Fault Diagnosis of Elevator Doors Using Control State Information

In this study, an integrated framework involving state classification, preprocessing, and classification is proposed for the fault diagnosis of elevator doors using control state information. During state classification, the door state is classified as operational or non-operational; moreover, based on the state information of the control board of an elevator door, the corresponding operational conditions are classified as opening or closing states. In the preprocessing phase, data processing and interpolation and feature manipulation are performed. Data are interpolated to synchronize each measurement with respect to the reference time; then, the state information is manipulated to create distinct features. In the classification phase, the operational states are classified, and nonlinear coordinate transformation is executed to transfer several features into a new nonlinear hyperspace by using an autoencoder. Two manifold features are extracted from the latent layer of the autoencoder; these become the principal axes for state classification using a support vector machine, indicating that three states are possible: normal with and without completion of a full stroke and abnormal stroke. The effectiveness of the proposed method was verified by performing field measurements on a control board during the operation of an elevator. Specifically, the autoencoder in the integrated framework effectively transformed an original space into a highly nonlinear yet efficient manifold, where classification was easy for different operational states. The proposed framework can be effective for real-world detection of elevator door faults because it exclusively uses state information measured from control boards.


I. INTRODUCTION
Elevators are a convenient and essential means of transportation in high-rise buildings. Research has shown that 54% of the world's population currently lives in urban areas [1]; thus, elevator systems have become indispensable components of apartments, commercial facilities, and office buildings. Elevators comprise several components, including mechanical, electrical, electronic, automatic control, and construction complexes; thus, faults in any elevator component may result in the stoppage of the elevator service. This downtime causes inconvenience to people and, in the worst case, can result in multiple passenger fatalities [2][3][4]. To guarantee the safe operation of elevators, monitoring the elevator status and detecting elevator system failures are essential, indicating the necessity of an effective fault diagnosis method.
Several studies have been conducted on the detection of faults in elevator components, such as winding machines, wire ropes, elevator doors, and guide rails [3,[5][6][7]. Among these components, elevator doors are considered as a critical component because if they are affected by faults, multiple passenger fatalities may occur. Therefore, numerous studies have been conducted to detect abnormalities in elevator doors by deploying many effective sensors, including optical cameras, microphones, accelerometers, and gyros [3,[8][9][10][11]. The hybridization of both acceleration and control information has been suggested to enhance the estimation accuracy [12]. Furthermore, studies on the monitoring and diagnosis of the elevator status in real time using Internet of Things (IoT) information have been conducted [13][14][15]. In these studies, additional sensor systems were employed to monitor elevator door systems, increasing that the total cost of elevator systems. Because of the competitive nature of the market, where the importance of economic feasibility in the installation of elevators is paramount, the increased costs prevent the regular deployment of fault-detection systems in commercial units. To reduce additional costs, a diagnostic method that uses only elevator state information was proposed [16]. In that study, normal operational states were predefined based on all the control-state information. Then, the state information violating the predefined normal operation was logged and reported to expert systems. These systems evaluated whether the newly sent information was faulty. However, the study did not involve an analysis of the quantitative comparison of the estimation accuracy of the proposed method with that of other methods.
Many novel methods have been studied from an academic perspective by measuring fault data using several sensors. Specifically, many machine-learning methods show excellent classification results and outperform traditional signalprocessing-based methods, indicating that fault detection using artificial neural networks (ANNs) is promising [7,[17][18][19]. These methods require the extraction of appropriate features. Hence, statistical methods have been widely deployed for feature extraction from measurements, including mean, root-mean-square (RMS), kurtosis, and crest factor for fault classification [20][21][22][23]. In addition, deeplearning methods have been recently developed to extract and classify features in an end-to-end manner [24,25]. Because of these features, minimal engineering effort is required for precise feature extraction and selection if sufficient data are available.
Machine-learning methods are based on empirical risk minimization (ERM) principles [26], indicating that these methods are trained with a focus on cost minimization. However, ERM does not minimize the actual error in the fault diagnosis because of two critical factors. One is the acquisition of insufficient training samples, and the other is the lack of an appropriate architecture [27]. These factors are also problems in end-to-end deep-learning architectures [28,29], implying that the extraction of features to separate faults is difficult because of insufficient abnormal data. It is difficult to provide sufficient fault data for the training of neural networks in most industrial systems, including elevator door systems; faults rarely occur in real-life instances. Moreover, different industrial systems have different complex characteristics and nonlinearity, suggesting that the selection of an appropriate neural network architecture requires considerable engineering efforts.
To overcome the limitations of both hardware and the method, an integrated framework is proposed in this study for the fault diagnosis of elevator doors using only control state information. The proposed method is cost efficient because it does not require additional sensor systems. The proposed framework is divided into three phases: state classification, preprocessing, and fault classification. The first phase involves the classification of the door state as operational or non-operational. Distinct features are effectively manipulated during the preprocessing phase. The combination of an autoencoder and a support vector machine (SVM) is implemented in the classification phase as a solution for imbalanced learning [30]. This approach effectively transfers high-dimensional data to a lowdimensional manifold [31], generating reduced lowdimensional data and preserving the key characteristics of high-dimensional inputs. Hence, the proposed framework ensures a high reliability, robustness, and accuracy. Specifically, the autoencoder effectively extracts distinct features and transforms them into a two-dimensional (2D) manifold map. Consequently, abnormal data are effectively separated from normal data because both data are located in different regions in the 2D manifold map. The linear SVM successfully classifies the current state among three different operations and faults with an optimal separating hyperplane (OSH). The effectiveness of the proposed method is verified by performing field measurements on a control board during elevator operation. The results indicate that the proposed framework exhibits excellent accuracy. Furthermore, indepth discussions of the confusion matrix and quantitative comparisons with other machine-learning methods provide profound insights into the intelligent prognostics and health management of complex industrial applications. The remainder of this paper is organized as follows. Section II details the experiments for field data measurements and data formats. The integrated framework for fault diagnosis of elevator doors is described in Section III. Section IV provides the analysis and discussion of the results of applying the proposed method to field measurements. Section V summarizes the conclusions and presents possible avenues for future research.

