In this study, a novel refractive index sensor structure was designed consisting of a metal-insulator-metal (MIM) waveguide with two rectangular baffles and a U-Shaped Ring Resonator (USRR). The finite element method was used to theoretically investigate the sensor’s transmission characteristics. The simulation results show that Fano resonance is a sharp asymmetric resonance generated by the interaction between the discrete narrow-band mode and the successive wide-band mode. Next, the formation of broadband and narrowband is further studied, and finally the key factors affecting the performance of the sensor are obtained. The best sensitivity of this refractive-index sensor is 2020 nm/RIU and the figure of merit (FOM) is 53.16. The presented sensor has the potential to be useful in nanophotonic sensing applications. Surface plasmon polaritons (SPPs) are electromagnetic surface waves generated by the interaction between an external light field and free electrons in metal, which can reach the maximum field intensity on the surface and decay exponentially along the direction perpendicular to the interface ,2. SPPs In recent years, refractive index sensors based on a metal-insulator-metal (MIM) waveguide have attracted wide attention because of their strong lateral confinement, easy manufacturability, low propagation loss, and shorter transmission length ,15. SensIn addition, Fano resonance is very sensitive to structural parameters and refractive index changes, which is very helpful for the preparation and improvement of refractive index sensors . It is aIn this article, a novel refractive index sensor structure consisting of a USRR and an MIM waveguide with two rectangular baffles is propounded theoretically. The USRR cavity can be represented with two parameters, which greatly reduces the difficulty of fabrication. Compared with other cavity structures, a USRR is more sensitive to the change in structural parameters, which is helpful for researching high sensitivity refractive index sensors. The standardized A schematic diagram of the designed structure is shown in aveguide . The TM mode equation is ,24:(1)taA 2D diagram can be used instead of a 3D diagram for simple calculation. The yellow and white parts were filled with silver and air, respectively. A sufficiently thick silver layer can be prepared on a silicon substrate by chemical vapor deposition (CVD). The desired structure can be obtained by electron beam etching on the silver layer. The silver was chosen as the filling metal, which is due to its higher electric field and lower power consumption. The relative permittivity of air is 1, and the relative permittivity of silver can be acquired using the Debye–Drude dispersion model:ion time ,26. The performances of the proposed structure can be evaluated by two parameters, sensitivity (S) and figure of merit (FOM), which can be reached as follows :(3)S=Δλ/Before the sensor was manufactured, the transmission spectrum of the structure was numerically simulated with COMSOL Multiphysics 5.4. Boundary conditions can be divided into absorptive boundary conditions and periodic boundary conditions. The absorbing boundary condition was established by a perfect matching layer to absorb spilled waves. By setting a high loss layer perfectly matching the dielectric impedance of the adjacent region in the boundary region, the electromagnetic wave decays rapidly without reflection until it is completely absorbed. The superfine mesh was selected to improve segmentation accuracy and guarantee perfect segmentation.Since Fano resonance plays a significant role in the sensitivity of the sensor, we will investigate the formation and characteristics of Fano resonance. The structural parameters are as follows: The blue line is a continuous curve with a narrow spectral width and low transmittance, and its transmission spectrum is similar to the shape of a Lorentz curve, showing a certain symmetry. Therefore, the transmission spectrum of single USRR can be considered as a discrete narrowband mode. As shown in The red line is a continuous sharp asymmetric curve with narrow spectral width and low transmittance, and its transmission spectrum is the standard Fano resonance. As shown in The Fano resonance wavelength Based on the above analysis of the causes of Fano resonance, we know that the linear shape of Fano resonance can be changed by varying the broadband mode and narrow band mode, thus improving the performance of the sensor. By changing the parameters of USRR structure that generates narrowband mode, the influence of narrowband mode on the transmission performance of the whole structure was evaluated. The influence of USRR Subsequently, the influence of the changed d of USRR on the whole structure’s transmission characteristics was evaluated, which were found to have increased from 175 to 215 nm. As Next, we investigated the broadband mode and evaluated the effect of broadband mode on the transmission performance of the whole structure by varying the parameters of the MIM waveguide structure that generates broadband mode. The MIM waveguide with two rectangular baffles structure and the MIM waveguide with single rectangular baffle structures were compared to explore the influence of different types of MIM waveguide on the transmission spectrum of the sensor. Both structures have the same parameters, which are set as: The influence of MIM waveguide structural parameters on system characteristics were further researched; we changed the height of rectangular baffle h from 115 to 155 nm and increased the distance between the two rectangular baffles l from 420 to 460 nm with an increase of 10 nm. As shown in Finally, the influence of the coupling gap was evaluated by changing the g from 10 to 30 nm. For optimal sensing performance, set the parameters to In this study, a novel refractive index sensor structure was designed consisting of a metal-insulator-metal waveguide with two rectangular baffles, coupled with a U-shaped ring resonator. The results show that Fano resonance, which results from the interaction of the successive wide-band mode and the discrete narrow-band mode, plays a significant role in the performance of the refractive index sensors. It was also found that the broadband mode mainly affects the line shape and FWHM of Fano resonance, and the narrowband mode mainly affects the sensitivity of sensor. A maximum sensitivity and FOM of this structure were achieved, which are 2020 nm/RIU and 53.16. The presented structure has the potential to be useful in nanophotonic sensing applications.


In this paper, we present an assistive mobility control for a robotic hip-knee exoskeleton intended for gait training. The robotic hip-knee exoskeleton is designed with an active flexion/extension and a passive abduction/adduction at each hip joint and an active flexion/extension at each knee joint to comply with the movement of lower limbs. While facilitating walking with the robotic exoskeleton, model-free linear extended state observer (LESO)-based controllers are proposed for gait control, in which the LESO is used to deal with each user’s different lower limb parameters and unknown exerted torques. Walking and ascending experiments were conducted to evaluate the performance of the proposed methods, and the results are shown with respect to walking parameters. Moreover, a preliminary study for an extended application to the recovery of normal gaits that relieves the freezing of gait (FOG) in Parkinson’s disease (PD) patients is also investigated in the paper. Walking is a fundamental prerequisite to almost all activities of daily living. Some movements such as stair ascent or slope ascent are far more demanding than normal walking in terms of metabolic energy, physical strength and joint torques . HoweverImpaired lower limbs always cause gait deficits. One way to remedy these is to execute rehabilitation training to help recover normal gait. According to the three different stages of rehabilitation exercises , the firA robotic exoskeleton is a wearable mechanical device whose links are strapped to human limbs . Recent Control technology for robotic lower limb exoskeletons plays the most critical role in providing safe and effective gait training. In general, the assistive control modes of robotic exoskeletons are classified to the user-active mode and user-passive mode according to the interactive modes of human–machine systems . In the In addition, another approach to the user-active mode was realized by the dynamic response of the human–exoskeleton system. An integral admittance shaping algorithm was proposed to control a robotic exoskeleton to achieve the desired dynamic response of the human–exoskeleton system . In 16]16], consIn the user-passive control mode, the robotic exoskeleton conveys forces to actuate the lower limbs to track the planned rehabilitation trajectory slowly, smoothly and safely for individuals who are incapable of walking without external assistance . The preMoreover, there always exist system uncertainties and human–robot interaction disturbances in robotic exoskeleton systems. The adaptive control scheme with the evolving forward learning model for disturbance approximation was derived for the control of a robotic exoskeleton . A modelThese referenced model-based control schemes can perform walking assistance well, but the algorithms developed from a dynamic model of the robotic exoskeleton system are computationally complicated and intensive . A modelA controller with a simpler structure but higher tracking performance is crucial for the real-time mobility assistance of robotic exoskeletons on gait training, because the complexity of control system can be minimized, and the processing time can be reduced to lower the computational load. Moreover, a model-free control strategy is eminent with a faster approach to the peak value and settling. In this study, a robotic hip-knee exoskeleton was developed with an active flexion/extension and a passive abduction/adduction at each hip joint and an active flexion/extension at each knee joint to comply with the movement of lower limbs. The robotic exoskeleton facilitates walking rehabilitation in passive mode control. The unknown system parameters and user exerted torques were grouped into the disturbances to the robotic hip-knee exoskeleton. A linear extended state observer (LESO) was designed to approximate the unknown disturbances. Then, the model-free LESO-based controllers were proposed to track the planned trajectories during the gait training. In comparison to the referred works in which the assistive controllers are only applied at the swing phase, our assistive mobility control is suitable for the complete gait training duration. A robotic hip-knee exoskeleton is used for gait training to improve impaired mobility, so the exoskeleton system is identified as a wearable human–machine device. As the robotic exoskeleton attaches closely to the human lower limbs, the robotic exoskeleton should be as lightweight as possible. In addition, for the user-passive mode, the robotic exoskeleton drives the lower limbs to execute the preplanned gait trajectories, so the robotic exoskeleton should provide natural motion for required degrees of freedom and reach the complete range of motion. In this way, the motion of the exoskeleton should comply with the movement of lower limbs in an anatomical structure. Inspired by the movement of lower limbs, the design of robotic exoskeletons should be in accordance with the ergonomic principles to guarantee that the system is kinematically compatible with the lower limbs ,34.The mechanical structure of the robotic hip-knee exoskeleton is shown in The building and wearing of the proposed robotic knee-hip exoskeleton is shown in The required actuation unit, angle