Sensor arrangement including a neural network and detection method using same

A sensor arrangement (1) comprising at least one measuring coil (2), at least one voltage source (3) for the measuring coil (2), and an evaluation unit (4) with means for detecting, processing, and evaluating measured signals. This sensor arrangement (1) is used to measure distances and thicknesses substantially independently of the material involved, without the user having to know the physicomathematical relations between the influencing quantities and the measured values. In order to evaluate the measured signals, the evaluation unit (4) of the sensor arrangement comprises a neural network (5) with an input layer, at least one hidden layer, an output layer, and connection weights for the individual layers. The connection weights are determined and stored in a learning phase by measurements taken on a plurality of different suitable learning objects with known actual values.

FIELD OF THE INVENTION 
The invention relates to a sensor arrangement comprising at least one 
measuring coil, at least one source of voltage for the measuring coil, and 
an evaluation unit with means for detecting, processing, and evaluating 
measured signals. 
BACKGROUND OF THE INVENTION 
Such sensor arrangements, for example with eddy-current sensors having a 
measuring coil, have been used for years for a large variety of 
measurements, such as, for example, for measuring the distance to an 
object, for measuring the thickness of a coating layer on an object, for 
measuring the conductivity and magnetic. permeability of a target, or for 
examining the homogeneity, and for detecting damage in the structure of 
the target surface. Normally, measurements with the known sensor 
arrangements require an extensive knowledge of physical relations between 
quantity being determined, the measured value, and possible disturbance 
variables. This knowledge must often be converted to measuring and 
evaluation electronics that are specially adapted to the measuring 
problem. Some measurements cannot be carried out at all, since different 
influence variables superpose, so that no clear statement of the 
measurements is obtained. When measuring the thickness of a conductive 
layer on a likewise conductive carrier with a known sensor arrangement, 
measuring errors will occur, for example, despite an adaptation to the 
particular target material. This applies, for example, to the existence of 
local inhomogeneities, magnetization, conductivity, effective 
permeability, temperature gradients, etc. When using known sensor 
arrangements of the state of the art, it will be necessary to find again 
for each measuring problem the mathematical relations between influence 
variables and measured values. The mathematical relations are in part 
complex and extremely nonlinear, so that this procedure, if possible at 
all, will take an enormous amount of time. 
The complexity of the mathematical relations between influence variables 
and measured values is to be demonstrated by the example of the 
noncontacting distance measurement by the eddy-current principle. The 
impedance of a coil (real part and imaginary part) varies upon approaching 
an electrically and/or magnetically conductive object. Thus, by measuring 
the impedance of a measuring coil, it is possible to determine the 
distance between the coil and the object being measured. In the object 
being measured, a current is induced, which counteracts the excitation of 
the coil. This reaction is again dependent on the electric conductivity 
and on the magnetic behavior of the measuring object, namely the material 
parameters. Same are again temperature-dependent. Furthermore, the 
impedance values are frequency-dependent, and nonlinearly related to the 
measuring distance. Reliable results of the measurement may be obtained 
only when all these influence variables are considered. 
SUMMARY OF THE INVENTION 
It is now the object of the invention to describe a sensor arrangement of 
the kind under discussion, which permits the user to perform largely 
material-independent measurements, without knowledge of the mathematical 
background. 
The sensor arrangement of the present invention accomplishes the foregoing 
object by providing a characteristic features of claim 1. Accordingly, 
providing a sensor arrangement which is configured such that the 
evaluation unit for evaluating the measured signals comprises a neural 
network of neurons or nodes arranged into layers including an input layer, 
at least one hidden layer, and an output layer, and connection weights for 
the nodes of the individual layers, and that the connection weights are 
determined and stored during a learning phase by measuring the outputs of 
the network produced when a plurality of different suitable learning 
objects with known actual values are input to the network, and using an 
algorithm to arrive at connection weights which produce the known actual 
values as outputs of the network. 
In accordance with the invention, it has been recognized that a detailed 
knowledge of the physicomathematical relations between disturbance 
variables and measured values is no longer needed, when a suitably trained 
neural network is used for the evaluation of the measured signals. It has 
further been recognized that the neural network of a sensor arrangement 
can also be trained for different kinds of measurements by a suitable 
selection of the learning objects and measurements in the learning phase. 
