed targeted improvement measures: improving locomotive utilization efficiency, strictly implementing marshalling plans, strengthening equipment maintenance, accelerating equipment upgrades, and integrating information systems to comprehensively improve the operational efficiency of the marshalling yard. Summary of the invention
[0016] An embodiment of the present invention provides a railway marshalling yard operation status assessment system based on machine learning, which is used to solve the problems existing in the prior art.
[0017] In order to achieve the above object, the present invention adopts the following technical scheme.
[0018] Railway marshalling yard operation situation assessment system based on machine learning, including:
[0019] Railway marshalling yard transportation production operation situation analysis module is used for:
[0020] Based on the four key transport production operation links from railway marshaling yard to unmarshaling, the transport production operation situation of railway marshaling yard is divided into four transport production operation situation subsets;
[0021] Analyze each transportation production operation situation subset from the perspective of vehicle flow input - system internal transportation production operation - vehicle flow output, and obtain the constituent elements of each transportation production operation situation subset;
[0022] Based on the constituent elements of each transport production operation situation subset, a railway marshalling yard transport production operation situation assessment model is constructed;
[0023] The railway marshalling yard transportation production operation situation scoring module is used to: solve the railway marshalling yard transportation production operation situation evaluation model through the entropy weight-CRITIC combined weighting method, and score the railway marshalling yard transportation production operation situation;
[0024] The K-Means-based situation grading module is used to: grade the transportation production operation situation of the railway marshalling yard based on the score of the transportation production operation situation of the railway marshalling yard through the K-Means clustering method;
[0025] The level of transportation production operation status of railway marshalling yard is used for transportation production operation of railway marshalling yard;
[0026] The model training module is used to: train a railway marshalling yard transportation production operation status assessment model based on the level of the railway marshalling yard transportation production operation status.
[0027] Preferably, the four key transport production operation links include: the transport production operation status of the arrival subsystem, the transport production operation status of the dismantling subsystem, the transport production operation status of the marshaling subsystem, and the transport production operation status of the departure subsystem.
[0028] Preferably, the entropy weight-CRITIC combined weighting method is used to solve the railway marshalling yard transportation production operation situation assessment model, and the assessment results of the railway marshalling yard transportation production operation situation are obtained, which specifically include:
[0029] Pass-through
[0030] X=(x hk ) m×n (1)
[0031] Construct a situation indicator data matrix; where x hkis the value of the kth situation indicator in the hth period to be evaluated, m is the number of periods to be evaluated for the transportation production operation situation of the railway marshalling yard, and n is the number of situation indicators;
[0032] By non-dimensionalizing the calculation formula of benefit-based indicators
[0033]
[0034] And the dimensionless calculation formula of cost-type indicators
[0035]
[0036] The situation indicator data matrix is dimensionless; where X max is the maximum value of the k-th situation indicator, X min is the minimum value of the k-th situation indicator;
[0037] Pass-through
[0038]
[0039] Calculate the probability p of the kth situation indicator appearing in the hth period to be evaluated hk ;
[0040] The information amount G of the k-th situation indicator is calculated by k
[0041]
[0042] Calculate the information entropy e of the k-th situation indicator k ; In the formula, suppose when p hk = 0, p hk Inp hk =0;
[0043] Pass-through
[0044]
[0045] Calculate the weight coefficient ω′ of the kth situation indicator k ;
[0046] Pass-through
[0047]
[0048] Calculate the correlation coefficient r of the situation index hk ; In the formula, is the mean value of the k-th situation indicator, x' hl is the value obtained by dimensionless processing of the lth situation indicator in the hth period to be evaluated, x' klis the value obtained by dimensionless processing of the lth situation indicator in the kth period to be evaluated;
[0049] Pass-through
[0050]
[0051] Calculate the information amount G of the kth situation indicator k ; In the formula, σ k is the standard deviation of the k-th situation indicator;
[0052] Pass-through
[0053]
[0054] Calculate the weight coefficient ω″ of the kth situation indicator k ;
[0055] Pass-through
[0056] ω k =βω' k +(1-β)ω″ k (10)
[0057] Calculate the combined weight ω of the kth situation indicator k ;Wherein, β=0.5;
[0058] Pass-through
[0059]
[0060] The dimensionless matrix X' in the situation indicator system is hk ) m×n Perform standardization to obtain a standardized evaluation matrix;
[0061] Through the situation index weight coefficient ω=(ω 1 ,ω 2 ,…,ω n ) and the standardized evaluation matrix X' after normalization and through the formula
[0062] z hk =ω k x″ hk (12)
[0063] Construct the weight matrix Z = (z hk ) m×n ;
[0064] Pass-through
[0065]
[0066] Determine the positive ideal solution Z +and negative ideal solution Z - ;
[0067] Pass-through
[0068]
[0069] Calculate the distance between each time period to be evaluated and the positive and negative ideal solutions; where, is the distance between the evaluation vector and the positive ideal solution in the hth period to be evaluated, is the distance from the evaluation vector to the negative ideal solution in the hth period to be evaluated, is a positive ideal solution Z + The kth component of is the negative ideal solution Z - The kth component of ;
[0070] Pass-through
[0071]
[0072] Calculate the railway marshalling yard transportation production operation status score Z in each evaluation period h .
[0073] Preferably, based on the score of the transportation production operation status of the railway marshalling yard, the transportation production operation status of the railway marshalling yard is graded by the K-Means clustering method, specifically including:
[0074] E1 randomly selects k sample points as the initial cluster centers;
[0075] E2 pass-through
[0076]
[0077] Calculate the Euclidean distance between each sample point and each cluster center in the data set, and then classify each sample point into the category corresponding to the cluster center with the shortest Euclidean distance; where x i is the set of objects classified into the i-th category, μ i is the centroid corresponding to category i, and n is the total number of features of the sample;
[0078] E3 calculates the mean of all sample points in each category and uses the mean point as the new cluster center;
[0079] E4 repeats steps E2 and E3 until the change of the cluster center is less than a preset threshold or reaches a preset maximum number of iterations;
[0080] E5 pass-through
[0081]
[0082] Calculate the silhouette coefficient of each sample; calculate the average of the silhouette coefficients of all samples to obtain the silhouette coefficient of the clustering result; in formula (18), b(i) 为样本 The average distance between sample i and other samples in the same category, and a(i) is the average distance between sample i and all samples that do not belong to the same category.
[0083] Preferably, the railway marshalling yard transportation production operation situation assessment model is a BP neural network-based model, including an input layer, a hidden layer and an output layer arranged in sequence along the direction of forward propagation of the information flow; the number of neurons in the hidden layer is calculated by the formula
[0084]
[0085] Calculated; where n is the number of neurons in the input layer, m is the number of neurons in the output layer, and a is a constant between 1 and 10;
[0086] The process of forward propagation of information flow in the railway marshalling yard transportation production operation situation assessment model includes:
[0087] Pass-through
[0088]
[0089] Input data to the neurons in the hidden layer; where w ij is the weight from hidden layer neuron i to input layer neuron j, x j is the input of neuron j in the input layer, θ i is the threshold of hidden layer neuron i, M is the total number of samples;
[0090] Pass-through
[0091]
[0092] Process the data input to the neurons in the hidden layer; and calculate the result y i As input to the output layer;
[0093] Pass-through
[0094]
[0095] Input data to the neurons in the output layer; where w ki is the weight from output layer neuron k to hidden layer neuron i, φ is the activation function of the hidden layer, a k is the threshold of neuron k in the output layer;
[0096] Pass-through
[0097]
[0098] Process the data input to the neurons in the output layer; and calculate the results o k As the output of the output layer; where, is the activation function of the output layer;
[0099] The process of information flow back propagation in the railway marshalling yard transportation production operation situation assessment model includes:
[0100] Pass-through
[0101]
[0102] Calculate the expected output of the network for each sample and the actual output o of the output layer k The error of k is the actual value of the kth neuron in the output layer, o k is the predicted value of the kth neuron in the output layer;
[0103] Pass-through
[0104]
[0105] Calculate the total error of all samples; where N is the total number of samples and L is the total number of neurons in the output layer;
[0106] Pass-through
[0107]
[0108] Calculate and obtain the correction amount of the output layer threshold, the correction amount of the hidden layer weight and the threshold correction amount;
[0109] Pass-through
[0110] △w ki =ηδ k y i (29)
[0111]
[0112] Calculate the weight of the output layer and the correction amount of the threshold; where δ k and δ i is the local gradient, η is the learning rate;
[0113] Pass-through
[0114] △w ij =ηδ i x j (31)
[0115] △θ i =ηδ i (32)
[0117] Calculate the hidden layer weights and threshold corrections.
