CN107358046B - Multi-life-part replacement strategy search algorithm considering structural correlation - Google Patents

Multi-life-part replacement strategy search algorithm considering structural correlation Download PDF

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CN107358046B
CN107358046B CN201710567229.7A CN201710567229A CN107358046B CN 107358046 B CN107358046 B CN 107358046B CN 201710567229 A CN201710567229 A CN 201710567229A CN 107358046 B CN107358046 B CN 107358046B
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付旭云
钟诗胜
张永健
林琳
王琳
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Shandong Tianlan Information Technology Co ltd
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Harbin Institute of Technology Weihai
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Abstract

The invention relates to the technical field of maintenance of aero-engines, in particular to a multi-life part replacement strategy search algorithm considering structural correlation, which establishes a multi-life part opportunity replacement problem optimization model by taking the lowest total replacement cost of life parts in a full life cycle as an optimization target on the basis of comprehensively considering the economic correlation and the structural correlation among life parts of an aero-engine; aiming at the characteristics of an optimization model, four model solution space reduction rules are provided, a search algorithm based on the reduction rules is provided based on the provided rules, and the algorithm can obtain the optimal solution of the model. And finally, evaluating and verifying the proposed algorithm by adopting a numerical experiment and an application case. The result shows that the algorithm can realize the accurate solution of the small-scale multi-life part opportunity replacement problem.

Description

Multi-life-part replacement strategy search algorithm considering structural correlation
The technical field is as follows:
the invention relates to the technical field of maintenance of aero-engines, in particular to a multi-life part replacement strategy search algorithm considering structural correlation.
Background art:
aeroengines are complex equipment with high requirements on safety, and the maintenance cost is very high. Among other things, the replacement cost of the life piece is an important component of the engine repair cost. Taking the CFM56-5B engine as an example, the cost of replacing a full life kit is approximately $ 260 ten thousand. A life piece is a component in an engine that has a mandatory life limit. During engine operation, the life piece is not allowed to last beyond its life limit and must be replaced before reaching the life limit. The life limits of the life members vary greatly due to differences in the materials, structures, operating conditions, etc. of the life members. A turbocharger rotor life limit, such as a CFM56-5B engine, is 30000 flight cycles and a high pressure turbine rotor disk life limit is 20000 flight cycles. If only the life-span part reaching the life-span limit is replaced during each maintenance, the maintenance frequency is too many, and the maintenance cost of the engine is greatly increased; if all the life parts are replaced every time of maintenance, a large amount of waste of the life parts is caused, and economic loss is caused to an airline company. Therefore, the determination of the optimal replacement strategy of the multi-life part has important significance for reducing the maintenance cost of the engine.
At present, an effective solving algorithm can be suitable for solving the problem that the engine multi-life component can be replaced, and the current research mainly develops around the economic relevance among the components, and the research on the structural relevance among the components is less. The engine generally adopts the structural design of a unit body. When a certain service life piece is replaced, the engine needs to be decomposed into a unit body state, and certain assembly and disassembly cost can be generated correspondingly; then, the unit body in which the life member is located needs to be further disassembled, and accordingly, the assembly and disassembly costs of the unit body occur, and the assembly and disassembly costs of the unit bodies are often different. The current research considers that the fixed maintenance cost is the same no matter which life member is replaced, and the influence of the unit body where the life member is located on the maintenance cost is not considered.
The invention content is as follows:
aiming at the defects and shortcomings in the prior art, the invention provides a multi-life-part replacement strategy search algorithm considering structural correlation.
The invention is achieved by the following measures:
a multi-life part replacement strategy search algorithm considering structural correlation, characterized by comprising the steps of:
step 1: establishing a multi-life part opportunity replacement problem optimization model, specifically comprising:
step 1-1: defining the parameters: considering the total life of the engine as TlimComprising p (p ≧ 1) unit bodiesAnd the opportunity replacement of n (n is more than or equal to p) life parts, and the fixed maintenance cost of the engine is recorded as cb,0Independent of the number of replacement life pieces; the kth unit body of the engine is Mk(k. 1, 2. cndot., p) comprising nkA life part ofThe assembly and disassembly costs are cb,k(ii) a Note the bookIs MkI th of (1)k(ik＝1,2···nk) A life member having a life limit ofAt a cost ofThe current service time of the engine is recorded as T,the time of use is recorded asResidual Life was recorded asIt is obvious thatRecording the minimum residual life of all life parts as tres,min(T) that isAs the value of T is increased, it is,the number of the channels is correspondingly increased,correspondingly reduce whenWhen the temperature of the water is higher than the set temperature,must be replaced, changedThe unit body M where the life part is located is required to be arrangedkDecomposition, resulting in unit body assembly and disassembly cost cb,kThus replacing the life partThe generated cost is After the replacement, the operation of the water pump is carried out,zeroing, restarting accumulation, in order to reduce the number of engine repairs over the life cycle,the engine can be replaced in advance when other life parts are replaced, so that the fixed maintenance cost of the engine and the assembly and disassembly cost of the unit body can be saved, a certain life part is wasted, and the engine is at TlimThe number of maintenance times is recorded as m, and the time of maintenance is recorded as Tj(j ═ 1,2,. cndot., m), m is different, T isjThe total cost C of the life parts in the whole life cycle of the engine is different if the life parts replaced in each maintenance are different; solving the problem of the replacement of multiple life parts at will is to determine the replacement strategy of the multiple life parts, namely to determine m and Tj(j ═ 1,2, ·, m), life pieces that are replaced at each repair, so that C is minimal, which can be formally expressed as formula (1):
