Optimization Method of Equipment Maintenance Resource Scheduling Based on Hidden Semi-Markov Model

In order to solve the problems of uneven distribution of maintenance resources, poor planning, and inaccurate forecasts in the process of coordinated maintenance of complex equipment, a complex equipment maintenance resource scheduling optimization method based on hidden semi-Markov model is proposed. Establish the transportation time matrix between the support points and the maintenance points, and propose the maintenance resource scheduling plan between the maintenance points and the support points. Make full use of existing resources, shorten the average waiting time for equipment to be repaired, restore the combat effectiveness of the equipment in a relatively short time, and maintain and restore the integrity of the equipment to the maximum.

At present, most of the research on resource scheduling problems is aimed at the management of emergency systems. Literature [1] proposes a multi-objective solution model based on fuzzy sets and decision satisfaction, and introduces weight coefficients in satisfaction and methods, so that program decision makers can configure different weights for multi-object satisfaction membership functions to make decisions [1]. However, research in this area focuses more on processing deterministic information, which has great limitations in practical applications. Literature [2] analyzed the relationship between the various elements of resource scheduling and the causes of resource conflicts based on the wartime equipment maintenance support resource scheduling system, and established a multi-maintenance point resource optimization scheduling model. A resource optimization scheduling method based on the priority of maintenance points is proposed [2], but the real-time health status of complex equipment cannot be accurately predicted, which makes resource scheduling uncertain. Literature [3] established a multi-demand-multi-supplier maintenance resource scheduling optimization model with soft time windows used by the scheduling optimization module in the system, and applied genetic algorithm to analyze the solution of the model [3]. However, the genetic algorithm parameters are more complicated and time-consuming, and are too dependent on the initial population selection. Literature [4] established a multi-objective optimization model, and transformed it into a single-objective model through objective priority decision-making. The adaptive genetic algorithm based on niche and the genetic algorithm based on spanning tree are used to solve the problem [4], but the research is mainly for the situation of a single maintenance demand point. Literature [5] established a highway network model and a mathematical model for optimal scheduling, and used dynamic programming and LINGO software to solve and calculate, and scientifically schedule maintenance resources [5]. However, the scheduling priority between maintenance points is not determined, resulting in poor scheduling efficiency.

Due to the complexity of the combat environment and resource allocation, the existing research methods have a narrow scope of application, strong limitations, strong specificity, and poor versatility. There is a lack of research on the optimal scheduling of maintenance support resources in the overall environment [6]. On this basis, this paper proposes an optimization method for complex equipment maintenance resource scheduling based on hidden semi-Markov model. Establish a hidden semi-Markov model based on the monitoring data of each maintenance point to evaluate the health status of the equipment, and calculate the importance and priority of each maintenance point based on the health status. Establish the transportation time matrix between the support points and the maintenance points, and propose the maintenance resource scheduling plan between the maintenance points and the support points [7].

Hidden Semi-Markov Model is an ideal mathematical model that uses observable sensor signals to predict unobservable health status. The Hidden Semi-Markov Model is constructed by adding the state duration to the defined Hidden Markov Model. Different from the state in the standard hidden Markov model, the generation of the state in the hidden semi-Markov model is an observable segment instead of a single observation set in the hidden Markov model. The parameters of the hidden semi-Markov model are: initial state distribution, transition matrix, state duration distribution, observation model. Only when the object of observation transfers from one state to another different state can the conditional independence between the past state and the future state be ensured [8]. The hidden semi-Markov model models the observation information between the state transition intervals, so it not only has the flexibility of the hidden Markov model to approximate the complex probability distribution, but also the flexibility of the semi-Markov model to express the state duration.

Before reaching the state to be repaired, complex equipment usually goes through several different operating states. Suppose the operating state is divided into n discrete states: 1,2,3,..., n-1 and F. The trained Hidden Semi-Markov Diagnostic Model can test the health status at each sampling time point, so it can be regarded as a random process: H = {H _t :t ≥ 0}.

H _{t = i, it means that the equipment is in state H i at time t.Assuming that when the equipment is in state H i , the transition probability Pij from the state of health to the next point in time j is fixed [9], for the hidden Markov chain, the conditional distribution of the future state H t+1 and the past state H 1,...,H t is:}

(1) P ( H t + 1 = j ∣ H t = i , H t − 1 = i t − 1 , … , H 2 = i 2 , H 1 = i 1 ) = P ( H t + 1 = j ∣ H t = i ) = P i j

The state of the segmented hidden semi-Markov model is called the macro state, and each macro state is composed of several individual micro states [10]. Suppose a macroscopic state sequence has n segment, let q_i be the time index of the end point (1≤i < n-1) of the i -th segment, and q_F be the time index of the end point F, the parameter mapping of the hidden semi-Markov model is shown in Figure 1.