[0118] It can be seen from the technical solutions provided by the above-mentioned embodiments of the present invention that the present invention provides a railway marshalling yard operation situation assessment system based on machine learning. The system takes the railway marshalling yard as the research object, and based on the situation assessment theory, combines machine learning, cluster analysis and other methods to conduct a comprehensive assessment of the transportation production operation status of the railway marshalling yard within a short time interval from four aspects: arrival, disintegration, marshalling and departure; proposes the concept of railway marshalling yard transportation production operation situation, and extracts the railway marshalling yard transportation production operation situation assessment indicators based on the railway marshalling yard operation process; the machine learning model used can accurately find the correlation between each sub-item assessment indicator and the railway marshalling yard transportation production operation situation level, and obtain objective and reasonable assessment results; based on the theoretical results of the research on the transportation production operation situation of the railway marshalling yard, the situation assessment is carried out through a visual interface to form a railway marshalling yard transportation production operation situation assessment system based on machine learning. The system provided by the present invention innovatively proposes a research method for transport production operation situation assessment based on machine learning, which effectively solves the problem of transport production operation situation assessment in railway marshalling yards; the system is strong; by comparing with the TOPSIS comprehensive evaluation method, the entropy weight-CRITIC-TOPSIS comprehensive evaluation method proposed in this paper can make the evaluation scheme more trending in the best and worst schemes, and finally manifests as a more obvious bias in the superiority and inferiority of the situation assessment results; the machine learning model used can better find the complex relationship between the situation indicators and the situation level of the transport production operation of the railway marshalling yard based on the K-Means clustering algorithm, and can make a more accurate evaluation result. By building a railway marshalling yard transport production operation situation assessment system based on machine learning, transport production personnel can monitor and evaluate the transport production operation situation of the railway marshalling yard in a timely, macro and comprehensive manner.
[0119] Additional aspects and advantages of the present invention will be given in part in the following description, which will become obvious from the following description, or may be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS
[0120] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.
[0121] Figure 1 A logical block diagram of a railway marshalling yard operation situation assessment system based on machine learning provided by the present invention;
[0122] Figure 2A schematic diagram of a railway marshalling yard transportation production operation situation assessment index system of a railway marshalling yard operation situation assessment system based on machine learning provided by the present invention;
[0123] Figure 3 A flow chart of railway marshalling yard transportation production operation situation assessment of the railway marshalling yard operation situation assessment system based on machine learning provided by the present invention;
[0124] Figure 4 A schematic diagram of the silhouette coefficients corresponding to different K values of the railway marshalling yard operation situation assessment system based on machine learning provided by the present invention;
[0125] Figure 5 A three-layer BP neural network topology diagram of the railway marshalling yard operation situation assessment system based on machine learning provided by the present invention;
[0126] Figure 6 A flow chart of the training and testing of the railway marshalling yard transportation production operation situation level assessment model based on BP neural network of the railway marshalling yard operation situation assessment system based on machine learning provided by the present invention;
[0127] Figure 7 A schematic diagram of the BP neural network training path of the railway marshalling yard operation situation assessment system based on machine learning provided by the present invention;
[0128] Figure 8 A schematic diagram showing a situation level assessment module of a railway marshalling yard operation situation assessment system based on machine learning provided by the present invention;
[0129] Fig. 9 A schematic diagram showing a situation scoring module of a railway marshalling yard operation situation assessment system based on machine learning provided by the present invention;
[0130] Fig.10 A schematic diagram showing a K-Means-based situation level classification module of a railway marshalling yard operation situation assessment system based on machine learning provided by the present invention;
[0131] Fig.11 A schematic diagram showing a machine learning training module of a railway marshalling yard operation situation assessment system based on machine learning provided by the present invention.
[0132] In the figure:
[0133] 101. Railway marshalling yard transportation production operation situation analysis module 102. Railway marshalling yard transportation production operation situation scoring module 103. K-Means-based situation level classification module 104. Model training module. DETAILED DESCRIPTION
[0134] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention.
[0135] It will be understood by those skilled in the art that, unless expressly stated, the singular forms "one", "said", and "the" used herein may also include plural forms. It should be further understood that the term "comprising" used in the specification of the present invention refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof. It should be understood that when we refer to an element as being "connected" or "coupled" to another element, it may be directly connected or coupled to the other element, or there may be intermediate elements. In addition, the "connection" or "coupling" used herein may include wireless connection or coupling. The term "and / or" used herein includes any unit and all combinations of one or more associated listed items.
[0136] To facilitate understanding of the embodiments of the present invention, several specific embodiments will be further explained below with reference to the accompanying drawings, and each embodiment does not constitute a limitation on the embodiments of the present invention.
[0137] The present invention provides a railway marshalling yard operation situation assessment system based on machine learning, which is used to solve the following technical problems existing in the prior art:
[0138] At present, many domestic and foreign experts and scholars have obtained rich and beneficial research results in the fields of situation assessment theory and railway marshaling yard evaluation. However, there are still some shortcomings in the existing research.
[0139] (1) Situation Assessment Theory
[0140] In terms of research methods, fuzzy comprehensive evaluation, hierarchical analysis method, multi-attribute decision analysis method, etc. are often used for situation assessment. However, in terms of research objects, the current situation research in the field of transportation is mainly carried out on road traffic, and there are relatively few studies related to railway transportation. Among the existing railway transportation situation studies, most of them focus on safety, and there are relatively few situation studies based on transportation organization. At the same time, there is no situation research on railway marshalling yards.
[0141] (2) Evaluation of Railway Marshalling Yards
[0142] At present, the evaluation research on railway marshalling yards mostly relies on traditional methods such as matter-element analysis, fuzzy network analysis and hierarchical analysis, and is still insufficient in the use of modern data analysis technologies such as machine learning. Machine learning technology has great application potential in the evaluation of railway marshalling yards with its powerful data processing and pattern recognition capabilities. Its lack undoubtedly limits the depth and breadth of the evaluation work. In terms of the timeliness of the evaluation research on railway marshalling yards, the existing studies often have a long evaluation cycle and are mostly aimed at evaluating railway marshalling yards over a long period of time (such as a month or a year). There are relatively few evaluation studies on the short-term operation of a single railway marshalling yard.
[0143] In summary, with the continuous advancement of railway transportation intelligence based on emerging information technology, new requirements have been put forward for the development of railway marshalling yard intelligent technology. At present, railway marshalling yards have formed a complete transportation production information collection system, but the overall transportation production operation status of railway marshalling yards still mainly depends on the experience and judgment of transportation production personnel. In order to ensure the efficient development of the dispatching and command work of railway marshalling yards and improve the level and efficiency of transportation production operations of railway marshalling yards, transportation production personnel need to conduct timely, macro and comprehensive monitoring and evaluation of the transportation production operation status of railway marshalling yards. A railway marshalling yard transportation production operation status evaluation system should be established, and machine learning algorithms should be introduced to achieve timely monitoring and evaluation of the transportation production operation status of railway marshalling yards.
[0144] See also Figure 1 The present invention provides a railway marshalling yard operation situation assessment system based on machine learning, comprising:
[0145] The railway marshalling yard transportation production operation situation analysis module 101 is used to:
[0146] Based on the four key transport production operation links from railway marshaling yard to unmarshaling, the transport production operation situation of railway marshaling yard is divided into four transport production operation situation subsets;
[0147] Analyze each transportation production operation situation subset from the perspective of vehicle flow input - system internal transportation production operation - vehicle flow output, and obtain the constituent elements of each transportation production operation situation subset;
[0148] Based on the constituent elements of each transport production operation situation subset, a railway marshalling yard transport production operation situation assessment model is constructed;
[0149] The railway marshalling yard transportation production operation situation scoring module 102 is used to solve the railway marshalling yard transportation production operation situation evaluation model through the entropy weight-CRITIC combined weighting method, and score the railway marshalling yard transportation production operation situation;
[0150] The K-Means-based situation level classification module 103 is used to: classify the transportation production operation situation of the railway marshalling yard by the K-Means clustering method based on the score of the transportation production operation situation of the railway marshalling yard;
[0151] The obtained level of the transportation production operation status of the railway marshalling yard is used for the transportation production operation management of the railway marshalling yard to optimize the operation process, improve operation efficiency and ensure operation safety.