sensors and main control board are integrated to the robotic hip-knee exoskeleton as presented in A robotic hip-knee exoskeleton integrates robot power and personal mobility in a collaboration to provide assisted rehabilitation or gait training. To increase assisted efficacy and user comfort, the locomotion of robotic lower limb exoskeleton must comply with human gait as closely as possible. According to the gait analysis of a human with a normal gait pattern, the walking cycle is basically composed of an alternating sequence of stance phase and swing phase. In the stance phase, one or two feet contact the ground. In the swing phase, the foot leaves the ground until the swing leg is put down to make the heel touch the ground again. In general, mathematical models of a robotic lower limb exoskeleton are considered for model-based gait control based on the walking phase. In the swing phase, the gait dynamics are developed by the oscillated serial links. In the stance phase, an inverted pendulum-like model is formulated for the dynamics.V, caused by the centrifugal force and Coriolis force, contains those terms that have any dependence on joint velocity; and the gravitational term G contains all those terms in which the gravitational constant g appears. The robotic hip-knee exoskeleton is a human–machine collaboration system, and thus the parameters of the user’s lower limbs and the exoskeleton are coupled to the gait dynamics. Without loss of generality, the dynamic model of one leg at the swing and stance can be expressed in a unified equation asAt the initial gait training stage, the general intent of the robotic exoskeleton is to help individuals with impaired mobility or muscular weaknesses to recover to the extent of a normal walking. As such, the desired gait trajectories are commanded to the robotic exoskeleton in a pre-recorded form from a normal walking pattern to execute gait training. However, system parameters, such as inertia, usually are uncertain and distinctive for each individual. Moreover, a human’s applied torques at the hip joints and knee joints are not known during walking. These uncertain effects are generally regarded as disturbances. Therefore, a model-free disturbance observer is used to estimate these uncertainties, and then a controller with disturbance compensation will be developed for the gait training control. LESO is a model-free disturbance observer that can estimate the unknown terms in real time without needing a detailed mathematic model . The metf accounts for the combined effects of uncertain dynamics and unknown human-exerted torques on joint angular acceleration. Moreover, the neglected coupling relationship of the hip joint of the other side on one leg model is regarded as the unmodeled dynamics. The unmodeled dynamics represent a disturbance included in f.Taking an inverse for the positive definite inertia matrix, and introducing a diagonal control gain matrix For gait training, the desired rehabilitation trajectory is planned by joint angles, and thus the disturbance observers can be designed individually for the hip joint and knee joint. Based on Equation (2), and including the disturbance as another state, the augmented state space is expressed asA = B =C =E =Combining Equation (3) leads to the compact formf, a linear extended state observer (LESO) is employed according to Equation (4),z is the estimated system state, z and To estimate the external disturbance oe = x − z, and then the error dynamics are derived asIn Equation (5), the pole placement approach can be used to determine the observer gain parameters . From EqThe observer gains are determined such that the characteristic polynomial The observer gain matrix is chosen ase of the observer will approach zero; that is, it implies zThe tracking error In general, the system estimation is more accurate for a larger observer bandwidth The LESO-based controller suggests that the unknown total disturbance can be tried to be eliminated if the total disturbance is estimated. That is, the trajectory tracking errors of the robotic exoskeleton are compensated by the total estimated disturbance If the servo portion is taken as ications . HoweverIt is well known that the primary feature of sliding mode control (SMC) is the robustness against system parameter uncertainties and external disturbances, and thus it is an effective technique to control uncertain and nonlinear systems ,39. Howeequ and reaching control ru, as the system presents a model imprecision or external disturbances. The nominal control iss zero. A sliding surface is to specify the desired closed-loop performance, and defined asC is related to the desired performance of the closed-loop system.SMC is composed of the nominal control FSMC maps two normalized inputs, s(t) and t), to linguistic output based on the Mamdani inferred rules, in which seven fuzzy partitions are adopted, namely, NB (Negative Big), NM (Negative Medium), NS , ZO (Zero), PS , PM (Positive Medium) and PB (Positive Big). The product inference with singleton fuzzification and centroid defuzzification methods were employed for the fuzzy implications. The fuzzy function is normalized, The fuzzy type of reaching control for the robotic exoskeleton is expressed asposed in . The memi = 1, …, n, with The input–output relationships in the fuzzy inference system are chosen according to a fuzzy logic IF-THEN rule base, in which rule The LESO-based FSMC is expressed asThe robotic hip-knee exoskeleton is controlled by the LESO-based FSMC (12). A Lyapunov candidate The stability is analyzed by taking the derivative of (13) asu for the robotic exoskeleton are synthesized through LESO-based FSMC, powering the DC motors to generate torques to drive the robotic exoskeleton to realize mobility assistance.The control structure of the LESO-based FSMC for the robotic hip-knee exoskeleton is shown in In comparison with the conventional FSMC, except for the error term p and q are coprime and with e = 0 in finite time given an initial state e(0)Based on the FTSMC field, the sliding surface is generally adopted to be (15)s=ΛeWhen The reaching control in a fuzzy type, Equation (11), is also introduced to overcome the estimation errors and suppress chattering. The total control for the LESO-based FFTSMC is expressed asThe performance of the proposed LESO-based controllers for the robotic hip-knee exoskeleton on gait training is investigated. As shown in , The required parameters for the proposed controllers are as follows: in the LESO-based PD controller, In the experiment, as shown in Since the above results demonstrate the superiority of the LESO-based FFTSMC, the following gait training experiment was conducted only by the LESO-based FFTSMC at a slower walking speed of 0.15 m/s. The gait trajectories for the left and right lower limbs were planned by an actual walking motion. In this locomotion, the left leg first lifted up, moved forward and then touched the ground to become a stance phase; the right leg was then actuated to start an alternate swing. In comparison with the tracking performance at a faster walking speed of 0.225 m/s, the RMSEs of joint trajectories for two different walking speed are presented in For an ascending test, a subject wore the robotic hip-knee exoskeleton to execute stair-climbing gait training with only the LESO-based FFTSMC, as shown in The trajectories of the hip and knee joints on both sides for ascending are displayed in Freezing of gait (FOG) often occurs in Parkinson’s disease patients who lack effective gaits. Because this particular type of gait disorder always results in disturbances of gait, such as sudden movement interruption or initiation hesitation, FOG increases the risk of fall and always leads to psychological anxiety due to the fear of fall . To alleviate FOG symptoms, many nonpharmaceutical treatments are performed to improve gait stability, such as visual and somatosensory cueing , auditorMore recent research indicates that the gait cycle becomes shorter than during normal gait and presents a shuffling gait of small steps before freezing . For thiThe healthy subject first wore the exoskeleton to perform walking exercises without powering the robotic exoskeleton. Supposing a significant reduction in gait cycle was indicated, the subject then triggered the robotic hip-knee exoskeleton by himself to execute a normal walking motion. In the preliminary study, the timing to trigger the robotic exoskeleton was set when a foot touches the ground and leaves the ground, and then a normal gait was recovered with the proposed LESO-based FFTSMC. The trajectories of hip joint and knee joint are shown in The proposed LESO-based FFTSMC for gait training is feasible for the complete walking duration without respective dynamic modeling at the stance phase and swing phase. In the experiment, the tracking stability is related to walking balance. Therefore, the walking balance control should be further considered at the stance phase, and the controller parameters at the stance phase may differ from the swing phase. When executing gait training, the left and right lower limbs are controlled independently through the respective preplanned trajectories. Because there is no communication for both lower limbs of the robotic exoskeleton, an unsmooth gait sometimes happens, especially at the transition from the stance to the swing, and vice versa. To guarantee a safe and smooth gait transition, the foot pressure sensors should be used for the communication of both lower limbs about the walking state. In particular, as the robotic hip-knee exoskeleton provides an active assistance solution to relieve FOG, the foot pressure sensors are required to detect and trigger the assistance timing. In the aforementioned references, the control designs and the associated results are only for the swing phase because the swing of the leg needs greater muscle strength. However, a complete gait cycle includes the stance phase that is related to the walking stability. Consequently, better tracking performance in the stance phase implies a stable gait. Moreover, in , a cascaThis work concludes with the realization of an assistive mobility controller for a proposed robotic hip-knee exoskeleton on gait training. To perform smooth and robust walking exercises, LESO was used to estimate a lumped disturbance that substitutes for the system uncertainty and unknown human-exerted torques, and then model-free LESO-based controllers were developed to eliminate disturbance and track the training trajectory. The walking experiments with the robotic hip-knee exoskeleton show that LESO-based FFTSMC gives superior performance in convergence and response over LESO-based PD and FSMC. Additionally, the investigation of walking speed suggests that a slower walking speed provides stable gait training. Moreover, the ascending training with the robotic exoskeleton validates the efficacy of stair-climbing assistance. The results also demonstrate that a larger error happens at the moment of starting a swing. The final tests indicate that the robotic exoskeleton with the assistive mobility control approach may become a promising assistive device for relieving FOG. The solution is to initiate the robotic exoskeleton to regulate the stride length and regain a normal gait before FOG. The results show that gait recovery is better when the robotic exoskeleton is triggered right at the beginning of a swing. In the future, the controller’s parameters will be further studied in an adaptive method for practical applications. In addition, clinical trials will be performed with individuals with lower limb hemiparesis, or PD patients. It is expected that the efficacy of such a robotic exoskeleton system can be fully assessed in providing gait training and recovery of a normal gait.


