Summarization of Remaining Life Prediction Methods for Special Power Plants

Abstract

With continuous improvements in integration, totalization and automation, remaining useful life predictions of mechanical equipment have become a key feature of technology and core element of equipment prediction and health management. The traditional method based on degradation mechanisms is not fully capable of predicting remaining useful life, especially for special power plants that use industrial transmissions, barrel launchers, etc. The expected service requirements are higher for condition monitoring and remaining service life prediction. The effective prediction of the remaining useful life of such special power plants is a major challenge and technical bottleneck in the industrial field and national defense equipment construction. This paper analyzes and expands on the research on the remaining life prediction methods for special power plants and analyzes the remaining life prediction methods of existing dynamic models, as well as data-driven and data–model fusion drives, and specific ideas for future research and development in four aspects, including remaining useful life prediction tests supplemented with soft measurements. Additionally, future research directions for the remaining life prediction of special power plants are provided.

1. Introduction

With the continuous improvements in integration, totalization and automation, the remaining useful life (RUL) prediction of mechanical equipment has become a key aspect of cutting-edge technology and a core aspect of equipment for prognostics and health management (PHM), providing a technical basis to improve equipment reliability [1,2]. Status monitoring and RUL predictions for mechanical equipment can effectively reduce maintenance costs, eliminate production downtime, and improve productivity. However, the increasingly stringent service environments of mechanical equipment and the increasingly diversified forms of structural failure have rendered traditional degradation-mechanism-based methods useless for RUL prediction [3], especially for special power plants with an industrial transmission device and barrel launcher as the application carrier, where the expected service demand leads to higher requirements for status monitoring and RUL prediction.

For example, transmissions carried out under an extreme reciprocating impact cause internal structure damage (Figure 1) and result in poor transmission or transmission failure. A barrel launcher is subjected to high-temperature, high-pressure, and high-frequency impact overloads, which lead to serious wear of the internal structure (Figure 2), resulting in a decrease in output dynamic energy and, in extreme cases, leading to barrel burst.

The working process of such special power plants cannot be effectively monitored, especially internal structural wear, damage, and other “internal injuries”, which are not easy to detect in a timely manner. Additionally, the means of data acquisition are seriously insufficient. Therefore, effectively predicting the RUL of such special power plants is a major challenge and technical bottleneck in the industrial field and national defense equipment construction [4,5].

The degradation of power plant performance is the main factor affecting a plant’s RUL. Research on the degradation mechanisms of conventional power mechanisms, such as rotating mechanisms, has reached a very mature stage, and a complete set of research theories have been formed. However, it is difficult to directly recreate research on conventional power mechanisms for special power plants, mainly due to the following three differences:

(1)

Different from rotating motion mechanisms such as those of gear boxes and rolling bearings, most parts of special power plants with structural wear or damage are reciprocating motion parts (Figure 1 and Figure 2), and the related research results [6,7] are not fully applicable in this field. Practical experience has shown that, due to the particularities of the working environment and the complexity of the task profile, the “internal injury” of special power plants is affected not only by the material and structure but also by dynamic parameters such as vibration, impact, and pressure in the process of work [8,9,10]. The degradation mechanism of these influencing factors in the reciprocating motion process is due to the different carriers of action. In the existing research process, the research theory of ordinary power plants cannot be fully followed, and improvements need to be made based on the motion characteristics of reciprocating mechanisms [11]. Therefore, the mapping relationship between a dynamic model constructed by integrating multiple degradation factors and equipment RUL is one of the key challenges in current research [12].

(2)

After constructing the mapping relationship between the dynamic model and the RUL of mechanical equipment, it is necessary to build a prediction model through multi-scale and multi-source data monitoring to realize the real-time prediction of the RUL of special power plants [13]. However, due to the generally poor working conditions of special power plants, traditional measurement methods for the dynamic parameters of power plants are usually not applicable in this environment, making it difficult to directly measure the dynamic parameters. This means that data acquisition methods are lacking [14]. At the same time, the traditional method of installing wired or wireless sensors at key structural points, collecting operational data, and analyzing modes or responses in power plants cannot effectively and objectively reflect the actual dynamic parameters, such as the vibration, impact, pressure, etc., of the special power plants’ internal mechanisms due to the complex transmission characteristics of the internal and external mechanisms. At this point, it is necessary to use soft-sensing technology to indirectly obtain dynamic data [15]. The so-called soft measurement method aims to obtain dynamic parameters that are difficult to measure for special power plants. Through the selection of auxiliary variables, data acquisition and processing, the construction of soft measurement models, and real-time correction, these parameters can be inferred or estimated [16]. Therefore, the question of how to soft-measure the dynamic parameters of special power plants and construct a mapping relationship between dynamic data and RUL is currently one of the key challenges in research [17].

(3)

Compared with ordinary power plants, the operating conditions of special power plants have state characteristics such as time-varying and discontinuous status. Moreover, their dynamic parameter measurement data have the characteristics of being non-stationary, single-measurement data and imbalanced, multiple-measurement data [18]. These specific features result in the inability to accurately characterize the complexity and randomness of the degradation process of conventional power plants based on their mapping relationship with RUL. The mapping relationship between the dynamic data established based on conventional power plants and RUL lacks interpretability, generalization, etc. [19]. In view of this, by combining the dynamic data of special plants with their structural characteristics and integrating the dynamic model-driven RUL prediction method with the dynamic data-driven RUL prediction method, breakthroughs can be made in terms of the interpretability and generalization of the model, and the expected results can be obtained [20]. Therefore, the question of how to effectively integrate dynamic models and data in order to establish RUL prediction methods is currently one of the key challenges in research [21,22].

