ABSTRACT: This journal is all about various kinds of automotive suspension configurations and how they affect ride quality, handling and durability of a vehicle and various methodologies used to design, analyse and physically test them along with their characteristics based on geometry and compliance. These are discussed in relation with the tyre and dynamics of the complete vehicle. As the technology is getting updated at a faster rate, especially in the field of automotive engineering, various design aspects also changes leading to more complicated suspension designs according to the application for which a vehicle is used for. Suspension of a vehicle governs the ride quality, safety, handling, and various other factors to a greater extent. Most of the automobile industries like Bentley, Aston martin, Jaguar, Audi etc. had already showed their interest in maximising the above mentioned qualities what a good car requires in a very innovative manner. Nowadays the dampers are available in varying types depending on the chief ingredient technologies adopted in them and they enhance the ride quality and other performance characteristics to a greater extent.
Suspension system of a vehicle governs the various ride characteristics, comfort and performance of a vehicle. It is the most important assembly in a vehicle as it supports all the mass of the vehicle in a stabilized condition allowing the vehicle to follow the path as driven by the driver in a more responsive manner. This journal deals with various suspension systems and modifications that can be done on them along with different optimization techniques used to improve ride quality and handling.
Ride quality of a vehicle is mainly concerned with the feel or sensation of a passenger in the environment of a moving vehicle. It depends upon the suspension as well as the body design of the vehicle. Vehicle oscillations are made to be maintained between 1 to 1.5 Hz as this is considered as the ideal frequency for humans. This was believed to be the ideal one by the early car manufacturers and they tried to maintain to impart frequencies of this range to the passengers inside so that they get a comfortable ride. It depends upon the type of suspension used and the various bushings which are fitted in the car. Thus cornerstone of a comfortable ride is still considered as the natural frequency. Static deflection of a vehicle is the deflection produced by the sprung mass of a vehicle (vehicle body). If the deflection produced by the sprung mass of a vehicle is 10 inches the frequency produced is equivalent to 1Hz. If the static deflection produced is 5in then the natural frequency produced is 1.4Hz and 3.13Hz for deflection of 1inch. 
It can be determined by using the formula:
The ratio of sprung and unsprung mass of a vehicle largely governs the vehicle ride quality and handling if the vehicle is extremely light weight vehicle. In today's commercial vehicles, the unsprung weight of the components is only 13 to 15 percent of the vehicle curb weight. A high sprung to unsprung weight ratio keeps the tyres more firmly in contact with the road and give a good ride.
Another cost effective method for improving handling is by reducing the wheel hop during a straight line drive. This gives a good ride quality along the straight lines. This can be done by using rear lowering trailing arms with tubular upper 3rd link. It will get the wheel hop under control and improves corner exit and straight line traction control. 
1. DOUBLE WISHBONE SUSPENSION
A double wishbone (consisting of upper and lower A-arm) suspension is an independent suspension design which uses two (at times parallel) wishbone-shaped arms to locate the wheel. Each arm or wishbone has two mounting points to the chassis and one joint at the knuckle is arm along with the shock absorber and coil spring mounted in order to control vertical movement of the wheels. Parameters like camber angle, toe pattern, caster angle, roll center height, scuff, scrub radius etc. can be controlled by the usage of double wishbone suspension design and it also allows the engineer to control the motion of the wheel along with the the suspension travel.
The double wishbone suspension which is also known as double 'A' arms, is known as a short-long arm suspension if the upper and lower arms are of unequal lengths. A single wishbone (A-arm ) can also be used in various other suspension types, such as MacPherson strut and Chapman strut. Double wishbone suspensions consist of a pair of upper and lower lateral arms. The upper arm is usually shorter than the lower arm in order to induce negative camber as the suspension jounces (rises) mainly during a bump or stopping of the vehicle. If we consider a vehicle taking a turn, positive cambers gain on the outside wheel resulting due to body roll which causes the outside wheel to jounce and gains negative camber due to the shorter upper arm. It can also be observed that weight transfer takes place to the outer tyre during a turn, which leads to more instability. The tyre can be kept perpendicular to the ground if these two effects are cancelled out by balancing them. This is what most of the suspension designers are focused on.
