US 5,146,541 AGrant
Signal Phase Pattern Sensitive Neural Network System and Method
Issue Date:1992-09-08
•10 Claims
•4 Drawing Sheets
Abstract
A signal phase pattern sensitive neural network system can discern persist patterns of phase in a time varying or oscillatory signal. The system employs duplicate inputs from each of its sensors to the processing elements of a first layer of its neural network, with the exception that one input is phase shifted relative to the other. The system also employs a modification of a conventional Kohonen competitive learning rule which is applied by the processing and learning elements of a second layer of its neural network.
Metadata
Assignee
- The United States of America as represented by the Secretary of the Navy
Inventor
- Steven L. Speidel
Application Information
Application Number:US 3685047
Filing Date:1989-06-19
Priority Date:1989-06-19
Art Unit:222
Classifications
IPC:
G06F 1518
Field of Search:
364200;900;133;513;213.9;273-277;972;972.1-972.4
Patent Drawings (4 sheets)
Description
BACKGROUND OF THE INVENTION
The present invention generally relates to parallel sensing and processing of signals and, more particularly, to a signal phase pattern sensitive neural network system and method for discerning persistent patterns of phase in time varying excitation.
An artificial neural network is a network of highly interconnected processing elements (PE's) which accomplish parallel processing and, to some extent, distributed processing. The neural network can be coupled with an array of sensors to form an artificial neural system for sensing and processing signals wherein learning and adapting occur in a way thought to simulate the human brain.
A typical neural network system is composed of multiple layers. In a layer of the neural network system where learning occurs, the layer is characterized by the fact that all the member PE's of the layer have the same learning rule. For example, consider the conventional neural network system 10 illustrated in FIG. 1. First layer 12 merely acts as a "fan-out" layer, connecting each sensor 14 with each member PE of second layer 16. No competition nor learning occurs in first layer 12.
The PEs of second layer 16 compete with one another. By way of example, competition between second layer PEs can occur in accordance with a learning rule that is known as the Kohonen competitive learning rule and is set out in detail in the text Self-Organization and Associative Memory by T. Kohonen, Springer-Yerlag, Germany, 1984. The Kohonen competitive learning rule provides for competition between PEs of second layer 16 on the basis of the equation: ##EQU1## The winner among PEs updates itself (or adjusts its weight) in accordance with the equation:
where x is typically a signal vector, W is a connectivity strength or weight vector which is modified during learning by the quantity W.sub.i for the ith PE, and alpha is a heuristically chosen learning constant.
Although each PE of second layer 16 operates locally upon the inputs it receives, only the winning PE, i.e., the one whose connection strength pattern most closely matches the incoming signals, is allowed to adapt. The connection strength patterns associated with the PEs form win regions or sectors for each PE in the manner of Kohonen competitive learning.
Heretofore, neural networks have been applied to preprocessed signals which are expressed as intensities or base-banded amplitude envelopes. However, there is growing interest in applying neural network technology to real world signals, for instance, to improve performance of weapon sensory systems (passive and active) against low Doppler targets, targets employing countermeasures, and targets in areas of high environmental noise.
SUMMARY OF THE INVENTION
The present invention relates to a signal phase pattern sensitive neural network system and method for discerning persistent patterns of phase in time varying or oscillatory excitation The novel features of the system of the present invention over the above-described conventional neural network system relate to (1) the provision of duplicate inputs from each sensor to the neural network except that one input is phase shifted relative to the other, and (2) the modification of the conventional Kohonen competitive learning rule applied by the processing elements of the second layer of the neural network. These features permit real-time, simultaneous detection of multiple, statistically significant phase patterns embedded in a time varying, or oscillatory, signal, for instance, a target signal masked in background or environmental signals.
OBJECTS OF THE INVENTION
Accordingly, it is the primary object of the present invention to provide a novel neural network system and method which achieves, simultaneously and in parallel, the formation of a set of bi-vectors which represent the phase pattern statistics (the probability density function of phase patterns) across an array of multiple sensors
Another object of the present invention is to provide a novel neural network system and method which employs phase shifted inputs to make evident a phase pattern characteristic of the signals incident across the multiple sensor array.
Still another object of the present invention is to provide a novel neural network system and method which employs a modified Kohonen competitive learning rule that allows a statistical partitioning or classification of the received signal pattern among the PEs of the layer employing the modified learning rule.