In conclusion, the realization of RUL predictions for special power plants faces the following challenges: First, the question of how to construct a dynamic model-driven RUL prediction method to measure the effects of vibration, impact, and pressure on mechanism wear and damage. The second problem is that it is difficult to directly measure the internal dynamic parameters of the device. How can a soft sensor be used? How can a dynamic data-driven RUL prediction method be built based on soft sensor data? Third, how should dynamic models and data effectively be integrated to ensure the interpretability and generalization of the prediction model? In view of the above three challenges, national and international scholars have carried out research on the RUL prediction of rotary motion mechanisms based on degradation mechanisms [23], deep learning [6,24], fusion methods [25], etc. However, they have encountered difficulties in exploring the RUL of reciprocating motion mechanisms. Based on “internal damage” phenomena such as wear and injury in the internal reciprocating motion mechanism of the special power plant, dynamic parameters such as vibration, impact, and pressure are the important factors used to determine its RUL. Therefore, based on the research results of the dynamic model, dynamic parameter soft sensor method, data-driven RUL prediction method, and other aspects, the RUL prediction method for special power plants can be converged to the RUL prediction method driven by a dynamic model, RUL prediction method driven by dynamic data, and RUL prediction method driven by dynamic data–model fusion [26].

Based on the research results of the above three aspects, it is important to consider multiple conditions, multiple factors, and different combination structures of dynamic analog-fusion-driven parametric RUL prediction models and clarify the mapping relationship between dynamic parameters and the RUL of the reciprocating motion mechanism. Revealing the dynamic degradation mechanism of special power plants provides theoretical and methodological guidance and important research directions for engineering applications, reliability improvements, and health management [27].

2. Research Status at Home and Abroad

RUL prediction is the premise guaranteeing the reliability of mechanical equipment. It allows one to establish relevant analysis methods and criteria and develop s corresponding life evaluation theory and technology with guaranteed safety. At present, national and international scholars’ research on the RUL prediction of mechanical equipment mainly focuses on degradation models and data-driven methods, while research on the data–model fusion method is relatively scarce. For special power plants, dynamic parameters are important factors used to determine RUL. Thus, this paper expands on the state of research at home and abroad, focusing on three aspects: dynamic models, dynamic data, and data–model fusion.

2.1. State of Research on Dynamic Model-Driven RUL Prediction Methods

Model-driven RUL prediction uses differential equations or difference equations to characterize the mapping relationship between mechanical equipment degradation processes and many degradation factors [28].

In classical models, physical quantities with practical significance such as stress, strain, fatigue damage, and energy are often used to characterize the degradation process of equipment. Experts and scholars at home and abroad have conducted a large number of studies on finite element model modification, rigid–flexible coupling analysis, the vibration characteristics of special beams, and the collision characteristics of multi-body structures [29,30].

Finite element model correction technology has a high accuracy and meets the need to provide a guiding confidence degree for practical engineering practice. According to the widespread nonlinear characteristics in a real structure, an important research direction for future computational finite element models is to constantly revise the structural linear simplification of the computational model [31,32].

Another key problem in dynamic analysis is the analysis of high displacement motion and flexible deformation for the computational model. At present, the analytical methods mainly include flexible modeling based on commercial dynamic analysis software [33,34] and coordinate system method numerical calculation analysis [35,36]. The combination of the two can better realize dynamic analysis. However, there is still significant room for improvement in terms of model refinement and computational efficiency.

The research on the dynamic characteristics of special power plants mainly focuses on the analysis of the collision characteristics of multi-body structures and the vibration characteristics of special beams. Among these aspects, research on the collision characteristics of multi-body structures mainly focuses on material deformation characteristics, contact crash mechanic models, friction and wear morphology, and the optimization characteristics of characteristic structures. The research on material deformation characteristics and contact crash mechanic models is interrelated and influential. The deformation characteristics of materials include elasticity, plasticity, and the critical point of transition between the two stages of deformation [37]. There are many factors influencing this characteristic, such as the working state of the device, the microstructure of the material, and the processing technology of the material. The action characteristics of a specific material need to be obtained by combining experimental and theoretical analyses [38]. The contact crash mechanic model is a mathematical simulation of the contact crash process that can be achieved by fully understanding the deformation characteristics of materials. By obtaining initial parameters such as the elasticity damping mass, the contact crash process can be reasonably simulated, and important variables such as the force and displacement in the process can be obtained [39]. At present, the Lankarani–Nikravesh model and other spring-damping mass models are commonly used to simulate the contact crash process. Through theoretical analysis and simulation experiments, the contact crash process of special power plants can be well-recreated with a multi-cycle reciprocating motion [40]. At present, contact crash experiments are mostly simulation experiments, and the obtained test results are mostly indirect verification results. The lack of testing techniques for deriving theoretical analysis results and the actual physical phenomena that occur in the research process of special power plants using this analytical method are key research directions in this stage. The study of friction and wear morphology should consider the impacts that the harsh working conditions within special power plants have on their specificity. At present, using the ablation degradation model, the friction degradation model can be used to quantitatively or, in part, qualitatively analyze the impacts of different matrix materials, coatings, surface structures, and physical strengthening methods on the degradation process of structural performance [41]. The intuitive manifestations of this structural performance degradation are the change in the contact crash feature results and the mapping relationship with contact crash friction wear [42], which are also key research directions in this stage. Research on the optimization characteristics of feature structures is based on suggestions regarding the above three aspects, aiming to change the structural morphology and strengthen the material properties of structures through physical–chemical means, from both macro- and micro-perspectives, in order to achieve the goal of slowing down the degradation process of special power plants [43,44].

The analysis of the vibration characteristics of special beams focuses on the following aspects: the correction of the dynamic differential solution method, extended based on the variational principle [45,46]; sensitivity analysis under coupling constraint and time-varying geometric characteristics [47]; the beam characteristic analysis of feature abstraction [48,49,50]; and coupling analysis based on structural correlation characteristics [51,52,53].

With further PHM research on mechanical equipment, basic theories such as fracture mechanics, fatigue damage, corrosion, and wear are constantly being enriched [13,14,54], and the classical Paris model [55] and Forman model [56] have been improved. New technologies and methods have been developed for material and strength testing, safety monitoring and control, and reliable operation and maintenance [1,2]. A series of standards, such as the environmental test method (MIL-STD-810G), dynamic environmental criteria (NASA-HDBK-7005), condition monitoring and diagnosis (GB/T 23713.1-2009), and RUL assessment (GB/T 34631-2017), have been proposed in the field of engineering applications [57,58,59,60]. When mechanical equipment has a simple composition and a single degradation factor, the prediction accuracy of the model-driven RUL is high [55]. However, with an enhancement of the structural composition and the complexity of the task profile, the time-varying nature and uncertainty of the degradation process increase, making it difficult to obtain an accurate model and achieve high-precision model-driven prediction results.

