Passenger seat is main part of vehicle which has direct effect on her/his convenience. Seat suspension can remove unwanted and harmful vibration if right parameters were selected. Each of human body organs has specific natural frequency. When vehicle vibration reaches to this natural frequency, resonance will occur, and this phenomenon is harmful in long term. Usually lumped models used to predict human body response to vibration. In this paper, via Kitazaki biodynamic model, the seat to head vibration transmissibility was minimized by artificial neural network method. By this method, the optimum spring constant, damper coefficient and mass values were found.

1. Conference paper at University of Cairo, Egypt. (December 2011)
L. Ali
Spinal Vibration Reduction in Vertical Vibration based on Artificial Neural Network
Optimization by Using of Kitazaki Biodynamical Model
Limam Ali
Faculty of Agriculture (Machinery), University of Cairo, Egypt.
_______________________________________________________________________________________
ABSTRACT
Passenger seat is main part of vehicle which has direct effect on her/his convenience. Seat suspension can
remove unwanted and harmful vibration if right parameters were selected. Each of human body organs has specific
natural frequency. When vehicle vibration reaches to this natural frequency, resonance will occur, and this
phenomenon is harmful in long term. Usually lumped models used to predict human body response to vibration. In
this paper, via Kitazaki biodynamic model, the seat to head vibration transmissibility was minimized by artificial
neural network method. By this method, the optimum spring constant, damper coefficient and mass values were
found.
KEY WORDS: Artificial Neural Network, Spinal Vibration, Kitazaki Biodynamical Model, Vertical Vibration.
INTRODUCTION
Nowadays, people have become more aware of vibration and they are looking for more comfortable
environments. One of the vibration and shock sources is traveling inside vehicles such as cars, buses, trains and
heavy construction machine such as tractors, loaders and bulldozers. Drivers are exposed to the whole body
vibrations due to the interaction between uneven roads or tracks with wheels. This leads to some injuries like spinal
disorder, weakness in sight, pain in internal tissues and heart problems in a long term. Many researchers studied
about human body responses to vibration, and how they can minimize the negative effects of shock to human body
(Paddan and Griffin, 1998, Boileau and Rakheja, 1998,Wang et al. , 2008) . The responses have been assessed in
terms of the apparent mass, driving point impedance and transmissibility. The forces and motion of pelvis and spine
are studied by the first two, and the third looks into the motion of chest, head and spine. The results of
transmissibility of seat-to-head from previous researchers indicate that the first principal response was found
between 4 and 6 Hz, and the second natural frequency appears at 8 to 12 Hz (ISO 5982).
The human body is a complex structure, and responses of that to the dynamic excitation are more complex. From
the results of many studies (Muksian and Nash, 1974, Suggs et al., 1969 , Wan and Schimmels, 1995, Liu et al.,
1998), several of biodynamical models are available to explain human body behavior exposed to the oscillation.
These models consist of lumped, multi body and finite element models. In the lumped model, human bodies are
considered as a set of masses, springs and dampers. Multi body models have a series of segments which are
interconnected by some kinematics joints. These joints are usually spherical, revolute or universal joints. In this type
of model, spine behavior is modeled by flexible elements. Finite elements methods consisting of several elements
were used to model the various parts of human organs, by meshing and stiffness matrix definition. This method can
also reproduce behavior of flexible and rigid parts with rheologic properties. Although lumped models are the
earliest generation in modeling, those are already applicable because of its simplicity.
Mechanical impedance, seat to head vibration transition, and apparent mass are important functions which are
used to driving model from experimental test, and also these are useful for optimization methods. Several
researchers have investigated on parameters which effect on the seat-to-head transmissibility (STH)( Paddan, and
Griffin, 2000). The variation of STH functions like as apparent mass and mechanical impedance is large. They
found that the posture, feet support and backrest can influence the STH. Boileu and Rakheja (1998) employed a four
degree of freedom (4-DOF) model to predict human responses to vertical vibration. They obtained first resonance
of STH at 4.8 Hz although experimental results showed at 5 Hz. Wan and Schimmle established a 4-DOF lumped
model that the total mass was 60.67 kg, and the first peak in STH appears at 4 Hz. The goodness-of-fit was 91% for
this model. Wang et al. (2008) studied the relationships between the apparent mass and seat to head transmissibility.
They conducted test with 12 males as subject who were exposed to whole body vibration in vertical direction.

