CN105528521A - Method for determining reconfiguration time of reconfigurable manufacturing system - Google Patents

Abstract

The invention discloses a method for determining reconfiguration time of a reconfigurable manufacturing system. The method is characterized in that a reconfiguration point of an RMS (reconfigurable manufacturing system) can be quickly and reasonably determined according to the change of an order, a processing function and a processing capability capable of meeting market requirements are rapidly reconfigured, and the features of low cost and quick response of the RMS are kept. The method comprises the following steps of firstly analyzing RMS dynamic complexity by utilization of information entropy, dividing the RMS dynamic complexity EX into a sum of an RMS active complexity Ep and an RMS negative complexity En, and analyzing RMS complexity change situation in the perspectives of the processing function and the processing capability; then constructing a potential function by utilization of a cusp catastrophe theory, wherein the catastrophe moment of the potential function is the reconfiguration time point of the RMS. The method disclosed by the invention has the advantages that reconfiguration point decision judgment evidence is provided for a decision maker, the system reconfiguration is performed in time, and the activity of the RMS is kept.

Description

A kind of Reconfigurable Manufacturing System reconstructs the defining method on opportunity

Technical field

The present invention relates to advanced manufacturing technology field, be specifically related to the defining method on a kind of Reconfigurable Manufacturing System reconstruct opportunity.

Background technology

Along with economic development, manufacturing industry intensified competition, customer demand is more cunning and diversified, cause being on the increase of product category, the fluctuating widely of the market demand, add the continuous innovation of science and technology, launch window reduces all the more, and existing manufacturing system appears gradually in defect, novel manufacturing system research becomes focus gradually, pursues with the high-quality product of low-cost production to obtain competitive edge.And Reconfigurable Manufacturing System (ReconfigurableManufacturingSystem, RMS) can provide accurate function and ability need according to customer requirement, become the focus of research gradually.

RMS can make the sudden change in market and responding fast, the process requirements various according to market, by the rapid adjustment of software and hardware facilities, reconstructs rapidly the machining functions and working ability that can meet the need of market.Can RMS after coming into operation, along with the carrying out of activity in production, under the combined action of the internal and external factors such as order variation, mechanical disorder, there is the phenomenon such as damp production, delivery extension, production scheduling difficulty increases, system effectiveness reduces, and RMS produces system reconfiguration demand.Consider the factors such as production cost, extension cost, reconfiguration cost, when be reconstructed and become responsive, the selection on reconstruct opportunity is significant for keeping the low cost of RMS, fast-response characteristic, inappropriate reconstruction point decision-making can cause the problem such as the increase of reconfiguration cost, the prolongation of reconstitution time, and this reconstruct even can be caused to lose meaning.Therefore, need to carry out decision analysis research to RMS reconstruction point.

RMS has good market outlook, and domestic and international researchist has carried out extensive and deep research, comprises the reconfigurability of RMS, system layout's planning, system performance analysis, workpiece race construction method etc.But at present almost not to the correlative study of RMS reconstruction point, and there are the following problems in system state research:

(1) be qualitatively analyze system state, the situation of change of system cannot be embodied intuitively.

(2) when analytic system complexity, just analyze static complexity, do not consider practical condition.

(3), during analyzing influence system state factor, simple analysis conditions of machine tool or work status, do not consider the state of workpiece and lathe.

(4) from the angle of machining functions and working ability, system state is not analyzed.

Summary of the invention

In view of this, the invention provides the defining method on a kind of Reconfigurable Manufacturing System reconstruct opportunity, can according to the change of order, fast, the reconstruction point of RMS is reasonably determined, reconstruct rapidly the machining functions and working ability that can meet the need of market, keep low cost, the fast-response characteristic of RMS.

Reconfigurable Manufacturing System of the present invention reconstructs the defining method on opportunity, comprises the steps:

Step 1, builds RMS DYNAMIC COMPLEX degree model according to information entropy theory, wherein, and RMS DYNAMIC COMPLEX degree E _xfor the positive complexity E of RMS _pcomplexity E passive of RMS _nsum; Wherein, E _pequal the feasible and unimpeded status information entropy of RMS, E _nequal feasible but blocked state information entropy and infeasible information entropy sum;

Step 2, adopting cusp catastrophe theory to build potential function is F (x)=v ₁x+v ₂x ²+ x ⁴, wherein, represent positive complexity control variable; represent passive complexity control variable; X is system state;

Step 3, the sudden change moment of solution procedure 2 potential function F (x), namely corresponding time point, this sudden change moment is the reconstitution time point of Reconfigurable Manufacturing System.

Further, described Reconfigurable Manufacturing System is made up of several manufacturing cells, and each manufacturing cell comprises several lathes, lathe of the same type has machining functions of the same race, the corresponding process route of each workpiece, this process route comprises several machining functions, then the positive complexity E of RMS _pcomplexity E passive of RMS _nbe respectively

$E_p=-\underset{i}{\overset{N}{\Σ}}\underset{j}{\overset{G_i}{\Σ}}\underset{k}{\overset{\left|S_{ij}\right|}{\Σ}}{p}_{ijk}^{1}1{\mathrm{bp}}_{ijk}^1---\left(3\right)$

$E_n=(-\underset{i}{\overset{N}{\Σ}}\underset{j}{\overset{G_i}{\Σ}}\underset{k}{\overset{\left|S_{ij}\right|}{\Σ}}{p}_{ijk}^{2}1{\mathrm{bp}}_{ijk}^2)+(-\underset{i}{\overset{N}{\Σ}}\underset{j}{\overset{G_i}{\Σ}}\underset{k}{\overset{\left|S_{ij}\right|}{\Σ}}{p}_{ijk}^{3}1{\mathrm{bp}}_{ijk}^3)---\left(4\right)$