To describe the time-varying and uncertainty qualities of the mechanical equipment degradation process, stochastic degradation models based on the framework of probability theory are introduced into RUL prediction, with the main methods including the Wiener process [61,62], gamma process [63,64], etc. The main idea of such prediction methods is to define RUL as the first arrival time at which the stochastic process reaches the failure threshold and to achieve RUL prediction by solving the probability distribution of the first arrival time. The Wiener process is suitable for describing the non-monotonic degradation process of mechanical equipment caused by a large number of small losses. In order to effectively reflect the non-Markov and multimodal properties of the degradation process, the degradation model based on fractional Brownian motion has become a focal point of research on the current Wiener process lifetime prediction theory [65,66]. The gamma process is used to describe mechanical equipment’s strictly monotonous degradation process and can better depict the slow degradation caused by continuous small impacts and the damage caused by a large impact, but the increments in the gamma process are related to a gamma distribution, and the mathematical form is complex, making real-time parameter estimation difficult; thus, it is mainly used to analyze the common lifetime characteristics of similar equipment. Therefore, it is difficult to achieve the high-precision prediction of individual equipment lifespans.

From the existing literature, in addition to the classical model and stochastic process model used to describe the degradation process of mechanical equipment, a regression model (such as a polynomial or exponential model, etc.) based on experience which is able to describe the mechanical equipment degradation process evolution rule can be used. In the case of a single piece of equipment and simple conditions, this method can accurately predict RUL. However, with the increasing complexity of mechanical equipment, their complex and changeable operating conditions, and the coupling interference of degradation factors, it becomes difficult to obtain an accurate degradation model, the cost of obtaining a degradation model becomes too high, and the generalization is not strong. However, the combination of a classical model and a stochastic degradation model cannot describe the dynamic performance degradation trend of mechanical equipment, especially for special power plants, for which a dynamic performance degradation model (hereinafter referred to as the “dynamic model”) has not yet been established.

2.2. State of Research on Dynamic Data-Driven RUL Prediction Methods

With the development and application of sensors, storage, network transmission, and other technologies, the monitoring of the operation processes of mechanical equipment has produced a large amount of data. These can be used to accurately predict RUL through the mining of the degraded information hidden in the data. To date, such methods have achieved some excellent results and been used to develop excellent public data sets (such as the FEMTO data set [67], Cincinnati data set [68], Xi’an Jiao-tong University data set [69]), and Siemens Predictive Maintenance Software Equipment Predictive Analytics (EPA), etc.). In conclusion, data-driven RUL prediction methods mainly consist of feature extraction, health indicator construction, and RUL prediction.

In obtaining accurate and reliable life prediction results, efficient feature extraction plays an important role. Data features are mainly divided into the time domain, frequency domain, and time–frequency domain. The time domain feature extraction method directly calculates the data’s statistical features, such as the mean, variance, root mean square, skewness, kurtosis, cliff, entropy, etc. The frequency domain feature extraction method uses Fourier transform to transform the time domain data into the frequency domain and then uses spectrum analysis to obtain the statistical features in the frequency domain. The time–frequency domain feature extraction method uses Hilbert–Huang transform, wavelet transform, empirical mode decomposition, etc. These methods can be used to expand the time domain data to a two-dimensional space, obtain the instantaneous frequency and amplitude at any time, and finally, obtain the time–frequency domain features [70,71,72,73]. The above feature extraction methods select the data from different perspectives, but the key features extracted for different types of mechanical equipment are still key problems for data-driven methods which have not been successfully solved.

Health indicator construction is the quantitative expression of the health state of mechanical equipment, which can be divided into two categories according to physical significance, namely, physical health indicators and virtual health indicators. Physical health indicators refer to the time domain, frequency domain, and time–frequency domain characteristics of mechanical equipment, which have physical significance but poor monotonicity and a poor trend and are seriously affected by noise [74]. Virtual health indicators refer to a type of indicators representing the running state of mechanical equipment, being obtained from the fusion of multiple physical health indicators or sensor data, which have no physical significance but can reflect the degradation trend and achieve good results in terms of monotonicity, trends, and scale similarity [75]. The main research methods include deep learning, principal component analysis, T-distributed random neighbor embedding, locally linear embedding, and the restricted Boltzmann machine [28,76].

Based on feature extraction and health indicator construction, representative methods of RUL prediction include convolutional neural networks, deep belief networks, recurrent neural networks, and transfer learning.

Convolutional neural networks have good feature extraction and generalization abilities, and their overall architecture includes an input layer, a convolutional layer (excitation layer, pooling layer, and fully connected layer), and an output layer. The stacked convolutional layers of the network and the pooling layer form a feature extractor, and the fully connected layer acts as a classifier or predictor, constituting an end-to-end network model. The model’s accuracy and robustness depend on the types of network layers, the network depth, the arrangement of various types of layers in the network, the features chosen for each layer, and the training data [77,78].

RUL prediction studies based on convolutional neural networks have the following characteristics [79,80]:

(1)

A convolutional neural network can process a large amount of raw data, which makes it suitable for large model computing processes.

(2)

Convolutional neural networks can realize automatic feature extraction and recognition without supervision and without human intervention.

(3)

A convolutional neural network has a strong processing ability with regard to mechanical signals, vibration signals, noise signals, optical signals, and other high-dimensional signals, and it has the function of automatic noise reduction during data processing.

(4)

A convolutional neural network has a relatively small number of parameters, which makes training more convenient and efficient and facilitates the construction of a deeper network structure.

(5)

A convolutional neural network is insufficient for data on time series feature extraction ability. Special power plants and other types of equipment with random degradation processes regarding the data information and characteristics of the equipment are often time-series-related, making it easy to lose important feature factors.

(6)

Convolutional neural network RUL prediction cannot quantitatively provide RUL uncertainty; thus, in this stage of the convolutional neural network, RUL prediction is often used in combination with other intelligent algorithms.

