A spare part prediction method based on a PSO-trained quantile neural network

Abstract

The application discloses a spare part prediction method based on a PSO training quantile neural network, combines a quantile regression neural network (QRNN) with a recurrent neural network (RNN) to construct a spare part demand prediction model, can more comprehensively capture the conditional distribution characteristics of the spare part demand through quantile regression analysis, and further provides deep insight into demand fluctuation, meanwhile, the introduction of the RNN enables the model to effectively process the time sequence dependency in time sequence data, so that the influence of past demand on current demand is considered in the prediction process, the efficiency of spare part management is effectively improved, the inventory cost is reduced, the quality and satisfaction of customer service are improved, important economic benefits and competitive advantages are brought to the manufacturing and service industries, therefore, the application has wide application prospects and can play an important role in various electronic products and after-sales services.

Description

Technical Field

[0001] The present invention belongs to the field of spare parts demand and artificial intelligence technology, and particularly 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 spare parts demand is crucial for ensuring after-sales service quality and improving customer satisfaction. With the accelerating pace of electronic product upgrades, many spare parts are becoming obsolete before the end of their product lifecycles, posing dual challenges for spare parts suppliers and service centers in inventory management and cost control. Traditional demand forecasting methods, such as time series analysis and regression models, can provide effective forecasts in certain situations, but they often rely on the continuity of historical data and are insensitive to shifts in demand patterns.

[0003] Furthermore, the demand for spare parts is often intermittent and influenced by a variety of factors, including customer choices (repair or purchase of new products), maintenance policies, and product failure rates, making it difficult for traditional models to cope with this intermittency and uncertainty. In recent years, the introduction of machine learning techniques has brought new perspectives to spare parts demand forecasting, especially artificial neural networks (ANNs) and support vector machines (SVMs), which can better capture complex patterns in the 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 on the market over a period of time, pre-process the collected product numbers, and construct an electronic product input sample set;

[0007] Step 2: Build a spare parts demand forecasting model based on the quantile regression neural network and the recurrent neural network. The spare parts demand forecasting model is expressed using 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, T0 is the initial time, T r is the termination time, ρ τ is the absolute value function;

[0013] Step 3: Use 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 forecasting 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 shown below:

[0016]

[0017] Where u is the variable to be calculated and τ is the conditional quantile.

[0018] Furthermore, in step 3, the method for completing the training of the spare parts demand forecasting model using the electronic product input sample set 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 updating the particle positions 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 forecasting model based on the electronic product input sample set.

[0019] Furthermore, the calculation formula for 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 i-th particle after the t-th 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, 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 i-th particle, is the updated velocity of the i-th 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. 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 velocity 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 stopping 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. This paper combines quantile regression neural network (QRNN) and recurrent neural network (RNN) to construct a spare parts demand forecasting model. Quantile regression analysis can more comprehensively capture the conditional distribution characteristics of spare parts demand, thereby providing deep insights into demand fluctuations. At the same time, the introduction of RNN enables the model to effectively handle the temporal dependencies in time series data, thereby taking into account the impact of past demand on current demand during the forecasting process. This effectively improves the efficiency of spare parts management, reduces inventory costs, and enhances the quality and satisfaction of customer service, bringing significant 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 optimum in the traditional stochastic gradient descent optimization method, optimizes the network training process, significantly improves the accuracy of the spare parts demand forecast, 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. 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 on 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) of electronic spare parts refers to the number of devices remaining in the market over a specific time period. IB is specifically divided into: IBL (Lifetime IB), which is the number of devices currently remaining in the market based on their expected useful life, and IBW (Warranty IB), which is the number of devices currently remaining in the market based on their warranty period. For each data sample x(t), IBL and IBW are calculated, taking into account the characteristics of spare parts demand forecasts, time tags, and the number of products sold x(t). These values ​​are 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 The maximum value of x in the current time period.

