Hypertrapezoidal fuzzy dynamic state interpreter

• US 6,272,477 B1
• Filed: 09/04/1998
• Issued: 08/07/2001
• Est. Priority Date: 09/05/1997
• Status: Expired due to Fees

• Current Assignee: Texas A&M University System
• Original Assignee: Texas A&M University System
• Inventors: Painter, John H., Kelly, Wallace E. III
• Primary Examiner(s): Davis, George B.
• Application Number:
  US09/148,523
• Time in Patent Office: 1,068 Days
• Field of Search: 706/5, 706/902
• US Class Current: 706/5
• CPC Class Codes: G06N 7/02 using fuzzy logic computing arrangements based on biological models G06N3/00; computing arrangements using knowledge-based models G06N5/00
• CPC Class Codes: Y10S 706/902 Application using ai with detail of the ai system

Abstract

An apparatus for determining the state of a dynamic system is disclosed. The apparatus comprises one or more sensors operable to sample physical parameters of a system, and a mode interpreter. The mode interpreter is operable to receive data from the sensor and determine the state of the dynamic system using hypertrapezoidal membership functions.

Claims

1. An apparatus for determining a state of a dynamic system comprising:

a sensor section operable to sample a plurality of different physical parameters of the system to produce a multi-dimensional sample; and

a mode interpreter operable to;

maintain a respective predetermined prototype point for each of a plurality of multi-dimensional fuzzy sets which each correspond to a respective one of a plurality of possible states of the system;

determine a degree of hypertrapezoidal fuzzy membership of said sample in each of said multi-dimensional fuzzy sets based on a calculation which is a function of said prototype points and said sample; and

select one of said states as a function of said determined degrees of hypertrapezoidal fuzzy membership.

2. An apparatus according to claim 1, further comprising a system advisor coupled to said mode interpreter and operable to advise a system user based on said state selected by said mode interpreter.

3. An apparatus according to claim 1, wherein the dynamic system is an aircraft.

4. An apparatus according to claim 3, wherein said states include taxi, take off, climb out, cruise, initial approach, final approach and landing.

5. An apparatus according to claim 3, wherein said physical parameters include aircraft power, indicated air speed, altitude, rate of climb, and parameters dealing with distance to fixed points.

6. An apparatus according to claim 3, further comprising a pilot assist system coupled to said mode interpreter and operable to receive said selected state from said mode interpreter and to formulate pilot assist information to assist a pilot in flight operations.

7. An apparatus according to claim 6 further comprising a presentation section coupled to said pilot assist system and operable to display said pilot assist information.

8. An apparatus according to claim 7, wherein said pilot assist system is operable to control a display mode of said presentation section based on said selected state.

9. An apparatus according to claim 1, wherein said mode interpreter is further operable to maintain a predetermined crispness value representative of how much of a space between respective pairs of said prototype points is fuzzy, said calculation being a function of said prototype points, said sample and said crispness value.

10. An apparatus according to claim 9, wherein said calculation includes solution of the following equations for every possible pair λ

_i and λ

_j of said prototype points;

${\mathrm{\rho <br><br>}}_{i|j}<br><br>\left(\mathrm{\Lambda <br><br>}\right)=\frac{|{\stackrel{\rightharpoonup <br><br>}{v}}_I<br><br>{|}^2<br><br>-|{\stackrel{\rightharpoonup <br><br>}{v}}_j<br><br>{|}^2}{|{\stackrel{\rightharpoonup <br><br>}{v}}_{\mathrm{ij}}<br><br>{|}^2}$${\mathrm{\mu <br><br>}}_{i|j}<br><br>\left(\mathrm{\Lambda <br><br>}\right)=\left\{\begin{array}{cc}0;<br><br>& {\mathrm{\rho <br><br>}}_{i|j}<br><br>\left(\mathrm{\Lambda <br><br>}\right)\ge <br><br>1-\mathrm{\sigma <br><br>}\\ 1;<br><br>& {\mathrm{\rho <br><br>}}_{i|j}<br><br>\left(\mathrm{\Lambda <br><br>}\right)\le <br><br>\mathrm{\sigma <br><br>}-1\\ \frac{{\stackrel{\rightharpoonup <br><br>}{v}}_{\mathrm{ij}}·<br><br>{\stackrel{\rightharpoonup <br><br>}{v}}_j-\frac{\mathrm{\sigma <br><br>}}{2}|{\stackrel{\rightharpoonup <br><br>}{v}}_{\mathrm{ij}}<br><br>{|}^2}{\left(1-\mathrm{\sigma <br><br>}\right)|{\stackrel{\rightharpoonup <br><br>}{v}}_{\mathrm{ij}}<br><br>{|}^2};<br><br>& \mathrm{otherwise}\end{array}\right\}$

