A Method for Real-Time Fault Detection of Liquid Rocket Engine Based on Adaptive Genetic Algorithm Optimizing Back Propagation Neural Network

sensors

Article A Method for Real-Time Fault Detection of Liquid Rocket Engine Based on Adaptive Genetic Algorithm Optimizing Back Propagation Neural Network

Huahuang Yu and Tao Wang *

School of Intelligent Systems Engineering, Sun Yat-sen University, Guangzhou 510006, China; [email protected] * Correspondence: [email protected]

Abstract: A real-time fault diagnosis method utilizing an adaptive genetic algorithm to optimize a back propagation (BP) neural network is intended to achieve real-time fault detection of a liquid rocket engine (LRE). In this paper, the authors employ an adaptive genetic algorithm to optimize a BP neural network, produce real-time predictions regarding sensor data, compare the projected value to the actual data collected, and determine whether the engine is malfunctioning using a threshold judgment mechanism. The proposed fault detection method is simulated and verified using data from a certain type of liquid hydrogen and liquid oxygen rocket engine. The experiment results show that this method can effectively diagnose this liquid hydrogen and liquid oxygen rocket engine in real-time. The proposed method has higher system sensitivity and robustness compared with the results obtained from a single BP neural network model and a BP neural network model optimized by a traditional genetic algorithm (GA), and the method has engineering application value. Citation: Yu, H.; Wang, T. A Method for Real-Time Fault Detection of Keywords: Liquid Rocket Engine Based on liquid rocket engine; liquid hydrogen and liquid oxygen rocket engine; genetic algorithm; Adaptive Genetic Algorithm back propagation neural network; fault detection Optimizing Back Propagation Neural Network. Sensors 2021, 21, 5026. https://doi.org/10.3390/s21155026 1. Introduction Academic Editors: Kim Phuc Tran, With the advent of key aerospace programs, such as deep space exploration, crewed Athanasios Rakitzis and Khanh T. spaceflight, lunar exploration, and space station construction, LRE serves as the central P. Nguyen power unit and component of the launch vehicle propulsion system. Its reliability and safe operation have become a focus of people’s attention [1]. Effective fault detection and Received: 4 June 2021 management systems for LRE can help reduce the likelihood of system failure during Accepted: 21 July 2021 operation and prevent unwarranted property damage. Published: 24 July 2021 Existing fault detection and diagnosis methods for LRE are often classified into three categories: model-driven methods, data-driven methods, and methods based on artificial Publisher’s Note: MDPI stays neutral intelligence [1–3]. The model-driven method needs to establish a system model according with regard to jurisdictional claims in to the law of system operation. The degree of conformity between the established model published maps and institutional affil- iations. and the actual circumstance determines the accuracy of the diagnosis results. However, LRE is a complicated nonlinear system with significant nonlinearity, non-stationarity, and uncertainty, making it challenging to develop an appropriate system model. This method is frequently used in conjunction with others. Ref. [4] performed real-time fault diagnosis on LRE based on the autoregressive moving average (ARMA) model. The data-driven Copyright: © 2021 by the authors. method analyzes the engine’s output signal with respect to the relationship between the Licensee MDPI, Basel, Switzerland. system’s output and the fault. This approach requires a large amount of high-quality data This article is an open access article to be supported. However, even for the same type of engine, the faults shown may vary distributed under the terms and conditions of the Creative Commons due to the engine’s working conditions. This method is more ideal for fault diagnostics and Attribution (CC BY) license (https:// alarming during the engine’s steady condition. Ref. [5] established an adaptive correlation creativecommons.org/licenses/by/ algorithm and envelope method for real-time fault detection and alarm during steady-state 4.0/). and startup processes of LRE. Methods based on artificial intelligence mainly include

Sensors 2021, 21, 5026. https://doi.org/10.3390/s21155026 https://www.mdpi.com/journal/sensors Sensors 2021, 21, 5026 2 of 15

expert systems, fuzzy theory, neural networks, and others. Ref. [6] developed an artificial neural network-based isolation and replacement algorithm for the fault management of LRE sensors. In the study of LRE fault diagnosis using BP neural network, Ref. [7] proposed a turbopump multi-fault diagnosis method based on a parallel BP neural network. Ref. [8] performed real-time fault diagnosis on LRE based on a dynamic cloud BP network. Ref. [9] proposed an LRE fault detection method based on quantum genetic algorithm optimized BP neural network. Ref. [10] proposed combining the improved particle swarm algorithm and BP neural network. The related research enhanced the convergence speed and defect detection accuracy of BP neural networks, resulting in pretty good results for offline engine fault diagnosis. It is noted that, in Ref. [11], the authors proposed an unsupervised method for diagnosing electric motor faults by utilizing a novelty detection approach based on deep autoencoders and discover that the multi-layer perceptron autoencoder provides the highest overall performance when compared to convolutional neural networks and long short-term memory. The authors of Ref. [12] suggested a technique for state estimation and, consequently, fault diagnostics in nonlinear systems and utilized a simulation of an SLFJR electric drive model to demonstrate their method. To overcome the drawbacks and flaws of fixed detection in cloud computing, Ref. [13] offered an adaptive and dynamic adjustment fault detection model based on support vector machines and decision trees. All of the studies mentioned above have made significant contributions to related subjects. The study investigates real-time fault detection in LRE and offers a method for real- time fault detection in LRE that utilizes an adaptive genetic algorithm (AGA) to optimize a BP neural network first, followed by a threshold judgment mechanism. The paper compares the suggested model to a single BP neural network and a typical genetic algorithm optimized BP neural network, with a certain type of liquid hydrogen and liquid oxygen rocket engine (LH2/LOX rocket engine) serving as the simulation object. The simulation results demonstrate that the suggested system is capable of real-time fault detection in LRE and that it is also capable of detecting defects more quickly. The rest of the paper is organized as follows. Section2 provides an overview of the LH2/LOX rocket engine. Section3 details the process of developing an AGA optimized BP neural network model. Section4 discusses how to use the model described in Section3 for real-time fault detection and introduces the method of threshold detection. Section5 is a validation of the suggested method using simulation. Section6 draws conclusions.