[0049] Step 2: Build a spare parts demand forecasting model based on the quantile regression neural network (QRNN) and recurrent neural network (RNN). The spare parts demand forecasting model is expressed using 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)where is the bias between the hidden layer and the output layer, l is the total number of hidden layer neurons, and m is the total number of input neurons.

[0052] Quantile Regression (QR) measures the central distribution of the regression variable, reveals more rich features of the data structure, and explores each part of the conditional distribution of the dependent variable through different quantile curves, so that the quantile regression error is used as the network loss function in the application, in order to improve the accuracy of prediction, the quantile regression error E under the condition of τ-quantile needs to be minimized τ The network loss function established in the application is as follows:

[0053]

[0054] wherein, is the predicted value, ξ(t) is the true value, T0 is the initial time, T r is the termination time, ρ τ is an absolute value function.

[0055] The application introduces an absolute value function ρ τ The positive error and the negative error are calculated respectively, as shown in the following formula:

[0056]

[0057] wherein, u is a variable to be calculated, and τ is a conditional quantile.

[0058] In the construction process of the spare parts demand prediction model, the quantile regression neural network is first introduced. The quantile regression neural network (QRNN) is a flexible network structure, which can model the nonlinear relationship between the input variable and the output variable without a predefined model structure. Unlike the fully connected neural network, the QRNN uses a quantile regression error function as its training loss function and generates a conditional quantile estimate as output, which can mine more rich data features. The network loss function is established to calculate the error between the network output value and the sample label, and the spare parts demand prediction model established in the application 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 in the application is as follows: an input layer containing m=4 input neurons, a hidden layer containing l=8 neurons, and an output neuron are included, and the output can be obtained according to the following formula for a given input x(t)

[0060]

[0061] in,

[0062] Furthermore, to improve the processing capabilities of the quantile recurrent neural network (QRNN) for time series data, this paper introduces an enhanced structure of the recurrent neural network (RNN). RNNs are widely used to capture long-term dependencies in time series data due to their superior performance in time series modeling. By combining the capabilities of RNNs, QRNNs can better handle the temporal characteristics present in spare parts demand forecasting and improve forecast accuracy. Specifically, the following steps are included:

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

[0064] The core advantage of RNNs lies in their memory capacity. The input at the current moment not only contains the current feature information but also retains information from the previous moment, forming a temporal dependency. This structure allows RNNs to reference previous spare parts demand trends when predicting current spare parts demand, thereby capturing dynamic temporal changes.

[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 a QRNN, the present invention not only captures the demand distribution at different quantiles through quantile regression, but also leverages the temporal dependency of RNNs 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 hidden layer output at the previous moment, thereby enhancing the model's ability to learn time-dependent and sequential data.

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

[0071]

[0072] By combining quantile regression neural networks and recurrent neural networks, the spare parts demand forecasting model constructed by the present invention can make more accurate predictions of 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 the data and improve the robustness of the overall prediction.

[0073] Step 3: The average value of the historical optimal positions is obtained by averaging the optimal positions of each particle in previous iterations. The average value of the historical optimal positions is used as a reference for particle position update to improve the particle swarm optimization algorithm and 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] Particle Swarm Optimization (PSO), an evolutionary algorithm, has been shown to be highly efficient and possesses strong global search capabilities when solving complex optimization problems. It is particularly advantageous for nonlinear problems and multidimensional parameter optimization. Compared to traditional gradient descent algorithms, PSO does not rely on gradient information, effectively avoiding local optimality and exhibiting rapid convergence.

[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 for 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 position and velocity of the particles, the global optimal solution is gradually approached. In PSO, each particle has a position vector X i and velocity vector V i , and the particle will be based on its historical optimal 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, c1 and c2 are learning factors, r1 and r2 are random numbers in the interval (0, 1), is the original velocity of the i-th particle, is the updated velocity of the i-th particle.

[0079] The position update formula is:

[0080]

[0081] By updating the speed and position described above, 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 weights and deviations.

