Spare Parts Management Strategy of High-Speed Railway Running Department Based on Performance Prediction

Abstract

Spare parts management is a critical aspect of high-speed train health management, playing a vital role in maximizing in-service time and minimizing maintenance costs. However, traditional spare parts management methods, which rely solely on historical experience and suggest spare parts quantities or ratios in equipment manuals, often lack practicality and fail to meet real-world demands. To address these limitations, this paper proposes a performance prediction-based spare parts management strategy for high-speed trains. The strategy comprises three main components. First, a performance degradation model is developed using performance evaluation results to define a performance degradation envelope. Next, the required quantity or ratio of spare parts for multiple devices in different performance states is determined using the expected performance score method. Finally, the timing of spare parts orders is scientifically optimized by accounting for production and transportation lead times. To demonstrate the effectiveness of the proposed strategy, we conducted experiments using the spare parts management of a specific high-speed train running gear as a case study and compared it with existing spare parts management methods.

1. Introduction

Spare parts refer to components that need to be prepared in advance for replacement during the maintenance process of high-speed railway operations [1,2]. As essential support materials, spare parts play a critical role in the routine maintenance and emergency handling of high-speed railway systems [3]. Proper spare parts management has become a crucial aspect of the operation and maintenance departments in high-speed rail, as it directly influences the railway’s maintenance duration, operational efficiency, and economic benefits. By preparing adequate spare parts for key components prone to wear and tear, degradation, or performance decline, the railway operation departments can significantly reduce downtime during maintenance, ensuring the efficient operation of high-speed rail systems. Therefore, developing a scientific and reasonable spare parts management strategy is essential for ensuring timely maintenance and replacement, reducing spare parts storage costs, and optimizing resource utilization [4,5,6,7,8].

In recent years, the development of spare parts management has generally been categorized into three approaches: model-driven, knowledge-driven, and data-driven.

Model-driven approaches solve spare parts management issues through mathematical or optimization models. For instance, Lin et al. [9] proposed a 0–1 programming model to optimize inventory and transportation of spare parts for high-speed trains. In contrast, Li et al. [10] designed an inventory optimization solution for train spare parts by integrating system reliability theory. Although these model-driven approaches address complex inventory and maintenance management problems, they rely heavily on model assumptions and parameters, which may limit their effectiveness when dealing with fluctuating demand or uncertainty. Additionally, these methods are computationally intensive, making them challenging to apply in large-scale systems.

Knowledge-driven approaches depend on domain specialists’ expertise and theoretical knowledge to make decisions by constructing rules. Hashemian [11] and Park [12] proposed predictive maintenance methods based on equipment degradation trends, using degradation models to predict equipment failure and enable preventive maintenance. While knowledge-driven approaches provide strong interpretability and are widely applied in equipment management, they are limited by their heavy reliance on expert knowledge. As a result, they may lack adaptability and scalability, making it difficult to apply them to new equipment or environments.

Data-driven approaches optimize decision-making by analyzing historical and real-time data. For example, Hong et al. [13] developed an unsupervised anomaly detection method based on tail probabilities to manage abnormal fluctuations in spare parts demand. Hao et al. [14] combined deep reinforcement learning with a Markov decision process to optimize condition-based maintenance and spare parts inventory management. Guo et al. [15] proposed a multi-period spare parts supply chain network optimization method using dynamic particle swarm optimization. The degradation envelope method is another data-driven application that analyzes historical and real-time performance data to evaluate equipment degradation trends and develop spare parts maintenance plans accordingly. This method ensures proactive and effective spare parts management by accurately assessing equipment conditions and predicting potential failure times. However, while powerful in handling large datasets, data-driven approaches require high-quality data, and incomplete or noisy data can reduce decision-making accuracy. Additionally, these methods lack causal interpretability, resulting in lower transparency.

Based on the specific operational characteristics of high-speed train running gear, this paper proposes a spare parts management method that integrates the advantages of both the knowledge-driven and data-driven approaches. By combining expert experience with large-scale data analysis techniques, the proposed method provides more reliable decision support in spare parts management.

In order to avoid the impact of uncertainty on spare parts management, multi-dimensional information such as test data, state characteristics, and the historical performance of the running parts can be used to evaluate the state of the running parts accurately, and the spare parts management can be carried out according to the evaluation results.

The research on spare parts management of high-speed railway running gears has two aspects of significance:

(1)

Enhancing the maintenance capabilities of the maintenance and support departments and improving the management and support levels will ensure the operational efficiency of high-speed rail.

(2)

Determining the reasonable quantity of various spare parts can reduce inventory quantity and spare parts inventory costs, thereby lowering high-speed rail’s operational and maintenance costs. This paper explores the spare parts management methods for key components based on the running gear’s performance evaluation results, considering the high-speed rail running gear’s actual working characteristics. The goal is to improve the running gear’s operational and maintenance management level and reduce maintenance costs.

This paper studies the spare parts management strategy for high-speed rail running gear, scientifically determining the required quantity of spare parts and the optimal ordering times. The main work of this paper includes:

• Obtaining the performance degradation envelope of the running gear based on performance evaluation results.
• Calculate the quantity or proportion of spare parts needed for multiple running gears in different performance states using the expected performance score method.
• Scientifically determine the ordering times for spare parts by considering their production and transportation time.

The remainder of this paper is organized as follows: Section 2 elaborates on the spare parts management issues for high-speed rail running gear; Section 3 applies the running gear performance degradation envelope method to spare parts management, detailing the working steps; and Section 4 conducts a case study on spare parts management for the running gear’s asynchronous motor using the proposed method.

