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Power spectral density moment of having defective 3D printed plastic beams under moving load based on deep learning

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Abstract

3D printing and 3D printing technology are increasingly popular in today’s world. However, there have not been many studies evaluating the quality of 3D printed products in real-life applications. This manuscript proposes a parameter for monitoring deterioration conditions of 3D printed plastic structures based on a multilayer perceptron network, using power spectral density (PSD) under a moving load. To create deterioration phenomena in the 3D printed plastic beam structures, simulations with cracks that change the stiffness of the structure are conducted. The features presented in this manuscript are constructed from the alteration forms of power spectral density used to detect the deterioration of a 3D printed plastic structure, accomplished by creating damage in beams and using a multilayer perceptron network in an input training dataset. Under these circumstances, the power spectral density is established by vibration signals obtained from acceleration sensors scattered along the 3D printed plastic beams. The results in this manuscript show that differences in the shapes of the PSD attributable to damage are more noticeable than those in the value of the basic beam frequency. This means that adjustments of shape in PSD will better allow the detection of damage in different 3D printed plastic beam structures. The determination of defects on 3D printed plastic beams by the power spectral density method has been used in research. However, the application of this deep learning model presents many new and positive effects.

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Abbreviations

x :

The location of points of the model

ωb :

The frequency damping of the model

t :

Time

f( t) :

The moving load

µ :

The self-weight of beam per unit length

υ:

The velocity of the mass

E :

The elastic modulus

I(x) :

The 2nd moment of the beam’s cross-section acreage

EI(x) :

The flexural rigidity

w( x,t) :

The displacement of the model in the z direction at position x at time t

φ j ( x) :

The jth shape function

q j :

The generalized coordinates

µ j :

The generalized mass on the jth movable type

F j(t):

The generalized load on the jth movable type

h j ( t) :

The response function of the jth movable type

ω dj :

The fundamental damper frequency of the jth movable type

\(\omega_{\nu } = \frac{n\nu }{l}\) :

The speed frequency of the load

f 0 :

The mean value elements of the force acting

f( t) :

The random elements of force

E[ .] :

The mathematical expectation

S q ( ω) :

The spectral density of responses in jth generalized coordinates

S F ( ω) :

The spectral density function of the generalized forces

ΔSM :

The spectral moment area ratio

p i :

The frequency value

A i :

The amplitude corresponding to the collected frequency value

z :

The standardized variable

Φ(z) :

The cumulative distribution of the function (CDF)

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Acknowledgements

This work was funded by Vingroup and supported by Vingroup Innovation Foundation (VINIF) under Project code VINIF.2020.DA15. The authors confirm that the intellectual content of this publication is the result of our own efforts, and that all outside aid or funds have been acknowledged.

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Authors and Affiliations

  1. Ho Chi Minh City University of Transport, Ho Chi Minh City, Vietnam

    Thanh Q. Nguyen

  2. Hospital of Odonto-Stomatology Ho Chi Minh City, Tran Hung Dao, Co Giang Ward, District 1, Ho Chi Minh City, Vietnam

    Nghi N. Nguyen

  3. Institute of Strategies Development, Thu Dau Mot University, Binh Duong, Vietnam

    Xuan Van Tran

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  1. Thanh Q. Nguyen
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  2. Nghi N. Nguyen
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Nguyen, T.Q., Nguyen, N.N. & Van Tran, X. Power spectral density moment of having defective 3D printed plastic beams under moving load based on deep learning. J Intell Manuf 35, 1491–1515 (2024). https://doi.org/10.1007/s10845-023-02120-5

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