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Structural Health Monitoring

Overview

This example applies digital twin methodology to structural health monitoring (SHM). The digital twin workflow shown below was developed for the SHM use cases.

DT workflow DT workflow

The complete source code for this example is available online.

Example Structure

This digital twin consists of:

  • SHM package: implements the digital twin workflow. The package also contains data recorded from the physical twin and replay functions that stream this data into the digital twin workflow.
  • replay.json: MQTT configuration file for replaying the recorded data

The package provides these experimental scenarios:

  • replay replays the recorded readings from the cantilever beam setup.
  • acceleration_readings shows how the Accelerometer class extracts accelerometer measurements from an MQTT data stream.

  • aligning_readings shows how the Aligner class collects and aligns accelerometer measurements from multiple MQTT data streams.

  • sysid demonstrates sysid with four cases:

    1. sysid-and-plot: plots natural frequencies.
    2. sysid-and-print: prints sysid output to the console.
    3. sysid-and-publish: publishes one set of sysid output via MQTT to the broker given in the sysid section of the config.
    4. live-sysid-publish: publishes sysid output continuously via MQTT to the broker given in the sysid section of the config.

  • Clustering demonstrates clustering with four cases:

    1. clustering-with-local-sysid: gets the sysid output by running sysid locally, then runs mode clustering.
    2. clustering-with-remote-sysid: gets the sysid output by subscribing, then runs mode clustering once.
    3. live-clustering-with-remote-sysid: gets the sysid output by subscribing, then runs mode clustering in a loop.
    4. live-clustering-with-remote-sysid-and-publish: gets the sysid output by subscribing, then runs mode clustering in a loop and publishes the cluster results.

  • mode-tracking demonstrates mode_tracking with three cases:

    1. mode-tracking-with-local-sysid: gets the sysid output by running sysid locally, then runs mode clustering and mode tracking.
    2. mode-tracking-with-remote-sysid: gets the sysid output by subscribing, then runs mode clustering and mode tracking once.
    3. live-mode-tracking-with-remote-sysid: gets the sysid output by subscribing, then runs mode clustering and mode tracking in a loop.

  • model-update demonstrates model_update with three cases:

    1. model-update-with-local-sysid: gets the sysid output, then uses it to update the model and get updated system parameters.
    2. live-model-update-with-remote-sysid: gets the sysid output by subscribing to an MQTT topic, then runs mode clustering and uses the result to update the model and get updated system parameters.
    3. live-model-update-with-remote-clustering: gets the mode clustering output by subscribing to an MQTT topic, then uses it to update the model and get updated system parameters.

The following scenarios can run in the automated execution mode:

  • acceleration_readings shows how the Accelerometer class extracts accelerometer measurements from an MQTT data stream.

  • aligning_readings shows how the Aligner class collects and aligns accelerometer measurements from multiple MQTT data streams.

  • sysid prints the sysid output to the console.

  • Clustering demonstrates sysid and clustering.

  • mode-tracking demonstrates sysid and mode_tracking.

  • model-update runs the digital twin workflow up to model_update.

Configuration

This example uses an MQTT broker to replay the data recorded from the physical twin. The configuration file is replay.json. Update the MQTT credentials in this file. If no local MQTT broker is available, you can use the Mosquitto test server.

Use

Run the program without arguments to list the available experimental scenarios:

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$example-shm
Usage: example-shm [OPTIONS] COMMAND [ARGS]...

Options:
  --config TEXT  Path to config file
  --help         Show this message and exit.

Commands:
  accelerometers
  align-readings
  clustering-with-local-sysid
  clustering-with-remote-sysid
  live-clustering-with-remote-sysid
  live-clustering-with-remote-sysid-and-publish
  live-mode-tracking-with-remote-sysid
  live-model-update-with-remote-clustering
  live-model-update-with-remote-sysid
  live-sysid-publish
  mode-tracking-with-local-sysid
  mode-tracking-with-remote-sysid
  model-update-with-local-sysid
  replay
  sysid-and-plot
  sysid-and-print
  sysid-and-publish

Run these examples with the replay.json config:

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$example-shm --config replay.json <experiment-name>
Usage: example-shm --config replay.json accelerometers

Automated Execution

The pipeline of this example runs two lifecycle scripts: lifecycle/sysid_print for system identification and lifecycle/model_update_local_sysid for model update. A truncated sample output follows, with the execution timestamps removed.

