Spatial behavior of a pipe conveying fluid is examined theoretically and experimentally under the condition that the pipe has an asymmetrical spring supported end. Three first-order ordinary differential equations, which govern the amplitudes and phase of the self-excited lateral pipe vibration, are derived from the nonlinear nonself-adjoint partial differential equations by the Liapnov-Schmidt reduction. The planar and nonplanar motion of the pipe exist depending on the flow velocity and the perturbed parameter of the spring coefficient. Furthermore the experiments were conducted with the silicon rubber pipe conveying water. The spatial displacements of the pipe were measured by the image processing system, which was based on the images from two CCD cameras. The typical feature of the self-excited pipe vibration, as predicted by the theory, was confirmed qualitatively.

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In this study, we proposed the technique to measure vibration of a turbine blade in a turn using an image processing. By using the CCD camera, we captured the end face of a blade in a turn and determined a position of a blade from an image data, and then estimated the amplitude of vibration statistically. The movement of the blade at high speed made a captured image blur, and degraded the estimation of the position of the blade. By processing the blurred image as the inverse problem, we could estimate the position of a blade precisely. Under a supposition that the blade vibrates sinusoidally, the probability density for the blade vibration can be calculated. By comparing the probability density for sine wave with the processed probalility density for the blade, the amplitude of blade vibration could be evaluated.

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In this paper, we verified a numerical dynamics simulator for a big size shaking table that we proposed. We applied the numerical simulator to the prototype facilities for the largest 3-dimensional vibration test facilities, and compared the actually measured data and the numerical simulator outputs to verify the numerical simulator. As a result, we show that our new numerical simulator can realize frequency characteristics and acceleration time response exactly.

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The largest 3-dimensional vibration test facility are planning to build in Hyogo prefecture. The objectives of this facility are to investigate the process of the collapsing phenomena of a full-scale structure under the earthquake. At the design stage, it is impossible to make sure the performance without the numerical simulation. Therefore, the mathematical simulation model was accurately constructed, and the simulation was performed. This paper describes the verification results based on the condition of a collapsing phenomena of the full-scale building.

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This paper describes vibration analysis using finite element method for an elastic block supported by a nonlinear concentrated spring. The restoring force of the spring has cubic nonlinearity. Finite element for the nonlinear spring is expressed and is connected to the elastic block modeled by linear solid finite elements. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. This transformation yields computation efficiency. Influences of Young's modulus on nonlinear frequency responses for the elastic block are clarified.

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The multiplication of Dynamic Vibration Absorbers (DVAs) has been studied for several years to improve its performance. However, the optimal regulation of DVA becomes practically difficult for increasing of number of DVAs. In this paper, two-series-mass DVA has been studied to improve vibration control performance and regulation easily. The optimal parameters of two-series-mass DVA have been calculated from compliance optimization, accelerance optimization and mobility optimization, so that optimal design diagrams and approximately formulas shall be conducted. The performance of vibration control is analyzed through the simulation and experiment. The results show that the two-series-mass DVA improves its performance, in the same total mass ratio, by about 20% than the one-mass DVA, and also it shows better results than even the four-parallel-mass DVA.

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Passive piezoelectric shunt damping is a vibration suppression method using a piezoelectric element which is electrically shunted by a passive electrical circuit. This paper shows a method of optimizing the values of the elements of the shunt circuits based on the robust performance index against the model uncertainties. For the optimization, the worst-case peak gain of the transfer function is selected as a cost function. From the results of the optimization for the LR shunt circuit, we investigate some required properties for the robustness of shunt circuits. As an example of the robust shunt circuits, the optimization for the LR-LRC shunt circuit is also presented. The experimental results demonstrate the efficiency of the proposed method.

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System identification of a real motorcycle is performed to design a control system for attitude stabilization of the motorcycle by front-wheel steering. In system identification, a front-steering impulse torque is used as the input signal and the roll angle response is used as the output signal. We reduce the identified model to the third order model and design the front-steering control system using the roll rate as the feedback signal by H_∞, control theory. It is verified from experimental results that the attitude of motorcycle against front-steering torque disturbance is stabilized by the H_∞ controller.

