Spare part prediction method of quantile neural network based on PSO training

Abstract

The invention discloses a spare part prediction method of a quantile neural network based on PSO training, a spare part demand prediction model is constructed by combining a quantile regression neural network (QRNN) and a recurrent neural network (RNN), conditional distribution characteristics of spare part demands can be more comprehensively captured through quantile regression analysis, and then deep insight in demand fluctuation is provided, so that the demand prediction accuracy is improved. Meanwhile, due to the introduction of the RNN, the model can effectively process the time sequence dependence in the time sequence data, so that the influence of the past demand on the current demand is considered in the prediction process, the spare part management efficiency is effectively improved, the inventory cost is reduced, and the customer service quality and satisfaction are improved. And important economic benefits and competitive advantages are brought to manufacturing and service industries, so that the method has a wide application prospect and can play an important role in various electronic products and after-sales services thereof.

Description

Technical Field

[0001] The invention belongs to the field of spare parts demand and artificial intelligence technology, and specifically relates to a spare parts prediction method based on a quantile neural network trained by PSO. Background Art

[0002] In modern supply chain management, forecasting the demand for spare parts is a key link in ensuring the quality of after-sales service and improving customer satisfaction. With the acceleration of the replacement of electronic products, many spare parts are eliminated before the end of the product life cycle, resulting in spare parts suppliers and product service centers facing the dual challenges of inventory management and cost control. Traditional demand forecasting methods, such as time series analysis and regression models, can provide effective forecasts in some specific cases, but these methods usually rely on the continuity of historical data and are not sensitive enough to changes in demand patterns.

[0003] In addition, the demand for spare parts is often intermittent and affected by many factors, including customer choice (repair or purchase of new products), maintenance policies, product failure rates, etc., which makes it difficult for traditional models to cope with this intermittency and uncertainty. In recent years, the introduction of machine learning technology has brought new perspectives to spare parts demand forecasting, especially artificial neural networks (ANNs) and support vector machines (SVM), which can better capture complex patterns in data. However, these methods still lack stability and accuracy when processing small sample data. Therefore, there is an urgent need for a new method that can effectively integrate time series features with historical demand data to improve the reliability and accuracy of spare parts demand forecasting. Summary of the invention

[0004] In view of this, the present invention provides a spare parts prediction method based on a quantile neural network trained by PSO, which realizes spare parts demand prediction with high accuracy.

[0005] The present invention provides a spare parts prediction method based on a quantile neural network trained by PSO, comprising the following steps:

[0006] Step 1: Collect the number of electronic product spare parts remaining in the market within a period of time, pre-process the collected product quantity, and construct an electronic product input sample set;

[0007] Step 2: Construct a spare parts demand forecasting model based on quantile regression neural network and recurrent neural network. The spare parts demand forecasting model is expressed by the following formula:

[0008]

[0009] in, is the normalized value of the network output at time t under the conditional quantile τ, and then after denormalization, it is obtained is the predicted value of the number of spare parts required; x i (t) is the input value of the i-th input neuron, and are the connection weight and bias between the i-th input neuron and the j-th hidden layer neuron, g j (t) is the value of the jth hidden layer neuron, is the connection weight of the hidden layer between consecutive time steps, is the connection weight between the jth hidden layer neuron and the output neuron, b (o) is the deviation between the hidden layer and the output layer, l is the total number of neurons in the hidden layer, and m is the total number of input neurons;

[0010] The network loss function is:

[0011]

[0012] Among them, E τ is the quantile regression error, ξ(t) is the true value, T 0 is the initial time, T r is the termination time, ρ τ is the absolute value function;

[0013] Step 3: Using the electronic product input sample set to complete the training of the spare parts demand prediction model;

[0014] Step 4: Collect the number of electronic product spare parts to be predicted that have remained on the market in the past period of time, use the normalized product quantity set as the data to be predicted, and input the data to be predicted into the trained spare parts demand prediction model to obtain the demand quantity of electronic product spare parts to be predicted.

[0015] Furthermore, the τ is the absolute value function in oblique form, as follows:

[0016]

[0017] Among them, u is the variable to be calculated, and τ is the conditional quantile.

