EP0757812A1

EP0757812A1 - Process for preparing for and accomplishing the fuzzification of a digital input signal at an input of a fuzzy processor

Info

Publication number: EP0757812A1
Application number: EP95915138A
Authority: EP
Inventors: Herbert Eichfeld
Original assignee: Siemens AG
Current assignee: Siemens AG
Priority date: 1994-04-29
Filing date: 1995-04-10
Publication date: 1997-02-12
Also published as: JPH09512366A; WO1995030186A1

Abstract

A fuzzy processor comprises a fuzzifier which calculates the appurtenance values of the relevant input-appurtenance functions from the digital input signal. To this end, the appurtenance functions must be stored. In order to reduce the storage space needed, especially at a high input signal resolution, it is of advantage to describe the appurtenance functions by shape-determined characteristics like restart points and slopes and store these. To save computing time, the definition range of the input signal is devided into equal segments. In the fuzzifiying process only the segment is considered in which the input signal to be fuzzified lies. This thus reduces the number of appurtenance functions to be considered, which reduces computing time. The result of the process is a fuzzification of the input signals using the minimum computing time without the need for excessively large storage space of the appurtenance functions.

Description

Method for preparing and performing the fuzzification of a digital input signal present at an input of a fuzzy processor

The structure and mode of operation of fuzzy processors are known (see, for example, H.Eichfeld, T.Künemund, M.Klimke "An 8b Fuzzy Coprocessor For Fuzzy Control", ISSCC 93, San Francisco, February 24-26, 1993, pages 180, 181, 286). Such a fuzzy processor also contains a fuzzy circuit, also called a fuzzifier, the task of which is to create a digital input signal that is to be fuzzified by means of input membership functions stored in a memory — also known as knowledge base memory to determine the membership values. To do this, it must first be determined which input membership functions (hereinafter referred to as membership functions) are affected by the input signal. The membership values to be assigned to the input signal can then be retrieved from the memory.

Until now, it was common to save membership functions point by point. Provided that the input signal is resolved with 8 bits, the membership functions were saved point by point with 256 points. This has advantages: The membership values are calculated using a memory access (scanning method). Any form of function is allowed. A disadvantage, however, is that the storage space requirement depends exponentially on the resolution of the input signals, so that the sampling method in e.g. a resolution with 12 bits leads to a large memory requirement.

When looking for other ways of storing the membership functions in which the memory requirement is lower, it must always be ensured that the time required to determine the membership values is not too great. The problem on which the invention is based is therefore to specify a fuzzification method which allows a maximum variety of forms of the membership functions with a minimal computing time, without the memory requirement for storing the membership functions becoming too great. This problem is solved according to the features of claim 1.

The method according to the invention is based on the idea of dividing the definition range or value range of the digital input signals into segments, preferably segments of the same size. Fuzzification only considers the segment in which the input signal to be fuzzified lies. This reduces the number of membership functions to be considered, which shortens the computing time. Any form of membership function is allowed, but the memory requirement is significantly reduced compared to the scanning method.

The memory requirement for the storage of the membership functions can be reduced by storing a shape information that includes the shape of the membership function. This form information contains features that define the form of the membership function, such as Support points at which the slopes change and the slopes between the support points. The start value and the end value of the membership function can be included in the form information as a support point.

In order not to buy the advantage of the lower memory requirement with a longer computing time, which is due to the fact that the shape of the membership functions that have been found must first be determined from the shape information and then the membership values, it is advantageous to divide the segments into the same size. Then the segment hit by an input signal to be fuzzified can be selected with the help of the higher order bits of the digital input signal and the exact value within the segment with the remaining lower order bits of the input signal. The search for membership functions taken by the input signal is facilitated in that the start values and the end values of the membership functions or the membership functions passing through the segment are stored for each segment. The determination of the membership functions taken per segment then requires determining whether membership functions pass through the segment without a start value and end value or whether the input signal is smaller than the end value of the membership function with a small number and is greater than the start values of the hit Membership functions with the following number. For this purpose, it is expedient to number the membership functions in ascending order.

To carry out this method, it is expedient not only to store in the memory the membership functions per segment, but also in each case the end values or start values and codes of the membership functions which pass through the segment. For this purpose, an end value memory and a start value memory can also be introduced in the memory. Then the memory receives a number memory, a start value memory and an end value memory for each input. In addition, an end value address memory and a start value address memory can be provided, for each input.