in the formula (I), the compound is shown in the specification,a solution vector formed by decision variables; n represents a natural number; representing the solution space made up of all the solution vectors,indicating the j-th maintenanceIf the replacement is not carried out, the replacement value is 1, otherwise, the replacement value is 0;is calculated as shown in equation (2):
in the formula, T0＝0，To representThe initial usage time of (a);
step 1-2: the problem of multi-life part replacement belongs to a combined optimization problem, and the solution space scale of the problem is shown as a formula (3):
the problem solution space is expressed as a tree, the root node of which represents the initial state(T＝T00) and is denoted by N0；N0Represents the 1 st repair (T ═ T)1) Is marked as N1(ii) a And so on; problem solution space treeing by N0Each node outside the node represents one maintenance, and any node N corresponding to the jth maintenancejThe decision variable involved is the maintenance opportunity TjAnd all life piece replacementm corresponds to the number from N0Length of path to leaf node, from N0The path to any leaf node corresponds to a solution to the problem;
step 2: executing a search algorithm based on a reduction rule, wherein the search algorithm specifically comprises the following contents:
step 2-1: optimizing model reduction rules, wherein the optimization model reduction rules comprise feasibility reduction rules, life part replacement reduction rules, maintenance opportunity determination reduction rules and cost reduction rules;
step 2-2: executing a search algorithm based on a reduction rule, wherein the feasibility reduction rule, the life part replacement reduction rule and the maintenance opportunity determine the reduction rule as a generation rule of the sub-nodes in the solution space tree, and the cost reduction rule is used as a sub-node search stopping rule in the solution space tree solving process;
assuming that in a certain maintenance, the life partAnd(k≠k*) All need to be replaced, then the unit body MkAndall the elements need to be decomposed, then when solving, the two unit bodies are combined into one unit body to be processed, so that the solution space of the problem can be effectively reduced, the solving efficiency is improved, the four types of reduction rules are also true for the combined unit body, and a child node generation method of the solution space tree is provided belowFor a more clear description of the child node generation method, the following is specified: at the time of maintenance TjAt a time, the collection of life-to-life parts isThe collection of the unit bodies where the life-to-life parts are located isThe collection of short-to-life parts isThe unit bodies with all life parts not reaching the life are collected intoTemporary replacement scheme life piece set is RmustAnd RchioceAnd the set of child nodes is R. Determining an arbitrary node NjChild node N ofj+1The steps of aggregation are as follows:
step1 orderWill SRESThe elements of (a) are arranged in a row from small to large, and the reduction rules determined by the maintenance opportunities can respectively determine the following sets: then
Step2 will gatherThe residual life of the life parts in the middle is sorted from small to large and respectively marked as r0,r2,···,rqThen, thenInitializing l to 0 (l is more than or equal to 0 and less than or equal to q), and recordingIs composed ofMiddle residual life less than or equal to rlOf the life-span member, i.e.
Step3 determining set of unit bodiesThe set of medium replacement life parts is:
step4 identifies a set of unit cells that do not contain life pieces,numbered according to the unit bodyThe unit bodies in the middle are arranged in a row, the number of the unit bodies isInitialization b is 1, and b is called slaveThe number of the selected unit bodies is increased,
step5 fromIn the process, b unit bodies are selected as the hair splitting objects to enableThen it sharesThe schemes are arranged in a row and are respectively marked asInitialization c 1, PcFor the c scheme, scheme PcCorresponding unit sets are
Step6 noteIs composed ofThe collection of all of the life pieces in the container,is composed ofThe set of life components with the shortest remaining life in the unit,will be provided withThe residual life of the life parts in the middle is sorted from small to large and respectively marked as r1,r2,···,rMThen, thenInitializing m to 0Is composed ofMiddle residual life of less than or equal tormOf the life-span member, i.e.
Step7 identifies the life piece replacement scheme for the unit cell not containing life pieces:the sub-node N of the life-span part replacement scheme can be determinedS: replacement of RchioceAnd RmustThe life span of the middle-sized or large-sized member,
step8 judges whether or notIf yes, continuing; otherwise, the scheme node N will be replacedSAdding into the replacement scheme child node set R, order
Step9, making M equal to M +1, judging whether M > M is satisfied, if yes, continuing, otherwise, jumping to Step7,
step10 judges whether or not c is c +1If so, continue, otherwise jump to Step6,
step11, if B is greater than B +1, judging whether B is greater than B; if yes, continuing; otherwise, the process jumps to Step5,
step12 judges whether l is greater than q by changing l to l + 1; if so, finishing the algorithm, and returning to the replacement scheme child node set R; otherwise, jumping to Step 3;
according to the child node generation method, a solving algorithm of the multi-life-part opportunistic replacement problem is provided, and the specific steps are as follows.