[0018] Furthermore, in the step 3, the method of using the electronic product input sample set to complete the training of the spare parts demand prediction model is as follows: the average value of the historical optimal positions is obtained by averaging the optimal positions of each particle in previous iterations, and the average value of the historical optimal positions is used as a reference for particle position update to improve the particle swarm optimization algorithm to establish an average optimal position strategy, and the average optimal position strategy is used to complete the training of the spare parts demand prediction model based on the electronic product input sample set.

[0019] Furthermore, the calculation formula of the average value of the historical optimal position is:

[0020]

[0021] Among them, pmean i is the average value of the historical optimal position of the i-th particle, pbest it is the optimal position of the ith particle after the tth iteration, pmean i is the average optimal position of the particle so far.

[0022] Furthermore, the speed update formula in the average optimal position strategy is:

[0023]

[0024] Among them, w p is the inertia weight, c 1 and c 2 are learning factors, r 1 and r 2 are random numbers in the interval (0, 1), gbest is the global optimal position, is the original velocity of the ith particle, is the updated velocity of the ith particle.

[0025] Furthermore, the process of completing the training of the spare parts demand prediction model using the electronic product input sample set in step 3 includes:

[0026] Step 3.1, initialize the position and velocity of each particle. The position represents the weight and bias of the network, and each particle represents a set of possible network parameter combinations;

[0027] Step 3.2: For each particle, use the current weight and bias to train the spare parts demand prediction model. The fitness function is defined using the quantile regression loss function, and the fitness value of each particle is calculated.

[0028] Step 3.3: Update the average optimal position and global optimal position of the particle according to its fitness;

[0029] Step 3.4: Use the improved particle swarm optimization algorithm to update the speed and position of each particle. The new position represents the updated value of the network weight and bias.

[0030] Step 3.5, repeat steps 3.2 to 3.4 until the preset number of iterations is reached or the stop condition is met;

[0031] Step 3.6: Output the global optimal position, that is, the optimal network weights and biases.

[0032] Beneficial effects:

[0033] 1. The present invention combines quantile regression neural network (QRNN) and recurrent neural network (RNN) to construct a spare parts demand forecasting model. The conditional distribution characteristics of spare parts demand can be more comprehensively captured through quantile regression analysis, thereby providing a deep insight into demand fluctuations. At the same time, the introduction of RNN enables the model to effectively handle the temporal dependency in time series data, thereby taking into account the impact of past demand on current demand in the forecasting process, effectively improving the efficiency of spare parts management, reducing inventory costs, and improving the quality and satisfaction of customer service, bringing important economic benefits and competitive advantages to the manufacturing and service industries. Therefore, it has broad application prospects and can play an important role in various electronic products and their after-sales services.

[0034] 2. The present invention adopts an improved particle swarm optimization (PSO) algorithm to complete the training of the spare parts demand forecasting model. By simulating the behavior of the particle swarm and dynamically adjusting the model parameters, it avoids falling into the local optimal situation in the traditional random gradient descent optimization method, optimizes the network training process, significantly improves the accuracy of spare parts demand forecasting, and reduces the prediction error. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 A schematic diagram of the processing flow of a spare parts prediction method based on a quantile neural network trained by PSO provided by the present invention.

[0036] Figure 2 The predicted curve and actual curve of S3 spare parts are obtained by using the spare parts prediction method based on the quantile neural network trained by PSO provided by the present invention. DETAILED DESCRIPTION

[0037] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0038] In order to facilitate the description of the technical solution of the present invention, a series of symbols representing time nodes are defined, and the symbols and their meanings are shown in Table 1.

[0039] Table 1 Symbolic representation of spare parts demand forecasting problem

[0040]

[0041] The present invention provides a spare parts prediction method based on a quantile neural network trained by PSO, and its processing flow is as follows: Figure 1 As shown, it mainly includes the following steps:

[0042] Step 1: Collect the number of electronic product spare parts remaining in the market within a period of time, pre-process the collected product quantity, and construct an electronic product input sample set.