The deep belief network is a joint distribution model combining observation data and labels which consists of multiple layers of restricted Boltzmann machines and one layer of a backpropagation neural network. The network is more expandable and can be used to perform unsupervised pre-training and supervised backpropagation on the data and, ultimately, obtain a good RUL mapping model [81,82].

The RUL prediction studies based on deep belief networks have the following characteristics [83,84]:

(1)

A deep belief network can solve the training difficulty problems of the depth model. Through layer-by-layer pre-training and the reverse fine-tuning strategy, the feature representation and extraction of data ranging from shallow to deep can be realized, and the distributed features of the input data can be discovered. The use of this method in the time domain signal does not need to satisfy the requirements of periodicity. The information from data on deep-level feature extraction plays a greater role.

(2)

The short-term prediction performance of the deep belief network is better, while the long-term prediction performance is worse.

(3)

The RUL prediction results obtained with deep belief networks cannot reflect the uncertainty of the prediction results and generally need to be combined with other prediction methods to reflect the uncertainty of the prediction results.

Recurrent neural networks have short-term memory; can be added to the gating mechanism to control information retention, discarding, and preservation in the memory unit; can learn the dependency relationship over a relatively long timespan; and can solve the phenomena of gradient disappearance, gradient explosion, etc. Typical recurrent neural networks are long short-term memory (LSTM) and gated recurrent unit (GRU) networks [85].

The study of RUL prediction based on recurrent neural networks has the following characteristics [86,87]:

(1)

In RUL prediction, recurrent neural networks are able to fuse the original learning samples with the updated learning model, which can retrain the samples and has the characteristics of a fast convergence speed and high stability while improving accuracy.

(2)

Recurrent neural networks have certain advantages in dealing with time-series data or before-and-after dependent degradation data but struggle to analyze and process multidimensional data.

(3)

Recurrent neural networks can effectively reduce the uncertainty caused by environmental perturbations through their unique gate structure. However, they can only realize the point estimation of RUL, and it is difficult to assess the confidence of the prediction results. The existing studies focus on the effect of network training rather than the time-varying stochastic and dynamic characteristics inherent in equipment performance degradation.

Transfer learning is the application of knowledge or patterns learned from the same type of equipment to new equipment or new problems, focusing on how to map the data in the source domain and the target domain from the original feature space to the target feature space and better utilize the existing labeled data samples in the source domain for RUL prediction [88,89].

RUL prediction research based on transfer learning has the following characteristics [90,91]:

(1)

Transfer learning can ignore the requirements regarding the same feature distribution of the model data and application data in traditional degradation models and data-driven models. The full-life performance degradation data of similar equipment types can be utilized, and their features can be transferred to the historical data of the target equipment through learning to realize the RUL prediction of the target equipment.

(2)

In this stage, transfer learning mainly focuses on research based on the deep transfer model and feature transfer model. The former reduces the complexity of the deep network to a certain extent, but the transfer effect mostly depends on the quality of the trained network. The latter requires prior knowledge of the characteristic differences in data distribution between the domains and an exploration of suitable mapping models. There are fewer reasonable explanations for transfer components and transfer tasks, and the theoretical research base is weak.

(3)

The effect of transfer learning is related to factors such as the volume of data, the quality of data, and the selection of transfer source domains. The applicability of the model under different conditions varies to some extent, and an adaptive adjustment of the transfer parameters is mostly used at present, which leads to a lack of theoretical explanations for the parameters of the model.

(4)

If there are large, dynamic changes in the learning source domain and target prediction domain of transfer learning, the iterative updating performance of transfer learning will become weak, resulting in a low prediction performance. The addition of an intermediate domain can reduce the impacts of dynamic changes on the transfer learning model, but the intermediate domain increases the complexity of the model; thus, the balancing of these two factors is a research focus at present.

In summary, the existing literature shows that one can obtain more accurate prediction results through data feature extraction, health indicator construction, and RUL prediction modeling, but the hyperparameters and network design are difficult, and the generalization of the model is poor. Additionally, the prediction results ignore the internal degradation mechanism of mechanical equipment and lack a strict dynamic theoretical basis and interpretability. Furthermore, the method requires a large amount data in order to train the network, which limits its use in mechanical equipment for which one cannot obtain a large amount of monitoring data or the expected prediction results. Therefore, the fusion of dynamic models and data and the study of data generation methods have become new trends in research on the RUL prediction of mechanical equipment [92,93].

2.3. State of Research on Data–Model-Fusion-Driven RUL Prediction Methods

With the continuous development of computer science, new application scenarios for integrating computational mechanic models and data science are constantly emerging. There are three main means of fusion [94]: The first method directly applies intelligent algorithms to solve linear dynamic models but still has a certain improvement interval in its ability to determine efficiency and limitations [95]. The second type produces a wide range of sample data through a dynamic model and uses an intelligent algorithm to extract the abstract mapping relations of the data combined with multi-source data [96,97,98]. The third is based on a “data driven” framework of computational mechanics, using random filtering (KF/EKF/UKF/PF) as a bridge and health indicators based on the characteristics of the project to select a suitable degradation model. The fusion filtering method is a random or parameter identification method used to determine the model’s parameters. Through the model’s extrapolation prediction results and the complementary advantages of implementing data mode methods, the prediction accuracy can be improved [99].

Kalman filtering (KF) addresses the optimal estimation problem of the linear system state with Gaussian noise for input and output data. This optimal estimation can be regarded as a filtering process because system noise and interference are included in the observed data. Both extended Kalman filtering (EKF) and unscented Kalman filtering (UKF) can handle nonlinear degradation processes with Gaussian noise. Of these methods, EKF establishes the Jacobi determinant based on the partial derivative of the nonlinear degradation process and then realizes linearization processing. UKF realizes an approximate calculation of the nonlinear degradation process via untrace transformation. The basic idea of this kind of method is to assume that the mechanical equipment degradation conforms to a certain degradation mechanism model, and the mathematical model and key parameters are fused into a discrete-time-state space model by establishing an extended vector [100]. Then, KF/EKF/UKF is used to realize the state updates and prediction. When studying RUL predictions of the rotation mechanism, the exponential function and its extension model [101] and the fusion curve model [102] are often selected as degradation mechanism models.

