基于CAN總線的電梯智能控制系統(tǒng)呼梯控制器設(shè)計與開發(fā),基于,can,總線,電梯,智能,控制系統(tǒng),控制器,設(shè)計,開發(fā) Elevator planning with stochastic multicriteria acceptability analysis Abstract Modern elevator systems in high-rise buildings consist of groups of elevators with centralized control. The goal in elevator planning is to configure a suitable elevator group to be built. The elevator group must satisfy specific minimum requirements for a number of standard performance criteria. In addition, it is desirable to optimize the configuration in terms of other criteria related to the performance, economy and service level of the elevator group. Different stakeholders involved in the planning phase emphasize different criteria. Most of the criteria measurements are by nature uncertain. Some criteria can be estimated by using analytical models, while others, especially those related to the service level in different traffic patterns, require simulations. In this paper we formulate the elevator planning problem as a stochastic discrete multicriteria decision-making problem. We compare 10 feasible elevator group configurations for a 20-floor building. We evaluate the criteria related to the service level in different traffic situations using the KONE Building Traffic Simulator, and use analytical models and expert judgments for other criteria. The resulting decision problem contains mixed type criteria. Some criteria are represented by the multivariate Gaussian distribution, others by deterministic values and ordinal (ranking) information. To identify configurations that can best satisfy the goals of the stakeholders, we analyze the problem using the stochastic multicriteria acceptability analysis (SMAA) method. Keywords: Stochastic multicriteria acceptability analysis (SMAA); Elevator planning; Multicriteria; Simulation Article Outline 1. Introduction 2. Elevator planning 3. The SMAA methods 4. Simulation model and simulation results 5. Decision-making problem and SMAA analysis 6. Conclusions Acknowledgements 1. Introduction In modern high-rise buildings workers and inhabitants are transported between floors mainly by means of multiple elevators. Elevators are usually operated by elevator group control systems in order to provide efficient transportation. When a high-rise building is designed, a suitable configuration for the elevator group has to be designed. The decision makers (DMs) should consider performance as well as price and other non-performance criteria of alternative elevator group configurations. Because analytical methods are limited to the up-peak traffic situation and cannot evaluate the effect of a group control algorithm, the performance has to be measured using computer simulation, which produces stochastic measurements for the performance criteria of alternative configurations. The performance of an elevator group can be measured using several criteria, such as the average waiting time (WT) or the average ride time of the passengers. The price and other non-performance criteria can usually be assessed with sufficient accuracy or by ranking the alternatives. Different DMs may have different preferences for the criteria. For example, some DMs pay attention to the average WT while others think that the percentage of long WTs is more important since it represents the fairness in service. The builder may stress the amount of floor space used by the elevator system. There are usually some trade-offs and dependencies between criteria. The problem of elevator planning can thus be considered as a discrete multicriteria decision-making problem with multiple DMs and stochastic criteria measurements. We are interested in finding a compromise solution which takes into account different possible preferences of DMs, and thus we have chosen to analyze the problem using the SMAA method. SMAA methods have been developed for discrete multicriteria decision-making problems, where criteria measurements are uncertain or inaccurate and where it is for some reason difficult to obtain accurate or any preference information from the DMs [1]. Usually the preference information is modelled by determining importance weights for criteria. The SMAA methods are based on exploring the weight space in order to describe the preferences that would make each alternative the most preferred one, or that would give a certain rank for a specific alternative. In the original SMAA method [2] the weight space analysis is performed based on an additive utility or value function and stochastic criteria measurements. The SMAA-2 method [1] generalized the analysis to a general utility or value function, to include various kinds of preference information and to consider holistically all ranks. The SMAA-O method [3] extends SMAA-2 for treating mixed ordinal and cardinal criteria in a comparable manner. SMAA is suitable for solving problems also when the uncertainties of criteria measurements are dependent [4]. Elevator planning research