A novel diagnosis method based on the rotor slip is proposed in the paper to correctly detect current and speed sensor failures during the induction motor drive (IMD) operation. In order to enhance reliability and avoid confusion in the diagnosis algorithm due to the influence of measured signal quality, each fault type is determined in a priority order defined by the diagnosis method. Based on the features of the IMD applying the field-oriented control (FOC) technique, an innovative model uses the measured currents and reference speed as the input signals to estimate the rotor slip for the current sensor fault detection. After verifying the quality of the feedback of the current signals, a speed sensor fault function is continued, and performs according to relations among the reference speed, estimated speed based on the sliding mode method, and measured rotor speeds. Finally, the estimated quantities are selected to replace the wrong measured current or speed signals. The feasibility of the proposed approach is verified by simulations using Matlab-Simulink software as well as by practical experiments using an IMD prototype with a rated power of 2.2 kW and a DSC-TMS320F28335-based control system. The obtained simulation and experimental results demonstrated the feasibility, effectiveness, and reliability of the proposed diagnosis technique in detecting sensor failures and maintaining the stable operation of the IMD. Set a reference value to IMDs corresponding to the specific requirement;Supply an initial voltage to start up the motor;Measure operational signals by the sensor system and send those feedback signals to the controller;The controller conducts the control algorithm and provides the control signal to the power inverter;The inverter supplies the corresponding voltage to the motor, then this is repeated.A three-phase induction motor is a widely manufactured electrical machine worldwide with applications in various fields such as cooling systems, chemical, textile, mining, petroleum industries, and especially in electric vehicles (EV) . In receThe performance of IMDs depends on the capacity and stability of all components of the system, where the stable structure of the motor, the analytical model, and the quality of the sensor signals plays an essential role in ensuring the effectiveness of the control process . There iThe field-oriented control (FOC), a typical method belonging to the vector control group, is a modern technique for IMDs. IMDs applying the FOC technique can precisely control torque and rotor flux based on the orthogonal current components in the rotation coordinate system ,8,9,10. The feedback speed from the encoder plays a crucial role in regulating the demand torque for executing the reference speed of IMDs that apply the FOC approach. If the speed sensor signal is faulty, it is necessary to be detected precisely and replaced as quickly as possible. In , an exteThe current sensor system of IMDs is classified into two types depending on the control structure: three current sensors and two current sensors. In a typical IMD system using three current sensors, the diagnosis method is based on Kirchhoff’s law principle: the sum of three-phase currents reaches zero at normal states. Three current observers are used to detect sensor failure, and each of them is composed of the corresponding two-phase currents. When a fault occurs with a specified current phase, the two observers corresponding to this phase current will be affected, while the other observer will be unaffected. As a result, the faulty phase will be correctly diagnosed ,18. In , the LO ults. In , the autults. In , an asymults. In . Similarults. In  has beenults. In ,25 has bSFD based on the comparison between the measured signal and the estimated signal, e.g., ,19,20,22SFD based on the comparison between the measured signal and the reference signal, e.g., ,16;SFD based on a self-test with a prior sample signal, e.g., ,24,25;SFD based on the change of a compound signal, e.g., ,18,21,23SFD based on a mixture of the above-mentioned methods (compound methods), e.g., ,23.Through the above-reviewed literature, various sensor fault detection (SFD) methods have been classified into five main specified groups, as shown below:In this paper, an innovative approach for the current sensor fault diagnosis based on the rotor slip estimation combined with the TDO technique is proposed to precisely locate a faulty phase current according to a predefined priority. It belongs to the compound methods, where the quality of both the current measurement and the speed encoder are verified and estimated simultaneously. Most existing sensor fault diagnosis methods do not mention random noises on feedback signals, which can lead to a mismatch diagnosis during the operation of IMDs. Therefore, the innovative standout of the proposed method from previous studies is the ability to distinguish between certain failures and random noises of the current sensors to make precise diagnosis decisions for increasing reliability in the control process. In the diagnosis method, the initial indication of a current sensor failure is first recorded by the TDO technique and then verified by the rotor slip comparison algorithm. The speed sensor fault diagnosis algorithm will be next performed as soon as the health status of the current sensors is verified. Therefore, by combining a reasonable diagnosis sequence, the proposed method has a faster sensor fault detection time than other diagnosis methods based on RMS values while ensuring high accuracy. Once the sensor fault is identified, the faulty measured signal will be replaced by an appropriate estimated signal to ensure the stable operation of the IMD. Moreover, most of IMD’s controllers achieve good performance when operating close to the nominal speed; however, they could face various difficulties at the low-speed region due to the influence of varying machine parameters, inverter nonlinearities, and a longer processing time . This paThe article is structured in five sections. The first part presents the introduction to research problems, and the second describes a mathematical description of the FOC and some sensor fault types. The following two parts, respectively, offer the simulation and experimental results in a low-speed range to prove the technical feasibility. The contributions and discussion of this research are described in the last section.Unlike DC motors, the relationships of induction motor (IM) electromagnetic quantities are complex and nonlinear. In the ial form , as beloIn order to satisfy the requirement of independent control of flux and torque, the FOC method is often used in high-performance variable-speed drives. In the FOC method, the complexity of the motor control model is linearized by decomposing the current space vector into two perpendicular components in the In the FOC loops, the two measured currents are converted to the In the In the normal operating condition, the rotor flux, according to the FOC method, is fixed as a constant value and By applying (10) to the dynamic modeling, we can obtain the characteristic control equations in the e system , as beloFrom (10) and (11), the stator current components can be determined by the following equations:The electrical rotor slip speed can be determined as (14):Generally, the accuracy of the feedback-measured signals, such as the stator currents and rotor speed, plays a vital role in the performance of control systems based on the machine model. If the quality of the feedback signals is inappropriate, the control algorithms will not be implemented correctly, leading to low control effectiveness or, worse, the collapse of the system completely. Abnormal situations of sensors can occur in various forms, which can be classified into two main types: partial failure and hard failure  ,29,30. PAs shown in The FTC outputs include two groups, status indicators  and feedback values -based comparison algorithm is proposed to cancel random noises in the current measurement system. The method uses the reference rotor slip determined from the reference components of the stator current vector and rotor time constant using the current model. The model inputs consist of the measured currents “tor slip  can be dApplying (5) and (14) with In a normal operation, as presented by (19), the reference RSL, This paper proposes an effective diagnosis strategy for both the current and speed sensors. The diagnosis algorithm proceeds with sequential checking steps, starting from the current sensor status and then the speed sensor condition. The flowchart presenting the proposed general fault diagnosis algorithm is described in As we can see in the flowchart, the current sensor diagnosis is first executed by two sub-steps, TDO and reference RSL. The TDO is used to determine any change in a specific phase current, and the reference RSL confirms a certain fault of the current sensors in the current measurement. The TDO method-based current fault detection algorithm, including three difference operators ,25,44, iIn normal operating conditions, the difference between the phase current values at two sampling times is very small, and the operators of the TDO method are also limited to a small range. However, if any sudden change in the phase current occurs due to either a noise or sensor fault, the indexes will significantly increase. Hence, in order to recognize a phase current change, the proposed current diagnosis algorithm applies the checking criterion based on the third difference operator of the stator currents defined in (21):The threshold eference  recommenAlthough the TDO technique is very sensitive to detecting changes in the current signal, it is not able to distinguish between permanent fault states and random noise. For example, when one pulse noise occurs at the time of 2 s in The reference RSL calculated by (19) is then applied to confirm a certain fault of the current sensors, not random noise in the current measurement. As shown in By applying the RSL technique, the fault diagnosis algorithm to determine the current sensor faults can be modified, as shown below:Remark: the value of As we can see in the flowchart, after checking the current sensor status, the diagnostic procedure for the speed sensor is then performed by comparing the reference and estimated speed with the measured rotor speed combined with a counter as a time-checker. It implies that the defective speed sensor signal should be verified by not only the value deviation but also the existence duration. The implementation can be described by the following steps:r speeds  and can Finally, the proposed FTC algorithm consists of various diagnosis blocks, each of which detects a specific type of sensor fault. The simulation model of the IMD is built using the nominal motor parameters see . The IMDThe control algorithms usually achieve high efficiency in the rated speed region because of the stability of the machine parameters. In contrast, control algorithms often reduce their efficiency when the IMD system works in the low-speed area due to changes in the motor parameters and the nonlinearity of the power converter. Therefore, to demonstrate the effectiveness of the proposed algorithm, simulations have been conducted to verify the capability to detect various sensor failures at 10% of the rated motor speed.First, the induction motor operates with all healthy sensors, then sudden damage to the speed sensor occurs at 2 s, as shown in The second simulation describes a disconnected failure of current sensors at phase A. As shown in Similarly, if there is a disconnection of the current sensor at phase C, the diagnosis algorithm can also determine exactly the phase damaged. After these three simulation cases, it can be stated that the proposed diagnosis algorithm has proved its