[0152] The model training module 104 is used to train the railway marshalling yard transportation production operation situation assessment model based on the assessment results of the railway marshalling yard transportation production operation situation, the score of the railway marshalling yard transportation production operation situation and the level of the railway marshalling yard transportation production operation situation.
[0153] Based on the four key transport production operation links from railway marshalling yard to disassembly and dispatch, the present invention divides the transport production operation situation of railway marshalling yard into the transport production operation situation of the above four subsystems, and analyzes the transport production operation situation constituent elements of each subsystem from the perspective of "vehicle flow input-system internal transport production operation-vehicle flow output", and constructs a railway marshalling yard transport production operation situation evaluation index system. Figure 2 shown.
[0154] The present invention solves the railway marshalling yard transportation production operation situation assessment model through the entropy weight-CRITIC combined weighting method. The entropy weight method is an objective method for weighting according to the discrete degree of indicator data. In the entropy weight method, if the information entropy value of an indicator is small, it means that its data distribution is relatively discrete, so the impact in the assessment will be greater; conversely, if the information entropy value is large, the weight is small, and the impact on the assessment result will be correspondingly weakened.
[0155] The CRITIC method takes into account the comparison strength and conflict between indicators when determining the indicator weights. In order to reduce the impact of data due to differences in dimensions and positive and negative signs, the standard deviation coefficient is used instead of the standard deviation, and the absolute value of the correlation coefficient is taken to ensure the accuracy of the weight calculation.
[0156] In order to more comprehensively reflect the weights of the evaluation indicators of the transportation production operation status of the railway marshalling yard, the present invention adopts the entropy weight-CRITIC combined weighting method. This method cleverly combines the advantages of the entropy weight method and the CRITIC method, not only deeply explores the intrinsic characteristics of the data, but also fully considers the complex relationship between the indicators, thereby obtaining a more scientific and reasonable weight distribution result. Compared with a single weighting method, the entropy weight-CRITIC combined weighting method has significant advantages, can more accurately reflect the real situation of the transportation production operation status of the railway marshalling yard, and provides strong support for railway operation management and decision-making.
[0157] The TOPSIS comprehensive evaluation method is based on constructing positive and negative ideal solutions to the evaluation problem. By calculating the relative closeness between the scheme to be evaluated and the two ideal solutions, the scheme is ranked in an orderly manner. This method cannot reflect the degree of correlation and importance between variables. The comprehensive use of the entropy weight-CRITIC-TOPSIS comprehensive evaluation method can solve the limitations of the traditional TOPSIS method in expressing the degree of correlation and importance between variables, and can more objectively and comprehensively reflect the dynamic changes in the transportation production and operation status of the railway marshalling yard, which helps the dispatching and commanding personnel to more accurately grasp the actual situation of the transportation production and operation status of the railway marshalling yard, and provide strong decision-making support for optimizing and improving the level of transportation organization.
[0158] The evaluation process of railway marshalling yard transportation production operation situation based on entropy weight-CRITIC-TOPSIS comprehensive evaluation method is as follows: Figure 3 shown.
[0159] In the preferred embodiment provided by the present invention, the steps of calculating the entropy weight-CRITIC combined weight are as follows:
[0160] Step 1: Construct a situation indicator data matrix. m is the number of time periods to be evaluated for the transportation production operation situation of the railway marshaling yard; n is the number of situation indicators. The value of the kth situation indicator in the hth time period to be evaluated is x hk , h=1,2…,m,k=1,2…,n, forming the situation indicator matrix X=(x hk ) m×n (1).
[0161] Step 2: Dimensionless processing. This aims to eliminate the dimension differences of different situation indicators and make the original data comparable. In practical applications, indicators are usually divided into two categories: benefit-based and cost-based. Benefit-based indicators pursue numerical maximization, while cost-based indicators hope to minimize numerical values. The dimensionless formulas for these two types of indicator data are as follows:
[0162] The dimensionless calculation formula of benefit-based indicators is as follows:
[0163]
[0164] Where X max ——The maximum value of the kth situation indicator;
[0165] X min ——The minimum value of the kth situation indicator.
[0166] The dimensionless calculation formula of cost-based indicators is as follows:
[0167]
[0168] According to the formula, the original data of the situation index is dimensionless, and we get X'=(x' hk ) m×n In the railway marshalling yard transportation production operation status indicator system established in Chapter 3, all 14 indicators are cost-based indicators.
[0169] Step 3 Calculate the probability p of the kth situation indicator appearing in the hth period to be evaluated hk , the calculation formula is as follows:
[0170]
[0171] Step 4 Calculate the information entropy e of the k-th situation indicator k , where it is assumed that when p hk = 0, p hk Inp hk =0, the calculation formula is as follows:
[0172]
[0173] Step 5 Calculate the weight coefficient of the k-th situation indicator (entropy weight method) ω' k , the calculation formula is as follows:
[0174]
[0175] Step 6 Calculate the correlation coefficient r of the situation index hk The correlation coefficient can overcome the different types and dimensions of indicators and reflect the degree and direction of correlation between variables. The calculation formula is as follows:
[0176]
[0177] In the formula ——The mean value of the k-th situation indicator, that is x' hl is the value obtained by dimensionless processing of the lth situation indicator in the hth period to be evaluated, x' kl It is the value obtained by dimensionless processing of the lth situation indicator in the kth period to be evaluated.
[0178] Step 7 Calculate the information amount G of the k-th situation indicator k The information content of each situation indicator is calculated according to the situation indicator correlation coefficient. The larger the value, the greater the role of the situation indicator in the entire situation indicator system. Information content G k The calculation formula is as follows:
[0179]
[0180] Where σ k——The standard deviation of the kth situation indicator.
[0181] Step8 Calculate the weight coefficient of the k-th situation indicator (CRITIC method) ω″ k , the calculation formula is as follows:
[0182]
[0183] Step 9 Calculate the combined weight ω of the kth situation indicator k In this paper, it is assumed that the two weighting methods have the same importance, and β = 0.5. The calculation formula is as follows:
[0184] ω k =βω' k +(1-β)ω″ k (10)
[0185] The specific calculation steps of the TOPSIS comprehensive evaluation method are as follows:
[0186] Step 1 Standardization. The dimensionless matrix X'=(x' hk ) m×n The standardized evaluation matrix is obtained by standardization, namely:
[0187]
[0188] Step 2: Construct a weighted matrix. According to the weight coefficient of the situation indicator obtained in the previous section, ω = (ω 1 ,ω 2 ,…,ω n ) and the standardized evaluation matrix X' after standardization to construct the weighted matrix Z = (z hk ) m×n ,in
[0189] z hk =ω k x″ hk (12)
[0190] Step 3 Determine the positive ideal solution Z + and negative ideal solution Z - .
[0191]
[0192] Step 4 calculates the distance between each time period to be evaluated and the positive and negative ideal solutions.
[0193]
[0194] In the formula ——The distance between the evaluation vector of the hth period to be evaluated and the positive ideal solution;
[0195] ——The distance from the evaluation vector of the hth period to be evaluated to the negative ideal solution;
[0196] ——Positive ideal solution Z + The kth component of ;
[0197] ——Negative ideal solution Z - The kth component of .
[0198] Step 5 Calculate the transportation production operation status score Z of the railway marshalling station in each evaluation period h , this paper converts the relative closeness score into a 100-point score and uses it as the railway marshaling yard transportation production operation status score. The calculation formula is as follows:
[0199]
[0200] z h The larger the value is, the closer the transportation production operation situation of the railway marshalling yard in the hth period is to the optimal level. h =100, the transportation production operation situation of the railway marshalling yard in the hth period is the best; when z h =0, the transportation production operation situation of the railway marshalling yard in the hth period is the worst.
[0201] The transportation production operation situation of a railway marshalling yard is a comprehensive description of the overall transportation operation status of a railway marshalling yard within a short time interval. In order to achieve an accurate portrayal of this situation, it is particularly important to select an appropriate evaluation interval. When determining this interval, the duration of the phase plan can be used as an important reference. The data of this embodiment comes from the realistic data of the transportation production operation of a railway marshalling yard from September to October 2023. After on-site investigation, it was learned that the phase plan of the railway marshalling yard is divided from 8 o'clock every day to 8 o'clock the next day, divided into stages of 3 hours. Therefore, this embodiment will divide 24 hours a day into 8 time periods at intervals of 3 hours to evaluate the transportation production operation situation. The transportation production operation time of each item is extracted from the data, and calculated according to the corresponding quantitative formula, and finally the transportation production operation situation index values of the railway marshalling yard for 250 time periods are obtained, and the initial evaluation matrix is constructed.