has a long history. The operative performance has been studied over decades [5] and [6]. The up-peak interval and the up-peak handling capacity has been analyzed in many publications in the 1960s, see, e.g. [7], [8] and [9]. The patience of passengers and what should be considered good service in different types of buildings has been studied since 1940s according to [10]. Earliest applications of simulation to elevator planning are from the 1960s [11] and [12]. There are also more recent applications in all areas of elevator planning, but in practice normal elevator groups are still designed using methods from the 1960s. In this paper we present a multicriteria method that allows to use stochastic simulator output in the decision analysis. We consider a realistic elevator planning problem, which consists of a 20-floor building for which one of 10 possible elevator group configurations has to be chosen. We will analyze the alternative configurations using the KONE Building Traffic Simulator. Based on the output of the simulator, we form a multicriteria decision-making problem, which we analyze using SMAA. To our best knowledge, we are the first to apply a stochastic MCDA method in elevator planning. We have chosen to use SMAA in the decision analysis, because it is the only MCDA methodology that allows multivariate Gaussian distributed criteria measurements. This paper is organized as follows: Section 2 introduces the reader to the area of elevator planning, and Section 3 to SMAA methods. In Section 4, we present the simulator that is used to generate the data, and the simulation results. We define the decision-making problem and present the SMAA analysis in Section 5. Section 6 ends this paper with conclusions. 2. Elevator planning The goal in elevator planning is to find a suitable elevator group to serve the traffic of a high-rise building. Because the buildings do not exist at the planning stage, the traffic must be estimated by using the building specifications: the number of floors, their heights, the floor area and the building type. The travel height can be calculated from the number of floors and their heights, and the total population can be estimated according to the type of building and the floor area. Building types have characteristic traffic profiles. For example, office buildings typically have up-peak traffic in the morning when employees enter the building, intense two-way or inter-floor traffic during the lunch time, and down-peak traffic when employees exit the building [13]. The performance of a group of elevators is mainly determined by the number and size of the cars and their speed. Also acceleration, door types and the group control algorithm affect performance. Usual performance criteria are the handling capacity and the interval calculated in the up-peak situation. The up-peak handling capacity is the percentage of population per 5?min that can be transported from the lobby to the upper floors. It is assumed that elevators are filled to 80% of rated load (although it is possible to fill elevator up to rated load that does not happen in practice). The (up-peak) interval is an interval between two starts from the lobby. The interval is also related to the WT. The up-peak is used since it is the most demanding situation considering elevator handling capacity at least in office buildings, and because there are analytical formulas for calculating the up-peak handing capacity and interval [14]. The usual recommendations state that the up-peak handling capacity for an office building should be 11–17% and interval 20–30s [15]. Non-performance criteria, such as cost and occupied floor area should also be considered. The cost of an elevator system consists of build and maintenance costs. The floor area occupied by the elevator group consists of the shaft space and the waiting area for passengers. In high-rise buildings the population is large and distances are long, thus the portion of shafts is large compared to the total floor area. This means more costs, since the rentable area is reduced. In some cases the building design constrains the occupied area, sometimes there is more freedom to use space. The elevator planning is not independent of building design; the architect should take advice from the elevator planner. Instead of considering only up-peak traffic, we take into account the entire daily traffic and consider all criteria simultaneously. In the study presented in this paper we consider the following six criteria. The cost and area criteria take into account the building owners point of view. Passengers point of view is taken into account by WT, journey time (JT), the percentage of WTs exceeding 60s (WT60), and the percentage of JTs exceeding 120s (JT120). The WT is measured from the moment a passenger enters the waiting area to the moment he/she enters the elevator. The JT is the total time from entering the waiting area to exiting the elevator. The last two criteria measure unsatisfactory service, which may happen especially in intense traffic peaks. 