IL264140B2 - A system and method for detecting deformations of elastic modes in a moving body - Google Patents

Description

SYSTEM AND METHOD FOR IDENTIFYING ELASTIC MODE DEFORMATIONS OF A MOVING BODY TECHNOLOGICAL FIELD The present invention is generally in the field of modal analysis of a moving body, and particularly relates to identification of structural deformations of a moving structure.

BACKGROUND A moving platform (e.g., land-vehicle, air-vehicle, marine-vehicle, space-vehicle) experience deformations (i.e., shape changes) during its motion, which may be affected by internal and/or external aero-dynamic loads (e.g., gusts), and/or movement of control surfaces, and/or changes in the payload carried by the platform (e.g., fuel/propellant exhaustion, disposable cargo such as airdrop and/or ammunition), which can reduce performance of the platform. In order to effectively and reliably control the motion of the platform the control system of the platform is required to monitor modal frequencies and elastic shapes of the platform, that occur as the mass of the platform is changed during its motion. Reliable real-time estimation of structural elastic mode states of a moving body is difficult to achieve. Typically, an array of sensor devices distributed over the moving body/platform are used to monitor natural frequency response during the motion of the body. However, in certain applications (e.g., in air/space vehicles, such as, but not limited to, missiles/launch vehicle) the number of sensors that can be used is very limited due to the mass penalty and complexity. Estimating modal frequencies and/or shapes from such limited number of sensor devices is inadequate for reliable real time motion control. Accordingly, accurate estimation of the modal elastic shapes for real-time motion control of a moving platform, requires mounting a large number of sensors over the body of the platform, which is mostly undesired due to the increased weight and complexity, and also due to the extensive wiring, which is heavy and susceptible to electromagnetic interferences. US Patent No. 9,073,623 proposes a hardware and software architecture for dynamic modal structural monitoring that uses a robust modal filter to monitor a potentially very large-scale array of sensors in real time, and tolerant of asymmetric sensor noise and sensor failures, to achieve aircraft performance optimization such as minimizing aircraft flutter, drag and maximizing fuel efficiency. US Patent Publication No. 2010/318336 suggests modelling dynamic behaviour of flight vehicles for simulation, analysis, and design. In this solution a user can define the complexity of a flight vehicle model, and such models may be simple rigid body models, models of medium complexity, or very complex models including high order dynamics comprising hundreds of structural flexibility modes and variables related to aero-elasticity, fuel sloshing, various types of effectors, tail-wags-dog dynamics, complex actuator models, load-torque feedback, wind gusts, and other parameters impacting flight vehicles. Multiple vehicle and actuator concepts and configurations, are accommodated and analysed, as defined in flight vehicle input data, which specifies flight vehicle parameters at a steady-state condition for modelling flight vehicle response to dynamic forces and flight control commands with respect to steady state operation. US Patent Publication No. 2013/238532 describes a method and apparatus for identifying deformation of a structure. Training deformation data is identified for each training case in a plurality of training cases. Training strain data is identified for each training case in the plurality of training cases. The training deformation data and the training strain data are configured for use by a heuristic model to increase an accuracy of output data generated by the heuristic model. A group of parameters for the heuristic model is adjusted using the training deformation data and the training strain data for each training case in the plurality of training cases, such that the heuristic model is trained to generate estimated deformation data for the structure based on input strain data. Hao Jiang et al., ("Real-Time Estimation of Time-Varying Bending Modes Using Fiber Bragg Grating Sensor Arrays", AIAA JOURNAL Vol. 51, No. 1, January 2013) suggest using fiber Bragg grating (FBG) sensor technology to locate a large number of sensing elements along a rocket's structure with a negligible mass penalty, for real-time modal estimation and control. A novel approach is suggested for real-time estimation of mode shapes on a variable mass structure using FBG sensor arrays. 30 GENERAL DESCRIPTION The application provides techniques for determining elastic modal shapes and frequencies of a moving structure which may have a time-varying mass, such as, but not limited to, an air/launch vehicle/missile, based on a numeric model calibrated utilizing strain vectors measured during a test maneuver/flight of the structure, or of a test model thereof. In some embodiments the determined elastic modal shapes and frequencies of the moving structure are used for filtering motion measurements obtained by an onboard measurement system of the moving structure (e.g., by an inertial measurement unit – IMU, also referred to herein as operative sensor arrangement), to remove from the motion measurement data elastic mode shapes of the moving structure, and feed a motion control system (e.g., flight control system) of the moving structure measured data/signals that are substantially/mainly indicative of rigid body modes of the moving structure. The strain vectors are measured during test maneuver/flight of the moving structure, responsive to internal and/or external load changes, and/or to mass/payload changes, of the moving structure during the test maneuver/flight. The measured strain vectors are processed to determine modal frequencies and modal elastic shapes of the moving structure as a function of the mass/payload of the moving structure, and to construct a repository of the determined modal frequencies and respective elastic shapes of the moving structure during its flight, which are thereafter used to filter displacements associated with the elastic modal shapes of the moving structure from data/signals measured by the onboard measurement system of the moving structure during operational flight. The repository can be arranged as a lookup table indicative of respective elastic modal shape and frequency for various different mass/payload conditions of the moving structure, to be used by the motion control of the moving structure to estimate elastic mode shape of the moving structure for real time modal filtering of data/signals measured by the onboard measurement system, and thereby reliably and efficiently control propulsion of the moving structure. One inventive aspect disclosed herein relates to a method of determining elastic mode shapes of a moving structure during its motion. The method comprising generating a repository of elastic mode shapes occurring in the moving structure based on strains measured during different motion-stages of the moving structure, or of a simulating structure thereof, each of the elastic mode shapes associated with a certain motion-stage of the moving structure during its motion, identifying a motion-stage of the moving structure during said motion, and extracting from the repository of elastic mode shapes a respective elastic mode shape based on the identified motion-stage of the moving structure. The extracted elastic mode shape can be indicative of elastic deformations in the moving structure while at the identified motion-stage. The method can comprise performing a test maneuver of with either the moving structure, or a simulating structure thereof, measuring strains in the moving structure, or in its simulating structure, by a plurality of sensors elements (e.g., implements using fiber Bragg grating) during motion thereof in the test maneuver, and determining the elastic mode shapes for the repository of elastic mode shapes from the measured strains. Optionally, but in some embodiments preferably, the method comprises determining a respective modal frequency for each of the determined elastic more shapes, and associating each of the elastic mode shapes in the repository of elastic mode shapes with its respective modal frequency. In some embodiments at least one property (e.g., mass, amount of fuel, shape, state of control surfaces, and/or center of mass) of the moving structure, or of its simulating structure, is being changed during the motion in the test maneuver, and the measuring of the strains is carried out at a plurality of motion-stages during the motion such that the measured strains are affected by the at least one property change. The method can thus comprise processing the measured strains obtained at each of the plurality of motion-stages to determine strain mode shapes of the moving structure, or of its simulating structure, at the plurality of motion-stages, and using a numerical model (e.g., a finite element model) associated with the structure, or with its simulating structure, for the determining of the elastic mode shapes from the determined strain mode shapes. The method can comprise associating at least one of the elastic mode shapes with a respective one of the motion-stages. The processing of the measured strains comprises in some embodiments performing spectral decomposition to obtain frequency components of the measured strains. Accordingly, the determining of the strain mode shapes can be based on imaginary portions of the frequency components of the strains measured by the sensors elements at a respective motion-stage in the test maneuver. The spectral decomposition can comprise a fast Fourier transform (FFT).