II. EXPERIMENTS
Data were collected for the period from April 01, 2020 to April 30, 2020. A testbed elevator is located in apartment X in Seoul, Korea. This elevator is hereafter designated as "Elevator X" for confidentiality purposes. The total number of the data records is 18 603 367. The control system of an elevator door measured 17 state information, as listed in Table I. The data comprised one time step and 16 other state information relevant to door control. Specifically, six sets of data were measured in the form of a digitized integer with a varied measurement range, including door floor, door position, door reference/feedback speeds, and door reference/feedback torques, whereas the others were binary signals, including door open/close, multibeam, safety edge, open/close limit, open/close command, hatch door limit, and gate door limit. This information is generally measured for elevator door control but not limited to all cases. Some elevator manufacturers may measure different data for control purposes. These signals were measured for door control and not for diagnosis, indicating that the proposed method can effectively detect faults and classify operational states without any new sensor installation. Subsequently, only the operational conditions are considered to identify the fault states of an elevator door. The second phase is data preprocessing, which involves data interpolation and feature manipulation. First, data are interpolated to synchronize each measurement with respect to the reference time with a uniform internal for each stroke because actual measurements are randomly varied from 8 to 10 Hz data. Then, the state information with a uniform internal is manipulated to create 28 categories of features based on the state information on a control board. The third phase is the classification of an operational state with distinct features as normal without interruption, normal with interruption, or faulty. In this phase, a nonlinear coordinate transformation is executed to transform several features into a new nonlinear hyperspace by using the autoencoder. Specifically, two major features are extracted from the latent layer of the autoencoder. Then, these 2D features become the main principal axes for state classification by employing the SVM, obtaining the current state among the three states of the elevator door: normal with completion of a full stroke, normal without completion of a full stroke, and abnormal stroke, that is, an elevator door fault. The first state indicates that the elevator door is opened or closed automatically, whereas the second state indicates that the elevator door is opened or closed with interruption during the opening or closing process. The third state indicates a problem or fault in the elevator door.  This information is beneficial for the detection of faults, because the difference between the reference and feedback represents an important metric of fault diagnosis. In addition, the close limit, gate door limit, and hatch door limit are released in the open state, implying that this binarynumbered information is also effective for identifying elevator door faults. The closed state is activated when the elevator is in motion. All state values are monitored to check the door states during this period because opening a door during the operation of an elevator might result in severe accidents, including passenger fatalities. During this period, close, hatch, and gate limits are activated, and the door position is at the minimum value. Fig. 2 presents the state information measured in the control system during the opening and closing of an elevator door. Once the open command is activated (Fig. 2(a1)), the reference speed and torque are input into the door motor, and the feedback speed and torque of the door motor are measured ( Fig. 2 (a2)). The feedback signals are used for closed-loop control of the door motor. Hence, the door is opened during the opening period ( Fig. 2(a3)). Several Boolean data types are also measured to mitigate safety concerns ( Fig. 2(a4)). This process is terminated when an open limit switch is activated. The elevator door closing process inversely mirrors the opening process. Initially, a close command is activated (Fig. 2(b1)). Then, the reference speed and torque are applied to a door motor, and the feedback speed and torque are measured for the closed-loop control of the door motor ( Fig. 2(b2)), resulting in the closing process as the door motor changes the door position ( Fig.  2(b3)). Several sets of Boolean information are also measured for safety ( Fig. 2(b4)) and control perspectives. This closing process terminates when a close-limit switch is activated. Each process is considered to be an independent stroke of the open or closed state, and each stroke is analyzed because operational information provides useful data for the detection of faults compared to operational data during the non-operational period. Note that the analysis of nonoperational data is cost-ineffective because the non-operational time is considerably longer than that considering the operational characteristics of elevators.