2. Liquid Hydrogen and Liquid Oxygen Rocket Engine Rocket engines used in aerospace mainly include solid rocket engines, solid-liquid hybrid rocket engines, conventional propellant engines, liquid oxygen kerosene rocket engines, liquid oxygen methane rocket engines, and LH2/LOX rocket engines. Among these, the LH2/LOX rocket engines powered by liquid hydrogen and liquid oxygen offer unmatched safety, adaptability, reliability, and economics, and have become the focal point of global launch vehicle power system development [14]. China, since the 1970s, has successfully developed a 4-ton YF-73 LH2/LOX rocket engine for the CZ-3, an 8-ton YF-75 LH2/LOX rocket engine, and a 9-ton YF-75D and 50-ton YF-77 LH2/LOX rocket engines for CZ-5, and has completed numerous major space launches, including multiple artiﬁcial satellites, lunar orbiting probes, lunar exploration projects, and laid the foundation for manned spaceship and space station projects. In the 21st century, when China demonstrated and researched the moon’s landing mode, heavy-duty launch vehicles, and power systems, it determined that the ﬁrst and booster stages would be powered by a 500-ton liquid oxygen kerosene rocket engine, while the second stage would use a 200-ton LH2/LOX rocket engine. The 200-ton LH2/LOX rocket engine’s operating principle and structure are depicted in Figure1[15–18]. Sensors 2021, 21, x FOR PEER REVIEW 3 of 15

The LH2/LOX rocket engine is mainly composed of a gas generation room, a thrust chamber, a hydrogen main valve, an oxygen main valve, a hydrogen turbo pump, an oxygen turbo pump, pipelines. The sensor data acquired by the system for the purpose of detecting rocket engine faults usually comprise temperature, pressure, speed, pressure, and vibration. [19–22]. The sensor parameters used in this article include hydrogen pump

inlet pressure Pih , oxygen pump inlet pressure Pio , generator pressure before hydrogen

injection Pgih , generator pressure before oxygen injection Pgio , combustion chamber pres-

sure Pc , hydrogen pump outlet pressure Peh , oxygen pump outlet pressure Peo , the

chamber pressure Pg of the combustion chamber, the temperature Teh after the hydro-

Sensors gen2021, 21pump,, 5026 the temperature Peo after the oxygen pump, and the temperature Tg of the 3 of 15 gas generator.

(a) (b)

FigureFigure 1. (1.a) ( Thea) The principle principle of 200-ton of 200-ton LH2/LOX LH2/LOX rocket engine; rocket (b )engine; the structure (b) the of astructure 200-ton LH2/LOX of a 200-ton rocket LH2/LOX engine [15]. rocket engine [15]. The LH2/LOX rocket engine is mainly composed of a gas generation room, a thrust chamber, a hydrogen main valve, an oxygen main valve, a hydrogen turbo pump, an 3. Model Building oxygen turbo pump, pipelines. The sensor data acquired by the system for the purpose In the real-timeof fault detecting detection rocket engineof LRE, faults this usually paper comprise employs temperature, an AGA to pressure, optimize speed, a BP pressure, neural network, andand obtains vibration. the [AGABP19–22]. The model. sensor parameters used in this article include hydrogen pump inlet pressure Pih, oxygen pump inlet pressure Pio, generator pressure before hydrogen injection Pgih, generator pressure before oxygen injection Pgio, combustion chamber pres- 3.1. BP Neural Networksure Pc, hydrogen pump outlet pressure Peh, oxygen pump outlet pressure Peo, the chamber The BP neural networkpressure P gwasof the proposed combustion in chamber, 1986 by the a team temperature of scientistsTeh after led the hydrogenby D.E. pump,Ru- the temperature P after the oxygen pump, and the temperature T of the gas generator. melhart and J.L. McClelland. It eois a multilayer feedforward network trainedg by an error back-propagation algorithm.3. Model Building The topology of the BP neural network consists of an input layer, hidden layer, andIn output the real-time layer. fault As detectiona typical of algorithm LRE, this paper in artificial employs anintelligence, AGA to optimize BP a BP neural networks haveshownneural network, that a and three-layer obtains the BP AGABP network model. can approximate any nonlinear

mapping relationship3.1. as BP long Neural as Network the parameters are appropriate. The BP neural network is widely used in systemThe control, BP neural pattern network recognition, was proposed image in 1986recognition, by a team and of scientists information led by D.E. processing. However,Rumelhart BP neural and J.L.networks McClelland. also It have is a multilayer disadvantages, feedforward such network as slow trained conver- by an error gence speed and easeback-propagation of falling into algorithm.local extreme The topology points. of Using the BP GA neural to optimize network consists BP neural of an input networks is a way tolayer, overcome hidden these layer, anddrawback output layer.s. This As study a typical employs algorithm an in AGA artificial to optimize intelligence, BP the performance of neuralBP neural networks networks. haveshown In thatthe aAGABP three-layer model, BP network the role can approximate of the BP anyneural nonlinear mapping relationship as long as the parameters are appropriate. The BP neural network is network is to performwidely regression used in systemfitting control, on the patternacquired recognition, sensor parameters. image recognition, and information processing. However, BP neural networks also have disadvantages, such as slow conver- 3.2. Adaptive Genetic genceAlgorithm speed and ease of falling into local extreme points. Using GA to optimize BP neural networks is a way to overcome these drawbacks. This study employs an AGA to optimize GA is an adaptivethe performanceprobability of optimization BP neural networks. technology In the AGABP based model,on biological the role ofgenetics the BP neural and evolutionary mechanisms,network is to performcreated regression by Professor fitting Holland on the acquired and his sensor students parameters. at the Uni- versity of Michigan in the United States, and is suitable for optimizing complex systems. GA is an efficient, parallel,3.2. Adaptive and Genetic global Algorithm search method. It can automatically acquire and accumulate informationGA about is an a adaptive search probability space during optimization the search technology process based and on adaptively biological genetics and evolutionary mechanisms, created by Professor Holland and his students at the Univer- sity of Michigan in the United States, and is suitable for optimizing complex systems. GA is an efficient, parallel, and global search method. It can automatically acquire and accumulate information about a search space during the search process and adaptively control all processes to find the optimal solution. In addition, there are many optimization algorithms based on bionics mechanisms for solving different technical applications [23–25]. Sensors 2021, 21, 5026 4 of 15

Numerous practices and research [26] have demonstrated that the standard GA has a serious drawback that its crossover and variation probabilities are fixed, implying that both good and bad individuals undergo the same crossover and variation operations. This impairs the algorithm’s local search ability and search efficiency in the late stages of evolution, making it susceptible to premature convergence. In order to overcome the disadvantages of the standard GA, in 1994, Ref. [27] proposed an AGA that dynamically adjusts the crossover probability and mutation probability according to the fitness value. In the early stages of population evolution, a higher crossover probability and variation probability are used to force the population to evolve globally in order to quickly find the optimal solution, while in the later stages, a lower crossover probability and variation probability are used to force the population to evolve locally in order to help the population converge. The adjustment formula used by the AGA is as follows:

0 ( k1( fmax− f ) 0 f ≥ favg p = fmax− favg (1) c 0 k2 f < favg

( ( − ) k3 fmax f f ≥ f fmax− favg avg pm = (2) k4 f < favg

In Formulas (1) and (2), pc represents the probability of crossover, pm represents the probability of mutation, fmax represents the maximum fitness value of the population, favg represents the average fitness value of the population, f 0 represents the larger fitness value of the two individuals to be crossed, and f represents the mutation value of the fitness value of the individual. In standard GA, the crossover probability is usually chosen randomly as a larger value and the mutation probability as a smaller value, usually in the range of 0.5–1.0 for the crossover probability and 0.001–0.05 for the mutation probability [28]. To avoid AGA slipping into local optimum solutions, the strategy of individuals with less than average fitness traversing the search space in search of the range containing the ideal solutions is applied. Individuals with poor fitness values should be disrupted as much as possible, while those with high fitness values should be preserved appropriately [29,30]. To accomplish this, in this paper, k1 = 0.6, k2 = 0.9, k3 = 0.01, k4 = 0.1. The article uses an AGA to optimize the initial weights and thresholds of a BP neural network, and locks the optimal global range in advance through optimization to speed up the BP neural network’s convergence and prevent it from falling into the local optimum.

3.3. Using AGA to Optimize BP Neural Network The process of optimizing BP neural network using AGA may be separated into three stages: determining the structure of the BP neural network; optimizing the BP neural network using AGA; using the optimized BP neural network to forecast. The ﬂow chart for optimizing the BP neural network using AGA is illustrated in Figure2. Sensors 2021, 21, x FOR PEER REVIEWSensors 2021 , 21, 5026 5 of 15 5 of 15

Encoding of Network Initial Determination of Neural Values Network Structure

Initialization of BP Neural Data Input Decode Network Data Assigning Values Preprocessing Calculation of to BP Network Fitness Training of the Decoding to Get Optimal Network Weight Thresholds Selection Calculation of Errors Crossover

N Assigning Values to BP Mutation Network

Calculation of Y Fitness

Judgment of the Prediction by Trained Conditions Model

Figure 2. The flow Figurechart 2.forThe optimizing ﬂow chart forthe optimizing BP neural the network BP neural using network AGA. using AGA.

3.3.1. Determining the3.3.1. Structure Determining of the the BP Structure Neural of theNetwork BP Neural Network A three-layer structure is chosen for the BP neural network in the article, including A three-layer structure is chosen for the BP neural network in the article, including an input layer, a hidden layer and an output layer. Using a certain type of LH2/LOX an input layer, a hiddenrocket layer engine and as an the output test object, layer. 11 sensors Using are a certain selected astype data of monitoring LH2/LOX points. rocket The gas engine as the test object,generation 11 sensors chamber are pressure selectedPg is as selected data asmonitoring the fitting network points. output, The gas and thegener- remaining ation chamber pressuresensor P data is is selected used as the as input the fitting to the BP network neural network. output, Therefore, and the the remaining number of input layer nodesg of this network is determined as 10 and the number of output layer nodes is 1. sensor data is used as theAccording input to to the empirical BP ne Formulaural network. (3), m is Therefore, the number ofthe hidden number layer of nodes, inputn is the layer nodes of this networknumber of is input determined layer nodes, as l10is and the number the number of output of layeroutput nodes, layer and nodesa is a constantis 1. between 1–10. After repeated simulation verification, the number of hidden layer nodes is determined to be 8, and then the network structure of the model is determined to be 10-8-1. According to empirical Formula (3), m is the number of hidden layer nodes, n is the √ number of input layer nodes, l is the number of outputm = n layer+ l + anodes, and a is a constant (3) between 1–10. After repeated simulation verification, the number of hidden layer nodes The computational complexity calculation method for single BP training of this pro- is determined to be 8, and then the network structure of the model is determined to be 10- posed BP Network is obtained by the following equation [31], 8-1. O(b × t × (n × m + m × l)) (4) mnla=++ (3) where b is the number of training samples and t is the number of iterations. The computa- The computationaltional complexity complexity of calculation the above model meth isod O(88 for bt) single by using BP Formula training (4). of It this can bepro- seen that posed BP Network isafter obtained determining by the the following network structure, equation the [31], computational complexity of this network is related to the number of samples b trained and the number of iterations t. The richer training samples helpOb(( to×× reduce t n × overfitting, m + m × l )) but also increase the computational complexity(4) of training. In addition, the size of the number of training iterations t has an impact on the where b is the numbercomputational of training complexity. samples and t is the number of iterations. The computational complexity of the above model is O(88 bt) by using Formula (4). It can be seen that after determining the network structure, the computational complexity of this network is related to the number of samples b trained and the number of iterations t. The richer training samples help to reduce overfitting, but also increase the computational complexity of training. In addition, the size of the number of training iterations t has an impact on the computational complexity. Figure 3 shows the structure of the BP neural network. The training sample of the network is the data of a certain type of LH2/LOX rocket engine during normal operation.

Sensors 2021, 21, 5026 6 of 15

Sensors 2021, 21, x FOR PEER REVIEW 6 of 15

Figure3 shows the structure of the BP neural network. The training sample of the network is the data of a certain type of LH2/LOX rocket engine during normal operation.