effectiveness in diagnosing various sensor failures at the low-speed range of induction motors. It has responded very fast and reliably to the damage states of both the speed and current sensors. The problem of the speed sensor is quickly resolved within 35 sampling cycles (3.5 ms), and the problem of the current sensors is certainly detected even faster, with only 20 sampling cycles (2.0 ms). It could help the IMD system switch from the normal to the fault-tolerant modes very smoothly due to the prompt and precise reaction of the proposed FTC method. During the fault-tolerant operation, the estimated quantities are used instead of the corresponding measured signals.To evaluate the ability of the proposed FTC method in practice, many practical experiments have been implemented by a real IMD system, as shown in In order to demonstrate the practical capability of the proposed approach, the experimental scenarios have been set up the same as the simulations mentioned in the previous section. The real induction motor drive parameters correspond to the motor parameters used for the simulation see . The expIn the first experiment, the induction motor drive operates in normal conditions with all healthy sensors from 0 to 2 s, as shown in The second experiment considers a disconnection of current sensors that occurs at 2 s in phase A, as shown in This part describes the performance of the proposed fault diagnosis algorithm for the real induction motor drive, where the experiments were set up in the same scenarios as the relevant simulations in the previous section. Both simulation and experimental results clearly demonstrate the capability and the superior of the proposed approach for this specific application. Moreover, the proposed diagnosis strategy is effective against various insufficient cases of the measuring system of IMDs in low-speed regions.The proposed sensor fault diagnosis method has demonstrated its effectiveness in dealing with both speed and current sensor failures. A new idea of using the rotor slip combined with the TDO has been proposed to precisely detect and locate the current sensors faults during the induction motor drive operation. In order to enhance reliability and avoid confusion due to the influence of random noise, an appropriate diagnosing strategy has been recommended where the sequentially specific order determines each fault type in the fault diagnosis unit. The disconnection of the current sensor, which is one of the most severe faults, can be quickly determined by the current sensor diagnosis function within 2 ms. Additionally, the speed sensor diagnosis function can reliably detect the inaccuracy of the speed sensor signal without being interfered with by random noises within 3–3.5 ms. The proposed diagnosis algorithm is more effective and convenient than other existing diagnosis methods. As a result, the IMD’s control system can operate more efficiently due to the lower calculation burden in the same operating conditions. Both simulation and practical experiments have proved the capability of the proposed method.


Lung cancer is one of the cancers with the highest mortality rate in China. With the rapid development of high-throughput sequencing technology and the research and application of deep learning methods in recent years, deep neural networks based on gene expression have become a hot research direction in lung cancer diagnosis in recent years, which provide an effective way of early diagnosis for lung cancer. Thus, building a deep neural network model is of great significance for the early diagnosis of lung cancer. However, the main challenges in mining gene expression datasets are the curse of dimensionality and imbalanced data. The existing methods proposed by some researchers can’t address the problems of high-dimensionality and imbalanced data, because of the overwhelming number of variables measured (genes) versus the small number of samples, which result in poor performance in early diagnosis for lung cancer.Given the disadvantages of gene expression data sets with small datasets, high-dimensionality and imbalanced data, this paper proposes a gene selection method based on KL divergence, which selects some genes with higher KL divergence as model features. Then build a deep neural network model using Focal Loss as loss function, at the same time, we use k-fold cross validation method to verify and select the best model, we set the value of k is five in this paper.The deep learning model method based on KL divergence gene selection proposed in this paper has an AUC of 0.99 on the validation set. The generalization performance of model is high.The deep neural network model based on KL divergence gene selection proposed in this paper is proved to be an accurate and effective method for lung cancer prediction. Lung cancer is the malignant tumor with the highest incidence and mortality . GloballMost lung cancers are diagnosed at an advanced stage, when the prognosis remains poor. Although LDCT screening has led to progress in early lung cancer detection, improvement in patient outcomes has been incremental and the accuracy is not satisfactory. With the rapid development of High-throughput sequencing, some researchers are beginning to explore the genomic evolution of premalignancy throughout the course of tumorigenesis . These sWith the rapid development of computer technology, machine learning methods are playing an increasingly important role in the diagnosis of lung cancer. Researchers continue to explore various lung cancer prediction algorithms, including support vector machines (SVM) , K-neareAt the same time, gene expression dataset has problems such as small dataset, high-dimensionality, unbalanced data, etc. There are tens of thousands of genes in a data set, but the number of samples is very small. Most genes have nothing to do with lung cancer, so we need exclude the irrelevant genes. If the existing machine learning methods are directly applied, the generalization performance of the model is very poor and it is difficult to converge, therefore, gene selection is needed. In the previous papers, difference analysis is usually used to select related genes. However, difference analysis requires data sets to conform to specific distributions and requires large data sets. At the same time, its calculation is more complicated, which leads to a small amount of data that cannot measure the importance of genes. There are also many researchers who try to use machine learning methods to select features, but gene expression data sets are unbalanced small data sets with high dimensionality, which leads to insufficient learning of machine learning methods and a underfitting model. The selected genes are often not the most relevant genes.In view of the shortcomings of traditional machine learning methods and the problems of gene expression level data sets, we hope to get a new simple and convenient method for gene selection, and on this basis, we can find a new machine learning method for lung cancer prediction. In recent years some deep learning researches in the biomedical field has been successful , which pIn order to solve the problem of high latitude of gene expression level data and few samples, this paper tries to use KL divergence for gene selection to build a deep neural network model. In order to solve the problem of imbalanced data, focal loss  is used The process of the deep neural network lung cancer prediction model based on KL divergence gene selection proposed in this paper is shown in Fig. https://dcc.icgc.org/). The TCGA dataset and ICGC dataset used in this paper is the RNA-seq gene expression data of lung adenocarcinoma (LUAD) samples from the TCGA dataset. The TCGA dataset contains 533 lung cancer samples and 59 normal samples. The ICGC dataset contains 488 lung cancer samples and 55 normal samples.The data we used were extracted from TCGA portal (https://tcga‐data.nci.nih.gov/tcga/) and ICGC portal . In practice, P represents the true distribution of the data, and Q represents the theoretical distribution of the data or the approximate distribution of P.KL divergence  Formula) is an aThe KL divergence is always greater than or equal to zero. When the two data distributions are the same, the value of the KL divergence is 0. The greater the difference between the two distributions, the greater the value of the KL divergence.For gene expression data, we can easily get the data distribution of each gene in the disease group and the control group. We can easily get the data distribution using a small sample data set, and then use KL divergence to measure the difference between the two distributions. If the two distributions are consistent, it means that the gene has nothing to do with the disease. If the two distributions are quite different, it means that the gene is related to the disease.KL divergence has the advantage of simple calculation. We can easily calculate the difference between the two distributions using small data set, which is suitable for small dataset such as gene expression dataset.This paper uses a deep neural network model to predict lung cancer. Deep neural network is inspired by the working principle of the brain and has been widely used in many fields. A deep neural network generates output based on input variables. Given a set of features and a target, it can learn to generate nonlinear function approximations value. Between the input and output, there are one or more nonlinear layers, called hidden layers. The deep neural network has multiple nonlinear hidden layers, which enable the deep neural network to learn complex nonlinear function relationships from high-dimensional raw data without the guidance of artificial rules .Figure input is the input information. W1 is the parameter of the first layer, relu(x) is a non-linear function, which is defined as Formula (sigmod function as the activation function[sigmod function is defined as shown in Formula (Formula  and Form Formula . Formula Formula  is the p function. The sig Formula , and itsThe binary classification model generally uses cross-entropy as the loss function, as shown in Formula , where y Formula . The croIn order to solve the problem of imbalanced data, we use focal loss function. Its formula is as shown in Formula . Focal lWe use the gradient descent method to adjust W1 and W2. Taking into account the shortcomings of existing methods and the characteristics of gene expression data sets, this paper uses TensorFlow to establish a three layers deep neural network and uses Adam as the gradient descent optimizer . In ordeWe evaluated the proposed method using k-fold cross validation method on the LUAD RNA-seq dataset, which comes from the TCGA dataset and ICGC dataset. These data sets include all stages of lung cancer, collected from patients of different clinical conditions and different ages and genders. The specific information of the data set is shown in Table This article analyzes the gene expression distribution of each gene in normal group and lung cancer group and calculates the KL divergence of two distributions. We believe that genes with larger KL divergence are genes that are related to lung cancer.After analysis and comparison, setting the KL divergence threshold to 3 can select lung cancer-related genes, the number of selected genes is small. In this paper, a total of 194 genes were selected.We use Accuracy, Recall, Precision to evaluate the performance of gene selection models and non-gene selection models. These indicators all rely on the confusion matrix  for calcThe accuracy rate is defined as the proportion of the predicted correct samples in the total samples, and the calculation formula is shown in Formula .9\documeThe recall rate is defined as the proportion of all samples whose true values are positive that are predicted to be