Therefore, the sensor arrangement of the present invention is capable of 
performing different kinds of measurements. Furthermore, it has been 
recognized that the suitable optimal selection of different learning 
objects also permits measurements of unknown measuring objects. The neural 
network in use approximates the relations such that it is also possible to 
determine correctly actual values that are between the learning points. A 
linearization or calibration as is common in conventional systems is thus 
no longer necessary. 
In the case of the noncontacting distance measurement, it is possible to 
eliminate the different influences of different materials in that during 
the learning phase measurements are performed on learning objects 
consisting of different suitable materials. If the actual measurements are 
to be made, for example on metallic materials, likewise metallic objects 
will be used for the learning phase by selecting, for example, learning 
objects of aluminum, iron, stainless steel, etc. These measurements supply 
input variables for the neural network, which assist in determining the 
connection weights of the neural network, since the actual values of the 
learning objects are known. In this connection, the system of equations 
for the connection weights is possibly repeatedly overdefined. In this 
case, a mean-square approximation is performed. Underdefined systems of 
equations or heavily correlated input values result in a lack of learning 
success. After the learning phase, the determined connection weights are 
held in a corresponding electronic element. The connection weights permit 
forwarding a mapping instruction of the input vector of input values to 
one or more output values. Thus, the neural network finds an approximation 
for a relation that cannot be solved in mathematically closed manner. In 
the measuring phase, this facilitates distance measurements also on 
measuring objects, which consist of a different material than any of the 
learning objects. 
In an advantageous embodiment of the sensor arrangement in accordance with 
the invention, a back-propagation network is used as neural network. Such 
network structures are already adequately known from the literature, so 
that it is not necessary to describe in more detail a concrete 
configuration of a back-propagation network. It should only be remarked 
that a back-propagation network has a network structure without feedback. 
There exist various possibilities of realizing such a network. Satisfactory 
results were obtained with a single-stage network structure, which has 
only one hidden layer. For example, different types of a single-stage 
network structure which yielded satisfactory results include: 
Type 1: eight input nodes, five nodes in the hidden layer, and one output 
node; 
Type 2: eight input nodes, one node in the hidden layer, and one output 
node; 
Type 3: six input nodes, five nodes in the hidden layer, and one output 
node; 
Type 4: four input nodes, four nodes in the hidden layer, and one output 
node; 
Type 5: two input nodes, two nodes in the hidden layer, and one output 
node. 
Possible, however, is also a two-stage network structure with two hidden 
layers. 
In a particularly advantageous embodiment of the sensor arrangement in 
accordance with the invention, a strictly monotonic and differentiable 
sigmoid function, which is adapted to the nonlinearity behavior of the 
measuring coil, is used as transfer function of the elements of a 
back-propagation network. Although there occurs an individual adaptation 
of the transfer function--and, thus, of the neural network--to the 
physical conditions of the measuring coil, the advantages of a sigmoid 
curve shape are however maintained. Any arbitrary input value is mapped to 
the interval between 0 and 1. Furthermore, input values which are close to 
0, are spread apart to a greater extent and, thus, are better separated by 
the slope of the curve in this range. Very high positive or negative 
values lead always to activities near 1 and respectively near 0. Their 
absolute magnitude is relatively irrelevant as a result of the very flat 
curve shape in these ranges. The sigmoid function has also the advantage 
that its differentiation is very simple. 
Preferably, the source of voltage is followed by a mixer arrangement, which 
generates selectively energizing voltages of different amplitude and 
frequency. These measurements of the impedance of the measuring coil at 
different frequencies represent a possibility of realizing uncorrelated, 
but physicomathematically connected input values for the neural network. 
To obtain now linearly independent measured values for input to the neural 
network, it is proposed to use as a component of the evaluation unit a 
four-wire-type circuit arrangement, which comprises one leg for detecting 
the voltage curve and another leg for detecting the current flow of the 
measuring coil. Both signals are also processed in the evaluation unit, in 
that they undergo an A-D conversion and complex division. In this manner, 
a complex impedance value is determined, which is independent of the 
amplitude and the phase of the energizing voltage. The evaluation unit may 
further comprise means for normalizing and scaling the measured signals. 
