CN105528521B - A kind of definite method on Reconfigurable Manufacturing System reconstruct opportunity - Google Patents
A kind of definite method on Reconfigurable Manufacturing System reconstruct opportunity Download PDFInfo
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Abstract
The invention discloses a kind of definite method on Reconfigurable Manufacturing System reconstruct opportunity.Can be according to the change of order using the present invention, reconstruction point that is quick, reasonably determining RMS, reconstructs rapidly the machining function and working ability that disclosure satisfy that the market demand, keeps low cost, the fast-response characteristic of RMS.The present invention analyzes rmc system DYNAMIC COMPLEX degree first with comentropy, by RMS DYNAMIC COMPLEX degree EXIt is divided into the positive complexity E of RMSpWith RMS passiveness complexities EnThe sum of, and from machining function and the angle analysis rmc system complexity situation of change of working ability；Then, potential function is built using cusp catastrophe theory, the mutation moment of the potential function is the reconstitution time point of Reconfigurable Manufacturing System.The present invention provides reconstruction point decision-making basis for estimation for policymaker, carries out system reconfiguration in time, keeps the vigor of rmc system.
Description
Technical Field
The invention relates to the technical field of advanced manufacturing, in particular to a method for determining reconfiguration time of a reconfigurable manufacturing system.
Background
With the economic development and the increased competition of the manufacturing industry, the customer demands are more popular and diversified, which leads to the continuous increase of product types and the large fluctuation of market demands. Reconfigurable Manufacturing Systems (RMS) can provide precise functions and capability requirements according to customer requirements, and are gradually becoming a hot point of research.
The RMS can make a quick response to the market mutation, and quickly reconstruct a processing function and a processing capacity which can meet the market demand through quick adjustment of software and hardware facilities according to the various processing demands of the market. After the RMS is put into use, with the progress of production activities, under the comprehensive action of internal and external factors such as order change, machine failure and the like, the phenomena of production stagnation, delivery delay and the like occur, the difficulty of production scheduling is increased, the system efficiency is reduced, and the RMS generates the system reconfiguration requirement. Considering factors such as production cost, delay cost, reconstruction cost and the like, when reconstruction becomes sensitive, the selection of reconstruction opportunity has important significance for keeping low cost and quick response characteristic of RMS, improper reconstruction point decision can cause the problems of reconstruction cost increase, reconstruction time extension and the like, and even can cause the reconstruction to lose significance. Therefore, decision analysis studies on RMS reconstruction points are required.
The RMS has a good market prospect, and researchers at home and abroad carry out extensive and intensive researches including reconfigurability of the RMS, system layout planning, system performance analysis, a workpiece family construction method and the like. However, there is almost no research on RMS reconstruction points, and the following problems exist in the system status research:
(1) The system state is only qualitatively analyzed, and the change condition of the system cannot be intuitively reflected.
(2) When the complexity of the system is analyzed, only the static complexity is analyzed, and the actual production condition is not considered.
(3) When the factors influencing the system state are analyzed, the state of the machine tool or the state of the workpiece are simply analyzed, and the states of the workpiece and the machine tool are not comprehensively considered.
(4) The system state is not analyzed from the viewpoint of the processing function and the processing capability.
Disclosure of Invention
In view of this, the present invention provides a method for determining a reconfiguration time of a reconfigurable manufacturing system, which can quickly and reasonably determine a reconfiguration point of an RMS according to a change of an order, quickly reconfigure a processing function and a processing capability that can meet market requirements, and maintain low cost and quick response characteristics of the RMS.
The method for determining the reconfiguration time of the reconfigurable manufacturing system comprises the following steps:
step 1, an RMS dynamic complexity model is constructed according to an information entropy theory, wherein the RMS dynamic complexity E X For RMS active complexity E p And RMS negative complexity E n Summing; wherein E is p Equal to RMS feasible and clear State information entropy, E n Equal to the sum of the feasible but congested state entropy and infeasible entropy;
step 2, adopting a cusp mutation theory to construct a potential function of F (x) = v 1 x+v 2 x 2 +x 4 Wherein, in the step (A),representing an aggressive complexity control variable;a control variable representing negative complexity; x is the system state;
step 3, solving the mutation time of the potential function F (x) in the step 2, namelyAnd the corresponding time point, namely the mutation moment is the reconstruction time point of the reconfigurable manufacturing system.