A knuckle with a spindle, between the outboard ends of the arms carries the wheel bearing and wheel and the Knuckles with an integral spindle are used to prevent wheel to be driven. If the wheel is to be driven, a bolt on hub design is commonly used. The arms are sometimes fitted with two bushings or ball joints at the body in order to resist fore-aft loads such as acceleration and braking.
In the scenarios where the steering loads have to be taken via a steering arm, single ball joints are typically used at the knuckle end, and the wishbones look A or L-shaped. In passenger vehicles, L-shaped arms are generally preferred since they allow a better compromise of handling and comfort to be enhanced in. A Pair of joints is sometimes used at both ends of the arms of a rear suspension of a vehicle in order to make them more H-shaped in plain view. As long as the shape of the other wishbone provides control of the upright, a fixed-length driveshaft can perform the function of a wishbone as well. This arrangement has now been successfully used in the Jaguar IRS. It is easy to work out the camber gain as the suspension is a 4-bar link in elevation view and other parameters for a given set of bushing or ball joint locations. The various bushings or ball joints do not have to be on horizontal axis which is parallel to the vehicle centre line. Antidive and Antisquat can be dialed in, if the various bushings and ball joints are set at an angle. 
2.A simple beam axle and leaf spring layout
In this type of suspension layout leaf springs are used to guide the road wheels on vertical direction, carry lateral loads and resist the moments applied by longitudinal forces in addition to their proper function as a spring medium. This was used in the early days as they didn't require any much effort in designing them. It reduced the manufacturing cost since it was simple and cheap. It is also called solid axle suspension since one set of wheels are connected to a shaft or a single beam laterally. The main advantages of using these suspensions are that they are simple and cheap to manufacture. The disadvantage of this type of suspension is that the wheels are restricted from behaving to the road pattern independently and the mass of the beam axle which acts as unsprung weight of the vehicle, affects ride quality of the vehicle. Even nowadays they are used since they are ideal for carrying heavy or varying loads because beam axles never exhibit camber change as the wheels travel through irregularities. Since the wheels have zero camber gain during body roll it has negative impact during cornering of a vehicle when compared to other suspension systems. This type of suspension system is used in heavy-duty trucks, light and medium duty pickup trucks and vans.
The main advantage of using a simple beam axle type suspension is that they provide better vehicle articulation. It is an important behaviour which is required for off road applications. Articulation or ramp travel index is a method of measuring a vehicles ability to flex its suspension. It is widely used in many, small front wheel drive cars and vans as they provide maximum internal volume.
Effect of number of leaves and thickness of leaf: Deflection for a small bump is too large while using a soft spring, all though it gives a comfortable ride along straight lines. Normal springs produce deflections proportional to load as they have a constant rate (Hooke's Law). When the lower leaves are set to a reverse camber, a stiffening-up of the spring occurs. This is known as "a progressive or variable-rate spring". The plates or leaves slide over each other causing inter-plate friction as the laminated spring deflects. This provides required damping effect, with a 'hard' ride, along with noise and wear, and minimises friction as much as possible. To provide some vital damping effect few features are incorporated with the spring instead of periodic spraying of penetrating oil, done earlier. These include,
- Fitting the synthetic rubber buttons at the ends of the leaves.
- Reducing the number of leaves, this however requires the increase in the width using inter-leaf plates of low friction material.
Note: Roll centre of a car is an imaginary point considered, about which the car rotates in a cross section while the points of tyre/road contact do not slide. 
HYDRAULIC FLUID AND AIR SUSPENSION: This suspension system is developed by combining hydraulic fluid and air without any air compressors. A cylinder forms the hydraulic part of each spring in this system and a plunger is attached to the wheel linkage to form the strut. Each cyclinder has spherical air chamber attached to the outer portion. This chamber is divided into two: upper and lower portion. The upper portion contains the air and the lower portion contains the hydraulic fluid. The two portions are separated by a diaphragm. Fluid communicates with cylinder through a two way restrictor valve. The dumping action is performed by the valve. It limits the movement of plunger since fluid will be moving back and forth. Thereby the dumping action controls the movement of wheel with respect to the portion of vehicle supported by springs. This is also known as pneumatic suspension.