[0043] The installed base IB (Installed Base) of electronic product spare parts refers to the number of devices remaining in the market within a certain period of time. IB is specifically divided into: the number of devices currently remaining in the market calculated based on the expected service life IBL (Lifetime IB) and the number of devices currently remaining in the market calculated based on the warranty period IBW (Warranty IB). For each data sample x(t), its IBL and IBW values ​​are calculated, taking into account the characteristics of spare parts demand forecasting as well as the time label and the number of products sold x(t), expressed as:

[0044]

[0045] Where t is the time point, S(t) is the sales volume of the product at time point t, IBL(t) is the IBL value of the product at time point t, and IBW(t) is the IBW value of the product at time point t.

[0046] In addition, in order to accelerate the convergence of weight parameters during neural network training and model fitting, the present invention uses the Min-Max Normalization method to normalize the input time series data vector x(t) to obtain x(t)′. The normalization formula is as follows:

[0047]

[0048] Among them, x min is the minimum value of x in the current time period, x max is the maximum value of x in the current time period.

[0049] Step 2: Build a spare parts demand forecasting model based on quantile regression neural network (QRNN) and recurrent neural network (RNN). The spare parts demand forecasting model is expressed by the following formula:

[0050]

[0051] in, is the normalized value of the network output at time t under the conditional quantile τ, and then after denormalization, it is obtained is the predicted value of the number of spare parts required; x i (t) is the input value of the i-th input neuron, and are the connection weight and bias between the i-th input neuron and the j-th hidden layer neuron, g j(t) is the value of the jth hidden layer neuron, is the connection weight of the hidden layer between consecutive time steps, is the connection weight between the jth hidden layer neuron and the output neuron, b (o) is the deviation between the hidden layer and the output layer, l is the total number of neurons in the hidden layer, and m is the total number of input neurons.

[0052] Quantile regression (QR) measures the central distribution of the regression variable, reveals richer features of the data structure, and explores various parts of the conditional distribution of the dependent variable through different quantile curves. Therefore, the present invention uses the quantile regression error as the network loss function. In order to improve the accuracy of the prediction, it is necessary to minimize the quantile regression error E under the conditional τ-quantile. τ The network loss function established by the present invention is as follows:

[0053]

[0054] in, is the predicted value, ξ(t) is the true value, T 0 is the initial time, T r is the termination time, ρ τ is the absolute value function.

[0055] The present invention introduces the absolute value function ρ in the form of tilt τ The positive error and negative error are calculated separately as shown in the following formula:

[0056]

[0057] Among them, u is the variable to be calculated, and τ is the conditional quantile.

[0058] In the process of constructing the spare parts demand prediction model proposed in the present invention, a quantile regression neural network is first introduced. Quantile Regression Neural Network (QRNN) is a flexible network structure that can model the nonlinear relationship between input variables and output variables without the need for a predefined model structure. Unlike a fully connected neural network, QRNN uses a quantile regression error function as its training loss function and generates conditional quantile estimates as output to mine richer data features. A network loss function is established to calculate the error between the network output value and the sample label. The spare parts demand prediction model established by the present invention can be solved and evaluated by minimizing the network loss function.

[0059] For example, the specific structure of the spare parts demand prediction model established by the present invention is: it consists of an input layer containing m = 4 input neurons, a hidden layer containing l = 8 neurons, and an output neuron. Specifically, for a given input x(t), the output can be obtained according to the following formula:

[0060]

[0061] in,

[0062] Furthermore, in order to improve the processing capability of quantile regression neural network (QRNN) for time series data, the present invention introduces an enhanced structure of recurrent neural network (RNN). RNN is widely used to capture long-term dependencies in time series data due to its superior performance in time series modeling. By combining the capabilities of RNN, QRNN can better handle the time series features in spare parts demand forecasting and improve the accuracy of forecasting. Specifically, the following steps are included:

[0063] Step 2.1. Structure and design of RNN.

[0064] The core advantage of RNN lies in its memory ability, that is, the input at the current moment not only contains the feature information of the current moment, but also retains the information of the previous moment, forming a temporal dependency transmission. Through such a structure, RNN can refer to the previous spare parts demand when predicting the spare parts demand at the current moment, thereby capturing the dynamic change rules in time.

[0065] Specifically, the hidden layer neurons are formulated as:

[0066]

[0067] Through this mechanism, the hidden layer can remember the state of the previous moment and integrate it into the input of the current moment to achieve modeling of time series dependencies.

[0068] Step 2.2: Combine RNN and QRNN.