Particle filter (PF) is a recursive Bayesian algorithm based on the Monte Carlo method. It uses sequential importance sampling to provide an approximate solution to the Bayesian optimal solution and is suitable for describing a nonlinear degradation process with non-Gaussian random noise. There are three main ideas aiming to improve the life prediction accuracy of the PF method: the selection of an appropriate degradation model [101], the improvement of PF [103], and integration with other methods [104].

With the development of machine learning, fusion research directly using machine learning and degradation models is also an important direction for data–model fusion. Its basic idea is based on multi-source sensor monitoring data, the construction of a virtual health indicator via weighted fusion, the use of stochastic process matching with a time-varying evolution trend, the optimization and adjustment of the fusion model and parameters using life prediction deviation to achieve an accurate prediction, and the quantitative analysis of forecast uncertainty [25,105,106,107]. However, the weighted fusion health indicators rely too much on subjective experience and lack objectivity in weight determination, which makes them unsuitable for the real-time prediction of mechanical equipment RUL.

According to the existing literature, the prediction accuracy of RULs driven by data–model fusion depends on three aspects: the selection of the stochastic degradation model, the determination of the fusion method, and the size of the data. For special power plants, whose performance degradation process mainly depends on dynamic parameters, the determination of the stochastic degradation model with a complex task profile is important. For real-time RUL prediction, a breakthrough in the data–model fusion method is also urgently needed. In addition, the acquisition of dynamic data is difficult, and it is necessary to design a reasonable measurement method.

2.4. Existing Problems

In conclusion, national and international scholars have conducted extensive research on mechanical equipment RUL, and a series of research results have been achieved, with good results in the field of rotating machinery. However, for the field of special power plants, breakthroughs are still needed regarding the creation of a dynamic stochastic degradation model with interpretability and generalization potential and the construction of mapping relationships between dynamic parameters and RUL. In summary:

(1)

The complexity of the special power plant and the variability of the operating conditions cause the coupling interference of a variety of degradation factors, which is not conducive to describing the degradation trends in the plant’s dynamic performance. This makes it difficult to obtain an accurate and generalized degradation model.

(2)

The RUL prediction of data-driven mechanical equipment requires one to monitor big data; thus, the data acquisition method is the first problem that needs to be solved. The existing data acquisition method often uses mechanical equipment with wired or wireless sensor external measuring equipment that runs incentive response parameters. This method of obtaining data leads to a high degree of random noise, and only the internal mechanism dynamic process is passed on to the external data. Therefore, this method cannot directly and effectively reflect the actual dynamic state of the internal mechanism.

(3)

For special power plants, the RUL prediction method driven by the dynamic model mainly builds a parametric mathematical model based on the dynamic degradation process but fails to combine the real-time monitoring data. This makes it difficult to reflect the actual state of the current operation; therefore, the prediction deviation is significant. The RUL prediction method driven by dynamic data lacks a strict dynamic theoretical basis and interpretability and has a poor generalization ability. Additionally, it is difficult to design hyperparameters for the network.

3. Future Research Directions

In view of the RUL prediction demands for special power plants, which are widely used in industrial manufacturing and national defense equipment, we discuss four aspects of the research on RUL prediction: dynamic models, dynamic data, data–model fusion, and test verification. The respective research contents, system, and hierarchy are shown in Figure 3. The overall technical route is shown in Figure 4.

3.1. Dynamic Model-Driven RUL Prediction Methods

To construct a dynamic performance degradation model of multi-factor coupling excitation, multi-working conditions and a different combined structure are used. First, the degradation mechanism should be extracted as a reciprocating movement mechanism, combining the dynamic model with the stochastic degradation model, and one should study vibrations, shock, and stress as a single factor under the random vibration. Then, a dynamic stochastic degradation model is constructed under one-factor excitation. Next, the mechanism of multi-factor coupling is analyzed, and the stochastic degradation dynamics model under multi-factor coupling excitation is constructed. Through the extraction of multi-factor features, the dynamic profile and performance degradation law of the reciprocating motion mechanisms under multi-working conditions are analyzed, and the construction of a dynamic stochastic degradation model of series, parallel, and hybrid structures is explored to clarify the performance degradation mechanism.

The key research contents can be summarized based on the following four aspects:

(1)

A study was carried out on a stochastic degradation model of dynamics under single-factor stochastic excitation;

(2)

A study was conducted on a stochastic degradation model of dynamics under multi-factor coupling excitation;

(3)

A study was conducted on a random degradation model under multi-working conditions;

(4)

A study was conducted on a stochastic degradation model with a combinatorial structure.

The implementation flowchart of RUL technology prediction using the model-driven dynamic method is shown in Figure 5.

3.1.1. Dynamic Stochastic Degradation Process under Single-Factor Random Excitation

By analyzing the actual operation process of a special power plant, it can be found that its internal rotating motion mechanism has a high level of reliability and is maintenance-free throughout the whole life-cycle. However, the internal reciprocating motion mechanism often undergoes fatigue damage and corrosion wear, which lead to the degradation of the dynamic performance. In extreme cases, the mechanism may be damaged. Through the analysis of the physical mechanism, the coupling effect of multiple dynamic excitation is induced (such as vibration, impact, pressure, etc.); thus, the classical Paris model and Forman model cannot accurately describe the degradation process of the mechanism’s dynamic performance. At the same time, the performance degradation of the reciprocating mechanism is caused by the comprehensive action of dynamic incentives, which should satisfy the infinite separability. However, the stochastic process models that mathematically satisfy the infinite separability are the Wiener process, gamma process, and inverse Gaussian process, and the degradation processes of different types of dynamic excitation are not the same. Therefore, the degradation model of a reciprocating motion mechanism using these three kinds of stochastic processes has strong explanatory power in terms of both statistics and dynamics. Starting from single-factor stochastic excitation, such as vibration, impact, and pressure, the stochastic degradation processes of different types of dynamic excitation are analyzed, and the performance degradation process of the reciprocating mechanism is studied in detail by modeling the stochastic degradation process caused by the single factor and identifying the model parameters. According to dynamic parameters such as vibration, impact, and pressure, the stochastic process model is constructed, being modeled through the expectation maximization (EM) algorithm so that the probability density distribution function and RUL distribution function of the single-factor stochastic degradation process can be obtained. The performance of different types of dynamic excitation degradation processes conforms to different stochastic processes; for example, vibration excitation degradation conforms to the Wiener process, shock excitation degradation conforms to the gamma process, and pressure excitation degradation conforms to the inverse Gaussian process. Therefore, based on the Wiener process, gamma process, and inverse Gaussian process, dynamic performance degradation probability density functions and RUL distribution functions can be obtained.