Step1 initializes the optimum value CminSet of optimal leaf nodes SminList of movable joints SLRoot node N0，CminIs set to a larger number, SminIs empty, SLIs empty;
step2 judges whether or not t is presentres,min(T0)≥Tlim. If so, Cmin＝0，Smin＝{N0Fourthly, the algorithm is ended; if not, N is added0Adding SL；
Step3 judgment SLWhether it is empty. If so, ending the algorithm; if not, S is specifiedLThe last node to be added is the current node Nc；
Step4 adopts child node generation method to generate current node NcThe child nodes of (1) form a set R;
step5 judges each child node in R in turnWhether or not to satisfyIf yes, removing the node from R, otherwise, continuing;
step6 successively judges whether all the life parts in each node in R can be used to TlimIf yes, calculating the objective function value corresponding to the element according to the formula (2-1), and adding the objective function value to CminComparing and updating CminAnd SminAnd removing the element from R; otherwise, the rest nodes are collected to a live node set SLReturning to the step 3;
as can be seen from the solving steps of the algorithm, the algorithm greatly reduces the problem solution space tree and can obtain the optimal solution of the problem which is replaced by a plurality of life parts of the engine.
The feasibility reduction rule in step 2-1 of the present invention is: for the problem of the chance replacement of the multi-life part shown in the formula (1), N is setj-1For solving any node in the spatial tree, if the node has a child node NjThen there areAt the same time, ifThen
The following two arguments can be easily derived from the constraint of equation (1):
introduction 1:and(i ≠ j) is a unit cell MkTwo life members of the same type, if T ═ TaWhen it is satisfied with the conditionWhen T > TaWhen it is suitable forAll are suitable for
2, leading: for the multiple-life part opportunity replacement problem shown in equation (1), it is assumed that there are two feasible solution pathsAndif there is a time point Ta So that(k＝1,2,···,p；ik＝1,2,···,nk) Then the pathIs also thatA feasible solution to this problem.
In step 2-1 of the present invention, the life-part replacement reduction rules include a life-part replacement reduction rule 1 and a life-part replacement reduction rule 2, where the life-part replacement reduction rule 1 is: for the problem of the chance replacement of the multi-life part shown in the formula (1), N is setjFor solving any node in the spatial tree, in the same unit body MkIn, if there is a life part satisfying Then there must be a node N not includedjAnd the feasible solution is not inferior to the feasible solution containing the node Nj(ii) a feasible solution; the rule states that when replacing life parts for an engine, the replacement of life parts should be performed in order of decreasing remaining life to increasing remaining life for a certain unit cell.
In step 2-1 of the present invention, the life-part replacement reduction rules include a life-part replacement reduction rule 1 and a life-part replacement reduction rule 2, where the life-part replacement reduction rule 2 is: for the problem of the chance replacement of the multi-life part shown in the formula (1), N is setjFor solving any node in the spatial tree, in the same unit body MkIn, if present Then there must be a node N not includedjAnd the feasible solution is not inferior to the feasible solution containing the node Nj(ii) a feasible solution; as can be seen from the life part replacement reduction rule 2, when the engine is repaired, the same unit body M is usedk(k 1,2, p), the life piece must be replaced by life; simultaneously, the life-span piece that is changed in the unit body needs to satisfy the condition:
maintenance opportunity determination reduction rules
The maintenance opportunity determination reduction rule in step 2-1 of the invention is as follows: for the problem of the chance replacement of the multi-life part shown in the formula (1), N is setjFor solving any node in the spatial tree, if any Then there must be a node N not includedjAnd the feasible solution is not inferior to the feasible solution containing the node NjThe feasible solution is determined by the maintenance opportunity, and when N is reached, the reduction rule is determinedjIs any node of the multi-life part opportunity replacement problem solution space tree, and the corresponding maintenance opportunity is Tj. If N is presentjPresence child node Nj+1Then N isj+1The maintenance timing of (A) can be determined as Tj+1＝Tj+tres，min(Tj)。
The cost reduction rule in step 2-1 of the present invention is: n is a radical ofaIs a node (non-leaf node) in the solution space tree, all containing node NaIs estimated by the cost of the objective function solution of (C)l(Na) The calculation can be made by equation (4):
in the formula-rounding to an integer; cost reduction rules: for the problem of the chance replacement of the multi-life part shown in the formula (1), set CminFor the global optimum of the objective function, NaTo a node in solution space (non-leaf node), if Cl(Na)＞CminThen node N is includedaIs not the optimal solution; tong (Chinese character of 'tong')From this rule, it can be seen that the lower bound value C is evaluated if the cost of the solution containing the current node is includedl(Na) Exceeds the global optimal solution C of the objective functionminThen the search path containing the current node should be terminated.
On the basis of comprehensively considering the economic relevance and the structural relevance among the life parts of the aero-engine, the total replacement cost of the life parts in the whole life cycle is the lowest as an optimization target, and a multi-life part opportunity replacement problem optimization model is established; aiming at the characteristics of an optimized model, four model solution space reduction rules are provided, a search algorithm based on the reduction rules is provided based on the provided rules, the algorithm can obtain the optimal solution of the model, and the accurate solution of the small-scale multi-life part opportunity replacement problem can be realized.