A. PHASE A: STATE CLASSIFICATION
Based on the operational data, two operational conditions can be classified: completion of a full stroke and normal without completion of a full stroke. Specifically, states were defined as full strokes when open or closed limits were activated, whereas elevator doors were classified as the other condition when they were inactivated. Then, abnormal strokes were classified by expert systems of the elevator, who actually conducted elevator operation and maintenance, because identifying abnormal strokes would be difficult considering the complex nature of the elevator operation. Abnormal strokes generally show different characteristics than normal strokes. Specifically, the measured information features a slow change in door position over time, a large difference between the feedback speed and reference command speed, no movement in the door position, initial locking of the door by the hatch door and gate doors, and limited movement of the door. These characteristics indicate the diversity of abnormal strokes, which hinders their definition in a single-feature format. Fig. 3

(a) shows the state information of an abnormal stroke during an open period.
Once the open command was activated ( Fig. 3(a1)), the reference speed and torque were input into the door motor, and the feedback speed and torque of the door motor were measured ( Fig. 3 (a2)). The feedback speed was considerably lower than the reference speed during 4-6 s, resulting in a higher torque ( Fig. 3 (a2)) than that in the normal state ( Fig.  2(a2)). Therefore, the door did not move during 5-8 s and then moved slowly ( Fig. 3 (a3)). Finally, the opening was interrupted, and the door was stopped ( Fig. 3(a3)); therefore, the open-limit signal was not activated at the end of the opening process ( Fig. 3 (a4)). Other Boolean signals were not activated in Fig. 3 (b4), except for the closed feedback signal at the end of the opening process, implying that these signals would provide effective information regarding faults. Fig. 3(b) shows the state information of the abnormal stroke during a closed period. In this abnormal state, the open limit signal is not activated, whereas the door-closing process normally starts with the activation of an open limit signal ( Fig. 3(b4)). Specifically, the reference speed and torque were input to the door motor when the close command was activated ( Fig. 3(b1)), and the feedback speed and torque of the door motor were measured ( Fig. 3 (b2)). The door moved slowly compared with the normal state ( Fig. 2(b2)). Finally, the closing process ended without completion and the door was stopped (Fig. 3(b3)).

B. PHASE B: PREPROCESSING
This subsection describes phase B (preprocessing), which comprises data interpolation and feature manipulation. The details of each process are as follows.
State information relevant to the elevator door is collected from the door control system. Preliminary analysis of time stamps on state information (Table I) suggests that the measurement frequency of the data varied between 8 and 10 Hz depending on the communication load, although the specification of the door control system indicates that all data were measured at 10 Hz. Hence, all state information was interpolated to ensure a uniform interval of measured states, because it was necessary to synchronize all information to the same time stamp for each stroke using the proposed method. To minimize deterioration and loss of data, the interpolation frequency was set to the lowest frequency of 8 Hz. A linear interpolation method with a round off was executed for a type of digitized integer number, including the door floor, door position, reference/feedback speeds, and reference/feedback torques. The linear interpolation method resulted in small differences, which were negligible when considering the measurement frequency, compared to the results of the actual measurement. Moreover, the Boolean state information was synchronized using the most accessible method because this is binary information [32].
Distinct features were extracted using a manipulation process. Fig. 4 shows a flowchart of feature manipulation. Overall, 11 measurements were obtained from the 16 state information listed in Table I. Five state information of the operation floor, open/close command, multi-beam, and safe edge were eliminated because they are less relevant to door faults. The state information for the multi-beam and safe edge was measured to prevent passengers from being trapped between doors. Open or closed commands were always activated during open or closed strokes. Moreover, the operating floor exclusively provided the location of the elevator. Statistical analysis of five state information with a type of digitized integer was conducted to extract statistical features, including the mean, RMS, and maximum of each feature for each stroke. These three features were addressed because they are effective for fault detection [23], [33]. Differences between the reference speed/torque and feedback speed/torque were also calculated to create two additional features because they provide crucial information regarding elevator door faults, resulting in a total of seven state information. Hence, statistical analysis of this seven-state information resulted in a total of 21 features for each open or closed stroke. In addition, six Boolean operational states were synchronized with respect to a timestamp, which started at zero when the open or close command was first activated. Thereafter, these six sets of binary information were summed to create six features for each open or closed stroke. Additionally, the total operational period of each stroke depends on various situations and interruptions from passengers; thus, it was calculated as a distinct feature. This indicates that the six features from the binary state information were highly correlated with the total operational period of operation at each stroke. In summary, 28 features were manipulated through this phase, comprising seven features related to operational states and 21 features extracted from statistical analysis. These features WERE normalized before training because the scales of each feature vary owing to the different physical quantities. Note that convergence is not guaranteed without normalization, and oscillations may occur during the optimization of the autoencoder. The normalization results in a similar effect of the input features on the output prediction in the neural network of the autoencoder. Two methods are widely used for normalization: min-max normalization (1) and z-score normalization (2), as follows: where , , , and , denote the th, minimum, and maximum values of feature , respectively.
where , and denote the mean value and standard deviation of feature , respectively. The min-max normalization changed the range of the features of interest to [0, 1]. This method is generally used for autoencoders with a sigmoid activation function because the range of sigmoid functions is the same. However, this method is difficult to use when the range of a feature is unpredictable. This problem can be solved by assuming an appropriate range for the normal value of each feature, and then considering outliers from a predefined range as the maximum or minimum values. By contrast, in z-score normalization, the range of each feature must not be defined. Moreover, the goal of the autoencoder is to create a manifold by learning more normal data than abnormal data [34], indicating that the scale of the normal data is important. This analysis suggests that z-score normalization is effective for detecting elevator door faults. Hence, the z-score normalization method is addressed in this study. The performance of the z-score normalization method is compared in detail in the Results and Discussion sections.