After the membership functions that have been found have been determined for an input signal to be fuzzified, the membership values must be calculated in a further step. For this purpose, the shape information which is also stored in the memory must be used. This form information relates to the form of the membership functions per segment. It is useful to define the typical forms of the membership functions that occur with the help of support points and slopes and to save them in a space-saving manner. The form address memory and segment address memory can then Form information of the membership functions taken are determined and the membership values are calculated therefrom.

Other developments of the invention result from the subclaims.

The invention is further explained on the basis of exemplary embodiments which are shown in the figures. FIG. 1 shows a possible division of membership functions in the definition range of the digital input signal, FIG. 2 shows a section of a segment, FIG. 3 curves in a segment that require special coding, FIG. 4 shows the organization of the memory with four inputs,

5 to 7 show a flow chart for determining the numbers of the membership functions taken,

8 shows the memory organization for calculating the membership values for four inputs, FIG. 9 to FIG. 14 flow diagrams for calculating the membership values,

15 to 17 the structure of the shape information memory, FIG. 18 an example to explain the method according to the invention.

The value range of a digital input signal E, which is divided here into 16 segments, results from FIG. The input signal E is e.g. resolved in n = 12 bits. Then the m = 4 upper bits (eo) can be used to address the 16 segments and the (n-m) lower bits (eu) can be used to address the points within the segment. Membership functions le are now distributed over the entire value range, as is the case e.g. can be seen from Figure 1. The possible degree of overlap is 2 here.

In the exemplary embodiment in FIG. 1, 15 membership functions le are arranged in a distributed manner. To differentiate between the functions, these can be numbered. Here, as FIG. 2 shows, for the membership functions present in a segment, the membership function with the smallest number is referred to as nrel, and the membership function with the largest number as nrei. In between are the other membership functions with the corresponding number. Furthermore, the designation of start values and end values per membership function results from FIG. The end value of each membership function is denoted by io, the start value by iu.

FIG. 2 shows some examples of membership functions, all membership functions ending, starting or starting and ending in the SG segment. However, courses of membership functions are also conceivable (see FIG. 1) which run through a segment SG without starting or ending there. Three cases result from FIG. 3. In case a), two membership functions run nreil and nrei through the segment SG. In case b) the one membership function runs neil through the segment SG, while a second membership function nrei starts in the segment and in case c) a membership function runs nrei through the segment SG, a membership function nreil ends in the segment SG and a third Membership function nre2 can possibly start in segment SG. In order to be able to recognize these cases in which at least one membership function runs through the segment, a number memory SP-N is provided for each input in a memory KBM, which is shown in FIG. 4, and contains a memory word for each segment SG The smallest number nreil and the largest number nrei of the membership functions per segment and the final value iol are stored in this memory word. Cases a) to c) can be recognized, for example, with the following codings in the memory word: For case a), nrel = nrei is set and iol = ooh. In case b) nrel = nrei is set and iol = ffh and in case c) nrei = fh, whereby two sub-cases are distinguished. In the first sub-case, a membership function begins in the segment. to Marking is set iu3 = ooh. This is not the case in sub-case c2. Accordingly, iu3 ≠ ooh.

The organization of the memory KBM (Knowledge Base Memory) is shown in FIG. 4. In the example in FIG. 4, it is assumed that the fuzzy processor has four inputs. Accordingly, four number memories, one for each input, are provided, these are called SP-N. The number memories contain the memory word defined above for each segment SG.

Additional memory areas are required to determine the membership functions that have been made. If several membership functions are contained in a segment, either the start value and / or the end value of such a membership function must be known during the check. The final values per input and per segment are in the final value memory SP-E, the initial values in the initial value memory SP-S. The end value memory or start value memory must be addressable, this is done via an end value address memory SP-AS per input and a start value address memory SP-AA per input. A possible organization of these partial memory areas in the memory can be seen from FIG. 4. The other use of the memory KBM for the descriptors KBD is known from the literature and is assumed.

The structure of the end value memory SP-E for the example in FIG. 1 can be found in Table 1 below.

