1. Introduction
As the size of high-rise buildings continues to increase, the demand for a quicker elevator speed is rising, and the use of high-speed and ultra-high-speed elevators is becoming more and more popular. Although increases in elevator speed have improved transportation efficiency, the problem of elevator passenger discomfort has gradually become prominent [
1,
2,
3,
4]. In addition, the loss of elevator structure stability will continue to increase during high-speed operation, mainly as a result of the difference between air pressures inside and outside of the elevator car. Air pressure compensation during elevator operation can effectively reduce air pressure difference and keep the elevator running smoothly and comfortably.
When a high-speed elevator runs fast in the hoistway, it will produce strong airflow disturbances and drastic pressure changes due to the small cross-section of the hoistway and the complex structure of the elevator, which could result in serious stability and comfort problems for the elevator. An elevator car is a closed passenger compartment structure with similar air pressure properties to other closed passenger compartment structures such as high-speed train and vehicle cars [
5,
6,
7,
8]. Schwanitz et al. [
9] simulated the pressure chamber TITAN to investigate pressure comfort for high-speed train passengers. They applied a generalized equation model to estimate the pressure change attributes that contribute to passenger discomfort, which could help improve train and tunnel designs. Diedrichs et al. [
10] analyzed the car body characteristics of high-speed trains inside tunnels. The results revealed that the influence of a low frequency mode increases as wall clearance narrows, corresponding to the nominal lateral position of the train.
The research mentioned above can assist in high-speed elevator aerodynamic analysis and help to improve the operations of high-speed elevators. In order to build a physical elevator model for simulation, Bai et al. [
11] carried out experiments by which to measure the aerodynamic characteristics of high-speed elevators. They analyzed the effects of different shapes of car and hoistway parameters on the aerodynamic characteristics of the elevator using experimental results. Duan et al. [
12] simulated the running status of an elevator according to different design parameters under various operating conditions, and measured the instantaneous velocity field of the different elevator car shrouds. Using an aerodynamic analysis of high-speed elevators, Zhu et al. [
13] found that traction ropes and counterweights have a great influence on airflow disturbances, which has been verified through high-speed elevator experiments. The aerodynamic characteristics of high-speed elevators obtained through experimental methods are high in accuracy as well as in cost. Numerical simulation analyses of the fluid mechanics inside hoistways has been widely used to save costs and improve efficiency. Shi et al. [
14] established a two-dimensional model of unsteady turbulence caused by a high-speed elevator system that focused mainly on the transient changes of aerodynamics when a counterweight moves in the hoistway, and obtained the aerodynamic characteristics of the elevator when the car-counterweight was staggered. Through the modeling and simulation analysis of high-speed elevators, Matsuda et al. [
15] concluded that high-speed elevator cars and airflow will produce strong airflow disturbances. Wang et al. [
16] utilized the static incompressible Navier–Stokes equation to numerically simulate the three-dimensional turbulence of a high-speed elevator hoistway. Through a simulation analysis of different blocking ratios, the results showed that as the blocking ratio decreased, the pressure and resistance of high-speed elevators also decreased.
To further improve the quality of elevator operation, elevator vibration factors should be studied as one of the five international standard elevator quality factors (ISO18738 (2012)). Taplak et al. [
17] predicted and analyzed the vibrations of an elevator system based on the proposed adaptive neural network predictor. The simulation results showed that its prediction performance was good. Jiang et al. [
18] established a traction dynamic model of a high-speed elevator with time-varying characteristics. This helped provide data on the mass, stiffness, damping, and dynamic characteristics of the system. After the analysis of the elevator system vibration causes, several damping methods were proposed. Zhang et al. [
19] used a linear motor to design an elevator car’s active shock absorber. Considering the effect of uncertain external excitations on the car system, they designed a back propagation neural network Proportion Integration Differentiation (PID) controller to intelligently and actively control the car’s vibrations. Tusset et al. [
20] pointed out that the horizontal response of the elevator in vertical operation had non-linear characteristics under the excitation of the deformation of the guide rails. They used a magnetorheological damper to dampen vibrations. The experimental results showed that this method could effectively suppress vibrations during elevator operation. Along with the vibration problem is the noise problem of elevator systems. Yang et al. [
21] proposed a mobile band-pass filter to improve the performance of active noise control in an elevator car. The noise control was able to be applied to dynamic systems with time-varying states, and the control effect was good. According to the principle of noise generated by the traction machine, Kawasaki et al. [
22] proposed a numerical calculation model of the structure sound based on the electromagnetic force of the traction machine. They further proposed a method to evaluate the noise of the traction machine.
