CN110654949B - Method for determining safe remaining service life of elevator under maintenance condition - Google Patents

Method for determining safe remaining service life of elevator under maintenance condition Download PDF

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CN110654949B
CN110654949B CN201810700390.1A CN201810700390A CN110654949B CN 110654949 B CN110654949 B CN 110654949B CN 201810700390 A CN201810700390 A CN 201810700390A CN 110654949 B CN110654949 B CN 110654949B
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elevator
maintenance
index
service life
preventive maintenance
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CN110654949A (en
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石振锋
李琪
孙尚
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Harbin Institute of Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B66—HOISTING; LIFTING; HAULING
    • B66B—ELEVATORS; ESCALATORS OR MOVING WALKWAYS
    • B66B5/00—Applications of checking, fault-correcting, or safety devices in elevators
    • B66B5/0006—Monitoring devices or performance analysers
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Abstract

The invention discloses a method for determining the remaining service life of elevator safety under the condition of maintenance, belonging to the field of determining the irregular maintenance time interval and the remaining service life of an elevator based on elevator operation and maintenance big data and relating to the establishment of a model and the innovation of an algorithm; the technical scheme is as follows: (1) determining an elevator safety residual service life model and a slope threshold; (2) determining the elevator performance after preventive maintenance through a performance recovery factor and a performance reduction rate expansion factor; (3) and determining a safe remaining service life model after the ith preventive maintenance according to the result of the step 2. The invention establishes an elevator safety residual service life model which can determine the maintenance time interval and predict the residual service life, so that the model has higher practicability, and the existing method is optimized and innovated by combining the specific industry background of elevator equipment, so that the model is more reliable. The model obtained by the invention has practicability and is more reliable.

Description

Method for determining safe remaining service life of elevator under maintenance condition
Technical Field
The invention belongs to the field of determining irregular maintenance time intervals and residual service lives of elevators based on elevator operation and maintenance big data, and relates to model establishment and algorithm innovation.
Background
With the continuous improvement of the urbanization level and the living standard of people in China, the number of elevators is increased in a blowout manner, and the elevators are used more frequently. The elevator as a travel tool is inseparable from the daily life of people, so that the elevator safety also becomes a civil engineering concerned by the people and media. In recent years, elevator safety accidents happen occasionally, and great psychological shadows are left for people in elevator people eating events, car type elevator sudden falling events and the like. The frequent occurrence of the elevator safety events indicates that the existing elevator maintenance system in China has certain disadvantages. The elevator is not in line with economic benefits because the elevator is scrapped without maintenance, the maintenance of the elevator is divided into post-fault maintenance and preventive maintenance, the former is emergency repair after the elevator breaks down, and the latter is preventive maintenance before the elevator breaks down, which is carried out by an elevator maintenance department according to an elevator maintenance system in China, so that the performance of the elevator is improved, and the service life of the elevator is prolonged. At present, China implements a regular maintenance system for elevators, namely, preventive maintenance is carried out on the elevators every 15 days, and the regular preventive maintenance of the elevators has certain disadvantages although the occurrence of elevator safety accidents can be avoided to a certain extent and the remaining service life of the elevator safety is prolonged. The elevator is a loss type device, and the elevator device can be divided into an early fault period, a sporadic fault period and a fault loss period according to the attenuation rule of the elevator performance. When the elevator enters a loss period, the failure rate of the elevator equipment gradually rises, the performance of the elevator gradually falls, and the risk of elevator safety accidents can be increased if preventive maintenance is still performed on the elevator every 15 days along with the accumulation of time.
Through the examination of relevant documents, most researches have been carried out to solve the optimal time interval and maintenance times in a given time region or directly predict the remaining service life of the equipment, although relatively remarkable research results are obtained in the field of maintenance time interval and remaining service life of mechanical equipment at present.
Disclosure of Invention
The main objective of this patent is based on the safe remaining life statistical model of elevator is established to elevator fortune dimension management big data, describes elevator safety remaining life curve, realizes the prediction to elevator preventive maintenance time interval and elevator time point of scrapping (promptly elevator safety remaining life), finally realizes applications such as the safety precaution to the elevator. In the research process, two situations of no maintenance and maintenance are considered, and the elevator safety residual service life model is respectively established, wherein the elevator is scrapped without maintenance in the case of no maintenance, and the elevator is scrapped after normal maintenance in the case of maintenance. Different research methods are fused and innovated, and a reliable elevator safety residual service life model is finally determined.
Firstly, the invention provides a method for determining the safe remaining service life of an elevator under the condition of no maintenance:
the performance of each part of the elevator equipment in the initial operation stage is good, the operation state is stable, and generally, maintenance is not needed. However, once the elevator equipment enters a loss period, the running reliability of the equipment is continuously reduced along with the accumulation of time, and when the running reliability of the equipment is reduced to a certain specified threshold value, the safety residual service life of the elevator is exceeded, and the equipment needs to be subjected to first preventive maintenance. Before the first preventive maintenance, a model of the remaining service life of the elevator safety without maintenance can be established, determining the time interval from the current moment to the first preventive maintenance. The process of model building is shown in fig. 1: (1) monitoring the elevator operation index at any moment, constructing an elevator operation index system, and selecting a relevant index to perform weighted average to obtain a subsystem comprehensive index; (2) dividing the monitoring samples containing the comprehensive indexes into elevator health running state grades for classifying the running indexes contained in the index system into a certain elevator health running state grade; (3) constructing an elevator life index according to an elevator operation index system; (4) predicting the life index of the elevator at the future moment based on a BP neural network algorithm; (5) and determining the safe remaining service life curve of the elevator under the condition of no maintenance by utilizing Weibull distribution.
The step (1) is specifically as follows: monitoring the elevator operation indexes at any moment to obtain monitoring samples, wherein each monitoring sample comprises all the elevator operation indexes obtained by monitoring at the moment; respectively determining the influence weight of the indexes of each subsystem on an evaluation object based on principal component analysis, respectively processing the indexes of each subsystem in a weighted average mode, and finally determining the respective comprehensive index X of each subsystem1,X2,X3,X4Respectively representing the healthy running states or the reliability of a car system, a tractor system, a door system and a dragging system of the elevator equipment; the indexes in the subsequent steps are all comprehensive indexes.
The related index is an index related to the service life of the elevator, namely the change condition of the index can represent the residual service life condition of the elevator equipment to a certain extent. According to the relevant data, the running system of the elevator is roughly divided into four parts, each subsystem corresponds to different specific running state indexes of the elevator, and the specific system division is shown in the table 1.
TABLE 1 Elevator operating status indicator System overview
Figure GDA0002750676650000021
The relevant index is the index described in the column "specific index" in table 1.
The occurrence of abnormality of any one relevant index can cause the service life of the elevator to be terminated, and the overall degradation of the index represents the sharp shortening of the residual service life of the elevator, so that the running state index of the elevator can be used for measuring and predicting the residual service life condition of the elevator.
Although the 17 indexes in table 1 all represent the operation state of the elevator, the too large sample dimension not only increases the complexity of the research, but also needs to select an index system because the collinearity among the indexes influences the final analysis result. Aiming at a specific elevator background, 17 indexes form four operation systems of the elevator, a principal component analysis theory is introduced, influence weights of the indexes of 4 subsystems on an evaluation object are respectively determined based on principal component analysis, and 4 comprehensive indexes X are finally determined in a weighted average mode1,X2,X3,X4Respectively, representing the healthy running state (or reliability) of the elevator equipment car system, the traction machine system, the door system and the dragging system. Through the index selection, the dimensionality is reduced, the complexity of subsequent research is reduced, the problem of collinearity among original indexes is solved, and the reliability of the model is guaranteed.
The step (2) is specifically as follows: clustering the elevator operation index monitoring data by using a fuzzy C-means clustering algorithm in unsupervised learning, dividing monitoring samples into three categories of 'excellent', 'good' and 'medium' to obtain three categories of clustering centers, and when fuzzy clustering is performed, using the clustering center determined by using a traditional system clustering method as an initial clustering center of the fuzzy clustering.
The health running state of the elevator can be judged by utilizing a data mining means through various monitoring index data of the elevator. The healthy operating state of an elevator is a measure of the operational reliability of an elevator installation. Along with the accumulation of time, the health state of the elevator equipment is worse and worse, the running reliability is gradually reduced, and when the health state is reduced to a certain degree, the elevator is scrapped, namely, the elevator reaches the retirement age. In order to qualitatively measure the healthy running state of the elevator, the healthy running state of the elevator can be classified into four grades of "excellent", "good", "medium" and "poor". And provides that the elevator is immediately taken out of service as soon as its operation monitoring data at a certain moment falls into the "bad" class, representing the end of life of the elevator. Therefore, when the monitoring data are classified and the health state grades of the elevators at different moments are judged, the monitoring data are classified into three types of "excellent", "good" and "medium", and the clustering centers of the three types are obtained.