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Noise reduction and vibration control at high speed railway are required to improve the interior noise characteristics of aluminum car body system, which is used shinkansen train and express train. However, it becomes difficult to maintain the vibration control of one link mechanism between the car body and the car bogie. In this paper, to improve the damping performances of one link mechanism, we have proposed a new type noise reduction link mechanism using granular materials. Factors which affect the damping performances are examined through a numerical simulation study. The present noise reduction link mechanism is studied via examining damping performance with granular mass effect and friction effect. Finally, in the numerical simulation by using the discrete element method (DEM), new type noise reduction link mechanism is improved by max. 4.6dB in comparison with the conventional one.

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As is well known, the abnormal sound detection is usually very difficult. In this paper, we present a new diagnostic method for abnormal sound using the Cellular Neural Network (CNN). The procedure of our method is 1) calculating the autoregressive model (AR model) coefficients from the abnormal sound by using the maximum entropy method ; 2) constructing the CNN whose memory patterns become standard abnormal sound patterns ; 3) making the coefficients obtained as an initial pattern and recalling one from the memory patterns, and then obtaining a diagnosis result. By using our method, the influence of the noise occurred from other normal parts can be avoided. Therefore the abnormal sound can be diagnosed by using CNN even when a man can not diagnoses the abnormal sound conventionally. The results demonstrate the advantages of our approach.

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This paper proposes a new technique based on the wavelet transform to detect knock in one combustion cycle. The fast wavelet transform algorithm for knock detection is discussed. The cylinder pressure in a spark-ignition engine is analyzed using wavelet transform. The frequency characteristic of resonance mode with crank angle change can be distinguished using wavelet transform. In view of the fact that plural resonance modes could not occur at same time, a knock detection algorithm is proposed with the comparison of scale power spectrum of plural resonance modes at the same crank angle. The results of simulation and experiment show that this technique is simple to implement and may provide practical utility for real time diagnostics of combustion.

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Car shake is arisen by imbalance and uniformity of tires. Typical car shake that is called the engine shake is occurred by the effect of bouncing resonance at a speed of midrange. In this paper, mechanism of this phenomenon is studied to reduce the vibration. It is cleared that engine shake are reduced by coupling mode with the pitching mode. The optimal condition for reducing the car shake is setting the engine pitching resonance coincided with the bouncing resonance of the engine. And optimum condition for reducing the vibration is expanded when the coupling coefficient is increased.

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Acceleration shock is due to a low frequency fore and aft vibration that is induced by rapid transient change of engine torque. And mechanism of vibration and force of transient torque was analyzed. The results are as follows. (1) Vibration of power train is minimized when resonance frequency of engine roll is equal to torsional resonance of power train. (2) This minimum condition is not feasible for vehicle with high gear ratio. (3) Quantitative evaluation of transient engine torque is calculated with excitation spectrum that is studied in this paper.

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We analyzed the drivers' braking behavior in view of the level of over-reliance on the system, for designing Forward Collision Avoidance Assistance System (ACAAS). In a condition when the system was activated at the timing showing Time to Collision is less than 1.7 s, no driver showed the over reliance on the system. In this condition, the drivers' braking timing was earlier than the system operation. We think that Time to Collision regarding the onset timing of the system will be an effective state variable for the analysis of the reliance level on the system, and the timing standing at Time to Collision is less than 1.7 s is one of the optimal conditions for the onset of FCAAS, in view of minimizing the over reliance on the system.

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A method for improving local optimal solutions of nonlinear programming problems by treating constraints directly, which is named "Modal Trimming Method", is proposed. This method combines a gradient method for searching local optimal solutions, with an extended Newton-Raphson method based on the Moore-Penrose generalized inverse of a Jacobian matrix of objective and constraint functions for searching initial feasible solutions used by the gradient method. A strategy for preventing traps into fathomed local optimal solutions is proposed. Some features of the method are investigated qualitatively, and it is found that they are suitable to improve local optimal solutions efficiently. The method is applied to a wide range of problems, and its performance is evaluated in terms of the global optimality of the suboptimal solutions. It turns out that the method has a high possibility of deriving the global optimal solutions by the suboptimal ones for a wide range of problems.

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The purpose of this study is to investigate the functional displacement of human foot complex during gait cycle. The methodlogy was to present the mathematical foot model which was three joints rigid rink 3 D model, consists of taroclural joint (TCJ), subtalar joint (STJ), and a foot arch as a single axis joint. And the angle motion and moments in each joints was determined using the inverse dynamics analysis method. The foot model parameter was sampled by anthropometric experimentation during a normal gait, and changed to the each joint coordinate system. The results of this study showed that the functional displacements of the three joints holding biomechanical relationships based on Elftman, and indicated the shape changes of the human foot complex during gait. We discussed that the muscle activities effect to the foot motion about the results of three joint moments in this 3 D model study.