2. Problem Description

Currently, the spare parts management for high-speed rail running gear is primarily conducted by experts who order the necessary spare parts based on the components’ consumption. This management approach relies entirely on the subjective judgment of experts. However, the high-speed rail running gear consists of multiple components, and their performance states are difficult to unify. Basing decisions solely on expert experience can lead to significant uncertainty in the decision-making process. The performance of the running gear reflects its working condition, and accurate performance evaluation helps in a timely understanding of the running gear’s operational status. When the performance of the running gear declines to a certain threshold, even if it can still function normally, sufficient spare parts should be prepared and replaced in advance to reduce losses or shorten downtime. Therefore, this chapter takes the performance evaluation of high-speed rail running gear as the basis and foundation for spare parts management. Currently, the principle for running gear spare parts management is “to be prepared for usefulness”, which has two implications:

• Appropriately increasing the spare parts inventory is necessary to ensure the smooth completion of daily tasks and prevent the malfunction of a single component from affecting the overall performance of the high-speed rail running gear.
• Since the high-speed rail running gear comprises various components, the quantity and variety of spare parts are substantial. The spare parts for critical positions are expensive, and excessive storage will increase management costs. Therefore, monitoring information on the running gear’s operational status to assess its performance, formulating corresponding maintenance strategies, and optimizing spare parts ordering times are of great significance in ensuring the working performance of the high-speed rail running gear and improving spare parts management.

In summary, conducting spare parts management research for high-speed rail running gear requires addressing the following two issues.

Issue 1: Due to the differences in operational status indicators among various running gears, these indicators, while reflective of the running gear’s performance, are challenging to use as a basis for spare parts management. The traditional spare parts management model relies on experts’ understanding of the performance variation patterns of the running gear. This method has subjective uncertainties, and is only sometimes convincing. Therefore, in conducting spare parts management, it is necessary to find an indicator that can reflect the performance level of the running gear. Compared to physically meaningful evaluation indicators, the performance degradation envelope of the running gear can more intuitively reflect the current performance state. Hence, Issue 1 focuses on obtaining the performance degradation envelope based on the evaluation results of the running gear.

Issue 2: The purpose of spare parts management for the running gear is to ensure that the running gear can remain in a normal working state and to shorten downtime caused by failures. Since the production and transportation of spare parts require time, time factors must be considered when formulating spare parts management strategies to prevent delays in delivering ordered spare parts to the site. Spare parts management mainly includes determining the required quantity of spare parts and the optimal ordering times. Therefore, Issue 2 is how to develop a reasonable spare parts management strategy based on the performance degradation envelope of the running gear.

The spare parts management strategy, which considers the performance degradation envelope of high-speed rail running parts, mainly includes two components, as shown in Figure 1. In Figure 1, $D_n$ represents the n-th reference level of the evaluation result. ${\varphi }_n\left(t\right)$ represents the belief degree of the reference level for the n-th evaluation result at time t, d represents the value for each reference level, and N is the number of the reference levels.

(1)

The performance envelope of the running parts is obtained by conducting the performance evaluation based on the evidence reasoning rule model of the multi-dimensional fault conclusion. Firstly, making full use of the condition monitoring information of the same type, the evidential reasoning rule method of multi-dimensional fault conclusion was used to model and evaluate, and then the established evaluation model was used to evaluate the existing running part.

(2)

Based on the performance degradation envelope of the running gear, the spare parts management strategy is formulated to comprehensively consider the order quantity and timing of spare parts, and the spare parts management is carried out.

3. Spare Parts Management Strategy of HSR Travel Department Considering Order Quantity and Timing

Firstly, spare parts management evaluates the performance of high-speed rail running gear using various types of information to leader their performance status. This ensures that spare parts can be replaced before downtime, shortening the downtime and ensuring that the running gears perform well and are always in a healthy working state.

For a complex device, when the performance of one component or device deteriorates or even fails, the performance of the whole device may be affected. If spare parts are available for the degraded or malfunctioning parts and equipment, they should be replaced immediately with new spare parts. If there are no corresponding spare parts, the equipment may need to be shut down to wait for spare parts to be ordered and replaced. For the high-speed railway running gear, due to the influence of production, transportation, and other factors, when spare parts are scarce, once the relevant components fail, it will lead to prolonged downtime and affect the operation or duty task. Therefore, it is necessary to scientifically determine the number of spare parts and order them in advance. In this section, the spare parts management strategy of the running gear will be studied from two aspects: the determination of spare parts quantity and the choice of ordering time.

3.1. Calculation Method of Spare Parts Quantity Based on Expectation of Performance Score

The performance evaluation results of high-speed railway running gears can be obtained using the evidential reasoning rule evaluation method based on multi-dimensional fault. The results obtained by this evaluation method are concrete physical quantities and have practical physical meanings. In this case, the evaluation indexes selected when evaluating different running gears are also different, and the physical meanings of the evaluation results are also different. When carrying out spare parts management work, the performance degradation envelope of the running gear can be used as a unified quantitative index of different equipment performance to express the availability level of the running gear. The method based on the matching degree function can transform the performance evaluation results of the running gear from the utility form to the performance envelope, which reflects the performance of the running gear gradually degrading from a good state to a poor state in the use process. Each point in the envelope is the performance score of the running gear. The performance score is expressed in the form of probability. It reflects the performance status of the running gear in the form of a percentage, which is also the basis for carrying out spare parts management. The matching degree function is used to transform the evaluation result’s expected utility into the performance degradation envelope as follows:

$$S\left(V_u\right)={\displaystyle \frac{V_u-Z_o^{-}}{Z_o^{+}-Z_o^{-}}},$$

(1)

where $V_u$ is the expected utility of the running gear performance evaluation result obtained at time u, $V_u$ is the performance score of the running gear obtained at time u. $Z_o^{+}$ is the upper bound of the output evaluation indicator, which is the optimal value of the output evaluation indicator, and $Z_o^{-}$ is the lower bound of the output evaluation indicator, which can also be considered the worst value of the evaluation indicator. The maximum and minimum reference values corresponding to the output evaluation indicator can be used as $Z_o^{+}$ and $Z_o^{-}$, respectively. In Equation (1), the denominator is used to obtain the interval value of the evaluation index. In the numerator, $V_u-Z_o^{-}$ represents the distance between the expected utility and the lower bound of the evaluation index. Dividing these values yields the final performance score for the running gear.