When analyzing the aerodynamic characteristics of high-speed elevators, both the performance parameters as well as the energy consumption of an elevator’s operation should be considered at the same time. Especially for ultra-high-speed elevators, energy consumption is often extremely high [
23,
24,
25]. Hu et al. [
26] developed a multi-objective genetic algorithm (MOGA) for elevator control in which the optimization goals were energy consumption and an acceptable waiting time for passengers. The optimization results showed that, compared to the traditional nearest-service principle method, MOGA could reduce energy consumption by 23.6%. Zhang et al. [
27,
28] proposed an optimization method for energy-saving dispatching measures during an elevator’s peak mode. By analyzing the optimization goals of elevator energy-saving dispatching, a robust scheduling optimization model was established to handle the elevator dispatching strategy under uncertain peak traffic flow. Finally, the proposed method was verified by the experiments’ effectiveness. Desdouits et al. [
29] improved the control method of elevator energy storage equipment. By setting two controllers—an advanced controller (based on linear rules) and a low-level controller (based on simple logic)—the elevator energy cost was optimized. Experimental results showed that this method could achieve 35% energy-saving efficiency. Based on a direct current (DC) micro-grid, Zhang et al. [
30] proposed an energy conservation approach for elevators. The method resulted in a high energy efficiency of 15.87–23.1% and 24.1–54.5% in the experimental test and field data collection, respectively.
With increases in elevator speed, problems with operation safety, structure stability, passenger comfort, and the dynamic characteristics of the elevator have gradually become complex and worth consideration. Kobayashi et al. [
31] proposed a magnetorheological fluid semi-active damper to improve the safety and reliability of elevators. The damper reduced impact force to passengers when the drives of the elevator failed. Wang et al. [
32] studied non-linear and uncertain load disturbances during elevator startup. They proposed an active disturbance rejection control strategy to ensure riding comfort, which suppressed sliding distance and speed to a certain extent. Elevator resonance can seriously affect elevator structure stability. Yang et al. [
33] studied the transverse vibrations of a super-high-speed elevator considering guide rail excitation and air disturbance. They constructed a four-degree-of-freedom model and employed the Newmark-
method to analyze transverse vibrations. Zhang et al. [
34] conducted a dynamics analysis of high-speed traction elevators. They constructed a time-varying dynamic model and used the fine integral method to analyze the vertical vibrations of a car-hoisting rope system. In addition, with the development of advanced technology, an innovative elevator has been developed to surpass the technical limitations of tradition elevators. Without the use of cables as a lifting system, a cableless elevator will not violently vibrate in high-rise and super-high-rise buildings. ThyssenKrupp Elevator introduced a product known as MULTI (ThyssenKrupp, 2016, Essen, Germany) [
35] in which multiple lift cars could be in the same hoistway and access power from a liner motor without hoist ropes. Multi-supported horizontal and vertical transportation, greatly increased flexibility and significantly reduced energy consumption.
The existing research on the performance of high-speed elevators has mainly focused on the fields of vibration and noise, most of which are single variables that do not consider the comprehensive impacts of multiple variables on performance, especially comfort. Furthermore, the air pressure regulation of an elevator car is realized through a high-coupling and non-linear air pressure compensation control system. The operation condition of a high-speed elevator in the shaft is repetitive and controllable. An effective design of the air pressure curve of an elevator car can provide a theoretical basis for the elevator car physical control system. To improve an elevator’s performance as well as passenger comfort, passive methods such as changing the external structure of the elevator car are often used. Studies on the active control of air pressure in the car have been performed less frequently. In view of this, an optimization method of the car air pressure curve has been proposed to improve elevator performance as well as the comfort of passengers’ ears. To resolve the design problem of high-speed elevator car air pressure curves, a theoretical elevator car air pressure adjustment curve is suitably selected. Based on the selected curve, a theoretical elevator car air pressure curve (THEC-APC) multi-performance optimization method utilizing (competitive mechanism based multi-objective particle swarm optimizer) CMOPSO is proposed. In addition, after the optimization solution is obtained, the THEC-APC is smoothed for the variable destination floor to reduce the effect of the sudden changes in the air pressure curve. A general depiction of the proposed method is shown in
Figure 1.
The remainder of this paper is organized as follows. Three theoretical car air pressure adjustment curves are introduced in
Section 2. The THEC-APC multi-performance optimization method is proposed in
Section 3, including multi-performance objectives, optimization variables, and the optimization algorithm. In
Section 4, the THEC-APC smoothing method is proposed. To verify the proposed method, a numerical experiment is conducted on a KLK2-type high-speed elevator design. Finally, a conclusion is presented in
Section 6.
