Journal of Sensors

Volume 2019, Article ID 9254315, 10 pages

https://doi.org/10.1155/2019/9254315

## Synthetic Sensor Array Training Sets for Neural Networks

Engineering Faculty, Ariel University, Ariel, Israel

Correspondence should be addressed to Nir Shvalb; li.ca.leira@hsrin

Received 11 June 2019; Accepted 10 August 2019; Published 10 September 2019

Academic Editor: Franz L. Dickert

Copyright © 2019 Oded Medina et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

It is often hard to relate the sensor’s electrical output to the physical scenario when a multidimensional measurement is of interest. An artificial neural network may be a solution. Nevertheless, if the training data set is extracted from a real experimental setup, it can become unreachable in terms of time resources. The same issue arises when the physical measurement is expected to extend across a wide range of values. This paper presents a novel method for overcoming the long training time in a physical experiment set up by bootstrapping a relatively small data set for generating a synthetic data set which can be used for training an artificial neural network. Such a method can be applied to various measurement systems that yield sensor output which combines simultaneous occurrences or wide-range values of physical phenomena of interest. We discuss to which systems our method may be applied. We exemplify our results on three study cases: a seismic sensor array, a linear array of strain gauges, and an optical sensor array. We present the experimental process, its results, and the resulting accuracies.

#### 1. Introduction

*Reconstruction problems* are of interest to the research community due to their importance in engineering applications. These have been studied with regard to heat source identification [1–5], shape reconstruction [6], wave source identification [7–9], inverse boundary conditions reconstruction [10, 11], and the problem of force identification on plates [12–17]. A notable example is [14] by Chierichetti and Ruzzene which uses the *confluence algorithm* to numerically reconstruct the dynamic response field of the structure from a limited number of experimental measurements (for a survey on analytic methods, see [18]). Another reconstruction problem is considered in [19] where an optical sensor array is used to position an IR (reflected) light source.

This paper offers a new line of thought on such problems. We gather sensor inputs taken in simple scenarios and manipulate them in accordance with the physical governing equations to form synthetic data in order to reconstruct more involved scenarios.

A sensor measures a physical quantity or its derivatives (for example, the change of an electrical analog signal is converted into the corresponding physical unit which is of interest [20, 21]). We distinguish between two conceptual cases:
(i)A sensor may be applied when a *single quantity* is to be detected. Examples include scalar quantities like velocity, temperature, distance, and light emission as the inputs to be estimated. Other examples are vector quantities like spatial orientation, detecting the location of a light source etc.(ii)A sensor may also be applied when *simultaneous quantities* are to be detected. Examples include scalar quantities like detecting all joint angles of a robotic arm [22], extracting the tensile stress field [6, 23], and measuring the motion of the sea bed [24]. Examples for simultaneous vector quantities to be detected include stress tensor field extraction and detecting the position of multiple light sources [25]

Using multiple sensors will not always detect simultaneous quantities. The reason for that is that in such cases, these quantities are aggregated into the sensor system—an *array of sensors*, in a complex manner. The same reasoning may apply also for the case where one is required to sense a wide range of a given physical quantity.

*Artificial neural networks* (ANN) are commonly used in computer vision [26] and regression problems. Though regression is a statistical process for estimating the relationships among variables, it can be used for computing arbitrary functions. Being available and due to the increasing computing power, the ANN usage has been accelerated in almost every domain of computer science [27, 28]. A neural network may be a good solution to analyze the sensor data described in (i) to estimate a physical quantity [29]. Of course, one needs to obtain a sufficiently large training set for convergence (c.f. in [30]). Obviously for simultaneous quantities to be detected, training the ANN would require to increase the training set exponentially in the power of which is unrealizable in many cases.

The training neural network for image recognition, 3D data, and video is typically an expensive task of collecting and annotating big data sets. The task of automatically generating such labeled data is an emerging field of research; see for example [31–33]. A new different approach is called *domain randomization* [34–37] where synthetic data is created by adding random textures to real images in order to force the ANN to learn the essential features. The underlying logic of this paper is somewhat similar to this approach.

In this paper, we introduce a way to analyze data from a sensor array by *bootstrapping synthetic training data* for an ANN. This way, the ANN “decomposes” the simultaneous quantity inputs and estimates its components individually. We also show how one can bootstrap synthetic training data for an ANN to analyze a wide range of input values.

*Remark. *The term *bootstrap* has various interpretations in literature. In computer science, the term may indicate a procedure for simulating discrete events [38] or be used to indicate a way to iteratively improve a classifier’s performance [39]. In statistics, bootstrap refers to a computational manipulation in order to establish certain statistical values [40]. Some other fields of research use the term in a totally different meaning. Here, we use the term bootstrap to indicate a procedure in which one manipulates real data from sensor arrays to form artificial sensor array data.

##### 1.1. Contribution and Paper Organization

The main concern of this paper is to construct synthetic physical measurements as data sets for ANNs. This is essential for cases were harvesting experimental data is out of reach (for reasons of time consumption, experimental setup complexity, etc.). For this end, we shall use basic ANNs provided by MATLAB.

The synthetic training data sets are bootstrapped out of a certain experimental set. More precisely, data is first collected from experiments; we then manipulate the sets to create a new training data. We discuss when such a method can be applied and exemplify our method for three cases of sensor arrays (cantilever deflection sensor, seismic sensors on a metal plate, and an optical sensor array).

This paper is organized as follows: Section 2 provides a mathematical formulation for situations where our method may be applied. Section 3 presents three sensor array study cases. Results for these cases where a single stimulus is of interest are provided in Section 5. In Section 6, we apply our bootstrapping method, and we conclude the paper in Section 7.

#### 2. A Mathematical Formalism

In what follows, we shall examine situations where one may desire to generate synthetic training data for a neural network. For clarity, we shall consider three examples for application and follow them throughout the paper:

##### 2.1. Study Case I

A horizontal cantilever beam with an unknown, nonconstant cross-section is included. A set of sensors (e.g., strain gauges) located along its axis, each on a different segment, measures the beam’s curvature (Figure 1). The beam is thought to be loaded by a *set of vertical forces* in which their position and magnitude are of interest. This sensor array was simulated using a finite element method. We used the finite element method (FEM) as a ground truth to train the ANN. Specifically, we used it to calculate the stress field and the resulting error function for training the ANN.