Seated pregnant subject biodynamics response enhancement against road irregularities using adaptive NeuroFuzzy control

Abstract

Human-beings in general and pregnant subjects (characterized by a sophisticated dynamic system) in particular are sensitive to whole-body vibrations (WBV) in sitting position while driving. The published literature is thickly populated with the investigation of WBV effects on non-pregnant subjects but sparsely populated with the biodynamic response enhancement of the pregnant subjects in driving conditions. In this paper, the biodynamic response analysis of eleven degrees of freedom (11-DoF) seated pregnant subject at the driver position is carried out while being exposed to vibrations induced by inherent road irregularities. An advanced adaptive NeuroFuzzy (AdaptNeuroFuzzy) control strategy for active suspensions of nineteen degrees of freedom (19-DoF) integrated vehicle-pregnant subject model is designed to attenuate harmful vibrations and protect the seated pregnant subject and fetus against the risk of damages. Matlab/simulink is employed to carry out simulations. Performance validation of the proposed advanced intelligent control strategy based suspension system is accomplished through comparison with the passive, PID, adaptive PID (AdapPID) and adaptive fuzzy logic control (AdapFLC) via standard performance indices, using an ISO-classified standard random road profile.

Keywords

Adaptive NeuroFuzzy control integrated vehicle-pregnant subject seated pregnant subject vibration attenuation whole body vibration

1 Introduction

In the present day’s highly mechanized society, most people are exposed to some doze of vibrations on a daily basis. Vibrations have harmful health effects on the human body depending upon the duration of exposure. Prolonged exposure to vibrations can cause temporary or permanent disability. Industrial employees and transport users are severely affected by vibrations. Car users are influenced by vibrations due to road-wheel interaction while traveling on uneven road surface causing occupants discomfort. The published literature suggests that low-back pain, neck pain, headache, vomiting and some other health-related problems are associated with prolonged and persistent exposure to vibrations as described in [1 –3]. A lot of research activities are presently taking place in the area of biodynamic response such as [4, 5].

The pregnant subject is a complex, highly sensitive and sophisticated dynamic system. The mother and fetus need extra care than a normal woman. The seated pregnant driver’s biodynamic response analysis exposed to vibrations is a new and special research topic. However, no significant research in the past is conducted in this area of special interest. Vibrations have varying effects on the seated pregnant subject (SPS) different body parts, depending upon the location, posture, type of vibrations and stage of pregnancy development. SPS is highly sensitive to road excitation. She has a complex biomechanical model that consists of an adult body and the fetus. Even a little carelessness can create complications for the mother and fetus. Moreover, a seated pregnant woman driver is comparatively more affected by vibrations as compared to the same group of a non-pregnant woman passenger. Vibrations due to road surface roughness are transmitted through the chain of wheels-suspension-chassis and driver seat to the pregnant subject organs. It initiates undesirable vertical oscillations and acceleration in the car chassis and SPS organs. The uncomfortable and awkward variations in displacement and acceleration create adverse physical and physiological effects on the organs.

Some low-frequency vibrations in the range of 4-8 Hz are extremely harmful. These are associated with a feeling of discomfort, reduced working ability, fatigue and health issues for all gender of people, especially pregnant subjects. An experimental study conducted on the biodynamic response of the pregnant woman in [6], suggested that vertical acceleration in the frequency magnitude of 7.7 Hz is extremely dangerous for a pregnant woman. They took measurements of the mechanical reaction of the frontal abdominal wall to the free-fall impact load during gravidity. Experiments were conducted on twelve women in the 32nd week of pregnancy. It was concluded from the experimental results that the risky critical frequency for the gravid abdomen of the pregnant female is 7.7 Hz in the vertical direction. Both the mother and the fetus will be at high risk in the stated frequency magnitude. According to the published literature, the first analytical investigation of the effects of the vibrations on the seated pregnant subjects (SPS) is conducted in [7]. The SPS model used in this investigation is based on the seated male driver model as given in [8]. The mass of SPS organ is taken as 60% of the mass of seated male driver’s corresponding organ.

To avoid the negative impact of the external disturbance and vibrations, on car occupants, an advanced suspension system is used. It supports the entire weight of the car and simultaneously absorbs most of the high frequency disturbing excitation. Three types of suspension models commonly used are passive, semi-active and active suspension systems as mentioned in [9]. The factory-fitted fixed parameters conventional passive suspension model has average performance. The damping fluids based semi-active suspension system provides better performance than the passive suspension system, however, they are least efficient than the active suspension. An active suspension system is the most efficient suspension model. It has an external power source that provides the desired damping force. Sensors and force actuators are the main components of the active suspension systems. They enable the car to adapt itself according to the demand for the varying road condition. This form of suspension provides improved ride quality and good road holding capability. Therefore, it remains an active research area for the past few decades.