Further, the reconfigurable manufacturing system is composed of a plurality of manufacturing units, each manufacturing unit comprises a plurality of machine tools, the machine tools of the same type have the same processing function, each workpiece corresponds to a process route, the process route comprises a plurality of processing functions, and the RMS positive complexity E p And RMS negative complexity E n Are respectively as
Wherein lb represents the base 2 logarithm; n represents the number of manufacturing units that the RMS contains; g i Indicates the type of the workpiece contained in the ith manufacturing unit; s ij Representing the process route of the jth workpiece of the ith unit;j-th workpiece usage S representing i-th cell ij The probability of being in a feasible and unblocked state for the kth processing function on the process route is equal to the usage S of the jth workpiece of the ith unit ij Probability of being in a feasible state at the kth processing function on the process routeUsing S with the jth workpiece of the ith cell ij Probability of being in a clear state at the kth processing function on the process routeThe product of (a);the jth workpiece of the ith cell is represented by using S ij The probability of feasible but blocked state at the k-th processing function on the process route is equal to the j-th workpiece use S of the i-th unit ij Probability of being in a feasible state at the kth processing function on the process routeUsing S with the jth workpiece of the ith unit ij Probability of being in a blocked state at the kth processing function on the process routeThe product of (a);the jth workpiece of the ith cell is represented by using S ij The probability of the k-th processing function on the process route being in an infeasible state is equal to the usage S of the j-th workpiece of the i-th unit ij Probability of being in an infeasible state at the kth processing function on the process route
Wherein the content of the first and second substances,
wherein the content of the first and second substances,the m machine tool of the kth machining function of the jth workpiece of the ith unit is in fault probability, and the m machine tool is empirically judged according to the fault characteristics of the machine tool;the probability that the mth machine tool which represents the kth machining function of the jth workpiece of the ith unit is in a machining state but does not play the machining function required by the workpiece is obtained through a data statistical result; m k Indicating the number of machine tools included in the kth processing function;representing the probability that the front buffer area of the machine tool has no workpiece;representing the probability that the rear buffer of the machine tool is full of workpieces;
wherein, the first and the second end of the pipe are connected with each other,
wherein, w ijk Indicating the productivity of the kth processing function of the ith manufacturing unit for processing the workpiece in the jth,indicating the productivity of the machine tool prior to the buffer,indicating the productivity of the next machine tool behind the cache region; h is the capacity of the buffer.
Has the advantages that:
the invention utilizes the information entropy to analyze the dynamic complexity of the RMS system, and realizes the quantitative description of the dynamic complexity of the RMS system. Meanwhile, the complexity change condition of the RMS system is analyzed from the aspects of processing function and processing capacity, and the essence of the state of the RMS system is reflected. And the identification of the state mutation time point of the RMS is realized by applying cusp mutation, so that a decision-making judgment basis of a reconstruction point is provided for a decision maker, the system reconstruction is carried out in time, and the activity of the RMS is kept.
Drawings
FIG. 1 is a schematic diagram of the reconstruction mechanism and implementation process of RMS.
FIG. 2 is a graphical representation of RMS system complexity vs. stability.
FIG. 3 is a diagram illustrating a state transition process of a cache area.
FIG. 4 is a schematic diagram illustrating the principle of cusp mutation.
Fig. 5 shows the cell division and machine tool distribution of the workshop.
Fig. 6 is a system state change trend chart.
FIG. 7 is a flow chart of the present invention.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention provides a method for determining reconfiguration time of a reconfigurable manufacturing system, considering that RMS system state is determined by interaction of workpieces and machine tools, the workpiece category provides processing function requirements for the manufacturing system, the workpiece number provides processing capacity requirements for the manufacturing system, and the machine tools are provided with one or more processing functions and a specific number of processing capacities as providers of the processing functions and the processing capacities. Therefore, the interaction relation between the workpiece and the machine tool can be well reflected by analyzing the complexity of the manufacturing system from the perspective of the processing function and the processing capacity, the state of the manufacturing system is substantially reflected, the RMS reconstruction point decision is carried out by combining the mutation theory, and the reasonable reconstruction opportunity can be given.
The invention provides a method for determining RMS reconstruction points based on information entropy and cusp mutation theory and considering the processing function and the processing capacity of RMS, which specifically comprises the following steps:
step 1, an RMS dynamic complexity model is constructed according to an information entropy theory.
Step 1.1, analyzing a reconfiguration mechanism of the reconfigurable manufacturing system.