correct. The calculation formula is shown in Formula .10\documThe precision is defined as the proportion of samples whose true values are positive among all samples whose predicted values are positive. The calculation formula is shown in Formula .11\documWe use the deep neural network model proposed in this article to train and evaluate all gene data and selected gene data respectively. The results are shown in Table We built a deep neural network model with two hidden layers, using focal loss as the loss function, taking the genes selected in the previous section as the model input, and then using k-fold cross validation method to evaluate the performance of the model, we set the value of k is five. After feature selection, the dimensionality of the data set is reduced, much lower than the sample size, which makes the application of deep neural network models possible.Compared with the SVM, LR, KNNThe AUC of the SVM, LR, KNN, RF model and the model proposed by this paper on TCGA and ICGC dataset are shown in Table In this paper, we found that the deep neural network model based on feature selection proposed in this paper has achieved better results than normal classification models in lung cancer prediction. Given the high incidence and mortality of lung cancer, early and accurate detection is very important. Therefore, computer artificial intelligence technology is of great help to improve the accuracy of lung cancer prediction.In this paper, we compare the deep learning model proposed in this paper with the SVM model. The SVM model has been widely used in disease prediction. The SVM can achieve better results on a balanced big data set, but on the gene expression data set, the generalization performance of SVM is poor. This is probably because the feature dimension is too high and the SVM cannot be fully learned, resulting in low prediction accuracy. Therefore, feature selection for high-dimensional data can reduce the cost of model learning, which makes it easier for the model to converge, so we can obtain better prediction accuracy.In addition, we observed that our deep learning-based model achieved higher accuracy and AUC scores than SVM. The result may be attributed to the inability of SVM to perform automatic feature crossover. The deep learning method we proposed can automatically learn the direct interaction and non-linear relationship of features and perform the best fit. Therefore, the accuracy of lung cancer prediction is higher. Our research results also confirm that deep learning has the ability to fit complex relationships, especially non-linear relationships, and does not require manual intervention. We believe that deep learning will become more and more important in the field of disease diagnosis and has a broad space for development.Finally, we need to point out that deep learning-based models require high computational costs. In order to overcome this problem, we use feature selection techniques in the data preprocessing stage, which greatly reduces model training and running time and makes the model easier to converge. With the rapid increase in the amount of gene expression data and the diversity of features, feature selection is a very important and necessary means. In general, in the discovery and research of important genes, feature selection is more and more worthy of attention.Aiming at the shortcomings of existing lung cancer prediction methods, this paper proposes a lung cancer prediction model based on KL divergence gene selection using deep neural network, which can solve the problem of high dimensionality, few samples, and model unfitting on gene expression data. Compared with traditional algorithms, it has the advantages of fast training and high accuracy, and it performs better on the verification data set.


In order to improve the diagnosis accuracy and generalization of bearing faults, an integrated vision transformer (ViT) model based on wavelet transform and the soft voting method is proposed in this paper. Firstly, the discrete wavelet transform (DWT) was utilized to decompose the vibration signal into the subsignals in the different frequency bands, and then these different subsignals were transformed into a time–frequency representation (TFR) map by the continuous wavelet transform (CWT) method. Secondly, the TFR maps were input with respective to the multiple individual ViT models for preliminary diagnosis analysis. Finally, the final diagnosis decision was obtained by using the soft voting method to fuse all the preliminary diagnosis results. Through multifaceted diagnosis tests of rolling bearings on different datasets, the diagnosis results demonstrate that the proposed integrated ViT model based on the soft voting method can diagnose the different fault categories and fault severities of bearings accurately, and has a higher diagnostic accuracy and generalization ability by comparison analysis with integrated CNN and individual ViT. The rolling bearing plays an important role in rotating machinery, its health is related directly to the overall operating conditions and the quality of the mechanical equipment. Bearing failure can lead to equipment failure and cause serious economic losses or casualties to the enterprise. Therefore, it is very important to monitor and diagnose the health status of rolling bearings through their vibration data to ensure normal production in enterprises ,4,5,6,7.In recent years, more and more deep learning models have been developed and applied to the fault diagnosis of rolling bearings because of the end-to-end diagnosis ability. The typical CNN neural network is widely applied in the field of bearing-fault diagnosis because of its simplistic network structure and high accuracy diagnosis ability ,9,10,11.To capture more fault-related information, some time–frequency signal-processing methods, such as wavelet transform (WT), empirical mode decomposition (EMD), etc., can not only denoise the original vibration signal but also decompose the signal into different scale components which are combined with a deep learning model to extract fault features for improving the diagnosis accuracy ,22. HoweIntegration learning has been widely applied to the fault diagnosis of bearings by flexibly fusing the preliminary diagnosis results of multiple base classifiers to obtain diagnosis results with higher accuracy and generalization ability because of the complementary classification behavior among different base classifiers. When integrated deep learning models combined with the different scale components of the original signal are utilized to diagnose the fault classes, higher diagnosis accuracy and generalization can be produced. Currently, some integrated deep learning models have been developed to apply to the field of fault diagnosis, and achieve good diagnosis results ,24,25.(1)The integrated ViT based on the soft voting fusion method is suggested to diagnose the bearing fault with high accuracy and generalization;(2)DWT is used to decompose the original signal into different subsignals in different frequency bands and denoise the subsignals. After that, CWT is utilized to transform the subsignals into time–frequency representation (TFR) maps which can describe the singularity of the different subsignals;(3)The ViT model can dig out more hidden fault-related information from the different TFR maps of the subsignals in different frequency bands.To the best of our knowledge, integrated learning has not been introduced into the ViT model to diagnose bearing faults. In order to improve the diagnosis accuracy and generalization of ViT, an integrated ViT model combined with wavelet transform and the soft voting method is proposed in this paper. The main contributions of the proposed diagnosis method are summarized as follows:The rest of the paper is organized as follows: n subsignals in different frequency bands by DWT, and these subsignals are transformed into the corresponding n TFR maps by CWT, and then n individual ViT models which consist of a linear projection of flattened patches (embedding layer), the transformer encoder and MLP head are utilized to diagnose these n TFR maps of subsignals to obtain the preliminary diagnosis results, respectively. Finally, the final diagnosis decision can be obtained by the soft voting method used to fuse all the preliminary diagnosis results.The integrated ViT model not only inherits the advantages of integrated learning but also inherits the advantages of the ViT model, which can improve the diagnosis accuracy and generalization. Referring to The discrete wavelet transform (DWT) can map any stationary or non-stationary signal to a set of base functions formed by wavelet scaling to obtain subsignals distributed in different frequency bands with complete information in the pass frequency range . Based oH denotes the low-pass filter, G denotes the high-pass filter, (1) Given a time series signal lgorithm , the decj and the high-frequency coefficients obtained from the decomposition of each level are reconstructed to obtain subsignals in different frequency bands. For example, A4 and a set of subsignals D4, D3, D2, D1 represent approximate signal and detailed signals with frequency from low to high respectively. The relationship between the decomposed components  and the original signal X can be expressed as(2) The obtained low-frequency coefficients can be decomposed repeatedly according to Equation (1). Thus, the low-frequency coefficients obtained from the decomposition of level The time–frequency analysis method is mainly used to reveal the time–frequency representation (TFR) of the subsignals in different frequency bands which can describe the relationship between the time and the frequency. At present, there are many time–frequency analysis methods used to analyze the time–frequency characteristics of vibration signals, such as short-time Fourier transform (STFT), Wigner–Ville distribution (WVD), and continuous wavelet transform (CWT). However, the STFT is unable to locate the time and frequency of non-stationary signals accurately ; the WVDψ is satisfied with ψ. The wavelet function is written as followsa is the scaling factor of changing the wavelet shape, b is the translation factor of the wavelet shift. Thus, the CWT for an arbitrary function f and ψ. fW  denotes the coefficients of the wavelet function with scale a and offset b, which represent the similarity between the wavelet function and the original signal, and both a and b are continuous variables.Assume that the mother wavelet or basic wavelet function In order to obtain the fault-related TFR of a subsignal in different frequency bands in this paper, the CWT is used to transform the signal into a TFR, which is described as follows:fs is the sampling frequency and cF is the wavelet center frequency, the actual frequency aF corresponding to scale a is written asAssuming that totalscal is the length of the scale series used in the wavelet transform of the signal, which is set as 256 here, and c is a constant.In order to make the transformed frequency sequence an equal difference sequence, the scale sequence must take the following values.c/totalscal should be sf/2. The value of the constant c can be calculated according to Equation (5), which can be obtained by the following equationOn the basis of the sampling theorem, the actual frequency corresponding to the scale Accordingly, the required scale sequence is obtained by substituting Equation (7) into Equation (6).fW  are obtained by applying the continuous wavelet transform principle of Equation (4). Then the scale sequence is converted into the actual frequency sequence f by Equation (5). Finally, the TFR map can be plotted.After determining the wavelet basis function and scale, the wavelet coefficients A transformer is a typical neural network model that relies entirely on