ELECTRONICS AND ACTIVE SUSPENSIONS: This suspension has various additional components apart from the normal air suspension components. The most important component is the computer which interrupts the input from various sensors. The simplest form maintains the level ride height. In four wheel systems height adjustments will lower the automobile's ride height to reduce the aerodynamic drag. It also improves fuel economy at highway drive. Driver can adjust the drive requirements manually by switching from soft mode to firm mode according to the requirement. The most advanced form will make automatic switching from soft mode to firm mode depending on the road conditions. The cost of this system is very high. This system is employed only in luxury cars.
The latest developments in suspension systems are the active suspension systems. This makes use of a microprocessor inorder to change the orifice size of the restrictor valve in a hydraulic suspension or shock absorber. The inputs are vehicle speed, load acceleration, lateral force or a driver preference. Thus these suspension systems are used inorder to provide maximum ride quality and handling. 
Hydropneumatic suspension is a kind of automotive suspension system which is invented by Citron and is widely used in Citron cars. This system is also used by other car manufacturers like Mercedes Benz, Peugeot and rolls Royce. The main aim of this system is to provide a comfortable and well controlled ride. This makes use of a nitrogen springing medium which is six times flexible than conventional steel spring. This system has a belt or camshaft driven pump from the engine which is used to pressurize a special hydraulic fluid. This in turn provides energy to operate brakes, suspension and power steering. This also provides energy to operate clutch system, turning head lamps and even power windows. The suspension system is also known as 'olopneumatique', simply emphasizing that oil and air are its main components. Many improvements have been made to this system from the initial development where the latest one consists of a simplified single pump-accumulator sphere combination.
The working/functioning of hydropneumatic suspension is as follows:
The system consists of a pressure sink and a suspension element. The suspension element is also known as spheres and is five or six in number. The spheres are distributed as one for every wheel. The system also has one main accumulator and special brake accumulator for certain models. For cars with antisink or active suspension there are totally nine spheres. This has a hollow metal ball which is open to the bottom and a flexible desmopan rubber membrane which is placed at the equator inside which separates the top and the bottom of the system. The top portion consists of nitrogen which is pressurized upto 75 bars. The bottom part is connected to the hydraulic fluid circuit of the car. The high pressure pump driven by the engine energizes the circuit and accumulator sphere at an operating pressure between 150 and 180 bars which powers the front brakes and then depending upon the model it is capable of providing energy to operate power steering, clutch and gear change. Pressure is transferred from the circuit to bottom parts there by providing energy to the wheel spears and rods which are connected to the suspension. This works by pushing the rod to LHM. This will compact the nitrogen in the upper part of the circuit. Damping is done by using a two way leaf valve present in the opening of the sphere. LHM squeeze back and forth through this two way valve causing resistance and controls the suspension movements in the circuit. This damper is of very simple architecture and also the most efficient. Car height connecting works are done by height connectors which are connected to front, rear and anti rollbars. These connectors will allow more fluid to travel to the spears under required pressure when the suspension is low. The fluid is returned to the system reservoir in low pressure when suspension is high. These connectors act with some delay to avoid the movements during normal suspension movements. Rear suspension spheres will power the rear brakes. 
HYDRACTIVE SUSPENSION: Hydractive Suspension is invented by French manufacturer, Citron in 1990. This development is an extension of hydropneumatic design developed in 1955. This is designed by the additional usage of electronic sensors which enhances great driver control by the suspension performance. In this system the driver can transform the vehicle to sport mode and also in a very comfortable mode. Sensors are used in brakes, steering, suspension, throttle pedal and gearbox. These sensors will feed information about the car speed, acceleration, road conditions to the on board computer. Accordingly these computers will switch to extra pair of suspension spheres in and out of the circuit inorder to allow the car to have a smooth supple drive in normal circumstances and high roll resistance while at the corners. This suspension system is mainly focussed on improving the comfort and handling while driving.
HYDRACTIVE 1 AND 2 SUSPENSION: Hydractive 1 has two preset modes for the driver: sport and auto. In Sport mode the car suspension setting is in firmest mode. In Auto mode the car suspension setting is transferred from firm mode to soft mode on temporary basis depending on the car speed by which the speed variations are detected by the sensors for brake pressure, steering wheel angle and body movements.
In hydractive 2, the preset modes are Sport and Comfort. In Sport mode the car suspension settings are not in firm mode instead it lowers the threshold for any of the sensor readings. In Comfort mode, same level of firmness is given while cornering and acceleration. There will be significant change in the ride quality in this mode while cruising.