C. PHASE C: CLASSIFICATION
This subsection describes phase C (classification), comprising the autoencoder and SVM. The autoencoder is a fully connected symmetric neural network composed of an encoder and a decoder. This neural network enables unsupervised learning to reconstruct features with the same characteristics and dimensions as input features [31]. The nonlinear activation functions at each layer enable nonlinear space transformation, implying that data interpretation is easier in a transformed hyperplane. Moreover, the autoencoder has a role in dimension reduction when features in the latent layers are used. In this study, two major features were used in the latent layer as 2D manifold because they provide sufficient information for door-fault detection.
To optimize the architecture of the autoencoder, the activation function for each layer and the number of nodes per layer should be determined. First, activation functions commonly used in machine learning include the rectified linear unit (ReLU), scaled exponential linear unit (SELU), sigmoid, and hyperbolic tangent. Note that a linear activation function is not used in the autoencoder because this function results in a linear transformation between the input and output and thereby yields the same result as principal component analysis (PCA). Hence, the proposed autoencoder applies only a linear activation function to the last layer to ensure the same range of data. ReLU and SELU were also excluded because the data could not be adequately restored. This factor can be explained by the fact that ReLU and SELU have filter roles below zero in the data. However, the autoencoder transforms the initial coordinates into hyperplanes for easy classification. Therefore, sigmoid and hyperbolic tangents were only considered as candidates for the activation functions of the autoencoder. Second, the number of nodes in each layer must be optimized. These two hyperparameters of the activation functions and the number of nodes at each layer were optimized by trial and error. Specifically, we changed the activation functions and numbers of nodes in each layer and monitored the loss of the object function with the Adam optimizer, which was defined by a mean square error. The architecture of the autoencoder with the smallest value of the object function was selected as the optimum architecture, as shown in Fig. 5(a). The autoencoder comprises eight layers, with four layers each for the encoder and decoder. Herein, 28-dimensional input features were passed through 32-, 16-, 8-, and 2dimensional layers in the encoder. Subsequently, 2dimensional data are decoded into 8-, 16-, and 32dimensional layers through the decoder and reach the final layer with 28-dimension, which is the same as the input data. The hidden nodes in each layer were trained to minimize the reconstruction errors between the original and reconstructed features. Sigmoid and hyperbolic tangent functions were used as activation functions in the encoder and decoder, respectively. Different activation functions for the encoder and decoder enabled a robust nonlinear space transformation. Fig. 5(b) depicts the training process of the autoencoder, which comprises three stages: pre-training, unrolling, and fine-tuning. Pre-training sets the initial values of each layer by using a random sampling method. Specifically, the first 32-dimensional layer of the encoder and the seventh layer of the decoder were trained with 28 feature inputs and the same output, resulting in a weight of 1 and bias of 1 . The same procedure was executed with different activation functions to determine the weight of 8 and the bias of 8 . Subsequently, trained weights and biases of 32 dimensions were used to train the second layer of the encoder and the sixth layer of the decoder with 16 dimensions, resulting in a weight of 2 and bias of 2 . Sigmoid and hyperbolic tangent functions were used to train the second layer of the encoder and decoder, respectively. This resulted in weights of 2 and 7 , and biases of 2 and 7 , for the encoder and decoder, respectively. The process was repeated to determine the weights and biases of the third and fourth layers of the encoder and decoder, respectively. After the pre-training process was completed, the layers on the system were unrolled to construct an entire autoencoder layer. Then, the weights and biases of the layers were fine-trained [31] for accurate prediction, resulting in n-dimensional manifolds for each layer. The architecture of the autoencoder indicates that the weights in the autoencoder form a transformation matrix that nonlinearly transforms distinct features in the original spaces to distinct features in a hyperspace, where the operational states can be easily classified. Furthermore, 2D features from the z-layer (fourth layer) were used in this study for the final classification. The SVM was addressed in this manifold to classify three operational states: normal with completion of full stroke, normal without completion of full stroke, and abnormal stroke. SVM aims to select the OSH between classes by training samples that lie at the edge of the class distributions, which are referred to as support vectors [35], [36]. In SVM, the training dataset of cases, represented by { , }, = 1, . . . , , ∈ {1, −1}, is used to form a classifier. The OSH represents the maximum margin between classes, where a hyperplane is defined as Here, , , and denote a point lying on the hyperplane, the weight defining an OSH that is normal to the hyperplane, and the bias, respectively. For a linearly separable space, a separating hyperplane can be defined for two classes. These two equations can be combined as follows: The margin represents the vertical distance from the OSH of the data closest to the OSH that divides the two classes. The margin value is defined as the inverse of (5). The proposed method has three categories, each of which is separated by an OSH. Hence, the three OSHs generated category-specific regions on the 2D feature map through each plane. The determination of the OSH in the SVM is an effective method for elevator door fault detection because SVM learns points in a space to maximize the gap width between each category. This implies that the proposed method can guarantee robustness when data inequalities occur in the training set. Specifically, fault data are relatively small compared with normal operational data in most cases. This serves as the rationale for referring to SVM in this study.