Other objects, advantages and novel features of the invention will become apparent from the following detailed description of the invention when considered in conjunction with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a diagrammatic representation of a conventional neural network system.
FIG. 2 is a diagrammatic representation of a signal phase pattern sensitive neural network system in accordance with the present invention.
FIG. 3 is a block diagram of a signal phase pattern sensitive neural network method in accordance with the present invention.
FIG. 4 is a diagrammatic representation of a bi-vector plane (W) and input vector (x) employed by a modified Kohonen competitive learning rule in accordance with the present invention.
FIG. 5 is a graph of beamforming results of the testing of the system of the present invention.
FIG. 6 is a graph of an original signal incident on one sensor and the processed signals derived from the PEs of the layer applying the modified competitive learning rule of the present invention.
FIG. 7 is a graph of synthetic target echoes used in experimental testing of the system of the present invention.
DETAILED DESCRIPTION OF THE INVENTION
Referring now to the drawings, and particularly to FIGS. 2 and 3, there is shown respective diagrammatic representations of the signal phase pattern sensitive neural network system 20 and method of the present invention. System 20 of the present invention is capable of discerning persistent patterns of phase in the time fluctuating excitation of a plurality of sensors 22 of system 20. The system can also learn and apply associations of these phase patterns with the directions of propagation of incoming waves and/or provide a beamforming function. In order to perform these functions, system 20 also includes a neural network 24 that is coupled with sensors 22 for sensing and processing signals. Neural network 24 is a network of highly interconnected processing elements (PE s) in first, second and third layers 26, 28 and 30 thereof, which accomplish parallel and, to some extent, distributed processing.
There are two, or a pair of, PEs 32 in first layer 26 for each sensor 22. The inputs from sensors 22 to first layer PEs 32 are analog signals. The PEs 32 of first layer 26 are digitizers, such as analog to digital (A/D) converters, which transform the analog inputs to digital signals for fanout to second layer 28. A pair of conductive leads 34A, 34B interconnect each of sensors 22 with a separate PE 32 of first layer 26.
One input signal is a substantial duplicate of the other except that it is phase shifted, under ideal conditions, by a quarter of a period of either a frequency component, or in the case of a narrowband signal, the center frequency. Lead 34B has a signal delay producing device 36, such as a time delay, interdisposed therein for producing the phase shift of the one input signal relative to the other from the same sensor 22.
The PEs 38 and 40 of second and third layers 28 and 30, respectively, are composed of digital logic circuits. The circuits of PEs 38 and 40 compose part of the circuitry of a general purpose digital computer, for example a Zenith 386 computer, operated by software, such as the computer program set forth in the Appendix. Alternatively, the digital logic circuits of PEs 38 and 40 can be implemented by a dedicated hardware/firmware architecture. Fan out of the digital signals from PEs 32 of first layer 26 to PEs 38 of second layer 28 is achieved by a bus 42 which provides the conductive leads connecting PEs 32 in first layer 26 with each of a plurality of PEs 38 in second layer 28.
This technique of providing phase shifted inputs makes evident a phase pattern characteristic of the signals across the array of sensors 22. It is also recognized in accordance with the inventive concept that by forming combinations of shifted and non-shifted signals, network PEs 38 of second layer 28 are capable of combining the sensor input signals with arbitrary relative phase. Array signals are presented to the neural network 24 in a manner which allows spatial sector discrimination by multi-phasic response to the sensor outputs. In the case where a system is processing narrowband signals or a frequency component of a signal, phasing among the PEs 32 of the first layer 26 may be accomplished by using the fact (trigonometric identity) that ##EQU2## Taking the initial signal from the ith sensor, .PSI..sub.i, to be A.sub.i cos(.omega.t+.phi..sub.i), the above expression may be rewritten as
where,
.PSI..sub.i =A.sub.i cos(.pi.t+.phi..sub.i)=weighted sensor signal,
.PSI..sub.i .pi./2 =A.sub.i cos(.omega.t+.phi..sub.i +.pi./2)=-A.sub.i sin(.omega.t+.phi..sub.i)=signal shifted by phase angle .pi./2,
.PSI..sub.i.phi. =A.sub.i cos(.omega.t+.phi..sub.i +.phi.)=phase shifted element signal.