Description of the drawings:
FIG. 1 is a schematic diagram of the spatial tree of the problem solution of the present invention.
Fig. 2 is an exemplary diagram of life piece replacement reduction rule 1 according to the present invention.
Fig. 3 is an exemplary diagram of life piece replacement reduction rule 2 according to the present invention.
FIG. 4 is an exemplary illustration of a maintenance opportunity determination reduction rule in accordance with the present invention.
The specific implementation mode is as follows:
the invention will be further described with reference to the accompanying drawings.
The invention comprehensively considers the structural correlation and the economic correlation among multiple life parts, and provides a multiple life part replacement strategy search algorithm considering the structural correlation, which specifically comprises the following contents:
firstly, establishing a multi-life part opportunity replacement problem optimization model, and considering the total life of an engine as TlimThe problem of the opportunistic replacement of p (p is more than or equal to 1) unit bodies and n (n is more than or equal to p) service life pieces is solved. Recording the fixed maintenance cost of the engine as cb,0Independent of the number of replacement life pieces. The kth unit body of the engine is Mk(k. 1, 2. cndot., p) comprising nkA life part ofThe assembly and disassembly costs are cb,k. Note the bookIs MkI th of (1)k(ik＝1,2···nk) A life member having a life limit ofAt a cost ofThe current service time of the engine is recorded as T,the time of use is recorded asResidual Life was recorded asIt is obvious thatRecording the minimum residual life of all life parts as tres,min(T) that isAs the value of T is increased, it is,the number of the channels is correspondingly increased,and is correspondingly reduced. When in useWhen the temperature of the water is higher than the set temperature,it must be replaced. Replacement ofThe unit body M where the life part is located is required to be arrangedkDecomposition, resulting in unit body assembly and disassembly cost cb,kThus replacing the life partThe generated cost is After the replacement, the operation of the water pump is carried out,return to zero and restart accumulation. To reduce the number of engine repairs over the life cycle,the engine can be replaced in advance when other life parts are replaced, so that the fixed maintenance cost of the engine and the assembly and disassembly cost of the unit body can be saved, and certain life parts are wasted. The engine being at TlimThe number of maintenance times is recorded as m, and the time of maintenance is recorded as Tj(j ═ 1,2,. cndot., m). m is different from TjUnlike, the total cost C of life parts over the engine life cycle varies as the life parts are replaced at each repair.
Solving the problem of the replacement of multiple life parts at will is to determine the replacement strategy of the multiple life parts, namely to determine m and Tj(j ═ 1,2, ·, m), life piece replaced at each repair, so that C is minimal, which can be formally expressed as equation (1).
In the formula (I), the compound is shown in the specification,a solution vector formed by decision variables; n represents a natural number； Representing the solution space made up of all the solution vectors,indicating the j-th maintenanceIf the replacement is not carried out, the replacement value is 1, otherwise, the replacement value is 0;is calculated as shown in equation (2).
In the formula, T0＝0，To representThe initial usage time of (a).
And (4) performing solution space analysis, wherein the problem of the replacement of multiple life parts belongs to a combined optimization problem. The solution space scale of the problem can be easily found according to the definition of each decision variable, as shown in formula (3).
It can be seen that the problem solution space scale is extremely large, and the main influencing factors are the number p of the unit bodies, the total number n of the service life parts and the total service life T of the enginelim. Even when the total life of the engine and the number of life pieces are not too large, it is almost impossible to obtain an optimal solution by completely traversing the solution space.
It is readily apparent that the engine maintenance has a natural chronological order over time. Thus, the problem solution space can be naturally expressed as a tree, as shown in FIG. 1. The root node of the tree represents the initial state (T ═ T)00) and is denoted by N0；N0Represents the 1 st repair (T ═ T)1) Is marked as N1(ii) a And so on. Problem solution space treeing by N0Each node outside represents a repair. Any node N corresponding to jth maintenancejThe decision variable involved is the maintenance opportunity TjAnd all life piece replacementm corresponds to the number from N0The length of the path to the leaf node. From N0The path to any leaf node corresponds to a solution to the problem.
The search algorithm based on the reduction rule is executed, and in order to improve the search effectiveness, the invention provides the search algorithm based on the reduction rule. The algorithm reduces the size of the solution space mainly by three aspects: (1) only traversing the feasible solution; (2) when the child node of a certain node is determined, only the child node which can obtain the optimal solution is reserved; (3) and terminating the search for the non-optimal node in time. First, optimizing a model reduction rule, wherein the feasibility reduction rule is as follows: for the problem of the chance replacement of the multi-life part shown in the formula (1), N is setj-1For solving any node in the spatial tree, if the node has a child node NjThen there areAt the same time, ifThen
The following two arguments can be easily derived from the constraint of equation (1):
introduction 1:and(i ≠ j) is a unit cell MkTwo life members of the same type, if T ═ TaWhen it is satisfied with the conditionWhen T > TaWhen it is suitable forAll are suitable for
2, leading: for the multiple-life part opportunity replacement problem shown in equation (1), it is assumed that there are two feasible solution pathsAndif there is a time point Ta So that(k＝1,2,···,p；ik＝1,2,···,nk) Then the pathIs also a viable solution to this problem. (1) Life piece change reduction rules: including life piece replacement reduction rule 1: for the problem of the chance replacement of the multi-life part shown in the formula (1), N is setjFor solving any node in the spatial tree, in the same unit body MkIn, if there is a life part satisfying Then there must be a node N not includedjAnd the feasible solution is not inferior to the feasible solution containing the node NjIs possible.