The method can comprise carrying out modal analysis to determine modal frequencies and shapes of the structure, or of its simulating structure, and calibrating the numerical model based thereon. The calibrated numerical model can be used to determine a respective strain mode shape, and a respective displacement mode shape of the structure, or of its simulating structure, for some, or all, of the determined modal frequencies and shapes. Optionally, but in some embodiments preferably, a transformation matrix is constructed from the determined strain mode shapes and their respective displacement mode shapes. The transformation matrix can be used for the determining of the elastic mode shapes from the determined strain mode shapes. Another inventive aspect disclosed herein relates to a mode shape filtering system comprising an input unit configured and operable to receive measurement data from a sensor system of a maneuverable structure, the measurement data comprising motion data indicative of deformations and/or displacements occurring in the maneuverable structure during its motion, and motion-state data indicative of at least one property of the maneuverable structure that is subject to changes during the motion, a repository of elastic mode shapes occurring in the maneuverable structure and derived from strains measured during different motion-stages of the maneuverable structure, or of a simulating structure thereof, each of the elastic mode shapes associated with a certain motion-stage of the maneuverable structure during its motion, a processing unit configured and operable to obtain from the repository of elastic mode shapes an elastic mode shape associated with the motion-state data, and a filtering unit configured to remove from the motion data components associated with the elastic mode shape obtained from the repository and generate respective filtered motion data. The system can be configured to provide the filtered motion data to a motion control system of the maneuverable structure for applying adjustments in motion control of the maneuverable structure. Optionally, the input unit is configured to receive from the sensor system new measurement data comprising new motion data indicative of deformations and/or displacements occurring in the maneuverable structure during its motion responsive to the motion control adjustments, and new motion-state data indicative of at least one property of the maneuverable structure that is subject to changes during the motion. The processing unit can be configured to obtain from the repository of elastic mode shapes a respective elastic mode shape associated with the new motion-state data, and the filtering unit can be configured to remove from the new motion data components associated with the elastic mode shape obtained from the repository of elastic mode shapes based on the new motion-state data. In some embodiments the at least one property of the maneuverable structure that is subject to changes during the motion comprises at least one of the following: internal aero-dynamic loads of the maneuverable structure, external aero-dynamic loads of the maneuverable structure, a payload of the maneuverable structure, state of control surfaces of the of the maneuverable structure, amount of fuel of the maneuverable structure, center of mass of the maneuverable structure, and/or a shape factor of the maneuverable structure. A yet another inventive aspect disclosed herein relates to a motion control system comprising a control unit configured and operable to receive location data from a position determining system of a maneuverable structure, the location data being indicative of a current location of the maneuverable structure during its motion, receive destination data from a destination determining system of the maneuverable structure, the destination data being indicative of a destination of the maneuverable structure, determine a direction of motion of the maneuverable structure for causing it to reach the desired destination, receive from the mode shape filtering system described hereinabove and/or hereinbelow filtered motion data of the maneuverable structure, and generate motion control data based at least partially on the filtered motion data. Optionally the destination determining system comprises a communication device configured to receive the destination data by transmission over a communication channel. A yet another inventive aspect disclosed herein relates to a system for generating a repository of elastic mode shapes occurring in a moving structure during its motion, the system comprising a structure properties determining unit configured to determine various properties of the moving structure and generate structure data indicative thereof, a modeling unit configured to generate a numerical model associated with said maneuverable structure based at least in part on the structure data, an analysis unit configured to determine modal properties of the maneuverable structure based on acceleration data indicative of accelerations measured in the maneuverable structure in response to excitations thereof in a free-free supported state, calibrate the numerical model based on the modal properties, and determine from the calibrated numerical model a transformation between strain and displacements associated with the maneuverable structure, and an elastic mode shapes determining unit configured to receive strain data indicative of strains measured in the maneuverable structure, or a simulating structure thereof, during different motion-stages thereof, use the determined transformation to generate from the strain data a displacement data of the repository being indicative of elastic mode shapes of the maneuverable structure, or its simulating structure, during its motion. Optionally, the elastic mode shapes determining unit is configured to determine for each elastic mode shape a respective modal frequency, and associate each elastic mode shape in the repository of elastic mode shapes with its respective modal frequency. The system comprises in some embodiments a motion-stage determining unit configured to receive at least one measured property of the maneuverable structure, or of its simulating structure, associated with the measured strains, the property is subject to changes during the motion in the test maneuver, and determine based thereon a respective motion-state indicator for each of the determined elastic mode shapes in the repository of elastic mode shapes. The system can be implemented by computer executable instructions of a computer program product.

