JP2008165310A - Multivariable model analysis system, method, program and program medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a multivariable analysis system capable of easily obtaining design variables having interactions. <P>SOLUTION: This system comprises a determination part which determines that, for other variable than predetermined variables, the other variables and the predetermined variables have interactions when the rate of change of conditions between a first cluster of a cluster set A and a first cluster of a cluster set B is different from the rate of change of conditions between a second cluster of the cluster set A and a second cluster of the cluster B. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a multivariable model analysis system, method, program, and program medium that extracts the principle of an analysis model by analyzing the relationship between a plurality of variables and characteristic values.

  With the recent development of computer technology, simulation systems and CAE (Computer-Aided Engineering) have been widely used in many fields. In the field of automobile design, the theoretical formula of the entire automobile was constructed by combining the theoretical formulas of the individual parts of the automobile, and the design was performed based on the simulation using this theoretical formula. The theoretical formula is expressed by a relational expression between design variables (design factors) such as the material, size, and shape of the structure and characteristic values such as riding comfort and noise. A desired design variable has been determined by simulating characteristic values using this theoretical formula.

  For example, the system described in Japanese Patent Application Laid-Open No. 2002-356106 is modeled on the basis of an input variable, a means for modeling a tire to be designed, a means for inputting a vehicle, a running condition, and the like as variables. Means for simulating the running of the tire. That is, this system is intended to perform a precise simulation by modeling a tire to be designed and defining many variables such as an actual running state and a vehicle structure.

  However, the greater the number of variables, the more complex the theoretical model of the design model, and it is not easy for the designer to understand the relationship between the variables and the characteristic values. That is, it is difficult to grasp the principle inherent in the design model from a complicated theoretical formula. In addition, if the theoretical formula becomes complicated, the amount of calculation and time required for the simulation become enormous, resulting in a problem that the design period and development cost increase.

  As another conventional technique, a design method described in JP 2000-315218 A has been devised. In this method, in the design of a structure model, optimization is calculated by calculating the sensitivity by evaluating the rigidity of each part of the design model, and setting the characteristics of the part having a relatively large sensitivity as a design variable. This reduces the number of design variables used. That is, according to this method, it is possible to perform optimization calculation with fewer variables by automatically selecting highly sensitive parts.

  However, this method merely makes it possible to reduce design variables by simply referring to the sensitivity of each part, and does not extract the principle inherent in the model to be designed. For this reason, it is impossible to extract the principle that connects the design variable and the characteristic value, and it is difficult for the designer to grasp the design policy.

  That is, in a complicated structure, the number of design variables increases and the theoretical formula becomes extremely complicated. Even if a simulation is performed by the response surface method, it is extremely difficult to determine how to determine a design variable in order to obtain a desired characteristic value. Furthermore, in the case of complex structures, enormous amounts of computation and time are required to perform model simulations that include the number of design variables and complex theoretical equations, and the design time and development costs are enormous. Can be.

A multivariable analysis system described in WO 2006/046737 by the applicant of the present application has been devised to show the direction for solving the above-mentioned problems. This system generates a plurality of models by substituting various values into design variables of a theoretical formula to be designed, and clusters models having approximate characteristic values. By extracting design factors whose correlation coefficient exceeds a predetermined value in each cluster, it becomes possible to extract the principles and laws inherent in the design model.
WO2006 / 046737

  In the above-described prior art, it has become possible to analyze the relationship between the design variable and the characteristic value, but no approach has been made to grasp the design variable having a so-called interaction. Although it is possible to grasp the interaction using the response surface method, the amount of calculation is enormous, and it is not suitable for the analysis of a complicated design model.

  Therefore, an object of the present invention is to provide a multivariable model analysis system that can easily grasp design variables having interaction.

  In order to solve the above-described problems, the present invention calculates a characteristic value of a model based on a model generation unit that generates a plurality of models each having a plurality of variables, the model model, and the model A characteristic value calculation unit for writing the variable and characteristic value of the first variable into the memory map, and for each of the two conditions A and B of the specific variable, at least first and second clusters of the model based on the magnitude of the characteristic value Are classified into the cluster set A corresponding to the condition A, the partial clustering unit for generating the cluster set B corresponding to the condition B, and the first cluster of the cluster set A for other variables than the specific variable. And the change rate of the condition between the first cluster of the cluster set B and the second cluster of the cluster set A and the second cluster of the cluster set B If different from the rate of change of condition between the clusters, and the other variables and the specific variable is determined to have interaction, and a determination unit for writing the determination result to the memory map.