After the RMS is built, a running-in period called a ramp-up period is required, and the system stability is low in this period, so that problems such as machine failure and unqualified products are prone to occurring. After a period of debugging and running-in, the problems of the new system are solved one by one, the system operates efficiently and stably, and the production activity with high quality, high yield and low cost can be carried out, and the period is called as a stable production period. With the running of the RMS, some random factors, such as machine tool faults, new production order insertion, etc., occurring inside and outside the system cause that the system cannot provide enough processing functions and processing capabilities, so that part of orders cannot be completed on schedule, the scheduling difficulty is increased, the production efficiency is reduced, the production is disordered, the system reconfiguration requirement is generated, and the system enters the final stage of production. At the appropriate time node, the RMS system is shut down, enters a reconfiguration period, and the machining function and capacity system of the RMS is reconstructed by adding, moving, removing, adjusting, etc. machine tools. After reconstruction is completed, the processing function and the processing capacity of the RMS are updated, the system capacity meets the new market demand, and the RMS also enters a new production cycle. Each reconstruction of the RMS continuously updates its own capabilities, thereby always maintaining high market response and production efficiency. Fig. 1 illustrates the reconstruction mechanism and implementation process of the RMS, and as can be seen from fig. 1, after a short ramp-up period, the RMS has the processing function and processing capacity required to provide the current production demand, the system can perform smooth production activities, and at the end of production, due to the combined effect of internal and external factors in the system, the processing function and processing capacity system of the RMS has the following three problems: 1) The processing function is satisfied but the processing ability is not satisfied; 2) The processing capability is satisfied but the processing function is not satisfied; 3) Neither the processing function nor the processing ability was satisfied. At the moment, the operation efficiency of the system is reduced, the capacity of the system is gradually reduced, the phenomenon of delayed delivery of orders occurs, the state of the manufacturing system is suddenly changed due to the deficiency of the processing function and the processing capacity at a certain time point, the system enters a reconstruction period, and a system for remodeling the processing function and the processing capacity enters the next production cycle.
The RMS system state is a result of interaction between the machining function and the machining capability driven by the order, and the fluctuation of the order, the failure of the machine tool, and the like cause the fluctuation of the machining function and the machining capability, and further cause the fluctuation of the system state. The RMS system complexity is a measure of the number of processing functions owned by the system and the fluctuation of the processing functions and the processing capability state, the less the processing functions are, the smaller the fluctuation of the processing capability state of the processing functions is, the easier the system state is to determine, the lower the system complexity is, and the lower the system stability is; on the contrary, the system state is difficult to determine, the system complexity is high, and the system stability is relatively high. The change of the system complexity can reflect the change situation of the system state stability, and in general, along with the gradual increase of the system processing function, the fluctuation of the processing function and the processing capacity is relatively stable, the system complexity can be gradually increased, and the system state stability is also gradually increased; when the processing function of the system gradually tends to be saturated and the fluctuation of the processing function and the processing capacity becomes large, the complexity of the system continues to increase, but the stability of the system state tends to be in an accelerated decline. Fig. 2 indicates the relationship between system complexity and system state stability.
In the initial stage of RMS production, because the number of units and machines is small, namely the processing function and the processing capacity are relatively deficient, the complexity of the system is low, the capacity of the system for coping with order fluctuation is insufficient, and the stability of the system is low; along with the progress of production activities, due to the change of orders, the processing functions of the system are gradually enriched, the processing capacity is gradually improved, the complexity of the system is gradually increased, the capacity of the system for responding to the change of the orders is improved, and the stability of the system is increased along with the change of the orders; after the phenomena of production stagnation, delivery delay and the like occur, the complexity of the system increases suddenly, the system is not smooth to operate, the efficiency of the system is reduced, the stability of the system begins to be reduced, the system state changes suddenly after the stability of the system is reduced to a certain degree, the production activity cannot be continued, and the system enters a reconstruction period. When the processing function or the processing capacity of the system cannot meet the order requirement, higher production stop cost is often caused if the system is immediately reconstructed; when a large amount of delays appear in the order, the system reconstruction difficulty is high, and the reconstruction cost is high. The decision of the reconstruction opportunity becomes a key step in the RMS implementation process, namely, at the end of production, the system stability state mutation point is searched by analyzing the system complexity change condition. When the system is mutated in a stable state, the cost for further production activities is increased suddenly; in addition, if the production activities are continued until the system is in an extremely unstable state, then the system reconstruction will be carried out at a high reconstruction cost, and the reconstruction time will be long. Therefore, when the system is subjected to mutation in the stable state, the system reconstruction is the best opportunity, the reconstruction time point is the RMS reconstruction point, and the RMS reconstruction point decision is completed by quantitatively analyzing the change condition of the system complexity based on the information entropy and combining the cusp mutation.