The neural network 24 is fabricated to have weights w.sub.i ' and w.sub.i '' in order to accommodate the sensor array inputs. Thus, the neural network 24 will be able to direct the array spatial response.
PEs 38 of second layer 28 are appropriately fabricated and interconnected to use a modified Kohonen competitive learning rule, in accordance with this inventive concept and as set forth in detail in the software of the computer program contained in the Appendix, to capture relative phase information in the sensed input signals. This modified learning rule allows for a statistical partitioning or classification of the received patterns of phase. Though each of PEs 38 of second layer 28 operates locally upon the inputs it is receiving, only the winning PE, i.e., the one whose connection strength pattern most closely matches the phase pattern of the incoming signals, is allowed to adapt. The connection strength patterns associated with PEs 38 form win regions or sectors for each PE in the manner of the modified form of the Kohonen competitive learning rule.
In contrast to its conventional form, the modified form of the Kohonen learning rule involves operations, to be described later on, which allow for processing of oscillatory signals in a manner which becomes sensitive to the relationship of the signal vector to a connectivity or weight plane or bi-vector in the multidimensional weight space. This capability allows the modified rule to respond particularly to the phase pattern feature of the signal vectors.
Thus, the finite population of open and solid PEs 38 in second layer 28, seen in FIG. 2, try to form a statistically optimal representation of the perhaps infinite number of received patterns Both use the same modified learning rule to capture the phase pattern and both have the same inputs. The distinction is that some are connected to the third layer 30 to act as what has come to be known as outstar sources which are developed thoroughly in the text Studies of Mind and Brain by S. Grossberg, D. Reidel Publishing Company, Boston, 1982. The outstar sources and other sources identified by Grossberg are used for beamforming output (through conjugation of the adapted weights). These are two examples of the purposes served by statistical capture of phase patterns. A detailed discussion of second layer operation rules follows this general discussion.
PEs 40 of third layer 30 of neural network 24 compose the boundaries of Grossberg outstars which learn according to the well-known Grossberg learning rule as set out in the Grossberg text. Second layer PEs 38 serve as the "sources" of these outstars. The appropriate outstar (or outstars) is activated when its source (an output from second layer 28) wins a competition. Those of PEs 40 serving as Grossberg outstars operate in two modes: (1) a learning or training mode and (2) a processing mode.
During learning, appropriate values are presented to the outputs of the third layer 30 simultaneously with the presentation of inputs at first layer 26. Each of PEs 38 adjust their response to inputs according to the modified learning rule. When operating in the processing mode, the PEs output the responses that they learned to associate with the particular source PE which is active at any given time. Thus, third layer 30 completes a pattern-to-pattern association--the particular signal array phase pattern is won by a PE in second layer 28 which subsequently activates a learned pattern in third layer 30. In this case, the third layer pattern has been trained to be the three direction cosines.
Given the above-described makeup of neural network system 20 of the present invention, the method of the invention is carried out in accordance with the steps represented by blocks A-E in FIG. 3. Block A represents the first step of sensing a signal emanating from an environment of interest, such as an environment containing a target signal. Block B represents the second step of transmitting the inputs of the signal sensed at each sensor 22 to each of the pairs of PEs 32 in the first layer 26 such that one input is phase shifted by a predetermined amount relative to the other. Block C represents the third step of fanning out the pairs of inputs from first layer PEs 32 to second layer PEs 38. Block D represents the fourth step of selecting and learning different segments of the sensed signal at second layer 28, in response to the inputs to the second layer PEs 38, in accordance with the modified Kohonen learning rule for partitioning the signal into the different segments. Block E represents the fifth step of transmitting the different partitioned signal segments from second layer PEs 38 to third layer PEs 40 where processing of the different partitioned signal segments takes place to identify a desired characteristic of the sensed signal, such as its directionality.
The functioning of second layer 28 is unique and a more detailed description of it now follows with reference to FIGS. 2-4. Given N sensors, the 2N inputs received by each PE 38 of second layer 28 are conceptualized, for the purpose of concise description, as components of a 2N component vector x. Since the excitation is a propagating wave, the pattern of amplitudes across sensors 22 will not remain fixed although the direction of incidence does.