[0202] The collected sample data is used to conduct situation assessment. The specific assessment steps are as follows.
[0203] 1. First, the initial matrix of the railway marshalling yard transportation production operation status indicators is dimensionless. The railway marshalling yard transportation production operation status indicators are all cost-type indicators, so the initial matrix corresponding to these indicators is dimensionless according to formula (3).
[0204] 2. According to the calculation steps of entropy weight-CRITIC combined weight, the information entropy e of 14 situation indicators is calculated according to formulas (4)-(6) respectively. k And the entropy weight coefficient ω′ k ; According to formula (7), the correlation coefficients between the 14 situation indicators are calculated, and according to formula (8), the information volume G of the 14 situation indicators is calculated. k According to formula (9), the weight coefficients ω″ of 14 situation indicators CRITIC are calculated. k ; According to formula (9), the combined weight ω of 14 situation indicators is calculated k ; Table 1 lists the information entropy e of the railway marshalling yard transportation production operation status indicators k , Entropy weight method weight coefficient ω' k , information volume G k , CRITIC weight coefficient ω″ k and the combined weight ω k .
[0205] Table 1 Information entropy, entropy weight coefficient, information volume, CRITIC weight coefficient and combined weight calculation results
[0206]
[0207]
[0208] (3) Combined with the calculation steps of the TOPSIS comprehensive evaluation method, the standard evaluation matrix is calculated according to formula (10), the weighted standard evaluation matrix is calculated according to formula (11), the distance to the positive and negative ideal solutions is calculated according to formulas (12)-(13), and the transportation production operation status score of the railway marshalling yard in each evaluation period is calculated according to formula (14). Some of the scoring results are shown in Table 2.
[0209] Table 2 Partial scoring results of the transportation production operation situation of railway marshalling yards
[0210]
[0211] In actual application scenarios, in order to comprehensively evaluate the transportation production operation situation of railway marshalling yards, multiple indicators need to be considered comprehensively. After clarifying the weight of each indicator, a comprehensive score can be obtained by weighted calculation of these indicators. This score can more comprehensively reflect the situation level of transportation production operations in railway marshalling yards. However, only obtaining a numerical score cannot intuitively reflect the pros and cons of the situation. Therefore, further dividing the situation score into different levels can more clearly help dispatching and commanding personnel understand the level of the current situation score, so as to make more informed decisions. The present invention uses the K-Means clustering algorithm to divide the situation level of the railway marshalling yard transportation production operation situation score based on entropy weight-CRITIC-TOPSIS.
[0212] In unsupervised learning, cluster analysis is an exploratory data analysis technique used to discover the inherent structure or pattern in a data set. For a limited number of samples, the K-Means algorithm is a widely used clustering method that divides the data set into k different categories based on the distance between samples.
[0213] The basic steps of the K-Means clustering algorithm are as follows:
[0214] (1) Initialize cluster centers: Randomly select k sample points as the initial cluster centers.
[0215] (2) Assign samples to the nearest cluster center: Calculate the Euclidean distance between each sample point in the data set and each cluster center, and then classify each sample point into the category corresponding to its nearest cluster center.
[0216] (3) Update the location of the cluster center: For each category, calculate the mean (i.e., centroid) of all sample points in that category, and use this mean point as the new cluster center.
[0217] (4) Iterate until convergence: Repeat steps (2) and (3) until the change in cluster center is no longer significant or the preset maximum number of iterations is reached.
[0218] The calculation formula of Euclidean distance is as follows:
[0219]
[0220] Where x i ——The set of objects classified into the i-th category;
[0221] μ i ——The centroid corresponding to category i;
[0222] n – the total number of features in the sample.
[0223] In practical applications, in order to optimize the clustering effect, it is crucial to select the best number of centroids. This process often requires trying multiple possible numbers of centroids one by one, and using the silhouette coefficient as an evaluation criterion to evaluate the pros and cons of the number of centroids selected. The silhouette coefficient is a parameter used to measure the clustering effect. After clustering is completed, the silhouette coefficient of each sample needs to be calculated, and the silhouette coefficients of all samples are averaged to obtain the silhouette coefficient of the entire clustering result. When the difference between samples in each category is small, and the difference between samples in different categories is large, it indicates that the clustering effect is good. The calculation formula of the silhouette coefficient is as follows:
[0224]
[0225] Where b(i) is the average distance between sample i and other samples in the same category;
[0226] a(i)——The average distance between sample i and all samples that do not belong to the same category.
[0227] The silhouette coefficient is an indicator that varies in the range of [-1,1] and is used to measure the quality of clustering. In this range, the closer the silhouette coefficient is to 1, the better the clustering effect is; on the contrary, if the value is closer to -1, the worse the clustering effect is.
[0228] The railway marshalling yard transportation production operation status score based on entropy weight-CRITIC-TOPSIS was used as a variable for K-Means cluster analysis. The optimal number of categories was determined by calculating the silhouette coefficient corresponding to different k values. The results are shown in the figure below. Figure 4 As shown in the figure, it can be found that when k = 5, the silhouette coefficient is the largest, so k = 5 is selected as the optimal number of categories.
[0229] Based on the optimal number of categories, the samples are divided into 5 levels, and the division criteria are shown in Table 3.
[0230] Table 3 Classification standards for transportation production and operation status of railway marshalling yards
[0231]
[0232] In summary, according to the K-Means clustering algorithm, the sample statistical results of the classification of the transportation production operation situation of the railway marshalling yard are shown in Table 4.
[0233] Table 4 Sample statistical results of the classification of transportation production operation status of railway marshalling yards
[0234]
[0235] The neural network model is designed to simulate the information transmission mechanism between neurons in the human brain. It is composed of a large number of simple neurons that are widely connected to form a complex network, aiming to reflect many basic characteristics of human brain function. In 1986, scientists Rumelhart and McClelland et al. conducted an in-depth analysis of the back propagation mechanism of errors in multi-layer feedforward neural networks, making the training of multi-layer neural networks possible, further promoting the development of neural networks and making their application in various fields more extensive.
[0236] The BP neural network is mainly composed of an input layer, a hidden layer, and an output layer. Its core features are: information transmission is positive, that is, it flows from the input layer to the output layer; while error correction is reverse, that is, it feeds back from the output layer to the input layer. The typical three-layer BP neural network topology is as follows: Figure 5 The number of neurons in the input and output layers is determined by the specific problem, while the number of neurons in the hidden layer is currently estimated by the empirical formula (18) and the trial and error method.
[0237]
[0238] Where n is the number of neurons in the input layer;
[0239] m——the number of neurons in the output layer;
[0240] a——a constant between 1 and 10.
[0241] The operation process of the BP neural network mainly includes two stages. First, it is the forward propagation stage of information. The external input information passes through the input layer, hidden layer in sequence, and finally reaches the output layer. Then it enters the reverse propagation stage of error. The error will follow the opposite path of forward propagation, that is, starting from the output layer, passing through the hidden layer, and finally tracing back to the input layer. In this process, the network will continuously adjust and optimize the weights and thresholds between layers to reduce the error until the error tends to zero or meets the preset error requirements.
[0242] In some feasible embodiments, the calculation process of the BP neural network is as follows:
[0243] 1. Information forward propagation process
[0244] The input net of hidden layer neuron i i :
[0245]
[0246] Where w ij ——The weight from hidden layer neuron i to input layer neuron j;
[0247] x j——The input of neuron j in the input layer;
[0248] θ i ——The threshold of hidden layer neuron i;
[0249] M – total number of samples.
[0250] The output y of hidden layer neuron i i :
[0251]
[0252] The input net of the output layer neuron k k :
[0253]
[0254] Where w ki ——The weight from output layer neuron k to hidden layer neuron i;
[0255] φ——activation function of the hidden layer;
[0256] a k ——The threshold of neuron k in the output layer.
[0257] The output o of neuron k in the output layer k :
[0258]
[0259] In the formula ——Activation function of the output layer.
[0260] 2. Error Back Propagation
[0261] The error is calculated based on the expected output and actual output of the network. The formula for calculating the error of the i-th sample is:
[0262]
[0263] Where T k ——The actual value of the kth neuron in the output layer;
[0264] o k ——The predicted value of the kth neuron in the output layer.