Wherein, the logarithm that it is the end that lb represents with 2; N represents manufacturing cell's quantity that RMS comprises; G _irepresent the workpiece kind that i-th manufacturing cell comprises; S _ijrepresent the process route of the jth kind workpiece of i-th unit; represent that the jth kind workpiece of i-th unit uses S _ijbe in feasible and unimpeded shape probability of state during kth on process route machining functions, the jth kind workpiece equaling i-th unit uses S _ijthe probability of able state is in during kth on process route machining functions s is used with the jth kind workpiece of i-th unit _ijunimpeded shape probability of state is in during kth on process route machining functions product; then represent that the jth kind workpiece of i-th unit uses S _ijbe in the feasible but probability of blocked state during kth on process route machining functions, the jth kind workpiece equaling i-th unit uses S _ijthe probability of able state is in during kth on process route machining functions s is used with the jth kind workpiece of i-th unit _ijthe probability of blocked state is in during kth on process route machining functions product; then represent that the jth kind workpiece of i-th unit uses S _ijbe in the probability of nonfeasible state during kth on process route machining functions, the jth kind workpiece equaling i-th unit uses S _ijthe probability of nonfeasible state is in during kth on process route machining functions

Wherein,

$p_{ijk}^B=\underset{m=1}{\overset{M_k}{\Π}}(p_{ijkm}^G+p_{ijkm}^{\stackrel{\‾}{J}})---\left(7\right)$

$p_{ijk}^K=1-p_{ijk}^B---\left(8\right)$

$p_{ijk}^C=(1-p_{ijk}^Q)\×(1-p_{ijk}^H)---\left(9\right)$

$p_{ijk}^D=1-p_{ijk}^C---\left(10\right)$

Wherein, represent that the m platform lathe of the kth kind machining functions of the jth kind workpiece of i-th unit is in the probability of fault, the fault characteristic experience according to lathe judges; represent that but the m platform lathe of the kth kind machining functions of the jth kind workpiece of i-th unit is in machining state does not play the probability of the machining functions needed for this kind of workpiece, obtained by data statistics result; M _krepresent the lathe quantity that kth kind machining functions comprises; represent the probability of the front buffer zone of lathe without workpiece; the probability of the full workpiece in buffer zone after expression lathe;

Wherein,

$p_{ijk}^Q=\left\{\begin{array}{cc}\frac{(1-\frac{w_{ijk}^R}{w_{ijk}^C})}{1-{\left(\frac{w_{ijk}^R}{w_{ijk}^C}\right)}^{h+1}}& w_{ijk}^R\≠w_{ijk}^C\\ \frac{1}{1+h}& w_{ijk}^R=w_{ijk}^C\end{array}\right.$

$p_{ijk}^H=\left\{\begin{array}{cc}\frac{{\left(\frac{w_{ijk}^R}{w_{ijk}^C}\right)}^h\·(1-\frac{w_{ijk}^R}{w_{ijk}^C})}{1-{\left(\frac{w_{ij}^R}{w_{ijk}^C}\right)}^{h+1}}& w_{ijk}^R\≠w_{ijk}^C\\ \frac{1}{1+h}& w_{ijk}^R=w_{ijk}^C\end{array}\right.$

Wherein, w _ijkrepresent the throughput rate of a kth machining functions of workpiece in the processing jth of i-th manufacturing cell, the throughput rate of a machine tool before expression buffer area, the throughput rate of a machine tool after expression buffer area; H is the capacity of buffer area.

Beneficial effect:

The present invention utilizes information entropy to analyze rmc system DYNAMIC COMPLEX degree, achieves the quantitative description of rmc system DYNAMIC COMPLEX degree.Meanwhile, from the angle analysis rmc system complexity situation of change of machining functions and working ability, the essence of rmc system state is reflected.And apply Cusp Catastrophe, achieve the identification of rmc system state mutation time point, thus provide reconstruction point decision-making basis for estimation for decision maker, carry out system reconfiguration in time, keep the vigor of rmc system.

Accompanying drawing explanation

Fig. 1 is Reconstruction Mechanism and the implementation process schematic diagram of RMS.

Fig. 2 is the relation schematic diagram of rmc system complicacy and stability.

Fig. 3 is the state migration procedure schematic diagram of buffer area.

Fig. 4 is Cusp Catastrophe principle schematic.

Fig. 5 is dividing elements and the lathe distribution situation in workshop.

Fig. 6 is system state change trend map.

Fig. 7 is process flow diagram of the present invention.

Embodiment

To develop simultaneously embodiment below in conjunction with accompanying drawing, describe the present invention.

The invention provides the defining method on a kind of Reconfigurable Manufacturing System reconstruct opportunity, consider that rmc system state is determined by the interaction of workpiece and lathe, workpiece classification is that manufacturing system proposes machining functions demand, piece count is the demand that manufacturing system proposes working ability, lathe, as machining functions and working ability supplier, has possessed the working ability of one or more machining functions and specific quantity.Therefore, carry out analyzing the interaction relationship that can embody workpiece and lathe well from the angle of machining functions and working ability to the complexity of manufacturing system, inherently embody the state of manufacturing system, then carry out the decision-making of RMS reconstruction point in conjunction with catastrophe theory, rational reconstruct opportunity can be provided.

