Polychromatic Sets Research Articles

Collaborative Optimization of Transfer Line Balancing and Buffer Allocation Based on Polychromatic Set

The transfer line balancing problem (TLBP) and the buffer allocation problem (BAP) are amongst the most studied problems on transfer line system. However, the two problems are usually solved separately, although they are closely interrelated. Traditional optimization of TLBP probably leads to a deviation of production rate from the actual performance which is used as the optimization objective of the following BAP, especially when the equipment reliability differences are relatively large. In this paper, an innovative approach, considering machining accessibility and machine reliability, is presented to solve the TLBP and BAP simultaneously. A polychromatic-set-based constraint model and a collaborative optimization algorithm are proposed. A group of Boolean constraint matrixes both for machining feature sets and their optional stations sets are constructed through polychromatic set theory. A new coding mode based on priority, which always keeps all schemes feasible in each iteration and suitable for GA, PSO and other intelligent algorithms, is presented to describe all the allocation information for station, process, buffer and configuration. Optimization objectives including production rate and production cost are evaluated through the COM interface with simulation software. Comparison experiments and a real case of a diesel engine block demonstrate both the validity and efficiency.

Process Sequence Planning Modeling Based on Polychromatic Sets

In view of the existing sequence planning problem, this paper presents a process scheduling model based on polychromatic sets theory. To attain the similarity and individuality of constraints of parts, the process route decision was divided into stages. A feature machining chain and process feature ranking model were built beginning with the factors that influence the processing stage and technology feature. The adoption of polychromatic sets theory simplifies the evaluation of process constraints; thus, knowledge can be expressed easily. This method not only ensures the versatility of the system, but also satisfies the customer-oriented process resource.

Optimization of line configuration and balancing for flexible machining lines

Line configuration and balancing is to select the type of line and allot a given set of operations as well as machines to a sequence of workstations to realize high-efficiency production. Most of the current researches for machining line configuration and balancing problems are related to dedicated transfer lines with dedicated machine workstations. With growing trends towards great product variety and fluctuations in market demand, dedicated transfer lines are being replaced with flexible machining line composed of identical CNC machines. This paper deals with the line configuration and balancing problem for flexible machining lines. The objective is to assign operations to workstations and find the sequence of execution, specify the number of machines in each workstation while minimizing the line cycle time and total number of machines. This problem is subject to precedence, clustering, accessibility and capacity constraints among the features, operations, setups and workstations. The mathematical model and heuristic algorithm based on feature group strategy and polychromatic sets theory are presented to find an optimal solution. The feature group strategy and polychromatic sets theory are used to establish constraint model. A heuristic operations sequencing and assignment algorithm is given. An industrial case study is carried out, and multiple optimal solutions in different line configurations are obtained. The case studying results show that the solutions with shorter cycle time and higher line balancing rate demonstrate the feasibility and effectiveness of the proposed algorithm. This research proposes a heuristic line configuration and balancing algorithm based on feature group strategy and polychromatic sets theory which is able to provide better solutions while achieving an improvement in computing time.

Workflow dynamic change and instance migration approach based on polychromatic sets theory

Dynamic changes refer to the modifications of workflow model in which some running instances are executing. When the dynamic changes occur, how to migrate the running instances from old workflow model to new workflow model is one of current research hotspots of workflow management technology. Based on polychromatic sets theory, this article proposes a new workflow dynamic change and instance migration approach for workflow management system. The frequent workflow dynamic changes are modelled and described formally. The workflow region is defined and its recognition algorithm is presented. The current running region and the dynamic change region are recognised and sorted in compound workflow model. According to the position sorting results, the selection of migration policies is implemented. A case study on order processing in manufacturing enterprise is provided to illustrate the feasibility and effectiveness of the workflow dynamic change and instance migration approach. With a formal mathematical foundation, the proposed approach reduces the problem size of workflow dynamic changes, decreases the computing complexity of workflow regions recognition, and has flexibility to take the different migration policies corresponding to the different workflow running instances dynamically.