In these two systems if the computer gets any abnormal sensor readings due to malfunctioning of electrical components then the setting will be shifted to the firm mode for rest of the ride.
HYDRACTIVE 3 : Hydractive 3 suspension is developed in 2001 by Citron for their 'C5'. While using this suspension system, the cars will remain at normal ride height even if the car is off for a very long period by using the elctronics. This also uses an orange fluid instead of green LHM mineral oil used in other vehicles with hydropneumatic suspension resulting improved performance characteristics. 
To improve safety and handling of cars, rear sway bar up-grade is an excellent solution. It is a very cost effective method for increased handling especially while driving through the corners. It will give improved steering input and will help in keeping the vehicle flat during hard cornering. This can be experienced during heavy load situations along with reduction of body roll and reduces tail wag while towing heavy loads. They contain polyurethane bushings and link end grommets with a mounting hardware kit. This system is mounted in front of the axle housing as it is a forward facing rear sway bar
The dynamics of a second sway bar offers tremendous handling characteristics especially when combined with other suspension products along with the end links mounting "mid frame". Suspension parameters are studied inorder to investigate their effect on a vehicle drifting to one side of the track during braking. In this situation , the driver must apply constant correction torque on the steering wheel inorder to maintain the vehicle to travel along a straight course. A graph representing vehicle drift vs time is given below.
Another technology used to improve the handling of a vehicle is by using traction bars. This enables more traction for the vehicle which can be mainly observed while driving it through rough and slippery surfaces. Traction bars work by solidly locating the rear axle to another point on the frame and thus prevents axle from wrapping up. The traction bars closely follow the angle of the rear leaf spring and the long bolts in the middle of the "T" pieces replace the existing front spring hangar bolt.Hence these bars almost make a true 4-link suspension. Traction bars keep the axle from twisting backwards and they forces the drive wheels to turn forward by completely eliminating leaf spring windup and keeping the rear drive wheels forced down to the pavement for superior traction. 
3. Panhard Rod:
A Panhard rod (also known as track bar/Panhard bar) is designed to prevent wheels to move forward or backward and from side to side. It is invented by the Panhard automobile company of France in the early twentieth century and is now widely used by most of the automobile companies. The panhard rod is connected in such a way that one of its ends is attached to the wheel axle and other on the body of the vehicle. Thus the panhard rod and the axle lie on a same plane. Panhard rod alone doesn't locate axle effectively in a longitudinal direction, thus it is used together with trailing arms which locates the axle in longitudinal direction. This arrangement is not required while using a leaf spring suspension since the leaf springs alone will produce enough of lateral rigidity. 
Suspension bushes are one of the chief ingredients in governing ride quality of a vehicle. There are different types of bushes available in the market nowadays depending upon the type of material used to make them. They are mainly available as rubber bushings. But for a long run, polyurethane bushings are now available. Polyurethane bushes enhance prolonged tyre life and improved vehicle performance. It also provides safety by increasing the braking stability of a vehicle. It has greater cost effectiveness than rubber bushings as they have a longer life. 
Polyurethane suspension bushes are not simply the replicas of original rubber bushes as they are individually designed to take full advantage of the various characteristics of polyurethane such as its durability, and exceptional friction-absorbing capability which cannot be attained by using rubber bushes. Pre-load, location factors and Critical crush are calculated and adjusted in such a way that, they can achieve positive and responsive driver feedback, which facilitates a vehicle's roadholding capability accompanied with ride quality. Finely finished polyurethane bushes which are not purely cosmetic either, where machine-finished and was appropriate for its purpose, ensured a precise fit - a vital part of the optimum crush, pre-load, and location equation. 
A suspension system governs a vehicle's durability to a greater extent depending upon various factors. It supports almost all the components of a vehicle in such a way that they get minimum vibrations that are absorbed by the vehicles wheel by using dampers and springs. This increases the life span of various components in a vehicle by preventing wear and tear among different components used in a vehicle.