[0265] Assuming there are N samples in total, the total sample error is:
[0266]
[0267] Where N is the total number of samples, and L is the total number of neurons in the output layer.
[0268] The actual output value of the network is o kIt directly depends on the weights and thresholds of each layer, that is, the error is actually a function of these weights and thresholds, and the error can be changed by adjusting the weights and thresholds. The correction value △w of the output layer weights using the error gradient descent method is ki After correction and given learning rate η (η>0), according to the partial derivative of formula (25), we have
[0269]
[0270] Similarly, the correction amount of the output layer threshold, the correction amount of the hidden layer weight and the threshold correction amount in the neural network are as follows:
[0271]
[0272]
[0273] According to the partial derivative of the formula and the formula, the local gradient is set to:
[0274]
[0275] Then the weight and threshold correction formula of the output layer can be obtained:
[0276] △w ki =ηδ k y i (29)
[0277]
[0278] In the formula, δ k and δ i is the local gradient and η is the learning rate.
[0279] Similarly defined:
[0280]
[0281] Then the hidden layer weight and threshold correction formula can be obtained:
[0282] △w ij =ηδ i x j (31)
[0283] △θ i =ηδ i (32)
[0284] BP neural network parameter update is an iterative process, and each update optimizes the current parameter value by adding a correction. In each iteration, the system calculates the error between the actual output and the expected output, and calculates the parameter correction amount based on this to adjust the network parameters. This process is repeated for each sample in the training set until the preset accuracy requirements are met or the maximum number of iterations is reached.
[0285] The training and testing process of the railway marshalling yard transportation production operation situation level assessment model based on BP neural network is as follows: Figure 6 As shown below, the design of BP neural network is explained.
[0286] 1. Determine the number of network layers. Based on the important theoretical support of Kolmogorov theorem. The theorem points out that without limiting the number of hidden layer nodes, a three-layer neural network consisting of only input layer, output layer, and hidden layer can theoretically approximate any nonlinear system. Although increasing the number of layers can improve training accuracy, it will also increase system complexity and reduce training efficiency. Therefore, this study adopts a basic three-layer network structure.
[0287] 2. Input layer neuron design. The number of input layer neurons is determined to be 14, based on the fact that the number of evaluation indicators for the transportation production operation status of the railway marshalling yard is 14.
[0288] 3. Output layer neuron design. The output data of the BP neural network should be the evaluation level of the transportation production operation situation of the railway marshalling yard in each period to be evaluated. There are 5 levels in total, which determines that the number of neurons in the output layer is 5.
[0289] 4. Hidden layer neuron design. Usually, we can use empirical formulas to narrow the range of the number of neurons, and then use trial and error to select the appropriate number of neurons.
[22] , the specific method is as follows:
[0290] (1) Determine the approximate range of the number of neurons in the hidden layer. The calculation formula is as follows:
[0291] In this network, the number of neurons in the input layer has been determined to be 14, and the number of neurons in the output layer has been determined to be 5. Substituting into equation (18), the number of neurons in the hidden layer should be in the range of [5,14].
[0292] (2) The final number of neurons in the hidden layer was determined by trial and error. The sample data was input into the network, and the maximum number of iterations was set to 1000, the minimum error to 0.0001, and the learning rate to 0.01. By adjusting the number of neurons in the hidden layer, 10 different training models were constructed. To reduce random errors, each model was run 10 times. The mean values of the Accuracy and Kappa coefficients of each model were compared. As shown in Table 5, it was found that when the number of neurons in the hidden layer was 13, the Accuracy and Kappa coefficients performed best. Therefore, the number of neurons in the hidden layer was determined to be 13.
[0293] Table 5 Comparison of the number of neurons in the hidden layer of BP neural network
[0294]
[0295] 5. Parameter design
[0296] (1) Training parameter settings: This study sets the learning rate to 0.01, the minimum error to 0.0001, and the maximum number of iterations to 1000, and the rest are filled with default values.
[0297] (2) Transfer function design. The MATLAB toolbox provides three transfer functions: logsig, purelin, and tansig. Purelin is a linear function, while logsig and tansig are nonlinear functions. The choice of transfer function is crucial to the classification accuracy. Therefore, this study keeps the training parameters unchanged and compares the Accuracy and Kappa coefficients of different transfer function combinations. The results are the average of 10 calculations, as shown in Table 6.
[0298] Table 6 Accuracy and Kappa coefficients of different transfer function combinations
[0299]
[0300]
[0301] From the results in Table 6, it can be seen that when the transfer function combination is logsig and purelin, the Accuracy and Kappa coefficients are the largest. Therefore, this study finally selects the hidden layer activation function as logsig and the output layer activation function as purelin.
[0302] (3) Training function design. There are 6 common training functions in MATLAB, each of which is based on a different algorithm. In order to determine the most suitable training function, the training parameters are kept unchanged. The Accuracy and Kappa coefficients under different training functions are compared. The results are the average of 10 calculations, as shown in Table 7.
[0303] Table 7 Comparison of training results of different training functions
[0304]
[0305] Based on the results shown in Table 7, this study finally decided to select trainbr as the training function. This is because while achieving the target error, the accuracy and Kappa coefficients of trainbr after training are better than those of other training functions, showing stronger model performance and classification accuracy, which is more suitable for the needs of this study.
[0306] Learning function settings. In most scenarios where BP neural networks are used, the choice of learning function is crucial. Among them, learngdm (BP learning rule with momentum term) has become the default learning function selection because it can accelerate the learning process, reduce shocks and improve stability. This embodiment also follows this principle and uses learngdm as the learning function in order to obtain better learning results and model performance.
[0307] The BP neural network with optimal parameters was used to train and test the samples. A total of 250 groups of samples were used in this study, which were randomly divided into training sets and test sets in a ratio of 8:2, that is, 200 groups of samples were used for training and 50 groups of samples were used for testing.
[0308] The BP neural network achieved the best training performance of 0.000093219 after the 47th training iteration, which met the performance conditions set by the network (i.e., the minimum training target error of 0.0001).
[0309] The confusion matrix of the training set is shown in Table 8. Based on the confusion matrix of the training set, the TP, FN, FP, and TN values of each category can be obtained as shown in Table 9.
[0310] Table 8 Confusion matrix of BP neural network training set
[0311]
[0312] Table 9 TP, FN, FP, TN values of each category in the BP neural network training set
[0313]
[0314] Based on Table 9 and the confusion matrix of the training set, it can be calculated that the Accuracy of the model on the training set is 100.00%, the Precision is 100.00%, the Recall is 100.00%, the Specificity is 1.0000, and the Kappa coefficient is 1.0000.
[0315] The confusion matrix of the test set is shown in Table 10. From the confusion matrix of the test set, the values of TP, FN, FP, and TN indicators of each category can be obtained as shown in Table 11.
[0316] Table 10 Confusion matrix of BP neural network training set
[0317]
[0318] Table 11 TP, FN, FP, TN values of each category in the BP neural network test set
[0319]
[0320]
[0321] Based on Table 11 and the confusion matrix of the test set, it can be calculated that the Accuracy of the model on the test set is 96.00%, the Precision is 97.08%, the Recall is 97.08%, the Specificity is 0.9889, and the Kappa coefficient is 0.9473.
[0322] The above analysis shows that the BP neural network model not only obtains good results on the training set, but also performs well on the test set. The overall prediction accuracy (248 / 250) is as high as 99.2%, and the prediction effect is excellent.
[0323] Random forest is a classification model that combines multiple decision trees as classifiers to train and predict samples. It inherits the advantages of decision trees and improves prediction performance through ensemble learning. The model was proposed by Leo Breiman and Adele Cutler in 2001.
[23] , which combines Breimans's "Bootstrap aggregating" idea and Ho's "random subspace" method. Its core lies in the random generation of multiple decision trees, so it is also called a random decision tree. Its basic principle is to use the bootstrap method to perform random sampling with replacement from the original data set to form multiple new training sample sets, each of which is used to build an independent decision tree. In the process of building these decision trees, not only randomly selected samples are used, but also a part of the features are randomly selected for consideration when each node splits. This double randomness increases the diversity and stability of the model. In the prediction stage, for classification problems, each tree in the random forest will give a classification result, and the final classification result is determined based on the voting results of these trees, that is, the class with the most votes is the class into which the sample is classified. For regression problems, the average of the prediction results of all trees is taken as the final prediction value.