A score of car models i.e., quarter-car, half-car, full-car and control techniques for vibrations attenuation are proposed in the published literature. Some are still under consideration as given in [10 –16]. Active suspension systems using multiple control solutions are developed in [17 –19]. A combined vehicle-driver biodynamic model is presented in [20]. The said model ignores the important system nonlinearities. Besides, a single parameter-PSD based analysis is carried out using sliding mode controller ignoring the important time and frequency domain analysis. Some solutions to improve the passive safety of pregnant women riding a car during accident is proposed in [21]. A linear 11-DoF pregnant subject model is only used for the experimental analysis. Biodynamic analysis of the seated pregnant subject is presented in [22]. However, 14-DoF linear coordinated model is used. The coordinated model is subjected to discrete type of external road excitation. No comprehensive biodynamic responses analysis is conducted in the work presented. In [23] a 5-DoF and an 11-DoF linear biodynamic models are presented. These models are experimentally investigated for better prediction of the human body responses. To the best of authors knowledge, no nonlinear coordinated vehicle-human model is developed. In the proposed work, an integrated 19-DoF vehicle-seated pregnant subject (IVSPS) biodynamic model with all forms of nonlinearities is presented.

An adaptive neural network (ANN) control is presented in [24] applied to a SISO system. The presented ANN control strategy which has embedded in its structure the human brain neuron model for better intelligent learning. However, it lacks the NeuroFuzzy system enhanced performance strategy which has embedded in its structure the good learning ability of the ANN system and the rule base of the fuzzy system to form an efficient system. A model free control strategy for vehicle lateral stability is presented in [25]. LQR theory is used for the solution of algebraic Riccati equation. Linearized state space dynamic model is used in the tracking of the yaw, roll and sideslip angles. A constrained adaptive robust sampled-data control to achieve the desired tracking performance under state and input constraints is proposed in [26]. The control techniques given in the literature ignores comprehensive vehicle-biodynamic analysis.

Based on the above discussion, the existing literature is abundantly rich with car models and vibrations attenuated techniques but lacks a comprehensive analysis and comparison of different control alternatives with special reference to SPS. More importantly, vibration analysis at the critical frequency of 7.7 Hz in the case of SPS at the driver’s position is another important key analysis.

In this paper, an advanced adaptive NeuroFuzzy (AdaptNeuroFuzzy) control algorithm for active suspension systems is developed and implemented on a highly nonlinear integrated vehicle-seated pregnant subject (IVSPS) model of 19-DoF subjected to standard random road excitation. To the best of authors knowledge, the current/existing literature lacks the application of such a coordinated control strategy used for IVSPS model to investigate the effects of vibrations on the pregnant subject.

Following are the main contributions of this study: i) Modeling of the integrated vehicle-seated pregnant subject (IVSPS) biodynamic model. The authors claim that the proposed model is nonlinear, coordinated (integrated) vehicle-human (pregnant-subject), 19-DOF which is developed for biodynamic response analysis and enhancement. To the best of authors knowledge, this type of mathematical model has never been used before for such studies. This model is more realistic and closed to actual model.

ii) Design and implementation of a modified adaptive NeuroFuzzy (AdaptNeuroFuzzy) control strategy. The authors claim that in the structure of NeuroFuzzy, a nonlinearity defined by T-norm (used for firing strength) has never been used and made adaptive before to the best of authors knowledge. In the literature either antecedent part, “IF " (membership functions) or consequent part, “THEN " (linear equation constant coefficients) are made online adaptive. But the authors claim that such T-nom (degree of fulfillment/firing strength) has never been made online adaptive. Therefore, the online adaptive tuning of the T-norm coefficients in the NeuroFuzzy structure for biodynamic response enhancement of a pregnant subject is a novel contribution in this area.

The rest of the paper is divided into 5 sections. Section 2 describes problem statement and control objectives. The proposed AdaptNeuroFuzzy control technique design is given in section 3. Section 4 gives the simulation results and discussion. Section 5 describes the conclusion.