Table 1 End value memory SP-E

EWA 4 io2 by le3 io3 by le4

EWA 9 io2 by le7 io3 by le8

EWA 9 + 1 io4 by le9 io5 by lelO

The organization of the end value memory presupposes that the end value (iol) of the membership function with the smallest number (nrel) is contained in the number memory. Then the end values of the membership functions are specified in the end value memory, which additionally end per segment.

The structure of the start value memory for the example in FIG. 1 is shown in Table 2.

Table 2 SP-S start value memory

SWA2 iu2 from le2 -

SWA3 iu2 from le3 -

SWA4 iu2 by le4 iu3 by le5

SWA8 iu2 by le6 iu3 by le7

SWA9 iu2 by le8 iu3 by le9

SWA9 + 1 iu4 by lelO iu5 by lell

SWA9 + 2 iu6 by lel2

SWA11 iu2 by lel3

SWA13 iu2 by lel4

SWA15 iu2 by lel5

The start values of the membership functions per segment are shown here.

It should be noted that the numbering of io and iu refers to the segment.

The addresses of the end value memory are designated by EWA, the addresses of the start value memory by SWA. The determination of the membership functions taken by an input signal is explained with the aid of FIGS. 5 to 7. Only the processes that are to be carried out to determine the membership functions that have been taken are shown without the address calculation being explained, which can be done in the usual way.

The input counter is set to the value ni of the input under consideration. Running variables j, k are set to 0. Depending on the input and the segment address (eo) contained in the input signal, the number memory SP-N assigned to the input and the memory word assigned to the segment are then addressed. The number nrel of the membership function with the smallest number contained in the memory word is entered into a number counter nrz. It is then checked whether one of the cases a and b given in FIG. 3 is present. If this is the case, the number nrz is stored in a latch and a further check is carried out to determine whether case a or case b exists. If case a is present, then a hit signal IKF is set which indicates that more than one membership function has been hit. The membership functions taken are then known, these are nrel and nrel + 1. However, if it turns out that case b is present, then it must still be examined whether nrei is hit by the input signal (Fig. 3). This examination is carried out in accordance with FIG. 7. Here the start value address memory is first addressed in order to obtain the start value of nrei (case b). The n-m least significant bits eu of the input signal are then examined to determine whether they are below iu. If this is the case, then nrei has not been hit. However, if this is not the case, then no hit has been made. The hit signal is set and the hit number of the membership function is saved.

If the comparison at the beginning of the process reveals that the condition nrz = nrei is not fulfilled, then it is checked whether the _β input signal has the membership function with the number nrel hits, eu> iol is queried. If this is not the case, then the membership function nrel is met. This is stored and case c) of FIG. 3 is then examined. If eu ≥ iol, then the membership function nrel has not been met, the number counter is increased by one unit and case c) is queried again. If it is not available, it is queried whether the membership function just examined is the last membership function contained in the segment and if this is the case the number is stored. If this is not the case, then the end value address memory must be addressed and the end value of the next membership function must be examined in comparison with eu. If nrei = fh, then nrz is saved as the number of the membership function taken. The method by which it is examined whether eu> io2 is shown in FIG. 6 and is understandable in itself. The process is carried out until a membership function is negative for the first time by comparing eu with io a membership function. Then the eu is compared to the following membership function. This then results from FIG. 7.

In general, it is first examined whether one of the special cases a) and b) is present and, if this is the case, the numbers of the membership functions passing through the segment are stored. It is then examined whether the input signal is within the segment to the left of the end value of the membership function with the smallest number. If this is the case, then this membership function is considered to have been met and the further investigation is carried out with the membership functions with an increasing number, namely with its initial value. If the membership function with the smallest number has not been met, the membership function with the next number is examined, again by comparing the input signal with the end value of this membership function. This method is carried out until a membership function is no longer met or the last membership function contained in the segment has been checked. A method carried out in this way to determine the membership functions taken brings about a time-optimal sequence.

A detailed explanation of the flow chart of Figures 5 to 7 does not appear necessary, since these are understandable in themselves.

After the functions have been determined, it is necessary to determine the membership values. To do this, the form of the functions must be known. The shape of the membership functions that occur is determined with the help of support points and slopes. Individual cases are shown in FIGS. 15 to 17, specifically as a curve and as shape information. The shape information is also stored in the memory KBM, namely a shape address memory SP-FA per input of the fuzzy processor, and a segment address memory SP-SG and a shape information memory SP-FO per segment. This structure is shown in Figure 8.