Equation (1) can be used to obtain the running gear’s performance degradation envelope. As the working time increases, the running gear’s performance will gradually decline, and the obtained performance score will also gradually decline. Therefore, the running gear’s performance degradation envelope should be a group of envelope curves with a gradual downward trend, as shown in Figure 2.

The shaded area in Figure 2 represents the performance envelope of a batch of running gear. The vertical axis is the performance score of the running gear. When the running gear is in working condition, the performance evaluation results of the running gear can be obtained based on the monitoring information of the input indicators. Since Equation (1) is a linear transformation, the performance degradation envelope can be obtained by simply transforming the boundary values of the expected utility of the running gear performance evaluation results. Since a single measurement information is an exact value, the exact value is used as the input information. Under the condition of using the exact value as monitoring information, the ER method is used to calculate the performance evaluation results. Assuming the evaluation result utility is V, the curve in Figure 2 shows that the possible continuous working time range for the running gear performance corresponds to $[u^{-},u^{+}]$. $[u^{-},u^{+}]$ indicates the possible working time range of the running gear under continuous working conditions.

In practical engineering, there is more than one running gear of this model in working condition, and there may be multiple running gears of the same model in working or in-use states, with potentially different performance states. When calculating the required quantity of spare parts, it is necessary to consider the number and performance of the running gears in use. Therefore, the required quantity of spare parts is calculated based on the number of running gears in use, distinguishing between two situations.

Situation 1: Suppose there are h running gears of a certain model in use, and all h units have operated for the same amount of time and are in the same performance state. h certain number of spare parts must be pre-stocked to ensure sufficient spare parts to replace the working equipment.

Under the constraint of the performance state, the number of spare parts required for this type of equipment at the current time $C_{S\left(x\right)}$:

$$C=\left[1-S\left(x\right)\right]\times d,$$

(2)

$$C_{S\left(x\right)}=⌈C⌉,$$

(3)

where $S\left(x\right)$ represents the performance score of the running gear at time x, and d represents the number of running gears with a performance score of $S\left(x\right)$. In Equation (2), $[1-S(x\left)\right]$ represents the performance degradation state of the running gear. After multiplying this by d, the overall performance degradation of all components within the running gear is obtained. $\lceil •\rceil$ represents the ceiling function, $\lceil C\rceil$ represents the smallest integer greater than C, C represents the required number of spare parts, and $C_{S\left(x\right)}$ represents the integer value of the required number of spare parts. Assuming the performance score of three components is 0.3, Equation (2) indicates that 2.1 components require replacement. To ensure the integrity of the components, the ceiling function is applied, resulting in the replacement of all three components.

Situation 2: In practical engineering scenarios, the performance scores of running gears may differ. By referring to Equations (2) and (3), we calculate the expected number of required spare parts based on the expected performance scores. Therefore, the required number of spare parts is determined accordingly.

$$C=\sum _{n=1}^N\left[\left(1-S\left(x_i\right)\right)\times d_i\right],$$

(4)

where $S\left(x_i\right)$ represents the performance score of the i-th running gear at time $x_i$, $d_i$ is the number of running gears with a performance score of $S\left(x_i\right)$, and N is the number of running gears with different performance scores.

If the running gear’s performance score range is $[S_i^{-},S_i^{+}]$, the required number of spare parts should also be a range value. Assuming the required number of spare parts is a range value $[C_{s_i^{-}},C_{s_i^{+}}]$, when the running gears’ performance scores in working conditions do not meet the usage requirements, to ensure sufficient spare parts for replacement, according to Equation (3), the required number of spare parts should satisfy the constraint condition $C_{S\left(x\right)}\ge C_{s_i^{+}}$.

3.2. Spare Parts Ordering Strategy Considering Time Factor

For running gears in use, their performance is constantly changing. Therefore, the required number of spare parts is also dynamically changing. To meet the working requirements of the running gear, when the number of spare parts is insufficient, timely ordering and replenishment are necessary. Due to the production and transportation time limitations of running gears, ordering spare parts only when there is a shortage will delay the optimal replacement time, leading to prolonged downtime of the running gear. Therefore, a preventive replacement strategy should be dynamically formulated based on the performance status of the running gear. Considering the time required for spare parts production and transportation, the spare parts ordering process is somewhat preventive, requiring spare parts to be ordered before the performance degrades to the critical threshold. Monitoring information on the running gear for future moments cannot be obtained in advance. The performance degradation envelope of the running gear, as a curve of its performance changes under working conditions, has typical characteristics. In the research process of spare parts ordering timing, the performance degradation envelope is used as the benchmark model, fully utilizing the relationship between degradation time and degradation degree to judge the performance score of the running gear under continuous working conditions.

Suppose there are a total of N individuals in the working state in the running gear of a certain type. The working status of the running gear described here corresponds to the inventory status. In other words, the running gear in working status is being used, not stored in a warehouse. Since each running gear has different working times, their performance also varies.