2 Problem statement and control objectives

The nonlinear 19-DoF IVSPS model is shown in Fig. 1. The model nonlinearities comprise car chassis geometrical and suspension’s dampers dry friction. The 8-DoF of car model denoted by Z_car includes vertical displacements of the four un-sprung masses, chassis heave, pitch motion, roll motion, and the driver’s seat vertical deflection. The 11-DoF of seated pregnant-subject model denoted by Z_preg includes the vertical excitation of the individual eleven SPS organs. The road surface disturbing inputs at the four wheels are represented by Z_dis. The five actuator forces at the four suspensions and driver seat is given by U. The nonlinear suspension’s dampers dry frictions at the four wheels are denoted by F (v_r). The four un-sprung masses, the driver seat mass, the car chassis mass, the pitch mass-moment-of-inertia, and the roll mass-moment-of-inertia are shown as M_car. The SPS eleven organ’s masses are denoted by M_preg. The damping co-efficient and the spring constants of the passive elements of the front and rear wheels suspensions are represented by C_s and K_s respectively. The car wheels are modeled as linear springs denoted by the constant K_t. The driver’s seat is represented by the damping co-efficient and spring constant as C_ds and k_ds respectively. The driver’s organs are modeled as linear dampers and springs, denoted by C_d damping co-efficient and K_d spring stiffness.

Fig. 1

Nonlinear full-car active suspension with pregnant subject biodynamic model and control algorithm.

Assumption: The integrated SPS system used in this study is assumed 1) time-invariant and 2) stable under the current test conditions. The energy induced in the IVSPS through suspension system by the road irregularities is dissipated in different parts of the system (springs and dampers) in finite time.

The entire 19-DoF IVSPS model is given by a nonlinear state-space model as in Equation 1.

Where F_car,1 (z), F_car,2 (z), F_preg,1 (z) and F_preg,2 (z) are the nonlinear continuous state functions of the IVSPS model, B_car and B_preg are the control matrices for the car and pregnant subject, G_car and G_preg are the inputs disturbance matrices and Q_car and Q_preg are the nonlinear dry friction matrices for the car and pregnant subject respectively. The subscript is defined as i = 1, 2, 3, 4. The “sin" and “cos" terms in the car chassis corners equations of displacement given by λ_c = λ₁, λ₂, ⋯ , λ₄ are the geometrical nonlinearity, while F (v_r) is the suspension dampers dry friction nonlinearity defined by the expression F (v_r) = C_sv_r. Where C_s is the damping coefficient and v_r is the relative velocity between the two ends of the suspension.

To optimize the closed-loop biodynamic system response in the critical frequency range of 4-8 Hz, the cost function defined by the following expression is minimized:

$\begin{matrix} ↓ J & = & \min \sum_{i = 1}^{5} J_{i} = \min [\frac{1}{2} (Γ_{d} - Γ_{m})^{2}] \\ = & \min \sum_{i = 1}^{5} \frac{1}{2} e_{i}^{2} \end{matrix}$ (2) subject to achieve the following system’s properties:

Where J is the cost function, e_i is the ith terms error, $a_{rms - org}^{ver}$ is the vertical RMS acceleration of the pregnant subject organs $a_{rms - abd}^{ver}$ is the vertical RMS acceleration of the pregnant subject abdomen, $a_{head}^{ver}$ is the head vertical acceleration, Γ_d is the reference (desired) vertical displacement of SPS organs and Γ_m is the actual vertical displacement of SPS organs.

vii. Some standard comfort limits are defined in the ISO 2631-1 of the 1997 standard for the problematic low-frequency range of 4-8 Hz based on the weighted RMS vertical acceleration described in [27]. A frequency weighting filter is used for the determination of weighted RMS acceleration in the sensitive low-frequency range as given by [28]. The values of weighted-RMS vertical acceleration of the SPS organs are kept within the comfort limits prescribed by ISO2631-1 of 1997 standard. The RMS vertical acceleration is determined by using a standard frequency weighting filter as shown in Fig. 2(a).

Fig. 2

(a) Frequency weighting filter. (b) AdaptNeuroFuzzy Architecture.

$a_{w . rms - org}^{ver} = \frac{1}{T} \int_{0}^{T} (a_{rms - org}^{ver})^{2} dt \leq 0.315 {ms}^{- 2}$

3 Adaptive NeuroFuzzy (AdaptNeuroFuzzy) control design

The proposed control algorithm uses the Fuzzy set theory of “IF " “THEN " rules. It relates the input-output of the nonlinear system. The design of the proposed control technique is based on a logical model i.e., Gaussian membership function covering the entire input membership degrees in the antecedent part between [0,1] and non-linguistic linear function in the consequent part.

Remark 1: Gaussian membership function provides a vernier and smooth coverage of the membership degrees between zero and one.

Remark 2: The proposed AdaptNeuroFuzzy control strategy is characterised by the following: 1) Fast processing speed (due to few number of rules) 2) simple structure 3) Online adaption 4) required less computational resources and space for storing data 5) easy to train and 6) add nonlinearity due to adaptive T-norm.

