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Analog Computing revisited: A fully analog and minimalistic Damage Detector for Ultrasonic Testing enabling Material-Integrated Structural Health Monitoring

Stefan Bosse

arXiv:2609.35478v1cs.ARcs.AI

TL;DR

The paper addresses analog sensor signals that are commonly digitized for processing, despite the resource requirements of digital systems. It demonstrates a discrete analog signal-processing and feature-extraction chain with an analog neural network for damage detection. The detector uses fewer than 100 transistors and estimates damage distance from three envelope-derived features in the tested scan path.

  • Problem

    Sensor signals are inherently analog but are commonly processed digitally after conversion, while analog circuits may reduce component, energy, and area requirements.

    Source: §1 · p. 2

  • Method

    The proof of concept uses an all-pass approximation of the Hilbert transform, analog envelope-based feature extraction, and an analog neural network for damage classification and distance regression.

    Source: §1 · p. 3, §5 · p. 12, §7 · p. 16

  • Results

    Fewer than 100 BJT and JFET transistors and 500 electronic components supported damage detection and distance estimation using three envelope-derived features.

    Source: §7 · p. 17

  • Takeaways & Limitations

    The authors estimate a circuit area below 400 mm2 as an outlook for material-integrated sensing with printed organic circuits.

    Source: §7 · p. 17

    The simplified magnitude approximation avoids analog multipliers but produces a less-smooth envelope with ripple.

    Source: §2 · p. 4

Abstract

from arXiv · show

Ultrasonic Testing (UT) is commonly used to detect damage in structures, e.g., metal plates. A sensor acquires Ultrasonic waves, e.g., by using PZT transducers. The time-resolved sensor signal must be processed with analog electronics, e.g., amplified and filtered. Commonly a digitalization follows using an Analog-to-Digital converter, finally processing the digital sensor signal, applying digital signal processing, feature extraction, and Machine Learning by using powerful microprocessor systems. The disadvantages of digital processing systems are their high number of transistors (microchip area), energy consumption, state-dependent processing and therefore sensitivity to energy supply interruption. Beyond silicon electronics, printed organic electronics gains interest. But printed electronics is still limited to low transistor and electronic component counts (typically 100). We will investigate and demonstrate a fully analog signal processing and feature extraction system consisting of an analog Hilbert transform deriving the signal envelope, simple analog arithmetic calculations for feature extraction, and finally damage classification and regression using an analog Artificial Neural Network. We expect a full damage detection system with less than 100 transistors. We will test our damage detection system with PZT transducer signals from Steel plates with circular defects. The focus of this work is the analog computation of the signal envelope (using all-pass filter networks for approximation of the Hilbert transform) and the analog feature extraction as well as the prediction of damage, forming an analog computer which can perform in-sensor computation, computing without a digital computer.

1. Introduction

This work investigates whether sensor-signal processing, feature extraction, and damage prediction can be performed with discrete analog electronics, typically using fewer than 100 transistors. The introduction motivates analog computation as a resource-conscious approach and points to printed organic circuits as a future route to material-integrated sensing.

1. Introduction

  • Damage detection compares a baseline signal’s information content with a damage-containing signal, using the difference and a narrowed time range to identify damage features.Source: §1 · p. 1
  • Ultrasonic testing minimally uses a pitch transmitter and catch receiver along at least one scan path, with configurations extendable to more transducers and paths.Source: §1 · p. 1
  • Sensor signals are inherently analog but are commonly processed digitally after analog-to-digital conversion.Source: §1 · p. 2
  • Analog circuits can approximate functional calculations with fewer components, generally reducing energy and area requirements while potentially improving explainability and stability to energy-supply disturbances.The paper connects supply stability particularly to autonomously supplied sensor nodes.Source: §1 · p. 2
  • Printed organic electronics are presented as relevant to flexible, material-integrated sensing, including structural monitoring and large-area printed circuits,,.Source: §1 · p. 3
  • The proof of concept tests whether discrete analog electronics can perform sensor-signal processing, feature extraction, and damage prediction with typically fewer than 100 transistors.The stated future goal of printed organic circuitry tightly coupled to sensors is not addressed directly in this work.Source: §1 · p. 3

2. Hilbert Transform and Analytical Signal

The section describes deriving an ultrasonic signal envelope from its analytical signal and approximating the Hilbert transform with all-pass phase-shifter networks. It also motivates a simplified magnitude calculation that avoids analog multipliers but produces ripple.