BRIEF DESCRIPTION OF THE DRAWINGS In order to understand the invention and to see how it may be carried out in practice, embodiments will now be described, by way of non-limiting example only, with reference to the accompanying drawings. Features shown in the drawings are meant to be illustrative of only some embodiments of the invention, unless otherwise implicitly indicated. In the drawings like reference numerals are used to indicate corresponding parts, and in which: Figs. 1A to 1C schematically illustrate construction and calibration of an initial model for a maneuverable structure according to some possible embodiments, wherein Fig. 1A is a flowchart demonstrating construction of a transformation matrix for the maneuverable structure, Fig. 1B schematically illustrates a setup that can be used to determine the mode frequencies and shapes of the maneuverable structure, and Fig. 1C is a flowchart demonstrating a process that can be used to extract the mode shapes; Fig. 2 shows time plots of signals measured by a sensor measurement setup according to a possible embodiment; Figs. 3A to 3C show graphical plots of first, second and third, mode shapes obtained from a finite element model, and from the sensor measurement setup, of some possible embodiments; Figs. 4A and 4B show graphical mode plots obtained with the sensor setup according to a possible embodiment, wherein Fig. 4A shows strain mode shapes plot and Fig. 4B shows displacement mode shape plots; Figs. 5A and 5B schematically illustrate adjusting of the calibrated initial model of the maneuverable structure according to changes occurring during motion of the structure according to some possible embodiments, wherein Fig. 5A demonstrates collection of data during motion of the maneuverable structure, and Fig. 5B is a flowchart demonstrating a process of adjusting the calibrated model to reflect changes occurring during motion of the structure; Figs. 6A to 6C show graphical plots demonstrating a process of determining elastic mode shapes of a maneuverable structure according to some possible embodiments, wherein Fig. 6A shows measurement data acquired by onboard measurement system of a maneuverable structure, Fig. 6B demonstrates determination of strain mode shapes based on spectral decomposition of the measurement data, and Fig. 6C demonstrates determination of the elastic mode shapes of the maneuverable structure based on the determined strain mode shapes; Fig. 7 is a flowchart schematically illustrating use of the adjusted and calibrated model for motion control during operation of the maneuverable structure; Fig. 8 is a block diagram schematically illustrating use of an elastic mode shapes filtering system with a motion control system according to some possible embodiments; and Fig. 9 is a block diagram schematically illustrating a repository generation system according to some possible embodiments.

DETAILED DESCRIPTION OF EMBODIMENTS One or more specific embodiments of the present disclosure will be described below with reference to the drawings, which are to be considered in all aspects as illustrative only and not restrictive in any manner. In an effort to provide a concise description of these embodiments, not all features of an actual implementation are described in the specification. Emphasis instead being placed upon clearly illustrating the principles of the invention such that persons skilled in the art will be able to make and use the embodiments hereof, once they understand the principles of the subject matter disclosed herein. This invention may be provided in other specific forms and embodiments without departing from the essential characteristics described herein. The application provides techniques for determining actual elastic modal shapes of a maneuverable platform/structure (e.g., an air vehicle) based on acceleration vectors measured along and/or about the maneuverable platform/structure while it is in a free-free supported sate (stationary suspended state), and based on strain vectors measured along and/or about the maneuverable platform/structure while it is in non-stationary (moving) states, during which it is being subject to changes affecting elastic modal shapes thereof. The acceleration vectors measured while the maneuverable platform/structure in the free-free supported state are used to calibrate a numerical model of the maneuverable structure, which is used to generate a transformation matrix by which displacement vectors of the maneuverable structure can be computed from strain vectors. The strain vectors measured while the maneuverable platform/structure is in the non-stationary/moving states, and the transformation matrix, are used to determine displacement vectors (also referred to herein as elastic shapes) of the maneuverable structure during various different motion-states of its movement in which its elastic shape is influenced by a certain payload/mass, and/or shape factor, and/or mass-center, and/or internal/external loads, of the structure. The numerical model of the maneuverable structure can be then modified to describe various different elastic shapes displayed by the maneuverable structure during its different motion-states. In some embodiments the modified model of the maneuverable structure is used for determining elastic modal shapes of the maneuverable structure while it is in motion in an operation state, based on a mass of the structure and/or other changing factors (e.g., detachment of fuel tanks, payload release, changes in control surfaces, and suchlike) that may occur during motion of the structure in the operational state. This is achieved in some embodiments by determining a motion-state indicator i.e., indicative of current payload/mass, and/or shape factors, and/or mass-center, and/or control surfaces states, of the maneuverable structure, and matching a respective actual modal frequency and shape of the maneuverable structure that corresponds to the determined instant motion-state indicator of the maneuverable structure.