The knowledge base of the fuzzy inference system is framed in the following generalized form: $R_{i} : If x_{1} is β_{i 1} and \dot{.} . and x_{n} is β_{in} THEN ℑ_{i} = a_{i 0} + a_{i 1} x_{1} + . . . + a_{in} x_{n}$ Where (x₁, x₂, . . . , x_n) ∈ Rⁿ are the real n-inputs, ℑ_i = (a_i0 + a_i1x₁ + . . . + a_inx_n) are the consequent output of the ith rule and (a_i0, a_i1, . . . , a_in) are the consequent parts constants. u = (u₁, u₂, . . . , u_n) ∈ R are the controller outputs. β_ij (j = 1, 2, . . . , n) are the fuzzy sets represented by gaussian membership function given as follows:

$μ_{ij} (x_{j}) = exp (- \frac{1}{2} (\frac{x_{j} - c_{i}^{j}}{σ_{i}^{j}})^{2})$ (3) Where $c_{j}^{i}$ and $σ_{j}^{i}$ are the mean and variance of the input membership function. Firing strength for the ith rule is given as follows:

$\begin{matrix} w_{i} & = & β_{i 1} (x_{1}) \times β_{i 2} (x_{2}) \times \dots \times β_{in} (x_{n}) \\ = & \prod_{j = 1}^{n} exp \frac{1}{2} (\frac{x_{j} - c_{i}^{j}}{σ_{i}^{j}})^{2} \end{matrix}$ (4) The corresponding generalized outputs of the AdaptNeoruFuzzy control is defined by the expression as: $u_{i} = \frac{\sum_{i = 1}^{n} w_{i} ℑ_{i}}{\sum_{i = 1}^{n} w_{i}} = \frac{w_{1} ℑ_{1}}{\sum_{i = 1}^{n} w_{i}} + \frac{w_{2} ℑ_{2}}{\sum_{i = 1}^{n} w_{i}} + \dots + \frac{w_{n} ℑ_{n}}{\sum_{i = 1}^{n} w_{i}} = \sum_{i = 1}^{n} ψ_{i} ℑ_{i}$ where $ψ_{i} = \frac{w_{i}}{\sum_{i = 1}^{n} w_{i}} = \frac{\prod_{j = 1}^{n} exp \frac{1}{2} (\frac{x_{j} - c_{i}^{j}}{σ_{i}^{j}})^{2}}{\sum_{i = 1}^{n} \prod_{j = 1}^{n} exp \frac{1}{2} (\frac{x_{j} - c_{i}^{j}}{σ_{i}^{j}})^{2}}$ is the ith rule basis function of the AdaptNeuroFuzzy control.

The AdaptNeuroFuzzy control structure as shown in Fig. 2(b) consists of six. Layer by layer detail is given as follows: Layer 1 is the first layer that consists of nodes which introduce crisp input to the fuzzy architecture. Layer-2 is the fuzzification layer. The nodes in this layer fuzzify the crisp input with linguistic terms, the Gaussian membership function is used to assign membership grade. Layer-3 is the fuzzy inference/rules firing layer. Rules are framed in this layer. Layer-4 is the basis function/normalization layer. Layers-5 is the deffuzzification layers. Layer-6 is the final output layer of AdaptNeuroFuzzy network. Parameters update: The cost function minimization depends upon the network parameters. Optimization of the network’s parameters results in cost function minimization. Parameters to be optimized include “mean" $c_{i}^{j}$ , and “variance" $σ_{i}^{j}$ , of the antecedent part and “constants" (a_0i, a_i1, ⋯ , a_in) of the linear function of the consequent part. Based on the gradient descent algorithm, the generalized update equation for the parameter optimization is given as follows:

$Λ_{k + 1} = Λ_{k} - α_{k} g^{k} = Λ_{k} - e α_{k} \frac{\partial}{\partial Λ_{k}} (u_{i})$ (5)

Where Λ_k is the kth update parameter, Λ_(k+1) is the (k + 1)th update parameter, α_k is the learning rate, g^k is the gradient of error w.r.t Λ_k and the partial derivative of the control output u_i w.r.t Λ_k. Parameters update laws:

The update laws for the system parameters based on Equation 3 are given as follows.