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Living in the gravitational environments, primates have various muscles as power souses. They have the muscular arrangements and muscular strength reflecting differences in their walking form. We have reported that coordination control among the three pair of antagonistic muscles contributed to the output force direction control in all round direction, the force/position control and the stiffness control at the endpoint of the extremities. In the present paper, relations between walking mode of various primates (human, chimpanzee and Japanese macaque) and the difference of their muscular strength were analyzed in terms of functional anatomy and of dynamics. The results that the muscular arrangements and size was reflected in their walking form in these Primates was obtained. They had the essential muscular arrangements and size to realize the force direction at the endpoint of the extremities.

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Robots have one motor at each joint, but animals have bi-articular muscle driving two joints simultaneously. The bi-articular muscle characterizes animals and is predicted to have special functions. To clarify these functions, a simple human model was emploved. The model was a Jumping Jack without the guide rail. Gastrocnemius, the bi-articular muscle in the lower leg, was modeled simply by wire. The clarified bi-articular muscle functions will contribute to development of simple controlled robots. Model experiments and computer simulations were executed with and without the wire. Ground reaction force and jump movement were analyzed both in the model experiments and computer simulations. In addition, energy transformation was analyzed in computer simulations. The wire simulating the bi-articular muscle (1) controlled the direction of the ground reaction force, (2) inhibited transformation into rotational energy from the potential energy of the spring, and (3) stabilized airborne movement.

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To achieve smooth motion of car-like robots, it is necessary to generate paths that satisfy the following conditions : maximum curvature, maximum curvature derivative, and curvature continuity. Another requirement is that human operators can manipulate the paths with ease. In this paper, a path expression methodology consisting of line segments, circular arcs, and clothoid arcs are presented. In addition, a method of global path generation with a visibility graph is proposed. To establish this method, the following steps are proposed : (a) the arrangement of subgoals (middle points) and (b) the construction of the graph for path generation. By using the proposed method, the paths were shortened by an averaee of 14%.

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In this paper a robust tracking control scheme without using adaptation and joint angular velocity measurements based on a state observer. The configuration of developed robust controller becomes very simple compared with that of regressor based adaptive controllers. It is shown that the Euclid norm of tracking errors can be arbitrarily reduced by using only one design parameter. Especially for a constant ideal trajectories, it is shown that Euclid norm of tracking errors converges to zero. Moreover, in the presence of quantization error in joint angle measurements, it is shown by numerical simulations and experiments that the proposed controller is more effective compared with the controller using Eular approximation of joint velocity.

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This paper presents a hybrid control system consisting of a distributed time-varying feedback control law and a behavior-based control framework to coordinate motions of multiple non-holonomic mobile robots with two wheels driven independently on capturing/enclosing a target by making troop formations. This motion coordination is a cooperative behavior for security against invaders in surveillance areas. Each robot in this control law has its own coordinate system and it senses a target/invader, other robots and obstacles, in order to achieve this cooperative behavior without making any collision between them. Each robot especially has a two-dimensional control input referred to as a "formation vector" and the formation is controllable by the vectors. As for determining the formation vectors, we use a behavior-based control framework in which the robot has some reactions heuristically designed according to this cooperative hunting behavior. The validity of this hybrid system is supported by computer simulations.

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This paper presents a measurement method and its results for a compliance of a vertical-multi-articulated robot. In order to calculate the compliance of a robot, a stiffness of each joint of the robot is required. In this paper, a stiffness of each joint of the robot is measured by using a force/torque sensor and a 3-D motion and position measurement system OPTOTRAK 3020. The proposed measurement method is applied for a 7-DOF robot PA-10 made by MITSUBISHI Heavy Industries, LTD. At first, an 11-DOF link model with 4-virtual joints, i. e. the link model includes virtual 4-DOF, is proposed. Then, a compliance matrix is obtained using a measured stiffness matrix of the PA-10 and a Jacobian matrix of the proposed 11-DOF link model. In order to investigate accuracy of the measured stiffness, and to confirm effectiveness of the measurement method for the stiffness and the proposed link model, experiments measuring the compliance of the PA-10 are conducted. In the experiments, the proposed 11-DOF link model is compared with a 7-DOF link model. Experimental results illustrate that the measured stiffness are accurate, and the measurement method and the proposed link model are effective for calculating the compliance of the PA-10.