3. The SMAA methods The SMAA-2 method [1] has been developed for discrete stochastic multicriteria decision-making problems with multiple DMs. SMAA-2 applies inverse weight space analysis to describe for each alternative what kind of preferences make it the most preferred one, or place it on any particular rank. The decision problem is represented as a set of m alternatives {x1,x2,…,xm} that are evaluated in terms of n criteria. The DMs’ preference structure is represented by a real-valued utility or value function u(xi,w). The value function maps the different alternatives to real values by using a weight vector w to quantify DMs’ subjective preferences. SMAA-2 has been developed for situations where neither criteria measurements nor weights are precisely known. Uncertain or imprecise criteria are represented by stochastic variables ξij with joint density function fX(ξ) in the space XRm×n. We denote the stochastic criteria measurements of alternative xi with ξi. The DMs’ unknown or partially known preferences are represented by a weight distribution with joint density function fW(w) in the feasible weight space W. Total lack of preference information is represented in ‘Bayesian’ spirit by a uniform weight distribution in W, that is, fW(w)=1/vol(W). The weight space can be defined according to needs, but typically, the weights are non-negative and normalized, that is; the weight space is an n-1 dimensional simplex in n dimensional space: (1) The value function is used to map the stochastic criteria and weight distributions into value distributions u(ξi,w). Based on the value distributions, the rank of each alternative is defined as an integer from the best rank (=1) to the worst rank (=m) by means of a ranking function (2) where ρ(true)=1 and ρ(false)=0. SMAA-2 is then based on analyzing the stochastic sets of favorable rank weights (3) Any weight results in such values for different alternatives, that alternative xi obtains rank r. The first descriptive measure of SMAA-2 is the rank acceptability index , which measures the variety of different preferences that grant alternative xi rank r. It is the share of all feasible weights that make the alternative acceptable for a particular rank, and it is most conveniently expressed percentage wise. The rank acceptability index is computed numerically as a multidimensional integral over the criteria distributions and the favorable rank weights as (4) The most acceptable (best) alternatives are those with high acceptabilities for the best ranks. The central weight vector is the expected center of gravity (centroid) of the favorable first rank weights of an alternative. The central weight vector represents the preferences of a ‘typical’ DM supporting this alternative. The central weights of different alternatives can be presented to the DMs in order to help them understand how different weights correspond to different choices with the assumed preference model. The central weight vector is computed numerically as a multidimensional integral over the criteria distributions and the favorable first rank weights using (5) The confidence factor is the probability for an alternative to obtain the first rank when the central weight vector is chosen. The confidence factor is computed as a multidimensional integral over the criteria distributions using (6) Confidence factors can similarly be calculated for any given weight vectors. The confidence factors measure whether the criteria measurements are accurate enough to discern the efficient alternatives. The uncertainty of the criteria measurements can be modelled very flexibly in SMAA methods by using an appropriate joint distribution fX(ξ). If the uncertainties are independent, then separate distributions fij(ξij) can be used for each measurement. Simple parametric distributions, such as the uniform and normal distribution may be suitable in many applications. When the uncertainties of the criteria measurements are dependent, then the dependent parameters can be represented by a joint distribution. The multivariate Gaussian (normal) distribution is particularly suitable, because it is theoretically well understood and yet it approximates well many real-life phenomena. Use of the multivariate Gaussian distribution with SMAA is described in more detail in [4]. There are several different ways to handle partial preference information in SMAA methods [1]. In the decision-making problem considered in this paper, we apply interval constraints for weights. For more information about this technique, see [16]. 