[0324] The main advantages of the random forest model include:
[0325] (1) High prediction accuracy: Due to the integration of multiple decision trees, random forests can usually provide higher prediction accuracy than a single decision tree. This integration effect makes random forests perform well in many fields, including bioinformatics, transportation, and chemical industry.
[0326] (2) Processing high-dimensional data: Random forests can effectively process data sets with a large number of features without the need for complex dimensionality reduction. This is because random forests randomly select features when building each tree, thereby reducing the impact of correlation between features on model performance.
[0327] (3) Feature importance assessment: Random forests can assess the importance of each feature in classification or regression problems. This is very helpful for understanding data, feature selection, and model optimization.
[0328] (4) Robustness to default values: Random forests have good tolerance for missing values in the input data and can handle data sets containing default values to a certain extent and give reasonable prediction results.
[0329] The main hyperparameters of the RF model are shown in Table 12.
[0330] Table 12 Main hyperparameters of RF model
[0331]
[0332]
[0333] The parameters max_depth and max_leaf_node are consistent in controlling the production of the tree, that is, controlling the maximum depth also controls the number of leaf nodes, so only one of the two needs to be considered; the parameters criterion, boostrap, min_samples_leaf, and min_impurity_split can all be selected with the default values. This paper mainly performs Bayesian optimization on the four hyperparameters of n_estimations, max_depth, max_features, and min_samples_split, and uses a five-fold cross-validation method to verify the model parameters, setting the value range of the n_estimators parameter to the interval [100,1000]; the value range of the max_depth parameter is set to the interval [2,25]; the value range of the max_features parameter is set to the interval [0.1,0.999]; the value range of the min_samples_split parameter is set to the interval [5,15]. The parameters are input into the python Bayesian optimization parameter adjustment model, and the output results are shown in Table 13. The optimal hyperparameters finally obtained in this study are [n_estimators: 288, min_samples_split: 5, max_features: 0.5257, max_depth: 12], and the optimal cross-validation accuracy at this time is up to 72.3%.
[0334] Table 13 Bayesian optimization parameter adjustment model
[0335]
[0336] After determining the optimal parameters of the RF model in the above text, the RF model with the best performance was obtained, and the divided training set and test set were trained and tested using it. The confusion matrix of the training set is shown in Table 14, and the confusion matrix of the test set is shown in Table 15.
[0337] Table 14 Confusion matrix of RF model training set
[0338]
[0339]
[0340] Table 15 RF model test set confusion matrix
[0341]
[0342] From the confusion matrix of the training set, the TP, FN, FP, and TN index values of each category can be obtained as shown in Table 16.
[0343] Table 16 TP, FN, FP, TN values of each category in the RF model training set
[0344]
[0345] Based on Table 16 and the confusion matrix of the training set, it can be calculated that the Accuracy of the model on the training set is 100.00%, the Precision is 100.00%, the Recall is 100.00%, the Specificity is 1.000, and the Kappa coefficient is 1.000.
[0346] From the test set confusion matrix, the TP, FN, FP, and TN index values of each category can be obtained as shown in Table 17.
[0347] Table 17 TP, FN, FP, TN values of each category in the RF model test set
[0348]
[0349]
[0350] Based on Table 17 and the confusion matrix of the test set, it can be calculated that the Accuracy of the model on the test set is 82.00%, the Precision is 88.13%, the Recall is 86.25%, the Specificity is 0.9489, and the Kappa coefficient is 0.7614.
[0351] From the above analysis, we can see that the RF model has an accuracy of 100.00% on the training set, but performs poorly on the test set, with an accuracy of only 82.00%. The overall prediction accuracy (241 / 250) reaches 96.4%.
[0352] The support vector machine classification model is a powerful and efficient supervised learning algorithm that is widely used in various classification problems. Its core idea is to find an optimal hyperplane to separate sample data of different categories to achieve accurate classification.
[24] The SVM classification model will be introduced in detail below.
[0353] The basic idea of the SVM classification model is to build a decision boundary by maximizing the classification interval based on the principle of structural risk minimization.
[25] In the binary classification problem, SVM tries to find a hyperplane that can completely separate positive and negative samples, and the distance from this hyperplane to the nearest point in the positive and negative sample sets is the largest, that is, the interval is maximized. Such a hyperplane has good generalization ability and can accurately classify unknown data.
[0354] In order to maximize the margin, SVM introduces the concept of kernel function. Kernel function can map the original data to high-dimensional space, making the originally linearly inseparable data separable in high-dimensional space. By selecting the appropriate kernel function, SVM can handle various complex data sets, including nonlinearly separable cases. Common kernel functions include Gaussian radial basis kernel (RBF), linear kernel and polynomial kernel. Different kernel functions have different mapping capabilities and characteristics, and need to be selected according to specific problems and data.
[0355] In the SVM classification model, support vectors play an important role. Support vectors refer to the sample points closest to the decision boundary, which play a decisive role in the model's decision. The SVM classification model only focuses on these support vectors and ignores the sample points far from the decision boundary, which makes the model more robust and computationally efficient. At the same time, since SVM only uses support vectors for training, it has better performance when processing high-dimensional data and large-scale data sets.
[0356] The SVM classification model has some other advantages. First, it is robust to noise and outliers because the principle of maximizing the interval makes the model insensitive to noise. Second, SVM is a non-parametric model that does not require assumptions about the distribution of data, so it can handle various types of data. In addition, SVM has high classification accuracy and good generalization ability, and can make accurate predictions on unknown data.
[0357] However, there are also some challenges and limitations in the SVM classification model. First, SVM is sensitive to the choice of parameters, including the type of kernel function and parameter settings, which will affect the performance of the model. Therefore, the parameters need to be carefully adjusted and optimized in practical applications. Second, when the dataset is large, the training process of SVM may become slower and require longer computing time. In addition, for multi-classification problems, SVM needs to construct multiple binary classifiers for combination, which may increase the complexity and computational cost of the model.
[0358] In summary, the support vector machine classification model is a powerful and efficient classification algorithm with excellent classification performance and generalization ability. By selecting appropriate kernel functions and parameter settings, SVM can handle various complex data sets and achieve high-precision classification. Although there are some challenges and limitations, in practical applications, through reasonable design and optimization, the SVM classification model can achieve satisfactory classification results.
[0359] The assessment of the transportation production operation status of railway marshalling yards involves many evaluation indicators, and the relationship between these indicators and the overall transportation production operation status level is complex and difficult to accurately describe with a simple linear formula. Therefore, it is a multi-classification nonlinear problem. Using the SVM algorithm to construct a railway marshalling yard transportation production operation status assessment model can effectively establish a relationship model between the transportation production operation status level and each evaluation indicator. The core of the design of the SVM model structure lies in the selection of the kernel function and the determination of the optimal parameters to obtain the corresponding support vector and Largrange operator. The specific decision function is as follows:
[0360]
[0361] Where a i ——Largrange multiplier, a i ≠0, the corresponding sample is the support vector;
[0362] K(x i ,x j )——kernel function, x i 、x j For input data;
[0363] b——Bias.
[0364] Therefore, the training and testing flow chart of the railway marshalling yard transportation production operation situation assessment model based on SVM is as follows: Figure 7 shown.
[0365] The specific design scheme is formulated according to the flowchart as follows. The input and output settings are the same as those of the BP neural network, so they are not repeated here:
[0366] 1. Selection of kernel function and determination of its optimal parameters
[0367] 1. Selection of kernel function. The RBF kernel function has excellent mapping ability and can map the original data to a high-dimensional space, making the data that was originally difficult to classify linearly separable. In addition, the RBF kernel function has the characteristics of few parameters, fast calculation speed, and strong versatility, and is suitable for processing various complex data sets. In this embodiment, considering the nonlinear and high-dimensional characteristics of the data, the selection of the RBF kernel function can better capture the inherent laws and structures of the data and improve the classification performance and generalization ability of the SVM model. Therefore, this embodiment uses the RBF kernel function to construct the SVM model in order to obtain better classification effect and prediction accuracy. The specific calculation form is:
[0368] K(x i ,x j ) = exp(-β||x i -x j || 2 ),β>0
[0369] Where β is the parameter in the RBF kernel function.