  The conditions A and B may be an upper limit value and a lower limit value given to the specific variable.

  The model generation unit may determine a plurality of variables using an orthogonal table.

  The present invention further includes an extraction unit that extracts variables determined to have an interaction by the determination unit.

  Furthermore, the present invention further includes a database that stores and retrieves the variables extracted by the extraction unit.

  The model may be a multi-layer package.

  In the present invention, the model generation unit generates a plurality of models each having a plurality of variables, and the characteristic value calculation unit calculates the characteristic value of the model based on the given model variable, and the variable of the model And write the characteristic value to the memory map. The partial clustering unit corresponds to the condition A by classifying the model into at least first and second clusters based on the magnitude of the characteristic value for each of the two conditions A and B of the specific variable. Cluster set A and cluster set B corresponding to condition B are generated.

  The determination unit determines that the change rate of the condition between the first cluster of the cluster set A and the first cluster of the cluster set B for the variables other than the specific variable is the second cluster and the cluster of the cluster set A. If the rate of change in the condition with the second cluster of set B is different, it is determined that the other variable and the specific variable have an interaction. Therefore, it is possible to grasp the relationship of interaction, that is, the relationship in which the condition of the other design variable is influenced by the condition of one design variable.

  According to the present invention, by using analysis by clustering, it is possible to easily grasp the interaction even for a complicated analysis model. That is, the present invention does not require complicated calculations as in the analysis by the response surface method.

  Further, by using the upper limit value and the lower limit value given to the specific variable as the condition A and the condition B, it becomes easy to grasp the change of the design variable. Furthermore, in generating a model, it is possible to generate a model without duplication by using an orthogonal table. Multiple variables can be determined.

  Further, by extracting variables determined to have an interaction and storing them in a database, it becomes easy to search for an optimal design value.

The best mode for carrying out the present invention will be described below with reference to the drawings.
(overall structure)
FIG. 1 shows an overall configuration diagram of an analysis system according to the present embodiment. This analysis system includes a simulation terminal 1, an emulator terminal 2, a hardware interface 3, a server 4, and a network 5. The simulation terminal 1 includes a computer main body, a display, a keyboard, and the like, and has a function of simulating an analysis model, clustering design variables, and extracting design variables. Further, the simulation terminal 1 can extract the principle inherent in the analysis model based on the extracted design variable, and can store this information as a database. Thereby, it is possible to search for desired design information according to a request from the user.

  The emulator terminal 2 includes a hardware interface 3 for measuring the physical quantity of the prototyped hardware. The emulator terminal 2 is used for performing detailed design by executing emulation by HIL (Hardware In Loop) based on the design variables calculated by the simulation terminal 1.

  The server 4 is connected to the simulation terminal 1 and the emulation terminal 2 via a network 5 such as a LAN or WAN, and executes predetermined calculation processing in response to requests from these terminals 1 and 2. is there. In the present embodiment, simulation processing, database search, and the like can be executed instead of the terminals 1 and 2 described above. The server 4 has a function of storing a simulation result such as a correlation coefficient and a model principle calculated by the simulation terminal 1 as a database, and searching the database in response to a request from the user.

  FIG. 2 is a hardware block diagram of the simulation terminal 1 described above. The simulation terminal 1 includes a CPU (central processing unit) 101, a bus 102, a memory 103, an HDD (hard disk drive) 104, an external storage device 105, an operation interface 106, a video controller 107, an input / output interface 109, and a NIC (network interface). Card) 110, display 108, and the like.

  The CPU 101 extracts a design variable area of a given analysis model and executes a simulation calculation of the design variable area. The bus 102 includes a data bus and an address bus, and is used to exchange data between the CPU 101 and a device such as a memory. The memory 103 is used as a work area for the CPU 101 to execute the analysis program, and the HDD 104 is used for storing the program and a database for simulation results.

  The external storage device 105 is a storage device for reading / writing data from / to various recording media such as MO, CD, CD-R, CD-RW, DVD, DVD-R, and DVD-RW. In addition to storing the analysis program according to the present embodiment on this recording medium, it is possible to save simulation results and the like.