D. EVALUATION
In this study, the K-fold cross-validation method was employed to evaluate the performance of the proposed fault detection method owing to the minimal data available on abnormal strokes in the measurements. Specifically, the main dataset was divided into 5 smaller datasets. One dataset was used as the test set and the other N-1 dataset was used as the training set. This process was iterated N times with different test sets at each iteration. Subsequently, the prediction accuracy was evaluated for each result using the F-score, which is an effective metric when there are minimal abnormal data in the dataset [37], [38]. The F-score is the harmonic mean of the model precision and recall and expressed as where is the recall and is the precision. Recall is the fraction of samples classified as positive among the total number of positive samples, whereas precision is the fraction of true-positive samples among the examples classified as positive. Therefore, recall is defined as the number of true positives divided by the number of true positives and false negatives, whereas precision is defined as the number of true positives divided by the number of false positives and true positives. Equation (6) can be applied to the problem of only two categories; however, this study aimed to classify these three categories. Therefore, we used the modified F-score. Specifically, one category was set and the F-score was computed by grouping the remaining categories. Three iterations were executed for each category. The F-score for each category was calculated using the following expression: where is the F-score of each category and is the total number of categories. Equation (7) is a macro F-score that calculates the F-score of more than two categories [39]. Therefore, the F-score obtained from (7) represents the overall performance of all categories. Finally, the calculated F-score was averaged for all iterations in which the K-fold cross-validation method was used. Moreover, the confusion matrix was addressed for a quantitative and reasonable analysis.

E. BAYESIAN OPTIMIZATION
The hyperparameters of the classifiers used in this study should be optimized to ensure the best results achieved for fair comparison. Hence, in this study, Bayesian optimization (BO) was applied to optimize the hyperparameters of all classifiers, which is a simple yet effective method widely used for hyperparameter optimization in machine-learning methods [40]- [42]. BO functions intervene in the construction of the posterior distribution because of the general fit of the Gaussian process to the results at a given data point, and select and use a new parameter space that is likely to be used in the next iteration. The choice of the second parameter at each iteration is determined by search strategies such as expectation improvement (EI) and defect posterior distribution, which determine the local maxima of the acquisition function. This process was repeated to determine the optimal variable. BO uses the initial values as prior knowledge, whose similar inputs produce similar outputs, and uses this learning to quickly refine and find optimal parameters. Specifically, μ( ) is the predictive mean function and ( , ′ ) is the predictive variance function under the prior Gaussian process. Based on the current data point, can predict the expected function, +1 ( ): +1 ( ) ~ ( ( ), ( , ′ )).
A new data point, +1 , is set based on function +1 ( ).
The new set data point is It is the data point with the greatest expected improvement obtained by utilizing the expectation function, +1 ( ), and max is the maximum output value for the current data point. Equations (8) and (9) were repeatedly applied to search for the improved optimal value, . Subsequently, the models were compared using the optimal hyper-parameter, , when training was completed.