The present invention is based on information entropy and cusp catastrophe theory, consider machining functions and the working ability of RMS, propose a kind of defining method of RMS reconstruction point, specifically comprise the steps:

Step 1, builds RMS DYNAMIC COMPLEX degree model according to information entropy theory.

Step 1.1, the Reconstruction Mechanism analysis of Reconfigurable Manufacturing System.

After RMS has built, need one period of running-in period of experience, be called oblique ascension period, this, system stability was lower in period, easily occurred the problem such as mechanical disorder, substandard product.After debugging after a while, break-in, new system Problems existing is settleed one by one, system high efficiency even running, can carry out the activity in production of high-quality, high yield, low cost, is called as steady production period this period.Along with the operation of RMS, internal system and outside some enchancement factors occurred, as machine failure, new production order insertion etc. causes system cannot provide enough machining functions and working ability, causes part order to complete on schedule, and scheduling difficulty increases, production efficiency declines, production falls into chaos, and produces system reconfiguration demand, and system enters produces latter stage.At reasonable time node, rmc system stops production, and enters the reconstruct phase, by increase, the movement of lathe, remove, adjustment etc., rebuild machining functions and the working ability system of RMS.After having reconstructed, machining functions and the working ability of RMS are upgraded, and system capability meets the new market demand, and RMS also enters new one and takes turns in production cycle.Reconstructing each time of RMS is all constantly updating the ability of self, thus remains higher market respond ability and production efficiency.Fig. 1 describes Reconstruction Mechanism and the implementation process of RMS, as shown in Figure 1, the after date when of short duration oblique ascension, RMS has possessed provides machining functions needed for current production requirements and working ability, system can carry out steady activity in production, producing latter stage, due to the combined action of system internal and external factor, the machining functions of RMS and working ability system there will be following three kinds of problems: 1) the satisfied still working ability of machining functions does not meet; 2) the satisfied still machining functions of working ability does not meet; 3) machining functions and working ability do not meet.Now, running efficiency of system reduces, system production capacity declines gradually, there is the phenomenon of order back order, at certain time point, the disappearance of machining functions and working ability result in the state mutation of manufacturing system, and system enters the reconstruct cycle, reinvent machining functions and working ability system, enter next production cycle.

Rmc system state is machining functions and working ability interactional result under order-driven market, and the factor such as fluctuation, machine failure of order can cause the variation of machining functions and working ability, and then causes the fluctuation of system state.Rmc system complexity is the tolerance that the machining functions quantity that has of system and machining functions and working ability state fluctuate, machining functions is fewer, and the fluctuation of machining functions working ability state is less, and system state is more easily determined, system complexity is lower, and system stability is lower; Otherwise system state is difficult to determine, system complexity is higher, system stability is relatively high.The change of system complexity can reflect the situation of change of system state stability, under normal circumstances, along with the progressively increase of system machining functions, machining functions is relative steady with working ability fluctuation, system complexity can progressively increase, and system state stability also progressively increases; When system machining functions is tending towards saturated gradually, machining functions and working ability fluctuate and become greatly, and system complexity continues to increase, but system state stability then can in accelerating downward trend.Fig. 2 indicates the relation between system complexity and system state stability.

RMS produces the initial stage, and because unit, machine quantity are less, namely machining functions is relative with working ability deficient, and system complexity is lower, the scarce capacity of system reply order fluctuation, and system stability is lower; Along with the carrying out of activity in production, due to the variation of order, the machining functions of system enriches gradually, and working ability improves gradually, and system complexity progressively increases, and system reply is ordered monotropic ability and improved, and system stability is along with increase; After there is the phenomenon such as damp production, delivery extension, system complexity increases suddenly, and system cloud gray model is not smooth, system effectiveness reduces, and system stability starts to reduce, and system stability is reduced to a certain degree, system state will be undergone mutation, and cannot proceed activity in production, and system enters the reconstruct cycle.When the machining functions of system or working ability cannot meet order requirements, if be reconstructed immediately, often cause higher shutdown cost; When a large amount of extension phenomenon appears in order, now system reconfiguration difficulty is large, and reconfiguration cost is higher.The decision-making on reconstruct opportunity becomes a committed step in RMS implementation process, namely in production latter stage, by analytic system complexity situation of change, and searching system stability status catastrophe point.When system stability state is undergone mutation, carrying out activity in production further needs the cost paid suddenly to increase; In addition, if continue activity in production until system is in extremely non-steady state, now carrying out system reconfiguration needs to pay larger reconfiguration cost, and reconstitution time also can be very long.Therefore, carrying out system reconfiguration when system stability state is undergone mutation is the best opportunity, and this reconstitution time point is RMS reconstruction point, herein by the situation of change based on information entropy quantitative analysis system complexity, in conjunction with Cusp Catastrophe, completes the decision-making of RMS reconstruction point.

Step 1.2, rmc system analysis of complexity.

In RMS reconstruction point decision process, need the situation of change investigating manufacturing system complexity.Manufacturing system complexity can be seen as two classes: static complexity and DYNAMIC COMPLEX degree.State residing when static complexity mainly considers that manufacturing system carries out activity in production by operation plan, but in actual production process, due to the impact of the uncertain factor such as market fluctuation, mechanical disorder, activity in production often departs from operation plan; State residing when DYNAMIC COMPLEX degree then describes manufacturing system actual motion, embodies the system state change situation of actual production activity.Therefore, in research process, system complexity is reduced to DYNAMIC COMPLEX degree herein, chooses the system state of DYNAMIC COMPLEX degree to RMS and analyzes.