  The operation interface 106 is an interface with an input device such as a keyboard and a mouse, and the user can specify an analysis model specification and a database search instruction to the simulation terminal 1 via these input devices. The video controller 107 includes a graphic memory, a 3D graphic controller, and the like, and has a function of converting an analysis model, a simulation result graph, and the like into a video signal. The display 108 is configured by a CRT, a liquid crystal display, or the like, and is for displaying an image based on a video signal from a video controller. The input / output interface 109 includes a USB, a serial port, a parallel port, and the like, and is used for connecting an external device such as a printer and the simulation terminal 1. The NIC 110 is a network adapter for connecting the simulation terminal 1 with Ethernet (registered trademark), the Internet, or the like. It is also possible to download an analysis program from the server 4 to the simulation terminal 1 via the NIC 110.

  FIG. 3 is a functional block diagram of the analysis system according to the present embodiment. In this figure, a theoretical formula input unit 11 is for determining a theoretical formula of a model to be analyzed. The theoretical formula expresses various models to be simulated for mechanical structures such as vehicles, electronic circuits, electronic parts, economic phenomena, etc., and includes multiple design factors (design variables) and characteristic values (function values). This is a mathematical expression. FIG. 4 shows a conceptual diagram of design variables, characteristic values, and theoretical expressions. In this figure, the thickness of the arrow represents the strength of correlation with the characteristic value. According to this embodiment, it is possible not only to extract design variables having a strong correlation with characteristic values, but also to extract design variables having a so-called interaction relationship.

  The model generation unit 12 is for generating various models by determining a plurality of design variable values in the theoretical formula input by the theoretical formula input unit 11. Here, an orthogonal table is used to determine uniform and unbiased design variables. This orthogonal table is constituted by a table in which the levels of factors (design variables) are all assigned equally. For example, an orthogonal table with four factors and two levels is composed of a table in which 1 and 2 are assigned evenly for each of the four factors, and each value of four design variables can be determined using this orthogonal table. It becomes possible. In this way, it is desirable to use an orthogonal table for the generation of uniform design variables, but the design variables may be generated in a pseudo-uniform manner using random numbers.

  It is possible to generate a plurality of orthogonal tables by rearranging the factors of a given orthogonal table, and to increase the number of design variables to be sampled using the plurality of orthogonal tables obtained in this way. is there. As a rearrangement technique, as shown in FIG. 5, each factor is shifted (rotated). For example, eight types of orthogonal tables can be generated by sequentially rotating an eight-factor orthogonal table seven times, and a total of 64 × 8 = 512 model design variables can be generated. That is, for N factor orthogonal tables, N types of orthogonal tables can be generated by rotating (N-1). Note that the arrangement may be changed by other methods, such as changing the arrangement of factors in the orthogonal table at random.

  The simulation calculation unit 10 is for substituting each design variable generated by the model generation unit 12 into a theoretical formula and calculating a characteristic value. For example, when 128 models are generated by the model generation unit 12, 128 data sets including characteristic values and design variable values are generated. The simulation calculation unit 10 is preferably capable of calculation with as high accuracy as possible, but can be configured using a general-purpose simulation system. As described above, since the number of design variables to be calculated is limited by the design variable generation unit 12, it is possible to minimize the calculation amount of the simulation calculation unit 10.

  The clustering unit 14 is for classifying models having approximate characteristic value changes using a hierarchical clustering technique. Among the plurality of models, there are a plurality of models whose characteristic value changes approximate each other, and these are classified into one cluster. That is, the distance between the characteristic value of one model and the characteristic value of another model is calculated for each design variable, and the models having the smallest sum of these distances are classified into the same cluster. In addition to the above shortest distance method, clustering can be performed using a method such as a group average method. The clustering unit 14 can generate the hierarchically classified clusters by sequentially classifying the clusters classified in this way as upper clusters (FIG. 6).

  In this way, by classifying models having approximate characteristic values into a uniform cluster, classification based on the value of a design variable having a large influence on the characteristic value can be performed. That is, it is possible to reduce the sensitivity of the design variable having a small influence on the characteristic value and extract the design variable having a large influence on the characteristic value.