Here, the elevator monitoring data is clustered using an algorithm of fuzzy C-means clustering in unsupervised learning, and fuzzy clustering is also one of the clustering algorithms. In fuzzy clustering, in order to reduce the iteration times and improve the iteration efficiency, the clustering center determined by the traditional system clustering method is used as the initial clustering center of the fuzzy clustering,
the step (3) is specifically as follows: the life index Ra of the elevator is expressed by a weighted rank-sum ratio WRSR, and the life index Ra comprises:
Figure GDA0002750676650000031
wherein, wjThe weight of the impact of the jth index on the evaluation object, rijThe rank of the jth index of the ith monitoring sample is obtained, and the ith monitoring sample contains all elevator operation indexes obtained by the ith monitoring; in step (2), the monitoring samples have been classified into three categories of "excellent", "good", and "medium", and the influence weight of each evaluation index is determined by calculating a correlation coefficient between each index and a category variable, which is known to be "excellent", "good", and "medium", of the three categories
xi＝(xi1,xi2,…,xim)(i＝1,2,…,n)
For n monitoring samples, c ═ c1,c2,…,cn) The fuzzy clustering result corresponding to each sample is the concrete representation form of the category variable, and the category variable is recorded
Figure GDA0002750676650000032
The absolute value of the correlation coefficient between the jth evaluation index and the category variable is shown, and the influence weight of the jth evaluation index on the evaluation result is as follows:
Figure GDA0002750676650000041
so that the life index Ra of the elevatoriThe calculation formula of (2) is as follows:
Figure GDA0002750676650000042
the elevator life index is a performance index which is constructed based on an original monitoring index of an elevator and can explain the health state of the elevator, the smaller the elevator life index is, the worse the health running state of the elevator is, the shorter the safe remaining service life is, and the value is between [0 and 1 ]. Thus, the elevator life index can be regarded as a measure of the overall performance change of the elevator, similar to the reliability of the elevator installation, which tends to decline over time.
And constructing an elevator life index by using a rank-sum ratio comprehensive evaluation method. The comprehensive rank-sum ratio evaluation method is widely applied at present, and prominent research results are obtained in the fields of quality control, forecast prediction, medical health and the like. In the patent, the method is expected to be applied to the field of mechanical equipment performance evaluation, and innovation of the application field is realized.
The RSR statistic value in the rank-sum ratio comprehensive evaluation method is between [0 and 1], and no matter what situation is, the larger the statistic is, the better the statistic is, the characteristics of the elevator service life index are met, and the comprehensive evaluation on the healthy running state of the elevator at different moments can be realized.
In this patent, the elevator life index Ra is represented by a weighted rank-sum ratio WRSR, and there are:
Figure GDA0002750676650000043
wherein, wjThe weight of the impact of the jth index on the evaluation object, rijRank of j index for ith monitor sample. In the fuzzy clustering, the detection samples have been classified into three categories of "excellent", "good", and "medium", and the influence weight of each evaluation index can be determined by calculating a correlation coefficient between each index and a category variable, which refers to three categories of "excellent", "good", and "medium", and is known
xi＝(xi1,xi2,…,xim)(i＝1,2,…,n)
For n monitoring samples, c ═ c1,c2,…,cn) The fuzzy clustering result corresponding to each sample is the concrete representation form of the category variable, and the category variable is recorded
Figure GDA0002750676650000044
The absolute value of the correlation coefficient between the jth evaluation index and the category variable is shown, and the influence weight of the jth evaluation index on the evaluation result is as follows:
Figure GDA0002750676650000051
therefore, the formula for calculating the life index Ra of the elevator is:
Figure GDA0002750676650000052
the step (4) is specifically as follows:
firstly, taking sample monitoring values of an elevator for any continuous p times as input nodes, taking sample monitoring values of the p +1 th time as output nodes, setting the number of hidden layer nodes as N, and training a BP neural network;
secondly, predicting the healthy running state of the elevator at the future time by using the trained BP neural network model:
calculating the distance between the prediction sample and the centers of three types of fuzzy clustering, namely 'excellent', 'good' and 'middle', and dividing the running state grade of a new prediction sample;
if the predicted samples are classified as "middle", then a distance threshold ε is set1Used for judging whether the running state of the elevator enters a 'difference' class or not, and once the distance between a prediction sample and a 'middle' class exceeds epsilon1If so, stopping prediction, and considering that the running state grade of the elevator is classified into a difference class, wherein the point is a scrapping point or a service life end point of the elevator; epsilon1The specific setting method is as follows:
calculating the distance d between all the monitored samples in the 'middle' class and the cluster center of the class by using the fuzzy clustering result3i(i ═ 1,2, …, n), and defines ε1＝max{d3i}(i＝1,2,…,n).
Suppose that the distance threshold ε is exceeded at the first prediction1The time monitoring interval between successive samples is known as Δ t*Then, without maintenance, the safe remaining life of the elevator is l x Δ t from the current moment*That is, the time interval from the current moment to the first preventive maintenance is obtained, namely the remaining service life of the elevator without maintenance.
The method has the advantages that the BP neural network is used for predicting the healthy running state of the elevator equipment at the future moment, so that the structural relation of continuous time point monitoring data can be accurately fitted, and the model error can be minimized. It is known that elevator equipment monitoring data are classified into three categories of "excellent", "good" and "medium" according to a fuzzy C-means clustering algorithm, and three categories of clustering centers are obtained; the elevator life index which integrally describes the healthy running state of the elevator at the current moment and the elevator life index of the center of each type can be obtained based on the original sample monitoring data through an order and ratio comprehensive evaluation method.
The method for predicting the healthy running state of the elevator at the future time based on the BP neural network algorithm comprises the following specific steps: (again assume that there are n monitoring samples x1,x2,…,xn)：
Firstly, as the monitoring data are all time sequence data, sample monitoring values of the elevator for any continuous p times can be used as input nodes, the sample monitoring value of the p +1 th time is used as an output node, the number of hidden layer nodes is set to be N, and a BP neural network is trained;
secondly, predicting the healthy running state of the elevator at the future time by using the trained BP neural network model;
and thirdly, calculating the distance between the prediction sample and the centers of the three types of fuzzy clustering, namely 'excellent', 'good' and 'middle', and dividing the running state grade of the new prediction sample. Since the healthy running state of the elevator is continuously attenuated along with the accumulation of time, the prediction samples can definitely show the trend of being always classified into the middle category as the prediction times are increased, the three categories can be completely separated at a certain time, the elevator enters the poor category, and the elevator is in a stop use state.
If the predicted sample is classified into the 'middle' class, setting a distance threshold epsilon1Used for judging whether the running state of the elevator enters a 'difference' class or not, and once the distance between a prediction sample and a 'middle' class exceeds epsilon1And stopping prediction, and considering that the running state grade of the elevator is classified into a difference class, wherein the point is a scrapping point or a service life end point of the elevator. Epsilon1The specific setting method is as follows:
calculating the distance d between all the monitored samples in the 'middle' class and the cluster center of the class by using the fuzzy clustering result3i(i ═ 1,2, …, n), may define ε1＝max{d3i}(i＝1,2,…,n).
Suppose that the distance threshold ε is exceeded at the first prediction1The time monitoring interval between successive samples is known as Δ t*Then, without maintenance, the safe remaining life of the elevator is l x Δ t from the current moment*I.e. the time interval from the current moment to the first preventive maintenance is obtained.
The step (5) is specifically as follows: the rule that the known elevator equipment has faults is subject to the distribution of a probability density function f (t), and the reliability function of the equipment is R (t). R (t) and f (t) have the following relationship:
Figure GDA0002750676650000061
where λ (t) is a fault rate function of the elevator installation;
the failure occurrence rule of the given elevator equipment follows Weibull distribution, and the corresponding equipment failure rate is expressed in the form that:
Figure GDA0002750676650000062
wherein alpha isiThe shape parameter represents the specific shape of the function curve of the failure rate of the mechanical equipment after the i-1 th preventive maintenance and before the i-th preventive maintenance; beta is aiThe scale parameter represents the time interval of two continuous failures of the equipment; the distribution function f (t) of the failure rate can be expressed as:
Figure GDA0002750676650000071
the reliability of the equipment is used for measuring the probability that the equipment can work stably, and the higher the reliability is, the better the elevator running state is; the elevator life index is used for measuring the healthy running state of the elevator, and the higher the elevator life index is, the healthier the running state of the elevator is, and the longer the remaining service life is. It can be found that the reliability has the same purpose as the elevator life index, and is used for measuring the running state of the elevator, and the higher the value is, the better the running state of the elevator is, so it can be guessed that the function form of the elevator life index is similar to the reliability function form, i.e. the distribution model of the remaining service life of the elevator can be represented by the reliability function of the elevator equipment, and there is ra (t) · r (t).
The relationship between the distribution model of the remaining service life of the elevator and the reliability of the elevator equipment after the i-1 th preventive maintenance and before the i-th preventive maintenance is as follows:
Figure GDA0002750676650000072
given that the elevator installation operates during the time period [0, t ], the reliability of the elevator at time t is defined as:
Figure GDA0002750676650000073
the left side and the right side of the formula (3) are simultaneously derived from the time t to obtain the following relation between the reliability function R (t) of the elevator equipment and the probability density function f (t) of the elevator fault occurrence rule:
Figure GDA0002750676650000074
the relationship between the reliability function of the elevator installation and the failure rate of the elevator is derived from equation (1), equation (2) and equation (4):
Figure GDA0002750676650000075
Figure GDA0002750676650000076
Figure GDA00027506766500000710
it is known that in the Weibull distribution,
Figure GDA0002750676650000077
and is provided with
Figure GDA0002750676650000078
The functional form of the safe remaining useful life curve after the i-1 th preventative maintenance to before the i-th preventative maintenance is therefore:
Figure GDA0002750676650000079
wherein alpha isi、βiDetermined by the specific elevator operating data; further, the functional form of the safe remaining service life curve under the condition of no maintenance, namely before the 1 st preventive maintenance, is determined as follows:
Figure GDA0002750676650000081
empirically, the curve should have a gradually decreasing trend and a gradually increasing rate of decrease. The general shape is shown in figure 2.
So far, the safety residual service life curve under the condition of no maintenance is well depicted, and the time point of first preventive maintenance of the elevator is determined.