Only then are the thus-determined impedance values supplied as input 
values to the neural network. 
Furthermore, the present invention relates to a method of detecting 
measured values with a sensor arrangement of the present invention. This 
method is intended to provide the user of the sensor arrangement in 
accordance with the invention with an automatism which permits the user to 
carry out different kinds of measurements without knowledge of the 
mathematical background. 
To this end, the detection of measured values must be performed such that 
for actual values that are to be determined, as many nonlinearly related, 
namely uncorrelated, but physicomathematically connected input values are 
determined for the neural network as there are input nodes. It has been 
recognized that, at different measuring frequencies, the impedance values 
of the measuring coil fulfill the requirements of the input values for 
neural networks. Therefore, in the measuring phase, the impedance values 
of the measuring coil are determined at different frequencies and applied 
accordingly normalized to the input of the neural network. To this end, 
the voltage curve and current flow are detected on the measuring coil at 
different frequencies. 
There exist various possibilities of determining the spectra of the 
digitized voltage curve and of the digitized current flow. In a 
particularly advantageous application of the method, the spectra of the 
digitized voltage curve and of the digitized current flow are determined 
by iteration with the use of a spectral estimator. In this connection, the 
spectrum is determined as 
##EQU1## 
where x.sub.n (t) is the sampling value at the time n, X.sub.n (f) the 
spectrum at the time n, and X.sub.n+1 (f) the newly calculated spectrum at 
the time n+1. With the term aT/T.sub.0 the desired spectral line is 
selected. As starting value of the iteration, one uses n=0, and X.sub.0 
(f)=0. X(f) is a complex quantity, X(t) is real. For nT=T.sub.0 (one 
period duration), the result corresponds exactly to that of a discrete 
Fourier transform. This applies likewise to integral multiples of a 
period. Thus, the method represents a spectral estimator. 
In a particularly advantageous variant of the method in accordance with the 
invention, a special square-wave voltage is used as energizing voltage for 
the measuring coil. The spectral proportion of higher harmonics drops in a 
pure square-wave voltage as the frequency increases. This is compensated 
by adding three additional square-wave signals of a lesser amplitude for 
the first four spectral lines. Such a compensation is advantageous, since 
the attainable resolution of the A-D converter is the same for all used 
frequencies, and in this manner it is possible to realize an optimal 
modulation of a high dynamic. Thus the square-wave voltage is 
advantageously formed by a periodically recurrent sequence of respectively 
one square pulse of a larger amplitude and three square pulses of a 
smaller amplitude. 
Furthermore, it will be advantageous, when the alternating energizing 
voltage of the measuring coil is superposed by a direct current component. 
The measured current facilitates conclusions as to the temperature of the 
measuring coil. The pure ohmic component of the coil impedance may be 
supplied to the neural network as additional input value, which achieves 
in a simple manner a temperature compensation of the sensor. 
Advantageously, the sensor arrangement of the present invention as well as 
the above-described method of detecting measured values with the sensor 
arrangement of the invention may be used for measuring distance and 
coating thickness. Thus, for example, it is possible to determine the 
thickness of metal foils or even the thickness of coatings. A further 
advantageous use of the sensor arrangement in accordance with the 
invention is the measurement of electric conductivity and effective 
permeability of surface coatings.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
Shown in FIG. 1 is a basic layout of a sensor arrangement 1 in accordance 
with the invention. The sensor arrangement 1 comprises a measuring coil 2 
as sensor element and a source of voltage 3 for the measuring coil 2. 
Further provided is an evaluation unit 4, which comprises means for 
detecting, processing, and evaluating measured signals. 
In accordance with the invention, the means for evaluating measured signals 
is a neural network 5 with an input layer, at least one hidden layer, an 
output layer, and connection weights for the individual layers. The 
connection weights are determined and stored in a learning phase by 
measurements on a plurality of different, suitable learning objects each 
with a known actual value. 
The illustrated neural network 5 is a back-propagation network with a 
single-stage network structure, i.e., the network structure has only one 
hidden layer. The input layer of the neural network has, for example, 
eight input nodes, whereas the hidden layer has five nodes, and the output 
layer is formed by a single output node. Used as transfer function of the 
neural network 5 is a sigmoid function adapted to the nonlinearity 
behavior of measuring coil 2 and having a strictly monotonic and 
differentiable curve. 