A. PHASE A: STATE CLASSIFICATION
The first phase of data selection in the proposed method ( Fig.  1)

1) STATISTICAL METHODS
Several statistical methods are effective for feature manipulation for fault classification, including skewness, kurtosis, crest factor, and shape factor [20], [22]. One common observation is that the estimation accuracy of fault diagnosis and classification may increase when more statistical features are addressed. Because this study addressed only three statistical features, we compared one extreme case with the proposed method to analyze this hypothesis. In the extreme case, nine additional statistical methods were applied to seven features, in addition to the mean, RMS, and peak, which were used in the proposed method, resulting in 84 features for the operational features of the digitized integer. Table Ⅶ in the appendix shows the formulas of the statistical methods used in this extreme case. The input and reconstructed layer dimensions were changed to 91 by the proposed autoencoder according to the shape of the input data developed by additional time-related static factors. In this subsection, the proposed method refers to the first case, whereas the extreme case refers to the second case. Table Ⅱ presents the classification results.
In the first case, all abnormal strokes were classified as abnormal in both open and closed states. All normal patients with complete stroke were correctly classified. Five of these states were identified as normal, without completion of the full stroke in closed states. Similarly, seventeen cases of normal without completion of full stroke were classified as normal with completion of full stroke in the open state. Therefore, the average F-score of the proposed method was 0.996, suggesting that the proposed method identifies faults in elevator doors with high accuracy, as illustrated in Fig. 6(a) and (b). All abnormal strokes were less than 0.5, for the second primary axis, that is, the vertical axis in Fig. 6(a), whereas two normal strokes exceeded 0.5, for this axis for closed states (Fig. 7(b)). This suggests that the characteristics of abnormal strokes differ from those of normal strokes in the transformed manifold. However, a small amount of normal data without the completion of full stroke overlapped with the normal data with the completion of full stroke in the transformed manifold because the measured data for both were similar. Specifically, interruptions from a passenger were triggered at the end of stroke completion, and thus did not have any effect on the operation of the elevator door. All the characteristics of the features in this case were very similar to that of the normal data with completion of full stroke, resulting in misclassification because the area overlapped in the manifold. However, this area was far from the abnormal stroke in the manifold and, thus, did not affect the classification of elevator door faults.
In the second case, two abnormal strokes were misclassified in the open state. Moreover, 17 and 29 misclassifications occurred in the open and closed states, respectively, resulting in an average F-score of 0.983, as shown in Fig. 6(c) and (d). Three abnormal strokes were located close to clusters of normal strokes without completion of full stroke in the open state, even though the abnormal stroke did not overlap with the normal strokes. This has resulted in the misclassification of abnormal strokes as normal strokes. One normal stroke was located between clusters of normal and abnormal states in the closed state. However, it was closer to abnormal strokes, resulting in misclassification. Some normal strokes also overlapped in this manifold in both the open and closed states, resulting in misclassification.
In summary, the dimensions of the input features cannot be increased owing to the challenges in hyperplane transformation. Thus, the three strokes were not clearly separated in the transformed manifold. A comparison of the two cases clearly shows that the characteristics of abnormal strokes differ from those of normal strokes when the hyperplane transformation is examined through the autoencoder. However, many input features encounter challenges in hyperplane transformation because of the dimension increase and the subsequent decrease in prediction accuracy for fault classification in the transformed manifold. Hence, the selection of appropriate features is important in accurate fault diagnosis.   Table Ⅲ presents the classification results.
In the first case, apart from one abnormal stroke in the closed state, all abnormal strokes were classified as abnormal in the open and closed states. Seventeen instances of normal without completion of a full stroke were misclassified in the open state, whereas 12 and 16 instances of normal with and without completion of a full stroke, respectively, were misclassified in the closed state, resulting in an average Fscore of 0.990. This score was lower than that of the proposed method, suggesting that six features from the difference calculation contributed to the increased fault classification accuracy. This result is explained by the manifold maps shown in Fig. 7(a) and (b). Normal strokes were separated from abnormal strokes in both the feature maps of the open and closed states, similar to those in the first case. However, one abnormal stroke was located close to clusters of two normal strokes and far from a cluster of abnormal strokes in the closed state, even though the abnormal stroke did not overlap with the normal strokes. This has resulted in the misclassification of abnormal strokes as normal strokes. The manifold maps also demonstrated the overlap area for the two normal strokes, resulting in misclassification.
In the second case, all the abnormal strokes were classified as abnormal strokes in the closed state. However, two abnormal strokes were considered normal with the completion of full stroke, and one abnormal stroke was considered normal without the completion of full stroke in the open state. Several misclassifications occurred in the two normal stroke classes in both the open and closed states, resulting in an average F-score of 0.988. These results are explained by the manifold maps shown in Fig. 7(c) and (d). Specifically, two abnormal strokes were in a clustered area of normal with the completion of full stroke, and one abnormal stroke was very close to the clustered area of normal without the completion of full stroke, resulting in this misclassification. Classification accuracy decreased by neglecting the features of the difference calculation and Boolean states. The third and fourth cases also had two misclassifications of abnormal strokes in the open state and several misclassifications in normal strokes, resulting in average Fscores of 0.990 and 0.972, respectively. The corresponding manifold maps in Fig. 7(e)-(h) show that misclassified abnormal strokes overlapped or were near the clusters of normal strokes.
In summary, a comparison of four cases with the proposed method demonstrated that the characteristics of abnormal strokes differed from those of normal strokes in the manifold transformed through the autoencoder. However, the limited availability of information decreased the accuracy of fault classification. In addition, we observed that adding Boolean features increased classification accuracy, implying that the sum of time for the Boolean state was effective in improving estimation accuracy. Furthermore, difference calculations provided additional effective information for fault diagnosis and classification, thereby increasing the estimation accuracy.