Input Layer Hidden Layer Output Layer

FigureFigure 3. 3. TheThe structurestructure of a BPof networka BP network (10-8-1). (10-8-1). 3.3.2. Optimizing the BP Neural Network Using AGA 3.3.2. OptimizingUtilizing AGA tothe optimize BP Neural the BP neural Network network’s Using initial AGA weights and thresholds, allows the network to converge more quickly during future training and avoids the problem ofUtilizing local optimization. AGA The to steps optimize to optimize the BP BP using neural AGA are network’s as follows: initial weights and thresholds, Step 1: Initial population. Use AGA to encode the initial value of the BP neural allowsnetwork the to network obtain the initial to converge population. more The population quickly refers during to the effectivefuture solution training in and avoids the prob- lemthe of problem local searchoptimization. space. In the The optimization steps process,to optimize a set of effective BP using solutions AGA refers are to as follows: a BPStep neural 1: networkInitial setpopulation. of weights and Use thresholds. AGA The to boundaryencode of the the neuralinitial network value of the BP neural net- weight and the threshold is set to [−1, 1]. As 10-8-1 is the structure of the BP neural worknetwork, to obtain the length the of theinitial chromosome population. in the AGA The is set population as 10 × 8 + 8 + refers 8 × 1 + 1to = 97. the The effective solution in the problempopulation search size determined space. inIn this the paper optimization is 20. The populations process, were formeda set of randomly effective on solutions refers to a this basis. BP neuralStep 2:network Calculate fitness.set of Calculate weights the and fitness thresholds. value of each individual The boundary in the pop- of the neural network weightulation. and The the fitness threshold value is the is criterion set to for [− judging1, 1]. theAs quality 10-8-1 of thisis the solution. structure In this of the BP neural net- article, the reciprocal of the root mean square error of the BP network fitting is used as the work,fitness the value. length of the chromosome in the AGA is set as 10 × 8 + 8 + 8 × 1 + 1 = 97. The populationStep 3: Selection.size determined Selection is the in process this ofpaper selecting is individuals20. The populations with strong vitality were formed randomly on inthis a group basis. to produce a new group. Individuals with higher fitness values are more likely to produce offspring. In the article, AGA employs a roulette wheel to assign probabilities toStep individuals 2: Calculate and selects fitness. them for Ca creatinglculate the nextthe generationfitness value proportional of each to their individual in the population.fitness The values. fitness value is the criterion for judging the quality of this solution. In this article, Step 4: Crossover. Crossover refers to the exchange of some genes between two paired thechromosomes reciprocal to of form the two root new mean individuals. square Crossover error is theof the primary BP methodnetwork to generate fitting is used as the fitness value.new individuals in GA, and it determines the global search ability of the algorithm. In this paper, the single-point crossover method is used for crossover operation. StepStep 3: 5: Selection. Mutation. Mutation, Selection the replacement is the process of gene of values selecting at some individuals locus in the with strong vitality in achromosomal group to produce coding strand a new of an individualgroup. Individuals with other alleles with of that higher locus, resultsfitness in values are more likely to produce offspring. In the article, AGA employs a roulette wheel to assign probabilities to individuals and selects them for creating the next generation proportional to their fitness values. Step 4: Crossover. Crossover refers to the exchange of some genes between two paired chromosomes to form two new individuals. Crossover is the primary method to generate new individuals in GA, and it determines the global search ability of the algorithm. In this paper, the single-point crossover method is used for crossover operation. Step 5: Mutation. Mutation, the replacement of gene values at some locus in the chro- mosomal coding strand of an individual with other alleles of that locus, results in the formation of a new individual. Mutation is an auxiliary method to generate new individuals and determines the local search ability of the GA. Step 6: Calculate the fitness value, check to see if the condition is satisfied, and if not, turn to Step 3 and continue the next round of genetic operation. Step 7: If the condition is satisfied, the individual with the best fitness value in the output population is used as the optimal solution.

Sensors 2021, 21, x FOR PEER REVIEW 7 of 15

Sensors 2021, 21, 5026 7 of 15 3.3.3. Using the Optimized BP Neural Network to Forecast After using the AGA to optimize the BP neural network, the optimal weights and thresholdsthe formation are of calculated, a new individual. the Mutationweights isand an auxiliarythresholds method to toAGABP generate are new assigned, and then individuals and determines the local search ability of the GA. the resultingStep 6: Calculate model the is fitness used value, to forecast check to. see The if the specific condition steps is satisfied, are as and follows: if not, turnStep to Step 1: 3 Assignment. and continue the The next roundvalues of geneticsolved operation. by the AGA optimization are assigned to the BP neuralStep 7: network If the condition as weights is satisfied, and the thresholds. individual with the best fitness value in the output population is used as the optimal solution. Step 2: Set training parameters. In this paper, the parameters of the BP neural net- work3.3.3. Usingare determined the Optimized as BP follows: Neural Network the maximum to Forecast number of iterations is 1000; the learning rate isAfter 0.01; using the thetraining AGA to target optimize is the 1× BP10 neural−10. The network, tansig the function optimal weightsis used and to define the transfer thresholds are calculated, the weights and thresholds to AGABP are assigned, and then the functionresulting modelbetween is used the to forecast.input and The specific hidden steps layers, are as follows: the logsig function is used to define the transferStep function 1: Assignment. between The values the solvedhidden by theand AGA output optimization layers, are and assigned the tonegative the gradient func- tionBP neuralis used network to create as weights the andtraining thresholds. function. StepStep 2: 3: Set Train training the parameters. network In to this get paper, the the expected parameters value. of the BP neural network are determined as follows: the maximum number of iterations is 1000; the learning rate is 0.01; the training target is 1× 10−10. The tansig function is used to define the transfer 4.function Real-time between Fault the inputDetection and hidden via layers,AGABP the logsig function is used to define the transfer function between the hidden and output layers, and the negative gradient function is usedThe to createreal-time the training fault function. detection based on AGABP is achieved by training the model firstlyStep using 3: Train historical the network data to get from the expected the normal value. engine. Then, the actual measurement data

from4. Real-Time the engine Fault Detectionbeing tested via AGABP is used as the input in the model to obtain the real-time pre- ′ ′ dictedThe value real-time Pg fault. Comparing detection based the on predicted AGABP is achieved value byPg training withthe the model actual ﬁrstly sensor measurement using historical data from the normal engine. Then, the actual measurement data from valuethe engine Pg being the residual tested is used is obtained, as the input and in the the model residual to obtain is the compared real-time predicted with the threshold to de- 0 0 terminevalue Pg .whether Comparing the the engine predicted is value malfunctioningPg with the actual or sensornot. Figure measurement 4 shows value the principle of the Pg the residual is obtained, and the residual is compared with the threshold to determine AGABP.whether the engine is malfunctioning or not. Figure4 shows the principle of the AGABP.