Summary of model building Process
Suppose that an index system capable of representing the healthy running state of the elevator is determined according to relevant literature data, and comprises 4 subsystems: the elevator equipment comprises a car system, a tractor system, a door system and a dragging system, and has 17 specific indexes. Based on the sample monitoring data of the 17 specific indexes of the elevator system, the process of establishing the elevator safety residual service life model under the condition of no dimension is summarized as follows:
firstly, respectively carrying out principal component analysis on the original indexes of each subsystem, determining the comprehensive influence weight of the original indexes on an evaluation object according to the principal component analysis result, and obtaining four comprehensive indexes X through weighted average1,X2,X3,X4Respectively representing the healthy running states of the four subsystems of the elevator equipment. The original indexes involved in the subsequent research refer to the four comprehensive original indexes;
secondly, monitoring data of the monitoring samples are divided into three types of excellent, good and medium by using a fuzzy C-mean algorithm, and in order to reduce iteration times and improve efficiency, an initial clustering center is determined by using a traditional system clustering method;
constructing an elevator life index based on a rank-sum ratio comprehensive evaluation method, calculating the elevator life index corresponding to each observation sample, simultaneously obtaining the elevator life index corresponding to three clustering centers of fuzzy clustering, and converting n multiplied by 17 dimensional sample monitoring data into n multiplied by 2 dimensional data sets, wherein 2 dimensions respectively represent the elevator life index and the grade of the elevator healthy running state at the current moment;
fourthly, the prediction of the life index of the elevator at the future moment is finished based on a BP neural network algorithm, and the time interval of the first preventive maintenance is determined by setting a limiting condition;
carrying out curve fitting on the life index Ra of the elevator from the beginning of monitoring to the end of prediction, and determining based on Weibull distribution, so that the functional form of the safe remaining service life curve under the condition of finally determining no maintenance is as follows:
Figure GDA0002750676650000082
wherein alpha is1、β1Are unknown parameters and can be determined by specific elevator operation data.
In addition, the invention also provides a method for determining the safe remaining service life of the elevator under the condition of maintenance, which comprises the following steps:
the elevator safety residual service life model under the maintenance condition is expected to complete the work of determining the time interval between two continuous maintenance, predicting the elevator performance curve after preventive maintenance, determining the elevator scrapping time point and the like on the basis of the established elevator safety residual service life model under the maintenance-free condition. And the influence of the maintenance cost and the maintenance times on the maintenance time interval of the elevator and the residual service life of the elevator is given from the theoretical point of view. In the specific establishing process of the model, the next maintenance time of the elevator is determined by considering the slope of the function, and whether the elevator should be stopped using is judged by introducing the skill index. The flow chart of the establishment of the elevator safety residual service life model under the maintenance condition is shown in the figure 3: (1) determining a slope threshold of an elevator safety residual service life model; (2) determining the elevator performance after preventive maintenance through a performance recovery factor and a performance reduction rate expansion factor; (3) determining a safe remaining service life model after the ith preventive maintenance according to the result of the step 2
Figure GDA0002750676650000083
The next preventative maintenance time point is determined based on the slope threshold.
The method specifically comprises the following steps:
the preventive maintenance time interval of the elevator refers to the time interval between two adjacent preventive maintenance, and the normal operation of the elevator can be ensured only by performing the preventive maintenance on the elevator according to the regulations, so that the service life of mechanical equipment is prolonged. The patent considers that when the elevator is in different operation stages, the preventive maintenance time intervals are different, because in the initial operation stage, the performance of the elevator is stable, and the preventive maintenance time intervals are long; as the elevator installation enters the wear phase, the time interval between two successive preventive repairs becomes shorter and shorter. The time interval between two adjacent preventive maintenance can be determined by introducing the concept of a slope threshold.
The elevator service life ending point under the condition of no maintenance is actually the first maintenance time point of the elevator under the condition of maintenance, so the slope of the service life ending point under the condition of no maintenance can be set as a slope threshold and is recorded as epsilon2. Once the slope of the elevator safety remaining service life curve reaches within the threshold value range, it is considered that preventive maintenance should be carried out on the elevator at that moment.
After the elevator is maintained, the service life index of the elevator is recovered, but the recovery degree is different along with the increase of the maintenance times; in addition, the decay rate of the life index of the elevator after maintenance is faster than that of the elevator before maintenance under the same life index. For the two problems, firstly, an elevator performance recovery factor eta and a performance reduction rate expansion factor delta are given, which are respectively used for representing the recovery degree of the elevator performance after maintenance and the expansion degree of the performance reduction rate.
The elevator performance recovery factor η is affected not only by the maintenance cost when the elevator is subjected to preventive maintenance, but also by the maintenance frequency. Setting etaiRepresenting the performance recovery factor after i-th maintenance of the elevator, can be calculated for etaiThe following definitions are made:
ηi＝(b·cpi)ci
wherein cpiMaintenance cost for the ith preventive maintenance; b is an adjustment parameter, which is the adjustment of the maintenance cost when the elevator is preventively maintained, and
Figure GDA0002750676650000091
c is an adjustment parameter, is the adjustment of preventive maintenance times of the elevator and is more than 0 and less than 1; etaiIs taken to be [0,1]]In the meantime.
Suppose that the maximum and minimum values of the elevator life index before the i-th service are divided into Rai maxAnd Rai minThe index of elevator life, recorded as Ra, recovers after the i-th maintenancei+1 maxAnd the degree of recovery of elevator performance after the i-th maintenance is known to be etai. It can be empirically concluded that as the number of repairs increases, the elevator life index after each repair tends to decrease and that the elevator performance in the time interval between the i-th repair and the i-1 st repair decreases, for example by Rai max-Rai minAfter preventive maintenance, the descending indicator is allowed to rise, etaiRelative to the descending amplitude Rai max-Rai minDegree of recovery of, i.e. etaiCan be seen as an adjustment parameter relative to the magnitude of the elevator performance decline prior to the i-th service. Therefore, the elevator life index after the i-th service, which can represent the overall performance of the elevator, is:
Rai+1 max＝Rai min+ηi(Rai max-Rai min)
suppose that the elevator life index models before and after the i-th preventive maintenance are Ra, respectivelyi(t) and Rai+1(t) the time consumed for the i-th preventive maintenance is Δ tiThe time interval from the end of the i-1 st repair to the i-th repair is recorded as Δ Ti(ΔTiIs according to Rai(t) decay Rate threshold, Rai(t) slope threshold. ) The model of the safe remaining service life without maintenance is a model depicting the change in the performance of the elevator before the first preventive maintenance, and according to the above definition, it can be written as Ra1(t) of (d). Below in Rai(t) analysis of Ra in the case of knowni+1(t) in a specific form, the elevator safety residual service life model after the ith maintenance is derived according to the elevator safety residual service life model before the ith maintenance, and the relevant steps are as follows:
firstly, the decay speed of the elevator service life index after maintenance is delta times larger than that of the elevator before maintenance under the same service life index, and the following can be obtained:
Figure GDA0002750676650000101
wherein, delta is regarded as a fixed value, the value is more than 1, and can be obtained according to the historical data of the elevator; rai'(t-(Δti+ΔTi) Represents Rai(t) moving to the right by Δ ti+ΔTiAnd the derivation is carried out after each unit. From the above relationship, the following can be derived:
Figure GDA0002750676650000102
equation (6) shows that the attenuation slope of the elevator safety residual service life model after the ith preventive maintenance can be regarded as that the elevator safety residual service life model under the condition of no maintenance is translated to the right
Figure GDA0002750676650000103
Linear transformation of the decay slope after a unit. In other words, if the timing problem is not considered, the elevator safety residual service life model after each preventive maintenance takes 0 moment as the model starting point, then for the same moment, the slope of the model after the ith maintenance at the point is delta times of the slope of the model before the ith maintenance at the point, and the phenomenon that the decay rate of the elevator safety residual service life model is faster and faster along with the increase of the maintenance times is reflectedThe characteristics of (1).
As can be seen from the formula (6):
Figure GDA0002750676650000104
wherein DiIs a constant. Ra1The specific form of (t) is known, and Ra is desiredi+1(t) determination of D onlyiAnd (4) finishing. It is known that the Ra after i-th maintenance of an elevator can be obtained according to an elevator performance recovery factori+1(t) Elevator safety residual service life model Rai+1(t) initial value, is
Figure GDA0002750676650000111
Similarly have Rai min＝Rai(hi max) And Rai max＝Rai(hi min) Then, there are:
Figure GDA0002750676650000112
wherein:
Figure GDA0002750676650000113
Figure GDA0002750676650000114
Figure GDA0002750676650000115
the function has an unknown constant, and the function value of a certain point is known, and the known function value is introduced into the function, so as to obtain DiThus, the life index model Ra of the elevator after the i-th maintenancei+1The specific form of (t) is determined.
To determine after the i-th repairTime interval delta T to i +1 th preventive maintenancei+1。Rai+1' (t) is Rai+1(t) the slope at time t can be used to represent the decay rate of the elevator life index. Has given a slope threshold epsilon2When Ra is presenti+1' (t) when the slope reaches the slope threshold, the next preventive maintenance time is considered to have been reached. The time point when the i +1 th preventive maintenance is reached is recorded as
Figure GDA0002750676650000116
Then can pass through
Figure GDA0002750676650000117
To determine
Figure GDA0002750676650000118
Is taken from a value of
Figure GDA0002750676650000119
ΔtiFor the time consumed in the ith preventive maintenance, with respect to Δ tiThe definitions of which will be described in detail later.
In addition, on the basis of the technical scheme, the scrapping time of the elevator can be further determined:
with the increase of maintenance times, the time interval between two continuous preventive maintenance is shorter and shorter, the maintenance cost is higher and higher, the great waste of resources and cost is caused, and the economic benefit is not met. Therefore, the elevator cannot be maintained for unlimited times, and when a certain limiting condition is met, the maintenance of the elevator is stopped, and the elevator is directly scrapped. This is, in fact, the point of inflection of the retirement time of the elevator.