where Λ

is said sensor output, σ

is said crispness value, {right arrow over (v)}_i is a vector from λ

_i to Λ

, {right arrow over (v)}_j is a vector from λ

_j to Λ

, and {right arrow over (v)}_ij is a vector from λ

_i to λ

_j, said calculation thereafter including solution for each of said prototype points of one of the following equations;

$\begin{array}{c}{\mathrm{\mu <br><br>}}_i<br><br>\left(\mathrm{\Lambda <br><br>}\right)=\frac{\underset{j=1\ne <br><br>i}{\overset{M}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\mu <br><br>}}_{i|j}<br><br>\left(\mathrm{\Lambda <br><br>}\right)}{\underset{k=1}{\overset{M}{\sum <br><br>}}<br><br>\left(\underset{j=1\ne <br><br>k}{\overset{M}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\mu <br><br>}}_{i|j}<br><br>\left(\mathrm{\Lambda <br><br>}\right)\right)}<br><br>\mathrm{for}<br><br>\text{\hspace{1em}<br><br>}<br><br>i=1,2,\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>M\\ {\mathrm{\mu <br><br>}}_i<br><br>\left(\mathrm{\Lambda <br><br>}\right)=\frac{\underset{j}{\min }<br><br>\left({\mathrm{\mu <br><br>}}_{i|j}<br><br>\left(\mathrm{\Lambda <br><br>}\right)\right)}{\underset{k=1}{\overset{M}{\sum <br><br>}}<br><br>\left(\underset{j}{\min }<br><br>\left({\mathrm{\mu <br><br>}}_{i|j}<br><br>\left(\mathrm{\Lambda <br><br>}\right)\right)\right)}<br><br>\mathrm{for}<br><br>\text{\hspace{1em}<br><br>}<br><br>i=1,2,\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>M.\end{array}$

11. An apparatus according to claim 10, wherein said selected state corresponds to the respective said prototype point having the largest calculated value of μ

_i(Λ

).

12. An apparatus according to claim 10, wherein said mode interpreter is operable to effect separate filtering of each said calculated value of μ

_i(Λ

).

13. An apparatus according to claim 1, wherein said mode interpreter is operable to effect separate filtering of each said determined degree of hypertrapezoidal fuzzy membership.

14. An apparatus according to claim 1, wherein said mode interpreter is further operable to determine a confidence value regarding the accuracy of said selected state.

15. An apparatus according to claim 14, wherein said mode interpreter is operable to determine said confidence value as a function of a difference between the largest and the second largest of said determined degrees of hypertrapezoidal fuzzy membership.

16. A method for determining a state of a dynamic system comprising:

sampling a plurality of different physical parameters of the system to produce a multi-dimensional sample;

maintaining a respective predetermined prototype point for each of a plurality of multi-dimensional fuzzy sets which each correspond to a respective one of a plurality of possible states of the system;

determining a degree of hypertrapezoidal fuzzy membership of said sample in each of said multi-dimensional fuzzy sets based on a calculation which is a function of said prototype points and said sample; and

selecting one of said states as a function of said determined degrees of hypertrapezoidal fuzzy membership.

17. A method according to claim 16, including the steps of:

maintaining a predetermined crispness value representative of how much of a space between respective pairs of said prototype points is fuzzy; and

carrying out said calculation of said determining step as a function of said prototype points, said sample and said crispness value.