The correlation coefficient calculation unit 13 is for calculating a correlation coefficient between design variables in each cluster. For example, when other variables or characteristic values related to the design variable are changed, the two design variables X and Y show a predetermined change. Here, the presence or absence of correlation between changes in two design variables can be expressed by the correlation coefficient of the following equation.
r = {(x1 x0) (y1 y0) + (x2 x0) (y2 y0) + ... (xn x0) (yn y0)} / (nδxδy)
In the above formula, x0 and y0 represent average values of x and y, and δx and δy represent standard deviations of x and y. The correlation coefficient r is a value of −1 ≦ r ≦ 1, and when the positive correlation is strong, r indicates a value close to 1, and when the negative correlation is strong, r indicates a value close to −1. .

  The fact that the correlation coefficient between design variables is strong is considered that these design variables influence the characteristic values while interlocking with each other. These correlated design variables exist in common in each cluster, and these design variables are closely related to the principle inherent in the model. Therefore, it is possible to extract the principle in the multivariable model by searching for variables having a strong correlation in each cluster.

  The partial clustering unit 19 performs partial clustering in order to determine which of the design variables a specific design variable has another interaction due to which of the other design variables. Specifically, the partial clustering unit 19 extracts only models of the upper limit value and the lower limit value for each of the other design variables and performs clustering, thereby corresponding to the set of clusters corresponding to the lower limit value and the upper limit value. Generate a set of clusters.

  As described above, the interaction generally means that the characteristic value for a certain design variable changes depending on the value of another design variable. That is, the influence of a single design variable on a characteristic value differs depending on the connection of two design variables in which an interaction is recognized. Therefore, it is possible to determine the presence or absence of interaction by generating a cluster set for each of the upper limit value and the lower limit value of a specific variable and examining changes in other design variables between the two cluster sets. .

  The determination unit 20 extracts a design variable that has an interaction with the specific design variable in each of the clusters obtained by the partial clustering unit 19. That is, the determination unit 20 determines that the rate of change in the condition of other design variables between the first cluster of the cluster set corresponding to the upper limit value and the first cluster of the cluster set corresponding to the lower limit value corresponds to the upper limit value. The other variable and the specific variable have an interaction when the rate of change in the condition is different between the second cluster of the selected cluster set and the second cluster of the cluster set corresponding to the lower limit value. Judge that. In addition, the determination unit 20 extracts variables determined to have an interaction and writes them in the memory map 22. Furthermore, the determination unit 20 can also calculate the correlation coefficient between design variables having an interaction relationship, and determine the degree of interaction.

  The extraction unit 15 extracts design variables determined to have interaction. Thus, by extracting design variables having an interaction, it becomes easy to determine an optimum value of, for example, a trade-off design variable.

  The extraction unit 15 can also extract the principle inherent in the model to be analyzed. An average of correlation coefficients in each cluster is calculated, and a connection of design variables having strong correlation in all clusters is obtained. These design variables work together to influence the characteristic values, and by modeling the relationship between these design variables and the characteristic values, it becomes possible to understand the principles underlying the model. . For example, when three design variables of a plurality of design variables have a strong positive correlation, it can be seen that a desired characteristic value is obtained by similarly changing these design variables. By graphing the relationship between these design variables and characteristic values, the user can grasp the principle of the model to be analyzed.

  Note that design variables can be automatically extracted by setting a correlation coefficient threshold value in advance. Further, the principle inherent in the model can be automatically extracted by calculating the relationship between the extracted design variable and the characteristic value by the simulation calculation unit 10 or the like. Note that the principle extraction process may be performed by the user by displaying the correlation coefficient or the like on a display or the like.

  The output unit 21 is for visually presenting the above processing result to the user. For example, it is possible to display classified clusters, correlation coefficients between design variables in each cluster, relational expressions between extracted design variables and characteristic values, design variables with interaction, degree of interaction, etc. It is. Further, the output unit 21 may transmit the processing result to another terminal through the network.

  The database 22 stores processing results as a database and enables retrieval. That is, by storing data such as classified clusters, correlation coefficients, extracted principles, and design variables having interactions in the database 22 in advance, desired data can be selected from a large number of stored processing data. Can be searched and used.