The individual shape information and the associated function profiles result from FIGS. 15 to 17. The individual curve profiles can always be seen per segment. A distinction is made between different types of shape information in order to be able to distinguish between the individual curve profiles. In case 15a) there is an individual value, a rectangle or a horizontal in the segment and accordingly the form information Fl consists only of the type specification (000) and the value y. In case 15b) the shape consists of a straight line with a positive slope, the corresponding shape information F2 specifies the initial value iu and the slope St in addition to the type (001). 15c) shows a variation, namely a positive one

Slope with y-section. Accordingly, the form information F3 contains, in addition to the type specification (010), the slope St and the section y. The case of the negative slope shows figure

15d). There, the form information F4 contains the end value io and the slope St. in addition to the type specification (011). The slope with the y section results from FIG. 16a, which contains the shape information F5, in addition to the type specification (100), the slope St and the section y. If the curve has the shape of a triangle, as shown in FIG. 16b), the shape information F6 contains, in addition to the type specification (101) and a distinction (SyB) of the triangle, an specification for the section y, the specification of the reference point x and the slopes Stl and St2 on both sides of the support point x. In the case of a symmetrical triangle, less information is required, as shown in FIG. 16b, second case, here the slope Stl is equal to St2. The case of the trapezoid can be seen from FIG. 16c. There are two support points xl and x2, at which the slope of the curve changes, and accordingly the shape information F7 contains, in addition to the value for y, the support points xl, x2 and the slopes Stl and St2. The shape information is simplified if the trapezoid is symmetrical, because then the slope Stl is equal to St2.

Finally, Figure 17 shows the most general case of a polygon as a membership function. In addition to the type specification (111), the support points x, y and the slopes between the support points must be included in the form information. Figure 17 then shows the structure of the shape information F8.

With the help of this form information, which is stored in the memory, the membership values for an input signal can be calculated. A flowchart showing this is shown in FIG. 9. First, the form address memory SP-FA of the corresponding input is addressed. In this form address memory there is a segment address SGA for each segment of each input. The segment address memory SP-SG is addressed with this address SGA and the number nrf of the membership function taken. It contains a form address FA for all nrel to nrei, with which the form information memory SP-F0 is finally addressed. The shape information store contains the shape information already described. The shape information is read from the memory and its type is queried. Ent- According to the type found, the membership value α can then be calculated and saved using the shape information. If, for example, the type = 000 is found, the membership value α has the value y, as can readily be seen from FIG. 15a. The run through the flowchart in FIG. 9 is repeated until all the membership functions that have been met have been processed. The hit signal IKF is used for this. If, for example, the overlap between two membership functions is a maximum of 2, then a maximum of two runs are required. The examination according to flow chart 9 thus reveals the type of membership function taken. The membership value α can then be determined from this using the shape information. The individual steps that have to be carried out for this purpose can be seen in FIGS. 10 to 14.

In the simplest case in FIG. 10a, which deals with the curve in FIG. 15a, the membership value is α = y.

In case 15b, the calculation according to FIG. 10b is carried out. The shape information is addressed and the slope St is multiplied by the difference eu-iu. This results in the belonging value α.

FIG. 10c deals with the case of FIG. 15c. It is understandable in itself.

The same applies to the cases in FIG. 15d and FIG. 16a, which are dealt with in FIGS. 11a and 11b, respectively.

The case of FIG. 16b of the triangle is somewhat more complicated.

This case is shown in Figure 12. A distinction is made between the symmetrical and non-symmetrical triangles.

The distance between the support point x and eu of the input signal is determined and from this the membership value is determined in accordance with FIG. The case of the trapezoid in FIG. 16c is shown in FIG. 13. Here it must be ascertained whether eu lies to the left of the support point xl, between the support points xl and x2 or to the right of the support point x2. Depending on this, the membership value is either y or results from the multiplication of the slope Stl or St2 by the distance eu -x of the corresponding support point.

The case of the polygon, FIG. 17, is shown in FIG. 14. Here it must be determined which support point is immediately adjacent to the left of the point eu and then the membership value is calculated using the slope St starting from this support point. The exact sequence is shown in FIG. 14.