Update law for the antecedent membership function “mean", c_i:

$\begin{matrix} c_{i (k + 1)} & = & c_{ik} - e α_{k} \frac{\partial}{c_{ik}} (u_{i}) \\ = & c_{ik} - e α_{k} (\frac{ℑ_{i} - \frac{\sum_{i = 1}^{n} w_{i} ℑ_{i}}{\sum_{i = 1}^{n} w_{i}}}{\sum_{i = 1}^{n} w_{i}}) \\ (\frac{x_{j} - c_{j}^{i}}{(σ_{j}^{i})^{2}}) w_{i} \end{matrix}$ (6)

Update law for the antecedent membership function “variance", σ_i: $\begin{matrix} σ_{i (k + 1)} & = & σ_{ik} - e α_{k} \frac{\partial}{σ_{ik}} (u_{i}) \\ = & σ_{ik} - e α_{k} (\frac{ℑ_{i} - \frac{\sum_{i = 1}^{n} w_{i} ℑ_{i}}{\sum_{i = 1}^{n} w_{i}}}{\sum_{i = 1}^{n} w_{i}}) \\ (\frac{(x_{j} - c_{j}^{i})^{2}}{(σ_{j}^{i})^{3}}) w_{i} \end{matrix}$ (7)

Update law for the consequent parameters “Constants" (a_i0, a_i1, . . . , a_1n):

Update law for, a_0i:

$\begin{matrix} a_{0 i} (k + 1) & = & a_{0 i} (k) - e α_{k} \frac{\partial}{a_{0 i} (k)} (u_{i}) \\ = & a_{0 i} (k) - e α_{k} ψ_{i} \end{matrix}$ (8)

Update law for, a_1i: $\begin{matrix} a_{1 i} (k + 1) & = & a_{1 i} (k) - e α_{k} \frac{\partial}{a_{1 i} (k)} (u_{i}) \\ = & a_{1 i} (k) - e α_{k} ψ_{i} x_{1} \end{matrix}$ (9)

Update law for, a_ji:

Similarly the update law for the jth constant is of the form:

\begin{matrix} a_{ji} (k + 1) & = & a_{ji} (k) - e α_{k} \frac{\partial}{a_{ji} (k)} (u_{i}) \\ = & a_{ji} (k) - e α_{k} ψ_{i} x_{j} \end{matrix}

(10)

The update parameters learning algorithm works in two passes. In the forward pass, firing strength w_i, basis function ψ_i and control output u_i are updated based on existing values of c_i, σ_i and (a_i0, a_i1, ⋯ , a_i1). While in the backward pass c_i, σ_i and (a_i0, a_i1, ⋯ , a_i1) are updated based on learning rate while using the aforementioned update laws.

3.1 Modification of the AdaptNeuroFuzzy control strategy

Adaptive T-norm is used to enhance the performance of the proposed control. Two additional parameters are added to the proposed control technique. The T-norm equation and the update laws for the two additional parameters, s_i and r_i are given as follows: T (μ₁, μ₂) = w_i = (μ₁ . μ₂) ^{s
_i} (μ₁ + μ₂ - μ₁ . μ₂) ^{r
_i} Where w_i is the firing strength of the ith rule and μ_s are the Gaussian input functions. The update law for the T-norm parameters s_i and r_i are presented as follows. Update law for T-norm parameter, s_i:

$\begin{matrix} s_{i (k + 1)} & = & s_{ik} - e α_{k} \frac{\partial}{s_{ik}} (u_{i}) \\ = & s_{ik} - e α_{k} (\frac{ℑ_{i} - \frac{\sum_{i = 1}^{n} w_{i} ℑ_{i}}{\sum_{i = 1}^{n} w_{i}}}{\sum_{i = 1}^{n} w_{i}}) \\ (w_{i} μ_{1}^{s_{i}} μ_{2}^{r_{i}} \ln (μ_{1})) \end{matrix}$ (11) Update law for T-norm parameter, r_i:

$\begin{matrix} r_{i (k + 1)} & = & r_{ik} - e α_{k} \frac{\partial}{r_{ik}} (u_{i}) \\ = & r_{ik} - e α_{k} (\frac{ℑ_{i} - \frac{\sum_{i = 1}^{n} w_{i} ℑ_{i}}{\sum_{i = 1}^{n} w_{i}}}{\sum_{i = 1}^{n} w_{i}}) \\ (w_{i} μ_{1}^{s_{i}} μ_{2}^{r_{i}} \ln (μ_{2})) \end{matrix}$ (12)

Remark 3: In fuzzy control, T-norm is used to connect different propositions in connection of and-operation. Weighted average requires that the rule base is complete and input fuzzy membership functions cover the input space. Otherwise, there is a danger to divide with zero. Systems using constants or linear functions in the consequence are clearly parameterized maps. Depending on the choice of T-norm and defuzzification, the expression above may change, but will always have similar structure.

Remark 4: By virtue of adaptive property augmented by the nonlinear T-norm coefficients, AdaptNeuroFuzzy control system handles 1) uncertainties due to system and 2) exhibits robustness against nonlinearities excited by road irregularities.

Remark 5: The control law embodies all the important constraints to avoid violations of thresholds imposed on various system key properties.