[0370] 2. Determine the optimal parameters. The penalty parameter c and the kernel parameter g play a vital role in SVM classification prediction, and their tuning is crucial to improving model performance. At present, the cross validation (CV) method is widely used in the optimization process of these two parameters. By gradually narrowing the value range of c and g, find the best parameter combination that can maximize the accuracy of training sample verification classification prediction. This paper chooses the five-fold cross validation method, sets the value range of log2c to [-2,5], that is, the value range of the penalty parameter c is [0.25,32], and the value range of log2g is set to [-4,4], that is, the value range of the kernel parameter g is [0.0625,16]. The parameters are input into the matlab cross validation model. After grid search, the optimal parameter combination c is 25.9921 and g is 0.353553. At this time, the optimal cross validation accuracy is 89%.
[0371] After selecting the kernel function of the SVM model and determining the optimal parameters, the SVM model with the best performance was obtained. The SVM model was used to train and test the divided training set and test set. The confusion matrix of the training set is shown in Table 18, and the confusion matrix of the test set is shown in Table 19.
[0372] Table 18 Confusion matrix of SVM model training set
[0373]
[0374]
[0375] Table 19 Confusion matrix of SVM model test set
[0376]
[0377] From the confusion matrix of the training set, the TP, FN, FP, and TN index values of each category can be obtained as shown in Table 20.
[0378] Table 20 TP, FN, FP, TN values of each category in the SVM model training set
[0379]
[0380] Based on Table 20 and the confusion matrix of the training set, it can be calculated that the Accuracy of the model on the training set is 97.50%, the Precision is 97.62%, the Recall is 98.06%, the Specificity is 0.9934, and the Kappa coefficient is 0.9671.
[0381] From the test set confusion matrix, the TP, FN, FP, and TN index values of each category can be obtained as shown in Table 21.
[0382] Table 21 TP, FN, FP, TN values of each category in the SVM model test set
[0383]
[0384] Based on Table 21 and the confusion matrix of the test set, it can be calculated that the Accuracy of the model on the test set is 94.00%, the Precision is 95.60%, the Recall is 89.23%, the Specificity is 0.9842, and the Kappa coefficient is 0.9206.
[0385] The above analysis shows that the SVM model has a good prediction effect on the training set, but performs slightly worse on the test set. The overall prediction accuracy (242 / 250) reaches 96.8%.
[0386] After using the optimal parameters for the three machine learning models of RF, SVM, and BP, the confusion matrix, accuracy, precision, recall, specificity, and Kappa coefficient of the test set were obtained as shown in Table 22.
[0387] Table 22 Confusion matrix, accuracy and Kappa coefficient of the test set of three machine learning models
[0388]
[0389] It can be analyzed from Table 22 that the accuracy of the three machine learning models on the test set is above 82%, and the Kappa coefficients of the BP neural network model and the SVM model are all above 0.8, indicating that the three machine learning models have good evaluation capabilities, and the evaluation results of the BP neural network model and the SVM model are almost completely consistent with the situation level classification results based on the K-Means clustering algorithm. Among them, the BP neural network model is superior to other models in terms of accuracy, precision, recall, and specificity indicators. This paper selects only 250 samples, and the number of samples is relatively small. The BP neural network model has obvious advantages in the small sample railway marshalling yard transportation production operation situation evaluation learning. The RF model is more suitable for processing problems with large sample capacity. Therefore, in the small sample railway marshalling yard transportation production operation situation evaluation model in this paper, the evaluation accuracy is relatively low.
[0390] In summary, these three models can better handle the complex relationship between the evaluation index of the transportation production operation situation of the railway marshalling yard and the transportation production operation situation level of the railway marshalling yard based on the K-Means clustering algorithm, and can make a relatively accurate evaluation. The BP neural network model is the best evaluation model based on the research sample of the transportation production operation situation of the railway marshalling yard. That is, the railway marshalling yard transportation production operation situation evaluation model based on machine learning can be used as a new means of evaluating the transportation production operation situation of the railway marshalling yard.
[0391] A statistical analysis was performed on the classification results of the model on the training set and the test set. Among the 250 samples, there were 233 samples, accounting for 93.2%, whose evaluation results of the railway marshalling yard transportation production operation situation based on machine learning were consistent with the railway marshalling yard transportation production operation situation classification results based on the K-Means clustering algorithm. There were 17 inconsistent evaluation results (see Table 23).
[0392] Table 23 Comparison of evaluation results of transportation production operation status of railway marshalling yards
[0393]
[0394]
[0395] The following conclusions can be drawn from the analysis of Table 23:
[0396] (1) For samples where the machine learning evaluation results are inconsistent with the grading results based on the K-Means clustering algorithm, the situation assessment scores calculated based on the entropy weight-CRITIC-TOPSIS comprehensive evaluation method are basically at the critical value of the grading. Since the evaluation at the critical point of the grade is uncertain and fuzzy, more sample data is needed to enhance the learning ability of the machine learning model and improve the accuracy of the evaluation.
[0397] (2) Samples 1, 4, 11, and 13 were evaluated as poor in the K-Means clustering algorithm, BP neural network, and SVM models, but were evaluated as medium in the RF model. This indicates that the RF model has a slightly lower accuracy in the evaluation process of small samples.
[0398] In actual business, the railway marshalling yard transportation production operation situation assessment model based on BP neural network can be embedded into the railway marshalling yard related system. The system is mainly divided into four modules:
[0399] Module 1: Railway marshalling yard transportation production operation situation analysis module 101. By inputting the railway marshalling yard transportation production operation situation evaluation index data, calling the above-mentioned trained BP neural network model for evaluation, the situation evaluation level can be displayed in the situation level result box. Assist the railway marshalling yard dispatching department to timely evaluate the situation level of the stage after the end of a stage, and understand the current railway marshalling yard transportation production operation status. The situation level evaluation module schematic diagram is shown in Figure 8 shown.
[0400] In order to detect whether the evaluation ability of module 1 is normal, three samples are randomly selected from the evaluation level results of the railway marshalling yard transportation production operation situation based on the K-Means clustering algorithm, and their indicator data are input into module 1 for evaluation. The evaluation level is compared with the evaluation level results of the railway marshalling yard transportation production operation situation based on the K-Means clustering algorithm to check whether module 1 is operating normally. The samples and their evaluation results are shown in Table 24.
[0401] Table 24 Samples and test results
[0402]
[0403] It can be seen from the above table that the transportation production operation situation level evaluated by module one is consistent with the actual level, so it can be concluded that the evaluation function of module one is normal.
[0404] The basic data of the model trained in Module 1 comes from the data set of 250 time periods covered by this embodiment. However, as the size of the data set increases, the existing model may not be able to adapt to the new evaluation requirements, so it is necessary to retrain the model through subsequent modules 2, 3, and 4 to obtain a new model that adapts to a larger data set.
[0405] Module 2: Railway marshalling yard transportation production operation status scoring module 102. By clicking the "Read data for status scoring" button, you can import the Excel file. Then, the system will automatically process and display the corresponding status indicator weights and status scoring results. The schematic diagram of the status scoring module is as follows Fig. 9 shown.
[0406] Module 3: Situation grading module based on K-Means 103. First, enter the range of the number of clusters in the input box, and then click the "Read data for situation grading" button to import the Excel file. Then, the system will automatically process and display the contour coefficient calculation results, the optimal number of clusters, and the situation grading results corresponding to each cluster number. The schematic diagram of the situation grading module based on K-Means is shown in the figure. Fig.10 shown.
[0407] Module 4: Machine learning model training module 104. First, according to the above learning and screening process, the optimal parameters of the railway marshalling yard transportation production operation situation level assessment model based on the BP neural network are re-determined, and then the number of hidden layer neurons, training function, hidden layer activation function and output layer activation function are set in the input box. Subsequently, the system will automatically train the model and save the trained model parameters for module 1 to call. The schematic diagram of the machine learning model training module is shown in the figure below. Fig.11 shown.