Step 1.2, RMS System complexity analysis.
In the RMS reconstruction point decision process, the variation of the complexity of the manufacturing system needs to be examined. Manufacturing system complexity can be seen in two categories: static complexity and dynamic complexity. The static complexity mainly considers the state of a manufacturing system when the manufacturing system carries out production activities according to a scheduling plan, but in the actual production process, the production activities often deviate from the scheduling plan due to the influence of uncertain factors such as market fluctuation, machine faults and the like; the dynamic complexity describes the state of the manufacturing system during actual operation, and represents the system state change condition of actual production activities. Therefore, the system complexity is reduced to dynamic complexity in the research process, and the dynamic complexity is selected to analyze the system state of the RMS.
The system complexity is a measure for describing a system uncertainty state, the information entropy represents the size of the information quantity contained in a system state, and the information entropy can well reflect the complexity change condition of the system: when the complexity of the system is low, the uncertainty of the system is low, and the system is in an ordered state, so that the amount of information required for describing the state of the system is less, and the entropy of the information of the system is less; on the contrary, when the complexity of the system is high, the state of the system is difficult to predict, which indicates that the system is in an unordered state, and the amount of information required for describing the system is large, and the entropy of the information of the system is large. Therefore, the system complexity of RMS is quantitatively analyzed herein based on the information entropy theory. The mathematical description of the information entropy is shown in formula (1).
p i ≥0 (1)
Wherein X represents a system, E (X) represents the information content contained in the system X, namely the information entropy value of the system X, and p i (i =1,2, ·, n) represents the probability that system X takes the ith symbol, and lb represents the base-2 logarithm.
The fast response capability of the RMS, according to the RMS definition analysis, depends on the process capability of the individual manufacturing units and the adjustment capability of the process function, i.e., the RMS reconstruction is driven by the adjustment of the process capability and the process function. Therefore, the processing capacity and the processing function of the RMS are selected as indexes for describing the complexity of the system, and the processing capacity and the processing function state probability of the RMS are analyzed at the end of each production cycle to construct an RMS system complexity information entropy model. When the processing capacity state of the system is analyzed, the machine tool productivity and the inventory of a cache area are selected as analysis indexes; and when the processing function state of the system is analyzed, selecting the processing state of the machine tool as an analysis index.
Step 1.3, RMS dynamic complexity model construction.
The RMS system performs machining activities according to workpiece families under the drive of orders, and the orders comprise machining information such as workpiece types, workpiece quantities, process routes and the like. The RMS is composed of a plurality of manufacturing units, each of which contains a certain number of machine tools, the same type of machine tools are classified into the same machining functions, the process route constructs the interrelationship between the machining functions, and the number of workpieces affects the productivity of the machine tools by considering the machining capability of the machine tools. RMS during operation, the machine tool is in a specific state, the number of machine tools in a cell and the machine state directly determine the cell state, and the cell states included in the system comprehensively determine the system state, so that the machine state in a cell needs to be identified.
When the machine tool is in normal operation and has a promoting effect on maintaining the stability of the system, the machine tool is in a feasible/unblocked state; when the machine tool has the capability of finishing the processing task but the efficiency is reduced, and the effect of maintaining the stability of the system is hindered, the machine tool is in a feasible/blocked state; when the machine tool stops production due to the fact that the machine tool cannot complete production tasks due to environmental disturbance (such as new orders, equipment faults and the like), the machine tool is in an infeasible state. The number of the machine tools and the fluctuation of the machine tool state jointly determine the system complexity, the type of the machine tool state determines the complexity type, the system complexity is divided into positive complexity and negative complexity according to the action condition of the machine tool state on the system stability, and a system dynamic complexity quantization model is constructed by combining an information entropy theory, wherein the formulas are shown as formulas (2), (3) and (4).