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Using docker image sha256:16f554efe9f9e182e2ec6b86ad37360138407a456a69982ed1b8261716ce5163 for python:3.12 with digest
$ cd digital_twins/shm
$ bash lifecycle/sysid_print
...

pyoma2.setup.base - INFO - Running SSIcovmm_mt... (base:123)
pyoma2.functions.ssi - INFO - Assembling Hankel matrix method: cov_mm... (ssi:82)
pyoma2.functions.ssi - INFO - ... uncertainty calculations... (ssi:94)
pyoma2.functions.ssi - INFO - SSI for increasing model order... (ssi:359)
JSON configuration loaded successfully.
on_connect: Connected with response code Success
Subscribing to topic: cpsens/recorded/1/metadata
on_subscribe: Subscription ID 1 with QoS levels [ReasonCode(Suback, 'Granted QoS 0')]
Extracted Fs from metadata: 256.0
on_connect: Connected with response code Success
Subscribing to topic: cpsens/recorded/1/data
on_subscribe: Subscription ID 1 with QoS levels [ReasonCode(Suback, 'Granted QoS 1')]
on_subscribe: Subscription ID 2 with QoS levels [ReasonCode(Suback, 'Granted QoS 1')]
on_subscribe: Subscription ID 3 with QoS levels [ReasonCode(Suback, 'Granted QoS 1')]
on_subscribe: Subscription ID 4 with QoS levels [ReasonCode(Suback, 'Granted QoS 1')]
on_subscribe: Subscription ID 5 with QoS levels [ReasonCode(Suback, 'Granted QoS 1')]
on_subscribe: Subscription ID 6 with QoS levels [ReasonCode(Suback, 'Granted QoS 1')]
on_subscribe: Subscription ID 7 with QoS levels [ReasonCode(Suback, 'Granted QoS 1')]
on_subscribe: Subscription ID 8 with QoS levels [ReasonCode(Suback, 'Granted QoS 1')]
Waiting for data for 0.1 seconds
Waiting for data for 0.2 seconds
Waiting for data for 0.3 seconds
...

sysid parameters: {'freq_variance_treshold': 0.1, 'damp_variance_treshold': 1000000, 'Fs': 256, 'model_order_min': 2, 'model_order': 15, 'block_shift': 30, 'mstab': 6, 'tMAC': 0.95, 'bound_multiplier': 2, 'allignment_factor': [0.05, 0.01], 'phi_cri': 0.8, 'freq_cri': 0.2, 'obj_cri': 0.1, 'tMAC_MU': 0.7, 'modes_search_paring': 6, 'pars_to_update': ['k_rot', 'm'], 'MU_start_values': array([10.   ,  0.015]), 'MU_bounds': [(0.01, 1000), (0, 1000)], 'MU_modes': [1, 2, 3]}

  0%|          | 0/16 [00:00<?, ?it/s]
100%|██████████| 16/16 [00:00<00:00, 23563.51it/s]
Cluster 0.4465797245502472 too short: 1 Must be: > 6
Cluster saved: 27.93849468231201
Updated parameters are:
k_rot: 12.04591179878987
m: 0.0
Model frequencies: [  4.13819299  26.68572155  80.22633861 164.67016633 180.37962416
  326.70816499] [Hz]
[DONE].

References

  1. This example corresponds to commit ce47244 of the example-shm repository.
  2. Talasila, P., Tcherniak, D., Jensen, A. M. D., Mahato, S., Schörghofer-Queiroz, A., Ulriksen, M. D., ... & Damkilde, L. (2025, July). Structural Health Monitoring of Engineering Structures Using Digital Twins: A Digital Twin Platform Approach. In International Conference on Experimental Vibration Analysis for Civil Engineering Structures (pp. 986-996). Cham: Springer Nature Switzerland.