=− Pg ek() | Pgg P '| Liquid Rocket Engine

Pg ' AGABP

FigureFigure 4. TheThe algorithm algorithm diagnosis diagnosis principle. principle. Figure5 shows the diagnosis process of the AGABP model. Speciﬁc steps are as follows:Figure 5 shows the diagnosis process of the AGABP model. Specific steps are as follows:Step 1: Data preprocessing. Step 2: Use normal engine measured data to train the AGABP model. StepStep 3:1: ProcessData preprocessing. the real-time engine measured data and import it into the estab- lishedStep AGABP 2: Use network normal model. engine Then, measured the model uses data the measuredto train the values AGABP of the other model. 10 sensorsStep obtained3: Process in real-time the real-time as input toengine predict measured the value ofthe data pressure and Pimportg in the gasit into the established generating chamber. AGABPStep network 4: Compare model. the predicted Then, valuethe model with the uses currently the measured collected gas values generating of the other 10 sensors chamber pressure Pg to obtain residual data. obtained in real-time as input to predict the value of the pressure Pg in the gas generating Step 5: Compare the residual error with the set threshold value. When the engine is chamber.working normally, the residual error value should be within the threshold value. If the residualStep error 4: valueCompare exceeds the the thresholdpredicted value, value that means with the the engine currently is malfunctioning. collected gas generating

chamber pressure Pg to obtain residual data. Step 5: Compare the residual error with the set threshold value. When the engine is working normally, the residual error value should be within the threshold value. If the residual error value exceeds the threshold value, that means the engine is malfunctioning.

Sensors 2021, 21, x FOR PEERSensors REVIEW2021 , 21, 5026 8 of 158 of 15

Sensor Data Pre-processing AGABP Forecasting Collection of Data

Real-time Real-time Comparison with the Threshold Judgment Residual

Figure 5. The diagnosis processFigure of AGABP. 5. The diagnosis process of AGABP.

4.1. Data Preprocessing 4.1. Data Preprocessing There are multiple sensors in the LH2/LOX rocket engine that can measure tem- There are multipleperature, sensors pressure, in the speed, LH2/LOX vibration, rocket and other engine types that of can signals. measure Different tempera- data collec- ture, pressure, speed,tors vibration, can be used and in the other LH2/LOX types rocketof signals. engine Different to collect data.data Whencollectors the system can is be used in the LH2/LOXoperational, rocket the engine data acquisition to collect system data. When collects the data system on the responsesis operational, of various the sen- data acquisition systemsors. These collects response data dataon the have responses a range of scalingof various and measurement sensors. These units response that vary. Pre- processing of the collected response data can reduce the interference of other factors on the data have a range predictionof scaling results. and measurement units that vary. Pre-processing of the collected response data can reduce the interference of other factors on the prediction results. 4.1.1. Select Data 4.1.1. Select Data The LH2/LOX rocket engine parameters change continuously with the change in the engine state, especially the change at the moment of ignition. To ensure the correctness of The LH2/LOXthe rocket experimental engine results,parameters data with chan obviousge continuously mistakes should with be the deleted change prior in to trainingthe engine state, especiallythe model, the change thereby reducingat the mome the influencent of ignition. of the error To data. ensure the correctness of the experimental results, data with obvious mistakes should be deleted prior to training 4.1.2. Normalization of Data the model, thereby reducing the influence of the error data. The LRE is a complicated nonlinear system that is related to mechanical, flow, and combustion processes, among others. The training samples have a greater influence on 4.1.2. Normalizationthe of model’s Data performance, and distinct sensor values have a range and dimension of their The LRE is a complicatedown. Prior to diagnosing nonlinear a system liquid rocket that engineis related failure, to themechanical, engine sensor flow, data and must be pre-processed to ensure that all input parameter components are given equal weight at combustion processes, among others. The training samples have a greater influence on the beginning to solve the numerical effects of the training data on the diagnostic model the model’s performance,due to orders and distinct of magnitudes. sensor This values paper have uses a the range method and of dimension normalizing of the their data for own. Prior to diagnosingdata preprocessing. a liquid rocket engine failure, the engine sensor data must be pre-processed to ensureThe that data all normalization input para processingmeter components formula is: are given equal weight at

the beginning to solve the numerical effects of the trainingx − xmin data on the diagnostic model xi = (5) due to orders of magnitudes. This paper uses the methodxmax −ofx normalizingmin the data for data preprocessing. Among them, xi is the normalized data, x is the original data, xmin is the minimum The data normalizationvalue of the dataprocessing change, and formulaxmax represents is: the maximum value of the data change. This formula transforms the data into the interval [0,1]. xx− x = min 4.2. Threshold Judgment Mechanismi − (5) xxmax min When the LH2/LOX rocket engine is working normally, its sensor parameters are Among them,stable x is within the normalized a speciﬁc dynamic data, range. x is the When original a fault data, occurs, x the sensor’s is the detectionminimum param- etersi will exceed the normal working range. As a result, themin simplest and most effective value of the data change,technique and to determine xmax represents whether a measuredthe maximum signal is value normal of is tothe compare data change. the observed This formula transformsvalue to the the permissibledata into the limit interval value (threshold [0,1]. value). This is the oldest and most generally used engineering processing method, as well as one of the most prevalent and widely used methods in spacecraft fault detection systems. 4.2. Threshold Judgment Mechanism When the LH2/LOX rocket engine is working normally, its sensor parameters are stable within a specific dynamic range. When a fault occurs, the sensor’s detection parameters will exceed the normal working range. As a result, the simplest and most effective technique to determine whether a measured signal is normal is to compare the observed value to the permissible limit value (threshold value). This is the oldest and most generally used engineering processing method, as well as one of the most prevalent and widely used methods in spacecraft fault detection systems.

Sensors 2021, 21, 5026 9 of 15

The most critical parameter of threshold-based fault detection is the threshold. Rea- sonable thresholds have an important impact on determining the time in fault and the stability of the system. Generally, a reasonable threshold is set based on historical experi- ence. When the difference between the two values exceeds the predeﬁned threshold, the system recognizes a problem and issues an early warning. If the threshold is set too high, the system will almost certainly overlook error warnings, but if it is set too low, the system will be overly sensitive and will issue false alarms. In the paper, the threshold setting is determined by the sensor’s average value to be tested in the normal test engine plus a tiny constant. In this method, the threshold is set to 0.2. The measured value is a random quantity. Assuming that x is the threshold of the difference between the critical sensors of the LH2/LOX rocket engine, −0.2 is the lower threshold of the normal working range of the sensor, and 0.2 is the upper threshold of the normal working range of the sensor. The normal range of the difference x is:

− 0.2 ≤ x ≤ 0.2 (6)

If only using the threshold criterion, it will quickly lead to misjudgment. To minimize misjudgment and enhance the system’s fault-tolerant alarm capability, the article employs a continuous judgment method; that is, if the residual error between the engine’s predicted and actual values exceeds the threshold ﬁve consecutive times, the engine is judged to be faulty; otherwise, it is considered normal.