2. Conference paper at University of Cairo, Egypt. (December 2011)
L. Ali
The frequency was in the range of 0.5-15 Hz, and the magnitudes of acceleration were 0.25, 0.5 and 1.0 m/s2
in
rms. The measurements were done in three postures: without backrest, vertical backrest and inclined position. Also,
two driver of hands position is considered such as hands in lap and hands on the steering wheel. The results showed
that both response functions (seat to head transfer and apparent mass) in primary resonances showed good
agreements between two postures. In addition, in secondary resonance there are considerable differences between
seat to head transmissibility and apparent mass for the two backrest positions. Seat to head transfer function is little
more sensitive than apparent mass in responding to the hand positions.
As a result, seat to head vibration transfer function shows wide variation in resonance first and second peaks
(from 3 Hz to 8 Hz) which are depended on posture, within or without backrest and feet supporter. The summation
of most important studies was represented as standard which is called ISO 5982. The seat to head transmissibility of
the seated human body is shown in Fig.1. In this standard, the first resonance in seat to head transmissibility is
between 3 to 5 Hz.
Fig.1. The seat to head transmissibility of the seated human body exposed to the vertical oscillation.
A modal analysis based on experimental data was made by Kitazaki (1992). This model is a biomechanical
lumped model which is able to explain biodynamical behavior of torso, head, and spine. In spite of simple base, this
model can reproduce first five modes of vibration in acceptable accuracy. Fig. 2 shows the parts of Kitazaki model
which has 15 degrees of freedom. The most important components of this model are the five vertebrae (T1, T6, T11,
L3 and S2) considered in the model as separate parts, and it is possible to monitor the modes shapes of them in the
analyses.
Fig.2. Human body biodynamical model and its degrees of freedom [10].
In vehicles, suspension systems are used to reduce unwanted vibration, and isolate the passengers. Most of heavy
duty vehicles remove the transition vibration by passive or active seat suspensions. In passive suspension systems,
finding the mass of seat, damping ratio and spring constant are essential for design.
Lumped parameter models are frequently used to find optimized values of damping and spring constant in
vehicle seat or suspension design. One of the methods which are useful in optimizing and mathematical modeling is
artificial neural network (ANN). This procedure was based on artificial intelligent method and machine learning
with some samples. These samples consist of sets of input and output values. Artificial neural network can trained
with examples which finally produce desired output values. This step is called training. After training, the network
will be able to simulate and predict the outputs for each entered values. ANN models can solve and simulate
nonlinear systems with acceptable accuracy. In this paper, artificial neural network was used to determine the seat

3. Conference paper at University of Cairo, Egypt. (December 2011)
L. Ali
suspension properties (mass, spring constant and damping ratio) that are able to minimize the vertical unwanted
vibration based on Kitazaki human body model.
Material and Methods
As mentioned in the literature review, Kitazki biodynamical model shows good results with regard to the real
conditions [10]. This model was considered as a benchmark for an establishment of an ANN model. Proposed model
includes human body parts (head, spinal column, visceral column and pelvis model) in sitting posture and seat
passive suspension system components. Optimizing suspension coefficients (mass, spring and damper) was done in
three steps:
1- Data preparation :
The human body modeled by using Working Model 2D software as shown in Fig. 3. The input function was a
harmonic sinusoidal acceleration with equation: tZ sin05.00  and srad1 ( Liang and Chiang, 2006).
The input acceleration (seat) and output values (head) in the time domain were obtained in this software for 20
seconds (Fig. 4). The seat to head (STH) function frequency peaks were calculated by using FFT (Fast Fourier
Transform) function in Matlab software. This step was repeated 11 times for 11 different values of mass, spring and
damper coefficients.
2- Optimization with neural network
The first two peaks of STH values were entered into neural network as input set (for 11 example). Also, the
values of mass, spring and damper were entered as output of network. The network was trained by these eleven
examples.
3- Validation of optimized system
The seat suspension system coefficients were set by the values obtained. Then, peak values of STH were
recalculated and were compared to the proposed values.
Fig.3. Human body and eccentric oscillator circle which was modeled in Working Model 2D

4. Conference paper at University of Cairo, Egypt. (December 2011)
L. Ali
Fig. 4. Vertical accelerations (m/s2
) of a) head and b) seat versus time (t).
Data Preparation: Human body mechanical modeling in Working Model 2D
Working Model 2D has some features like as mechanism modeling and dynamic analyses. Parts of human body
were modeled with rigid components, torsion spring and damper components as illustrate in Fig.3. The displacement
of masses was constrained in the vertical axes. The components properties were set according to Table 1 (Kitazaki,
1992). An eccentric circle and a rotary engine were located under the model to produce harmonic movement
according to tZ sin05.00  . The neural network model needs some examples for training and optimization, thus
the values of seat mass, spring and damper were set to eleven values. These values are listed in Table 2. It is
observed that the amplitudes of the first 2 peaks in STH are low for mass in the range of 14 to 15 kg, damping
coefficient 125 to 130 Ns/m and spring stiffness from 8100 to 8150 N/m. The acceleration of input point (seat) and
output point (head) were achieved in separate diagrams which these values are time dependents. In the next step,
these two acceleration values were keying into the program which was written in Matlab environment. This program
divided the accelerations values of head to seat. The output values were converted to frequency by using Fast
Fourier transformation function to determine the peak values of seat to head transmissibility (STH).
Table.1. Stiffness and damping values of the lumped model (Kitazaki, 1992).
Articulations K (Nm/rad) C (Nms/rad)
C0 18 0.1
T1 20 0.8
T6 625 0.8
T12 92 0.2
L3 224 0.9
S2 643 0.1
Table. 2. Seat mass, spring, damper coefficients, first and second peaks of STH in each of 11 examples.
Example No. Mass (kg) C(N.s/m) K(N/m)
Amplitude of
first peak in
STH
Amplitude of
second peak in
STH
1 15 125 8100 0.756 0.174
2 13 120 8150 1.316 1.004
3 15 130 8150 0.743 0.177
4 14 128 8100 0.751 0.174
5 16 120 8200 0.754 0.181
6 13 130 8000 1.31 0.99
7 13 100 8100 0.8 0.178
8 14 125 8130 0.753 0.176
9 11 120 8200 0.754 0.181
10 7 80 7500 1.084 0.935
11 17 120 8200 1.325 1.009