Assume $S_i^{+}$ and $S_i^{-}$ represent the upper and lower bounds of the performance score of the i-th running gear $\left(i=1,2,\dots ,N\right)$, as shown in Figure 3.

When the performance score range of the i-th running gear is $[S_i^{-},S_i^{+}]$ at a certain time, its corresponding working time is $[u_i^{-},u_i^{+}]$. $S_{th}$ is the spare parts replacement threshold for this type of running gear, typically determined by domain experts based on the performance characteristics and operational requirements of the running gear. The spare parts replacement threshold varies for different running gears. When the performance score of the running gear falls below $S_{th}$, spare parts must be immediately used to replace the equipment.

To ensure that the stored spare parts quantity meets the needs, when calculating the required number of spare parts, the lower bound of the performance score range $[S_i^{-},S_i^{+}]$ of the running gear is considered the performance score of the running gear, and the corresponding continuous working time of the running gear is taken as the maximum value $u_i^{+}$. The spare parts quantity calculated in this way can maximally meet the operational needs. $\Delta u_i$ can be considered the time required for the i-th running gear to continuously work until it reaches the performance threshold $R_{th}$ for spare part replacement, $\left(i=1,2,\dots ,N\right)$. This time is relatively conservative, representing the shortest time required for the running gear to degrade to the spare parts replacement threshold under continuous operation.

At the initial time $u_0$, the method proposed in Section 3.1 can be used to determine the required number of spare parts as $C_{S\left(u_0\right)}$. Suppose the number of spare parts in stock is $\tilde{C}$. If $C_{S\left(u_0\right)}\le \tilde{C}$, it indicates that there are enough spare parts in the warehouse, and no additional replenishment is needed; if $C_{S\left(u_0\right)}>\tilde{C}$, the spare parts in stock may not be sufficient to meet the demand, and timely replenishment is necessary. Since ordering and transporting spare parts also require time, ordering spare parts in advance is necessary. To minimize equipment downtime, the optimal time to order spare parts should be determined, and orders should be placed in advance.

Before researching the timing of spare parts ordering, the following assumptions are made:

• Since running gear is critical for the regular operation of the equipment, minimizing repair time during spare parts replacement is essential. Therefore, it is assumed that the time consumed in the replacement process is not considered as long as there are sufficient spare parts in stock, allowing for immediate replacement. This assumption is made to simplify the research analysis, eliminating interference from other variables and focusing on optimizing the timing of spare parts ordering. Given that running gear failure directly affects equipment operation, ensuring the timely supply of spare parts is crucial to reducing downtime.
• The time from ordering spare parts to their delivery at the designated warehouse impacts the overall efficiency of the supply chain. It is assumed that this time is denoted as $\Delta u_{tr}$, which includes all stages such as spare parts production, transportation, and storage. The purpose of this assumption is to simplify the research process by standardizing the time factor, allowing the focus to remain on optimizing the timing of spare parts orders. By defining this time parameter, we can more accurately assess the time consumption of the supply chain, ensuring that spare parts are replenished in a timely manner when demand arises, thus avoiding equipment downtime due to delays.
• Considering that the replaced spare parts are not original equipment manufacturer (OEM) parts, there may be issues with compatibility due to differences in specifications, materials, or manufacturing processes. Therefore, it is assumed that the performance score of the running gear after spare parts replacement is $[0.93,0.97]$, indicating that the performance cannot fully recover to its optimal state and can only be partially restored. This assumption is made to better reflect the potential impact of non-OEM parts on the overall performance of the equipment, enabling a more accurate assessment of how spare parts replacement affects operational efficiency in the analysis.

As the running gear’s usage time increases, its performance gradually decreases, and the required number of spare parts increases. Suppose that the n-th running gear has the lowest performance score among all N running gears in use. From the initial time $u_0$, after $\Delta u_n$ time of operation, when the performance score of the n-th running gear reaches the critical value $S_n^{-}=S_{th}$, the required number of spare parts $C_{S\left(u_0+\Delta u_n\right)}$ reaches its maximum value within the time range $[u_0,\Delta u_n+u_0]$, and replacement is needed.

When the performance score of the n-th running gear reaches the replacement threshold, and the spare parts are replaced, the number of stored spare parts decreases by one. Suppose that the $\overline{n}$-th running gear has the lowest performance score among the remaining running gears in use. While replacing spare parts for the n-th running gear, the performance of the $\overline{n}$-th running gear might also be approaching the spare parts replacement threshold. Therefore, it is necessary to determine whether the remaining spare parts in stock can meet the replacement requirements of the running gear. Based on the time required for the running gear to continuously operate from the initial time to reach the performance critical threshold for spare parts replacement, the time can be divided into two periods, $\Delta u^1$ and $\Delta u^2$, both equal to the time required for ordering and transporting spare parts, i.e., $\Delta u^1=\Delta u^2=\Delta u_{tr}$.

In this case, it is necessary to study the relationship between the transportation time and the timing of spare parts ordering. At the initial time $u_0$, if $\Delta u_n>\Delta u_{tr}$, it indicates that ordering spare parts at time $u=\left(u_0+\Delta u_n-\Delta u_{tr}\right)$ will ensure that the ordered spare parts are received before the performance of the n-th running gear reaches the replacement threshold, and the ordered quantity is $\left(C_{S\left(u_0+\Delta u_n\right)}-\tilde{C}\right)$. If $\Delta u_n<\Delta u_{tr}$, the ordering and transportation time $\Delta u_{tr}$ will be longer than the time $\Delta u_n$ required for the n-th running gear to reach the replacement threshold from working. In this scenario, no matter when the order is placed, the n-th running gear will not receive the ordered spare parts when its performance reaches the replacement threshold. If the stored spare parts quantity $\tilde{C}$ is insufficient, it may lead to downtime due to the running gear’s performance failing to meet operational needs. To minimize the downtime of the running gear, spare parts for this model must be ordered and replenished immediately at time $u_0$. In this case, the shortest possible downtime is $\left(\Delta u_{tr}-\Delta u_n\right)$. Therefore, the research on the timing of spare parts ordering can be divided into two scenarios.