E X ＝E p +E n (2)
Wherein E is x Representing RMS dynamic complexity, E p Indicating RMS active complexity, E n Represents RMS negative complexity; RMS dynamic complexity equals the sum of the active complexity, which equals the feasible/clear state information entropy, and the passive complexity, which equals the sum of the feasible/blocked and infeasible information entropy; n represents the number of manufacturing units the RMS contains; g i Indicating the type of the workpiece contained in the ith cell; s ij The process route of the jth workpiece representing the ith cell, for example, the manufacturing cell contains 2 kinds of workpieces, and the process routes of the workpieces 1 and 2 are { a b c } and { a c d }, respectively, then S 1 ＝{a b c}，S 2 = { a c d }, a, b, c, d representing machining functions, each machining function possibly comprising a plurality of machine tools, | S ij L represents the process route length;the jth workpiece of the ith cell is represented by using S ij Probability of being in a feasible/unblocked state at the kth processing function on the process route;the jth workpiece of the ith cell is represented by using S ij Probability of being in a feasible/blocked state at the kth processing function on the process route;the jth workpiece of the ith cell is represented by using S ij Probability of being in an infeasible state at the kth processing function on the process route.
The machine tool comprises three states of feasible/unblocked, feasible/blocked and infeasible, wherein the feasible and infeasible belong to the category of processing functions, and the unblocked and blocked belong to the category of processing capabilities. The machining function and the machining capacity are independent, so that the feasibility/infeasibility and the smoothness/blockage are independent, the state probability of the machine tool can be regarded as the joint probability of two types of states of the machining function and the machining capacity, namely the probability of the feasible/unblocked state is equal to the product of the probability of the machine tool in the feasible state and the probability of the unblocked state, and the probability of the feasible/blocked state is equal to the product of the probability of the machine tool in the feasible state and the probability of the blocked state. In summary, the probability solving method for the three states of the machine tool is shown in the formula (5).
Wherein the content of the first and second substances,j-th workpiece usage S for i-th cell ij Probability of being in a feasible state at the kth processing function on the process route;j-th workpiece usage S representing i-th cell ij Probability of being in a smooth state at the kth processing function on the process route;j-th workpiece usage S representing i-th cell ij Probability of being in a blocked state at the kth processing function on the process route;j-th workpiece usage S representing i-th cell ij Probability of being in an infeasible state at the kth processing function on the process route.
And 2, performing probability analysis according to the characteristics of the processing function and the processing capacity.
Each machine tool may have a plurality of machining functions, that is, the machine tool and the machining function are in a one-to-one or one-to-many relationship, and the same machine tool may exert different machining functions at different machining stages of a workpiece, so that machine tools having similar machining functions in a unit are classified into the same type of machining function, and the relationship between the machine tool and the machining function can be expressed by equation (6).
Wherein, N i The total number of machine tools of the i-th manufacturing unit representing RMS; n represents the type of processing function contained in the manufacturing unit; d ij The number of machine tools of the jth machining function of the ith manufacturing unit is indicated.
In the machining process, the machine tool comprises a machining state, a fault state and an idle state, when the machine tool is in the fault state, all machining functions contained in the machine tool are in an infeasible state, namely, when all the machine tools belonging to a certain machining function are in the fault state, the machining function is infeasible; when the machine tool is in a machining state, the machine tool only performs one machining function, and other machining functions of the machine tool are in a non-feasible state. Therefore, for a workpiece, the machine tool corresponding to the processing function on the process route is in a processing state, but the processing function is not required by the workpiece, so that the processing function required by the workpiece is not feasible. In conclusion, a probability calculation method for whether the processing function is feasible or not can be obtained, as shown in formulas (7) and (8).
Wherein the content of the first and second substances,the probability that the mth machine tool of the kth machining function of the jth workpiece of the ith unit is in fault is shown;a probability that the mth machine tool, which indicates the kth machining function of the jth workpiece of the ith cell, is in a machining state but does not perform the machining function required by the jth workpiece; m k The number of machine tools included in the kth machining function is shown.
In summary, the probability analysis of the machining function is completed, including the feasible state probability and the infeasible state probability of the machining function.
When the machining function is in a feasible state, the clear, blocked state of the relevant machine tool (in this case, the machine tool that machines the workpiece is determined, i.e., the machining function and the workpiece are defined in a one-to-one relationship) needs to be further analyzed to obtain the machining capability state. When the front cache region of the machine tool has inventory and the rear cache region has a vacancy, the machine tool is in a smooth state; when the current cache region has no stock or the rear cache region has no vacancy, the machine tool is in a blocked state. The state of the buffer reflects the state of the machine tool, and therefore the probability of the machining capacity is calculated by analyzing the states of the buffer before and after the machine tool, as shown in equations (9) and (10).