a self-attention mechanism to establish the relationship between input and output, which can consider the global information comprehensively and be trained in parallel because of the parallel architecture that is completely different from the sequential structure of the traditional recurrent neural network (RNN). In order to solve this problem, the vision transformer (ViT) was proposed by Dosovitskiy . ViT hash denotes the height of the image, w denotes the width of the image, and c denotes the number of channels of the image; the image is split into N image patches with length p and width p firstly, and then the image is flattened into a one-dimensional sequence D dimension vector space.The embedding layer is mainly for implementing the linear projection of flattened image patches and retaining the positional information and one-dimensional feature vector and class labels of the image patches. Suppose the input image Additionally, the class label and the positional information of the image patch are all added to the outputs of embedding layer. Thus, a new sequence of image patches that contains the image features and the positional and class label information is obtained, which is the input of the transformer encoder.Sublayer(x) indicates the multiheaded self-attentive function and MLP function in each sublayer, LayerNorm(▪) denotes the normalization function.Each transformer encoder layer consists of multiple identical modular layers arranged in a stack, its internal structure is shown in The internal structure of the MLP layer and the multihead self-attention layer are described as follows.MLP layerx denotes the input, and erf(▪) denotes the Gaussian error function.The internal structure of the MLP is shown in Multiheaded self-attention layerQ is the query matrix, K is the key matrix, V is the value matrix. These three matrices are obtained by multiplying the input feature matrix fX with the parameter matrices QW, KW and VW respectively, d is the dimension of Q, K and V.The self-attention mechanism allows the network model to extract local valid features, but a single attention mechanism can only learn relevant information in one representation space. To synthetically extract long-distance features from a global image, a multiheaded self-attention mechanism is used to jointly focus on features from different representation subspaces at different locations. The structure of the multihead attention layer is shown in ith attention head Q, K and V, OW is the weight matrix of multihead attention, h is the number of attention heads, Concat function is to concatenate the output values of each attention head.The multihead self-attention mechanism is a combination of multiple self-attention mechanisms, which use multiple self-attention heads to learn features from different representation subspaces, respectively, and then the multiple attention value is combined and transformed linearly, thus the final attention value is obtained to realize the representation under these different constraint conditions. The multihead self-attention mechanism equation can be expressed as followsGenerally, the standard MLP head layer of ViT consists of a fully connected layer and activation function, which is used to diagnose the fault classes. In order to reduce the calculation workload of the ViT model, a Gaussian error linear unit (GELU) activation function is adopted in this paper. Thus, the input data processed by the transformer encoder layer is input into the MLP head to obtain the probability value of each fault class, and the final fault class can be obtained according to the maximum probability value.ky(kx) of the time–frequency map kx produced by the kth base classifier {Mk) is taken as the final classification result, which is defined as followskx denotes the CWT time–frequency map of the subsignal in the kth frequency bands decomposed by DWT on the original data samples x, max denotes the maximum function, K is the number of base classifiers.When the output of a single classifier is the probability value of each fault class, the fusion is most generally performed by the soft voting method . ConsideThe diagnosis flowchart based on the proposed integrated ViT model is shown in K is the number of fault classes, N is the number of training samples, iyk, is the symbolic function (0 or 1), which takes 1 if the true fault class of sample i is equal to k, take 1, otherwise it is 0. ipk, denotes the probability value of fault class k that the data sample i belongs to. The parameters of each individual ViT model are trained by the TFR maps, respectively.In addition, the number of the individual ViT model is determined by the number of the subsignals in different frequency bands, which is set as five here. The loss functions of all ViT models are all cross entropy loss functions which are written as follows:In order to verify the effectiveness of the proposed integrated ViT model for the fault diagnosis of the rolling bearing, the diagnosis method was utilized to diagnose the fault signals obtained from the Case Western Reserve University (CWRU) Bearing Data Center ,35. As sThe electrical discharge machining (EDM) method was used to simulate the different fault categories and severity of the bearings. Three different diameters of single point damage  on the inner ring, outer ring and rolling element of the bearing were introduced, respectively. The statistics of the dataset are described in Considering that the shape of Daubechies (Db) wavelet function is similar to the waveform of bearing vibration signal, and in order to obtain a better frequency band division effect and reduce the calculation time, DWT based on Db5 wavelet function was used to decompose the data sample into different subsignals in frequency bands in this paper. In order to obtain the TFR maps of subsignals in different frequency bands to describe the relationship between time and frequency, the different detail subsignals D1, D2, D3, D4 and the approximation subsignal A4 was transformed by the CWT based on the cmor3-3 wavelet basis function which was selected because its shape is similar to the impact signal of a bearing fault. In order to verify the effectiveness of the integrated ViT models based on wavelet transform and the soft voting method, the TFRs of five different detail and approximation subsignals in different frequency bands of size 64 × 64 × 3, were input to five individual ViT models, respectively, to preliminarily diagnose the fault of the bearing, and then the soft voting method was used to fuse all the preliminary diagnosis results to obtain the final diagnosis result.X-axis denotes the test data sample number and Y-axis denotes the fault-class labels. From the figure, it can be seen that the diagnosis accuracy produced by ViT model with the detail subsignal D1 achieved 95.07%, which is the highest among all diagnosis accuracy produced by all the individual ViT models with other detailed and approximate subsignals; the diagnosis accuracy produced by the individual ViT model with the detailed subsignal D2, D3 and D4 was 94.80%, 76.47%, respectively, the diagnosis accuracy produced by the individual ViT model with approximate subsignal A4 was 74.40%, which was only higher than that of the individual ViT model with D4, the diagnosis accuracy of the individual ViT model with D4 was the lowest, only 73.73%. This is mainly because the different detailed and approximate subsignals in the different frequency bands contained different amounts of fault-related information, and the amount of fault information in different frequency bands can affect the diagnosis accuracy of the individual ViT model directly.X-axis and the Y-axis indicate the names of the detailed and approximate subsignals and the diagnostic accuracy, respectively; the histogram indicates the diagnosis accuracy of the individual ViT with different TFR maps of the subsignals in different frequency bands, the curve indicates the diagnostic accuracy of the integrated ViT model with the first n TFR maps of subsignals in different frequency bands. From the figure, it can be seen that the diagnosis accuracy of the integrated ViT models increased with the number of individual ViT models involved in the integration. The diagnosis accuracy of the integrated ViT models with first two individual ViT models can reach 99.13%, and the diagnosis accuracy of integrated ViT with the five individual ViT models achieved 100.00%, which exceeded the accuracy of all individual ViT models and the accuracy of other integrated ViT models with different numbers of individual ViT models. The diagnostic accuracy of all the integrated ViT models with different numbers of individual ViT models was consistently higher than the highest diagnostic accuracy of the individual ViT model. All these indicate that the integrated ViT model based on the soft voting method has a superior diagnosis performance to the individual ViT model, integrated learning can improve the diagnosis accuracy of the individual ViT model.The final diagnosis results of the integrated ViT model using the soft voting method for decision making to fuse all the preliminary results of five individual ViT models with five different detailed and approximate subsignals in different frequency bands were obtained and are shown in To verify the superiority of the integrated ViT model, the TFRs of the subsignal in different frequency bands were also input into the integrated CNN models based on the soft voting method to diagnose the bearing fault. The structure parameters of the individual CNN are shown in In addition, to verify the stability of the proposed integrated ViT model, the five diagnosis tests were conducted by the individual ViT model, the integrated ViT model and the integrated CNN model, respectively. To validate the generalization of the proposed integrated ViT model based on the soft voting method, the fault diagnosis analysis of the three diagnosis models was conducted on three different datasets under three different working conditions  which are referred to as dataset 1, dataset 2 and dataset 3, for convenience. Each dataset contained 10 fault classes, the number of samples for each fault class was 200, including 140 training samples and 60 test samples. Thus, each dataset had 1400 training samples and 600 test samples. Each sample had 1024 data points. From This paper proposes an integrated ViT model with the TFR maps of subsignals in different frequency bands based on the soft voting method to diagnose bearings. In the diagnosis process, DWT is used to decompose the vibration signal into different subsignals in different frequency bands and CWT is utilized to obtain TFRs of subsignals in different frequency bands, and then the TFR maps of the different subsignals are input into multiple individual ViT models to diagnose the fault preliminarily, and lastly, the final diagnosis result is obtained by the fusion method based on the soft voting method.The effectiveness and generalization of the proposed integrated ViT model were verified by comparison with the integrated CNN model based on the soft voting method and individual ViT model. Through a multifaceted comparison of the three methods on different experimental datasets, the diagnosis results demonstrated that the proposed integrated ViT has higher diagnosis accuracy and generalization than the integrated CNN and individual CNN model for fault diagnosis of rolling bearings. All these show that the integrated ViT has a promising development prospect in the field of fault diagnosis of mechanical equipment. However, it was found that the number of ViT models used for integrated learning affected the diagnosis accuracy in the process of fault diagnosis, so how to select the number of ViT models with subsignals in different frequency bands will be studied further in future.