In order to deal with the cyclical fluctuation, the input vector x may be considered to be rotating or oscillating in a plane in the 2N dimensional space if it is maintaining a set relative phase pattern. Proof of this relationship is as follows. When a sinusoidal excitation is applied at a sensor 22 (FIG. 2), two vector components u.sub.i,v.sub.i are formed at the input to the neural network 24:
Thus, for the entire sensor array of n sensors 22 the input vector x is:
where x is a function of time. At sample times t.sub.1,t.sub.2,t.sub.3 the input vectors are:
It may be shown that the vectors x.sub.1,x.sub.2,x.sub.3 fall in a plane by showing that the third is linearly dependent on the first and second. To do this, the components of x.sub.3 are expanded as follows:
also
and
where n.sub.31,n.sub.32 are constants, and, by induction,
Similarly, it can be shown that
Thus, any two of the vectors x(t.sub.k),x(t.sub.l) form a basis for all others and the time evolving vectors therefore lie in a plane within the hypersphere.
Further, as seen in FIG. 4, the input sensitivities (W) for each PE's set of inputs describe an additional plane. If the plane of the vector x and the plane of W are the same, then their phase patterns are matched. This fact is taken advantages of in the design of the present invention. During learning, PEs 38 of the second layer 28 adjust their input sensitivity planes (W) to match the planes of the input vectors (x). While doing this, they continually compete in the manner of the modified Kohonen learning rule so that they reserve "win regions" about some particular phase patterns, i.e., each PE's learned W plane is a statistically weighted expectation representing the inputs which it has won.
A similar competition is used in the processing mode as is used in the learning mode. When a given second layer PE 38 wins, it acts as an outstar "source" and a particular Grossberg outstar is invoked. The association of the phase pattern with the direction of the incident wave is accomplished this way and the Grossberg outstars produce the average values of the direction number triples that were presented to them coincidently with associated input vectors at the second layer during training. In FIG. 2, the outstars are indicated by the dashed lines between second and third layers 28 and 30. The solid output lines from the second layer allow for "beam" outputs, i.e., sums of the products of the components of phase conjugate of w and x (the dot product). A "window function" may also be applied for narrowing of the beams.
The phase conjugate is formed to enable the transforming of weights for beamforming in accordance with the following relationships. For beamforming, transform the weights (sensitivities) w to vector b, which when multiplied times an input vector x of a particular phase pattern will cause the inputs to add in phase. Given 2N inputs, let
and, for some input pair from the ith sensor,
where,
.PSI..sub.i is the original transduced signal on sensor i,
.PSI..sub.i .pi./2 is the delay signal,
and
.PSI..sub.i.phi. =cos(.omega.t+.phi..sub.x) is the phase shifted signal.
We want to find b
such that
where .phi..sub.ix -.phi..sub.iw is independent of i if the learned pattern matches the incoming one. Expanding, get ##EQU4## Thus, the result is that
The operations of the neural network 20 can be summarized in mathematical form as follows:
Learning
First layer 26: no learning, fanout only.
Second layer 28: learning in accordance with the modified Kohonen competitive learning rule:
where W.sub.i, is the "weight plane",expressed as a bi-vector, of the ith PE of layer 2, .alpha. is the learning rate, d.sub.ik =x.sub.k 19 W.sub.i (the bar denotes normallization), c.sub.ik is the projection of x.sub.k onto W.sub.i, normallized to unit length, and the symbol denotes the wedge product An alternative form of the learning rule for the second layer 28 is as follows. Given input vector:
use any pair (x.sub.j ',x.sub.j ") as a phase reference
For each pair,
find
Likewise, for w, find
Form the difference
and adjust w according to the formula
Third layer 30: Grossberg "outstars" with sources at the second layer as set forth the Grossberg text. For example,
and
Processing
First layer 26: fanout only
Second layer 28:
o.sub.i =.omega..sub.i .multidot.x, where .omega..sub.i is the phase conjugate of .omega..sub.i,
Third layer 30: Output learned values of direction numbers (approaches average) according to Grossberg rule.
System 20 of the present invention is not limited to any particular application. By way of example, in a sonar application of system 20, sensors 22 could be piezoelectric crystals, whereas in an application of the system to testing signals in an electrical circuit, sensors 22 could be taps on the circuit paths. As mentioned earlier, PEs 32 of the neural network 24 are A/D converters, whereas PEs 38 and 40 of the neural network 24 are digital circuit portions of a general purpose computer, such as the Zenith 386, directed and controlled by software, such as contained in the Appendix.