Wherein the content of the first and second substances,representing the probability that the buffer area in front of the machine tool is not stored;representing the probability of no empty space in the machine tool rear buffer.
Further analyzing the probability of the cache region, and if the capacity of the cache region is h, the inventory can be divided into h +1 states from no inventory to full inventory, and when a machine tool in the front of the cache region finishes processing one workpiece, the state of the cache region is transferred backwards by one unit, namely the productivity of the front machine tool is the input transfer rate of the cache region; the state of the buffer area is shifted forward by one unit every time a machine tool behind the buffer area starts to process one workpiece, namely the productivity of the machine tool behind the buffer area is the output transfer rate of the buffer area, and the buffer area state transfer process is shown in fig. 3.
The state transition equation is constructed by the above analysis, as shown in equation (11).
Wherein the content of the first and second substances,representing the probability of the ith state of the cache region; when l =0, the signal strength of the signal is high,i.e. the probability that the buffer has no stock; when l = h, the ratio of the total of the components is as follows,i.e. the probability of no empty space in the buffer;indicating the productivity of the machine tool prior to the buffer,the productivity of the machine tool after the buffer, i.e., the productivity of the kth machining function of the ith unit that machines the workpiece in the jth.
And solving the cache region state transition equation set (11) to obtain the cache region state probability as shown in the formula (12).
When the buffer area before the machine tool is out of stock, l =0 in equation (12), and the probability when the buffer area before the machine tool is out of stock is as shown in equation (13).
When the buffer area has no vacancy after the machine tool, l = h of formula (12), and the probability that the buffer area has no vacancy after the machine tool is shown as formula (14).
Therefore, the probability analysis of the processing capacity is completed, and the smooth and blocking conditions under the condition that the processing function is feasible are analyzed and calculated.
And 3, constructing an RMS reconstruction point decision model based on cusp mutation, analyzing and solving the RMS reconstruction point decision model, and identifying RMS reconstruction points.
The components with different complexity control the running condition of the system, the stability of the system is determined, and when the positive complexity for maintaining the stability of the system is in absolute advantage, the system has higher stability and production efficiency; when the negative complexity component causing the system instability is in absolute advantage, the system stability is greatly reduced, even the system state is suddenly changed, thereby causing the occurrence of the system reconfiguration event. The above shows that the RMS system has state mutation in the operation process due to the effect of external and internal factors of the system such as new order addition, machine tool failure and the like, and the mutation theory proposed by french mathematician THOM in 1972 provides a common adaptive method for studying transition, discontinuity and sudden qualitative change, and the mutation theory takes a system potential function consisting of state variables and external control parameters as a study object, and obtains the critical point of the system equilibrium state through potential function operation. Therefore, the reconstructed point correlation solution analysis is carried out by combining mutation theory on the basis of analyzing the dynamic complexity of the RMS system.
In the THOM study, when the manipulated variable is not greater than 4 and the state is not greater than 2, there can be 7 basic mutation models at most, and 4 are commonly used, which are a folding mutation, a cusp mutation, a dovetail mutation and a butterfly mutation, respectively. The state change of the sharp point mutation is shown in fig. 4, which shows a creased mutation manifold. The curved top and bottom lobes are stable equilibrium states and the middle lobe is unstable equilibrium state, which has the same characteristics as the stable period including a smooth-running period and the unstable period including a ramp-up period per production cycle in the RMS implementation shown in fig. 1. In an ideal case, the RMS system state varies smoothly along AB, the system is in dynamic equilibrium; in the actual production process, due to uncontrollable factors such as order change, machine tool faults and the like, the state of the system can change along a CD path, namely, the RMS can generate state mutation after undergoing a period of stable operation, namely mutation occurs at the E point, the system enters a reconstruction period from the production period, the system enters a new production period after reconstruction is completed, the system enters a new stable operation period after running-in of a ramp-up period, the process is called RMS circulation, the dynamic complexity of the system dynamically reflects the circulation process, the active complexity and the passive complexity serve as two control variables to maintain the state of the system in mutual balance, and when the active complexity occupies a dominant position, the system is in the stable operation period; when the negative complexity dominates, the system state changes suddenly; when the active complexity and the passive complexity are equal, the system may be in a ramp-up period or a late-producing period, if the system is in the ramp-up period, the active complexity gradually occupies the upwind, and if the system is in the late-producing period, the passive complexity gradually occupies the upwind.