2. Theoretical Elevator Car Air Pressure Adjustment Curve Selection
Before formulating the air pressure compensation scheme for high-speed elevator cars, the THEC-APC needs to be designed to obey the air pressure compensation system. The theoretical curve should be converted into stored data that can be generated online or offline, according to certain principles; this establishes the pressure compensation control. Unlike elevator speed curves, which have been heavily studied, there is not enough research to standardize the THEC-APC. According to the existing research on high-speed elevator car air pressure adjustment schemes, the THEC-APC can be summarized into the following three types:
In this situation, there are no air pressure compensation measures conducted for the inside of the elevator car. The air inside and outside the elevator car are freely exchanged through the ventilation fan and the leaking gap. At this time, the air pressure curve in the car changes with the height of the elevator. In general, the air pressure adjustment curve changes slowly when the elevator starts and brakes, and changes drastically in the middle high-speed stage, which is shown as the black curve in
Figure 2.
- (b)
Fixed Adjustment Type
In this situation, the inlet ventilation fan performs simple active compensations for the air pressure inside the car. The air compensation rate remains constant, which shapes the fixed-adjustment-type air pressure adjustment curve into a straight line. This is shown as the blue curve in
Figure 2. Compared with the non-control-type curve, the fixed-adjustment-type curve can slightly reduce the rate of air pressure change in the middle high-speed stage.
- (c)
Stepped-Segmentation Adjustment Type
In this situation, the adjustment curve is divided into several segments. Through this multiple-stepped-segmentation air pressure control, passengers can achieve air flow between the outside world and their middle ear cavities in a short period of time, thereby eliminating ear pressure and reducing the time of discomfort. This is shown as the red curve in
Figure 2.
In this paper, the stepped-segmentation adjustment-type curve is utilized as it is shown in
Figure 3. In this adjustment-type curve, the air pressure in the elevator car increases in steps. The air pressure in the elevator car is first compensated with a large air pressure change rate in a short period of time. In this period, the passenger can be fully aware of the pressure change and perform active swallowing actions to balance the air pressure inside and outside the ear canal. At the mean amount of time, this helps to ease the abnormal feeling of the ear [
36,
37]. For the subsequent period of time, the air pressure is maintained within a small variation range so that passengers are given enough time to adjust. The lines with arrows in
Figure 3 represents the amounts and the directions of compensation required for the air pressure adjustment.
The stepped-segmentation air pressure adjustment method can eliminate the ear blocking feeling caused by pressure change in an elevator car, and can greatly reduce a passenger’s discomfort time. Following
Figure 3, a curve function model is established as follows:
where
denote the air pressure change rate in each segment of the adjustment curve, and
denotes the
k-th segment point on the THEC-APC.
4. THEC-APC Smoothing for Variable Destination Floor
The THEC-APC obtained using the CMOPSO algorithm is only a simple segmented polyline. In practice, there is a sudden change in the air pressure change when the fan compensates for the car, which the pressure compensation system cannot achieve. Therefore, it is necessary to smooth the THEC-APC. For computational complexity, a Bezier curve is adopted to smooth the THEC-APC. To ensure that the compensation amount of the fan does not change suddenly during the entire compensation phase, the Bezier curve can be determined according to the position vector (
) of given
N + 1 points:
where
is the basis function for the following calculation method:
Meanwhile, the Bezier curve should satisfy the following conditions:
If the curve function of the THEC-APC is expressed as
P(
t), the adjustment amount of one of the corresponding curves is
. To prevent sudden changes in the barometric compensation rate at the turning point and to avoid drastically changing the shape of the THEC-APC, two reference points (
) on both sides of the turning point are selected. These two reference points along with the turning point can be used for the Bezier curve smoothing. The second-order Bezier curve equation connecting these three points can be expressed as:
In the actual high-speed elevator operating cases, the destination floor is not fixed. When the destination floor changes, there will be a pressure difference between the inside and outside of the car, and this will cause the car door to become difficult to open and passengers to feel uncomfortable when the door is opened due to the sudden air flow. To this end, the THEC-APC should be further adjusted, as shown in
Figure 9. Suppose a scenario in which a high-speed elevator moves from departure floor a to destination floor b; if the passengers at any time modify the destination floor to floor c, then the curve dynamic adjustment function can be expressed as:
where
is the exact time that the target floor changes;
and
denote each corresponding THEC-APC before dynamic adjustment, respectively;
denotes the THEC-APC after dynamic adjustment; and
.