The matched actual modal frequency and shape of the maneuverable platform/structure can be used to assist in motion (e.g., flight) control of the maneuverable platform/structure by discriminating components of the matched actual modal shape from body deformations/displacement measurement data measured by its sensor elements e.g., inertia measurement unit – IMU, during motion in the operational state. For example, strain vectors measured while the maneuverable structure experiencing the various different motion-states during a test maneuver of the maneuverable platform/structure, can be processed to determine respective elastic modal shapes of the platform/structure and construct a repository of its modal shapes at the various different motion-states. The constructed repository can be then used to filter elastic body displacements associated with the elastic modal shapes of the platform/structure from data measured by the sensor elements of the vehicle during operational maneuvers. The terms moving body, maneuverable platform, and maneuverable structure, are interchangeably used herein to refer to a movable body (e.g., air crafts), and particularly to a movable body in which changes affecting elastic modal shapes of the body occur during its motion (e.g., changes in weight, and/or payload, and/or shape, and/or center of mass, and/or internal/external loads, and suchlike). The term maneuver is generally used herein to refer to propulsion of a movable body for moving it in a desired direction. It is noted that although the embodiments disclosed herein mostly relates to the maneuverable structure being an air craft, it is clear that the disclosed subject matter can be similarly used/applied, mutatis mutandis, with/to other maneuverable structures, such as, but not limited to, sea vehicles, land vehicle, and space vehicles. Motion of any maneuverable structure is affected by environmental/ambient conditions of the medium surrounding it. Thus, such maneuverable structures can use an operative sensor arrangement to measure motion components, forces applied thereto, inter alia, due to the surrounding environmental/ambient conditions, and other parameters indicative of its state/condition. Control unit of the maneuverable structure can use the data/signals measured by the operative sensor arrangement to adjust/correct propulsion forces applied by the maneuverable structure in order to place it in a correct path/trajectory for accurately reaching its target destination.

The techniques disclosed herein can be used to calibrate a numerical model of a maneuverable structure, and adjust it to reflect/describe changes that occur in the maneuverable structure during motion while being in different motion-states. This way a modified numerical model of the maneuverable structure is obtained that can be used to accurately determine/describe elastic mode shapes of the maneuverable structure while in various different motion-states during its motion, in which changes affecting its elastic body properties occur, and thereby enable to filter out artifacts introduced into signals/data measured by operative sensor arrangement of the maneuverable structure due to the elastic deformations thereof during motion. More particularly, the signals/data measured by the operative sensor arrangement of the maneuverable structure combines rigid and elastic body measurement components, but only the rigid body measurement components are needed to properly control the motion of the maneuverable structure. Thus, the elastic body measurement components combined in the signals/data measured by the operative sensor arrangement of the maneuverable structure are referred to herein as undesired artifacts, that can erroneously cause motion control of the maneuverable structure to apply propulsion forces in wrong directions, and thereby deteriorate performance, and even divert the maneuverable structure from its intended path/trajectory. It is a difficult task to correctly determine elastic mode shapes of a moving structure, and particularly in applications wherein the maneuverable structure is subject to changes while in different motion-states during its motion that affect its elastic modal shapes and frequencies. The embodiments disclosed herein can be used to calibrate and modify a numerical model of a maneuverable structure to reflect/describe changes occurring in the maneuverable structure during its motion, based on signals/data a priori obtained from strain gauge and/or acceleration sensors setup coupled to the maneuverable structure during one or more test procedures. Particularly, signals measured in one or more stationary modal excitation test procedures (ground vibration testing - GVT) conducted with the maneuverable structure (or using a prototype thereof) are used to calibrate a numerical model (e.g., finite element model - FEM) of the maneuverable structure, and signals measured during test maneuver(s) conducted with the maneuverable structure (or using a prototype thereof) are used to modify the calibrated numerical model to reflect changes occurring in the maneuverable structure during its motion, thereby enabling accurately determining elastic modal shapes and frequencies of the elastic modal shapes of the maneuverable structure during its motion, as the changes occur therein. Signals/data can be measured by a sensors setup coupled to the maneuverable structure in a first test procedure, while the maneuverable structure is in a free-free suspended state and being subject to structural excitations (e.g., applied by a modal hammer or shaker device). For example, and without being limiting, the sensors setup can be implemented by an array of acceleration or strain sensors attached to/in the maneuverable structure, e.g., by one or more fiber optic Bragg grating sensors. The signals/data measured during the first test procedure can be used to calibrate a numerical model constructed to describe/evaluate physical conditions and/or states occurring in the maneuverable structure in response to external forces. Optionally, but in some embodiments preferably, in a second test procedure signals/data are measured by the same, or by a different, sensors setup, while the maneuverable structure is in various different motion-states during motion, while changes affecting the elastic modal shapes of the maneuverable structure occur therein. The signals/data measured during the second test procedure can be used to adjust/modify the numerical model to also reflect/describe changes occurring in the maneuverable structure while being in various different motion-states, as it is being operatively in motion. The changes occurring in the maneuverable structure during its motion can include changes in the mass/weight of the maneuverable structure e.g., due to discharge of one or more payloads thereby carried and/or fuel consumption, and/or change of shape of one or more elements of the maneuverable structure, and/or changes in center of mass of the maneuverable structure, and/or internal/external loads, and/or any other change that affect elastic modal shapes and frequencies of the maneuverable structure, and any combination thereof. In some embodiments the maneuverable structure is an air vehicle, such as, but not limited to, an air craft, a missile, a launch vehicle, or suchlike, and the numerical model is calibrated to adjust elastic modal shapes of the maneuverable structure, as described by its numerical model, according to the signals/data measured in the first test procedure responsive to the structural excitations. The calibrated numerical model is then adjusted/modified based on the signals/data measured in the second test procedure to also reflect/describe changes occurring in the maneuverable structure during motion, while it is in various different motion-states. In some embodiments the calibrated and adjusted/modified numerical model is used by a flight control unit of the air vehicle to filter out from signals/data measured by operative sensor arrangement of the air vehicle introduced thereto due to elastic modal shapes of the maneuverable structure. Optionally, but in some embodiments preferably, the operative sensor arrangement is implemented by a type of inertia measurement unit (IMU) configured to measure linear and angular motion components of the maneuverable structure. However, the signals/data measured by such operative sensor arrangements superposition elastic body displacements/deformations and rigid body motions of the maneuverable structure, which thus can cause motion/flight control of the maneuverable structure to misinterpret measured signals/data and output undesired propulsion instructions that can steer the maneuverable structure out of its desired path/trajectory. Therefore, in order to accurately control propulsion actuators e.g., engines of the maneuverable structure, the elastic body displacements/deformations components should be removed from the data/signals measured by the operative sensor arrangement, by accurately determining elastic mode shapes of the maneuverable structure in various different motion-states during each and every stage of its motion. In order to accurately discriminate the elastic body displacements/deformations components obtained in the data/signals measured by the operative sensor arrangement, modal frequencies of the maneuverable structure should be identified, and the elastic mode shapes of the maneuverable structure should be determined in each modal frequency. Thus, in some embodiments, the signals/data measured by such operative sensor arrangements is transformed into the frequency domain (e.g., by FFT) for filtering out the elastic mode shapes artifacts. Imprecise evaluation of the elastic mode shapes of the maneuverable structure inevitably deteriorates the performance of the maneuverable structure, and can even divert it away from reaching its target destination. As will be explained hereinbelow in details, the techniques disclosed herein can be used to accurately determine elastic mode shapes and frequencies of a maneuverable structure while it is in motion and subject to various changes affecting its elastic mode shapes. For an overview of several example features, process stages, and principles of the invention, the examples of calibrating and adjusting a numerical model of a maneuverable vehicle illustrated schematically and diagrammatically in the figures are intended for an air craft (e.g., air plane, missiles, launch vehicle). These techniques and their embodiments are shown as one example implementation that demonstrates a number of features, processes, and principles used to accurately determine elastic mode shapes of a moving structure, but they are also useful for other applications and can be made in different variations. Therefore, this description will proceed with reference to the shown examples, but with the understanding that the invention recited in the claims below can also be implemented in myriad other ways, once the principles are understood from the descriptions, explanations, and drawings herein. All such variations, as well as any other modifications apparent to one of ordinary skill in the art and useful for applications of propelling/maneuvering bodies/structures may be suitably employed, and are intended to fall within the scope of this disclosure In a possible embodiment elastic mode shapes of a moving body are determined based on signals/data measured at the beginning and at the end of a test maneuver. The measured signals/data are used to determine respective initial and final elastic mode shapes of the maneuverable structure, which can be then used to estimate (e.g., interpolate) intermediate elastic mode shape occurring during various stages of the movement. For example, if used with an air vehicle, the initial modal properties (i.e., elastic mode shape and frequency) can correspond to a fully fueled state of the vehicle, and the final modal properties can correspond to a full (or near full) fuel consumption state of the vehicle. However, this approach is inaccurate, since it can only provide a general approximation of possible elastic mode shapes of the maneuverable structure during its motion, which is not reliable enough for accurately controlling motion/flight of the maneuverable structure along a desired path/trajectory. The techniques described hereinbelow, and illustrated in the drawings, enable accurately determining elastic mode shapes of a maneuverable platform at any intermediate stage of its motion, by calibrating a numerical model of the structure, such as a FEM, and adjusting/modifying it to also describe/reflect intermediate elastic mode shapes occurring in the maneuverable structure during its motion. This way, the motion/flight control system of the maneuverable structure can reliably filter out elastic displacements/deformations occurring in the maneuverable structure during various stages of its motion/flight and introduced into signals/data measured by its operative sensor arrangement. The disclosed techniques were tested and successfully verified in various different experiments.