According to the analysis, based on a cusp mutation theory, an RMS reconstruction point decision model is constructed by taking the system stability as a potential function and the system complexity as a control variable, and RMS reconstruction points are obtained by solving the model mutation points. The potential function mathematical model in the cusp mutation is shown as formula (15).
F(x)＝v 1 x+v 2 x 2 +x 4 (15)
Wherein, F (x) is a potential function of the RMS reconstruction point decision model, namely representing the stability of the RMS system; v. of 1 、v 2 For two control variables in the model, the values of the control variables depend on the active complexity and the passive complexity, the ratio of the components with different complexity to the total complexity of the system is used as the value of the control variable, v 1 Representing the active complexity control variable, v 2 The negative complexity control variable is expressed, and the negative complexity control variable value is taken into account to have negative effect on the stability of the system, namely v 2 <, 0. The RMS system state control variable solving method is shown in equations (16) and (17).
The system state mutation process can be described by using a corresponding state surface, wherein the state surface is a set of all points enabling the first derivative of the potential energy function to be 0, and the set of all points together form a mutation manifold. And the set of points satisfying that the second derivative of the energy function is 0 is called the set of non-isolated singularities, i.e., the system state critical points.
First, the first derivative is obtained on both sides of the equation (15) to construct a sudden change manifold equation, which is shown in the equation (18).
F′(x)＝v 1 +2v 2 x+4x 3 ＝0 (18)
And solving the second derivative of the equation (15) to construct a singular point manifold equation as shown in the equation (19).
F″(x)＝2v 2 +12x 2 ＝0 (19)
The equation (18) and (19) are eliminated by x to obtain a divergent equation, which is shown in equation (20).
When delta>0，The method is established, namely the active complexity occupies absolute advantage, the RMS is in a dynamic stable state, and no reconstruction requirement exists; when the ratio of the Δ =0,the method comprises the following steps that (1) the positive complexity and the negative complexity are in a dynamic balance state, the RMS is in a critical point, and the state of the RMS system is possibly mutated due to slight interference to generate a reconstruction requirement; when delta<0，It is true that the negative complexity dominates the absolute and the RMS steady state is mutated and needs to be reconstructed immediately.
The following is a further description with reference to specific examples.
The RMS plant contains three process units, unit 1 contains M 11 、M 12 、M 3 、M 4 Four machine tools, unit 2 containing M 3 、M 5 、M 6 、M 7 、M 8 Six machine tools, unit 3 contains M 1/2 、M 5 、M 8 Three machine tools, wherein M 11 、M 12 Showing that both machine tools have a machining function 1; machine tool M 1/2 The machine tool has the processing functions of 1 and 2, the processing functions can be switched according to requirements, other machine tools only have one processing function, each machine tool can only process one workpiece at the same time, the processing rule of first-come first-serve is adopted, and if different processing functions of the same machine tool are needed, the later workpieces automatically enter a waiting queue. Each machine tool comprises a buffer area in front of and behind each machine tool, and the capacity of the buffer area is 5; the system of process functions and process capabilities of an RMS system is shown in figure 1. The first batch of orders comprises 6 workpieces, corresponding process routes are compiled according to workshop processing functions and processing capacity, a processing task table is produced, as shown in table 1, the serial numbers of the workpieces in the table represent the types of the workpieces, the process routes represent the processing function codes required for completing the processing of the corresponding workpieces, the quantity represents the requirements of the workpieces on the processing capacity, and as shown in the process route 6,7,9 of the workpiece 03, the machine tool M required for processing the workpiece is represented 6 、M 7 、M 9 And (4) jointly completing. The total time required to machine each type of workpiece and the machining time of each process are shown in table 2 based on the machining capacity of the existing machine tool in the workshop, each row indicating the process and machining time each workpiece has passed through, and each column indicating the type of workpiece and machining time each machine tool needs to machine.
TABLE 1 processing assignment table
TABLE 2 Single piece processing schedule for different workpieces
According to the distribution of the processing time in table 2, the states of the machine tool and the workpiece of the system are counted every 10 minutes, and the probability of the processing function and the processing capability is calculated, and the machine tool M is used because the data volume is large 1/2 For example, probability calculation including work of machining is performedProbability of feasibility of a capability p K ijk Probability of infeasibility p B ijk Probability of failure p G ijkm Probability of undesired functional processingUnblocked probability p of processing capacity C ijk Probability of clogging p D ijk Pre-buffer probability p Q ijk Post-buffer probability p H ijk (ii) a Probability p of possible/unblocked machine tool 1 ijk Probability of feasibility/blocking p 2 ijk Probability of infeasibility p 3 ijk As shown in table 3.