4 Simulation results and discussion

To evaluate the performance and effectiveness of the proposed advanced adaptive NeuroFuzzy (AdaptNeuroFuzzy) control, the 19-DoF IVSPS model is subjected to standard category-D type of external random road profile defined by ISO-8608 standard. This form of the road surface reflects the actual road precision to which vehicles are daily exposed. This paper analyzes SPS biodynamic response both in the time domain and frequency domain. The effectiveness of the proposed control is validated through comparison with passive, PID, AdapPID and AdapFLC control using standard performance indices. Values of different parameters of IVSPS model are provided in appendix A, while the benchmark controllers and their parameters are given in appendix B. The total mass of SPS is considered as 66 kg including mass of the fetus. Simulation results both in the time domain and frequency domain of the SPS biodynamic response are given in Figs. 3 through 10 and tabulated in Tables 1 and 2.

Fig. 3

Vertical displacements of organs (a) pelvis (b) abdomen (c) lumber spine (d) neck (e) head.

Table 1

Comparison of the power absorbed and percentage reduction in the power absorbed by the seated subject organs with AdaptNeuroFuzzy control

Mag:of power Absorbed with (J/s (*10^-3))					% imp: with AdaptNeuroFuzzy
Organs	Passive	PID	AdapPID	AdapFLC	AdaptNeuro Fuzzy	Passive	PID	AdapPID	AdapFLC
Palvis	853	454	149	96	81	91%	80%	46%	16%
Abdomen	263	143	59	29	19	93%	87%	68%	34%
Diaphragm	9.67	5.34	2.4	1.06	0.61	94%	89%	75%	43%
Thorax	11.6	6.4	2.9	1.3	0.72	94%	89%	67%	43%
Torso	228	124	51	25	17	93%	87%	57%	34%
Upper-arm	5.73	3.14	1.13	0.64	0.49	92%	84%	57%	24%
Lower-arm	1.4	0.77	0.28	0.16	0.12	92%	85%	58%	24%
Lumbar-spine	236	122	46	26	19	92%	84%	58%	27%
Thoracic-spine	223	115	43	25	18	92%	84%	58%	27%
Neck	2.66	0.8	0.53	0.29	0.23	91%	71%	57%	23%
Head	1.65	0.48	0.34	0.21	0.16	91%	67%	53%	23%

Table 2

Comparison of the pregnant subject abdominal RMS acceleration at the critical frequency of 7.7 Hz

	Mag: of RMS Acc: with (*10^-2)					% imp: with AdaptNeouroFuzzy
Organs	Passive	PID	Adap PID	Adap FLC	Adapt-Neuro-	Passive	PID	Adap PID	Adap FLC
Abdomen	1.41	1.13	0.69	0.33	0.21	85%	81%	70%	37%

4.1 Pregnant subject biodynamic response analysis in the time domain

Comparison of the time response of SPS five vital organ’s vertical displacement for the passive, PID, AdapPID and AdapFLC controls with AdaptNeuroFuzzy control is shown in Fig. 3. The corresponding integral time absolute error (ITAE) result for vertical displacement of all SPS organs is shown in Fig. 5(a). The results show that with the proposed AdaptNeuroFuzzy control, the overshoot in the vertical displacements of the organs are effectively damped as compared to response with the passive, PID, AdapPID, AdapFLC controls. The analysis reveals that the transient response of the AdaptNeuroFuzzy is fast and it produces sufficient damping effect to attenuate the harmful vibrations as compared to the effect produces by other control techniques. It is obvious from Fig. 5(a) that ITAE of the vertical displacements for all SPS organs with the proposed AdaptNeuroFuzzy control is much smaller as compared to the rest of the control techniques. Thus the proposed control exhibits quick response and hence enhanced the ride comfort of the pregnant subject significantly.

Fig. 4

Weighted rms vertical acceleration of organs (a) pelvis (b) abdomen (c) lumber spine (d) neck (e) head.

Fig. 5

(a) ITAE vertical displacement of organs (b) ITAE weighted rms vertical acceleration of organs.