We present a workflow for clinical data analysis that relies on Bayesian Structure Learning (BSL), an unsupervised learning approach, robust to noise and biases, that allows to incorporate prior medical knowledge into the learning process and that provides explainable results in the form of a graph showing the causal connections among the analyzed features. The workflow consists in a multi-step approach that goes from identifying the main causes of patient’s outcome through BSL, to the realization of a tool suitable for clinical practice, based on a Binary Decision Tree (BDT), to recognize patients at high-risk with information available already at hospital admission time. We evaluate our approach on a feature-rich dataset of Coronavirus disease (COVID-19), showing that the proposed framework provides a schematic overview of the multi-factorial processes that jointly contribute to the outcome. We compare our findings with current literature on COVID-19, showing that this approach allows to re-discover established cause-effect relationships about the disease. Further, our approach yields to a highly interpretable tool correctly predicting the outcome of 85% of subjects based exclusively on 3 features: age, a previous history of chronic obstructive pulmonary disease and the PaO2/FiO2 ratio at the time of arrival to the hospital. The inclusion of additional information from 4 routine blood tests  increases predictive accuracy to 94.5%. Coronavirus disease COVID-19) first appeared in China in November 2019 and it is caused by the new coronavirus SARS-CoV-2. Its spreading was immediately very fast, prompting WHO to declare a pandemic status on March 12, 2020. Currently, COVID-19 counts over 116M accumulated cases worldwide with more than 2.5M deaths [9 first aSince the pandemic outbreak, several algorithms have been proposed to evaluate predictive scores helping in management of COVID-19 patients. These systems are based on both standard statistical approaches and Machine Learning (ML) methodologies –5. The aet al. [Another critical issue that needs careful consideration is the fact that commonly adopted ML approaches to diagnosis or outcome prediction are almost uniquely from the family of the supervised learning models. As such, they work on a purely associative approach, by identifying correlations between input data, such as symptoms, clinical history and treatments, and the target variable. Many examples show that the inability to distinguish correlation from causation can produce classifications that are misleading to the point of being potentially dangerous . For inset al.  describeA good option to avoid this kind of problems is given by Bayesian Structure Learning (BSL) approaches , which ait is intrinsically interpretable given that it produces a graph representing the causal relationships among the input data;it allows to include domain knowledge , i.e. itit naturally avoids overfitting  and it iit has shown good performances also with small sized dataset , a commoOn a less rigorous note, it has been observed that building causal graphs with BSL forces the researchers to think clearly about the topic, and articulate that thinking in the form of the graph, which is often beneficial in and of itself , 15, 16.All these features make BSL an optimal tool for medical research. In fact, it has found good application in the analysis of genetic data , 18, eleFollowing these considerations, the main objective of this paper is to introduce the use of a BSL-based methodology to study the causal relationship between various predictors and mortality in COVID-19 patients. We aim at verifying whether BSL can reproduce and/or improve our current understanding of causal pathways of COVID-19 risk of mortality using a single-centre but feature-rich clinical dataset  which inIn conclusion, the present work addresses the need of explainable and causally grounded approaches to learn clinical useful knowledge from retrospective data, which is a mainly unexplored research topic, especially in the emergency context of COVID-19. This is achieved by presenting a novel clinical data analysis framework that provides a multi-step approach that goes from the identification of causal relationships between medical data, using BSL, to the realization of a clinically suitable tool, based on a BDT. This tool is suitable for patients triage and is easy to use, straightforward to interpret and has solid clinical bases behind its predictions.The dataset includes COVID-19 diagnosed patients admitted between the 3rd of March 2020 and the 30th of April 2020 from three different units of the Pisa University Hospital  . All datData collection was performed according to the principles stated in the Declaration of Helsinki and it conforms to standards currently applied in our country. No minors were involved in the study. The use of the data was approved by the Comitato Etico Area Vasta Nord Ovest  under the IRB number 230320 and the patient’s informed consent was obtained in conformity with safety protocols adopted in the hospital during the emergency. In particular, oral consent was obtained and recorded in the medical chart by nurses from patients at the moment of admission. This procedure was approved by IRB in face of the extraordinary conditions present at the time of the first wave of COVID-19.The main outcome of the data cohort is dismissal at home or death. The subjects included in the study are 265, of whom 71 died for COVID-19 or for its complications. The death rate of this sample is thus 26.8%. The original dataset included 125 variables. Among the various features collected during the triage and the hospitalization, 63 are missing in less than 50 subjects and thus are included in the study. For the purpose of this study, these features are grouped into six different logical categories as illustrated in The methodology put forward in this paper is articulated in three steps, leveraging different machine learning and statistical methods. First we apply BSL to analyze how the variables of the sample are causally interconnected. Then, we evaluate with Bivariate Statistical Tests (BST) the strength of the connections between the outcome and its neighbours in the BSL graph. This second analysis may seem redundant with respect to the first step. However, while BSL performs a multivariate analysis taking into consideration also latent variables and the possibility of mediated connections, the second one evaluates singularly how each variable affects the outcome. Thus, on the one hand, the causal graph obtained with BSL helps to understand the logical cause-effect sequence bringing to the outcome and to select the features of interest; on the other hand, BST helps to rank the dependency between each feature and the outcome. The third step targets selecting the most relevant features to train a Binary Decision Tree (BDT) useful for clinical practice.The following sections provide a synthetic background on Bayesian Networks, describe the BSL algorithm used and the workflow of the three analyses discussed above.G, P), where P is a joint probability of random variables XV =  associated with nodes V = {1, …, N}. Each random variable Xi can possibly be of different nature . The graph G =  is a directed acyclic graph (DAG) whose edges E encode the joint probabilistic relationships among the N random variables. The graph is a visual representation of the joint distribution of the data, where a directed edge eij from node i to j indicates that i is the parent of j as part of a conditional dependence relationship between the two nodes [BNs are graphical models . For this reason, heuristic search algorithms are usually employed to avoid testing a combinatorial number of cases . As a coQuantifying causal effects. For every DAG identified by FCI, we estimate the effect that each variable has on the variables it is connected to, representing an indicator of the strength of their causal connection, using covariate adjustment. Basically, for each pair of variables, X and Y, we compute a linear regression of Y on X using the parent set of X, extracted from the DAG, as covariate adjustment. When multiple DAGs are available, we average the effects estimated from each DAG. However, in this study we have observed that the DAG is usually estimated without ambiguity and thus the cases in which multiple different effects are found are very rare. Note that this method describes the effect that a unitary increase in X has on Y and, therefore, it is highly sensitive to the range of both X and Y. In order to be able to qualitatively compare the effects, we standardized the variables before this calculation, applying a Z-score transformation.BSL strategy on our cohort. The application of the BSL pipeline described in the previous subsection followed some considerations related to the nature of the dataset available in our study. First, it has to be noted that only a portion of the features in The BSL algorithm attempts to infer causal relationships from input data, which are unavoidably biased, because the sample analyzed is composed by subjects whose medical conditions required hospitalization. Thus, the results from this analysis should be interpreted as representative of the most severe situations.The causal graph analysis pipeline discussed so far has been repeated under two different conditions. In the first we provide to the BSL process a conservative list of prohibited causal connections , whose severance is enforced during the graph identification process. The second one, instead, comprises a fully data driven setting, where no prior knowledge is supplied to the BSL algorithm. This second condition is tested for comparison, to assess the capability of the method to autonomously identify causal relationships that are not blatantly in contrast with widely agreed clinical knowledge.The focus of this step of our analysis is to study how the outcome depends singularly from each relevant feature identified at the previous stage. To this end, we use the Fisher Exact Test (FET)  for cateBDT models are characterized by an inferential process which has some resemblance with human reasoning, which makes them amenable to human