2. Hilbert Transform and Analytical Signal

  • The signal hull, or envelope, is obtained from the magnitude of the analytical signal, which combines the real signal with its Hilbert transform.The Hilbert transform supplies a quadrature component for the analytical signal.Source: §2 · pp. 3–4
  • Approximating the analytical-signal magnitude without squaring avoids analog multipliers, but the simplified envelope calculation loses smoothness and shows ripple.Source: §2 · p. 4
  • An all-pass frequency phase-shifter network approximates the Hilbert transform by shifting the original signal by 90° independently of frequency,.Source: §2 · p. 4, Figure 3 · p. 5
  • The design uses first-order all-pass filters because second-order filters are unsuitable for the discrete-transistor analog processor, although second-order filters have been advocated.A network of order n requires 2n first-order filters split between paths A and B.Source: §2 · pp. 5–6
  • Pole frequencies are designed for a specified frequency range and filter order; the example uses 10–300 kHz and n=4, with a table of pole frequencies for the 90° phase-shift network.Source: §2 · p. 5, Table 1 · p. 6

3. Signal Processing Architecture

The system derives an ultrasonic signal envelope and extracts main-peak features through a sequence of analog operations. Two measurement runs supply peak, timing, and area signals for damage diagnostics.

3. Signal Processing Architecture

  • The signal-processing architecture calculates the ultrasonic signal envelope and derives features from its main peak.The authors note that these calculations are straightforward digitally but challenging to implement with analog circuits.Source: §3 · pp. 6–7, Figure 4 · p. 7
  • The extracted features are the main peak’s relative time and height, its width at a chosen fraction of peak height, and its area at that fraction.The width may be expressed as full width at half maximum when the fraction is k=0.5.Source: §3 · pp. 6–7
  • The measured signal passes through all-pass phase-shifter paths, whose outputs are combined and low-pass filtered before controlled switches select peak-detector paths.The architecture uses two measurements because the analog system cannot play a signal backward.Source: §3 · p. 7, Figure 4 · p. 7
  • In the second run, integrators record two peak-relative times and the area above a selected fraction of peak height; peak and integrator outputs provide diagnostic features.The area fraction is typically 20%–50% of peak height.Source: §3 · p. 8

4. Analog Signal Processing System: Feature Extraction

The feature-extraction system approximates the signal envelope with a discrete transistor all-pass network and analog circuits for rectification, peak detection, and addition. Its envelope and peak-detector outputs are reported to approximate their targets with errors below 10%.

4. Analog Signal Processing System: Feature Extraction

  • The fourth-order discrete all-pass network uses single-transistor amplifiers in each path, with resistor-capacitor pairs setting filter frequencies and equal resistors fixing the amplifier’s DC operating point.Because those resistors must be equal, the pole frequency is determined by the capacitor.Source: §4 · p. 8
  • The single-order filter design has phase error below 1.5° within the specified bandwidth because two RC networks cannot be decoupled in the single-transistor setup.Second-order filters are described as superior, but interacting RC networks would introduce significant phase errors in this implementation.Source: §4 · p. 8, Figure 6 · p. 10
  • The analog feature circuits include an active full-wave rectifier, a capacitive-storage peak detector, and an adder with low-pass filtering.JFETs in the peak detector’s difference-amplifier stage are used to avoid leakage of the stored peak value.Source: §4 · pp. 8–9, Figure 9 · p. 11
  • Error is below 10% for the envelope approximation relative to the mathematical Hilbert transform and for the peak detector across its input scale.The envelope retains some ripple from the complex-magnitude approximation; low-pass filtering shifts its phase slightly, which the authors say is not critical for subsequent calculations.Source: §4 · p. 11, Figure 10 · p. 12

5. Analog Artificial Neural Network: Combined Classification and Regression

The proposed diagnostic model targets both damage detection within the scan path and estimation of damage position. A normalized output can encode both classification and regression, while the illustrated AANN neuron architecture is described but is not part of this work.