System complexity is the tolerance of a description systematic uncertainty state, information entropy then represents the size of the quantity of information that a system state comprises, information entropy can reflect the complexity situation of change of system well: when system complexity is very low, systematic uncertainty is low, illustrative system is in a kind of orderly state, quantity of information then needed for descriptive system state is less, and the information entropy of system is less; Otherwise when system complexity is very high, system state is difficult to prediction, and illustrative system is in a kind of unordered state, then the quantity of information needed for descriptive system is more, and the information entropy of system is larger.Therefore, herein based on the system complexity of information entropy theory quantitative test RMS.The mathematical description of information entropy is such as formula shown in (1).

$E\left(X\right)=-\underset{i=1}{\overset{n}{\Σ}}{p}_{i}1{\mathrm{bp}}_i$

p _i≥0(1)

$\underset{i=1}{\overset{n}{\Σ}}{p}_i=1$

Wherein, X represents a system, and E (X) represents the quantity of information that system X comprises, and is the information entropy of system X, p _i(i=1,2, n) represent that system X gets the probability of i-th symbol, the logarithm that it is the end that lb represents with 2.

According to RMS defined analysis, the capability of fast response of RMS depends on the working ability of each manufacturing cell and the adjustment capability of machining functions, and namely RMS reconstruct is driven by the adjustment of working ability and machining functions.Therefore choose the working ability of RMS and the machining functions index as descriptive system complexity, in each latter stage production cycle, the working ability of rmc system and machining functions state probability are analyzed, builds rmc system complexity information entropy model.When analytic system working ability state, the tank farm stock of selecting machine tool throughput rate and buffer area is as analysis indexes; When analytic system machining functions state, selecting machine tool machining state is as analysis indexes.

Step 1.3, RMS DYNAMIC COMPLEX degree model construction.

Rmc system carries out processing activity according to workpiece race under order-driven market, and order comprises the machining informations such as workpiece type, piece count and process route.RMS is made up of several manufacturing cells, each manufacturing cell comprises the lathe of some, and lathe of the same type is divided into machining functions of the same race, and process route then constructs the mutual relationship between machining functions, piece count then can test the working ability of lathe, namely affects the throughput rate of lathe.RMS is in operation process, and lathe can be in specific state, and the lathe quantity in unit and conditions of machine tool directly determine location mode, and the location mode that system comprises comprehensively determines system state, therefore needs to identify the conditions of machine tool in unit.

When lathe runs well, and when playing a driving role to maintenance system stability, lathe is in feasible/unimpeded state; When lathe has possessed the ability of processing tasks but efficiency declines, when playing inhibition to maintenance system stability, lathe is in feasible/blocked state; When lathe due to environmental perturbation (as new order, equipment failure etc.) cannot complete production task cause stopping production time, lathe is in nonfeasible state.The quantity of lathe, the fluctuation of conditions of machine tool determine system complexity jointly, the type of conditions of machine tool then determines complexity type, according to the operative condition of conditions of machine tool to system stability, system complexity is divided into positive complexity and passive complexity, combining information entropy theory constructing system DYNAMIC COMPLEX metrization model, shown in (2), (3), (4).

E _X＝E _p+E _n(2)

$E_p=-\underset{i}{\overset{N}{\Σ}}\underset{j}{\overset{G_i}{\Σ}}\underset{k}{\overset{\left|S_{ij}\right|}{\Σ}}{p}_{ijk}^{1}1{\mathrm{bp}}_{ijk}^1---\left(3\right)$

$E_n=(-\underset{i}{\overset{N}{\Σ}}\underset{j}{\overset{G_i}{\Σ}}\underset{k}{\overset{\left|S_{ij}\right|}{\Σ}}{p}_{ijk}^{2}1{\mathrm{bp}}_{ijk}^2)+(-\underset{i}{\overset{N}{\Σ}}\underset{j}{\overset{G_i}{\Σ}}\underset{k}{\overset{\left|S_{ij}\right|}{\Σ}}{p}_{ijk}^{3}1{\mathrm{bp}}_{ijk}^3)---\left(4\right)$

Wherein, E _xrepresent RMS DYNAMIC COMPLEX degree, E _prepresent the positive complexity of RMS, E _nrepresent the passive complexity of RMS; RMS DYNAMIC COMPLEX degree equal positive complexity and passive complexity and, positive complexity equals feasible/unimpeded status information entropy, and passive complexity equals feasible/blocking and infeasible information entropy sum; N represents manufacturing cell's quantity that RMS comprises; G _irepresent the workpiece kind that i-th unit comprises; S _ijrepresent the process route of the jth kind workpiece of i-th unit, such as manufacturing cell comprises 2 kinds of workpiece, and the process route of workpiece 1,2 is { abc}, { acd}, so S respectively ₁={ abc}, S ₂=acd}, a, b, c, d represent machining functions, and often kind of machining functions may comprise multiple stage lathe, | S _ij| represent process route length; then represent that the jth kind workpiece of i-th unit uses S _ijfeasible/unimpeded shape probability of state is in during kth on process route machining functions; then represent that the jth kind workpiece of i-th unit uses S _ijthe probability of feasible/blocked state is in during kth on process route machining functions; then represent that the jth kind workpiece of i-th unit uses S _ijthe probability of nonfeasible state is in during kth on process route machining functions.