Fig. 1A is a flowchart schematically illustrating a process 7 of calibrating a numerical model of a maneuverable structure, and generating a strain to displacement transformation matrix of the maneuverable structure. Initially, a numeric model is constructed for the maneuverable structure, such as, but not limited to, a FEM, that can numerically describe the response of the maneuverable structure to excitations applied thereto. The numeric model expresses stiffness properties of the maneuverable structure, combining materials and geometrical properties thereof (e.g., expressed as Young's modulus of the materials, and inertia moments), and loads/weight (e.g., fuel, payload) thereby carried. The numeric model is constructed in some embodiments using commercially available finite element analysis (FEA) software e.g., NASTRAN™ and ANSYS™. The numerical model of the maneuverable structure is determined in step S0 e.g., using finite element analysis. In step S1 modal analysis of the maneuverable structure (modal excitation test), or a simulation body/prototype thereof, is carried out, during which acceleration vectors data/signals are measured therealong and/or thereabout. The modal excitation test (experimental modal analysis - EMA) aims to find modal frequencies of the maneuverable structure, and the elastic mode shapes of the maneuverable structure in each of the identified modal frequencies. In step S2 the measured acceleration vectors data/signals are processed to determine frequency modes (natural frequencies) of the maneuverable structure, and modal shapes corresponding to the determined frequency modes. Is step S3 the numerical model of the maneuverable structure is calibrated to comply with the modal frequencies and shapes determined in step S2 . The calibrated numerical model is then used in step S4 to extract strain mode vectors (Ψn) and displacement mode vectors (Φn) of the maneuverable structure. The strain mode vectors (Ψn) and displacement mode vectors (Φn) can be computed by specialized computer programs, such as, but not limited to, NASTRAN™ and ANSYS™. In step S5 the extracted strain mode vectors (Ψn) and displacement mode vectors (Φn) are used to construct a strain-to-displacement transformation matrix [ Tds ]. Fig. 1B schematically illustrates a setup 10 for carrying out modal analysis of a maneuverable structure 11 , according to some possible embodiments, utilizing an array of sensors 11s , and excitation device 12 , and a control unit 13 . During the modal excitation test the maneuverable structure 11 should be in a free-free state, which can be achieved to some extent by suspending the maneuverable structure via elastic rubber bands 10a or pressurized air (air cushion/bed), and/or supporting it by soft support means 10b , such as, but not limited to, foam mats, soft cushions, and suchlike. In order to approximate free-free state the modal frequencies of the bands/support cushions/mats should be substantially smaller than (e.g., at least 1/5 of) the first modal frequency of the maneuverable structure 11 . The modal excitation test is carried out using an excitation device 12 , such as, but not limited to, a modal shaker and/or hammer, configured to cause vibrations/shakes in the maneuverable structure 11 by inducing wideband vibrations. An array of acceleration sensors 11s coupled along and/or about the maneuverable structure 11 , is used to generate signals/data 11d indicative of accelerations along and/or about the maneuverable structure 11 in response to the vibrations/shakes caused by the excitation device 12 . Fig. 2 shows graphical plots of strain measurement signals/data obtained in a modal analysis process from twelve sensor elements attached to a tested maneuverable structure 11 in a possible embodiment. The generated signals/data 11d are then processed by the control unit 13 to identify modal frequencies of the maneuverable structure 11 , and to determine for each identified modal frequency a respective elastic mode shape. In some embodiments the control unit 13 is configured to process the generated signals/data 11d to identify only some modal frequencies of interest, and/or modal frequencies within some predefined range, and to determine their respective elastic mode shape. The control unit 13 can be a computerized device comprising one or more processors 13p and memories 13m , and it may be configured and operable to communicate data/signals with the excitation device 12 , for controlling operation of the excitation device 12 . The control unit 13 can also comprises an analysis module 13c configured and operable to determine modal frequencies and shapes of the structure 11 the signals/data 11dgenerated by the sensor array 11s , responsive to the vibrations/shakes caused by the excitation device 12 . Optionally, the modal frequencies and shapes can be determined utilizing specialized computer programs, such as, but no limited to, IMS™, GVT™, MEscope™. A calibration module 13c can be used in the control unit 13 to calibrate the numerical model of the structure ( 11 ) in order for it to properly reflect/describe the modal frequencies and shapes determined in the in the modal analysis by the analysis module 13c .