The rule states that when replacing life parts for an engine, the replacement of life parts should be performed in order of decreasing remaining life to increasing remaining life for a certain unit cell. Life piece replacement reduction rule 2: for the problem of the chance replacement of the multi-life part shown in the formula (1), N is setjFor solving any node in the spatial tree, in the same unit body MkIn, if present Then there must be a node N not includedjAnd the feasible solution is not inferior to the feasible solution containing the node NjIs possible.
As can be seen from the life part replacement reduction rule 2, when the engine is repaired, the same unit body M is usedk(k 1,2, p), the life piece must be replaced by life; simultaneously, the life-span piece that is changed in the unit body needs to satisfy the condition:this rule can be illustrated in fig. 3.
(3) The maintenance opportunity determines a reduction rule: for the problem of the chance replacement of the multi-life part shown in the formula (1), N is setjFor solving any node in the spatial tree, if anyThen there must be a node N not includedjAnd the feasible solution is not inferior to the feasible solution containing the node NjIs possible.
The reduction rule is determined according to the maintenance time when N isjIs the task of changing the problem solution space tree by multiple life partsA node with a corresponding maintenance time of Tj. If N is presentjPresence child node Nj+1Then N isj+1The maintenance timing of (A) can be determined as Tj+1＝Tj+tres,min(Tj)。
(4) Cost reduction rule, NaIs a node (non-leaf node) in the solution space tree, all containing node NaIs estimated by the cost of the objective function solution of (C)l(Na) The calculation can be made by equation (4):
in the formulaRound is an integer.
Cost reduction rules: for the problem of the chance replacement of the multi-life part shown in the formula (1), set CminFor the global optimum of the objective function, NaTo a node in solution space (non-leaf node), if Cl(Na)＞CminThen node N is includedaIs not the optimal solution.
This rule is clearly true. From this rule, it follows that the lower bound value C is evaluated if the cost of the solution containing the current node is includedl(Na) Exceeds the global optimal solution C of the objective functionminThen the search path containing the current node should be terminated.
Executing a search algorithm based on the reduction rule, wherein the search algorithm is a solving algorithm based on the reduction rule: the feasibility reduction rule, the life part replacement reduction rule and the maintenance opportunity determination reduction rule are used as generation rules of the sub nodes in the solution space tree, and the cost reduction rule is used as a sub node search stopping rule in the solution space tree solution process.
At present, when an engine is maintained, the engine needs to be firstly decomposed into unit bodies, and then subsequent maintenance activities are carried out. Assuming that in a certain maintenance, the life partAndall need to be replaced, then the unit body MkAndthe decomposition is needed, and then when the solution is carried out, the two unit bodies are combined into one unit body for processing, so that the solution space of the problem can be effectively reduced, and the solution efficiency is improved. The four types of reduction rules also hold for the merged unit.
The method for generating child nodes of the solution space tree is given below. For a more clear description of the child node generation method, the following is specified: at the time of maintenance TjAt a time, the collection of life-to-life parts isThe collection of the unit bodies where the life-to-life parts are located is The collection of short-to-life parts isThe unit bodies with all life parts not reaching the life are collected intoTemporary replacement scheme life piece set is RmustAnd RchioceAnd the set of child nodes is R. Determining an arbitrary node NjChild node N ofj+1The steps of aggregation are as follows:
step1 orderWill SRESThe elements are arranged in a row from small to big, and the reduction rules determined by the maintenance time can be respectively determined asThe following sets: then
Step2 will gatherThe residual life of the life parts in the middle is sorted from small to large and respectively marked as r0,r2,···,rqThen, thenInitializing l to 0 (l is more than or equal to 0 and less than or equal to q), and recordingIs composed ofMiddle residual life less than or equal to rlOf the life-span member, i.e.
Step3 determining set of unit bodiesThe set of medium replacement life parts is:
step4 identifies a set of unit cells that do not contain life pieces,numbered according to the unit bodyThe unit bodies in the middle are arranged in a row, the number of the unit bodies isInitialization b is 1, and b is called slaveThe number of the selected unit cells.
Step5 fromIn the process, b unit bodies are selected as the hair splitting objects to enableThen it sharesThe schemes are arranged in a row and are respectively marked asInitialization c 1, PcFor the c scheme, scheme PcCorresponding unit sets are
Step6 noteIs composed ofThe collection of all of the life pieces in the container,is composed ofThe set of life components with the shortest remaining life in the unit,will be provided withThe residual life of the life parts in the middle is sorted from small to large and respectively marked as r1,r2,···,rMThen, thenInitializing m to 0Is composed ofMiddle residual life less than or equal to rmOf the life-span member, i.e.
Step7 identifies the life piece replacement scheme for the unit cell not containing life pieces:the sub-node N of the life-span part replacement scheme can be determinedS: replacement of RchioceAnd RmustThe life piece of (1).