Lathe comprises feasible/unimpeded, feasible/blocking, infeasible three kinds of states, the feasible and infeasible category belonging to machining functions, and unimpeded and blocking is then the category belonging to working ability.Because machining functions and working ability are independent mutually, therefore feasible/infeasible and unimpeded/block separate, the state probability of lathe can regard the joint probability of machining functions and working ability two type state as, namely feasible/unimpeded shape probability of state equals the product that lathe is in able state probability and unimpeded state probability, and feasible/blocked state probability equals the product that lathe is in able state probability and blocked state probability.In sum, lathe three kinds of shape probability of state method for solving are such as formula shown in (5).

$\left\{\begin{array}{c}{p}_{ijk}^1=p_{ijk}^K\·p_{ijk}^C\\ p_{ijk}^2=p_{ijk}^K\·p_{ijk}^D\\ p_{ijk}^3=p_{ijk}^B\end{array}\right.---\left(5\right)$

Wherein, represent that the jth kind workpiece of i-th unit uses S _ijthe probability of able state is in during kth on process route machining functions; represent that the jth kind workpiece of i-th unit uses S _ijunimpeded shape probability of state is in during kth on process route machining functions; represent that the jth kind workpiece of i-th unit uses S _ijthe probability of blocked state is in during kth on process route machining functions; represent that the jth kind workpiece of i-th unit uses S _ijthe probability of nonfeasible state is in during kth on process route machining functions.

Step 2, according to machining functions and working ability feature, carries out probability analysis.

Every platform lathe may possess multiple machining functions, namely lathe and machining functions are one to one or the relation of one-to-many, same lathe may play different machining functions at the different processing stages of workpiece, therefore the lathe in unit with similar machining functions is divided into same class machining functions, the relation of lathe and machining functions can represent with formula (6).

$\underset{j=1}{\overset{n}{\Σ}}{D}_{ij}\≥N_i---\left(6\right)$

Wherein, N _irepresent the lathe total amount of i-th manufacturing cell of RMS; N represents the machining functions kind comprised in manufacturing cell; D _ijrepresent the lathe quantity of the jth kind machining functions of i-th manufacturing cell.

In process, lathe comprises machining state, malfunction, idle state, when lathe is in malfunction, illustrate that all machining functions that this lathe comprises all are in nonfeasible state, that is, when all lathes belonging to certain machining functions are all in malfunction, this machining functions is infeasible; When lathe is in machining state, now, lathe only plays a kind of machining functions, and other machining functions of lathe are all in nonfeasible state.Therefore, for workpiece, the lathe that on process route, machining functions is corresponding is in machining state, but the machining functions played is not this workpiece demand, and so the machining functions of this workpiece demand is infeasible.To sum up, the method for calculating probability that whether feasible machining functions is can be obtained, shown in (7), (8).

$p_{ijk}^B=\underset{m=1}{\overset{M_k}{\Π}}(p_{ijkm}^G+p_{ijkm}^{\stackrel{\‾}{J}})---\left(7\right)$

$p_{ijk}^K=1-p_{ijk}^B---\left(8\right)$

Wherein, represent that the m platform lathe of the kth kind machining functions of the jth kind workpiece of i-th unit is in the probability of fault; represent that but the m platform lathe of the kth kind machining functions of the jth kind workpiece of i-th unit is in machining state does not play the probability of the machining functions needed for this kind of workpiece; M _krepresent the lathe quantity that kth kind machining functions comprises.

To sum up, complete the probability analysis of machining functions, comprise able state probability and the nonfeasible state probability of machining functions.

When machining functions is in able state, need to analyze associated machine tool further (now, the lathe of processing work is determined, namely machining functions and workpiece are that relation is defined as man-to-man relation) unimpeded, blocked state to obtain working ability state.When buffer area before lathe in stock, when rear buffer area is had vacant position, lathe is in unimpeded state; When the not in stock of current cache district or rear buffer area are without room, lathe is in blocked state.The state of buffer area embodies the state of lathe, therefore by the buffer state analyzed before and after lathe come calculating processing ability probability, shown in (9), (10).

$p_{ijk}^C=(1-p_{ijk}^Q)\×(1-p_{ijk}^H)---\left(9\right)$

$p_{ijk}^D=1-p_{ijk}^C---\left(10\right)$

Wherein, represent the probability of lathe front buffer zone not in stock; after expression lathe, buffer zone is without the probability in room.

Further analysis buffer area probability, suppose that the capacity of buffer area is h, so tank farm stock can be divided into h+1 state from not in stock to full stock, the previous lathe of buffer area often processes a workpiece, buffer state shifts a unit backward, and namely the throughput rate of last lathe is the input rate of transform of buffer area; After buffer area, a lathe often starts to process a workpiece, and buffer state shifts forward a unit, and namely, the throughput rate of a lathe is the Output transfer rate of buffer area, and buffer state transfer process as shown in Figure 3.

State transition equation is built, shown in (11) by above-mentioned analysis.

$\left\{\begin{array}{c}-w_{ijk}^R{p}_{ijk}^0+w_{ijk}^C{p}_{ijk}^1=0\\ w_{ijk}^R{p}_{ij1}^0-(w_{ijk}^R+w_{ijk}^C)p_{ijk}^1+w_{ijk}^C{p}_{ijk}^2=0\\ \begin{array}{cc}.& .\end{array}\\ \begin{array}{cc}.& .\end{array}\\ \begin{array}{cc}.& .\end{array}\\ -w_{ijk}^R{p}_{ijk}^{h-1}+w_{ijk}^C{p}_{ijk}^h=0\end{array}\right.---\left(11\right)$

$\underset{l=0}{\overset{h}{\Σ}}{p}_{ijk}^l=1$

Wherein, represent l shape probability of state of buffer area; As l=0, the i.e. probability of buffer area not in stock; As l=h, namely buffer area is without the probability in room; the throughput rate of a machine tool before expression buffer area, represent the throughput rate of a machine tool after buffer area, i.e. the throughput rate of a kth machining functions of workpiece in the processing jth of i-th unit.