The numeric model initially constructed (step S0 in Fig. 1A ) is calibrated based on the identified modal frequencies, and the determined respective elastic mode shapes. The calibration can be carried out manually by the researcher, by specialized computer program developed on-sight by the researcher, and/or by commercially available software e.g., NASTRAN™, MEscope™, FEMtools™ , e.g., by correlating the identified modal frequencies, and/or the elastic mode shapes, and/or gains, or any combination thereof. Fig. 3A shows graphical plots of a first mode shape as originally defined/described by the numerical model ( 31a ) and as determined by the modal analysis ( 31b ) in a possible embodiment, Fig. 3B show graphical plots of a second mode shape as originally defined/described by the numerical model ( 32a ) and as determined by the modal analysis ( 32b ) in a possible embodiment, and Fig. 3C show graphical plots of a third mode shape as originally defined/described by the numerical model ( 33a ) and as determined by the modal analysis ( 33b ) in a possible embodiment. The calibration module 13cis configured in some embodiments to fit the modal frequencies and shapes defined/described by the numerical model to the modal frequencies and shapes determined in the modal analysis by the analysis module 13m . The calibrated numerical model obtained after this calibration step can reliably describe/define the maneuverable structure in terms of its modal frequencies and its elastic mode shapes, and can be used to extract strain mode shape vectors (Ψn, n=1,2,…,N, where n>0 and N>0 are integers) and displacement mode shape vectors (Φn) of the maneuverable structure e.g., using specialized computer programs. Fig. 1C is a flowchart demonstrating a process 8 for extracting the mode frequencies and shapes from the generated signals/data ( 11d ), according to some possible embodiments. In step T1 the signals/data ( 11d ) generated by the sensor array ( 11s ) responsive to the vibrations/shakes caused by the excitation device ( 12 ) undergo spectral decomposition, using any spectral decomposition process, such as, but not limited to, fast Fourier transform (FFT), suitable for frequency domain presentation of the signals/data ( 11d) . In step T2 the frequency domain presentation of the signals/data is analyzed to identify therein modal frequencies (Fn), and in step T3 a strain mode vector (Ψn) is constructed for each determined modal frequency. The construction of a strain mode vectors (Ψn) for a specific modal frequency (Fn) can be carried out by combining imaginary components of frequency domain presentation of the signals/data ( 11d ) from the different sensors. This way, for example, if the sensors ( 11s ) are arranged along the length of the structure ( 11 ), combining a sequence of imaginary components of frequency domain presentation of the signals/data ( 11d ) from the lengthwise sequence of sensors provides a lengthwise presentation of the strains along the structure. Alternatively, or additionally, the strain mode vectors (Ψn) are determined from the signals/data ( 11d ) using advanced mathematical techniques e.g., operation displacement shapes, and/or by specialized computer programs, such as, but not limited to, NASTRAN™ and IMS™. Fig. 4A shows strain mode shape plots of a first modal frequency F1 ( Ψ1 ), a second modal frequency F2 ( Ψ2 ), and of a third modal frequency F3 ( Ψ3 ), in a modal analysis process, of a possible embodiment. Fig. 4B shows displacement mode shape plots obtained for the first modal frequency F1 ( Φ1 ), a second modal frequency F2 ( Φ2 ), and of a third modal frequency F3 ( Φ3 ), of a possible embodiment. The [Tds] matrix is constructed from the strain mode shape vectors (Ψn), and the displacement mode shape vectors (Φn), extracted from the calibrated numerical model of the maneuverable structure, which can be expressed as: [Tds] = [ΦN]([ΨN]T[ΨN])-1[ΨN]T. (1) The [Tds] matrix is used in some embodiments to compute the displacements {d} occurring in the maneuverable structure based on measured strain vector {s}, as follows: {d} = [Tds]{s}. (2) Referring now to Fig. 5A , for the test maneuver an array of sensor elements 11s is attached along and/or about the maneuverable structure 11 (or a prototype thereof), for measuring the strain vectors occurring therealong and/or thereabout during the test maneuver 50 . The location of the sensor elements 11s can be determined using any suitable optimization techniques, that are well known to those versed in the field of this application. The sensor elements 11s can be implemented by any suitable strain gauge. During the test maneuver 50 the strain measurement is carried out using a sampling frequency that is greater than the highest modal frequency (Fn) that is of interest for the maneuverable structure 11 . Optionally, but in some embodiments preferably, the sensor elements 11s are implemented by a type of FBG sensors, equipped with respective optical measurement units configured to measure signals indicative of the strains forces occurring therealong and thereabout during the test maneuver. The use of FBG sensors to measure the strain is advantageous in that they substantially lightweight, it is simple and easy to deploy them over the tested structure, they are not affected by temperature changes, they are immune to electromagnetic interferences, and they are not expensive. The maneuverable structure 11 utilizes in some embodiments a control unit 17 , comprising one or more processors 17p and memories 17m , configured and operable to sample the strain signals/data vectors from the sensor elements 11s during the test maneuver 50 . The control unit 17 comprises in some embodiments a transceiver 17t configured to communicate data and/or instructions with a (ground) control center 23 . The control unit 17 can thus store the strain signals/data vectors from the sensor elements 11s in the memory 17m , and optionally process the stored strain signals/data as will be described hereinbelow, and/or transmit the strain signals/data from the sensor elements 11s to the control center 23 for storage and/or processing. Accordingly, the control center 23 comprises a transceiver 23t configured to communicate data and/or instructions with the control unit 17 of the maneuverable structure 11 , and one or more processors 23p and memories 23m , configured and operable to process the strain signals/data vectors as will be described hereinbelow. The strain vectors are measured by the sensor elements 11s at various time instances during the test maneuver 50 in order to collect data indicative of the elastic mode shapes of the structure while changes affecting its elasticity occur. The strain vectors measurements can be thus conducted periodically, continuously, or intermittently whenever such changes can occur. In this specific and non-limiting example a payload 15 of the maneuverable structure 11 changes during the test maneuver 50 . The payload 15 can reflect fuel state of the maneuverable structure 11 , which is fully fueled at the beginning ( I ) of the test maneuver 50 , and as the fuel is gradually consumed during the intermediate stages ( II ), ( III ) and ( IV ), of the test maneuver 50 the fuel level is decreased, and consequently the mass/payload of the maneuverable structure 11 , until the end stage ( V ) of the test maneuver 50 , wherein all of the fuel is consumed, and the fuel tank is emptied. This way, strain vectors signals/data Vs(I),… Vs(II) ,… Vs(III) ,… Vs(VI), ,… Vs(V), are measured for all motion-states of the maneuverable structure 11 .