The processing elements referred to throughout this application are simulated in the illustrative embodiment in the referred to Zenith computer in accordance with the program of the Appendix. Optionally the processing elements could be fabricated from a plurality of general purpose CPUs, such as the Motorola 68,000 series or Intel 8086 series, that are suitably programmed in accordance with known techniques by one skilled in the art to which the invention pertains to carry out the mathematical operations set forth above. Such implementation by the CPUs or transputers could be carried out without requiring undue experimentation or ingenuity outside of the scope of the teachings of the concept.
Beamforming Test Results
Each of PEs 40 of the bi-vector beamforming (or third) layer 30 is capable of forming a beam. Thus, by setting the number of PEs in the layer, the maximum number of beams is determined. If a large number of PEs are included, then training might not occur on all of them. Just a few of the PEs may continually capture the incoming signal vector depending on the statistics of the incoming signal. For the testing which is described below, five PEs were used, the number being arbitrarily chosen. For the test data which was used, all of the PEs trained at some time during the ping cycle.
Referring now to FIGS. 5-7, the sea-test data came from an experiment performed by Acoustic Research Laboratory/Pennsylvania State University personnel in Dabob bay. It consisted of nine channels representing summed outputs from the rows of elements of a transducer. Thus, the dimension of freedom was the vertical. Synthetic target echoes were introduced into the signal by computing the root mean square (RMS) levels of the target and the environment within the time window of the target return. A signal-to-noise (S/N) ratio could then be selected and the target and environment added in the appropriate proportion. The scenario used for generation of the target echo was matched to that of the sea test. The source was 30 meters deep and moving at 15 knots. The bottom was approximately 200 meters. The target was chosen to be stationary and placed at 100 meters in horizontal range and at 30, 90, and 130 meters in depth. All signals were base-banded. FIG. 5 shows beamforming results, in terms of sensitivity versus angle, with target depth equal to 130 meters. Up and down are reversed on these plots. That is, the +45-degree target is directed toward the bottom.
By feeding the data into the beamformer in sections, the effect of each segment of the ping cycle series upon the PEs 40 could be seen. As it turned out, there were two unexpected object returns within the record. One was an anomalous return from some unknown object in the water. The other was caused by an error in the target echo which caused there to be two targets instead of one. The other target was giving a very brief return from an apparent angle of 26 degrees while the main return was at 45 degrees. Two of the beams responded to the 26-degree target, which can be seen in FIG. 5.
FIG. 6 shows the original time series signal on channel 5 and the processed signals derived by passing them through the trained beams. The time series signal looks as if it is all of uniform amplitude, whereas on the beam outputs one can discern the accentuation of where the target is and the squelching down of the rest of the signal relative thereto.
Actually, the beams are constantly changing so this is not exactly the true-beam response. But it shows how particular parts of the record are being emphasized by the beams. The arrow on the top trace is at the end of the 26-degree target (tar26) and the beginning of the 45 degree target (tar45).
FIG. 7 shows the phase nature of the artificial target echoes and the channel to channel phase difference produced by target reflection alone.
The present invention and many of its attendant advantages will be understood from the foregoing description and it will be apparent that various changes may be made in the form, construction and arrangement of the parts thereof without departing from the spirit and scope of the invention or sacrificing all of its material advantages, the forms hereinbefore described being merely exemplary embodiments thereof. ##SPC1##
Claims
Having thus described the invention, what is claimed is:
1. A signal phase sensitive neural network system, comprising: (a) a plurality of means for sensing a signal emanating from an environment of interest; (b) a first layer means composed of a plurality of pairs of processing elements; (c) means interconnecting each said sensing means with a pair of said plurality of pairs of processing elements of said first layer for transmitting one input representative of said sensed signal to one processing element of each said pair of processing elements and another input representative of a phase shifted said sensed signal; and (d) a second layer means composed of a plurality of processing and learning elements, each of said first layer processing elements being connected to all of said second layer processing and learning elements for fanning out said sensed signal and said phase shifted sensed signal to all of the processing and learning elements of said second layer means, each processing and learning elements of said second layer means being capable of selecting out and learning different segments of the sensed signal in accordance with a predetermined competitive learning rule that partitions the signal into said different segments.