Solve buffer state equation of transfer group (11), buffer state probability can be obtained, shown in (12).

$p_{ijk}^l=\left\{\begin{array}{cc}\frac{{\left(\frac{w_{ijk}^R}{w_{ijk}^C}\right)}^l\·(1-\frac{w_{ijk}^R}{w_{ijk}^C})}{1-{\left(\frac{w_{ijk}^R}{w_{ijk}^C}\right)}^{h+1}}& w_{ijk}^R\≠w_{ijk}^C\\ \frac{1}{1+h}& w_{ijk}^R=w_{ijk}^C\end{array}\right.---\left(12\right)$

When before lathe during buffer area not in stock, the l=0 of formula (12), the probability before lathe during buffer area not in stock is as shown in such as formula (13).

$p_{ijk}^Q=\left\{\begin{array}{cc}\frac{(1-\frac{w_{ijk}^R}{w_{ijk}^C})}{1-{\left(\frac{w_{ijk}^R}{w_{ijk}^C}\right)}^{h+1}}& w_{ijk}^R\≠w_{ijk}^C\\ \frac{1}{1+h}& w_{ijk}^R=w_{ijk}^C\end{array}\right.---\left(13\right)$

When buffer area after lathe is without room, the l=h of formula (12), after lathe buffer area without the probability in room such as formula shown in (14).

$p_{ijk}^H=\{\begin{array}{cc}\frac{{\left(\frac{w_{ijk}^R}{w_{ijk}^C}\right)}^h\·(1-\frac{w_{ijk}^R}{w_{ijk}^C})}{1-{\left(\frac{w_{ij}^R}{w_{ijk}^C}\right)}^{h+1}}& w_{ijk}^R\≠w_{ijk}^C\\ \frac{1}{1+h}& w_{ijk}^R=w_{ijk}^C\end{array}---\left(14\right)$

To sum up, complete the probability analysis of working ability, analytical calculation has been carried out to unimpeded, stopping state under the feasible prerequisite of machining functions.

Step 3, builds the RMS reconstruction point decision model based on Cusp Catastrophe, and carries out analysis and solution to RMS reconstruction point decision model, identifies RMS reconstruction point.

Different complexity Composition Control the ruuning situation of system, decide the stability of system, and when the positive complexity maintaining system stability is in absolute predominance, system has higher stability and production efficiency; When causing the passive complexity composition of system instability to be in absolute predominance, system stability greatly reduces, and even causes system state to produce sudden change, thus causes the generation of system reconfiguration event.Above-mentionedly show that rmc system can add due to new order in operation process, state mutation occur under the effect of the system internal and external factors such as machine failure, French mathematician THOM provide just a kind of method of common adaptation studying transition, uncontinuity and suddenly qualitative change in the catastrophe theory that 1972 propose, the system potential function that catastrophe theory is formed with state variable and external control parameter, for research object, obtains the critical point of system balancing state by potential function computing.Therefore, herein on the basis analyzing rmc system DYNAMIC COMPLEX degree, be reconstructed a little to be correlated with in conjunction with catastrophe theory and solve analysis.

In the research of THOM, when control variable is not more than 4, when state is not more than 2, can have at most 7 kinds of basic catastrophic models, conventional has 4 kinds, is respectively fold catastrophe, Cusp Catastrophe, Coattail catastrophe and butterfly sudden change.Wherein, as shown in Figure 4, what show in figure is a catastrophe manifolx having fold to the state situation of change of Cusp Catastrophe.The top of curved surface and bottom leaf are stable equilibrium states, and the middle period is unstable equilibrium state, and the amphibolic stage of the stationary stage and oblique ascension period that comprise an even running phase with each production cycle in the RMS implementation process shown in Fig. 1 has identical feature.In the ideal case, rmc system state is along AB smooth change, and system is in dynamic balance state, in actual production process, owing to there is order variation, the uncontrollable factors such as machine failure, system state can along CD path change, namely can there is state mutation in RMS after date when experienced by one section of even running, namely undergo mutation at E point, system enters the reconstruct cycle from the production cycle, after system reconfiguration completes, enter the new production cycle, after the break-in in oblique ascension period, enter new even running period, this process is called that RMS circulates, the then dynamic reflection cyclic process of the DYNAMIC COMPLEX degree of system, positive complexity and passive complexity maintain the state of system as two control variable in mutual containing, when positive complexity dominate, system is in even running period, when passive complexity dominate, system state can be undergone mutation, when positive complexity and passive complexity are matched each other in strength, system may be in oblique ascension and also may to be in period and to produce latter stage, if be in oblique ascension period, positive complexity can be got the upper hand gradually, otherwise produce latter stage if be in, passive complexity can be got the upper hand gradually.

According to above-mentioned analysis, based on cusp catastrophe theory, take system stability as potential function, system complexity is that control variable builds RMS reconstruction point decision model, obtains RMS reconstruction point by solving model catastrophe point.In Cusp Catastrophe, potential function mathematical model is such as formula shown in (15).