Figure 1.

(2) q i j ( k ) = P ( H t + 1 = j , X j = k ∣ H t = i )

q_ij (K) is the initial state distribution from state i to state j, the result depends on when the equipment is in state H_i at the previous moment t and t+1 is in state H_j at the latter moment, and X_j is the duration of a certain state j expressed as a non-negative integer ^k .

Figure 2 shows the flow chart of maintenance resource scheduling optimization based on hidden semi-Markov model.

Figure 2.

a. Collect the monitoring data of each maintenance point, and monitor the trend of the data as the time point increases.

b. Establish a hidden semi-Markov model to evaluate the real-time health status of the equipment.

c. Introduce the importance and priority of each maintenance point, determine the judgment matrix of the weight of each index, and sort the maintenance points according to the calculation results of the importance and priority.

d. Establish the transportation time matrix between the support point and the maintenance point.

e. Establish a maintenance resource scheduling plan.

In order to evaluate the optimization performance of the proposed complex equipment maintenance resource scheduling optimization method based on the hidden semi-Markov model in the complex equipment maintenance resource scheduling, the electrical subsystem of a certain type of self-propelled gun is used to test it [16]. The electrical subsystem of a certain type of self-propelled artillery is mainly composed of three subsystems: fire control system, follow-up system, and electrical system. The factory allowable values of the state characteristic parameters of each subsystem component are set, and the limit values are known. And use the sensors on the subsystem to obtain the monitoring values of the state parameters to evaluate the health of the all-gun electrical system of the self-propelled artillery.

In this experimental study, it is assumed that the maintenance unit needs to maintain 4 maintenance points, namely artillery A, artillery B, artillery C, and artillery D. Use the monitoring data of the sensors on the artillery to evaluate the repair status of the self-propelled artillery. The monitoring data of 4 artillery is selected to show the change trend of the sensor monitoring data in the case of increasing time points, and data preparation is carried out for evaluating the health status of the artillery [17]. Table 1 shows the monitoring data of the maintenance point sensors.

The training curve of the Hidden Semi-Markov Model is shown in Figure 3.

Figure 3.

According to Figure 3, during the model training process, as the number of iterations increases, the health of the artillery gradually deteriorates. But when the importance and priority are introduced, the increase of the log-likelihood estimation probability value curve is gradually slow, and the convergence error is limited to a fixed value. The log-likelihood estimation probability values of the four artillery can reach the set error within less than 50 iterations, indicating that the method has strong real-time signal processing capabilities. Among them, artillery A maintains a fixed value after the 12th iteration, artillery B maintains a fixed value after 15 iterations, artillery C maintains a fixed value after 20 iterations, and artillery D maintains a fixed value after the 10th iteration.

This paper proposes an optimization method for complex equipment maintenance resource scheduling based on hidden semi-Markov model. Establish a hidden semi-Markov model based on the monitoring data of each maintenance point to evaluate the health status of the equipment, and calculate the importance and priority of each maintenance point based on the health status. Establish the transportation time matrix between the support points and the maintenance points, and propose the maintenance resource scheduling plan between the maintenance points and the support points. The advantages of this method are:

1) Taking into account the maintenance support situation of the entire combat environment, a hidden semi-Markov model is introduced to evaluate the health status of complex equipment, and the real-time health status of complex equipment is taken as one of the priority considerations for resource scheduling.

2) Introduce the importance and priority of each maintenance point. The accuracy of the priority of the maintenance point is 1.2% higher than the importance of the maintenance point. Therefore, the calculation result of the priority of the maintenance point is selected to establish the transportation time matrix and the scheduling plan between the support point and the maintenance point. It can ensure the priority supply of key troops, key directions, and key equipment maintenance support resources.

3) Establish a transportation time matrix between the support point and the maintenance point, which improves the efficiency of resource protection in terms of time and reduces the maintenance cost.

4) In view of the complexity of the combat environment and resource allocation, a multi-maintenance point-multiple support point scheduling optimization plan was considered. This makes the method applicable to a wide range, reduces the limitation on the basis of the previous method, and improves the versatility.