3.1.2. Dynamic Stochastic Degradation Process under Multi-Factor Coupling Excitation

Based on the degradation model of dynamic performance under single-factor random excitation, according to the infinite separability of the degradation process, the parameters of the stochastic degradation model are extracted, and the parameter matrix is constructed. The matrix contains characteristic information on the degradation of the dynamic performance. The significance of the eigenvalues is positively correlated with the magnitude of the eigenvalues of the matrix. Therefore, by solving the eigenvalues of the parameter matrix, the feature space of dynamic performance degradation is constructed. The parameter optimization of the feature space can be carried out using a Particle Swarm Optimization (PSO) algorithm, and the multi-parameter fusion degradation model can be obtained; that is, the dynamic performance degradation model under multi-factor coupling excitation can be obtained.

3.1.3. RUL Prediction Model under Multiple Working Conditions

For special power plants, one tends to constantly adjust the working conditions according to the task profile, and the dynamic parameters of the internal reciprocating motion mechanism will also change under different working conditions (mean, variance, etc.). A dynamic performance degradation model obtained under a single working condition cannot fully describe the performance degradation law under all working conditions. Therefore, the similar trajectory method (STM) can be combined for the prediction of RUL under multiple operating conditions to achieve RUL prediction for special power plants under multiple operating conditions.

First, according to the dynamic performance degradation model obtained under multi-factor coupling excitation, the dynamic performance degradation trajectory under different conditions can be established. Then, the similarity of the trajectory can be evaluated, Euclidean distance similarity evaluation criteria can be obtained, the performance degradation trajectory can be integrated under different working conditions, and the RUL prediction model can be formed under multiple working conditions.

3.1.4. RUL Prediction Model for Different Combined Structures

Considering that there is a series, parallel, or series–parallel mixed structure in the reciprocating motion mechanism of the special power plant, while the load-sharing mechanism is present in the combined structure, the dynamic excitation factors are the same, the physical locations of the mechanisms are adjacent, and the degradation processes of different mechanisms have certain correlations. The dynamic profile of the combined structure in the operation stage will affect the degradation process of each component mechanism, defining the affected dynamic performance degradation parameters as the covariates. Each mechanism in the combined structure is also subject to a shared load or a dynamic profile, and there is a shared covariate. Therefore, the shared covariates are used as a “bridge” to connect the degradation models of different mechanisms in order to describe the correlation between the degradation laws of various mechanisms in the combined structure.

Based on the state space model, a combinatorial structure stochastic degradation model is established considering the shared covariates. Covariates are introduced into the state space to establish a state space model of the combined structural dynamics containing the covariates. Secondly, the degradation of the combined structure at a certain time point is defined as a state, and the degradation model of its dynamic performance is transformed into the state transition equation in the state space model. The unknown parameter estimation model in the dynamic state space model can be constructed based on the particle filter (PF) algorithm. The RUL prediction model of the combined structure is obtained by extrapolating the estimated degradation parameters. Based on this process, RUL prediction models with different combined structures can be studied.

3.2. Dynamic Data-Driven RUL Prediction Method

To decrease the difficulty of obtaining the dynamic data of special power plants, based on the random, non-contact test theory, the incentive transfer models and boundary conditions such as vibration, impact, and pressure are studied. Based on the dynamic data obtained from single-working-condition and multi-working-condition tests, the RUL prediction method of special power plants with small-sample and unbalanced data can be researched, the mapping relationships between different types of trial data and RUL can be analyzed, and the change rule of RUL under different types and levels of random incentives can be explored. Then, the method of dynamic data acquisition and pretreatment can be researched for different combined structures, such as series, parallel, and hybrid structures. The dynamic data characteristics are analyzed, and dynamic data-driven RUL prediction models are constructed for different combinatorial structures. RUL prediction methods for complex institutions can be explored. The key research contents can be summarized according to the following four aspects:

(1)

Theoretical research is conducted on the soft measurement method for the follow-up dynamic parameters;

(2)

Research is conducted on RUL prediction methods using small samples and non-equilibrium data conditions;

(3)

Research is conducted on the RUL prediction method driven by dynamic data under multiple working conditions;

(4)

Research is conducted on the RUL prediction method driven by dynamic data under different combination structures.

The implementation flowchart of RUL technology prediction using the data-driven dynamic method is shown in Figure 6.

3.2.1. Theoretical Research on the Soft Measurement Method of Follow-Up Dynamic Parameters

The dynamic parameters of the special power plant cannot be measured directly. The traditional measurement method is based on indirect measurement on the outside of the device, equipped with wired or wireless sensors for the internal institutions’ excitation response parameters (Figure 7). The use of such methods to obtain data leads to a high degree of random noise, and only the internal mechanism dynamic process is transmitted to the external data. Therefore, such a method cannot directly and effectively reflect the actual operating state of the internal mechanism. Therefore, this paper proposes a soft measurement method for follow-up dynamic parameters. The basic idea is to integrate the sensor into the special power plant dynamic object, follow the movement of the test mechanism (reciprocating movement mechanism) through the dynamic action object, and directly measure the vibration, impact, pressure, and other dynamic parameters, as shown in Figure 8. Because this method is based on the follow-up sensor group, accompanied by the motion of the dynamic object to measure its dynamic parameters, and further supplemented by the dynamic excitation transfer matrix to deduce the dynamic data of the tested mechanism, it is called the soft measurement method of dynamic parameters.