Step8 judges whether or notIf yes, continuing; otherwise, the scheme node N will be replacedSAdding into the replacement scheme child node set R, order
Step9 makes M equal to M +1, judges whether M > M is satisfied, if yes, continues, otherwise, jumps to Step 7.
Step10 judges whether or not c is c +1If so, continue, otherwise jump to Step 6.
Step11, if B is greater than B +1, judging whether B is greater than B; if yes, continuing; otherwise jump to Step 5.
Step12 judges whether l is greater than q by changing l to l + 1; if so, finishing the algorithm, and returning to the replacement scheme child node set R; otherwise, jump to Step 3.
According to the child node generation method, a solving algorithm of the multi-life-part opportunistic replacement problem is provided, and the specific steps are as follows.
Step1 initializes the optimum value CminSet of optimal leaf nodes SminList of movable joints SLRoot node N0，CminIs set to a larger number, SminIs empty, SLIs empty.
Step2 judges whether or not t is presentres,min(T0)≥Tlim. If so, Cmin＝0，Smin＝{N0Fourthly, the algorithm is ended; if not, N is added0Adding SL。
Step3 judgment SLWhether it is empty. If so, ending the algorithm; if not, S is specifiedLThe last node to be added is the current node Nc。
Step4 adopts child node generation method to generate current node NcThe child nodes of (1) form a set R.
Step5 judges each child node in R in turnWhether or not to satisfyIf satisfied, the node is removed from R, otherwise, the process continues.
Step6 successively judges whether all the life parts in each node in R can be used to TlimIf yes, calculating the objective function value corresponding to the element according to the formula (2-1), and adding the objective function value to CminComparing and updating CminAnd SminAnd removing the element from R;otherwise, the rest nodes are collected to a live node set SLIn (5), return to step 3.
As can be seen from the solving steps of the algorithm, the algorithm greatly reduces the problem solution space tree and can obtain the optimal solution of the problem which is replaced by a plurality of life parts of the engine.
And (4) carrying out algorithm verification, and evaluating the provided algorithm by adopting a method of randomly generating the multiple-life-piece chance replacement problem through a numerical experiment. Let cb,0～U(100000,300000)，cb,k～U(4500,20000)，p＝1，(TlimN) ∈ {60000+10000 · k | k ═ 0,1,2,3} × {5+ k | k ═ 0,1, …,7 }. For any one (T)limN) all randomly generated 10 questions. The algorithm is implemented by Java. And solving each group of problems by adopting a proposed algorithm on a common computer. The average elapsed time t for the algorithm to solve is recorded. The table shows the results of the experiment.
As can be seen from the table, with the full life cycle TlimAnd the number n of the service life pieces is increased, the time for solving the problem is increased, and when the problem scale is large, the memory overflow occurs. For example, when Tlim60000, the solution time increases with increasing n, and when n is 11, the memory overflows.
TABLE 1 results of the experiment
Taking a certain engine of an airline company as an example, the method provided by the invention is adopted to solve the problem of the chance replacement of the multi-life part. This model of engine contains 20 life parts, and the cost of replacing a set of life parts is about $ 260 ten thousand. The table is a unit body list of the engine with the model and the life parts, and the table is a life part list of the engine with the model. Let cb,0$ 160000, Tlim60000 flight cycles. The table shows the results of the solution.
The algorithm of the invention takes 14.64min in total, 1 optimal solution is obtained, and the corresponding objective function value is $ 8142147. Application cases show that the algorithm provided by the invention is suitable for the problem of the replacement of multiple life parts of an aircraft engine.
TABLE 2 Unit body List
TABLE 3 list of life parts
TABLE 4 results of solution
On the basis of comprehensively considering the economic relevance and the structural relevance among the life parts of the aero-engine, the total replacement cost of the life parts in the whole life cycle is the lowest as an optimization target, and a multi-life part opportunity replacement problem optimization model is established; aiming at the characteristics of an optimization model, four model solution space reduction rules are provided, a search algorithm based on the reduction rules is provided based on the provided rules, and the algorithm can obtain the optimal solution of the model. And finally, evaluating and verifying the proposed algorithm by adopting a numerical experiment and an application case. The result shows that the algorithm can realize the accurate solution of the small-scale multi-life part opportunity replacement problem.