The measure of weighted RMS vertical acceleration, $a_{w . rms}^{ver}$ is a valuable time domain response performance evaluation index which is the basic statistical measure of the random motion. $a_{w . rms}^{ver}$ is determined using the standard frequency weighting filter based on the ISO 2631-1 of 1997 guidelines. The $a_{w . rms}^{ver}$ response for five vital SPS organs and the corresponding ITAE of the $a_{w . rms}^{ver}$ for all organs are shown in Figs. 4 and 5(b) respectively. Results reveal that with the proposed AdaptNeuroFuzzy control, values of $a_{w . rms}^{ver}$ for vital SPS organs are negligibly small and within the comfort limits prescribed by the standard while the values with other control techniques are more than the comfort limits. The corresponding ITAE for all SPS organs with the proposed control also depicts a small change in the performance index than the values with other control techniques. It can be seen that with the proposed control strategy, the variation in the vertical RMS acceleration is very small which exhibits a negligibly small slope throughout the travel. The response has a flat profile which depicts a negligible disturbance caused to the SPS organs as compared to other control techniques. Therefore, the proposed AdaptNeuroFuzzy control provides a comfortable ride travel. It effectively damps the harmful vibrations and well segregates the SPS organs and fetus from the adverse impact of the road surface excitation than the conventional and non-conventional control schemes.

Discomfort analysis based on absorbed power is an important performance evaluation key. The power absorbed is frequency-dependent which induces strain in the organ tissues causing muscle damage. The organs, therefore, need to be isolated against the power transfer from the road surface irregularities. The SPS organs absorb power through chassis and seat which dissipate throughout the body. The organs closed to the source and parallel to the line of action of the force, absorb maximum power. Pelvis and the back column are the organs that absorb a significant amount of power due to their closed location to the point of contact. A small amount of power is transferred to the organs far from the seat due to a series of damping components. A comparison of the power absorbed by the SPS organs with AdaptNeuroFuzzy and passive, PID, AdapPID and AdapFLC controls are shown in Figs. 6 and 7 and tabulated in Table 1. The response curves of power absorbed for the five vital SPS organs with the proposed control are almost a straight line with negligible small slope i.e., the values of power absorbed are very small as compared to the values with the rest of the control schemes. It is evident from the results that the proposed control provides good performance in terms of power absorbed. The corresponding ITAE for the entire organs with the proposed control also shows a flatten performance index as compared to the rest of the control techniques which further validate the better performance of the proposed control. Values of the absorbed power by all SPS organs with the five control techniques along with percentage improvement for the proposed AdaptNeuroFuzzy control are tabulated in Table 1. Pelvis absorbs the maximum amount of power followed by the abdomen and lumber-spine. While lower arm absorbs a minimum amount of power followed by the head. The percentage reduction in the power absorbed by the organs is averaging around 92% which is highly encouraging for the proposed control strategy. It is found from the above analysis that the proposed adaptive control provides an exceptional good shield to the SPS organs against the harmful impact of power transfer.

Fig. 6

Absolute power absorbed by organs (a) pelvis (b) abdomen (c) lumber spine (d) neck (e) head.

Fig. 7

Absolute power absorbed of organs.

4.2 Pregnant subject biodynamic response analysis in the frequency domain

To analyze the SPS biodynamic response in the frequency domain, another performance evaluation key is the power spectral density (PSD) of the $a_{w . rms}^{ver}$ of organs. PSD quantifies the frequency content of the acceleration which is obtained by taking derivative of $a_{w . rms}^{ver}$ with respect to frequency. The area under the PSD curve is the measure of the RMS value of acceleration for various frequency bands. Greater the area under the curve tantamount to more RMS acceleration for the organs. Thus, creates more discomfort perception for the SPS organs. Fig. 8 shows the comparison of the PSD for $a_{w . rms}^{ver}$ of the SPS vital organs with the five control strategies in the critical frequency range of 4-8 Hz. It is obvious from the results that for the proposed AdaptNeuroFuzzy, the SPS organs have the smallest area under the PSD curve as compared to the passive, PID, AdapPID, AdapFLC controls. Hence, the proposed AdaptNeuroFuzzy control provides a better ride environment by significantly reducing the vibration effects on the body organs as compared to passive, PID, AdapPID, AdapFLC controls.

Fig. 8

Power spectral density of organs (a) pelvis (b) abdomen (c) lumber spine (d) neck (e) head.

Most of the organs have their natural frequency falling in the range of 4-8 Hz which causes muscle damage. WBV consequences on human beings depend upon the magnitude of frequency and the amount of vibration transmitted to the organs. The peaks in the $a_{w . rms}^{ver}$ might cause severe damage to the organs and hence create discomfort perception. It is desired to eliminate the peaks in the $a_{w . rms}^{ver}$ to maximize the ride comfort. A comparison showing the mapping of $a_{w . rms}^{ver}$ for the five vital SPS organs in the critical frequency range of 0-10 Hz with the five control techniques is shown in Fig. 9. Results reveal that with the proposed control, the peaks in the $a_{w . rms}^{ver}$ of the SPS organs at the problematic resonant frequency are mostly damped as compared to the peaks with passive, PID, AdapPID, AdapFLC control. Hence, the AdaptNeuroFuzzy enhances the ride comfort of the SPS and provides protection against the harmful WBV. Moreover, with the proposed control technique, the travel duration is significantly enhanced without the SPS organs being subjected to discomfort symptoms.