Claims (25)

264140/ - 26 - CLAIMS:

1. A method of determining elastic mode shapes of a moving structure during its motion, the method comprising: generating a repository of elastic mode shapes occurring in said moving structure based on strains measured during different motion-stages of said moving structure, or of a simulating structure thereof, each of said elastic mode shapes associated with a certain motion-stage of the moving structure during its motion; identifying a motion-stage of the moving structure during said motion; performing a test maneuver of either said structure, or of a simulating structure thereof, measuring strains in said structure, or its simulating structure, by a plurality of sensors elements during motion thereof in said test maneuver, and determining the elastic mode shapes of for the repository of elastic mode shapes from the measured strains; and extracting from said repository of elastic mode shapes a respective elastic mode shape based on the identified motion-stage of the moving structure, the extracted elastic mode shape is indicative of elastic deformations in said moving structure while at the identified motion-stage; wherein, the method comprises determining a respective modal frequency for each of the determined elastic mode shapes, and associating each of said elastic mode shapes in said repository of elastic mode shapes with its respective modal frequency.

2. The method of claim 1 wherein at least one property of the structure, or of its simulating structure, is being changed during the motion in the test maneuver, and wherein the measuring of the strains is carried out at a plurality of motion-stages during said motion such that said measured strains are affected by said at least one property change.

3. The method of claim 2 comprising processing the measured strains obtained at each of the plurality of motion-stages to determine strain mode shapes of said structure, or of its simulating structure, at said plurality of motion-stages, and using a numerical model associated with said structure, or its simulating structure, for the determining of the elastic mode shapes from the determined strain mode shapes 264140/ - 27 -

4. The method of claim 3 comprising associating at least one of the elastic mode shapes with a respective one of the motion-stages.

5. The method of any one of claims 3 and 4 wherein the processing of the measured strains comprises performing spectral decomposition to obtain frequency components of the measured strains.

6. The method of claim 5 wherein the determining of the strain mode shapes is based on imaginary portions of the frequency components of the strains measured by the sensors elements at a respective motion-stage in the test maneuver.

7. The method of any one of claims 5 and 6 wherein the spectral decomposition comprises a fast Fourier transform.

8. The method of any one of claims 3 to 7 comprising carrying out modal analysis to determine modal frequencies and shapes of the structure, or of its simulating structure, and calibrating the numerical model based thereon.

9. The method of claim 9 comprising using the calibrated numerical model for determining a respective strain mode shape, and a respective displacement mode shape of the structure, or of its simulating structure, for of the determined modal frequencies and shapes.

10. The method of claim 9 comprising constructing a transformation matrix from the determined strain mode shapes and their respective displacement mode shapes, said transformation matrix is used for the determining of the elastic mode shapes from the determined strain mode shapes.