5. Conference paper at University of Cairo, Egypt. (December 2011)
L. Ali
Neural Network Modeling and Seat Suspension Optimization
Neural networks are robust tools which can solve non-linear equation in optimization problem. In this research,
the problem was stated in mathematic relationship as multi input-output function which has a polynomial nature. In
fact, seat to head transmissibility peak values ( 1p and 2p ) is a function of mass, spring constant and damper
coefficient.
),,(),( 21 KCmfppSTH 
A feed forward back propagation architecture network was chosen for this modeling because this case is
optimization problem. Two matrices were made for input data and output. The first matrix was 2*11 which includes
first and second peaks of STH values with eleven examples. The output matrix was 3*11 which three rows were
mass, spring and damper coefficients. Various training functions, adaptation learning function, threshold function
and error reduction function were tested to obtain best model fitting with high accuracy. Due to this aim the
TRAINLM function (Levenberg-Marquardt backpropagation algorithm) was considered as training function, and
adaptation learning function was LEARNGDM (gradient descent with momentum weight and bias learning
function). This architecture has 4 layers in total which it has 3 hidden layers with ten neurons (Fig. 5). Also,
TANSIG (Hyperbolic tangent sigmoid transfer function) was selected in Matlab software for threshold function and
minimumsquired error (MSE) was function to error reduction and weight adjusting loop.
Fig.5. The architecture of neural network for optimization.
After network training, the performance graph and gradient were obtained. Furthermore, the regression graph
between the target and output was plotted. In addition, R2
for all regressions was calculated. Finally, the network
was simulated to find the output with first and second STH peaks. The outputs of the network will be the optimum
values of suspension coefficients (m, C, and K) which produce minimum value of seat to head transmissibility.
RESULTS AND DISCUSSION
After the network was entered with examples, six epochs were done to complete the training. The R2
for training,
validation, test and in overall were 0.99994, 1, 1 and 0.99995, respectively (Fig. 6). To find the best values of mass,
spring and damper constants, the amplitudes of first and second peak of STH were considered 0.5 and 0.09. These
values were entered to the trained network to find outputs of that. These value were obtained as 15.88, 8000 and
128.748 for seat mass, spring and damper coefficient, respectively.

6. Conference paper at University of Cairo, Egypt. (December 2011)
L. Ali
Fig.6. Correlation coefficients in neural network model in training, validation, test, and all steps, respectively (T is
target values, Y is predicted output by model, and R correlation coefficient between output of model and target
values).
For evaluation of result, seat suspension was adjusted again in Working Model and acceleration of head and seat
were reached. STH diagram was plotted with new values of suspension parameters. Fig. 7 illustrates the STH in
optimized seat properties, and this ratio decreased to below 1 which means that purposed results were obtained as
desired.
Fig.7. First and second STH peak in optimized seat suspension.
In Fig.7, amplitude of STH in optimized seat suspension system were0.76 and 0.18, and it appears that the first
and second natural frequencies are in the desired range according to ISO 5989. Alizadeh et al. (2008) found out that
the seat mass, damper and spring coefficients were 14 Kg, 125 Ns/m and 8130 N/m, respectively by Quasi- Newton
method. The STH after optimization in their test was near 1.8 while optimized seat to head vibration by Kitazaki

7. Conference paper at University of Cairo, Egypt. (December 2011)
L. Ali
(1992) model have better reduction in vertical vibration transmissibility, and it looks this model can be considered as
reference model for simulation and optimization.
CONCLUSION
Optimizing the seat properties (spring, damper and mass) by neural network is very useful in reducing the
vertical vibration transmissibility. The result of this study shows that it is possible to consider spinal column motion
exposed to vibration for optimization. In addition, if a suitable seat suspension is used, the vibration which is
transmitted to the head can be reduced by 94%.
ACKNOWLEDGEMENTS
The author would like to thanks from University of Cairo.
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