[0069] By embedding the RNN structure into QRNN, the present invention can not only capture the demand distribution at different quantiles through quantile regression, but also use the time-dependent characteristics of RNN to more accurately predict demand changes. Specifically, the output of the hidden layer depends not only on the current input data, but also on the output of the hidden layer at the previous moment, thereby enhancing the model's ability to learn time dependency and sequence data.

[0070] Thus, the spare parts demand prediction model constructed by the present invention is obtained, that is, the network output calculation formula is as follows:

[0071]

[0072] Through the combination of quantile regression neural network and recurrent neural network, the spare parts demand forecasting model constructed by the present invention can make more accurate predictions on future spare parts demand at different time points. Especially for scenarios with large fluctuations in spare parts demand, RNN can better capture the dynamic change trend of data and improve the robustness of the overall prediction.

[0073] Step 3: The average value of the historical optimal position is obtained by averaging the optimal position of each particle in previous iterations. The average value of the historical optimal position is used as a reference for particle position update to improve the particle swarm optimization algorithm to establish an average optimal position strategy. The average optimal position strategy is used to complete the training of the spare parts demand prediction model based on the electronic product input sample set.

[0074] As an evolutionary algorithm, Particle Swarm Optimization (PSO) has been proven to be highly efficient and has strong global search capabilities in solving complex optimization problems, especially for nonlinear problems and multi-dimensional parameter optimization. Compared with the traditional gradient descent algorithm, PSO does not rely on gradient information, can effectively avoid falling into the local optimum, and has the characteristics of fast convergence speed.

[0075] PSO finds the optimal solution by simulating the collaborative search behavior of individuals (i.e. particles) in the group in the solution space. Each particle represents a possible solution of the network parameters (i.e. weights and biases). The particle's position vector represents the value of the weights and biases. The particle's velocity vector has no practical meaning and is only used to calculate the position vector. By continuously adjusting the particle's position and velocity, the global optimal solution is gradually approached. In PSO, each particle has a position vector X i and the velocity vector V i , and the particle will be based on its historical best position pbest i And the global optimal position gbest to update its position and velocity.

[0076] The existing speed update formula is as follows:

[0077]

[0078] Among them, w p is the inertia weight, c 1 and c 2 are learning factors, r 1 and r 2 are random numbers in the interval (0, 1), is the original velocity of the ith particle, is the updated velocity of the ith particle.

[0079] The position update formula is:

[0080]

[0081] Through the above-mentioned speed and position updating method, particles gradually approach the historical optimal solution and the global optimal solution until the optimal network parameters are found.

[0082] In order to improve the training efficiency and prediction accuracy of the spare parts demand prediction model constructed by the present invention, the present invention improves the particle swarm optimization algorithm (PSO) and uses the improved particle swarm optimization algorithm (PSO) to optimize the network weight and deviation.

[0083] Specifically, the present invention improves the standard PSO and proposes an average optimal position strategy. In the standard PSO, the particle position update only depends on the individual historical optimal position pbest i , but this may cause individual particles to fall into local optimality. To solve this problem, the present invention introduces the average value pmean of the historical optimal position i , take the average of the optimal position of each particle in previous iterations as a reference for position update.

[0084] The average value of the historical optimal position is calculated as follows:

[0085]

[0086] Among them, pbest it is the optimal position of the ith particle after the tth iteration, pmean i is the average optimal position of the particle so far.

[0087] The speed update formula is improved to:

[0088]

[0089] Through this improvement, particles not only rely on their historical best positions during the update process, but also refer to their historical average best positions, which enhances the local search capability and further improves the global convergence performance of PSO. This method can effectively reduce the possibility of particles falling into local optimality while maintaining the search efficiency of the global optimal solution.

[0090] Based on the average optimal location strategy established by the present invention, the weights and deviations of the spare parts demand forecasting model optimization network are trained. The specific training process is as follows:

[0091] Step 3.1, Initialize the particle swarm: Initialize the position and velocity of each particle. The position represents the weight and bias of the network. Each particle represents a set of possible network parameter combinations.