The technical index aims to measure the maintenance cost of the elevator in unit time or the support time of the maintenance cost of the elevator in unit time, wherein the smaller the former is, the better the economic benefit is, and the larger the latter is, the better the economic benefit is. Let T be the total operating time, C be the total cost of maintenance, then the formula of calculation of skill index is:
Figure GDA00027506766500001110
wherein K' represents the unit cost support time, the larger the better; k represents the maintenance cost per unit time, and the smaller the size, the better.
Given a technical index threshold epsilon, taking the maintenance cost K in unit time as an example3If the slope threshold is used to find the maintenance time for the next preventive maintenance, the technical index of the point exceeds the given index threshold epsilon3If the elevator is maintained again, the maintenance is not in accordance with the economic benefit, the elevator stops being used immediately, and the elevator is selected to be scrapped; if the skill index does not exceed the threshold value epsilon3And then, the continuous maintenance is more economic than the direct scrapping and replacement of new equipment.
The total maintenance cost of an elevator is mainly composed of three parts: maintenance cost C for elevator failuremI.e. the cost spent in the failed repair; preventive maintenance cost C of elevatorpI.e. the cost spent in performing preventive maintenance; loss of equipment outage cost ClI.e. the loss due to elevator down-time during the time spent in preventive maintenance.
Maintenance cost C for elevator faultm
Setting a time interval T between the i-1 th repair and the i-th repairiInner elevator equipment co-generates FiThe maintenance cost per time of fault maintenance is a fixed value CmrThen the total failed repair cost for the elevator before the i-th repair is made is:
Figure GDA0002750676650000121
wherein FkCan be regarded as a risk function from the k-1 th preventive maintenance to the k-th preventive maintenance in the maintenance period before this maintenance, FkThe specific calculation method comprises the following steps:
Figure GDA0002750676650000122
wherein λk(u) is a function of the failure rate of the elevator installation in the maintenance period from the (k-1) th preventive maintenance to the (k) th preventive maintenance, [ k1, k2 ]]For this maintenance period the elevator is operated for a period of time and there are:
Figure GDA0002750676650000123
wherein Δ Ti、ΔtiThe time interval after the i-1 th preventive maintenance until the i-th preventive maintenance and the time consumed by the i-th preventive maintenance, respectively. When k is 1, k1 is 0, and k2 is Δ T1。
② preventive maintenance cost of elevator Cp
The preventive maintenance of elevators requires a certain expenditure, which can be generally divided into a fixed preventive maintenance cost CpfAnd varying preventive maintenance costs CpvThen preventive maintenance cost C at kth maintenancepkCan be expressed as:
Cpk＝Cpf+ΔtkCpv
wherein C ispf、CpvThe fixed maintenance cost and the variable maintenance cost in the k preventive maintenance are constant values, delta tkIs the time consumed in the kth maintenance, so CpvBut also as a fluctuating cost per unit time.
Therefore, before the ith maintenance, the total preventive maintenance cost of the elevator is as follows:
Figure GDA0002750676650000131
loss charge C of equipment shutdownl
It takes a certain time to perform preventive maintenance. Furthermore, it is known from experience that as the number of maintenance operations increases, the time consumed for preventive maintenance increases, assuming that the time consumed for the k-th preventive maintenance operation is Δ tkThe time consumed in the k-1 th preventive maintenance is Deltatk-1Then Δ tkAnd Δ tk-1There is the following relationship between:
Δtk＝sΔtk-1,k＝2,3,…
where s is the maintenance time adjustment factor, a constant greater than 1, so that finally:
Δtk＝sk-1Δt1,k＝2,3,…
assuming that the loss cost per unit time is a certain value CluThen the cost of loss C during the kth preventive maintenancelkComprises the following steps:
Clk＝ΔtkClu
total loss cost C for preventive maintenance period before ith maintenancelThe total loss cost from the 1 st preventative maintenance to the i-1 st preventative maintenance, over the total down time period, can be expressed as:
Figure GDA0002750676650000132
in summary, it can be seen that the total maintenance cost C of the elevator before the i-th maintenance is:
Figure GDA0002750676650000133
taking the maintenance cost K in unit time as an example, the technical indexes corresponding to the maintenance benefits of the elevator equipment can be obtained as follows:
Figure GDA0002750676650000141
has given a maintenance cost threshold epsilon per unit time3Once K > ε3If the elevator is not preventively repaired, the elevator should be selected to be immediately discarded and the elevator reaches the inflection point of the retirement time.
Summarizing the model establishing process:
assuming that the function form of the elevator safety residual service life curve under the condition of no maintenance is determined based on the elevator safety residual service life model under the condition of no maintenance:
Figure GDA0002750676650000142
Figure GDA0002750676650000143
can be regarded as a model of the safe remaining service life of the elevator before the first maintenance, wherein alpha1,β1Model parameters respectively representing the elevator safety residual service life curve before the first maintenance can be calculated by using elevator operation data. The establishment process of the elevator safety residual service life model under the maintenance condition is summarized as follows:
the method comprises the following steps: determining a slope threshold for an elevator safety remaining life model
According to the elevator safety residual service life model under the condition of no maintenance
Figure GDA0002750676650000144
Figure GDA0002750676650000145
The end point of the curve corresponds to the time point h on the time axis1 max，
Figure GDA0002750676650000146
The slope at this point is the given elevator performance degradation rate threshold epsilon2Then, there are:
Figure GDA0002750676650000147
step two: determining elevator performance after preventive maintenance based on performance recovery factor
Assuming that the i-th preventive maintenance has been completed on the elevator, the elevator performance recovery factor after the maintenance is:
ηi＝(b·cpi)ci
wherein C ispi＝Cpf+ΔtiCpv＝Cpf+si-1Δt1CpvB and c are adjustment parameters of the preventive maintenance cost and the maintenance frequency respectively, and can be given manually. Suppose that the elevator life index after the i-th preventive maintenance is restored to
Figure GDA0002750676650000148
The calculation formula is as follows:
Figure GDA0002750676650000149
wherein the content of the first and second substances,
Figure GDA00027506766500001410
and
Figure GDA00027506766500001411
represents the elevator safety residual service life model before and after the ith preventive maintenance respectively, and
Figure GDA0002750676650000151
according to a given slope threshold, using Rai(hi max)＝ε2Can solve h reverselyi max，
Figure GDA0002750676650000152
ΔTi＝hi max-hi minSame principle of
Figure GDA0002750676650000153
Is to utilize
Figure GDA0002750676650000154
And (4) carrying out inverse solution. Herein, the
Figure GDA0002750676650000155
Model of elevator life index after i-th maintenance
Figure GDA0002750676650000156
The starting point of (2).
Step three: determining a safe remaining service life model after an ith preventative maintenance
Figure GDA0002750676650000157
The time consumed by the ith maintenance is known as deltatiThe time interval from the end of the last repair to the i-th repair is recorded as Δ TiAnd the decay speed of the elevator life index after maintenance is delta times larger than that of the elevator before maintenance under the same life index, and the elevator safety residual service life model after the ith maintenance can be determined according to the following formula
Figure GDA0002750676650000158
Figure GDA0002750676650000159
Where i is 2,3, …. And is provided with
Figure GDA00027506766500001510
Description of h2 max,h3 max… are time points for performing preventative maintenance, 2 nd, 3 rd.
Judging whether the (i + 1) th maintenance should be carried out or not based on skill index
Assuming that the model of the safe remaining service life of the elevator after the i-th service has been determined, the following threshold value epsilon based on the skill index K3To judge whether the elevator should be repaired for the (i + 1) th time. Calculation of maintenance cost K per unit time before i +1 th maintenanceThe formula is as follows:
Figure GDA00027506766500001511
wherein, CmrFixed maintenance costs for each failure; cpf、CpvRespectively fixed maintenance cost and variable maintenance cost in each preventive maintenance; cluLoss costs per unit time for preventive maintenance of the elevator; alpha is alphak、βkRespectively model of the remaining service life of the elevator before the kth maintenance
Figure GDA0002750676650000161
The model parameters in (1); s is a maintenance time adjustment coefficient, which is a constant greater than 1; Δ t1The time consumed for the first preventive maintenance.
When K isi+1＞ε3If so, the maintenance is not carried out for the (i + 1) th maintenance, the elevator is scrapped after the service life is ended, namely the elevator reaches the inflection point of the retirement time; if Ki+1＜ε3And returning to the step two, which shows that the maintenance of the elevator is more in line with economic benefit than the direct scrapping.
Advantageous effects
The invention analyzes the elevator wear-out period performance and predicts the irregular maintenance time of the elevator according to the elevator performance change trend, thereby not only improving the economic benefit, but also greatly reducing the elevator safety accident risk; in addition, the invention establishes an elevator safety residual service life model which can determine the maintenance time interval and predict the residual service life on the basis of the existing research, so that the model has higher practicability, and the existing method is optimized and innovated by combining the specific industry background of the elevator equipment, so that the model is more reliable.
Drawings
FIG. 1 is a flow chart of elevator safety remaining service life model building under a maintenance-free condition;
FIG. 2 is a schematic shape of a curve of the remaining life of the elevator without maintenance;
FIG. 3 is a flow chart of the elevator safety remaining service life model building under the maintenance condition;
FIG. 4 is a model of elevator safety remaining service life without maintenance;
fig. 5 model of the remaining life of elevator safety in the case of maintenance.