3.2.2. RUL Prediction Method under Small-Sample and Non-Equilibrium Data Conditions

The dynamic data obtained using the soft sensor method of follow-up dynamic parameters are limited and pertain to small samples. At the same time, in the short term, the sample size of the dynamic data is much larger than that of the degenerate state, which contains unbalanced data. Therefore, the dynamic data of special power plants are characterized by a small sample size and non-equilibrium conditions. The following steps can be taken to model and analyze the RUL of special power plants based on small-sample and non-equilibrium dynamic data:

(1)

Data preprocessing based on the GSA-IFCM method.

The data obtained through measurements of the accompanying sensor group are periodic time series data containing noise interference, which need to be filtered and de-noised according to the operating frequency before extracting the unit cycle sequence. Then, the actual dynamic data in the unit cycle can be reversed through the dynamic excitation transfer matrix. The Improved Fuzzy C-Means (IFCM) algorithm and Genetic Simulated Annealing (GSA) algorithm can be combined to extract the cluster center of the maximum value of the unit time series, and the t-Mean Square Value (t-MSV) method can be used to calculate the energy curve of the time series by setting a time window to determine the start and end points of the unit period time series in order to adaptively extract the unit period time series. A basic flowchart of the data preprocessing steps based on the GSA-IFCM method is shown in Figure 9.

(2)

Data enhancement based on the SAE-ACGAN method.

On the basis of data preprocessing (1), a sparse auto-encoder (SAE) is combined with ACGANs based on auxiliary classifier generative adversarial networks (ACGANs). Thus, a data enhancement method based on a time–frequency diagram and SAE-ACGANs is formed, as shown in Figure 10. Firstly, the SAE is applied for the in-depth extraction of high-dimensional data features. Then, an SAE structure is added as the extractor of the image features in the ACGAN framework, the raw data are encoded as hidden variables, noise is added through the standard normal distribution, and this is then input into the generator in order to strengthen its ability to represent the hidden variables related to the image category and reduce the generator range required to learn the real sample feature space, so that the image category features can be effectively maintained in the model training and recognition stage to improve the discriminator performance. This data enhancement method can be used to amplify small-sample and disequilibrium data.

(3)

Construction of an RUL prediction model based on the RCNN-ABi-LSTM method.

On the basis of data enhancement, the good feature extraction ability and generalization ability of convolutional neural networks (CNNs) are used to construct a residual convolutional neural network attentional bidirectional long- and short-term memory (RCNN-Abi-LSTM) network RUL prediction model for special power plants. When extracting depth feature vectors from multi-dimensional sensor signals via CNN, the residual network structure is used to solve the problem of gradient disappearance caused by the deep CNN network. In view of the sequential correlation of sensor data, bidirectional long- and short-term memory (Bi-LSTM) networks can be used to learn the dynamic changes in the features proposed by the CNN and capture the long-distance-related features in the time series. In addition, the attention mechanism is introduced to provide different probability weights into the Bi-LSTM implicit states so as to strengthen the expression of key information regarding RUL prediction.

The basic structural diagram of an RUL prediction model based on the RCNN-ABi-LSTM method is shown in Figure 11.

3.2.3. RUL Prediction Method under Multi-Working Conditions

For the multi-working conditions of special power plants, the kurtosis and cliff degree characteristics can be extracted according to the measurement data in order to effectively identify each working condition, which can be transformed into the RUL prediction problem driven by small-sample and non-equilibrium dynamic data. The dynamic data obtained through the soft sensor method of dynamic parameters under each working condition can be analyzed according to the above steps. Finally, based on the similar trajectory method (STM), a dynamic data-driven multi-working condition RUL prediction model is constructed.

3.2.4. RUL Prediction Methods under Different Combined Structure Conditions

Combined structures can be simplified and abstracted into series, parallel, and mixed structures, as shown in Figure 12. Based on the dynamic data obtained using the soft measurement method of dynamic parameters, the temporal domain and frequency domain characteristics can be analyzed, the combined structure can be identified, and the data of each subsystem can be extracted. An RUL prediction model can be constructed for each subsystem. An RUL prediction model is proposed as follows:

Cascaded structure: $\mathrm{RUL}=\min \left({\mathrm{RUL}}_1,{\mathrm{RUL}}_2,{\mathrm{RUL}}_3\right)$.

Parallel structure: $\mathrm{RUL}=\max \left({\mathrm{RUL}}_1,{\mathrm{RUL}}_2,{\mathrm{RUL}}_3\right)$.

Composite construction: $\mathrm{RUL}=\min \left(\max \left({\mathrm{RUL}}_1,{\mathrm{RUL}}_2\right),{\mathrm{RUL}}_3\right)$.

For cases where the combination structure is relatively complex and there are many subsystems, an analogy can be made according to the above situation on the basis of the RUL prediction model.

3.3. RUL Prediction Method Driven by Data–Model Fusion

Focusing on the problems of the interpretability and generalization of RUL prediction, typical health indicators were used to characterize the health status of special power plants, and the construction method for health indicators under multi-factor coupling excitation was studied to explore the quantitative expression method for the health status of special power plants. Based on this aim, to study the RUL prediction method for special power plants, a parametric degradation process model was constructed with dynamic data–model fusion, and the model uncertainty and data uncertainty were quantitatively analyzed. The influences of the uncertainty factors on the prediction accuracy were explored. Research was conducted on the construction method of the data–model fusion RUL prediction model based on complex task profiles, the real-time correction mechanism of dynamic data for the prediction models was analyzed, and a real-time prediction method for the RUL of special power plants was explored. The key research contents can be summarized according to the following three aspects:

(1)

Research on the construction method of health indicators under multi-factor coupling excitation;

(2)

Research on the parameterized RUL prediction model based on health indicators;

(3)

Research on the real-time prediction method of RUL based on complex task profiles.

The detailed technical route is shown in Figure 13.