(1)

The performance of a single travel unit decreases to a critical value during the transportation cycle.

In this case, during period $\Delta u^1$, only one running gear is in use, the n-th unit, and the performance of other units is better than that of the n-th running gear, as shown in Figure 4. $\Delta u_n>\Delta u_{tr}$. In this scenario, ordering spare parts in advance can prevent downtime.

In Figure 4, because the cumulative working time difference between the n-th unit and the $\overline{n}$-the running gear is greater than the spare parts ordering and transportation time, $\left(u_n^{+}-u_{\overline{n}}^{+}\right)>\Delta u_{tr}$, when the n-th running gear reaches the spare parts replacement threshold, the cumulative working time of the $\overline{n}$-th running gear has not yet reached the spare parts ordering time, so ordering is not required. Therefore, it is only necessary to consider the number of spare parts required when the n-th running gear reaches the spare parts replacement time. At time $u=u_0+\Delta u_n$, the required number of spare parts $C_{S\left(u_0+\Delta u_n\right)}$ is the maximum, and the number of spare parts to be ordered is $C_{S\left(u_0+\Delta u_n\right)}-\tilde{C}$. Since the time required from ordering to transporting the spare parts is $\Delta u_{tr}$, the ordering time should be $\left(u_0+\Delta u_n-\Delta u_{tr}\right)$. At this point, the replacement of the first running gear’s spare parts is completed, and the running gear needs to be retested, its performance evaluated, and the above process repeated.

(2)

During the transportation cycle, the performance of several travel units decreases to the critical value.

In this case, during period $\Delta u_1$, there are multiple running gears in use, numbered as the n-th, $\overline{n}$-th, and so on, and the performance of other running gears is better than that of the n-th running gear, as shown in Figure 5.

Due to the issue’s complexity in this scenario, the ordering and replacement process for spare parts will be illustrated using the example of three running gears, as shown in Figure 6.

When the performance of each running gear degrades to the replacement threshold, the required number of spare parts reaches its maximum in a short period. Considering the spare parts ordering and transportation time, it is necessary to order spare parts at time $\Delta t_{tr}$ before each running gear reaches the replacement threshold. In this case, the degradation of the running gears from the current time to the spare parts replacement time must be considered.

In Figure 6, $\Delta u^1$ and $\Delta u^2$ are two periods, and $\Delta u^1=\Delta u^2=\Delta u_{th}$. The working times of the second and third running gears fall within period $\Delta u^1$. When replacing spare parts, it is essential to consider whether the spare parts inventory can meet the replacement demand for all running gears in use within period $\Delta u^1$ when they reach the replacement time. When ordering spare parts, it is also necessary to ensure that all running gears in period $\Delta u^1$ can meet the spare parts demand when needed. In Figure 6, the spare parts replacement time for the third running gear is $\left(u_0+\Delta u_3\right)$, and the corresponding spare parts ordering time is $\left(u_0+\Delta u_3-\Delta u_{tr}\right)$. After replacing the spare parts for the third running gear, the performance score of the second running gear approaches the replacement threshold. If the remaining spare parts in stock cannot meet the demand when the second running gear reaches the replacement time, it will lead to system downtime. Therefore, when ordering spare parts at $\left(u_0+\Delta u_3-\Delta u_{tr}\right)$, it is necessary to consider whether the total of the ordered spare parts and the stock spare parts can meet the replacement needs when the performance of both the second and third running gears degrades to the replacement threshold after a period of operation. This approach can prevent downtime of the running gears and avoid repeated short-term spare parts orders, saving transportation costs.

According to the above analysis, the number of spare parts to be ordered is $C^{\prime }$

$$C^{\prime }=C_{S\left(u_{th}^{-}\right)}-\tilde{C},$$

(5)

$$C_{S\left(u_{th}^{-}\right)}=max[C_{S_3\left(u_0+\Delta u_3\right)},C_{S_2\left(u_0+\Delta u_2\right)}],$$

(6)

where $C_{S_3\left(u_0+\Delta u_3\right)}$ is the number of spare parts required for the third running gear when its performance degrades to the replacement threshold at time $\left(u_0+\Delta u_3\right)$, and $C_{S_2\left(u_0+\Delta u_2\right)}$ is the number of spare parts required for the second running gear when its performance degrades to the replacement threshold at time $\left(u_0+\Delta u_2\right)$.