Detailed Description
Example 1
The method for determining the safe remaining service life of the elevator under the condition of no maintenance comprises the following steps:
the performance of each part of the elevator equipment in the initial operation stage is good, the operation state is stable, and generally, maintenance is not needed. However, once the elevator equipment enters a loss period, the running reliability of the equipment is continuously reduced along with the accumulation of time, and when the running reliability of the equipment is reduced to a certain specified threshold value, the safety residual service life of the elevator is exceeded, and the equipment needs to be subjected to first preventive maintenance. Before the first preventive maintenance, a model of the remaining service life of the elevator safety without maintenance can be established, determining the time interval from the current moment to the first preventive maintenance. The process of model building is shown in fig. 1: (1) monitoring the elevator operation index at any moment, constructing an elevator operation index system, and selecting a relevant index to perform weighted average to obtain a subsystem comprehensive index; (2) dividing the monitoring samples containing the comprehensive indexes into elevator health running state grades for classifying the running indexes contained in the index system into a certain elevator health running state grade; (3) constructing an elevator life index according to an elevator operation index system; (4) predicting the life index of the elevator at the future moment based on a BP neural network algorithm; (5) and determining the safe remaining service life curve of the elevator under the condition of no maintenance by utilizing Weibull distribution.
The step (1) of selecting relevant indexes specifically comprises the following steps:
monitoring the elevator operation indexes at any moment to obtain monitoring samples, wherein each monitoring sample comprises all the elevator operation indexes obtained by monitoring at the moment; respectively determining the influence weight of the indexes of each subsystem on the evaluation object based on the principal component analysis, respectively processing the indexes of each subsystem in a weighted average mode,finally determining respective comprehensive index X of each subsystem1,X2,X3,X4Respectively representing the healthy running states or the reliability of a car system, a tractor system, a door system and a dragging system of the elevator equipment; the indexes in the subsequent steps are all comprehensive indexes.
The related index is an index related to the service life of the elevator, namely the change condition of the index can represent the residual service life condition of the elevator equipment to a certain extent. According to the relevant data, the running system of the elevator is roughly divided into four parts, each subsystem corresponds to different specific running state indexes of the elevator, and the specific system division is shown in the table 1.
TABLE 1 Elevator operating status indicator System overview
Figure GDA0002750676650000171
The relevant index is the index described in the column "specific index" in table 1.
The occurrence of abnormality of any one relevant index can cause the service life of the elevator to be terminated, and the overall degradation of the index represents the sharp shortening of the residual service life of the elevator, so that the running state index of the elevator can be used for measuring and predicting the residual service life condition of the elevator.
Although the 17 indexes in table 1 all represent the operation state of the elevator, the too large sample dimension not only increases the complexity of the research, but also needs to select an index system because the collinearity among the indexes influences the final analysis result. Aiming at a specific elevator background, 17 indexes form four operation systems of the elevator, a principal component analysis theory is introduced, influence weights of the indexes of 4 subsystems on an evaluation object are respectively determined based on principal component analysis, and 4 comprehensive indexes X are finally determined in a weighted average mode1,X2,X3,X4Respectively, representing the healthy running state (or reliability) of the elevator equipment car system, the traction machine system, the door system and the dragging system. Through index selection, not only the dimensionality is reduced, but also the later dimension is reducedThe complexity of continuous research also solves the problem of collinearity between original indexes, and ensures the reliability of the model.
The step (2) of dividing the grade of the healthy running state of the elevator is specifically as follows:
the health running state of the elevator can be judged by utilizing a data mining means through various monitoring index data of the elevator. The healthy operating state of an elevator is a measure of the operational reliability of an elevator installation. Along with the accumulation of time, the health state of the elevator equipment is worse and worse, the running reliability is gradually reduced, and when the health state is reduced to a certain degree, the elevator is scrapped, namely, the elevator reaches the retirement age. In order to qualitatively measure the healthy running state of the elevator, the healthy running state of the elevator can be classified into four grades of "excellent", "good", "medium" and "poor". And provides that the elevator is immediately taken out of service as soon as its operation monitoring data at a certain moment falls into the "bad" class, representing the end of life of the elevator. Therefore, when the monitoring data are classified and the health state grades of the elevators at different moments are judged, the monitoring data are classified into three types of "excellent", "good" and "medium", and the clustering centers of the three types are obtained.
Here, the elevator monitoring data is clustered using an algorithm of fuzzy C-means clustering in unsupervised learning, and fuzzy clustering is also one of the clustering algorithms. In fuzzy clustering, in order to reduce the iteration times and improve the iteration efficiency, the clustering center determined by the traditional system clustering method is used as the initial clustering center of the fuzzy clustering,
step (3) constructing an elevator life index specifically as follows:
the elevator life index is a performance index which is constructed based on an original monitoring index of an elevator and can explain the health state of the elevator, the smaller the elevator life index is, the worse the health running state of the elevator is, the shorter the safe remaining service life is, and the value is between [0 and 1 ]. Thus, the elevator life index can be regarded as a measure of the overall performance change of the elevator, similar to the reliability of the elevator installation, which tends to decline over time.
And constructing an elevator life index by using a rank-sum ratio comprehensive evaluation method. The comprehensive rank-sum ratio evaluation method is widely applied at present, and prominent research results are obtained in the fields of quality control, forecast prediction, medical health and the like. In the patent, the method is expected to be applied to the field of mechanical equipment performance evaluation, and innovation of the application field is realized.
The RSR statistic value in the rank-sum ratio comprehensive evaluation method is between [0 and 1], and no matter what situation is, the larger the statistic is, the better the statistic is, the characteristics of the elevator service life index are met, and the comprehensive evaluation on the healthy running state of the elevator at different moments can be realized.
In this patent, the elevator life index Ra is represented by a weighted rank-sum ratio WRSR, and there are:
Figure GDA0002750676650000181
wherein, wjThe weight of the impact of the jth index on the evaluation object, rijRank of j index for ith monitor sample. In the fuzzy clustering, the detection samples have been classified into "excellent", "good", and "medium", and the influence weight of each evaluation index can be determined by calculating the correlation coefficient between each index and the category variable, knowing that
xi＝(xi1,xi2,…,xim)(i＝1,2,…,n)
For n monitoring samples, c ═ c1,c2,…,cn) Respectively corresponding to the fuzzy clustering result of each sample
Figure GDA0002750676650000191
The absolute value of the correlation coefficient of the jth evaluation index and the category variables, namely "excellent", "good" and "medium", is shown, then the influence weight of the jth evaluation index on the evaluation result is:
Figure GDA0002750676650000192
so that the life index Ra of the elevatoriThe calculation formula of (2) is as follows:
Figure GDA0002750676650000193
predicting a future life index based on a BP neural network algorithm:
the method has the advantages that the BP neural network is used for predicting the healthy running state of the elevator equipment at the future moment, so that the structural relation of continuous time point monitoring data can be accurately fitted, and the model error can be minimized. It is known that elevator equipment monitoring data are classified into three categories of "excellent", "good" and "medium" according to a fuzzy C-means clustering algorithm, and three categories of clustering centers are obtained; the elevator life index which integrally describes the healthy running state of the elevator at the current moment and the elevator life index of the center of each type can be obtained based on the original sample monitoring data through an order and ratio comprehensive evaluation method.
The method for predicting the healthy running state of the elevator at the future time based on the BP neural network algorithm comprises the following specific steps: (again assume that there are n monitoring samples x1,x2,…,xn)：
Firstly, as the monitoring data are all time sequence data, sample monitoring values of the elevator for any continuous p times can be used as input nodes, the sample monitoring value of the p +1 th time is used as an output node, the number of hidden layer nodes is set to be N, and a BP neural network is trained;
secondly, predicting the healthy running state of the elevator at the future time by using the trained BP neural network model;
and thirdly, calculating the distance between the prediction sample and the centers of the three types of fuzzy clustering, namely 'excellent', 'good' and 'middle', and dividing the running state grade of the new prediction sample. Since the healthy running state of the elevator is continuously attenuated along with the accumulation of time, the prediction samples can definitely show the trend of being always classified into the middle category as the prediction times are increased, the three categories can be completely separated at a certain time, the elevator enters the poor category, and the elevator is in a stop use state.
If the prediction sample is alreadyFall into the "middle" category, under which a distance threshold ε is set1Used for judging whether the running state of the elevator enters a 'difference' class or not, and once the distance between a prediction sample and a 'middle' class exceeds epsilon1And stopping prediction, and considering that the running state grade of the elevator is classified into a difference class, wherein the point is a scrapping point or a service life end point of the elevator. Epsilon1The specific setting method is as follows:
calculating the distance d between all the monitored samples in the 'middle' class and the cluster center of the class by using the fuzzy clustering result3i(i ═ 1,2, …, n), may define ε1＝max{d3i}(i＝1,2,…,n).
Suppose that the distance threshold ε is exceeded at the first prediction1The time monitoring interval between successive samples is known as Δ t*Then, without maintenance, the safe remaining life of the elevator is l x Δ t from the current moment*I.e. the time interval from the current moment to the first preventive maintenance is obtained.
The Weibull distribution of the step (5) determines that the curve of the safe remaining service life of the elevator under the condition of no maintenance is specifically as follows:
the life index Ra of an elevator from the monitoring moment to the period when the elevator is out of service without maintenance is obtainediThe next step is to describe the life index Ra of the elevator by taking time as the abscissa under the condition of no maintenanceiThe curve of the remaining service life of the elevator is the ordinate. Empirically, the curve should have a gradually decreasing trend and a gradually increasing rate of decrease. The general shape is shown in figure 2.
Assuming that the rule of failure of the elevator equipment is known to follow the distribution of the probability density function f (t), the reliability function of the equipment is R (t). R (t) and f (t) have the following relationship:
Figure GDA0002750676650000201
where λ (t) is a function of the failure rate of the elevator installation.