Fig. 9

RMS vertical acceleration v/s frequency of organs (a) pelvis (b) abdomen (c) lumber spine (d) neck (e) head.

The pregnant subject is a special passenger highly sensitive to WBV which needs extra care during travel. Motion sickness causes nausea and vomiting which can be harmful to the SPS and her fetus. Human beings are sensitive to WBV in the low-frequency range of 0.1-0.5 Hz in the horizontal direction which causes motion sickness. SPS therefore needs to be protected against the negative impact of the harmful vibrations in this special sensitive frequency range. To avoids, motion sickness, the head acceleration, a_head of the SPS needs to be minimized in the problematic frequency range. Fig. 10(a) shows the comparison of the a_head for the five control techniques. The results reveal that with the proposed AdaptNeuroFuzzy control, the overshoot in a_head in the problematic frequency range of 0.1-0.5 Hz is effectively damped as compared to the overshoot with passive, PID, AdapPID, AdapFLC control. Therefore, the proposed AdaptNeuroFuzzy control provides an improved comfort environment to the SPS as compared to the comfort level with the other control strategies.

Fig. 10

(a) Motion Sickness (pregnant subject) (b) Pregnant subject abdomen frequency.

Experiments conducted on the pregnant subject [7], suggest that vertical acceleration of the abdomen ( $a_{abd}^{ver}$ ) at the frequency magnitude of 7.7 Hz causes fetus damage. To isolate the mother and her fetus against the harmful ( $a_{abd}^{ver}$ ) in the problematic frequency, the control objective is to minimize the magnitude of ( $a_{abd}^{ver}$ ). Fig. 10(b) shows a comparison of the ( $a_{abd}^{ver}$ ) of SPS for the critical frequency with the five control techniques. It can be seen from the results that with AdaptNeuroFuzzy control, the peaks in the ( $a_{abd}^{ver}$ ) are effectively eliminated/damped as compared to the peaks with the passive, PID, AdapPID and AdapFLC controls. The analysis shows that the proposed AdaptNeuroFuzzy control protects the fetus in a better way against the harmful abdomen acceleration as compared to the rest of the control techniques. The percentage reduction in the ( $a_{abd}^{ver}$ ) with the proposed adaptive control as compared to passive, PID, AdapPID and AdapFLC controls are tabulated in Table 2. The results show that for the proposed AdaptNeuroFuzzy control, the percentage reduction in the magnitude of ( $a_{abd}^{ver}$ ) for critical frequency as compared to passive, PID, AdapPID, AdapFLC controls are 85%, 81%, 70%, 37% respectively. These inspiring improvements suggest that the proposed adaptive control provides sufficient protection to the mother and fetus. The mother and fetus are, therefore, well protected against the adverse effect of WBV.

Therefore, it is evident from the above investigations that with the proposed AdaptNeuroFuzzy control strategy, all the objectives are effectively achieved. Hence, it is concluded that the proposed control strategy based active suspension system of the integrated vehicle-seated-pregnant subject model provides better performance as compared to the conventional passive, PID, AdapPID and intelligent AdapFLC control alternatives.

5 Conclusion

This paper analyzed the biodynamic response of SPS against the road roughness induced vibrations. A 19-DoF nonlinear full-car IVSPS model is used in the analysis. The biodynamic response of the integrated model is performed by subjecting the model to standard road profile. The performance of AdaptNeuroFuzzy control is validated both in the time domain and frequency domain. Results of the AdaptNeuroFuzzy control are compared with passive, PID, AdapPID and AdapFLC controls. The excellent performance of the AdaptNeuroFuzzy control (in terms of ride comfort improvement, vertical displacement minimization, weighted RMS vertical acceleration minimization, absorbed power minimization and elimination of the resonant and critical frequency of the seated-pregnant-driver subject organs) is validated by the simulation results. Given the above facts, it is observed that with the proposed control, all the objectives are achieved efficiently. It is, therefore, concluded that the proposed AdaptNeuroFuzzy control is a better control technique for the integrated vehicle-pregnant subject model is an excellent control alternative as compared to the passive, PID, AdapPID and AdapFLC controllers.

Future work: Further, nonlinearities in the form of nonlinear passive component i.e., spring & dampers and nonlinear biodynamic model can be incorporated in the proposed mathematical model. Investigation of vibrations on the SPS can be carried out in the different seat-positions of the car. Performance comparison of the proposed control scheme under parametric variations.

Footnotes

Appendix

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