3) NORMALIZATION METHOD
This subsection presents the classification results based on the normalization methods addressed in this study. A case study was conducted because the fault classification depends on the normalization method [45], [46]. Normalization has a critical role in the rescaling of inputs that measure different physical quantities, thereby resulting in similar weights for all features. Two normalization methods widely used in autoencoders are the z-score and min-max methods. Because the z-score was used in the proposed method, we employed the min-max method, expressed by (2), for comparison. Table Ⅳ presents the results of this study.
In the case of addressing the min-max normalization method, three abnormal states were misclassified in both the open and closed states. Specifically, two abnormal strokes were classified as normal with completion of full stroke, and one abnormal stroke was considered normal without completion of full stroke in the open state, whereas three abnormal strokes were considered normal without completion of full stroke in the closed state. Moreover, 20 and 38 misclassifications occurred for normal strokes in open and closed states, respectively, resulting in an average Fscore of 0.947. Fig. 8 presents the results of the misclassifications. Three abnormal strokes occurred in clusters of normal strokes in the open state. Interestingly, many misclassifications occurred in this area, implying that the min-max normalization method can only separate nonidentical characteristics in this area, rather than identical characteristics. One abnormal stroke was also in a cluster of normal without completion of full stroke, and two abnormal strokes were located close to the misclassified abnormal stroke in the closed state. These three abnormal strokes were far from a cluster of abnormal strokes, suggesting that normalizing features via the min-max normalization method is less effective in the creation of distinct manifolds through the autoencoder.  A comparison of the normalization methods clearly shows that the selection of an appropriate normalization is important for securing fault diagnosis and classification, and the z-score normalization method is more appropriate than the min-max normalization method for the data used in this study. The superiority of the z-score normalization method can be explained by the fact that the feature was normalized with a standard deviation. Compared with other features, this allows other data in this feature to be less affected by outliers when converting physical quantities to the same scale. In contrast, the min-max normalization method is significantly affected by abnormal data, which likely originate from a fault. For example, one abnormal datum, that is, an outlier, is added when the value of two features is already set equal.
These abnormal data exceed the range of the current data in one feature but fall within the range of the current data in another feature. In z-score normalization, abnormal data have a minimal effect on the scale of features that are out of range. However, the min-max normalization method has a significant impact on the scale of the out-of-range features. Abnormal data in existing data, which are well-found features by the changed scale feature, may not be well found by the changing feature scale. This results in improved performance of the z-score normalization method in learning autoencoders for abnormal detection.

1) AUTOENCODER
The autoencoder projects data in a high-dimensional space onto data in a low-dimensional space [47], [48]. The nonlinear activation function enables a nonlinear hyperplane transformation. Apart from the last layer, the same activation function is typically used for each layer to match the range of the output and input data when training the AE. However, the proposed method addresses varying activation functions of encoders and decoders to impose more nonlinear characteristics in the hyperplane transformation. Three cases were compared to analyze the contribution of this strategy. The first method is the proposed method. In the second case, the sigmoid function was used for both the encoder and decoder to train the autoencoder, whereas the hyperbolic tangent function was used for both the encoder and decoder in the third case. In all cases, the output layer used a linear activation function. The classification results are listed in Table V. In the first case, all abnormal states were detected and the average F-score was 0.996, as mentioned in Section 4.2.1. The average margins of all iterations between the normal with complete stroke and abnormal stroke and between normal without complete stroke and abnormal stroke were 0.29 and 0.10 in open states and 0.18 and 0.09 in closed states, respectively.
In the second case, all abnormal strokes were classified as abnormal strokes in closed states, whereas one abnormal stroke was considered normal without completion of full stroke. Moreover, 29, 78, 6, and 18 misclassifications occurred during normal stroke with completion of full stroke in the open state, normal stroke without completion of full stroke in the open state, normal stroke with completion of full stroke in the closed state, and normal stroke without completion of full stroke in the closed state, respectively, resulting in an average F-score of 0.975. The average margins of all iterations between the normal with complete stroke and the abnormal stroke and between the normal without complete stroke and the abnormal stroke were 0.08 and 0.02 in open states and 0.05 and 0.04 in closed states, respectively. This observation implies that the margin of the second case is lower than that of the first case, suggesting that the distribution of the data according to the state of each data point is closer than that of the first case. The result for the misclassification is clearly identified by the manifold maps presented in Fig. 9(a) and (b). Specifically, some abnormal strokes were located close to clusters of normal strokes, even though the abnormal strokes did not overlap with normal strokes. This resulted in the misclassification of abnormal strokes as normal and normal strokes as abnormal.
In the third case, the classification of all abnormal strokes was similar to that in the second. All abnormal strokes were classified as abnormal strokes in closed states, whereas one abnormal stroke was considered normal without the completion of full stroke. However, 16, 15, and 16 misclassifications occurred at normal stroke without completion of full stroke in the open state, normal with completion of full stroke in the closed state, and normal stroke without completion of full stroke in the closed state, respectively, resulting in an average F-score of 0.993. The misclassification results were clearly identified by the manifold maps presented in Fig. 9(c) and (d). Specifically, normal without the completion of full stroke clusters between clusters of abnormal states and one abnormal state in the open state. This would be closer to normal strokes, resulting in misclassification. A comparison of the three cases clearly shows that the characteristics of abnormal strokes differ from those of normal strokes when the hyperplane transformation is conducted through the autoencoder. However, the consideration of one type of activation function in the autoencoder results in difficulties in space transformation, thereby decreasing the prediction accuracy for fault classification in the transformed manifold. Addressing different nonlinear activation functions on the encoder and decoder strengthens the capability of the nonlinear hyperplane transformation, exhibiting the best accuracy. Specifically, the normal data were trained to not cross the region of the abnormal data when addressing the sigmoid activation function, whereas the margin between the normal and abnormal data was observed to be large when addressing the hyperbolic tangential activation function. The proposed method achieved the advantages of both activation functions, suggesting that addressing different activation functions for the encoder and decoder is effective for the separation of complex yet similar operational strokes in a transformed manifold.