5. Numerical Experiment Verification
The KLK2-type high-speed elevator from Canny Elevator Co., Ltd. is utilized as the verification elevator. The proposed method is used in the KLK2 (Canny Elevator Co., Ltd., 2015, Suzhou) high-speed elevator THEC-APC design process. A random generating method is adopted to initial the air pressure parameter samples of the KLK2 elevator car. The initial samples are optimized based on the CMOPSO optimization algorithm. The particles can be expressed as
, where
k denotes the
k-th generation particle population during sample update,
i denotes the
i-th particle in a specific particle population, and
j denotes the
j-th steps. To address the problem of the traditional particle swarm algorithm with many parameter settings and irrational parameter values, the CMOPSO algorithm based on a competition mechanism was selected to solve the THEC-APC multi-objective optimization problem. The particle swarm was initiated according to the optimization parameters, with an initial population number of 200 and a termination of iterations number set to 200. The algorithm parameters of CMOPSO
and
were 0.8. The maximum inertia factor was 1.2 while the minimum inertia factor was 0.1. When the number of iterations was 32, the optimal solution in the offspring population reached the iteration termination condition. The optimal solution of THEC-APC for 100 high-speed elevator cars is shown in
Table 2. The height of the selected elevator test tower was 280 m, and the pressure difference between the departure floor and the destination floor was about 3300 Pa. In the verification test, the elevator started from the bottom of the test tower and ran uninterrupted to the top of the test tower. As is illustrated in
Section 3, the pressure change of each segment of the segmented adjustment curve was set to a reasonable range of 500–2000 Pa. Therefore, in this verification test, the most reasonable number of segments for the TC-TAPC was three segments, and the eight design parameters that followed are listed in
Table 2. Meanwhile, the objective function values for 100 optimal solutions are shown in
Table 3.
The Pareto optimal solution distribution is shown in
Figure 10 after 32 iterations.
,
,
denote the passenger comfort index, energy-saving index, and precision pressure adjustment index, respectively.
When selecting the optimal solution, the principle of first ensuring the accuracy of the compensation then ensuring passenger comfort should be followed. Therefore, from the 200 optimal solutions obtained, the solution with the smallest difference in internal and external air pressure was selected (with a value of 5.7 Pa). The passenger comfort index (a value of 8921.5) was also acceptable in the optimal solution; meanwhile, the energy-saving index was 28275.6 J, and the precision pressure adjustment index was 5.7 Pa, corresponding to scheme No. 55. The detail of scheme No. 55 is shown in
Table 2. The THEC-APC can be determined by the optimized solution, as shown in
Figure 10. The smoothed THEC-APC is shown in
Figure 11 as well. The comparison results between the optimal stepped-segmentation curve and the non-control curve are shown in
Table 4.
Since the non-control-type curve only requires the exhaust fan to run at a constant speed to achieve the ventilation function, the total accumulation was lower than the segmented adjustment-type curve, and the compensation accuracy index was not much different. The segmented adjustment-type curve was significantly more comfortable for passengers than the non-control-type curve, which proves the practicability of the segmented adjustment-type curve. To ensure that the selected algorithm did not fall into the local optimal solution, two other typical non-dominant genetic algorithms were used to again determine the ideal air pressure adjustment curve of the elevator car and compared with the CMOPSO algorithm. The optimal solutions of each algorithm were selected as shown in
Table 5.
Table 5 shows that, based on the same optimal solution selection rules, the evaluation indexes corresponding to the optimal solution obtained by the CMOPSO algorithm were significantly better than the ones obtained by the MOPSO algorithm. At the same time, they were similar to the ones obtained by the NSGA-III algorithm, which proves the reliability and accuracy of the solution obtained by the CMOPSO algorithm. Considering the initialization of the multi-objective optimization algorithm, the certain randomness of the final result, and the subjectivity of the selection rule of the optimal solution, the convergence iterative process of the algorithms needed to be compared again, as shown in
Figure 12 and
Table 6.
Table 6 illustrates that, to obtain the optimal solutions with fewer iteration steps and an acceptable computation time, the CMOPSO algorithm showed a better algorithm performance than the NSGA-III and MOPSO algorithms. (Generation distance (GD) and inverted generation distance (IGD) reflect the similarity degree between the Pareto solution obtained by the algorithm and the real Pareto solution, for which the smaller, the better).