2. The system of claim 1 further comprising: a third layer means composed of a plurality of processing elements connected to said second layer means for processing said different segments to identify a desired characteristic of the emanated signal.
3. The system of claim 1 wherein said transmitting means includes: first and second conductive leads connecting said each sensing means with said processing elements of said first layer means; and a signal delay producing device disposed in one of said leads.
4. The system of claim 1 wherein said competitive learning rule is a modified Kohonen competitive learning rule in accordance with the expression: where W.sub.i is the weight plane, expressed as a bi-vector, of the ith PE of layer 2, .alpha. is the learning rate, d.sub.ik =x.sub.k .multidot.W.sub.i the bar denotes normalization, c.sub.ik is the projection of x.sub.k onto W.sub.i, normalized to unit length, and the symbol denotes the wedge product
5. A signal phase sensitive neural network system, comprising: (a) a plurality of means for sensing a signal emanating from an environment of interest; (b) a first layer means composed of a plurality of processing elements connected to said plurality of sensing means for receiving inputs representative of said sensed signal; and (c) a second layer means composed of a plurality of processing and learning elements, each of said processing elements of said first layer means being connected to all of said processing and learning elements of said second layer means for fanning out said inputs to all of the processing and learning elements, each of said processing and learning elements being capable of selecting out and learning different segments of the signal in accordance with a predetermined competitive learning rule that partitions the signal into said different segments, said competitive learning rule being a modified Kohonen competitive learning rule in accordance with the expression: where W.sub.i is the weight plane, expressed as a bi-vector, of the ith PE of layer 2, .alpha. is the learning rate, d.sub.ik =x.sub.k .multidot.W.sub.i the bar denotes normalization, c.sub.ik is the projection of x.sub.k onto W.sub.i, normalized to unit length, and the symbol denotes the wedge product.
6. The system of claim 5 further comprising: a third layer means composed of a plurality of processing elements connected to said processing and learning elements of said second layer means for processing the different signal segments into identify a desired characteristic of the emanated signal.
7. A signal phased sensitive neural network method, comprising the steps of: (a) sensing a signal emanating from an environment of interest; (b) transmitting pairs of the sensed signal to each pair of a plurality of pairs of processing elements of a first layer thereof such that the signals of the sensed signal pair of substantial duplicates except that one is phase shifted by a predetermined amount relative to the other; (c) fanning out the sensed signal pair from the first layer processing elements to each of a plurality of processing and learning elements of a second layer; and (d) selecting out and learning different segments of the emanated signal, from the sensed signal pair at the second payer of processing and learning elements, in accordance with a predetermined competitive learning rule for partitioning the signal into the different segments.
8. The method of claim 7 wherein said competitive learning rule is a modified Kohonen competitive learning rule in accordance with the expression: where W.sub.i is the weight plane, expressed as a bi-vector, of the ith PE of layer 2, .alpha. is the learning rate, d.sub.ik =x.sub.k .multidot.W.sub.i the bar denotes normalization, c.sub.ik is the projection of x.sub.k onto W.sub.i, normalized to unit length, and the symbol denotes the wedge product.
9. The method of claim 7 further comprising: transmitting the different signal segments from the second layer processing and learning elements to a plurality of processing elements of a third layer; and processing the different signal segments at the third layer to identify a desired characteristic of the emanated signal.
10. A signal phase sensitive neural network method, comprising the steps of: (a) sensing a signal emanating from an environment of interest; (b) transmitting inputs of the sensed signal to each of a plurality of processing elements of a first layer; (c) fanning out the inputs from the first layer processing elements to each of a plurality of processing and learning elements of a second layer; and (d) selecting out and learning different segments of the signal, form the inputs at the second layer, in accordance with a predetermined competitive learning rule for partitioning the signal into the different segments, said competitive learning rule being a modified Kohonen competitive learning rule in accordance with the expression: where W.sub.i is the weight plane, expressed as a bi-vector, of the ith PE of layer 2, .alpha. is the learning rate, d.sub.ik =x.sub.k .multidot.W.sub.i the bar denotes normalization, c.sub.ik is the projection of x.sub.k onto W.sub.i, normalized to unit length, and the symbol denotes the wedge product.