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In this paper, we consider a design method of approximate feedback linearization for non-linear systems to which the exact linearization method is not applicable. We adopt a two-step procedure to solve the approximate linearization. First, a state transformation matrix is settled, so that the non-linear system is transformed approximately into the controllable canonical form. Second, a standard non-linear linearization method is used to transform the controllable canonical form into a stable linear system. Finally, the application of the proposed method to the Acrobot, which is known as a system to which the exact linearization method cannot be applied, is shown to illustrate the effectiveness of the proposed method.

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We have developed a Pipe-Diagnostic Robot System with Ultrasonic Sensor. The robot is able to detect the flaws at the elbows in addition to strait pipes. This robot is composed of a six-link parallel mechanism, a ring-rail and a diagnostic end-effecter which has a ultrasonic probe. In order to measure the thickness of pipes accurately, it is important to adjust the posture of the ring-rail to the pipe elbow geometry, and to contact the ultrasonic probe to the surface of pipes closely. We have introduced schemes to control the position and posture of the ring-rail and to judge the status of the probe's contact, and shown the results of the experiments.

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In order to detect corrosions on the inside of pipes accurately, it is very important to set the posture of the ultrasonic probe normal to the surface of the pipes. It is indispensable for an inspection robot which moves on pipe lines autonomously to have an ability adjusting the posture of the probe. We propose an algorithm to adjust probe posture, which uses a characteristic of ultrasonic echo depending on posture of probes. In this paper, we will explain about the algorithm and describe about a posture adjusting experiment with a five DOF of robot manipulator newly designed. And we will propose a method to make a pipe-corrosion-map with pipe thickness data that are measured by automatic inspection robot.

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A new type of passive element with variable mechanical impedance is proposed in this paper. Since the proposed elements are lighter, smaller and softer than the previous passive elements, these elements have possibility of develop wearable mechanical systems. In this paper, the principles of the variable mechanical impedance of the proposed elements are explained and the basic experimental results demonstrate the performance of the proposed elements. Moreover, a wearable mechanical system for virtual reality is developed by using the proposed elements and it is shown that the developed system can be utilized as a force display in virtual world.

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This paper proposes a new type of output coupling mechanisms which consists of a couple of differential gears. The mechanism uses the input surplus power through distributing it to the other outputs, which enables us to use the input power more effectively. The fundamental equations of the mechanism with respect to velocity and efficiency of input/output are obtained. Furthermore, its effectiveness is demonstrated with an experimental device.

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In this study, the SiO₂ micro injectors, the diameters of which were about 10∼1000 μm, were fabricated using MEMS technology. In order to inject minute liquid into a cell, the characteristics of micro channels were investigated. When minute liquid is driven by pressure, it turns out that the smaller the aspect ratio of the channel became and the less a flux became, the smaller pressure loss due to the friction became. Since the pressure loss of the injector with the diameter of 10 μm and the length of 25 mm at the flow rate of 1n 1/s was about 100 kPa, this injector can inject minute liquid by pressure. The stiffness of the injector was measured by the minute force measuring experiment. The fracture load is about 460 μN. Since this injector can be inserted into about 100 μm and 1 mm egg cells, it became clear that the fabricated injector had sufficient strength.

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It is difficult for human beings to transfer their skills to someone directly. It requires a lot of time and effort. We develop the "Skill Coaching System" to attempted to decrease time and effort when the skill is transferred. In this paper, in order to accelerate acquisition of skill, how to change the supporting method by the degree of acquisition of skill is examined. The method of evaluating the degree of acquisition of skill is important. A coherence function is used as a method of evaluating the degree of acquisition of skill. Moreover, the GMDH (Group Method of Data Handling) technique is used in order to evaluate by few data. It turns out by these methods that man's internal model is formed and the coefficient of the internal model becomes large by the degree of acquisition of skill. Since the degree of skill evaluated by real time by this method, it turns out that this method is suitable for evaluation of the degree of acquisition of skill in the coaching system for skill.

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This study aims at the realization of running a powered-wheelchair safely and comfortably by voice commands. In this report, the experiments of running by voice in such a narrow space as toilet was done using a real powered-wheelchair equipped with a personal computer. From the results, the possibility of running the powered-wheelchair in a narrow space using a voice commands was assured by introducing macro-command.