5. Experiment and Simulation Analysis The following computer platform was used in this article: CPU Intel Core i7-10700, 2.90 GHz eight-core, 64 GB memory. The model was implemented and tested in MATLAB R2020b. Meanwhile, in order to better observe the simulation results, the simulation in this paper used data of the whole test cycle of a certain type of LH2/LOX rocket engine, mentioned in a previous section. Among them, 730 sets were collected for normal test runs, and 6001 sets of data for faulty test runs were collected. During the test, no interruption simulation processing was performed on the fault. To facilitate comparison of the proposed models’ progress, the methods employing a single BP neural network, an optimized BP neural network using a standard GA, and an optimized BP neural network using an AGA followed by fault detection via a threshold detection mechanism were referred to as the BP model, GABP model, and AGABP model, respectively.

5.1. Results about AGABP Model This paper uses the proposed AGABP model to diagnose the entire process of a certain type of LH2/LOX rocket engine. Figures6 and7 are the model’s sensor prediction output of the normal measured data and the measured data at the time of malfunction. As can be seen, the AGABP model provides an accurate diagnosis of the issue, and the 0.2 threshold is reasonable. Sensors 2021, 21, x FOR PEER REVIEW 10 of 15

Sensors 2021, 21, x FOR PEER REVIEW 10 of 15

Sensors 2021, 21, 5026 10 of 15

Figure 6. AGABP fault detection—normal.

Figure 7. AGABP fault detection—fault.

5.2. Simulation Result and Analysis Figure 7. AGABP fault detection—fault. In order to evaluate the model proposed in this paper, this paper uses both the BP neural network and the standard GA to optimize the BP neural network to diagnose the 5.2. Simulation Result and Analysis faults of the same LH2/LOX rocket engine. In this paper, we ensure that the training pa- rametersIn order of all to BP evaluate networks the are model consistent, proposed while in for this the paper, GABP this model, paper the uses crossover both the prob- BP abilityneural isnetwork set to 0.9 and and the the standard mutation GA probabilit to optimizey is theset toBP 0.1, neural which network is consistent to diagnose with thethe maximumfaults of the crossover same LH2/LOX probability rocket and engine. maximum In this variationpaper, we probabilityensure that ofthe the training AGABP pa- model.rameters In oforder all BP to networksevaluate the are quality consistent, of ea whilech model, for the the GABP following model, standards the crossover are used prob- as testability indicators: is set to 0.9 and the mutation probability is set to 0.1, which is consistent with the maximum crossover probability and maximum variation probability of the AGABP model. In order to evaluate the quality of each model, the following standards are used as test indicators:

Sensors 2021, 21, 5026 11 of 15

5.2. Simulation Result and Analysis In order to evaluate the model proposed in this paper, this paper uses both the BP neural network and the standard GA to optimize the BP neural network to diagnose the faults of the same LH2/LOX rocket engine. In this paper, we ensure that the training parameters of all BP networks are consistent, while for the GABP model, the crossover probability is set to 0.9 and the mutation probability is set to 0.1, which is consistent with the maximum crossover probability and maximum variation probability of the AGABP model. In order to evaluate the quality of each model, the following standards are used as test indicators: (1) Mean Square Error (MSE). MSE is an estimation function T for the unobservable parameter θ. Deﬁned as: MSE(T) = E((T − θ)2) (7) (2) Model Forecast Time (MFT). MFT refers to the time when different network models are used to forecast the output results. The time here in this article is the time for predicting a data set for a test cycle. Table1 shows the MSE and MFT of each model in processing normal measured data and fault data. The time unit is second.

Table 1. The MSE and MFT of each model in normal data and fault data.

Normal Data (730 Sets) Fault Data (6001 Sets) Model MSE MFT (s) 1 MSE MFT (s) 2 BP 0.0027 0.0231 0.0703 0.0665 GABP 0.0026 0.0067 0.0597 0.0073 AGABP 0.0062 0.0054 0.1053 0.0071 1 The MFT here refers to the time used to predict 730 sets of data. 2 The MFT here refers to the time used to predict 6001 sets of data.

It can be seen from Table1 that, among the three detection models tested in this paper, the BP neural network models optimized by genetic algorithm (GABP and AGABP) are far superior to the single BP neural network in terms of computing time. The AGABP model offers a superior detection effect on fault data in MSE evaluation. Figures8 and9 are the output and residual diagrams of the measured data from the three models. It can be seen that each model can correctly judge that the engine is in a normal working state under the condition of a threshold of 0.2. Comparing the results of the three models shows that in the judgment of normal data, the overall performance of the BP model is more stable. In contrast, the performance of the GABP and AGABP models is relatively volatile. When the engine is ignited (the sample point in the picture is around 200), the changes in each model are drastic, and it is also quite easy to make an error at this time. Figures 10 and 11 are the output and residual diagrams of the three models when diagnosing fault data. Under the condition that the threshold value of each model is 0.2, the three models can correctly judge that the engine is in a fault state. In the data analysis of the failure test, it can be seen that AGABP can diagnose the failure more effectively, and as illustrated in Figure 11, the AGABP model has a faster diagnosis time, a broader range of change, and a more vivid display of failure information. Sensors 2021, 21, x FOR PEER REVIEW 11 of 15

(1) Mean Square Error (MSE). MSE is an estimation function T for the unobservable parameter θ. Defined as:

MSE() T=− E (( T θ ))2 (7)

(2) Model Forecast Time (MFT). MFT refers to the time when different network models are used to forecast the output results. The time here in this article is the time for predicting a data set for a test cycle. Table 1 shows the MSE and MFT of each model in processing normal measured data and fault data. The time unit is second.

Table 1. The MSE and MFT of each model in normal data and fault data.

It can be seen from Table 1 that, among the three detection models tested in this paper, the BP neural network models optimized by genetic algorithm (GABP and AGABP) are far superior to the single BP neural network in terms of computing time. The AGABP model offers a superior detection effect on fault data in MSE evaluation. Figures 8 and 9 are the output and residual diagrams of the measured data from the Sensors 2021, 21, 5026 three models. It can be seen that each model can correctly judge that12 of the 15 engine is in a normal working state under the condition of a threshold of 0.2.

Sensors 2021, 21, x FOR PEER REVIEW 12 of 15

FigureFigure 8. 8.The The output output of the of three the models—normal.three models—normal.

FigureFigure 9. 9.The The output output residuals residuals of the threeof the models—normal. three models—normal.