Method of Calculating the Assembly Error Transfer Path Based on JSS Matrix

Joint surface error is described by small displacement torsors theory, error transfer properties of common assembly joint surface are analyzed. Assembly joint surface symbols with engineering semantics are defined to describe the type of joint surface and cooperate relationship. Combined with the polychromatic sets theory, joint surface and error relationship contour matrix(called joint surface symbols(JSS) matrix) that can describe assembly relationship, joint surface type and error transfer properties is established. Assembly error transfer path search method based on JSS matrix is proposed, the actual error transfer property matrix of joint surface is established, and the method of obtaining the transfer path of each error component is discussed. In view of the uncertainty problem in parallel error transfer path, highest precision is put forward as the basis of distinguishing error transfer effective path, then the effective error transfer paths of error component which is associated with the assembly precision requirements are obtained based on the error model that is established based on Jacobian-torsor theory. The feasibility and practicability of the research method is verified by an example of a typical assembly error transfer path solution.

A Scheme Design and Configuration Model of Mechanical Equipment Processing Technology based on Polychromatic Sets Theory

Various factors concerning design and producing need to be taken into account while designing and configuring the processing scheme of complex mechanical equipment. The quality of the processing scheme is directed related to the quality and function of the products. It is of great significance to make effective processing schemes for complex mechanical equipment processing. Thus, based on research and analysis of design and configuration of processing schemes of complex mechanical equipment, this paper presents a design and configuration model for designing processing scheme of complex mechanical equipment based on polychromatic sets theory. It obtains various designs and configuration schemes up to the standard of processing through using the concept of polychromatic graph and polychromatic set algorithm, and evaluates potential processing schemes based on multi-attribute fuzzy evaluation, to achieve the best processing scheme for complex mechanical equipment. Finally, this paper proves the efficacy and feasibility of the algorithm and the model through examining specific and concrete schemes.

A Method of Coordinate Measuring Path Planning Based on Polychromatic Sets

In order to improve the intelligent level of path planning in coordinate measurement, the algorithm of path planning based on theory of polychromatic sets and ant colony algorithm is proposed. The model of the relation about measured geometrical features, probe angles and inspection planes is established, and the sub path is got by grouping for the global path on the basis of conjunctive operation of polychromatic sets. The global path is optimized by planning the sub paths with ant colony algorithm. The practical example verified the validity and reliability of the proposed method.

PCB Assembly Process Optimization based on Constraint Model

The structure and assembly process of Chip Shooter (CS) machine are studied. The factors of engineering practice such as the component size and machine structure etc. are considered. The assembly optimization model of Printed Circuit Board (PCB) on CS machine is formulated. A hybrid genetic algorithm (HGA) which combine with Polychromatic Sets (PS) and Genetic Algorithm (GA) is presented. A binary piece-wise coding method is proposed. In the individual chromosome, feeder arrangement and component placement sequence is described simultaneously. Constraint model is used to consider the impact of component size on the assembly speed and the feeder arrangement of CS machine. Meanwhile the constraint model improved the quality of initial population, ensured the effectiveness of GA operation and narrowed the search space of GA obviously. Calculation example indicated that HGA optimize the component sequence and feeder arrangement simultaneously and achieve excellent practicability. The assembly efficiency of CS machine is improved obviously.

A Computable Model for PCB Assembly Optimization Based on Polychromatic Sets

A modeling methodology is presented for printed circuit board(PCB) assembly optimization based on polychromatic sets(PS) theory. A computable model framework with hierarchical structure includes three layers, which are set layer(SL), logic layer(LL) and numerical layer(NL). Based on the hierarchical model and the mapping relationship among each layer, a computable model is formulated to describe the PCB assembly optimization problem in multiple PCB assembly tasks and multiple machines. The computable model not only involves various computation parameters, complicate constraint relationships such as process constraints, resource constraints and so on in PCB assembly optimization, but also describes the shortage of component, machine failure, order change and other uncertain factors. The optimization problems of PCB assembly in low-volume environment and multiple tasks can be solved efficiently.

An assembly tolerance representation model based on spatial relations for generating assembly tolerance types

The main advantage of polychromatic sets-based assembly tolerance representation model is that the number of feature types to be processed is larger. However, the number of recommended assembly tolerance types generated by the model is somewhat large for the same feature surfaces. Furthermore, the model cannot be directly applied to further assembly tolerance analysis and synthesis due to the fact that the information of degrees of freedom cannot be processed in polychromatic sets. To further reduce the number of recommended assembly tolerance types and to lay foundation for further assembly tolerance analysis and synthesis, a spatial relation layer is introduced into the polychromatic sets-based model and an assembly tolerance representation model based on spatial relations for generating assembly tolerance types is proposed. The proposed model is hierarchically organized and consists of part layer, assembly feature surface layer, spatial relation layer and assembly tolerance type layer. Each layer is defined with an adjacency matrix, respectively. By the mapping from spatial relations to assembly tolerance types, the number of recommended assembly tolerance types generated by the mapping from feature surfaces to assembly tolerance types is able to be further reduced. In addition, the information of degrees of freedom can be attached in the elements of adjacency matrices when recommended assembly tolerance types are generated by spatial relations so that the proposed model can be directly applied to further assembly tolerance analysis and synthesis. The effectiveness of the proposed model is demonstrated by an approach for generating assembly tolerance types and a practical example.