1. USE OF SUSPENSION SYSTEM HAVING INTEGRATED LINK, SPRING AND ANTI-ROLL BAR
A suspension system in any automobile supports almost all the components of a vehicle and keeps them resistant from wear and tear by absorbing almost all the vibrations caused during a wheel travel. It works with a combined effort and forces acting on tyres, unit body (frame), wheel bearings, brakes, wheels, and steering system to provide comfortable and a safe mode of transportation. Several vital roles of a suspension system are, allowing the tyres to move up and down in accordance to the road irregularities, eliminating excessive body squat when accelerating, supporting various components of an automobile, allowing immediate cornering without any much body roll or body sway, keeping the tyres firmly on road surfaces, allowing the directional change of front wheels to turn side to side, for steering, to eliminate excessive body dive while braking and keeping the wheels in correct alignment. The various suspensions in a vehicle support engine, vehicle's frame, body and powertrain above the wheels. All these above mentioned assemblies constitute what is called us sprung mass. All the structural components, wheels, brake assemblies and tyre, which are not supported by the springs, constitute what is called as un-sprung mass. There will be drastic characteristic change - which is not good, in vehicle handling when the un-sprung weight is high and thus reduced un-sprung weight is desirable. Around 3 - 4 linkages are connected between wheel axle and frame to carry driving and braking torque. They also support vertical loads due to road irregularities, and lateral loads during cornering. For the up and down movements of wheel assembly, the lower arms are pivoted in the frame members and these lower arms sometimes even supports rear coil springs of a vehicle. All these linkages cause an increase in the un-sprung mass of a vehicle and increases complexity and part count.
In addition to all these components, anti roll bars are sometimes used to prevent side sway (body roll) of the body and to support the rear axle housing in alignment with the frame. Thus it further increases complexity of suspension systems. The disadvantage of conventional techniques could be overcome with new technique which integrates multiple automotive vehicle suspension into one integrated unit. This should reduce complexity and part count while potentially reducing noise vibration and harshness. This can be done by using a rear wheel suspension having an integrated link, spring and anti-roll bar. Thus a rear wheel suspension replace the lower control arms, coil springs, and anti roll bar assembly with a simple composite beam. By designing the shape of the beam, the material system and the pivot locations, the ride and roll rates, camber and toe characteristics of the old suspension design can be restored. Thus it facilitates multiple automotive suspension functions in one unit. 
Durability and fatigue testing can be carried out on special purpose rigs:
- Hydraulic Con-Rod and Torsion Rigs
- Suspension Rig (with varying number of channels)
- Seat Test Rigs including Seat Test KUKA Robot
- Load/Force/Deflection Rigs
- Vehicle Four-Poster Rig
- General Servo-Hydraulic Rigs
D.METHODOLOGIES USED FOR THE OPTIMIZATION FOR BOTH RIDE COMFORT AND HANDLING
The Dynamic-Q method and Sequential Quadratic Programming algorithm the are the two approximation methods used for the optimisation for both handling and ride comfort. The function values are determined by using computer integrated numerical simulations. A vehicle is modelled in ADAMS, and coupled to MATLAB for the execution of the optimisation process. The ADAMS model of a vehicle consists of a load-dependent tyre model, suspension kinematics, as well as non-linear springs and dampers. Suspension characteristics up to four design variables are considered for the modelling purpose. Thus cost is determined by the number of simulations that has to be carried out for the proposed optimisation process. Various optimisation algorithms used are the dynamic -Q method, the SQP method and gradient approximation methods.
THE DYNAMIC-Q METHOD
As per the book published by the professors of UNIVERSITY OF PRETORIA on vehicle dynamics (chapter 3), the method called the Dynamic-Q method consists of applying the dynamic trajectory optimization algorithm to successive quadratic approximations of the actual optimization problem. This method may be considered as an extension of the unconstrained SQSD model which is capable of solving general constrained optimization problems. This is method is most suitable where the number of variables n is particularly large as well as the storage requirements of the dynamic-Q method are very less.
The identical entries along the diagonal of the the above three Hessian matrices indicates that the approximate sub problems P[i] are spherically quadratic.
For i=0, a linear approximation is formed by setting the curvatures a, bj and ck to zero. The curvatures a, b and ck are chosen so that the approximating functions interpolate their corresponding actual fujnctions at both xi and xi-1. These conditions imply that for i = 1,2,3....
If the gradient vectors are not known analytically, they may be approximated from functional data by means of first-order forward finite differences. Since the second derivatives of the objective constraints are approximated using function and gradient data, the calculations and storage locations which would usually be required for these second derivatives, are not needed. The computational and storage resources for the dynamic-Q method are thus reduced to. At most 4+p+q+r+n+s n-vectors need to be stored (where p, q, r and s are respectively the number of inequality and equality constraints and the number of lower and upper limits of the variables). These savings become significant when number of variables become large. For this reason it is expected that the dynamic-Q methods is well suited, for example, to engineering problems such as structural optimization where large number of variables are present.