When calculating $C_{S_3\left(u_0+\Delta u_3\right)}$, it is important to note that the usage time of the third running gear has increased by $\Delta u_3$. For the i-th and second running gears, their working times may fall within the range of $[0,\Delta u_3]$. To ensure enough spare parts for replacement, the working times of the i-th and second running gears are set to $\Delta u_3$. Currently, the performance scores of the i-th and second running gears are $U_i\left(u_0+\Delta u_3\right)$ and $S_2\left(u_0+\Delta u_3\right)$, respectively. When calculating $C_{S_2\left(u_0+\Delta u_2\right)}$, similar to the calculation of $C_{S_3\left(u_0+\Delta u_3\right)}$, it is necessary to recalculate the performance scores of all running gears after $\Delta u_2$ time from the initial time $u_0$. At this point, the performance score of the i-th running gear is $S_i\left(u_0+\Delta u_2\right)$. Since the third running gear has already been replaced, according to the third assumption mentioned earlier, its performance score starts at 0.93 and gradually decreases with the increased usage time. As shown in Figure 6, the continuous usage time corresponding to a performance score of 0.93 is $u_{in}$. When the second running gear reaches the replacement threshold, the performance score of the third running gear is $S_3\left(u_{in}+\Delta u_2-\Delta u_3\right)$. By comparing $C_{S_3\left(u_0+\Delta u_3\right)}$ and $C_{S_2\left(u_0+\Delta u_2\right)}$, the maximum value is determined, and the difference between this maximum value and the stock of spare parts is the number of spare parts that should be ordered at the ordering time $u^{\prime }$. The ordering time should be $u^{\prime }=\left(u_0+\Delta u_3-\Delta u_{tr}\right)$, and the determined $u^{\prime }$ indicates that spare parts should be ordered $\Delta u_3-\Delta u_{tr}$ after the initial time $u_0$. During the transportation period, if the performance of more than two running gears degrades to the replacement threshold, the above process can be referenced to calculate the required number of spare parts and the ordering time.

3.3. Implementation Process of Spare Parts Management Strategy for High-Speed Railway Running Gear Based on Performance Degradation Envelope

The main process of the spare parts ordering strategy for high-speed rail running gear based on the performance degradation envelope is as follows:

• Determine the number of running gears in use and inventory: First, it is necessary to count the number of running gears currently in use and the number of running gears in stock. Next, the degradation data of equipment similar to the running gear is used to evaluate its performance and draw a performance degradation envelope. This envelope diagram is usually established by analyzing the historical usage data of the running gear and combining key performance indicators (such as working hours, failure rate, etc.). This step aims to understand the current status of the running gear and predict its future performance degradation trend.
• Determine the spare parts replacement threshold and timing: Once the performance degradation envelope has been obtained, the next step is to define the replacement criteria. This is obtained by setting the spare parts replacement threshold $S_{th}$, which indicates the minimum acceptable performance level before a replacement is necessary. Additionally, the replacement timing $u_{{th}^{-}}$ must be determined, which indicates the optimal time for replacing the spare parts to avoid failure or excessive wear. These thresholds and timings are established based on expert experience, historical data, and the working mechanism of the running gears.
• Calculate the spare parts ordering and transportation time: The third step involves logistical considerations. It is important to calculate the actual time $\Delta u_{tr}$ required for the spare parts to be ordered from the manufacturing factory and transported to the warehouse. This time must include any delays due to distance, shipping, and processing. Additionally, values for $\Delta u^1$ and $\Delta u^2$ are set, where $\Delta u^1=\Delta u^2=\Delta u_{tr}$. These values represent the time intervals required for monitoring the performance and ordering parts. In this step, the continuous working time $u_{in}$ corresponding to a performance score of 0.93 is also calculated, indicating the duration the running gears can operate before their performance significantly deteriorates.
• Evaluate current running gears and analyze spare parts inventory: Set the initial time to $u_0$, perform performance tests on multiple running gears in use, use the test information to evaluate their performance, and calculate their corresponding performance scores. Next, predict whether any running gear will reach the time for spare parts replacement within the future time $\Delta u^2$. If any running gear reaches the replacement threshold within this time, it is necessary to analyze whether the number of spare parts in the inventory is sufficient to meet the replacement demand. If the existing inventory is insufficient, spare parts should be ordered immediately at the initial moment to minimize system downtime. Conversely, if no running gear will reach the replacement threshold within this time, it is necessary to determine the number of running gears $\overline{n}$ within a shorter time (i.e., within $\Delta u^1$).
• Calculate the required spare parts quantity and ordering timing: To ensure sufficient spare parts are available for replacement without causing system downtime, it is crucial to analyze the spare parts needs in advance. Analyze and calculate the number of spare parts needed when $\overline{n}$ running gears reach the replacement threshold after the corresponding working time, find the maximum value $C_{S\left(•\right),max}$ of the required spare parts quantity $\overline{n}$, the ordering timing $\left(u_0+\Delta u_3-\Delta u_{tr}\right)$, and the number of spare parts to be ordered $\left(C_{S\left(•\right),max}-\tilde{C}\right)$. This ensures that the necessary parts are ordered in a timely manner, reducing the risk of delays caused by insufficient inventory.
• Repeat the process for future replacement needs: Once the spare parts replacement has been completed for all running gears that reached the replacement threshold within the time $\Delta u^1$, the process loops back to step 4. This ensures a continuous evaluation and replacement cycle, ensuring that spare parts are always available when needed and that replacements are performed before performance degradation impacts the system.

In this process, Figure 7 illustrates the main flow of spare parts ordering and replacement. By following the steps outlined above, the required number of spare parts and the optimal timing for both ordering and replacement can be determined, thus minimizing downtime and optimizing the spare parts management strategy.

4. Case Study

To visually demonstrate the implementation process of this method, the experiment utilized fault log data provided by a company on 27 July 2017, with a focus on the temperature faults of small and medium-sized motors in the operating mechanism. By comparing and analyzing the frequency, causes, and impact range of motor temperature faults during this period, the fault diagnosis results included data on fault types and severity. The performance evaluation results, obtained using a multidimensional fault conclusion evidence reasoning rule model, were applied to manage the spare parts for the asynchronous motor, determining the required quantity of spare parts and the appropriate ordering timing. The asynchronous motor is a crucial component of the high-speed rail running gear, playing a key role in the starting, stopping, and smooth operation. In practical engineering, multiple asynchronous motors are embedded within the high-speed rail running gear. Therefore, spare parts management for the asynchronous motor is to replace the old motor with a new one when it is found that a motor in the running gear cannot meet the operational requirements. The required spare parts refer to the asynchronous motor, not the entire running gear.