Description of System Fault Behavior Model Based on Polychromatic Sets

The system fault behavior model was investigated by the author first. Sys tem fault behavior model describes the occurrence and development process of malfunction in product, and analyzes the transmission process of unit malfunction in system and effects of various factors on system. In order to realize simulation of system fault b ehavior, it is necessary to perform formalized process of system fault behavior model, so as to acquire the mathematic description required by computer simulation. So the formalized description of fault behavior model (FBM) based on polychromatic sets theory was introduced. With consideration of the characteristics of model hierarchy and information variety of current fault behavior model, the method of polychromatic sets and polychromatic graph was adopted to describe the information such as objects, behaviors, restrictio n and relevant correlation in model. Formalized description of fault behavior model and convenient model for computer expression and operation were realized, which laid down a further solid foundation for simulation of system fault behavior.

Workflow process modelling and resource allocation based on polychromatic sets theory

In workflow management, studying the relationship between workflow process activities and resource allocation is one of the interesting research topics. Polychromatic sets theory (PST) is a relatively new mathematical theory which is especially suitable for treating such problems. Based on PST, this paper proposes a framework of workflow process modelling and resource allocation. As the theoretical foundation, polychromatic sets (PS), polychromatic graph (PG) and isolation operation (IO) of the PS are introduced. Special net structure (SNS), a special PG with colourless nodes and concolourous edges, is also introduced, and a new workflow process model and its verification algorithm are presented. Furthermore, a workflow resource model based on the entity of PS is developed. Based on IO of PS, the allocation mechanism that considers workflow process and workflow resource is proposed. Finally, a case study is provided to demonstrate the effectiveness of the above-mentioned theory and method.

Scalable Routing Modeling for Wireless Ad Hoc Networks by Using Polychromatic Sets

Graph theory is a traditional mathematical method to analyze computer networks, including intelligent wireless networks, such as ad hoc networks, sensor networks, and wireless mesh networks. Because of the variety of the network nodes and wireless links, conventional graph theory and set theory used to describe the element of the network (node and link) are not suitable to model the modern complex wireless networks. Recent research in weighted graph and random graph theories that place a weight on the links and a probability to decide the existence of the link or not is a further step to model the wireless network in a near real-life scenario. However, it lacks the ability to describe the properties of the network node. In this paper, a new mathematical tool, polychromatic sets (PS-sets), is introduced in modeling the complex wireless networks. PS-sets have the ability to describe the property of each element, which we believe will be a perfect tool to describe the network nodes and links of wireless networks. This paper demonstrates a scalable network modeling using PS-sets theory and a routing scheme based on this model. Evaluation results show that it is simple and scalable, and its performance is superior to other conventional routing schemes. The PS-sets theory could become a new tool in studying modern complex wireless networks.

A dynamic assembly model for assembly sequence planning of complex product based on polychromatic sets theory

PurposeAssembly Sequence Planning integrating assembly Resources (ASPR) is a trend in industry. Because of the introduction of resource, the complexity of ASPR for complex product increases drastically; besides, the dynamic property of resource and the co‐existence of assembly sequence and disassembly sequence (ASDS) make the problems in ASPR more difficult. The dynamic assembly model (DAM) based on polychromatic sets (PS) theory was proposed to address these issues.Design/methodology/approachFirst, a strategy was presented to simplify ASPR, taking advantage of assembly sequence generated in the phase of assembly design which considers no resource. Secondly, the concept of DAM was discussed, and some principles/criteria for DAM modeling were generalized from experience. Then, the DAM was modeled by formalizing its incidence relations as PS matrix, and refined based on the formalized criteria, which were expressed as PS locating and collision relation models. Finally, an application case was studied to demonstrate the effectiveness of the method.FindingsThe approach could reduce the complexity of ASPR significantly, and was able to identify dynamic resource, model DAM and handle the co‐existence of ASDS effectively.Practical implicationsThe method may change the manual pattern of ASPR in simulation environment, and become a potential tool to change the pattern of traditional ASP which comes to work from scratch, by utilizing the upstream information of product design.Originality/valueDifferent from traditional assembly model, DAM was a local model which consists of partial components of product and resource, and the DAM‐based ASPR approach would make the computational complexity of product assembly become more linear than exponential.