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This paper presents the results of an experimental study of the performance of a novel electrostatic separator. The separator consists of a conductive belt conveyor equipped with a plate electrode. The separation tests were performed on a sample containing 50% polyvinylchloride (PVC) and 50 aluminum. The influence of electric field strength and belt speed on the separation efficiency was investigated. Numerical experiments have shown the feasibility of obtaining extract contents of aluminum and PVC in excess of 99.99% and 99.46%, respectively.

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The fan blade has the shape twisted the with aerodynamic design. However, the blade produces the deformation in the direction of which the twist is returned by centrifugal force under rotation. The method for measuring the return of the twist of this blade by the discharge was devised, and using the cascade in which the return of the twist was generated suspected, this measurement was tried. Measurement principles are as follows. In the casing wall, needle electrode of several pieces is installed on the axial straight for the blade tip. The high tension is applied to this electrode, and the spark discharge is generated in the electrode and between blade tips. A time difference occurs in produced discharge waveform, when one blade passes several electrodes, because blade shape axially faces it, and because it is not straight line. The difference of the length in each electrode is proven, when this time difference is multiplied by circumferential speed, and as this result, it is possible to obtain the external form of pressure surface of the one blade. The discharge continues during the transit time, when the blade passes the electrode. In it, the shape of the suction surface of the blade can be also measured, if it proves discharge end. As the result that it manufactured the equipment and measured at 16.7m/s circumferential speed, the measurement accuracy of about ± 2 mm was obtained in the pressure surface edge, and about ± 1 mm was obtained in the suction surface edge.

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The innovative measuring method for transmission error of final reduction gearboxes has been developed. Because laser speed sensors measure the rotary movement of the flanges connected rigidly to a gear pair, obtained data express the transmission error precisely. It has been confirmed that the transmission error measured by the method are in the relation of direct proportion to the vibration level of final reduction gearboxes. This has proven that the proposal of hypoid gears with involute helicoid tooth form is nonsense to reduce gear noise of final reduction gearboxes.

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This paper deals with the running torque of ball bearings with the polymer lubricant. The experimental results showed that the measured running torque of the ball bearings with the polymer lubricant are affected by the enclosure form of the polymer lubricant. The measured running torque difference between the ball bearings with different enclosure form of the polymer lubricant was not affected significantly by the rotational speeds and the axial loads. The analytical results showed that the running torque difference was caused mainly by the friction (depending on the enclosure form of the polymer lubricant) between the balls and the polymer lubricant (or the cage).

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A new cutting lubrication method employing solid lubricant has been proposed for green machining. In this method, nm order silica particles were selected for the lubrication agent, referring to glass extrusion process. Glass has not only an ability to lublicate, but also it has some great advantages, for example, the strong electrostatic to manipulate its motion. Therefore paying attention to electrophoresis in particular, the lubrication method, spraying nm order silica particles under colloidal condition around cutting area and guide them to the cutting point, was tried out. The result showed the good prospect of the method, such as reduction of cutting force and burr, long tool life since glass particles promote better chip flow, and that also proved this method was efficient for environment.

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For improving the machinability of aluminum alloys without adding low melting-temperature elements such as Pb or Bi, effects of the addition of Si and Cu, solely or in combination, on the chip breaking were examined for peak-aged (T8) Al-1.0 mass%Mg-0.8 mass%Si alloy (A 6061 alloy) under lathe machining at cutting speeds V = 0.83∼3.33 m/s in dry and wet atmospheres. The magnitude of chip breaking N = (the number of chips) / (100 g of chips) increased with a dcrease in V and with the addition of Si and Si+Cu in both cutting atmospheres. The value of N amounted to ∼22000/100 g, that is ∼6 times larger than that of 6061 alloy and is large enough for practical machining operation, at the smallest V of 0.83m/s in the wet atmosphere where the adhesion of work material on the tool surface scarcely occurred. Such a notable improvement of chip breaking by the combined addition of Si and Cu was ascribed to the existence of large Si particles at which micro-cracks appear and along which they propagate, and also to the solution and precipitation hardening of the matrix which results in the loss of fracture ductility.