Thus approximate sub-problem, constructed at xi thus becomes P[i]:
With solution x*i. In the dynamic-Q method the sub-problems generated are solved using the dynamic trajectory or "leap frog" (LfopC) method of Snyman [101, 102]for unconstrained optimization applied to penalty function formulations ( Snyman et al. , Snyman  of the constrained problem.
A dynamic-Q method is thus a robust and efficient method for non linear optimization, with minimal storage requirements compared to those of the SQP method. The particular methodology proposed is made possible by the special properties of the LfopC optimization algorithm (Snyman ), which isused to solve the quadratic sub-problems. 
This journal dealt with various suspension systems and modifications that can be done which affect vehicle ride quality, handling and vehicle durability. It also dealt with various optimization techniques used for both handling and ride comfort and how they can be implemented for improving vehicle performance characteristics in a very cost effective manner. It can be concluded that the future developments which can be implemented on vehicle suspension systems are Active Stabilizer Suspension System and electro dynamic suspension system. This will results in better vehicle performance characteristics than the present day conventional suspension systems resulting in better ride quality handling and vehicle durability.
 Jo Yung Wong. Vehicle Ride Characteristics from Theory of Ground Vehicles. Edition: 3 - 2001, 431-432.
 Heinz Heisler. Technology and engineering/automotive, Advanced Vehicle Technology Volume - 10, publisher - Butterworth-Heinemann, Edition: 2 - 2002, pp418.
 Al Kirschenbaum. The Official Ford Mustang 5.0: Technical Reference & Performance Handbook : 1979 Through 1993, Bentley Publishers, 2003. pp 331.
 Tim Gilles. Automotive Chassis: Brakes, Suspension and Steering, Section 4 - suspension and steering, 2004, page 327 - 328
 J.R. Ellis. Vehicle Handling Dynamics. Chapter Four, Suspension Characteristics. 1994, 91-95.
 Malcolm James Nunney. Light and Heavy vehicle Technology. Air Suspension System, Published by Elsevier Limited, Fourth Edition, 2007, pp 447
 Jack Erjavec. Automotive Technology: a systems approach, Electronic And Active Suspensions, Fourth Edition, Chapter 44, 1140-1141
 Colin Campbell. New Directions In Suspension Design: making the car faster, Hydropneumatic suspension. 1999, Chapter 9, 143-149.
 Eric Chowanietz. Automobile Electronics. Hydractive suspension. Publisher: Butterworth-Heinemann, 1995, 178-181
 Khalid Hussain, Andrew Day, & Nihal Mirza. Vehicle Handling And Stability Investigation To Causes Of vehicle Drifting During Straight Line Braking, http://www.eng.brad.ac.uk/eqi/downloads/courses/kh_veh+eqifi.pdf
 Four Wheeler Magazine. Four-Wheeler Chassis and Suspension Handbook, Publisher: MotorBooks/MBI Publishing Company, 2004, pp94
 Dennis Parks. American Hot Rod: How To Build A Hot Rod With Boyd Coddington, Chasis, Publisher: MotorBooks/MBI Publishing Company- 2005, Chapter 2, 48-50.
 Tim Gilles. Automotive chassis: brakes, suspension, and steering, Suspension And Steering, Cengage Learning, 2004 - Chapter 15, Section 4, 350-352
 Mike Ancas. Mazda RX-7 performance handbook - PERFORMANCE HANDBOOK SERIES, Chassis and Suspension, Publisher: MotorBooks/MBI Publishing Company, 2001, 40-42
 Lawson et al.. Wheel Suspension having Integrated Link, Spring and Anti-Roll Bar, United States Patent, Patent No. US 6,530,587 B2, Filed: May 30, 2001, Publication on Jan 03, 2002, date of Patent Mar 11, 2003, 1 - 5.
 Els, P.S., Uys, P.E., Snyman, J.A. and Thoresson, M.J., 2006, Gradient-based approximation methods applied to the optimal design of vehicle suspension systems using computational models with severe inherent noise, Mathematical and Computer Modelling, Vol. 43, pp. 787- 801.