F(x)＝v ₁x+v ₂x ²+x ⁴(15)

Wherein, F (x) is the potential function of RMS reconstruction point decision model, namely represents the stability of rmc system; v ₁, v ₂for the control variable of two in model, the value of control variable depends on positive complexity and passive complexity, and employing acts on different complexity composition and the total complexity ratio of the system value as control variable, v ₁represent positive complexity control variable, v ₂represent passive complexity control variable, consider the negative consequence of passive complexity to system stability, cancelling pole complexity control variable value is negative value, i.e. v ₂<0.Rmc system state control variable method for solving is such as formula shown in (16), (17).

$v_1=\frac{E_p}{E_X}---\left(16\right)$

$v_2=-\frac{E_n}{E_X}---\left(17\right)$

System state mutation process can be described by corresponding state curve surface, state curve surface be make the first order derivative of potential-energy function be 0 set a little, jointly form catastrophe manifolx.And meet be can the second derivative of function be 0 point set be collectively referred to as non-isolated singularity set, i.e. system state critical point.

First first order derivative is asked to formula (15) both sides, build catastrophe manifolx equation, shown in (18).

F′(x)＝v ₁+2v ₂x+4x ³＝0(18)

Again second derivative is solved to formula (15), build singular point stream shape equation, shown in (19).

F″(x)＝2v ₂+12x ²＝0(19)

Bifurcation equation is drawn, shown in (20) by formula (18), (19) cancellation x.

$\mathrm{\&Delta;}=27v_1^2+8v_2^3=0---\left(20\right)$

As Δ >0, set up, namely actively complexity occupies absolute predominance, and RMS is in dynamic steady state, does not have reconfiguration requirement; When Δ=0, set up, positive complexity and passive complexity are in dynamic balance state, and RMS is in critical point, and slightly interference just may cause rmc system state to be undergone mutation, and produces reconfiguration requirement; As Δ <0, set up, passive complexity occupies absolute predominance, and RMS steady state (SS) is undergone mutation, and needs to reconstruct immediately.

Be further described below in conjunction with concrete example.

RMS workshop comprises three machining cells, and unit 1 comprises M ₁₁, M ₁₂, M ₃, M ₄four lathes, unit 2 comprises M ₃, M ₅, M ₆, M ₇, M ₈six lathes, unit 3 comprises M _1/2, M ₅, M ₈three lathes, wherein M ₁₁, M ₁₂represent that these two lathes all possess machining functions 1; Lathe M _1/2represent that this lathe has machining functions 1 and 2, machining functions can be switched according to demand, other lathes only have a machining functions, every platform lathe can only process a workpiece simultaneously, adopt the processing rule of First Come First Served, if desired use the different machining functions of same a machine tool, the workpiece arrived afterwards enters waiting list automatically.All comprise a buffer area before and after every platform lathe, the capacity of buffer area is 5; The machining functions of rmc system and working ability system are as shown in Figure 1.First batch of order comprises 6 kinds of workpiece, corresponding process route is worked out according to workshop machining functions and working ability, production and processing task list, as shown in table 1, in table, workpiece sequence number represents workpiece classification, and process route has represented the machining functions code name that the processing needs of corresponding workpiece are used, quantity represents the demand of workpiece to working ability, process route 6,7,9 as workpiece 03 represents that this workpiece of processing needs lathe M ₆, M ₇, M ₉jointly complete.According to the working ability of the existing lathe in workshop, process T.T. that every class workpiece needs and process time of each operation as shown in table 2, every a line represents operation and the process time of each workpiece process, and the workpiece kind that every platform lathe needs are processed and process time are shown in each list.

Table 1 processing tasks table

The single-piece work timetable of table 2 different workpieces

According to distribution situation process time of table 2, the every 10 minutes lathes to system and work status are once added up, and calculating processing function and working ability probability, because data volume is comparatively large, with lathe M _1/2for example carries out probability calculation, comprise the feasible Probability p of machining functions ^k _ijk, infeasible Probability p ^b _ijk, probability of malfunction p ^g _ijkm, non-required function processing probability the unimpeded Probability p of working ability ^c _ijk, blocking probability p ^d _ijk, front buffer area Probability p ^q _ijk, rear buffer area Probability p ^h _ijk; Feasible/unimpeded Probability p of lathe ¹ _ijk, feasible/blocking probability p ² _ijk, infeasible Probability p ³ _ijk, as shown in table 3.

Table 3 lathe M _1/2dependent probability analysis

Feasible/unimpeded Probability p of each lathe of each unit is obtained by data statistics and analytical calculation ¹ _ijk, feasible/blocking probability p ² _ijk, infeasible Probability p ³ _ijk, and the algorithm combining this paper calculates rmc system complexity and RMS Cusp Catastrophe reconstruction point decision data, as shown in table 4.

Table 4 complexity and reconstruction point decision data

According to the Δ Plotting data rmc system state variation tendency figure of table 4, as shown in Figure 2.Can find out As time goes on, system state Testing index Δ data trend: when Δ value is more than or equal to 0, illustrative system can normally run, and does not need to be reconstructed; At the 50th minute, Δ value crossed over critical point, and meet the state mutation condition of Cusp Catastrophe, illustrative system state there occurs sudden change, needs to carry out rmc system reconstruct immediately.