2) SVM
Several methods, including SVMs, ANNs, and decision trees, are widely used for classification [49]. This subsection compares the two other methods to the SVM as a classifier. For a fair comparison of each model, 20% of the data were optimized through BO [40][41][42], implying that the hyperparameters of SVM, decision tree, and ANN would be designated as suitable values for the data used. The hyperparameters of each classifier are presented in Table VI.
In the case of ANNs, all abnormal strokes were classified as abnormal strokes in both open and closed states. Similarly, all normal with completion of full stroke were classified as being in open states, whereas five of these states were identified as normal with completion of full stroke in closed states. Seventeen normal cases without completion of full stroke were classified as normal with completion of full stroke in the open state. Sixteen normal cases without completion of full stroke were classified as normal with completion of full stroke, resulting in an average F-score of 0.996. These values were the same as those of the SVM.
In the case of the decision tree, all abnormal strokes were classified as abnormal strokes in both the open and closed states. However, 3 cases of normal with completion of full stroke were classified as normal without completion of full stroke, and 17 cases of normal without completion of full stroke were classified as normal with completion of full stroke in open states. Sixteen cases of normal with completion of full stroke were classified as normal without completion of full stroke, and 15 cases of normal without completion of full stroke were classified as normal with completion of full stroke in closed states, resulting in an average F-score of 0.995. A comparison of these cases shows that the SVM, ANN, and decision-tree classifiers have similar accuracies. In addition, all abnormal strokes were classified as abnormal strokes in all cases. These results again confirm that the autoencoder effectively transforms the original spaces into manifold maps, where two types of normal and abnormal data can be separated.
However, the calculation times of the SVM, decision tree, and ANN were 0.078, 0.041, and 685 s, respectively, suggesting that a deep neural network of ANN requires 1000 times heavier computational effort than SVM and decision tree. Moreover, the decision tree requires two more hyperparameters to be selected than the SVM, implying that more engineering effort is required to optimize the decision tree. This result also suggests that the decision tree easily converges to a local minimum and thereby has estimation accuracy. For example, misclassifications for normal with and without completion of full stroke are larger in the decision tree compared to those in ANN and SVM, even after conducting BO. Therefore, the SVM is the most accurate classifier among the three analyzed.

V. CONCLUSIONS
In this study, a fault diagnosis and classification method is proposed for elevator doors based on the exclusive use of control state information. The proposed method comprises three phases. The first phase extracts operational state information from the control state information of the elevator doors. This phase is intended to minimize computational efforts for fault detection because elevators are in a nonoperational state in most periods. In the second phase, distinct features are manipulated for fault diagnosis. In the third phase, autoencoders and an SVM are used to effectively classify the three operational states. Actual field measurements indicated that the proposed method has high estimation accuracy for fault diagnosis. A systematic analysis of the field measurements provides the following findings.
-The selection of appropriate statistical methods increases the estimation accuracy of fault diagnosis methods. The use of numerous statistical methods increases the dimensions related to problem solving, creating difficulties in nonlinear hyperplane transformations. -Feature manipulation, including difference calculation and normalization, has a critical role in fault diagnosis because a high correlation between distinct features and different operational conditions ensures a high estimation accuracy. -The autoencoder effectively transforms the original space into manifold space for fault diagnosis. Moreover, the implementation of different activation functions in the autoencoder improves the capability of the nonlinear hyperplane transformation. Future work includes the validation of the proposed method by acquiring data from elevator doors and applying them to other complex systems to demonstrate the effectiveness and robustness of the proposed method.