Comparing the results of the three models shows that in the judgment of normal data, the overall performance of the BP model is more stable. In contrast, the performance of the GABP and AGABP models is relatively volatile. When the engine is ignited (the sample point in the picture is around 200), the changes in each model are drastic, and it is also quite easy to make an error at this time. Figures 10 and 11 are the output and residual diagrams of the three models when diagnosing fault data. Under the condition that the threshold value of each model is 0.2, the three models can correctly judge that the engine is in a fault state. In the data analysis of the failure test, it can be seen that AGABP can diagnose the failure more effectively, and as illustrated in Figure 11, the AGABP model has a faster diagnosis time, a broader range of change, and a more vivid display of failure information.

Figure 10. The output of the three models—fault.

Sensors 2021, 21, x FOR PEER REVIEW 12 of 15

Figure 9. The output residuals of the three models—normal.

Comparing the results of the three models shows that in the judgment of normal data, the overall performance of the BP model is more stable. In contrast, the performance of the GABP and AGABP models is relatively volatile. When the engine is ignited (the sample point in the picture is around 200), the changes in each model are drastic, and it is also quite easy to make an error at this time. Figures 10 and 11 are the output and residual diagrams of the three models when diagnosing fault data. Under the condition that the threshold value of each model is 0.2, the three models can correctly judge that the engine is in a fault state. In the data analysis of the failure test, it can be seen that AGABP can diagnose the failure more effectively, Sensors 2021, 21, 5026 and as illustrated in Figure 11, the AGABP model has a faster diagnosis13 of 15 time, a broader range of change, and a more vivid display of failure information.

Sensors 2021, 21, x FOR PEER REVIEW 13 of 15

FigureFigure 10. 10.The The output output of the of three the models—fault.three models—fault.

FigureFigure 11. 11.The The output output residual residual of the three of the models—fault. three models—fault.

6. Conclusions The article studies a real-time fault detection method of LRE based on an adaptive genetic algorithm optimized BP neural network, and simulates and analyzes a certain type of LH2/LOX rocket engine as an example. The following conclusions can be obtained: (1) By using a BP neural network to forecast sensor data and then determining whether a fault occurs via a threshold detection mechanism, the technology can serve as an effective early warning system for engine failure. (2) In the detection process, the real-time fault detection method based on AGA optimized BP neural network meets the real-time requirements and has engineering application value. (3) The AGABP model can accurately, stably, and timely output the predicted value of the physical quantity to be measured. It is not easy to fall into the optimal local solution. Using the AGABP model to detect the measured data of a certain type of LH2/LOX rocket engine, the detection results are closer to the actual situation and faster response than those of the BP model, indicating that the method can be well applied to the fault detection of this type of LH2/LOX rocket engine. (4) Compared with the BP and GABP models, the AGABP model is more suitable for detecting this type of LH2/LOX rocket engine.

Author Contributions: Conceptualization, H.Y. and T.W.; methodology, H.Y. and T.W.; software, H.Y.; validation, H.Y.; formal analysis, H.Y. and T.W.; investigation, H.Y. and T.W.; resources, T.W.; data curation, H.Y. and T.W.; writing—original draft preparation, H.Y.; writing—review and editing, H.Y. and T.W.; visualization, H.Y. and T.W.; supervision, T.W.; project administration, T.W.; funding acquisition, T.W. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data is not publicly available as it involves sensitive information. Acknowledgments: We appreciate the previous research works from the references. And also, many thanks for the valuable suggestion of the reviewers.

Sensors 2021, 21, 5026 14 of 15

6. Conclusions The article studies a real-time fault detection method of LRE based on an adaptive genetic algorithm optimized BP neural network, and simulates and analyzes a certain type of LH2/LOX rocket engine as an example. The following conclusions can be obtained: (1) By using a BP neural network to forecast sensor data and then determining whether a fault occurs via a threshold detection mechanism, the technology can serve as an effective early warning system for engine failure. (2) In the detection process, the real-time fault detection method based on AGA optimized BP neural network meets the real-time requirements and has engineering application value. (3) The AGABP model can accurately, stably, and timely output the predicted value of the physical quantity to be measured. It is not easy to fall into the optimal local solution. Using the AGABP model to detect the measured data of a certain type of LH2/LOX rocket engine, the detection results are closer to the actual situation and faster response than those of the BP model, indicating that the method can be well applied to the fault detection of this type of LH2/LOX rocket engine. (4) Compared with the BP and GABP models, the AGABP model is more suitable for detecting this type of LH2/LOX rocket engine.

Author Contributions: Conceptualization, H.Y. and T.W.; methodology, H.Y. and T.W.; software, H.Y.; validation, H.Y.; formal analysis, H.Y. and T.W.; investigation, H.Y. and T.W.; resources, T.W.; data curation, H.Y. and T.W.; writing—original draft preparation, H.Y.; writing—review and editing, H.Y. and T.W.; visualization, H.Y. and T.W.; supervision, T.W.; project administration, T.W.; funding acquisition, T.W. Both authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data is not publicly available as it involves sensitive information. Acknowledgments: We appreciate the previous research works from the references. And also, many thanks for the valuable suggestion of the reviewers. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Abbreviations The following abbreviations are used in this manuscript: AGA Adaptive genetic algorithm AGABP Adaptive genetic algorithm optimized BP neural network ARMA Autoregressive moving average BP Back propagation GA Genetic algorithm GABP Standard genetic algorithm optimized BP neural network LH2/LOX Liquid hydrogen and liquid oxygen LRE Liquid rocket engine MFT Model Forecast Time MSE Mean Square Error

References 1. Wu, J.J.; Zhu, X.B.; Cheng, Y.Q.; Cui, M.Y. Research Progress of Intelligent Health Monitoring Technology for Liquid Rocket Engines. J. Propuls. Technol. 2021, 1–13. 2. Wu, J.J.; Cheng, Y.Q.; Cui, X. Research Status of the Health Monitoring Technology for Liquid Rocket Engines. Aerosp. Shanghai Chin. Engl. 2020, 37, 1–10. 3. Li, Y.J. Study on Key Techniques of Fault Detection and Diagnosis for New Generation Large-Scale Liquid-Propellant Rocket Engines. Ph.D. Thesis, School of National University of Defense Technology, Changsha, China, 2014. Sensors 2021, 21, 5026 15 of 15