The failure occurrence rule of the given elevator equipment follows Weibull distribution, and the corresponding equipment failure rate is expressed in the form that:
Figure GDA0002750676650000202
wherein alpha isiThe shape parameter represents the specific shape of the function curve of the failure rate of the mechanical equipment after the i-1 th preventive maintenance and before the i-th preventive maintenance; beta is aiThe time interval between two consecutive failures of the device can be represented as a scale parameter. The distribution function f (t) of the failure rate can be expressed as:
Figure GDA0002750676650000203
the reliability of the equipment is used for measuring the probability that the equipment can work stably, and the higher the reliability is, the better the elevator running state is; the elevator life index is used for measuring the healthy running state of the elevator, and the higher the elevator life index is, the healthier the running state of the elevator is, and the longer the remaining service life is. It can be found that the reliability has the same purpose as the elevator life index, both for measuring the operating state of the elevator, and the higher the value, the better the operating state of the elevator, so it can be guessed that the functional form of the elevator life index is similar to the reliability functional form, i.e. the elevator remaining service life distribution model can be represented by the reliability function of the elevator equipment, there is a
Figure GDA0002750676650000211
Given that the elevator installation operates during the time period [0, t ], the reliability of the elevator at time t can be defined as:
Figure GDA0002750676650000212
the left side and the right side of the formula (3) are simultaneously derived from the time t, and the relation between the reliability function R (t) of the elevator equipment and the probability density function f (t) of the elevator fault occurrence rule can be obtained as follows:
Figure GDA0002750676650000213
from equation (1), equations (2) and (4) the relationship between the reliability function of the elevator installation and the elevator fault rate can be derived:
Figure GDA0002750676650000214
Figure GDA0002750676650000215
Figure GDA0002750676650000216
it is known that in the Weibull distribution,
Figure GDA0002750676650000217
and is provided with
Figure GDA0002750676650000218
The functional form of the safe remaining useful life curve after the i-1 th preventative maintenance to before the i-th preventative maintenance is therefore:
Figure GDA0002750676650000219
wherein alpha isi、βiDetermined by the specific elevator operating data; further, the functional form of the safe remaining service life curve under the condition of no maintenance, namely before the 1 st preventive maintenance, is determined as follows:
Figure GDA00027506766500002110
so far, the safety residual service life curve under the condition of no maintenance is well depicted, and the time point of first preventive maintenance of the elevator is determined.
Summary of model building Process
Suppose that an index system capable of representing the healthy running state of the elevator is determined according to relevant literature data, and comprises 4 subsystems: the elevator equipment comprises a car system, a tractor system, a door system and a dragging system, and has 17 specific indexes. Based on the sample monitoring data of the 17 specific indexes of the elevator system, the process of establishing the elevator safety residual service life model under the condition of no dimension is summarized as follows:
firstly, respectively carrying out principal component analysis on the original indexes of each subsystem, determining the comprehensive influence weight of the original indexes on an evaluation object according to the principal component analysis result, and obtaining four comprehensive indexes X through weighted average1,X2,X3,X4Respectively representing the healthy running states of the four subsystems of the elevator equipment. The original indexes involved in the subsequent research refer to the four comprehensive original indexes;
secondly, monitoring data of the monitoring samples are divided into three types of excellent, good and medium by using a fuzzy C-mean algorithm, and in order to reduce iteration times and improve efficiency, an initial clustering center is determined by using a traditional system clustering method;
constructing an elevator life index based on a rank-sum ratio comprehensive evaluation method, calculating the elevator life index corresponding to each observation sample, simultaneously obtaining the elevator life index corresponding to three clustering centers of fuzzy clustering, and converting n multiplied by 17 dimensional sample monitoring data into n multiplied by 2 dimensional data sets, wherein 2 dimensions respectively represent the elevator life index and the grade of the elevator healthy running state at the current moment;
fourthly, the prediction of the life index of the elevator at the future moment is finished based on a BP neural network algorithm, and the time interval of the first preventive maintenance is determined by setting a limiting condition;
fifthly, the life index Ra of the elevator from the beginning of monitoring to the end of predictioniPerforming curve fittingAnd is determined based on the Weibull distribution, so the functional form of the safe remaining service life curve in the case of finally determining no maintenance is as follows:
Figure GDA0002750676650000221
wherein alpha isi、βiAre unknown parameters and can be determined by specific elevator operation data.
Example 2
The method for determining the safe remaining service life of the elevator under the condition of maintenance comprises the following steps:
the elevator safety residual service life model under the maintenance condition is expected to complete the work of determining the time interval between two continuous maintenance, predicting the elevator performance curve after preventive maintenance, determining the elevator scrapping time point and the like on the basis of the established elevator safety residual service life model under the maintenance-free condition. And the influence of the maintenance cost and the maintenance times on the maintenance time interval of the elevator and the residual service life of the elevator is given from the theoretical point of view. In the specific establishing process of the model, the next maintenance time of the elevator is determined by considering the slope of the function, and whether the elevator should be stopped using is judged by introducing the skill index. The flow chart of the establishment of the elevator safety residual service life model under the maintenance condition is shown in the figure 3: (1) determining an elevator safety residual service life model and a slope threshold; (2) determining the elevator performance after preventive maintenance through a performance recovery factor and a performance reduction rate expansion factor; (3) determining a safe remaining service life model after the ith preventive maintenance according to the result of the step 2
Figure GDA0002750676650000222
The method specifically comprises the following steps:
the preventive maintenance time interval of the elevator refers to the time interval between two adjacent preventive maintenance, and the normal operation of the elevator can be ensured only by performing the preventive maintenance on the elevator according to the regulations, so that the service life of mechanical equipment is prolonged. The patent considers that when the elevator is in different operation stages, the preventive maintenance time intervals are different, because in the initial operation stage, the performance of the elevator is stable, and the preventive maintenance time intervals are long; as the elevator installation enters the wear phase, the time interval between two successive preventive repairs becomes shorter and shorter. The time interval between two adjacent preventive maintenance can be determined by introducing the concept of a slope threshold.
The elevator service life ending point under the condition of no maintenance is actually the first maintenance time point of the elevator under the condition of maintenance, so the slope of the service life ending point under the condition of no maintenance can be set as a slope threshold and is recorded as epsilon2. Once the slope of the elevator safety remaining service life curve reaches within the threshold value range, it is considered that preventive maintenance should be carried out on the elevator at that moment.
After the elevator is maintained, the service life index of the elevator is recovered, but the recovery degree is different along with the increase of the maintenance times; in addition, the decay rate of the life index of the elevator after maintenance is faster than that of the elevator before maintenance under the same life index. For the two problems, firstly, an elevator performance recovery factor eta and a performance reduction rate expansion factor delta are given, which are respectively used for representing the recovery degree of the elevator performance after maintenance and the expansion degree of the performance reduction rate.
The elevator performance recovery factor η is affected not only by the maintenance cost when the elevator is subjected to preventive maintenance, but also by the maintenance frequency. Setting etaiRepresenting the performance recovery factor after i-th maintenance of the elevator, can be calculated for etaiThe following definitions are made:
ηi＝(b·cpi)ci
wherein cpiMaintenance cost for the ith preventive maintenance; b is an adjustment parameter, which is the adjustment of the maintenance cost when the elevator is preventively maintained, and
Figure GDA0002750676650000231
c is an adjustment parameter, is the adjustment of preventive maintenance times of the elevator and is more than 0 and less than 1; etaiIs taken to be [0,1]]In the meantime.
Suppose the maximum and maximum values of the elevator life index before the i-th serviceSmall value is marked as Rai maxAnd Rai minThe index of elevator life, recorded as Ra, recovers after the i-th maintenancei+1 maxAnd the degree of recovery of elevator performance after the i-th maintenance is known to be etai. It can be empirically concluded that as the number of repairs increases, the elevator life index after each repair tends to decrease and that the elevator performance in the time interval between the i-th repair and the i-1 st repair decreases, for example by Rai max-Rai minAfter preventive maintenance, the descending indicator is allowed to rise, etaiRelative to the descending amplitude Rai max-Rai minDegree of recovery of, i.e. etaiCan be seen as an adjustment parameter relative to the magnitude of the elevator performance decline prior to the i-th service. Therefore, the elevator life index after the i-th service, which can represent the overall performance of the elevator, is:
Rai+1 max＝Rai min+ηi(Rai max-Rai min)
suppose that the elevator life index models before and after the i-th preventive maintenance are Ra, respectivelyi(t) and Rai+1(t) the time consumed for the i-th preventive maintenance is Δ tiThe time interval from the end of the i-1 st repair to the i-th repair is recorded as Δ Ti(ΔTiIs according to Rai(t) decay Rate threshold, Rai(t) a slope threshold. ) The model of the safe remaining service life without maintenance is a model depicting the change in the performance of the elevator before the first preventive maintenance, and according to the above definition, it can be written as Ra1(t) of (d). Below in Rai(t) analysis of Ra in the case of knowni+1(t) in a specific form, the elevator safety residual service life model after the ith maintenance is derived according to the elevator safety residual service life model before the ith maintenance, and the relevant steps are as follows:
firstly, the decay speed of the elevator service life index after maintenance is delta times larger than that of the elevator before maintenance under the same service life index, and the following can be obtained:
Figure GDA0002750676650000241
wherein, delta is regarded as a fixed value, the value is more than 1, and can be obtained according to the historical data of the elevator; rai'(t-(Δti+ΔTi) Represents Rai(t) moving to the right by Δ ti+ΔTiAnd the derivation is carried out after each unit. From the above relationship, the following can be derived:
Figure GDA0002750676650000242
equation (6) shows that the attenuation slope of the elevator safety residual service life model after the ith preventive maintenance can be regarded as that the elevator safety residual service life model under the condition of no maintenance is translated to the right
Figure GDA0002750676650000243
Linear transformation of the decay slope after a unit. In other words, if the timing problem is not considered, the elevator safety residual service life model after each preventive maintenance takes the 0 moment as the model starting point, and for the same moment, the slope of the model after the ith maintenance at the point is delta times of the slope of the model before the ith maintenance at the point, so that the characteristic that the decay rate of the elevator safety residual service life model is faster and faster along with the increase of the maintenance times is reflected.