(1)

Study of health indicators under multi-factor coupling incentives

The operation data of the special power plant, obtained using the soft sensor method of dynamic parameters with follow-up, are periodic time series of vibration, impact, and pressure with noise interference, which are filtered and de-noised according to the operating frequency to form the vibration data set, impact data set, and pressure data set. The health indicator (HI) construction procedure of this institution is as follows:

(a)

The dynamic excitation transfer matrix constructed based on the research contents described in Section 3.2 is used to infer the actual dynamic data of the device.

(b)

Considering the degradation process of the dynamic performance of the device as a random process, the parameter variables of the stochastic processes are taken as the health indicators of institutions. Vibration HI, impact HI, pressure HI, etc., are extracted based on the vibration data set, impact data set, and pressure data set, respectively. These HIs have practical physical significance, and the change process is highly interpretable.

(c)

The parameter matrix is constructed using each HI constructed based on the random process parameter (b), and the eigenspace is constructed by solving the eigenvalues of the parameter matrix.

(d)

After optimizing the feature space with the parameters, HI can be fused with multiple parameters. This parameter contains the feature information on dynamic performance degradation, and the degree of degradation is positively related to its value.

(2)

Research on the RUL parametric prediction model based on health indicators

Based on the multi-parameter fusion HI obtained through the above process, the parametric prediction model of data–model fusion can be obtained by substituting it into the multi-parameter fusion degradation model that is constructed. In order to preserve generality, the individual differences incorporated into the degradation model are reflected in the uncertainty of stochastic degradation processes based on the dynamic model. At the same time, the multi-parameter fusion HI, based on dynamic data, also contains measurement errors, which manifest as data uncertainty. These two kinds of uncertainty can be treated according to a mutually independent normal distribution, that is, the model uncertainty f(x) ~ N (μ_m, σ_m) and the data uncertainty g(x) ~ N (μ_d, σ_d). The sum, difference, and product of the two follow a normal distribution. Finally, the upper and lower boundaries of the confidence interval of the prediction result 100(1 − α)% can be obtained.

(3)

Research on the real-time prediction method of RUL for a complex task profile

A complex task profile essentially constitutes the conditions of special power plants, such as the change in gear transmission speed, the barrel launcher firing rate, and the changes in conditions which can lead to dynamic profile changes. Changes in dynamic data segmentation, thinning, and the amount of data are characterized by the small sample size and disequilibrium of the data. These aspects can also reveal random parameter drift in the random process. Therefore, the real-time prediction of RUL for special power plants with a complex task profile must be based on the historical measurement data set, which can be implemented using the following technical route:

(a)

The real-time dynamic measurement data of a complex task profile can be extracted and preprocessed. The actual dynamic data of special power plants can be obtained, and the dynamic section can be constructed.

(b)

One extracts the random parameters based on the dynamic profile and the parametric model constructed in (2).

(c)

Based on Bayesian theory, the random parameters of the data–model-fusion-parameterized model are updated to obtain a real-time RUL prediction model for special power plants.

3.4. Research on RUL Prediction Tests Aided by Soft Measurements

The correctness of the RUL prediction of special power plants is directly determined by the correctness of the soft sensor method and theory of follow-up dynamic parameters, which affects the potential engineering application value of the research. Therefore, it is necessary to synthesize and verify the correctness of the research through experimental work. Through the design and testing of follow-up dynamic parameter measurement devices under a variety of working conditions, the dynamic data of the operation process can be extracted, the dynamic profile can be analyzed under a variety of working conditions, and the incentive input of the experimental platform can be preset. Throughout the whole process of the dynamic data measurement test, the RUL-parameterized prediction model and RUL real-time prediction method can be verified. The key research contents can be summarized according to the following two aspects:

(1)

Trial production and test research on soft measuring equipment with follow-up dynamic parameters;

(2)

Research measuring the full life-cycle dynamic parameters of the special power plant.

The test principle is detailed as follows:

(1)

Trial production and the testing of soft measuring equipment for the accompanying dynamic parameters.

The internal reciprocating motion mechanism of the special power plant is taken as the test object for the trial production and testing of a soft sensor with dynamic parameters, and its structure is simplified. The test setting is shown in Figure 14. The reciprocating motion mechanism is fixed on the vibration test bench, the vibration test bench controller stimulates excitation on the vibration test bench, and the motion controller drives the reciprocating movement mechanism through the motor. The follow-up sensor group is closely connected to the moving part of the reciprocating motion mechanism to collect dynamic data, such as vibration and impact data, during the mechanism’s movement. An analysis of the collected data verifies the correctness of the soft measurement method of random dynamic parameters.

(2)

Testing of dynamic parameters’ measurement throughout the whole life-cycle of special power plants.

On the basis of the soft sensor method based on follow-up dynamic parameters, an experiment can be conducted, the dynamic transmission of flat, lift, swing processes of the dynamic data can be obtained, the dynamic profile can be extracted, and a console preset incentive can be set. The test principle is shown in Figure 15. The leveling mechanism and the lift and swing mechanism have a series structure. Two sets of lift and two sets of swing mechanisms comprise the parallel structure, and the follow-up sensor set is built into the transmission load (center of gravity). Using the vibration, impact, and other dynamic data under actual working conditions, such as single-load and multi-load conditions, a dynamic life-cycle data set is constructed to verify the proposed RUL prediction model.

4. Conclusions

This paper mainly summarizes the state of research on the RUL prediction methods of special power plants and analyzes the problems in the present stage of this research. In order to further study the RUL prediction methods of special power plants, the research contents and ideas regarding four aspects are summarized: the dynamic model-driven method, the data-driven method, the data–model-fusion-driven method, and the RUL prediction test assisted by soft-sensor technology.

The main future research directions can be divided into the following three aspects:

(1)

On the basis of the existing research on random degradation models, the mechanism and theory of the effects of dynamic degradation factors could be explored further, and a degradation effect model that is more aligned with special power plants could be constructed, objectively and effectively furthering RUL prediction research for special power plants.

(2)

Focusing on special power plants, a reasonable and effective soft sensor method could be designed for dynamic environments to directly measure dynamic data and then predict the RUL based on the dynamic data.

(3)

Furthermore, the dynamic models and data should be effectively fused to develop an RUL prediction method for special power plants with interpretability and generalization ability.