18. A method according to claim 17, wherein said calculating step includes the step of solving the following equations for every possible pair λ

_i and λ

_j of said prototype points;

${\mathrm{\rho <br><br>}}_{i|j}<br><br>\left(\mathrm{\Lambda <br><br>}\right)=\frac{|{\stackrel{\rightharpoonup <br><br>}{v}}_I<br><br>{|}^2<br><br>-|{\stackrel{\rightharpoonup <br><br>}{v}}_j<br><br>{|}^2}{|{\stackrel{\rightharpoonup <br><br>}{v}}_{\mathrm{ij}}<br><br>{|}^2}$${\mathrm{\mu <br><br>}}_{i|j}<br><br>\left(\mathrm{\Lambda <br><br>}\right)=\left\{\begin{array}{cc}0;<br><br>& {\mathrm{\rho <br><br>}}_{i|j}<br><br>\left(\mathrm{\Lambda <br><br>}\right)\ge <br><br>1-\mathrm{\sigma <br><br>}\\ 1;<br><br>& {\mathrm{\rho <br><br>}}_{i|j}<br><br>\left(\mathrm{\Lambda <br><br>}\right)\le <br><br>\mathrm{\sigma <br><br>}-1\\ \frac{{\stackrel{\rightharpoonup <br><br>}{v}}_{\mathrm{ij}}·<br><br>{\stackrel{\rightharpoonup <br><br>}{v}}_j-\frac{\mathrm{\sigma <br><br>}}{2}|{\stackrel{\rightharpoonup <br><br>}{v}}_{\mathrm{ij}}<br><br>{|}^2}{\left(1-\mathrm{\sigma <br><br>}\right)|{\stackrel{\rightharpoonup <br><br>}{v}}_{\mathrm{ij}}<br><br>{|}^2};<br><br>& \mathrm{otherwise}\end{array}\right\}$

where Λ

is said sample, σ

is said crispness value, {right arrow over (v)}_i is a vector from λ

_i to Λ

, {right arrow over (v)}_j is a vector from λ

_j to Λ

, and {right arrow over (v)}_ij is a vector from λ

_i to λ

_j, and wherein said calculating step includes the step of solving, for each of said prototype points, one of the following equations;

$\begin{array}{c}{\mathrm{\mu <br><br>}}_i<br><br>\left(\mathrm{\Lambda <br><br>}\right)=\frac{\underset{j=1\ne <br><br>i}{\overset{M}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\mu <br><br>}}_{i|j}<br><br>\left(\mathrm{\Lambda <br><br>}\right)}{\underset{k=1}{\overset{M}{\sum <br><br>}}<br><br>\left(\underset{j=1\ne <br><br>k}{\overset{M}{\prod <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\mu <br><br>}}_{i|j}<br><br>\left(\mathrm{\Lambda <br><br>}\right)\right)}<br><br>\mathrm{for}<br><br>\text{\hspace{1em}<br><br>}<br><br>i=1,2,\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>M\\ {\mathrm{\mu <br><br>}}_i<br><br>\left(\mathrm{\Lambda <br><br>}\right)=\frac{\underset{j}{\min }<br><br>\left({\mathrm{\mu <br><br>}}_{i|j}<br><br>\left(\mathrm{\Lambda <br><br>}\right)\right)}{\underset{k=1}{\overset{M}{\sum <br><br>}}<br><br>\left(\underset{j}{\min }<br><br>\left({\mathrm{\mu <br><br>}}_{i|j}<br><br>\left(\mathrm{\Lambda <br><br>}\right)\right)\right)}<br><br>\mathrm{for}<br><br>\text{\hspace{1em}<br><br>}<br><br>i=1,2,\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>M.\end{array}$

19. A method according to claim 18, including the step of carrying out said selecting step by selecting one of said states which corresponds to the respective said prototype point having the largest calculated value of μ

_i(Λ

).

20. A method according to claim 18, including the step of effecting separate filtering of each said calculated value of μ

_i(Λ

).

21. A method according to claim 16, including the step of effecting separate filtering of each said determined degree of hypertrapezoidal fuzzy membership.

22. A method according to claim 16, including the step of determining a confidence value regarding the accuracy of said selected state.

23. A method according to claim 22, including the step of determining said confidence value as a function of a difference between the largest and the second largest of said determined degrees of hypertrapezoidal fuzzy membership.