[0083] Specifically, the present invention improves the standard PSO and proposes an average optimal position strategy. In the standard PSO, the position update of the particle 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 formula for calculating the average value of the historical optimal position is:

[0085]

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

[0087] The speed update formula is improved as follows:

[0088]

[0089] This improvement allows particles to update not only based on their best historical position but also based on their average historical best position, enhancing local search capabilities and further improving the global convergence performance of the PSO. This approach effectively reduces the likelihood of particles falling into local optimality while maintaining the efficiency of searching for the global optimal solution.

[0090] Based on the average optimal location strategy established by the present invention, the spare parts demand forecasting model is trained to optimize the weights and biases of the network. 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, and 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 in the fitness function is less than a predetermined threshold;

[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 weights and deviations, for the final spare parts demand forecast.

[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 network output after normalization.

[0098] The improved PSO algorithm can quickly and effectively optimize the network parameters of QRNNs. Compared with traditional gradient descent methods, PSO has significant advantages, including: strong global search capability: PSO can effectively avoid local optimal traps, ensuring that network training converges to the global optimal solution; independence from gradient information: PSO is suitable for highly nonlinear and gradient-free information optimization, and is particularly well-suited for complex spare parts demand forecasting problems in time series data; fast convergence: 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 forecasting model trained in step 3 to obtain the number of electronic product spare parts to be predicted that will remain on the market in the future.

[0100] Experimental results show that the QRNN network trained using PSO demonstrates excellent performance in spare parts demand forecasting, which can significantly improve forecast 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 PSO training method, the present invention can effectively cope with complex spare parts demand forecasting scenarios, especially when facing highly volatile time series data, and the model shows strong robustness and adaptability.

[0102] The following table compares the prediction results of different algorithms for several types of spare parts using real data, which provides guidance for result analysis. M1, M2, and the autoregressive moving average model (ARMA) represent three fitting algorithms, which are derived from the following models:

[0103] M1:log(ξ(t))=b0+log(IB(t))+b2×t

[0104] M2:log(ξ(t))=b0+b1log(IB(t))+b2×AGE(t)

[0105] The parameters b0, b1, and b2 are fitted to the IB value by their corresponding spare parts demand values, and AGE(t) represents the average life of the IB in time period t.

[0106]

[0107] Among them, 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 indicators 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 indicators 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 for prediction. From the results, it can be seen that our invention is better than other algorithms in different categories of spare parts and evaluation indicators, and can provide after-sales service providers with a more reliable guide to purchase the appropriate number of spare parts.

[0118] As can be seen, 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 for our prediction algorithm. Taking into account the advantages of QRNN and RNN in time series prediction and the advantages of 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 the demand prediction of spare parts in the case of 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 were tested. 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 effectiveness of our proposed PSO-QRNN in spare parts demand forecasting is verified by comparing the results with some advanced forecasting methods.

[0119] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection 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 on the market over a period of time, pre-process the collected product numbers, and construct an electronic product input sample set; Step 2: Build a spare parts demand forecasting model based on the quantile regression neural network and the recurrent neural network. The spare parts demand forecasting model is expressed using 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: Use the electronic product input sample set to complete the training of the spare parts demand prediction model; Step 4: Collect the quantity of electronic product spare parts remaining in the market over the past period of time, use the normalized quantity set as the data to be predicted, and input the data to be predicted into the trained spare parts demand forecasting model to obtain the demand quantity of the electronic product spare parts to be predicted; The method for completing the training of the spare parts demand forecasting model using the electronic product input sample set in step 3 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 forecasting model based on the electronic product input sample set; 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. 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 velocity 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 stopping condition is met; Step 3.6: Output the global optimal position, that is, the optimal network weights and biases.

2. The spare parts prediction method according to claim 1, characterized in that: The p τ is the absolute value function in oblique form, as shown below: Where 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 calculation formula for 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 in is the optimal position of the i-th particle after the n-th iteration, pmean i is the average optimal position of the particle so far.

4. The spare parts prediction method according to claim 3, 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 i-th particle, is the updated velocity of the i-th particle.

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