  The memory map 22 shows the processing results in each of the theoretical formula input unit 11, model generation unit 12, simulation calculation unit 10, correlation coefficient calculation unit 13, clustering unit 14, extraction unit 15, partial clustering unit 19, and determination unit 20. It is for holding. Each processing unit can pass the processing result to another processing unit via the memory map 22.

Next, the operation of the analysis system according to this embodiment will be described with reference to the flowchart of FIG. In the following description, the design of a multilayer package is taken as an example, but the present invention is not limited to the design of a multilayer package.
(Theoretical formula input).

  As shown in FIG. 9, the multilayer package includes a chip flat board, a chip mounted thereon, a resin for sealing the chip, and a printed circuit board (hereinafter referred to as “PCB”). It is configured. The board and printed circuit board are connected by solder bumps. If the design values of the thickness, Young's modulus, and thermal expansion coefficient of each layer of resin, board, etc. are inappropriate, solder bumps may be peeled off. A malfunction will occur. Therefore, how to determine these design variables is extremely important.

  Here, chip thickness, substrate thickness, PCB thickness, resin thickness, substrate Young's modulus, substrate linear expansion coefficient (CTE), PCB Young's modulus, PCB linear expansion coefficient (CTE), resin Young's modulus, resin wire The theoretical formula of the multilayer package is determined using the expansion coefficient (CTE) as a design variable and the total equivalent nonlinear strain range Δεin as a characteristic value. Further, the size of the chip, the substrate, and the PCB is determined as shown in FIG. 6, and the size of the solder bump is determined as shown in FIG. Furthermore, the basic characteristics of each material are determined as shown in FIG. 11, for example. The theoretical formula thus determined is input to the theoretical formula input unit 11 by the user (step S101).

  FIG. 12 shows the relationship between the PCB thickness and resin thickness and the total equivalent inelastic strain range Δε. As shown in this figure, it can be confirmed that the total equivalent inelastic strain range Δε changes depending on the values of the PCB thickness and the resin thickness. In addition, other design variables affect the characteristic values, and there are combinations having an interaction among these design variables.

(Model generation)
The model generation unit 12 specifically determines the values of the ten design variables in the determined theoretical formula, and generates a plurality of models (step S102). The range of each design variable is determined as shown in FIG. 13, for example. That is, the value of each design variable is determined within the range of the lower limit value and the upper limit value shown in this figure. Further, as described above, by defining each design variable using an orthogonal table, it is possible to generate a plurality of models that are equal and do not overlap. It is desirable that the number of generated models is sufficient to determine the interaction. In the present embodiment, for example, 90 models are generated. The model generated in this way is stored in the memory map 22.

(Characteristic value calculation)
Subsequently, the simulation calculation unit 10 performs simulation of the generated model (step S103). That is, the simulation calculation unit 10 substitutes the value of the specifically determined design variable into the theoretical formula, and calculates the total equivalent inelastic strain range Δεin that is the characteristic value. The combination of the characteristic value calculated in this way and the design variable is stored in the memory map 22 as one data set.

(Clustering)
The clustering unit 14 performs clustering by calculating the distance between the characteristic values of each model (step S105). For example, there are 90 models with approximate changes in characteristic values, and the distance between such characteristic values is short. The clustering unit 14 classifies models having characteristic values with a short distance from each other into one cluster. The characteristic value changes of the two models classified in this way are approximate to each other.

  FIG. 14 shows an example of the clustering result. As shown in this figure, the 90 models are rearranged in the order of the characteristic values, and finally classified into four clusters (1) to (4).

(Correlation coefficient calculation)
Subsequently, the extraction unit 15 calculates an average value of design variables in each of the clusters (1) to (4). And as FIG. 15 shows, the average value of ten design variables is plotted about each of cluster (1)-(4). The extraction unit 15 determines what correlation the design variable of each cluster has with the characteristic value. The correlation can be determined based on the correlation coefficient calculated by the correlation coefficient calculation unit 13 (step S107).

  In FIG. 15, when the substrate Young's modulus increases, the characteristic value also increases. Therefore, it can be confirmed that the substrate Young's modulus has a positive correlation with the characteristic value. In addition, since the characteristic value decreases as the resin thickness, PCB CTE, and resin Young's modulus increase, these variables have a negative correlation with the characteristic value. Furthermore, even if each of the PCB thickness and the PCB Young's modulus changes, the characteristic value hardly changes. Therefore, it can be determined that there is almost no correlation between these variables and the characteristic value. Each of the chip thickness, the substrate thickness, the resin CTE, and the characteristic values other than the above-described design variables does not correspond to any of the above-described correlations (monotonically increasing, monotonously decreasing, or unchanged). From this, it can be determined that the chip thickness, the substrate thickness, the substrate CTE, and the resin CTE are likely to be design variables having an interaction.