The method is explained again using an example which is shown in FIG. A simple curve course of the membership functions has been selected and there are only three membership functions Iel, le2 and le3. The value range of the input signal E is divided into 16 segments, which are designated in FIG. 18. From Table 3 below

Table 3

Address content

KBDl + Oh nrel = lel = 0, nrei = lel = 0.00 <iol <ffh

KBDl + lh same

KBDl + 2h same

KBDl + 3h nrel = lel = 0, nrei = lel = 0, iol = ffh (special case b)

KBDl + 4h nrel = lel = 0, nrei = lel = 0, iol = 00h (a)

KBDl + 5h same

KBDl + 6h nrel = lel = 0, nrei = fh, iol von lel ("<= 2)

KBDl + 7h nrel = le2 = l, nrei = le2 = l, 00h <iol <ffh

KBDl + 8h same

KBDl + 9h nrel = le2 = l, nrei = le2 = l, iol = ffh (special case b)

KBDl + Ah nrel = le2 = l, nrei = le2 = l, iol = 00h (special case a)

KBDl + Bh ditto

KBDl + Ch nrel = le2 = l, nrei = fh, iol from le2 ("c2)

KBDl + Dh nrel = le3 = 2, nrei = le3 = 2.00 <iol <ffh

KBDl + Eh ditto

KBDl + F ditto

The organization of the number memory then results.

Table 3 shows the special cases a, b, c. It can be seen that whenever the special case a or b is present, nrel = nrei is set and the coding of the final value iol shows whether the special case a or b is present. The special case c is recognized in that nrei = fh is set, the two cases being distinguished by iol.

The flow chart of FIGS. 5, 6, 7 can then be run through with the aid of this information from the number memory. In the event that the input signal is in the segments 0, 1, 2, 4, 5, 7, 8 A, B, D, E, F, a branch is made to 3. If the input signal is in segment 3 or 9, there is a branch to 2 and if the input signal is in segment 6 or C. branches to 2 or 3, depending on which values have eu or iol. It follows from this that an end value address or end value memory is not required in this example. On the other hand, start addresses are required, Table 4 shows the structure of the start value address memory:

Table 4 Address content y + Oh not used lh II n

2h II B

3h SWA3

4h not occupied

5h II II

6h SWA6

7h not occupied

8h and II

9h SWA9

Ah not used

Bh II II

Ch SWA12

Ie not occupied

Eh not occupied

Fh not used

with y = KBD1 + 2Oh (NI + 1) + 10h ni

The structure of the start value memory can be found in Table 5: Table 5

Address content

SWA3 iu2 from le2, iu3 any

SWA6 iu2 any, iu3 ≠ 00h

SWA9 iu2 from le3, iu3 any

SWA12 iu2 any, iu3 ≠ 00h

To calculate the membership value α, the form address memory must first be read, the structure of which is shown in Table 6:

Table 6

Address content

KBD2 + ni * 10h + 0h SGA0

• •

+ Fh SGA15 t eo

Then the segment address memory is addressed. If the same shapes are defined in two segments, shape information is sufficient for a shape address FA in the segment address memory. This would be e.g. this is the case in segments 1, 2, 3, 8, 9 and 14 to 16, since there is only a horizontal level of the same height. In this way, the segment address memory can be constructed to save space.

The organization of the segment address memory is shown in Table 7: Table 7 Address content

SGA0 = SGA1 = = SGA2: = SGA7 + 1 = FAO

SGA8 + l = SGA13 + 2 = = SGAl4 + 2 = SGA15 + 2

SGA3 FA1

SGA3 + 1 FA2

SGA4 FA3

SGA4 + 1 FA4

SGA5 FA5

SGA5 + 1 FA6

SGA6 FA7

SGA6 + 1 FA8

SGA9 + 1 FA9

SGA9 + 2 FA10

SGA10 + 1 FA11

SGA10 + 2 FA12

SGA11 + 1 FA13

SGA11 + 2 FA14

SGA12 + 1 FA15

SGA12 + 2 FA16

Finally, the form information memory can be controlled via the form addresses FA. Table 8 shows the organization of the shape information store:

Table 8 Address content Address content

FAO Horizontal FA10 positive

FA1 triangle FA10 + 1 slope

FA1 + 1 FA11 negative slope

FA1 + 2 FA11 + 1 with y

FA2 positive FA12 positive climb.

FA2 + 1 slope FA12 + 1 with y

FA3 negative FA13 negative climb.