4. Xue, W.; Zhang, Q.; Wu, X.P. Based on the ARMA Model for the Liquid Rocket Propulsion Fault Detection. Comput. Meas. Control 2019, 27, 4–7. 5. Liu, H.G.; Wei, P.F.; Xie, T.F.; Huang, Q.; Wu, J.J. Research of Real-time Fault Detection Method for Liquid Propellant Rocket Engines in Ground Test. J. Astronaut. 2007, 28, 1660–1663. 6. Flora, J.J.; Auxillia, D.J. Sensor Failure Management in Liquid Rocket Engine using Artiﬁcial Neural Network. J. Sci. Ind. Res. India 2020, 79, 1024–1027. 7. Zhang, W.; Zhang, Y.X.; Huang, X.X. Multi-fault Diagnosis for Turbo-pump Based on Neural Network. J. Propuls. Technol. 2003, 24, 17–20. 8. Liu, Y.J.; Huang, Q.; Cheng, Y.Q.; Wu, J.J. Fault Diagnosis Method for Liquid-propellant Rocket Engines Based on the Dynamic Cloud-BP Neural Network. J. Aerosp. Power 2012, 27, 2842–2849. 9. Xu, L.; Zhao, S.; Li, N.; Gao, Q.; Wang, T.; Xue, W. Application of QGA-BP for Fault Detection of Liquid Rocket Engines. IEEE Trans. Aerosp. Electron. Syst. 2019, 55, 2464–2472. [CrossRef] 10. Li, N.; Xue, W.; Guo, X.; Xu, L.; Wu, Y.; Yao, Y. Fault Detection in Liquid-propellant Rocket Engines Based on Improved PSO-BP Neural Network. J. Softw. 2019, 14, 380–387. [CrossRef] 11. Principi, E.; Rossetti, D.; Squartini, S.; Piazza, F. Unsupervised Electric Motor Fault Detection by Using Deep Autoencoders. IEEE/CAA J. Autom. Sin. 2019, 6, 441–451. [CrossRef] 12. Kazemi, H.; Yazdizadeh, A. Optimal State Estimation and Fault Diagnosis for a Class of Nonlinear Systems. IEEE/CAA J. Autom. Sin. 2020, 7, 517–526. [CrossRef] 13. Zhang, P.Y.; Shu, S.; Zhou, M.C. Adaptive and Dynamic Adjustment of Fault Detection Cycles in Cloud Computing. IEEE Trans. Ind. Inform. 2021, 17, 20–30. [CrossRef] 14. Ding, X.L.; Jiao, H.; Sui, Y. Current Status of Foreign Hydrogen-oxygen Engine Detection Technology. Aerodyn. Missile J. 2019, 5, 90–95. 15. Tan, Y.H. Research on Large Thrust Liquid Rocket Engine. J. Astronaut. 2013, 34, 1303–1308. 16. Zheng, D.Y.; Tao, R.F.; Zhang, X.; Xiang, M. Study on Key Technology for Large Thrust LOX/LH2 Rocket Engine. J. Rocket Propuls. 2014, 40, 22–27, 35. 17. Huang, D.Q.; Wang, Z.; Du, D.H. Structural Dynamics of the Large Thrust Liquid Rocket Engines. SCIENTIA SINICA Phys. Mech. Astron. 2019, 49, 23–34. [CrossRef] 18. Long, L.H. Discussion of the Technical Route for China Manned Lunar-landing. Front. Sci. 2008, 2, 29–38. 19. Dong, L.S.; Fan, J.; Luo, Q.J. System Design of Tripropellant Liquid Rocket Engine Based on YF-75 Rocket Engine. Missiles Space Veh. 2005, 4, 1–6. 20. Tian, L.; Zhang, W.; Yang, Z.W. Application of Elman Neural Network on Liquid Rocket Engine Fault Prediction. J. Proj. Rocket. Missiles Guid. 2009, 29, 191–194. 21. Xie, T.F.; Liu, H.G.; Huang, Q.; Wu, J.J. Selection of Real-time Fault Detection Parameters for Liquid-propellant Rocket Engines in Ground Tests. Aerosp. Control 2008, 26, 77–81. 22. Huang, Q.; Wu, J.J.; Liu, H.G.; Xie, T. Implementation of Real-time Fault Detection Algorithms Based on Neural Network for Liquid Propellant Rocket Engines. J. Natl. Univ. Def. Technol. 2007, 29, 10–13. 23. Zapata, H.; Perozo, N.; Angulo, W.; Contreras, J. A Hybrid Swarm Algorithm for Collective Construction of 3D Structures. Int. J. Artif. Intell. 2020, 18, 1–18. 24. Kaur, G.; Gill, S.S.; Rattan, M. Whale Optimization Algorithm for Performance Improvement of Silicon-On-Insulator FinFET. Int. J. Artif. Intell. 2020, 18, 63–81. 25. Precup, R.E.; David, R.C.; Roman, R.C.; Petriu, E.M.; Szedlak-Stinean, A.I. Slime Mould Algorithm-Based Tuning of Cost-Effective Fuzzy Controllers for Servo Systems. Int. J. Comput. Intell. Syst. 2021, 14, 1042–1052. [CrossRef] 26. Feng, X.B.; Ding, R. Improved Genetic Algorithm and Its Application; Metallurgical Industry Press: Beijing, China, 2016. 27. Srinivas, M.; Patnaik, L.M. Adaptive Probabilities of Crossover in Genetic. IEEE Trans. Syst. Man Cybern. 1994, 24, 656–667. [CrossRef] 28. Chen, C.Z.; Wan, N. Adaptive Selection of Crossover and Mutation Probability of Genetic Algorithm and Its Mechanism. Control Theory Appl. 2002, 19, 41–43. 29. Gao, S.C.; Zhou, M.C.; Wang, Y.R.; Cheng, J.J.; Hanaki, Y.; Wang, J.H. Dendritic Neuron Model with Effective Learning Algorithms for Classiﬁcation, Approximation, and Prediction. IEEE Trans. Neural Netw. Learn. Syst. 2019, 30, 601–614. [CrossRef][PubMed] 30. Zhao, S.L.; Liu, Y. An Fault Detection Method Based on Compensation of SVMR. In Proceedings of the International Conference on Software Intelligence Technologies and Applications and International Conference on Frontiers of Internet of Things, Hsinchu, China, 4–6 December 2014; pp. 351–354. 31. What Is the Time Complexity of Training a Neural Network Using Back Propagation? Available online: https://qastack.cn/ai/57 28/what-is-the-time-complexity-for-training-a-neural-network-using-back-propagation (accessed on 20 July 2021).