Claims (6)

1. A multi-life part replacement strategy search algorithm considering structural correlation, characterized by comprising the steps of:
step 1: establishing a multi-life part opportunity replacement problem optimization model, specifically comprising:
step 1-1: defining the parameters: considering the total life of the engine as TlimThe problem of the opportunistic replacement of p (p is more than or equal to 1) unit bodies and n (n is more than or equal to p) service life parts is solved, and the fixed maintenance cost of the engine is recorded as cb,0Independent of the number of replacement life pieces; recording the kth sheet of the engineElement is Mk(k-1, 2 …, p) containing nkA life part ofThe assembly and disassembly costs are cb,k(ii) a Note the bookIs MkI th of (1)k(ik＝1,2…nk) A life member having a life limit ofAt a cost ofThe current service time of the engine is recorded as T,the time of use is recorded asResidual Life was recorded asIt is obvious thatRecording the minimum residual life of all life parts as tres,min(T) that isAs the value of T is increased, it is,the number of the channels is correspondingly increased,correspondingly reduce whenWhen the temperature of the water is higher than the set temperature,must be replaced, changedThe unit body M where the life part is located is required to be arrangedkDecomposition, resulting in unit body assembly and disassembly cost cb,kThus replacing the life partThe generated cost is After the replacement, the operation of the water pump is carried out,zeroing, restarting accumulation, in order to reduce the number of engine repairs over the life cycle,the engine can be replaced in advance when other life parts are replaced, so that the fixed maintenance cost of the engine and the assembly and disassembly cost of the unit body can be saved, a certain life part is wasted, and the engine is at TlimThe number of maintenance times is recorded as m, and the time of maintenance is recorded as Tj(j ═ 1,2, …, m), m is different, TjThe total cost C of the life parts in the whole life cycle of the engine is different if the life parts replaced in each maintenance are different;
solving the problem of the replacement of multiple life parts at will is to determine the replacement strategy of the multiple life parts, namely to determine m and Tj(j ═ 1,2, …, m), life piece replaced at each repair, so that C is minimal, which may formalize the chartShown as formula (1):
in the formula (I), the compound is shown in the specification,a solution vector formed by decision variables; n represents a natural number; representing the solution space made up of all the solution vectors,indicating the j-th maintenanceIf the replacement is not carried out, the replacement value is 1, otherwise, the replacement value is 0;is calculated as shown in equation (2):
in the formula, T0＝0，To representThe initial usage time of (a);
step 1-2: the problem of multi-life part replacement belongs to a combined optimization problem, and the solution space scale of the problem is shown as a formula (3):
the problem solution space is expressed as a tree, the root node of which represents the initial state (T ═ T)00) and is denoted by N0；N0Represents the 1 st repair (T ═ T)1) Is marked as N1(ii) a And so on; problem solution space treeing by N0Each node outside the node represents one maintenance, and any node N corresponding to the jth maintenancejThe decision variable involved is the maintenance opportunity TjAnd all life piece replacementm corresponds to the number from N0Length of path to leaf node, from N0The path to any leaf node corresponds to a solution to the problem;
step 2: executing a search algorithm based on a reduction rule, wherein the search algorithm specifically comprises the following contents:
step 2-1: optimizing model reduction rules, wherein the optimization model reduction rules comprise feasibility reduction rules, life part replacement reduction rules, maintenance opportunity determination reduction rules and cost reduction rules;
step 2-2: executing a search algorithm based on a reduction rule, wherein the feasibility reduction rule, the life part replacement reduction rule and the maintenance opportunity determine the reduction rule as a generation rule of the sub-nodes in the solution space tree, and the cost reduction rule is used as a sub-node search stopping rule in the solution space tree solving process;
assuming that in a certain maintenance, the life partAndall need to be replaced, then the unit body MkAndwhen solving, the two unit bodies are merged into one unit body to process, which can effectively reduce the solution space of the problem and improve the solving efficiency, the above four types of reduction rules also hold for the merged unit body, the method for generating child nodes of the solution space tree is given below, and for more clearly explaining the method for generating child nodes, the following rules are provided: at the time of maintenance TjAt a time, the collection of life-to-life parts isThe collection of the unit bodies where the life-to-life parts are located is The collection of short-to-life parts isThe unit bodies with all life parts not reaching the life are collected intoTemporary replacement scheme life piece set is RmustAnd RchioceDetermining any node N, wherein the child node set is RjChild node N ofj+1The steps of aggregation are as follows:
step1 orderWill SRESThe elements of (a) are arranged in a row from small to large, and the reduction rules determined by the maintenance opportunities can respectively determine the following sets: then
Step2 will gatherThe residual life of the life parts in the middle is sorted from small to large and respectively marked as r0,r2,…,rqThen, thenInitializing l to 0 (l is more than or equal to 0 and less than or equal to q), and recordingIs composed ofMiddle residual life less than or equal to rlOf the life-span member, i.e.
Step3 determining set of unit bodiesThe set of medium replacement life parts is:
step4 identifies a set of unit cells that do not contain life pieces,numbered according to the unit bodyThe unit bodies in the middle are arranged in a row, the number of the unit bodies isInitialization b is 1, and b is called slaveThe number of the selected unit bodies is increased,
step5 fromIn the process, b unit bodies are selected as the hair splitting objects to enableThen it sharesThe schemes are arranged in a row and are respectively marked asInitialization c 1, PcFor the c scheme, scheme PcCorresponding unit sets are
Step6 noteIs composed ofThe collection of all of the life pieces in the container,is composed ofThe set of life components with the shortest remaining life in the unit,will be provided withThe residual life of the life parts in the middle is sorted from small to large and respectively marked as r1,r2,…,rMThen, thenInitializing m to 0Is composed ofMiddle residual life less than or equal to rmOf the life-span member, i.e.