[0408] In summary, the present invention provides a railway marshalling yard operation situation assessment system based on machine learning. The system takes the railway marshalling yard as the research object, and based on the situation assessment theory, combines machine learning, cluster analysis and other methods, comprehensively assesses the transportation production operation status of the railway marshalling yard within a short time interval from four aspects: arrival, disintegration, marshalling and departure; proposes the concept of railway marshalling yard transportation production operation situation, and extracts railway marshalling yard transportation production operation situation assessment indicators based on the railway marshalling yard operation process; the machine learning model used can accurately find the correlation between each sub-item assessment indicator and the railway marshalling yard transportation production operation situation level, and obtain objective and reasonable assessment results; based on the theoretical results of the research on the transportation production operation situation of the railway marshalling yard, the situation assessment is visualized through a visual interface to form a railway marshalling yard transportation production operation situation assessment system based on machine learning. The system provided by the present invention innovatively proposes a research method for transport production operation situation assessment based on machine learning, which effectively solves the problem of transport production operation situation assessment in railway marshalling yards; the system is strong; by comparing with the TOPSIS comprehensive evaluation method, the entropy weight-CRITIC-TOPSIS comprehensive evaluation method proposed in this paper can make the evaluation scheme more trending in the best and worst schemes, and finally manifests as a more obvious bias in the superiority and inferiority of the situation assessment results; the machine learning model used can better find the complex relationship between the situation indicators and the situation level of the transport production operation of the railway marshalling yard based on the K-Means clustering algorithm, and can make a more accurate evaluation result. By building a railway marshalling yard transport production operation situation assessment system based on machine learning, transport production personnel can monitor and evaluate the transport production operation situation of the railway marshalling yard in a timely, macro and comprehensive manner.
[0409] Those skilled in the art can understand that the accompanying drawings are only schematic diagrams of an embodiment, and the modules or processes in the accompanying drawings are not necessarily required to implement the present invention.
[0410] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.
Claims
1. Railway marshalling yard operation situation assessment system based on machine learning, characterized by: include: Railway marshalling yard transportation production operation situation analysis module is used for: Based on the four key transport production operation links from railway marshaling yard to unmarshaling, the transport production operation situation of railway marshaling yard is divided into four transport production operation situation subsets; Analyze each transportation production operation situation subset from the perspective of vehicle flow input - system internal transportation production operation - vehicle flow output, and obtain the constituent elements of each transportation production operation situation subset; Based on the constituent elements of each transport production operation situation subset, a railway marshalling yard transport production operation situation assessment model is constructed; The railway marshalling yard transportation production operation situation scoring module is used to: solve the railway marshalling yard transportation production operation situation evaluation model through the entropy weight-CRITIC combined weighting method, and score the railway marshalling yard transportation production operation situation; A K-Means-based situation grading module is used to: grade the transportation production operation situation of the railway marshalling yard based on the score of the transportation production operation situation of the railway marshalling yard by using the K-Means clustering method; The level of transportation production operation status of railway marshalling yard is used for transportation production operation of railway marshalling yard; The model training module is used to: train the railway marshalling yard transportation production operation status assessment model based on the level of the railway marshalling yard transportation production operation status.
2. The system according to claim 1, characterized in that The four key transport production operation links include: the transport production operation status of the arrival subsystem, the transport production operation status of the dismantling subsystem, the transport production operation status of the marshaling subsystem, and the transport production operation status of the departure subsystem.
3. The system according to claim 1, characterized in that The entropy weight-CRITIC combined weighting method is used to solve the railway marshalling yard transportation production operation situation assessment model, and the assessment results of the railway marshalling yard transportation production operation situation are obtained, which specifically include: Pass-through X=(x hk ) m×n (1) Construct a situation indicator data matrix; where x hk is the value of the kth situation indicator in the hth period to be evaluated, m is the number of periods to be evaluated for the transportation production operation situation of the railway marshalling yard, and n is the number of situation indicators; By non-dimensionalizing the calculation formula of benefit-based indicators And the dimensionless calculation formula of cost-type indicators The situation indicator data matrix is dimensionless; where X max is the maximum value of the k-th situation indicator, X min is the minimum value of the k-th situation indicator; Pass-through Calculate the probability p of the kth situation indicator appearing in the hth period to be evaluated hk ; The information amount G of the k-th situation indicator is calculated by k Calculate the information entropy e of the k-th situation indicator k ; In the formula, suppose when p hk = 0, p hk Inp hk =0; Pass-through Calculate the weight coefficient ω' of the kth situation indicator k ; Pass-through Calculate the correlation coefficient r of the situation index hk ; In the formula, is the mean value of the k-th situation indicator, x' hl is the value obtained by dimensionless processing of the lth situation indicator in the hth period to be evaluated, x' kl is the value obtained by dimensionless processing of the lth situation indicator in the kth period to be evaluated; Pass-through Calculate the information amount G of the kth situation indicator k ; In the formula, σ k is the standard deviation of the k-th situation indicator; Pass-through Calculate the weight coefficient ω of the kth situation indicator k ; Pass-through oh k =bo' k +(1-β)ω” k (10) Calculate the combined weight ω of the kth situation indicator k ;Wherein, β=0.5; Pass-through The dimensionless matrix X' in the situation indicator system is hk ) m×n Perform standardization processing to obtain a standardized evaluation matrix; Through the situation index weight coefficient ω=(ω1,ω2,…,ω n ) and the standardized evaluation matrix X' after normalization and through the formula z hk =ω k x” hk (12) Construct the weight matrix Z = (z hk ) m×n ; Pass-through Determine the positive ideal solution Z + and negative ideal solution Z - ; Pass-through Calculate the distance between each time period to be evaluated and the positive and negative ideal solutions; where, is the distance between the evaluation vector and the positive ideal solution in the hth period to be evaluated, is the distance from the evaluation vector to the negative ideal solution in the hth period to be evaluated, is a positive ideal solution Z + The kth component of is the negative ideal solution Z - The kth component of ; Pass-through Calculate the railway marshalling yard transportation production operation status score Z in each evaluation period h .
4. The system according to claim 3, characterized in that The scoring of the transportation production operation status of the railway marshalling yard and the classification of the transportation production operation status of the railway marshalling yard by the K-Means clustering method specifically include: E1 randomly selects k sample points as the initial cluster centers; E2 pass-through Calculate the Euclidean distance between each sample point and each cluster center in the data set, and then classify each sample point into the category corresponding to the cluster center with the shortest Euclidean distance; where x i is the set of objects classified into the i-th category, μ i is the centroid corresponding to category i, and n is the total number of features of the sample; E3 calculates the mean of all sample points in each category and uses the mean point as the new cluster center; E4 repeats steps E2 and E3 until the change of the cluster center is less than a preset threshold or reaches a preset maximum number of iterations; E5 pass-through Calculate the silhouette coefficient of each sample; obtain the silhouette coefficient of the clustering result by calculating the average of the silhouette coefficients of all samples; in formula (18), b(i) is the average distance between sample i and other samples in the same category, and a(i) is the average distance between sample i and all samples that do not belong to the same category.
5. The system according to claim 4, characterized in that The railway marshalling yard transportation production operation situation assessment model is a BP neural network-based model, including an input layer, a hidden layer and an output layer arranged in sequence along the direction of forward propagation of information flow; the number of neurons in the hidden layer is calculated by the formula Calculated; where n is the number of neurons in the input layer, m is the number of neurons in the output layer, and a is a constant between 1 and 10; The process of forward propagation of information flow in the railway marshalling yard transportation production operation situation assessment model includes: Pass-through Input data to the neurons of the hidden layer; where w ij is the weight from hidden layer neuron i to input layer neuron j, x j is the input of neuron j in the input layer, θ i is the threshold of hidden layer neuron i, M is the total number of samples; Pass-through Process the data input to the neurons in the hidden layer; and calculate the result y i as input to the output layer; Pass-through Input data to the neurons of the output layer; where w ki is the weight from output layer neuron k to hidden layer neuron i, φ is the activation function of the hidden layer, a k is the threshold of neuron k in the output layer; Pass-through Process the data input to the neurons in the output layer; and calculate the result o k As the output of the output layer; where, is the activation function of the output layer; The process of information flow back propagation in the railway marshalling yard transportation production operation situation assessment model includes: Pass-through Calculate the expected network output of each sample and the actual output o of the output layer k The error of k is the actual value of the kth neuron in the output layer, o k is the predicted value of the kth neuron in the output layer; Pass-through Calculate the total error of all samples; where N is the total number of samples and L is the total number of neurons in the output layer; Pass-through Calculate and obtain the correction amount of the output layer threshold, the correction amount of the hidden layer weight and the threshold correction amount; Pass-through △w ki =hd k y i (29) Calculate the weight of the output layer and the correction amount of the threshold; where δ k and δ i is the local gradient, η is the learning rate; Pass-through △w ij =hd i x j (31) △θ i =hd i (32) The weights of the hidden layer and the correction amount of the threshold are obtained by calculation.
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