(Partial clustering)
In order to search for design variables having an interaction, the partial clustering unit 19 performs partial clustering (step S109). For example, in order to determine which other design variable causes the chip thickness to have an interaction, the partial clustering unit 19 determines each of the other nine design variables other than the extracted chip thickness. The models with the maximum and minimum values are extracted and clustered with these models. FIG. 16 shows the result of clustering of the substrate thickness design variables among the nine design variables. In this figure, black dots represent a set of model clusters having a minimum substrate thickness (300 μm), and white dots represent a set of model clusters having a maximum substrate thickness (500 μm). These models are arranged in order of the magnitude of the total equivalent nonlinear distortion Δεin, which is a characteristic value, and are classified into two clusters (1) and (2) (partial clustering). In this way, partial clustering is performed for each of the other design variables.

(Judgment of interaction)
Based on the result of the partial clustering described above, the determination unit 20 determines which of the other design variables causes the design variable to be determined to have an interaction (step S110). That is, when the other design variables are changed from the lower limit value to the upper limit value, the determination unit 20 examines a change in the design variable to be determined in order to obtain a desired characteristic value.

  FIG. 17 shows how design variables change in a model that is partially clustered based on numerical values from the lower limit value to the upper limit value of the substrate thickness. In this figure, as the model substrate thickness in cluster (1) increases from 300 μm to 500 μm, the chip thickness also increases. However, if the model substrate thickness in cluster (2) increases in the same way, the chip thickness decreases conversely.

  That is, if the substrate thickness is decreased to reduce the characteristic value of the total equivalent inelastic strain range Δεin (cluster (2) → (1)), the chip thickness must be increased. Conversely, in order to increase the total equivalent inelastic strain range Δεin (cluster (1) → (2)), the chip thickness must be decreased when the substrate thickness is increased. As described above, it can be determined that the substrate thickness and the chip thickness have an influence on each other because the influences on the lifetime of the multilayer package are reversed.

  Similarly, the determination unit 20 determines whether or not there is an interaction with the chip thickness for all other design variables. In this way, design variables recognized as having an interaction are written into the memory map 22. Furthermore, the model, cluster, interaction determination result, etc. generated as described above are all stored in the database 23. The user can search for desired data from the data stored in the database 23 and use it for design and the like.

Therefore, according to the present embodiment, it is possible to extract variables having an interaction by performing partial clustering on two different conditions of a specific variable and examining the influence on other design variables. As a result, it is possible to easily grasp how the design value should be determined in order to realize a desired characteristic value, and it is possible to perform an efficient design.

  Although the present embodiment has been described above, the present invention is not limited to the above-described configuration and can be changed without departing from the spirit of the present invention. For example, the present invention is not limited to the above-described design field. The present invention can be applied to any design field in which simulation calculation is possible. For example, the present invention can be applied to a wide range of fields such as electronic circuit simulation, structural design, software design, stock price prediction, and traffic congestion prediction.

  In the present invention, not only the software program for executing the above-described processing is installed in the computer but also downloaded from a server or a download site for use. Further, the program software may be installed from a storage medium such as a CD-ROM. Further, the encrypted program may be distributed to the user, and only the user who has paid the price may be notified of the decryption key. Further, any operating system for executing the program may be used, and the form of hardware for executing the program is not limited.