A possibility of realizing voltage source 3, measuring coil 2, and the 
means for detecting the measured signals within the scope of evaluation 
unit 4 is shown in FIG. 2. The actual voltage source 3 is followed by a 
mixer arrangement 6, which generate selectively energizing voltages of 
different amplitudes and frequencies. The illustrated mixer arrangement 6 
facilitates realization of an energizing voltage in the form of a 
square-wave signal, which is formed by a periodically recurrent sequence 
of respectively one square pulse of a larger amplitude and three square 
pulses of a smaller amplitude. Such a signal curve is shown in FIG. 3. The 
associated graph in the frequency range may be noted from FIG. 4. As best 
seen in FIG. 4, a signal with four substantially equally strong frequency 
components is generated by adding several square pulses of smaller 
amplitudes to a square pulse of a larger amplitude. 
As a result of energizing the measuring coil 4 with such a square signal, 
it is possible to determine the impedance values of measuring coil 2 at 
these four different frequencies. 
Shown in FIG. 2 is that portion of the evaluation unit 4, which detects the 
measured signals, namely the voltage curve U.sub.x and the current flow 
I.sub.x on measuring coil 2. The voltage curve is detected parallel to the 
measuring coil 2, whereas the current flow is detected serial to the 
measuring coil 2. This circuit arrangement is realized by the four-wire 
circuit method, wherein the individual current branches are shielded. 
Both the voltage signal and the current signal undergo an A-D conversion 
and complex division. In this process, uncorrelated impedance values of 
measuring coil 2 result at the different frequencies, which are 
independent of the amplitude and phase of the energizing voltage. 
The circuit shown in FIG. 2 is followed by processing means, which form 
likewise a part of evaluation unit 4. More specifically, they include 
means for digitizing, namely an A-D converter 7, means for carrying out a 
Fourier analysis for voltage and current 8, means for complex dividing at 
different frequencies 9, and finally means for complex normalizing and 
scaling 10. Only next to these signal processing stages are the input 
nodes of the neural network 5, as shown in FIG. 1. 
In FIG. 5, the headings of the test diagrams of distance measurements are 
to be interpreted as follows: 
In all ten tests single-stage neural networks were used, which have only 
one hidden layer. Type 8/5/1 indicates a network structure with eight 
input nodes, five nodes in the hidden layer, and one output node. 
Indicated next thereto are the materials used during the training, such 
as, for example, copper, iron, or V2A steel. The test was always conducted 
with ten different metals. The two axes correspond to the desired distance 
or the distance estimated by the network. Starting with test 7, the number 
of used measuring frequencies was reduced. As can be noted, effective of 
at least two frequencies, usable results are obtained by the method, this 
means a good correlation between the actual distance and the detected 
distance. However, for a higher number of measuring frequencies, a better 
approximation quality will result. 
As a whole, the following statements can be made: 
The material properties of metals, which have not been learning objects are 
correctly recognized and are interpolated or extrapolated. This allows to 
shorten the calibrating operation significantly. 
The classification algorithm of the learning phase determines the material 
parameters, for example, conductivity and effective permeability of the 
material, and it compensates for their influence on the distance 
measurement. 
Material parameter fluctuations caused by temperature changes in the object 
being measured do not influence the distance measurements. 
Thus, the neural network finds an approximation for a relation which cannot 
be solved in mathematically closed manner. However, it is not simple to 
extract the approximation from the trained connection weights. Tests with 
different input values and network structures furnish experimental 
statements on solubility and necessary minimal requirements of also 
similar problems. 
As regards advantageous embodiments of the sensor arrangement in accordance 
with the invention, as well as the method of the present invention for the 
detection of measured values with this sensor arrangement, which have not 
be considered in the foregoing description of the Figures, the general 
description of the invention is herewith incorporated by reference. 
Finally, it should expressly be remarked one more time that the sensor 
arrangement of the present invention may be used not only for measuring 
distance and thickness, but also for measuring material parameters, such 
as electric conductivity and effective permeability.