Polychromatic set theory-based spectrum access in cognitive radios

In this study, the authors have investigated a dynamic spectrum access method for cognitive radio (CR) networks by using polychromatic sets (PS) theory. First, a power control model is proposed in which the transmission power at a CR node can be calculated by considering both the primary radio (PR)-to-CR and PR-to-PR interference under a specific outage probability. In order to allocate the available spectrum among the CR nodes in a spectrum overlay scenario, the authors further propose a channel selection algorithm based on PS. This study also gives a framework of the PS-based method and concludes with future work describing the practical implementation of the proposed framework. Effectiveness of proposed method is demonstrated through an example application.

Formalized and Semantic Modeling of Manufacturing Process Data

Based on the summary of the manufacturing process data content and the analysis of current expression approach for manufacturing process data,a formalized and unified mathematical architecture to integrate the activity,object and relationship with the process as its core based on polychromatic sets theory is proposed.A mapping of polychromatic sets-based manufacturing process data model to process specification language(PSL) core ontology is carried out.Meanwhile,the extension of PSL core semantic is also conducted to realize the semantic description of manufacturing process data.A gear shaft manufacturing process application instance with formalized and semantic definition is given to illustrate the capability and effectiveness of the proposed model for providing unified organization structure,representing associated relationship and maintaining consistent semantic of manufacturing process data.

Study on the Optimization Process Technology in NC Machining Based on the Polychromatic Sets Theory

Polychromatic sets theory is used for boxes parts CAPP expert system so as to store knowledge rules of selecting machining method in form of contour matrix. Through the logic operation of coloring in the knowledge based, the machining schemes relating to the features can be obtained. Genetic algorithm is used to sequence machining step in the machining center to make the process of sequencing machining step more flexible and convenient, and the result of sequencing machining step more reasonable.

Assembly Modeling for 3D Component Based on Polychromatic Sets

In order to improve the efficiency of assembly modeling and provide a complete assembly model for assembly sequence planning (ASP), a method of assembly modeling based on polychromatic sets (PS) is proposed. Firstly, the assembly information of 3D Component is obtained by API function in SolidWorks. In addition, assembly incident matrix, information matrix and mapping matrix are built. On the basis of these matrixes, a method of location modeling is explored. The interference relation matrix is developed by judging the spatial location and analyzing dynamic interference relation among parts. Finally, a case study is given to verify the method.

A New Knowledge Representation and Processing Method of Radar Fault Diagnosis

In order to solve the problem of complex faults of radar and bottleneck problem in the expert system, a fault diagnosis system based on hierarchical fault tree and a new method of knowledge storage for radar is developed. The radar faults are divided into subjective faults and objective faults through the analysis of knowledge for some types of radar faults. Aimed at objective faults, a knowledge base structure based on polychromatic sets theory is proposed, which solves the problems of inconvenient storage of fault tree and lacking unified mathematical model, puts forward the description method of knowledge base and realizes the intelligent knowledge reasoning. Aimed at subjective faults, a knowledge base structure based on the method of conventional production rule is founded. The system is verified using VC++6.0. The result shows that knowledge bases with different methods are built respectively according to different types of faults, which improves efficiency and accuracy of the location of faults, providing a new way on the research of radar fault diagnosis system.

A Method for Designing Assembly Tolerance Networks of Mechanical Assemblies

When designing mechanical assemblies, assembly tolerance design is an important issue which must be seriously considered by designers. Assembly tolerances reflect functional requirements of assembling, which can be used to control assembling qualities and production costs. This paper proposes a new method for designing assembly tolerance networks of mechanical assemblies. The method establishes the assembly structure tree model of an assembly based on its product structure tree model. On this basis, assembly information model and assembly relation model are set up based on polychromatic sets (PS) theory. According to the two models, the systems of location relation equations and interference relation equations are established. Then, using methods of topologically related surfaces (TTRS) theory and variational geometric constraints (VGC) theory, three VGC reasoning matrices are constructed. According to corresponding relations between VGCs and assembly tolerance types, the reasoning matrices of tolerance types are also established by using contour matrices of PS. Finally, an exemplary product is used to construct its assembly tolerance networks and meanwhile to verify the feasibility and effectiveness of the proposed method.