11. The method of any one of claims 3 to 10 wherein the numerical model is based on a finite element model of the structure, or of its simulating structure. 264140/ - 28 -

12. The method of any one of claims 3 to 11 wherein the plurality of sensors elements comprises a fiber Bragg grating sensor.

13. The method of any one of claims 3 to 12 wherein the at least one property change comprises a changes in a mass, in an amount of fuel, in a shape, state of control surfaces, and/or center of mass, of the structure or of its simulating structure.

14. The method of any one of the preceding claims wherein the moving structure is a sea vehicles, a land vehicle, a space vehicles, or an air vehicle.

15. The method of any one of the preceding claims wherein the structure is an airplane, a missiles, or a launch vehicle.

16. A mode shape filtering system comprising: an input unit configured and operable to receive measurement data from a sensor system of a maneuverable structure, said measurement data comprising motion data indicative of deformations and/or displacements occurring in said maneuverable structure during its motion, and motion-state data indicative of at least one property of the maneuverable structure that is subject to changes during the motion; a repository of elastic mode shapes occurring in said maneuverable structure and derived from strains measured during different motion-stages of said maneuverable structure, or of a simulating structure thereof, each of said elastic mode shapes associated with a certain motion-stage of the maneuverable structure during its motion; a processing unit configured and operable to obtain from the repository of elastic mode shapes an elastic mode shape associated with the motion-state data; and a filtering unit configured to remove from the motion data components associated with the elastic mode shape obtained from said repository and generate respective filtered motion data wherein the system is configured to provide the filtered motion data to a motion control system of the maneuverable structure for applying adjustments in motion control of said maneuverable structure, and wherein the input unit is configured to receive from the sensor system new measurement data comprising new motion data indicative of deformations and/or displacements occurring in said maneuverable structure during its 264140/ - 29 - motion responsive to said motion control adjustments, and new motion-state data indicative of at least one property of the maneuverable structure that is subject to changes during the motion, and wherein said processing unit is configured to obtain from the repository of elastic mode shapes a respective elastic mode shape associated with said new motion-state data; and wherein the filtering unit is configured to remove from the new motion data components associated with the elastic mode shape obtained from the repository of elastic mode shapes based on the new motion-state data.

17. The system of claim 16, wherein at least one property of the maneuverable structure that is subject to changes during the motion comprises at least one of the following: internal aero-dynamic loads of the maneuverable structure, external aero-dynamic loads of the maneuverable structure, a payload of the maneuverable structure, state of control surfaces of the of the maneuverable structure, amount of fuel of the maneuverable structure, center of mass of the maneuverable structure, and/or a shape factor of the maneuverable structure.

18. The system of any one of claims 16 to 17 wherein the maneuverable structure is a sea vehicles, a land vehicle, a space vehicles, or an air vehicle.

19. The system of any one of claims 16 to 18 wherein the maneuverable structure is an airplane, a missiles, or a launch vehicle.

20. A motion control system comprising a control unit configured and operable to: receive location data from a position determining system of a maneuverable structure, said location data being indicative of a current location of said maneuverable structure during its motion; receive destination data from a destination determining system of said maneuverable structure, said destination data being indicative of a destination of said maneuverable structure; determine a direction of motion of the maneuverable structure for causing it to reach said desired destination, receive from a mode shape filtering system 264140/ - 30 - filtered motion data of the maneuverable structure, and generate motion control data based at least partially on said filtered motion data wherein said mode shape filtering system comprising: an input unit configured and operable to receive measurement data from a sensor system of a maneuverable structure, said measurement data comprising motion data indicative of deformations and/or displacements occurring in said maneuverable structure during its motion, and motion-state data indicative of at least one property of the maneuverable structure that is subject to changes during the motion; a repository of elastic mode shapes occurring in said maneuverable structure and derived from strains measured during different motion-stages of said maneuverable structure, or of a simulating structure thereof, each of said elastic mode shapes associated with a certain motion-stage of the maneuverable structure during its motion; a processing unit configured and operable to obtain from the repository of elastic mode shapes an elastic mode shape associated with the motion-state data; and a filtering unit configured to remove from the motion data components associated with the elastic mode shape obtained from said repository and generate respective filtered motion data.

21. The motion control system of claims 20 wherein the destination determining system comprises a communication device configured to receive the destination data by transmission over a communication channel.

22. A system for generating a repository of elastic mode shapes occurring in a moving structure during its motion, the system comprising: a structure properties determining unit configured to determine various properties of the moving structure and generate structure data indicative thereof; a modeling unit configured to generate a numerical model associated with said maneuverable structure based at least in part on said structure data; an analysis unit configured to determine modal properties of said maneuverable structure based on acceleration data indicative of accelerations measured in said maneuverable structure in response to excitations thereof in a free-free supported state, calibrate said numerical model based on said modal properties, and determine from the 264140/ - 31 - calibrated numerical model a transformation between strain and displacements associated with said maneuverable structure; and an elastic mode shapes determining unit configured to receive strain data indicative of strains measured in said maneuverable structure, or a simulating structure thereof, during different motion-stages thereof, use the determined transformation to generate from said strain data a displacement data of said repository being indicative of elastic mode shapes of said maneuverable structure, or its simulating structure, during its motion.

23. The system of claim 22 wherein the elastic mode shapes determining unit is configured to determine for each elastic mode shape a respective modal frequency, and associate each elastic mode shape in said repository of elastic mode shapes with its respective modal frequency.

24. The system of any one of claims 22 to 23, comprising a motion-stage determining unit configured to receive at least one measured property of the maneuverable structure, or of its simulating structure, associated with the measured strains, said property is subject to changes during the motion in the test maneuver, and determine based thereon a respective motion-state indicator for each of the determined elastic mode shapes in said repository of elastic mode shapes.

25. The system of any one of claims 22 to 24 implemented by computer executable instructions of a computer program product.