5. Analog Artificial Neural Network: Combined Classification and Regression

  • The model is intended to predict whether damage lies within the scan path and the damage’s distance from the sending transducer.The first target is classification; the second is regression.Source: §5 · p. 12
  • A normalized output below 0.5 indicates no damage, while an output above 0.5 indicates damage and estimates its position.The proposed encoding divides the output range into [0,0.5) for classification and [0.5,1] for regression.Source: §5 · p. 12
  • The paper illustrates an AANN neuron using three-transistor OpAmp circuits and a sigmoid circuit, but states that the AANN implementation is not part of this work.The sigmoid circuit’s input range is [-10V,10V] and its output range is [0,10V].Source: §5 · p. 12, Figure 11 · p. 13

6. Ultrasonic Damage Detector

The detector was evaluated with simulated ultrasonic signals for a steel plate with a 20 mm hole, using three extracted features to predict damage and its distance from the sender. The AANN output encodes no-damage classification separately from damaged-case distance estimates.

6. Ultrasonic Damage Detector

  • The evaluation used simulated signals for a 500 by 500 mm steel plate with a 20 mm hole along the transducer axis.The detector is specific to this use case, so the authors did not perform rigorous statistical analysis.Source: §6 · p. 13
  • The analog feature extractor generated T1, T2, and A1 from 20 damage cases and one undamaged baseline case.T1 marks the main peak, T2 the time at 20% of its height, and A1 the integrated area between them.Source: §6 · p. 14
  • The three features were passed to a two-layer AANN with three neurons and sigmoid activation functions.The reported trained weights and biases were all below 20 for analog implementation.Source: §6 · p. 15
  • The AANN output uses values below 0.5 for no detected damage and values from 0.5 to 1 for detected damage and distance estimates.The distance range is 100–200 mm from the sending transducer.Source: §6 · p. 15

7. Conclusion

The conclusion reports a functionally suitable pure-analog ultrasonic damage detector built with fewer than 100 transistors. It extracts envelope-based features with a fourth-order all-pass network and estimates damage distance, with printed organic circuits proposed as a next step.

7. Conclusion

  • A fourth-order discrete-transistor all-pass network approximates the signal envelope with errors below 10%.The conclusion describes phase shifts and peak-detection nonlinearity; second-order filters are preferred, but RC-network interference introduces phase errors in the single-transistor setup.Source: §7 · p. 16
  • The demonstrated detector uses fewer than 100 BJT and JFET transistors and 500 electronic components.It detects damage along a scan path between two transducers and estimates distance using three signal features.Source: §7 · p. 17
  • The proposed next step is printed organic electrochemical transistors on non-conducting substrates for material-integrated sensing.The estimated circuit area is less than 400 mm2 assuming transistor area below 1 mm2.Source: §7 · p. 17

8. Appendix A

Appendix A lists component values for the all-pass filter, rectifier, peak detector, adder, and sigmoid circuits, along with supply voltages.

8. Appendix A

  • The all-pass filter component table lists Q11-Q15 and Q21-Q25 as 2N3904 transistors, with R101 and R201 at 100 kΩ and C10 and C20 at 500 nF.Source: §8 · p. 17, Table 2 · p. 18
  • Component-value tables are provided for the rectifier, peak detector, and adder circuits.Source: Table 3 · p. 18, Table 5 · p. 19, Table 4
  • The appendix identifies component values for the sigmoid circuit used in the AANN, derived through particle-swarm optimization and electronic simulation.Source: Table 6 · p. 19
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