As can be seen from the formula (6):
Figure GDA0002750676650000244
wherein DiIs a constant. Ra1The specific form of (t) is known, and Ra is desiredi+1(t) determination of D onlyiAnd (4) finishing. It is known that the Ra after i-th maintenance of an elevator can be obtained according to an elevator performance recovery factori+1(t) Elevator safety residual service life model Rai+1(t) initial value, is
Figure GDA0002750676650000245
Similarly have Rai min＝Rai(hi max) And Rai max＝Rai(hi min) Then, there are:
Figure GDA0002750676650000246
wherein:
Figure GDA0002750676650000247
Figure GDA0002750676650000251
Figure GDA0002750676650000252
the function has an unknown constant, and the function value of a certain point is known, and the known function value is introduced into the function, so as to obtain DiThus, the life index model Ra of the elevator after the i-th maintenancei+1The specific form of (t) is determined.
The time interval Δ T from the i-th repair to the i + 1-th preventive repair is determined as followsi+1。Rai+1' (t) is Rai+1(t) the slope at time t can be used to represent the decay rate of the elevator life index. Has given a slope threshold epsilon2When Ra is presenti+1' (t) when the slope reaches the slope threshold, the next preventive maintenance time is considered to have been reached. The time point when the i +1 th preventive maintenance is reached is recorded as
Figure GDA0002750676650000253
Then can pass through
Figure GDA0002750676650000254
To determine
Figure GDA0002750676650000255
Is taken from a value of
Figure GDA0002750676650000256
ΔtiThe time consumed for the ith preventive maintenance.
Summarizing the model establishing process:
assuming that the function form of the elevator safety residual service life curve under the condition of no maintenance is determined based on the elevator safety residual service life model under the condition of no maintenance:
Figure GDA0002750676650000257
Figure GDA0002750676650000258
can be regarded as a model of the safe remaining service life of the elevator before the first maintenance, wherein alpha1,β1Model parameters respectively representing the elevator safety residual service life curve before the first maintenance can be calculated by using elevator operation data. The establishment process of the elevator safety residual service life model under the maintenance condition is summarized as follows:
the method comprises the following steps: determining a slope threshold for an elevator safety remaining life model
According to the elevator safety residual service life model under the condition of no maintenance
Figure GDA0002750676650000259
The point of time h at which preventive maintenance is first required can be obtained1 max，
Figure GDA00027506766500002510
The slope at this point is the given elevator performance degradation rate threshold epsilon2Then, there are:
Figure GDA00027506766500002511
step two: determining elevator performance after preventive maintenance based on performance recovery factor
Assuming that the i-th preventive maintenance has been completed on the elevator, the elevator performance recovery factor after the maintenance is:
ηi＝(b·cpi)ci
wherein C ispi＝Cpf+ΔtiCpv＝Cpf+si-1Δt1CpvB and c are adjustment parameters of the preventive maintenance cost and the maintenance frequency respectively, and can be given manually. Suppose that the elevator life index after the i-th preventive maintenance is restored to
Figure GDA0002750676650000261
The calculation formula is as follows:
Figure GDA0002750676650000262
wherein the content of the first and second substances,
Figure GDA0002750676650000263
and
Figure GDA0002750676650000264
represents the elevator safety residual service life model before and after the ith preventive maintenance respectively, and
Figure GDA0002750676650000265
according to a given slope threshold, using Rai(hi max)＝ε2Can solve h reverselyi max，
Figure GDA0002750676650000266
ΔTi＝hi max-hi minSame principle of
Figure GDA0002750676650000267
Is to utilize
Figure GDA0002750676650000268
And (4) carrying out inverse solution. Herein, the
Figure GDA0002750676650000269
Model of elevator life index after i-th maintenance
Figure GDA00027506766500002610
The starting point of (2).
Step three: determining a safe remaining service life model after an ith preventative maintenance
Figure GDA00027506766500002611
The time consumed by the ith maintenance is known as deltatiThe time interval from the end of the last repair to the i-th repair is recorded as Δ TiAnd the decay speed of the elevator life index after maintenance is delta times larger than that of the elevator before maintenance under the same life index, and the elevator safety residual service life model after the ith maintenance can be determined according to the following formula
Figure GDA00027506766500002612
Figure GDA00027506766500002613
Where i is 2,3, …. And is provided with
Figure GDA00027506766500002614
Description of the invention
Figure GDA00027506766500002615
… points areTime points for preventive maintenance were performed, except 2 nd, 3 rd.
Example 3
Application of the model:
in order to verify the feasibility of the model, 1000 sample data can be randomly generated based on the normal value range of 17 specific indexes. And assuming that the first set of sample data is collected at time 0, the time interval between two consecutive sets of sample data is 2 hours.
(1) Data preprocessing and index selection
In order to avoid the influence of dimension problems on the effectiveness of the model, the original data needs to be preprocessed, namely each index is subjected to non-dimensionalization, and the value of each index is [0,1]]In the meantime. A degradation function can be introduced, and after each index is converted by the degradation function, the data can be converted into 0,1]In addition, the elevator state is better as the index value is larger. And respectively converting the deterioration degrees of the 17 original indexes according to the types of the indexes to finally obtain 1000 groups of dimensionless sample data, wherein the larger the index value is, the better the performance of the representative elevator is. 17 indices, in the order of Z in Table 11～z17To represent
Although 17 indexes of the elevator healthy operation index system can represent the healthy operation state of the elevator, the dimensionality is overlarge, and the correlation among the indexes greatly increases the complexity and the unreliability of a model, so that the selection of the indexes based on a certain technology is necessary. The elevator operation index system can be divided into 4 subsystems, in order to achieve the purpose of simultaneously reducing and storing original index information as much as possible, a method for determining index weight through a principal component analysis theory is adopted, and a comprehensive index is respectively extracted from each subsystem to respectively represent the healthy operation states (or the reliability) of an elevator equipment car system, a tractor system, a door system and a dragging system. Finally 4 comprehensive indexes X are obtained1,X2,X3,X4：
Figure GDA0002750676650000271
(2) Elevator safety residual service life model under maintenance-free condition
The elevator safety residual service life model under the condition of no maintenance is mainly characterized in that a BP neural network algorithm and an FCM algorithm are combined at first to complete the prediction of the elevator health running state at the future time, the time point of first preventive maintenance is determined, and the elevator safety residual service life model under the condition of no maintenance is carved based on Weibull distribution.
Based on historical experience, when the distance from the prediction point to the center of the "middle" category exceeds 1.2d to 0.3879338, it can be considered that the healthy running state of the elevator at that time completely enters the "bad" category, and prediction should be stopped. And finally, 17 predicted elevator life indexes are obtained, and the time interval between every two adjacent predicted values is 2 hours. The predicted values for the elevator lifetime index at future times and the distance from the cluster center of the "middle" class are summarized in table 2.
TABLE 2 prediction of elevator Life index at future time
Figure GDA0002750676650000272
Figure GDA0002750676650000281
Based on 1017 sets of sample data, Ra was obtained using the associated software1Specific functional form of (t):
Figure GDA0002750676650000282
namely alpha1＝1.449，β11318, and the fitting degree of the model reaches 99.75%, so that the fitting effect is good. The curve of the remaining service life of the elevator without maintenance is shown in fig. 4.
Up to this point, the curve of the remaining service life of the elevator without maintenance is established, which is the basis for establishing the model of the remaining service life of the elevator without maintenance, and if the last monitoring sample time is taken as the current time, the first preventive maintenance should be performed after 34 hours.
Note: since the monitoring time is assumed to start from the time 0, the sample number is multiplied by the monitoring time, that is, the monitoring time is 2 times the sample number, and the effect of the elevator life index on the scatter diagram of the sample number is the same as the effect of the elevator life index on the scatter diagram of the monitoring time.
(3) Elevator safety residual service life model under maintenance condition
The scrapping of the elevator without maintenance is not in accordance with economic benefits, the residual service life of the elevator can be prolonged through multiple preventive maintenance, but the elevator cannot be maintained endlessly, and the situation that the elevator is scrapped directly at a certain time point is more in accordance with economic benefits than the situation that the elevator is subjected to preventive maintenance again. The purpose of this program is mainly two: determining a second, third preventative maintenance time point; the point in time of the scrapping of the elevator is determined.
The slope of the end-of-life point without maintenance is used as the slope threshold, so2＝-0.0004926559。
For some values involved in the model that need to be determined based on historical elevator operation and maintenance data and actual experience, the following assumptions are made, as shown in table 3:
table 3 empirical value assignment in model
Figure GDA0002750676650000283
Figure GDA0002750676650000291
And simulating the elevator safety residual life service model under the condition of maintenance by using related statistical software based on the empirical value in the given model. Since the monitoring time of the first sample monitoring point is known to be 0 time, the time interval from 0 time to the first preventive maintenance time can be 2032 hours as the time interval before the first preventive maintenance. The simulation result shows that when the 9 th preventive maintenance is needed, the value of the technical index is larger than 10, so that the preventive maintenance is carried out on the elevator, the economic benefit is not met, and the elevator should be directly scrapped. Namely, after 8 times of preventive maintenance is carried out on the elevator, the time point when the elevator reaches the preventive maintenance again is the elevator scrapping point. The time interval from the last preventive maintenance to the current preventive maintenance of the elevator, the technical index when the current preventive maintenance is reached, and the time consumed by the current preventive maintenance are shown in table 4.