Step7 identifies the life piece replacement scheme for the unit cell not containing life pieces:the sub-node N of the life-span part replacement scheme can be determinedS: replacement of RchioceAnd RmustThe life span of the middle-sized or large-sized member,
step8 judges whether or notIf yes, continuing; otherwise, the scheme node N will be replacedSAdding into the replacement scheme child node set R, order
Step9 makes M equal to M +1, judges whether M > M is satisfied, if yes, continues, otherwise, jumps to Step7,
step10 judges whether or not c is c +1If so, continue, otherwise jump to Step6,
step11 judges whether B > B by changing B to B + 1; if yes, continuing; otherwise, the process jumps to Step5,
step12 judges whether l > q by changing l to l + 1; if so, finishing the algorithm, and returning to the replacement scheme child node set R; otherwise, jumping to Step 3;
according to the child node generation method, a solving algorithm of the multi-life-part opportunistic replacement problem is provided, and the method specifically comprises the following steps:
step1 initializes the optimum value CminSet of optimal leaf nodes SminList of movable joints SLRoot node N0，CminIs set to a large number, SminIs empty, SLIs empty;
step2 judges whether or not t is presentres,min(T0)≥TlimIf so, Cmin＝0，Smin＝{N0Fourthly, the algorithm is ended; if not, N is added0Adding SL；
Step3 judgment SLWhether the algorithm is empty or not, if so, the algorithm is ended; if not, S is specifiedLThe last node to be added is the current node Nc；
Step4 adopts child node generation method to generate current node NcThe child nodes of (1) form a set R;
step5 judges each child node in R in turnWhether or not to satisfyIf yes, removing the node from R, otherwise, continuing;
step6 successively judges whether all the life parts in each node in R can be used to TlimIf yes, calculating the objective function value corresponding to the element according to the formula (1), and converting the objective function into the objective functionNumerical value and CminComparing and updating CminAnd SminAnd removing the element from R; otherwise, the rest nodes are collected to a live node set SLIn, go back to Step 3; as can be seen from the solving steps of the algorithm, the algorithm greatly reduces the problem solution space tree and can obtain the optimal solution of the problem which is replaced by a plurality of life parts of the engine.
2. The algorithm for searching multiple life-part replacement strategy considering structural correlation according to claim 1, wherein the feasibility reduction rule in step 2-1 is: for the problem of the chance replacement of the multi-life part shown in the formula (1), N is setj-1For solving any node in the spatial tree, if the node has a child node NjThen there areAt the same time, ifThen
3. The algorithm for searching multiple life-part replacement strategy considering structural correlation according to claim 1, wherein the life-part replacement reduction rules in step 2-1 include life-part replacement reduction rule 1 and life-part replacement reduction rule 2, wherein the life-part replacement reduction rule 1 is: for the problem of the chance replacement of the multi-life part shown in the formula (1), N is setjFor solving any node in the spatial tree, in the same unit body MkIn, if there is a life part satisfying Then there must be a node N not includedjAnd the feasible solution is not inferior to the feasible solution containing the node Nj(ii) a feasible solution; the rule states that when replacing life parts for an engine, the replacement of life parts should be performed in order of decreasing remaining life to increasing remaining life for a certain unit cell.
4. The algorithm for searching multiple life-part replacement strategy considering structural correlation according to claim 1, wherein the life-part replacement reduction rules in step 2-1 include life-part replacement reduction rule 1 and life-part replacement reduction rule 2, wherein the life-part replacement reduction rule 2 is: for the problem of the chance replacement of the multi-life part shown in the formula (1), N is setjFor solving any node in the spatial tree, in the same unit body MkIn, if present Then there must be a node N not includedjAnd the feasible solution is not inferior to the feasible solution containing the node Nj(ii) a feasible solution; as can be seen from the life part replacement reduction rule 2, when the engine is repaired, the same unit body M is usedk(k 1,2, …, p), the life piece must be replaced by its lifetime; simultaneously, the life-span piece that is changed in the unit body needs to satisfy the condition:
5. the algorithm for searching multiple life parts replacement strategy considering structural correlation according to claim 1, wherein the repair opportunity determination reduction rule in step 2-1 is: for the problem of the chance replacement of the multi-life part shown in the formula (1), N is setjFor solving any node in the spatial tree, if any Then there must be a node N not includedjAnd the feasible solution is not inferior to the feasible solution containing the node NjThe feasible solution is determined by the maintenance opportunity, and when N is reached, the reduction rule is determinedjIs any node of the multi-life part opportunity replacement problem solution space tree, and the corresponding maintenance opportunity is TjIf N is presentjPresence child node Nj+1Then N isj+1The maintenance timing of (A) can be determined as Tj+1＝Tj+tres,min(Tj)。
6. The algorithm for searching multiple life-parts replacement strategy considering structural correlation according to claim 1, wherein the cost reduction rule in step 2-1 is: n is a radical ofaIs a node (non-leaf node) in the solution space tree, all containing node NaIs estimated by the cost of the objective function solution of (C)l(Na) The calculation is performed by equation (4):
in the formula-rounding to an integer; cost reduction rules: for the problem of the chance replacement of the multi-life part shown in the formula (1), set CminFor the global optimum of the objective function, NaFor a node in solution space, a non-leaf node, if Cl(Na)>CminThen node N is includedaIs not the optimal solution; from this rule, it follows that the lower bound value C is evaluated if the cost of the solution containing the current node is includedl(Na) Exceeds the global optimal solution C of the objective functionminThen the search way containing the current nodeThe path should be terminated.
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