TABLE 3 machine tool M 1/2 Correlation probability analysis of
Obtaining the feasible/unblocked probability p of each machine tool of each unit through data statistics and analysis calculation 1 ijk Probability of feasibility/blocking p 2 ijk Probability of infeasibility p 3 ijk And computing RMS system complexity and RMS cusp mutation reconstruction point decision data in conjunction with the algorithm herein, as shown in table 4.
TABLE 4 complexity and reconstruction point decision data
The RMS system state change trend was plotted against the delta data of table 4, as shown in figure 2. It can be seen that over time, the system state detection indicator Δ data trend: when the delta value is greater than or equal to 0, the system can normally operate without reconstruction; at 50 minutes, the delta value crosses the critical point, and the state mutation condition of cusp mutation is met, which indicates that the system state is mutated and RMS system reconstruction is required to be carried out immediately.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (1)
1. A method for determining a reconfiguration time of a reconfigurable manufacturing system, comprising the steps of:
step 1, constructing an RMS dynamic complexity model according to an information entropy theory, wherein the RMS dynamic complexity E X For RMS active complexity E p And RMS negative complexity E n Summing; wherein E is p Equal to RMS feasible and clear state information entropy, E n Equal to the sum of the feasible but congestion status entropy and infeasible entropy;
wherein the reconfigurable manufacturing system is composed of a plurality of manufacturing units, each manufacturing unit comprises a plurality of machine tools, the machine tools of the same type have the same processing function, each workpiece corresponds to a process route, the process route comprises a plurality of processing functions, and the RMS active complexity E p And RMS negative complexity E n Are respectively as
Wherein lb represents the base 2 logarithm; n represents the number of manufacturing units that the RMS contains; g i Indicates the type of the workpiece contained in the ith manufacturing unit; s ij Representing the process route of the jth workpiece of the ith unit;j-th workpiece usage S for i-th cell ij Kth processing function on process routeThe probability of being in a feasible and unblocked state is equal to the using S of the jth workpiece of the ith unit ij Probability of being in a feasible state at the kth processing function on the process routeUsing S with the jth workpiece of the ith cell ij Probability of being in a clear state at the kth processing function on the process routeThe product of (a);the jth workpiece of the ith cell is represented by using S ij The probability of being in a feasible but blocking state at the k-th processing function on the process route is equal to the usage S of the j-th workpiece of the i-th unit ij Probability of being in a feasible state at the kth processing function on the process routeUsing S with the jth workpiece of the ith cell ij Probability of being in a blocked state at the kth processing function on the process routeThe product of (a);the jth workpiece of the ith cell is represented by using S ij The probability of the k-th processing function on the process route being in an infeasible state is equal to the usage S of the j-th workpiece of the i-th unit ij Probability of being in an infeasible state at the kth processing function on the process route
Wherein, the first and the second end of the pipe are connected with each other,
wherein the content of the first and second substances,the m machine tool of the kth machining function of the jth workpiece of the ith unit is in fault probability, and the m machine tool is empirically judged according to the fault characteristics of the machine tool;the probability that the mth machine tool representing the kth machining function of the jth workpiece of the ith unit is in a machining state but does not exert the machining function required by the workpiece is obtained through data statistics; m k Indicating the number of machine tools included in the k-th machining function;representing the probability that the front buffer area of the machine tool has no workpiece;representing the probability that the rear buffer of the machine tool is full of workpieces;
wherein, the first and the second end of the pipe are connected with each other,
wherein, w ijk Indicating the productivity of the kth processing function of the ith manufacturing unit for processing the workpiece in the jth,indicating the productivity of the machine tool prior to the buffer,indicating the productivity of the next machine tool behind the cache region; h is the capacity of the buffer area;
step 2, adopting a cusp mutation theory to construct a potential function of F (x) = v 1 x+v 2 x 2 +x 4 Wherein, in the step (A),representing an aggressive complexity control variable;representing a negative complexity control variable; x is the system state;
step 3, solving the mutation time of the potential function F (x) in the step 2, namelyAnd the corresponding time point, namely the mutation moment is the reconstruction time point of the reconfigurable manufacturing system.
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