TABLE 4 time intervals from last preventive maintenance and skill index before this maintenance
Figure GDA0002750676650000292
Since the skill index before the 9 th service exceeds the threshold 10, a direct scrapped elevator should be selected at the 9 th preventive maintenance time point. Then, if the last sample monitoring time is assumed to be the current time, on the premise of normal maintenance, after 1722 hours from the current time, the elevator reaches the inflection point of the retirement time, that is, the safety remaining service life of the elevator is 72 days.
And finally, according to the simulation result, depicting an elevator safety residual service life model under the condition of maintenance, as shown in figure 5.
As can be seen from fig. 5, the elevator performance recovers after preventive maintenance as the number of preventive maintenance increases, but the recovery value becomes lower and lower; the inclination degree of the elevator safety residual service life model after each preventive maintenance is larger than that of the safety residual service life model before maintenance, which shows that the performance attenuation speed of the elevator is faster and faster along with the increase of the preventive maintenance times and conforms to the actual experience.

Claims (3)

1. A method for determining the remaining service life of elevator safety under maintenance condition comprises the following steps: the method is characterized in that: the method comprises the following steps: (1) determining an elevator safety residual service life model and a slope threshold; (2) determining the elevator performance after preventive maintenance through a performance recovery factor and a performance reduction rate expansion factor; (3) determining a safe remaining service life model after the ith preventive maintenance according to the result of the step 2
Figure FDA0002750676640000011
The step (1) is specifically as follows: a. monitoring the elevator operation indexes at any moment to obtain monitoring samples, wherein each monitoring sample comprises all the elevator operation indexes obtained by monitoring at the moment; respectively determining the influence weight of the indexes of each subsystem on an evaluation object based on principal component analysis, respectively processing the indexes of each subsystem in a weighted average mode, and finally determining the respective comprehensive index X of each subsystem1,X2,X3,X4Respectively representing the healthy running states or the reliability of a car system, a tractor system, a door system and a dragging system of the elevator equipment; indexes in the subsequent steps are all comprehensive indexes; b. clustering elevator operation index monitoring data by using a fuzzy C-means clustering algorithm in unsupervised learning, dividing monitoring samples into three types of 'excellent', 'good' and 'medium' to obtain three types of clustering centers, and when fuzzy clustering is performed, using the clustering center determined by using a traditional system clustering method as an initial clustering center of the fuzzy clustering; c. the life index Ra of the elevator is expressed by a weighted rank-sum ratio WRSR, and the life index Ra comprises:
Figure FDA0002750676640000012
wherein, wjThe weight of the impact of the jth index on the evaluation object, rijThe rank of the jth index of the ith monitoring sample is obtained, and the ith monitoring sample contains all elevator operation indexes obtained by the ith monitoring; in step b, the monitoring samples have been divided into "The evaluation index is determined by calculating a correlation coefficient between each index and a category variable, namely, the category variables of "excellent", "good" and "medium", which are known to be excellent
xi＝(xi1,xi2,…,xim)(i＝1,2,…,n)
For n monitoring samples, c ═ c1,c2,…,cn) The fuzzy clustering result corresponding to each sample is the concrete representation form of the category variable, and the category variable is recorded
Figure FDA0002750676640000013
The absolute value of the correlation coefficient between the jth evaluation index and the category variable is shown, and the influence weight of the jth evaluation index on the evaluation result is as follows:
Figure FDA0002750676640000014
so that the life index Ra of the elevatoriThe calculation formula of (2) is as follows:
Figure FDA0002750676640000021
d. firstly, taking sample monitoring values of an elevator for any continuous p times as input nodes, taking sample monitoring values of the p +1 th time as output nodes, setting the number of hidden layer nodes as N, and training a BP neural network;
secondly, predicting the elevator life index at the future moment by using the trained BP neural network model:
calculating the distance between the prediction sample and the centers of three types of fuzzy clustering, namely 'excellent', 'good' and 'middle', and dividing the running state grade of a new prediction sample;
if the predicted samples are classified as "middle", then a distance threshold ε is set1Used for judging whether the running state of the elevator enters a 'difference' class or not, and once the distance between a prediction sample and a 'middle' class exceeds epsilon1If so, stopping prediction, and considering that the running state grade of the elevator is classified into a difference class epsilon1Namely the scrapping point or the service life end point of the elevator; epsilon1The specific setting method is as follows:
calculating the distance d between all the monitored samples in the 'middle' class and the cluster center of the class by using the fuzzy clustering result3i(i ═ 1,2, …, n), and defines ε1＝max{d3i}(i＝1,2,…,n).
Suppose that the distance threshold ε is exceeded at the first prediction1The time monitoring interval between successive samples is known as Δ t*Then, without maintenance, the safe remaining life of the elevator is l x Δ t from the current moment*Namely, the time interval from the current moment to the first preventive maintenance is obtained, namely the elevator safety residual service life under the condition of no maintenance is obtained;
e. setting the rule of the known elevator equipment with faults to obey the distribution of a probability density function f (t), and setting a reliability function of the equipment as R (t); r (t) and f (t) have the following relationship:
Figure FDA0002750676640000022
where λ (t) is a fault rate function of the elevator installation;
the failure occurrence rule of the given elevator equipment follows Weibull distribution, and the corresponding equipment failure rate is expressed in the form that:
Figure FDA0002750676640000023
wherein alpha isiThe shape parameter represents the specific shape of the function curve of the failure rate of the mechanical equipment after the i-1 th preventive maintenance and before the i-th preventive maintenance; beta is aiThe scale parameter represents the time interval of two continuous failures of the equipment; the distribution function f (t) of the failure rate can be expressed as:
Figure FDA0002750676640000031
the relationship between the distribution model of the remaining service life of the elevator and the reliability of the elevator equipment after the i-1 th preventive maintenance and before the i-th preventive maintenance is as follows:
Figure FDA0002750676640000032
given that the elevator installation operates during the time period [0, t ], the reliability of the elevator at time t is defined as:
Figure FDA0002750676640000033
the left side and the right side of the formula (3) are simultaneously derived from the time t to obtain the following relation between the reliability function R (t) of the elevator equipment and the probability density function f (t) of the elevator fault occurrence rule:
Figure FDA0002750676640000034
the relationship between the reliability function of the elevator installation and the failure rate of the elevator is derived from equation (1), equation (2) and equation (4):
Figure FDA0002750676640000035
Figure FDA0002750676640000036
Figure FDA0002750676640000037
it is known that in the Weibull distribution,
Figure FDA0002750676640000038
and is provided with
Figure FDA0002750676640000039
The functional form of the safe remaining useful life curve after the i-1 th preventative maintenance to before the i-th preventative maintenance is therefore:
Figure FDA00027506766400000310
wherein alpha isi、βiDetermined by the specific elevator operating data; further, the functional form of the safe remaining service life curve under the condition of no maintenance, namely before the 1 st preventive maintenance, is determined as follows:
Figure FDA00027506766400000311
Figure FDA00027506766400000312
the end point of the curve corresponds to the time point on the time axis
Figure FDA00027506766400000313
Figure FDA00027506766400000314
The slope at this point is the given elevator performance degradation rate threshold epsilon2Then, there are:
Figure FDA00027506766400000315
once the slope of the elevator safety remaining service life curve reaches within the threshold value range, it is considered that preventive maintenance should be carried out on the elevator at that moment.
2. The method of claim 1, further comprising: the step (2) is specifically as follows: if the i-th preventive maintenance is finished on the elevator, the performance recovery factor of the elevator after maintenance is as follows:
ηi＝(b·cpi)ci
wherein cpiI is the maintenance cost for the preventive maintenance of the ith time, b is the adjustment parameter, is the adjustment of the maintenance cost for the preventive maintenance of the elevator, and has
Figure FDA0002750676640000041
c is an adjustment parameter, is the adjustment of preventive maintenance times of the elevator and is more than 0 and less than 1; etaiIs taken to be [0,1]]To (c) to (d); suppose that the elevator life index after the i-th preventive maintenance is restored to
Figure FDA0002750676640000042
The calculation formula is as follows:
Figure FDA0002750676640000043
wherein the content of the first and second substances,
Figure FDA0002750676640000044
and
Figure FDA0002750676640000045
represents the elevator safety residual service life model before and after the ith preventive maintenance respectively, and
Figure FDA0002750676640000046
is known, according to a given slope threshold, using
Figure FDA0002750676640000047
Is reversely solved to
Figure FDA0002750676640000048
Figure FDA0002750676640000049
Figure FDA00027506766400000410
The time interval from the end of the i-1 th maintenance to the i-th maintenance is recorded as delta TiSame principle of
Figure FDA00027506766400000411
By using
Figure FDA00027506766400000412
Performing inverse solution;
Figure FDA00027506766400000413
elevator life index model after considering i-th maintenance
Figure FDA00027506766400000414
The starting point of (2).
3. The method of claim 2, further comprising: the step (3) is specifically as follows: the time consumed by the ith maintenance is known as deltatiThe time interval from the end of the last repair to the i-th repair is recorded as Δ TiAnd the decay speed of the elevator life index after maintenance is delta times larger than that of the elevator before maintenance under the same life index, and the elevator safety residual service life model after the ith maintenance can be determined according to the following formula
Figure FDA00027506766400000415
Figure FDA00027506766400000416
Wherein i is 2,3, …; and is provided with
Figure FDA00027506766400000417
Figure FDA00027506766400000418
Time points for performing preventive maintenance were 2 nd, 3 rd.
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