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An approach is presented to predict the chip formation and the three components of cutting force in the machining with the curved-edge end mill, which has the tool geometries changing with the cutter height. Those geometrical parameters are defined as the functions of the cutter height. The chip formation in the milling process is modeled as a pilling up of orthogonal cuttings along the cutting edge. The orthogonal cuttings are made in the planes containing the cutting velocities and the chip flow velocities so that chip flows up to a certain direction as a rigid body. The chip flow direction can be given to minimize the cutting energy, which can be given as the sum of the shear energy on shear plane and the friction energy on rake face. The cutting force, then, can be predicted with the chip formation having the minimum cutting energy. The presented approach is applied to the prediction of cutting process in the machining with the insert-ball end mill. The predicted results are verified to be accurate enough in a variety of depth of cut. The change of the chip flow angle and that of the orthogonal cutting model during a rotation of the cutter can be shown in the presented approach.

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It is well known that the diameter of cutting tool should be the same as the diameter of cam follower, otherwise it is impossible to fabricate the precise cam track. However, if the error is permissibly small during the roughing mill-process the use of a smaller cutter is preferred due to the cost. For the case of cylindrical cam with translating follower, the tool offset and the offset error have been studied. Here a plainer methodology to obtain the tool offset and offset error of the smaller cutting tool for a cylindrical cam with translating and oscillating followers is proposed, then the offset error is evaluated accordingly based on the analytical procedures. The evaluation of error is useful to determine the minimum size of cutting tool for finishing milling and grinding process. As a result of the simulations, it becomes clear that one or two rank size down cutter can be used to mill the cam track.

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In sheet metal bending, bending die is designed in prospect of spring back after unloading. Although accuracy of spring back analysis has been improved, slight variation of thickness or material properties depending on production lot of sheet metal causes scatter of bend angle in mass production, which is a serious problem especially in bending high strength steels or low priced sheets. As a countermeasure, a new method for compensation of bend angle is proposed in this paper. When sheet metal is partially sheared with negative punch-die clearance, it is slightly bent by the gradient of plastic strain normal to bend axis developed in the sheared zone. By controlling this deformation, accurate and adjustable bending was studied. Change of bend angle depending on punch penetration, clearance, tool edge condition and lubrication was investigated experimentally for two kinds of pure aluminum sheets 0.8 mm in thickness. Among test parameters, punch penetration was found to be most influential one and to have linear relationship with bend angle, which suggests good angle-controllability of this method. Strength of bent portion was tested and sufficient strength was assured up to 20% punch penetration against sheet thickness under the optimum condition. Moreover, spring back was little observed since plastic strain is much higher than that by moment bending. These results were studied with strain distribution estimated by elastoplastic finite element analysis.

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Design of latching type electromagnetic solenoids becomes more important recently especially for micro switching devices such as optical switches for optical network communications, and electrical switches for electro communications and power electronic devices with low impendence. Design and characteristics of a micro electro magnetic solenoid with 7 mm × 4 mm × 2.2 mm are reported in this paper : (1) general discussion of potential structures, (2) electromagnetic design using finite element method, (3) design and characteristic of the prototype, and (4) small limits of electrical current and activating period for switching are shown.

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If a system is composed of only one element, it is possible to evaluate the stability of the system with the Stress-Strength model. However, it is impossible to evaluate the stability of a complex system in which huge amounts of element are linked to each other. To estimate the stability of a complex system, we need to consider the whole structure of the system including interaction between the elements. In this paper, we propose a hierarchized Cellular Automata (HCA) for rational and quantitative system management. In the HCA method, the system is expressed as a lamination structure, which is composed of some hierarchies. Each hierarchy is composed of some elements ; each element has a characteristic status value, inputs and outputs. With the HCA method, we can understand the stability of the whole system in terms of probability, by considering local interactions between the elements. As a numerical example, the HCA method is applied to a model of a human organization's conscious changing process. The stability of this model is calculated by numerical simulation, and a probability distribution of the stability of the system is obtained. In conclusion, it is found that the stability of the whole system can be evaluated using the probability distribution.

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In the bag-packing problem, several items are selected so that the sum weight should be closest to the target weight. In order to obtain an optimal solution, all the candidate solutions must be enumerated. But when the number of candidate solutions increases, it takes too much time to obtain an optimal solution. So such enumeration method is not efficient. Therefore the following system is developed ; such conditions can be derived as would exclude useless, superfluous searches and by checking whether the conditions are satisfied or not, the number of candidate solutions that must be enumerated can be decreased. Many of the simulation results seem to prove the proposed system to be effective.

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