[0092] Step 3.2, fitness calculation: For each particle, use the current weight and bias to train the spare parts demand prediction model, the fitness function is defined using the quantile regression loss function, and the fitness value of each particle is calculated;

[0093] Step 3.3, update the optimal position: according to the fitness of the particle, update its average optimal position and global optimal position;

[0094] Step 3.4, position and velocity update: Use the improved PSO algorithm to update the velocity and position of each particle. The new position represents the updated value of the network weight and bias.

[0095] Step 3.5, iterative optimization: repeat steps 3.2 to 3.4 until the preset number of iterations is reached or the stopping condition is met, such as the change of the fitness function is less than a predetermined threshold, etc.;

[0096] Step 3.6: Output the optimal network parameters: When the stopping condition is met, output the global optimal position, that is, the optimal network weight and deviation, which are used for the final spare parts demand prediction.

[0097] After network training and processing, the total normalized network output is It needs to be inverse normalized to get the output The inverse normalization formula is: in, is the maximum value of the network output after normalization, is the minimum value of the normalized network output.

[0098] The improved PSO algorithm can quickly and effectively optimize the network parameters of QRNN. Compared with the traditional gradient descent method, PSO has great advantages, including: strong global search ability: PSO can effectively avoid the local optimal trap and ensure that the network training can converge to the global optimal solution; no reliance on gradient information: PSO is suitable for highly nonlinear and gradient-free information optimization, especially for processing complex spare parts demand forecasting problems in time series data; fast convergence speed: by introducing the average optimal position strategy, the improved PSO has a faster convergence speed and can find the optimal solution in fewer iterations.

[0099] Step 4: Collect the number of electronic product spare parts to be predicted that have remained on the market in the past period of time, and use the normalized product quantity set as the data to be predicted. Input the data to be predicted into the spare parts demand prediction model trained in step 3 to obtain the number of electronic product spare parts to be predicted that will remain on the market at a future moment.

[0100] Experimental results show that the QRNN network trained using PSO demonstrates excellent performance in spare parts demand forecasting, which can significantly improve forecasting accuracy, reduce inventory management costs, and improve the response efficiency of the supply chain.

[0101] Through the detailed description of the RNN enhancement mechanism and the PSO training method, the present invention can effectively cope with complex spare parts demand forecasting scenarios, especially when facing highly volatile time series data, the model shows strong robustness and adaptability.

[0102] The following table is a comparison of the indicators of the prediction results of several types of spare parts using different algorithms under real data, which is of guiding significance for the result analysis. Among them, M1, M2 and autoregressive moving average model (ARMA) represent three fitting algorithms, which are obtained from the following models respectively:

[0103] M1:log(ξ(t))=b 0 +log(IB(t))+b 2 ×t

[0104] M2:log(ξ(t))=b 0 +b 1 log(IB(t))+b 2 ×AGE(t)

[0105] Among them, parameter b 0 , b 1 and b 2 The IB value is fitted by its corresponding spare parts demand value, and AGE(t) represents the average life of the IB in time period t.

[0106]

[0107] Where μ is the average value of the sequence ξ(t), and θ i is the i-th lag coefficient and lag error coefficient, p and q are the orders of the autoregressive model and the moving average model, and ε(t) is the error at time t.

[0108] The following six indicators are used in this invention to characterize the accuracy of the prediction results, and the expressions are as follows:

[0109]

[0110]

[0111] Table 2 Comparison of PSO-QRNN, M1, M2 and ARMA algorithms for S1 spare parts prediction

[0112]

[0113] Table 3 Comparison of indicators of PSO-QRNN, M1, M2 and ARMA algorithms for S2 spare parts prediction

[0114]

[0115] Table 4 Comparison of PSO-QRNN, M1, M2 and ARMA algorithms for S3 spare parts prediction

[0116]

[0117] The detailed flowchart of using PSO-QRNN for prediction is as follows Figure 1 As shown, in order to verify the performance of the present invention, we compared the quantile neural network prediction method trained by PSO-QRNN with other algorithms. From the results, it can be seen that our invention is superior to other algorithms in different categories of spare parts and evaluation indicators, and can provide a more reliable guide for after-sales service providers to purchase an appropriate number of spare parts.