4. Simulation model and simulation results To obtain stochastic criteria measurements for the performance criteria, we executed simulations with the KONE Building Traffic Simulator [17] and [18]. The simulation model consists of the elevator model and traffic generation. Features of the model are: ? Floors have landing call buttons. Entering passenger gives a call to the (up/down) direction where he is heading. ? The group control algorithm allocates the call to the most suitable elevator. The algorithm is a genetic algorithm [19], which optimizes WTs. The group control has also a returning algorithm which sends the elevator back to the lobby to wait for a call. The returning algorithm is necessary in the incoming traffic situation. ? A stopping elevator opens doors, exiting passengers get out, entering passengers get in and the doors are closed. The simulator has delays related to door opening, entrance, exit and door closing. ? An elevator can take passengers up to the maximum load, which is about 80% of the cars rated load. If the load exceeds bypass load (about 80% of maximum load), an elevator does not accept new landing calls. The loads are expressed in persons. ? An elevator cannot reverse direction with passengers aboard. ? An elevator accelerates smoothly to the rated speed, provided that the distance is long enough. The smoothness is modelled by the acceleration derivative jerk, which is . The deceleration is an inverse to the acceleration phase. ? The passengers arrive to different floors approximately according to a Poisson process. This means that the inter-arrival times follow the exponential distribution, f(x)=αe-αx, where α is the arrival rate. ? There is one entrance floor and rest of the floors are populated floors. Traffic consists of three components: incoming, outgoing and inter-floor components. Incoming passengers travel from an entrance floor to populated floors, outgoing passengers from populated floors to the entrance floor and inter-floor passengers between populated floors. Intensity of traffic and the percentages of incoming, outgoing and inter-floor passengers are determined by traffic parameters. The traffic profile determines the intensity and the portions of traffic components at each moment. The intensity is expressed as portion of population per time unit. The passengers are generated as follows: (1) The simulator generates the expected number of passengers to a 5-min period and assigns them random entry times. The number of passengers is the total population multiplied by the traffic intensity. (2) The traffic component of passenger (incoming, outgoing or inter-floor) is chosen randomly according to the traffic profile. (3) The component determines whether the arrival and destination floors are entrance or populated floors: (a) If the floor is a populated floor, the probability of the floor is proportional to the floor population. (b) If independently generated arrival and destination floors happen to be equal (can happen with an inter-floor passenger), the floor generation is repeated. Table 1 shows characteristics of the simulated building. The building has a lobby floor and 19 populated floors. The estimated number of people is 60 per floor. Table?1. Characteristics of the simulated building Characteristic Value Floors 20 Floor height (m) 4.2 Travel (m) 78 Floor area (m2/floor) 1000 Rentable area (m2/floor) 800 Persons per floor 60 Persons total 1140 Fig. 1 shows the intensities of incoming, outgoing and inter-floor passengers during the day from 7?a.m. to 7.15?p.m. The traffic profile is measured from an office building. The profile shows typical morning, lunch time and afternoon traffic peaks. When passengers are generated according to the traffic profile, the expected number of passengers are 11?502. Since total population of the building is uncertain, the traffic is varied between 80% and 120% of forecasted traffic. With these parameters, we generated 21 traffic situations according to the traffic profile. The same passengers were used for all 10 alternatives in order to reduce the covariance between the measurements of different alternatives. Fig.?1.?Traffic profile of the simulated building [13] Siikonen ML, Lepp?l? J. Elevator traffic pattern recognition. In: Proceedings of the fourth world congress of the international fuzzy systems association, Brussels, Belgium; 1991. p. 195–8.[13]. Table 2 shows 10 alternative configurations. The number of elevators varies between 6 and 8, rated load from 13 to 24 and speed from 3.5 to 5?m/s. Area is the shaft space plus waiting area space. The exact costs are unknown. The costs are ranked from 1 to 10, where 1 is the cheapest and 10 is the most expensive. All alternatives are feasible with respect to up-peak handling capacity and interval. Table?2. Alternative configurations of the elevator group Name Elevators Rated load Speed (m/s) Acceleration (m/s2) Area (m2) Cost E6L17S4 6 17 4.0 1.0 69.8 1 E6L21S4 6 21 4.0 1.0 77.4 2 E6L17S5 6 17 5.0 1.0 71.4 3 E6L24S4 6 24 4.0 1.0 87.2 4 E7L17S35 7 17 3.5 0.8 87.5 5 E7L17S4 7 17 4.0 1.0 87.5 6 E7L13S5 7 13 5.0 1.0 76.0 7 E7L17S5 7 17 5.0 1.0 89.5 8 E8L13S35 8 13 3.5 0.8 79.4 9 E8L17S35 8 17 3.5 0.8 93.5 10 Simulation results are presented in Fig