4.1. Performance Degradation Envelope of Induction Motor Based on Matching Degree Function

The obtained performance evaluation results for the asynchronous motor include its deviation value, and the performance degradation envelope of the asynchronous motor can be derived using a multidimensional fault conclusion evidence reasoning rule model. When calculating the performance degradation envelope of the asynchronous motor, the maximum and minimum reference values corresponding to the output evaluation indicators are taken as $Z_o^{+}$ and $Z_o^{-}$, respectively, i.e., $Z_o^{+}=85.2$ m, $Z_o^{-}=0$. According to Equation (1), the performance degradation envelope of this type of asynchronous motor can be obtained, as shown in Figure 8.

In Figure 8, the blue bar area represents the performance envelope of the asynchronous motor. The performance envelope gradually decreases as the motor’s usage time increases, reflecting the accumulation of errors in the motor, which leads to a gradual decrease in its performance score—A decreasing process. Maintenance or spare parts replacement can improve the performance of equipment like motors. Using the performance degradation envelope of the motor as a basis provides theoretical support for conducting spare parts management.

4.2. Calculation of Spare Parts Quantity Based on Expectation of Performance Score

The performance variation of the asynchronous motor is the basis and foundation for conducting spare parts management. The number of spare parts required for multiple motors in simultaneous operation can be calculated using the performance envelope of the asynchronous motor obtained earlier.

In Figure 8, the horizontal axis represents the sample sequence, arranged in chronological order of the testing times. Therefore, the sample sequence can be converted into testing time based on the testing time intervals. Assuming the interval between each sample is 15 h, the resulting graph can be seen in Figure 9.

Assume that four asynchronous motors of this type are in use. At the initial time, state monitoring and performance evaluation are conducted for the four motors, resulting in performance evaluation scores of $S_1=[0.78,0.83]$, $S_2=[0.64,0.73]$, $S_3=[0.77,0.79]$, and $S_4=[0.43,0.52]$, respectively. According to Equation (4), the required number of spare parts at the current time is calculated as follows:

$$C=\underset{k=1}{\sum ^4}\left(1-S_k\right),$$

(7)

Formula (8) is used to calculate $C=[1.13,1.38]$. The quantity should be at least the smallest integer to ensure sufficient spare parts. This means that the current required number of spare parts is 2.

Since the current spare parts stored in the warehouse might not be exactly 2, discovering that the number of spare parts in storage does not meet the required quantity could impact the normal operation of the equipment, causing prolonged downtime. Therefore, if the number of spare parts in the warehouse is less than 2, it is necessary to order them immediately. Assuming there are 2 spare parts in the warehouse at the initial time, there is no need to order spare parts now.

4.3. Timing Determination of Spare Parts Ordering Considering Transportation Time

An asynchronous motor, also known as an induction motor, is a motor that relies on the principle of electromagnetic induction for energy conversion. Its most common form is the three-phase asynchronous motor, which is widely used in industrial production and life. Its working principle is based on the rotating magnetic field generated by the stator, in which the conductor in the rotor cuts the magnetic field lines, induces a current, generates a torque and drives the rotor to rotate [16]. Based on the extensive practical experience of multiple engineers in the field of high-speed rail bogies, the spare parts replacement threshold is set at 0.2. This threshold was developed using historical performance data and long-term field operations rather than solely relying on subjective individual judgment. When the performance score lower bound of the asynchronous motor reaches 0.2, it is necessary to replace the parts to ensure optimal functionality. Currently, there are two spare parts stored in the warehouse. According to the performance envelope obtained in Section 4, if the motor’s performance score is 0.2, the corresponding minimum working time is $u_{th}^{-}=2085$ h. Based on the performance scores of the four motors, the respective continuous working time intervals can be obtained, namely $u_1=[751,1128]$ h, $u_2=[927,1361]$ h, $u_3=[837,1145]$ h, and $u_4=[1318,1723]$ h. The maximum continuous working time of the four motors is taken as the actual working time to ensure sufficient spare parts and avoid downtime due to a lack of spare parts. Assume that the minimum time required from ordering to delivering the spare parts to the warehouse is $\Delta u_{tr}=350$ h. Therefore, the time $u^{\prime }$ for ordering spare parts is longer than the time $u^{\prime }>u_{4,max}$ required for the fourth equipment to operate until reaching the critical threshold. This equation indicates that ordering spare parts at the current moment allows the ordered spare parts to be obtained before performance degrades to the replacement threshold. This process is illustrated in Figure 10.

In Figure 10, $\Delta u^1=\Delta u^2=350$ h, while $u_{4,max}-\Delta u^1=1373$ h $>u_{2,max}$. Therefore, when the fourth motor continues to operate until the spare parts replacement threshold time $u_{th}^{-}$, the second motor’s usage time has not yet reached the spare parts ordering time $u^{\prime }$. When ordering spare parts at time $u^{\prime }$, it is only necessary to consider the number of spare parts required after $\Delta u_4=\left(u_{th}^{-}-u_{4,max}\right)$ time for the fourth motor’s performance to degrade to the replacement threshold. Thus, after four asynchronous motors have been running for $\Delta u_4=362$ h, when it is necessary to replace the fourth motor with spare parts, the required number of spare parts is calculated. At this point, the required number of spare parts is the maximum value needed during the first spare parts ordering cycle. Assume the initial time is $u_0=0$, and after $\Delta u_4=362$ h, the fourth motor reaches the performance critical threshold for spare parts replacement and needs to be replaced. The upper and lower boundary functions of the previously obtained performance envelope can be used to determine the performance scores of the motors at different times. Based on this, the performance scores of the asynchronous motors at various times during the degradation process can be obtained.