interpretation. However, they are known to severely suffer from overfitting , thus itThe scope of our BDT analysis is two-fold. On the one hand we would like to identify a compact BDT to provide an interpretable and procedural view on what are the discriminative cut-point values for the features identified by the BSL causal analysis, and if those values are in agreement with clinical knowledge. On the other hand, we would like to measure the predictive value of such candidate features on our dataset.The first objective (interpretation) has been addressed by training a BDT with a depth fixed to 4 levels, considering only those features present in the integrated graph and only those subjects having those features fully available. Other BDT parameters relevant to reproduce this work are recapitulated in The interpretable BDT is trained on the full data , as it is never used for prediction. To assess the impact of the identified causal features on predictive performance, we train two additional models. The first is a BDT with the same structural constraints and features of the intepretable one, but it is trained and assessed in a 10-fold cross-validation scheme. Its predictive performance is assessed as the average accuracy on the 10 validation folds. The second is a permutation test BDT, again trained and evaluated in 10-fold cross-validation, but using features randomly drawn from the set of features in The comparison between the last two BDTs is intended to verify the effectiveness of the feature identified by the BSL causal analysis. However, a fair comparison requires to ensure that the two BTDs have a comparable number of subjects in training, otherwise it is impossible to understand whether a performance reduction is to be imputed to the lower training size or to the different features. Thus, in the permutation test, we train about 1000 different BDTs of depth-4 with number of training subjects and features matching those used for training the causal BDT.As already said at the beginning of this paragraph, the choice of using a BDT is mainly motivated by its interpretability and ease of clinical usage, but at the same time we want to maximize the prediction performance, otherwise the benefit deriving from an interpretable tool would be less useful. Thus, we performed an additional analysis to compare the performance of the BDT with 3 commonly adopted machine learning algorithms: logistic regression (LR) and support vector machine (SVM) with linear and polynomial kernels. In this analysis the algorithms are trained only with the same features used by the BDT, following the same steps of the BDT analysis: train-all, 10-fold cross-validation and permutation test using random features.We report the main results of the empirical analysis run on our COVID-19 dataset following the three-fold structure of our methodology. A pictorial overview of the experimental analysis is provided in The results of the BSL step run separately on the single feature categories are provided in relevant we mean that these features are connected to the outcome within 2 hops. To ease intepretation of the results we report also, in the second (third) within the brackets, the death (recovery) excess factors with respect to the occurrence in the whole dataset.The first line in Finally, the additional comparison with less interpretable but well regarded algorithms such as LR and SVM , COPD is the only pathology in direct causal relationship with mortality. This result was recently confirmed by a meta-analysis on the associations between respiratory diseases and COVID-19 outcomes .As regards prior (non-respiratory) diseases (graph a), not surprisingly, cardiovascular disease has a direct relationship with the outcome . Furtherab origin and it is detectable by the gender bias in hospitalized patients.Age is one of the most cited risk factors due to its close relationship with mortality in COVID-19 patients . AccordiThe BSL analysis applied to treatment features (graph d) shows also a direct connection between the assumption of anticoagulant before/during Coronavirus infection and the outcome. As it can be noted from Results from the analysis of the symptoms present at hospital admission (graph e) are particularly intriguing. In fact, only a relatively small number of symptoms show a direct causal relationship with the outcome. Among these, myalgia seems to be protective against the risk of mortality. This fact, which has been recently confirmed by Zheng et al. , could bAmong laboratory tests (graph f), only three parameters have a direct causal relationship with mortality. PF ratio is an index of respiratory function and, given that the respiratory system is one of the systems most affected by COVID-19, its causal relationship with mortality is highly understandable. This connection can be observed both in the single-category as well as in the integrated causal graph. Other clinical variables selected by our automatic method are BUN and creatinine. Elevated levels of both BUN and creatinine can be associated to chronic kidney disease which was already demonstrated in direct causal relationship with mortality. Furthermore, a link between creatinine, BUN and mortality has already been observed in COVID-19 patients by other authors .The study of causality between classes of clinical variables and mortality in COVID-19 patients revealed some already known relationships as well as offering some new insights. However, the picture becomes more clear when all clinical variables are used together to assess causal effects on the outcome as in the integrated causal graph of Moving to the BDT illustrated in As it emerges from this discussion, various limitations exists in this study:the limited size of the dataset;the dataset is unavoidably biased towards locally resident subjects with severe symptoms requiring hospitalization;patient-reported data may be very noisy: such as clinical history details, ongoing treatments, symptoms before hospitalization, etc.Except for the first limitation, all the remaining ones represent common issues in the medical field. However, the coherence between the results obtained with this methodology on such a limited dataset, with the results available in literature, suggests that the implemented approach is resilient to this kind of issues. Overall, a percentage of 5.5% of misclassified subjects using solely data available at the triage suggests that the 3-step methodology presented in this paper could be successfully adopted to design an operative flowchart for clinical use when paired with a larger dataset and after an extensive validation.Our work took place on the claim that causal learning, and in particular BSL methodologies, provide useful tools for delivering a robust and interpretable exploratory analysis of clinical data. We have put forward an integrated methodology, rooting on causal graph learning, that provides practitioners with a pipeline of analytical steps amenable toidentify and measure the strength of causal association between features and outcomes in a fully-multivariate fashion;select causally relevant features and assess how they impact, separately, the outcome;provide a compact and interpretable procedural description of the outcome-determination process to support clinical decision making.We have demonstrated the effectiveness of our approach on a COVID-19 case study, where we evaluated the causality relationship between clinical parameters and mortality in a cohort of COVID-19 patients, confirming existing results. The analysis was carried out both splitting the clinical variables into classes as well as using them altogether into an integrated causal graph. Our clinical discussion provides compelling evidence of the robustness of the causal relationships identified by our causal learning approach. The results of the causal analysis were further used to build a highly explainable predictive model of mortality as a decision tree that could be easily implemented in a real clinical context. Our empirical validation against a permutation test setting, confirms the quality and relevance of the features identified by our method, also in a predictive setting.Thus, we propose the adoption of this workflow to discover complex cause and effect relationships in clinical high dimensional dataset, also for other applications. For instance, one possible future work may consist in the study of targeted drugs by applying the presented methodology to the data about the effects of such drugs on subjects with different symptoms, comorbidities, personal and familial clinical history. Within the context of this Coronavirus emergency, we hypothesize this multi-step approach may be useful for investigating how the symptomatology, the care received and the clinical history of the patient impact on COVID long-term effects, which are still very unclear , 56.Finally, future improvements of the methodology itself may rely on the adoption of supervised deep learning models using causal inference , that haS1 TableParameters used for the BSL and BDT analyses.(PDF)Click here for additional data file.S2 TableResults obtained with the SVM  and Logistic Regression algorithms. In all the 3 cases, the permutation test using random features shows significantly inferior results with respect to the features chosen with the causal analysis. Note that the results of the permutation tests are the average of those obtained from 1,000 permutations.(PDF)Click here for additional data file.S1 FigImage showing the BSL analysis applied to different categories of features. All the illustrated graphs are generated without taking the information provided by clinicians into account.(TIF)Click here for additional data file.S2 FigGraph generated with the most relevant features found from the graphs shown in (TIF)Click here for additional data file.S3 FigResults of the permutation test conducted with the logistic regression algorithm.(TIF)Click here for additional data file.S4 FigResults of the permutation test conducted with the linear kernel SVM.(TIF)Click here for additional data file.S5 FigResults of the permutation test conducted with the polynomial kernel SVM.(TIF)Click here for additional data file.