1 is an overall view of an analysis system according to the present invention. It is a hardware block diagram of the analysis system concerning the present invention. It is a functional block diagram of the analysis system concerning the present invention. It is a conceptual diagram of the analysis object model which concerns on this invention. It is a figure showing the orthogonal table which concerns on this invention. It is a conceptual diagram of the clustering which concerns on this invention. It is a flowchart showing operation | movement of the analysis system which concerns on this invention. It is sectional drawing of the multilayer structure package of the analysis object model which concerns on this invention. It is a figure showing the design conditions of the multilayer structure package of the analysis object model which concerns on this invention. It is a figure showing the design conditions of the solder bump of the analysis object model which concerns on this invention. It is a figure for demonstrating the design variable of the analysis object model which concerns on this invention. It is a graph showing the relationship between the design variable and characteristic value of the analysis object model which concerns on this invention. It is a table | surface showing the upper limit and lower limit of the design value of the analysis object model which concerns on this invention. It is a graph showing the clustering result of the analysis object model which concerns on this invention. It is a graph showing the average value of each cluster of the analysis object model concerning the present invention. It is a graph showing the result of the partial clustering of the analysis object model which concerns on this invention. It is a graph showing the change of the design variable of the analysis object model which concerns on this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Simulation calculation part 11 Theoretical-expression input part 12 Model production | generation part 13 Correlation coefficient calculation part 14 Clustering part 15 Principle extraction part 19 Partial clustering part 22 Memory map 23 Database

Claims (9)

A model generation unit for generating a plurality of models each having a plurality of variables;
A characteristic value calculation unit that calculates the characteristic value of the model based on a given model variable, and writes the variable and characteristic value of the model to a memory map;
For each of the two conditions A and B of a specific variable, the cluster set A corresponding to the condition A by classifying the model into at least first and second clusters based on the magnitude of the characteristic value; A partial clustering unit that generates a cluster set B corresponding to the condition B;
For other variables than the specific variable, the rate of change in the condition between the first cluster of cluster set A and the first cluster of cluster set B is the second cluster of cluster set A and the second cluster set of cluster set B. A determination unit that determines that the other variable and the specific variable have an interaction when the rate of change of the condition between the two clusters is different and writes the determination result to the memory map; Multivariable model analysis system.   The multi-variable model analysis system according to claim 1, wherein the condition A and the condition B are an upper limit value and a lower limit value given to the specific variable.   The multivariable model analysis system according to claim 1, wherein the model generation unit generates the model by determining a plurality of variables using an orthogonal table.   The multivariable model analysis system according to claim 1, further comprising an extraction unit that extracts design variables determined to have an interaction by the determination unit.   The multivariable model analysis system according to claim 1, further comprising a database that stores and retrieves design variables extracted by the extraction unit.   The multivariable model analysis system according to claim 1, wherein the model represents a multilayer structure package. Generating a plurality of models each having a plurality of variables;
Calculating a characteristic value of the model based on a given model variable, and writing the variable and characteristic value of the model to a memory map;
For each of the two conditions A and B of a specific variable, the cluster set A corresponding to the condition A by classifying the model into at least first and second clusters based on the magnitude of the characteristic value; Generating a cluster set B corresponding to condition B;
For other variables than the specific variable, the rate of change in the condition between the first cluster of cluster set A and the first cluster of cluster B is the second cluster of cluster set A and the second of cluster set B. A multi-variable having a step of determining that the other variable and the specific variable have an interaction when different from a rate of change of the condition with the cluster, and writing the determination result to the memory map Model analysis method. Generating a plurality of models each having a plurality of variables;
Calculating a characteristic value of the model based on a given model variable, and writing the variable and characteristic value of the model to a memory map;
For each of the two conditions A and B of a specific variable, the cluster set A corresponding to the condition A by classifying the model into at least first and second clusters based on the magnitude of the characteristic value; Generating a cluster set B corresponding to condition B;
For other variables than the specific variable, the rate of change in the condition between the first cluster of cluster set A and the first cluster of cluster B is the second cluster of cluster set A and the second cluster of cluster B. Multi-variable model including a step of determining that the other variable and the specific variable have an interaction and writing the determination result in the memory map Analysis program. Generating a plurality of models each having a plurality of variables;
Calculating a characteristic value of the model based on a given model variable, and writing the variable and characteristic value of the model to a memory map;
For each of the two conditions A and B of a specific variable, the cluster set A corresponding to the condition A by classifying the model into at least first and second clusters based on the magnitude of the characteristic value; Generating a cluster set B corresponding to condition B;
For other variables than the specific variable, the rate of change in the condition between the first cluster of cluster set A and the first cluster of cluster B is the second cluster of cluster set A and the second of cluster set B. A multi-variable having a step of determining that the other variable and the specific variable have an interaction when different from a rate of change of the condition with the cluster, and writing the determination result to the memory map Model analysis program medium.

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