FA3 + 1 climb, with y FA13 + 1 with y

FA4 positive FA14 positive climb.

FA4 + 1 climb, with y FA14 + 1 with y

FA5 neg. F 15 negative climb.

FA5 + 1 neg. With y FA15 + 1

FA6 positive climb. FA16 triangle

FA6 + 1 with y FA16 + 1

FA7 neg.FA16 + 2

FA7 + 1 slope

FA8 triangle

FA8 + 1

FA8 + 2

FA9 triangle

FA9 + 1

FA9 + 2

Claims

1. Method for preparing and carrying out the fuzzification of a digital input signal (E) present at an input of a fuzzy processor a) in which the possible value range assigned to the input for the input signal (E) is divided into segments (SG), b) in the membership functions (le) available in the respective segment are stored, c) in which, when fuzzifying an input signal, the segment into which the input signal falls is determined, and thus the membership functions available in the segment, d) in which it is determined Which of the membership functions available in the segment are met by the input signal, e) and in which the membership value of the input signal is determined for each membership function taken.

2. The method as claimed in claim 1, in which the membership functions are stored with the aid of shape information (F) representing the shape of the membership functions, using reference points and slopes between the reference points.

3. The method according to claim 2, in which the start value and the end value of the accessory function can be determined from the shape information.

4. The method according to any one of the preceding claims, wherein the segments have the same size.

5. The method according to claim 4, in which the input signal is represented in n-bit (n integer) and the m (m integer) bits of higher order define the segment and the nm lower-order bits determine the position of the input signal in the segment.

6. The method according to claim 5, in which the membership functions are assigned numbers (nre) in ascending order and for each segment the smallest and the largest number are stored by the membership functions available in the segment.

7. The method according to claim 6, in which the end value of the membership function with the smallest number is also stored.

8. The method according to claim 7, in which, in the event that several membership functions end in a segment, the end values are stored in an end value memory except for the end value already stored.

9. The method according to claim 7 or 8, in which, in the event that membership functions begin in a segment, the start values are stored in a start value memory.

10. The method according to any one of claims 6 to 9, in which in a segment existing in the segment non-ending and non-beginning membership functions are identified by a coding.

11. The method according to claim 10, in which the following steps are carried out to determine the membership functions taken by an input signal: a) the segment is selected with the aid of the m higher-order bits of the input signal, b) each membership function present in the segment is examined to determine whether it is a start and end value in

Segment has and if this is not the case, their number is saved as hit, c) otherwise the end value or start value of the membership functions lying in the segment is examined in ascending order of numbers to determine whether the input signal

- is less than the end value of the membership functions and if this is the case, this membership function is saved as hit, then it is examined whether the input signal is greater than the starting value of the following membership functions and as long as this is the case, the membership functions are saved as hit, c) the number of hits saved if this is greater than 1.

12. The method according to claim 11,

-in which the numbers of the membership functions are stored in a number memory for each input,

in which the end values required for determining membership functions are stored in a end value memory per input and their addresses in a end value address memory,

in which the start values required for determining the membership functions taken are stored in a start value memory per input and their addresses in a start address memory.

13. The method as claimed in claim 11, in which the following steps are carried out in preparation for determining the membership value of an input signal: a segment address is stored in a form address memory for each segment,

a shape address is stored in a segment address memory for each membership function,

- The shape information per segment is stored in a shape information memory.

14. The method as claimed in claim 13, in which the following steps are carried out to determine the membership value of an input signal for each membership function taken: the form address memory is addressed and the segment address assigned to the segment concerned is read, the segment address memory is addressed with the segment address and the determined number of the membership function that has been determined, and the address of the shape information assigned to the membership function that is encountered is read out — the shape information assigned to the membership function that is met is read out with the address of the shape information,

The membership value for the input signal is determined from the input signal and the form information read out.

15. The method according to claim 13 or 14, in which the shape information is formed for each section of a membership function running in a segment in the following manner: a) a type designation is assigned to each different curve section, b) reference points are stored, that are given

-in the case of a change in the slope within the segment, -in the presence of only a starting value without further change in the segment,

- If there is a final value in the segment without changing the slope within the segment, c) the slopes originating from the support points are stored.

16. The method according to any one of the preceding claims, in which at most two membership functions overlap.