[0118] It can be seen that this paper considers and develops a prediction method for spare parts demand, studies the characteristics of spare parts demand, and uses them as input features of our prediction algorithm. Considering the advantages of QRNN and RNN in time series prediction and PSO in network training, a QRNN trained by improved PSO is designed and proposed to predict spare parts demand. This network architecture is specially designed to handle spare parts demand prediction under small sample data. The implementation of the algorithm includes steps such as data processing, network training and prediction. Using sales and demand data from real after-sales service cases, a variety of spare parts are tested, among which the verification results for S3 spare parts are as follows: Figure 2 As shown in the figure, the good performance of the RNN structure and the network training mechanism based on the improved PSO is verified. In addition, the comparison results with some advanced prediction methods verify the effectiveness of our proposed PSO-QRNN in spare parts demand forecasting.

[0119] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A spare parts prediction method based on quantile neural network trained by PSO, characterized in that: The following steps are involved: Step 1: Collect the number of electronic product spare parts remaining in the market within a period of time, pre-process the collected product quantity, and construct an electronic product input sample set; Step 2: Construct a spare parts demand forecasting model based on quantile regression neural network and recurrent neural network. The spare parts demand forecasting model is expressed by the following formula: in, is the normalized value of the network output at time t under the conditional quantile τ, and then after denormalization, it is obtained is the predicted value of the number of spare parts required; x i (t) is the input value of the i-th input neuron, and are the connection weight and bias between the i-th input neuron and the j-th hidden layer neuron, g j (t) is the value of the jth hidden layer neuron, is the connection weight of the hidden layer between consecutive time steps, is the connection weight between the jth hidden layer neuron and the output neuron, b (o) is the deviation between the hidden layer and the output layer, l is the total number of neurons in the hidden layer, and m is the total number of input neurons; The network loss function is: Among them, E τ is the quantile regression error, ξ(t) is the true value, T0 is the initial time, T r is the termination time, ρ τ is the absolute value function; Step 3: Using the electronic product input sample set to complete the training of the spare parts demand prediction model; Step 4: Collect the number of electronic product spare parts to be predicted that have remained on the market in the past period of time, use the normalized product quantity set as the data to be predicted, and input the data to be predicted into the trained spare parts demand prediction model to obtain the demand quantity of electronic product spare parts to be predicted.

2. The spare parts prediction method according to claim 1, characterized in that: The τ is the absolute value function in oblique form, as follows: Among them, u is the variable to be calculated, and τ is the conditional quantile.

3. The spare parts prediction method according to claim 1, characterized in that: The method of using the electronic product input sample set to complete the training of the spare parts demand prediction model in step 3 is: by averaging the optimal position of each particle in previous iterations to obtain the average value of the historical optimal position, using the average value of the historical optimal position as a reference for particle position update to improve the particle swarm optimization algorithm to establish an average optimal position strategy, and using the average optimal position strategy to complete the training of the spare parts demand prediction model based on the electronic product input sample set.

4. The spare parts prediction method according to claim 3, characterized in that: The calculation formula of the average value of the historical optimal position is: Among them, pmean i is the average value of the historical optimal position of the i-th particle, pbest i is the optimal position of the ith particle after the tth iteration, pmean i is the average optimal position of the particle so far.

5. The spare parts prediction method according to claim 4, characterized in that: The speed update formula in the average optimal position strategy is: Among them, w p is the inertia weight, c1 and c2 are learning factors, r1 and r2 are random numbers in the interval (0, 1), gbest is the global optimal position, is the original velocity of the ith particle, is the updated velocity of the ith particle.

6. The spare parts prediction method according to claim 3, characterized in that: The process of completing the training of the spare parts demand prediction model using the electronic product input sample set in step 3 includes: Step 3.1, initialize the position and velocity of each particle. The position represents the weight and bias of the network, and each particle represents a set of possible network parameter combinations; Step 3.2: For each particle, use the current weight and bias to train the spare parts demand prediction model. The fitness function is defined using the quantile regression loss function, and the fitness value of each particle is calculated. Step 3.3: Update the average optimal position and global optimal position of the particle according to its fitness; Step 3.4: Use the improved particle swarm optimization algorithm to update the speed and position of each particle. The new position represents the updated value of the network weight and bias. Step 3.5, repeat steps 3.2 to 3.4 until the preset number of iterations is reached or the stop condition is met; Step 3.6: Output the global optimal position, that is, the optimal network weights and biases.

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