At the time $u=362$ h, the lower bounds of the performance scores for the four motors are $S_{1,min}=0.4357$, $S_{2,min}=0.3223$, $S_{3,min}=0.4253$, and $S_{4,min}=0.2$, respectively, as shown in

Table 1. Performance scores of four asynchronous motors at different times.

Number	At Time u = 0, the Continuous Working Time of the Motor	At Time u = 362 h, the Continuous Working Time of the Motor	Lower-Bound of Performance Score
1	1128 h	1490 h	0.4357
2	1361 h	1723 h	0.3223
3	1145 h	1507 h	0.4253
4	1723 h	2085 h	0.2

.

At time $u_0=0$ h, using the previously mentioned method for calculating the number of spare parts, the required number of spare parts is calculated to be $C_{max}\left(0\right)=1.38$, which, when rounded, results in 2 spare parts needed. From time $u_0=0$ to time $u=362$ h, the motors remain in operation, with their performance gradually degrading and the required number of spare parts gradually increasing. At time $u=362$ h, the fourth motor needs to be replaced with a spare part, requiring $C_{max}(362$ h$)=2.62$ spare parts, which rounds to 3 spare parts needed. Therefore, starting from $u=0$ h, after 12 h, at the first spare parts ordering time $u^{\prime }$, the required number of spare parts is three. Assuming only two spare parts are in stock, ordering one spare part at a time is necessary.

After replacing the spare part for the fourth motor, there are two spare parts left in the warehouse. The second motor has the longest usage time among the four motors. To accurately assess the equipment’s performance, it is necessary to retest the equipment, obtain monitoring information, and conduct performance evaluations to determine the performance scores of the four motors. Then, repeat the above analysis process to determine the required number of spare parts and the ordering timing to meet the continuous operation needs of the equipment. The above analysis process determines the required spare parts and the ordering timing for the asynchronous motor.

Although this study primarily validates the spare parts management strategy for asynchronous motors in high-speed train running gear, the method has certain scalability. Adjusting key parameters such as the performance degradation curve and threshold can be applied to the management of other complex equipment. For example, industrial robots, aircraft engines, and ship propulsion systems also experience similar performance degradation issues. Therefore, appropriate adjustments can allow the model to meet the spare parts management needs of these types of equipment.

Taking aircraft engines as an example, the key components may experience a faster rate of performance degradation, so the model would need a higher performance threshold to ensure safe operation. Additionally, spare parts procurement for aviation equipment may involve longer production cycles. Therefore, the spare parts delivery time parameters in the model should be adjusted to ensure parts arrive before performance reaches the critical threshold.

Future research will further validate the applicability of the model in managing other types of equipment, especially in the industrial and maritime sectors. The model’s generalizability and scalability will be more comprehensively verified through field testing.

5. Conclusions

This study proposes a high-speed train spare parts management strategy based on performance prediction aimed at extending the operational life of high-speed trains and reducing maintenance costs. Simulation experiments have verified the feasibility and effectiveness of this approach, demonstrating its ability to reduce downtime, improve resource allocation, and enhance overall maintenance efficiency. This strategy represents a key advancement in condition-based maintenance, contributing to more intelligent and adaptive maintenance systems with broader applications in other complex mechanical environments. Compared to existing approaches [9,11,12], the proposed method combines the strengths of knowledge- and data-driven techniques. This hybrid approach allows for more flexibility and adaptability in dealing with real-world operational challenges while improving decision-making accuracy by integrating historical and real-time performance data.

The main contributions of this paper are composed of three parts: First, a transformation method based on a matching function is proposed to convert equipment performance evaluation results from utility form to the form of a performance degradation envelope. Second, using the performance degradation envelope, a spare parts quantity calculation method based on the expected performance score is proposed to determine the number of spare parts required during the operation of high-speed trains. Finally, the timing of spare parts orders is determined by considering the spare parts’ transportation time. Implementing spare parts management based on the proposed strategy is a concrete realization of the “condition-based maintenance” concept in health management. Compared to traditional spare parts management methods that rely solely on historical experience, this strategy provides a systematic approach to spare parts management, improving resource utilization and reducing maintenance costs for high-speed trains. Compared to traditional spare parts management methods that rely solely on historical experience, this strategy provides a more dynamic and data-driven approach. While earlier models focused on optimizing stock levels under fixed assumptions, our approach enhances resource allocation by incorporating real-time performance degradation data, enabling more accurate and timely decision-making for spare parts replacement.

Future research efforts will concentrate on several important areas. First, to address the current limitation of lacking a benchmark model, future studies will incorporate such models to further validate the method’s effectiveness. Additionally, the applicability of the proposed strategy will be expanded to more complex and dynamic environments, particularly for other equipment operating under extreme conditions and experiencing irregular degradation. We aim to develop an online spare parts management system with real-time assessment, enabling on-site real-time data collection and implementation evaluation. Moreover, utilizing recent operational data will ensure the model remains relevant and accurate within current operational contexts. Finally, more advanced predictive techniques, such as machine learning and deep learning models, will be introduced to enhance the model’s ability to handle complex operational conditions and optimize spare parts management for high-speed rail systems.

In conclusion, while this study provides a solid foundation for performance-based spare parts management in high-speed railway operations, further research is necessary to broaden its applicability and refine its adaptability to more varied and complex contexts.