In sum, these are only preferred embodiment of the present invention, be not intended to limit protection scope of the present invention.Within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (2)

1. Reconfigurable Manufacturing System reconstructs the defining method on opportunity, it is characterized in that, comprises the steps:

Step 1, builds RMS DYNAMIC COMPLEX degree model according to information entropy theory, wherein, and RMS DYNAMIC COMPLEX degree E _xfor the positive complexity E of RMS _pcomplexity E passive of RMS _nsum; Wherein, E _pequal the feasible and unimpeded status information entropy of RMS, E _nequal feasible but blocked state information entropy and infeasible information entropy sum;

Step 2, adopting cusp catastrophe theory to build potential function is F (x)=v ₁x+v ₂x ²+ x ⁴, wherein, represent positive complexity control variable; represent passive complexity control variable; X is system state;

Step 3, the sudden change moment of solution procedure 2 potential function F (x), namely corresponding time point, this sudden change moment is the reconstitution time point of Reconfigurable Manufacturing System.

2. Reconfigurable Manufacturing System as claimed in claim 1 reconstructs the defining method on opportunity, it is characterized in that, described Reconfigurable Manufacturing System is made up of several manufacturing cells, each manufacturing cell comprises several lathes, lathe of the same type has machining functions of the same race, the corresponding process route of each workpiece, this process route comprises several machining functions, then the positive complexity E of RMS _pcomplexity E passive of RMS _nbe respectively

$E_p=-\underset{i}{\overset{N}{\&Sigma;}}\underset{j}{\overset{G_i}{\&Sigma;}}\underset{k}{\overset{\left|S_{ij}\right|}{\&Sigma;}}{p}_{ijk}^1{\mathrm{lbp}}_{ijk}^1---\left(3\right)$

$E_n=(-\underset{i}{\overset{N}{\&Sigma;}}\underset{j}{\overset{G_i}{\&Sigma;}}\underset{k}{\overset{\left|S_{ij}\right|}{\&Sigma;}}{p}_{ijk}^2{\mathrm{lbp}}_{ijk}^2)+(-\underset{i}{\overset{N}{\&Sigma;}}\underset{j}{\overset{G_i}{\&Sigma;}}\underset{k}{\overset{\left|S_{ij}\right|}{\&Sigma;}}{p}_{ijk}^3{\mathrm{lbp}}_{ijk}^3)---\left(4\right)$

Wherein, the logarithm that it is the end that lb represents with 2; N represents manufacturing cell's quantity that RMS comprises; G _irepresent the workpiece kind that i-th manufacturing cell comprises; S _ijrepresent the process route of the jth kind workpiece of i-th unit; represent that the jth kind workpiece of i-th unit uses S _ijbe in feasible and unimpeded shape probability of state during kth on process route machining functions, the jth kind workpiece equaling i-th unit uses S _ijthe probability of able state is in during kth on process route machining functions s is used with the jth kind workpiece of i-th unit _ijunimpeded shape probability of state is in during kth on process route machining functions product; then represent that the jth kind workpiece of i-th unit uses S _ijbe in the feasible but probability of blocked state during kth on process route machining functions, the jth kind workpiece equaling i-th unit uses S _ijthe probability of able state is in during kth on process route machining functions s is used with the jth kind workpiece of i-th unit _ijthe probability of blocked state is in during kth on process route machining functions product; then represent that the jth kind workpiece of i-th unit uses S _ijbe in the probability of nonfeasible state during kth on process route machining functions, the jth kind workpiece equaling i-th unit uses S _ijthe probability of nonfeasible state is in during kth on process route machining functions

Wherein,

$p_{ijk}^B=\underset{m=1}{\overset{M_k}{\&Pi;}}(p_{ijkm}^G+p_{ijkm}^{\stackrel{\&OverBar;}{J}})---\left(7\right)$

$p_{ijk}^K=1-p_{ijk}^B---\left(8\right)$

$p_{ijk}^C=(1-p_{ijk}^Q)\&times;(1-p_{ijk}^H)---\left(9\right)$

$p_{ijk}^D=1-p_{ijk}^C---\left(10\right)$

Wherein, represent that the m platform lathe of the kth kind machining functions of the jth kind workpiece of i-th unit is in the probability of fault, the fault characteristic experience according to lathe judges; represent that but the m platform lathe of the kth kind machining functions of the jth kind workpiece of i-th unit is in machining state does not play the probability of the machining functions needed for this kind of workpiece, obtained by data statistics result; M _krepresent the lathe quantity that kth kind machining functions comprises; represent the probability of the front buffer zone of lathe without workpiece; the probability of the full workpiece in buffer zone after expression lathe;

Wherein,

$p_{ijk}^Q=\left\{\begin{array}{cc}\frac{(1-\frac{w_{ijk}^R}{w_{ijk}^C})}{1-{\left(\frac{w_{ijk}^R}{w_{ijk}^C}\right)}^{h+1}}& w_{ijk}^R\&NotEqual;w_{ijk}^C\\ \frac{1}{1+h}& w_{ijk}^R=w_{ijk}^C\end{array}\right.$

$p_{ijk}^H=\left\{\begin{array}{cc}\frac{{\left(\frac{w_{ijk}^R}{w_{ijk}^C}\right)}^h\&CenterDot;(1-\frac{w_{ijk}^R}{w_{ijk}^C})}{1-{\left(\frac{w_{ijk}^R}{w_{ijk}^C}\right)}^{h+1}}& w_{ijk}^R\&NotEqual;w_{ijk}^C\\ \frac{1}{1+h}& w_{ijk}^R=w_{ijk}^C\end{array}\right.$

Wherein, w _ijkrepresent the throughput rate of a kth machining functions of workpiece in the processing jth of i-th manufacturing cell, the throughput rate of a machine tool before expression buffer area, the throughput rate of a machine tool after expression buffer area; H is the capacity of buffer area.