31 results about "Sensitivity equation" patented technology

The invention discloses a voltage out-of-limit adjusting method in the technical field of power supply system control. The voltage out-of-limit adjusting method comprises the following steps of: obtaining power flow interface data and determining nodes which take part in voltage adjustment; calculating power flow distribution of a power supply system according to the power flow interface data, so as to obtain voltage of each node; correcting and checking each node which takes part in the voltage adjustment, determining a voltage out-of-limit node and the voltage out-of-limit node with a maximum voltage out-of-limit value, and recording the node with the maximum voltage out-of-limit value as a node N*; carrying out sensitivity analysis on the node N*, calculating a reactive voltage sensitivity matrix of all the nodes which take part in the voltage adjustment to the node N*, and determining adjustment equipment taking part in the voltage adjustment; establishing a comprehensive sensitivity equation and calculating an adjustment amount of each adjustment equipment taking part in the voltage adjustment; adjusting each adjustment equipment taking part in the voltage adjustment according to the adjustment amount; calculating the adjusted voltage of each node; and if no voltage out-of-limit node exists, stopping adjusting. According to the voltage out-of-limit adjusting method disclosed by the invention, the adjustment capacity of the adjustable equipment can be rapidly and accurately calculated, and the security and the reliability of the power supply system are improved.

The invention discloses a finite element model correction method based on a positive substructure. The finite element model correction method includes the steps: firstly, dividing an integral structure finite element model into independent substructure models; building an integral structure characteristic equation according to the substructure models to obtain an integral structure characteristic solution; building an integral structure characteristic sensitivity equation according to the integral structure characteristic equation to obtain an integral structure characteristic solution sensitivity matrix; building a target function according to residual errors of the integral structure characteristic solution and a measured integral structure test mode; adjusting structural parameters of the substructure and minimizing the target function to obtain optimal structural parameters; adjusting structural parameters of the finite element model and correcting the finite element model; recognizing structural damage according to change of result parameters of the finite element model. When a structure is locally damaged and a local area needs to be corrected, large structure finite element model correction efficiency and precision are effectively improved only by iteratively analyzing the local substructure models without repeatedly analyzing the integral structure model.

The invention discloses a method for calibrating an airborne interference synthesis aperture radar (SAR) under the squint condition. By the method, the problems of insufficient calibration accuracy and unstable and unreasonable calibration result in the calibration of the airborne interference SAR are solved. The method comprises the following steps of: calculating squint angles at which calibration points are positioned by geometrical relationship between the calibration points and a main antenna; establishing a system delayed calibration equation under the squint condition according to processing geometry which is adopted in a squint SAR imaging algorithm, and completing the calibration of system delay by utilizing the obtained squint angles; establishing a target elevation equation under the squint condition according to the squint geometrical relationship of the interference SAR, solving partial derivatives of interference parameters to obtain an elevation sensitivity equation, and establishing a squint interference calibration model; and substituting initial interference parameters, airborne interference SAR elevation measuring values and elevation information of the calibration points into the squint interference calibration model to obtain a calibration equation set, so that interference parameter errors are calculated.

Provided is a static equivalence method of an external network in an interconnected power grid. The static equivalence method comprises a static equivalence model which is established on a boundary and provided with a non-generator node; two sensitivity equations before and after equivalence are equaled; and a virtual generator voltage, an equivalence injection current, an equivalence branch to ground and the like are deduced after static equivalence of the external network. In the aforementioned computation processes, the boundary of the static equivalence model is additionally provided with the equivalence branch to ground of the non-generator node of the boundary. A maximum safety error and a relative error of a line inactive injection power and an active injection power of an internal network are both improved, and a node maximum voltage amplitude relative error in the internal network is also improved so that higher static equivalence accuracy of the external network is obtained, and static safety analysis on the internal network can be better performed. When static safety analysis is performed on the internal network, a more accurate current value is also obtained.

The invention belonging to the field of the rotating shaft error measuring instrument of the non-contact R-test five-axis numerical control machine tool discloses a structural parameter optimization method for a non-contact R-test measuring instrument. The method comprises: step one, establishing a structural model of a non-contact R-test measuring instrument with an eddy current displacement sensor and preprocessing a coordinate of the structural model; step two, constructing a measurement sensitivity equation based on induced voltages measured in the step one and by the sensor to obtain a sensor elevation angle corresponding to sensitivity maximization; step three, calculating a measurement constraint equation of each sensor based on the structural model with the maximum sensitivity; andstep four, calculating the number, being the measuring space volume, of measuring points meeting a measurement constraint equation simultaneously and then acquiring a sensor central space corresponding to measuring space maximization, thereby completing the structural parameter optimization. Therefore, problems of low sensor reading sensitivity and low measuring precision of the existing contactR-test measuring instrument due to the contact wearing and the mechanical structure are solved; and the accurate measurement of the measuring instrument is realized.

The invention discloses an optimal arrangement method for urban water supply pipe network flow monitoring points. The method comprises the following steps that a water supply pipe network hydraulic model is constructed; a water supply pipe network flow monitoring point optimal arrangement model is constructed, constraint conditions of the model are a pipe network node flow continuity equation, a pipe network node water pressure constraint condition and a pipe network energy conservation equation, and a sensitivity equation of pipe network node flow to pipe network node pressure is established;Pearson correlation analysis on the sensitivity equation is adopted in the optimized arrangement model for calculating the flow monitoring points of the water supply pipe network, a simple normalization equation is solved, the arrangement positions of the pressure monitoring points and strong correlation points of the pressure monitoring points are solved, and an optimal flow monitoring point scheme is determined. According to the method, the arranged pressure monitoring points can well reflect the change condition of the node pressure, the reliability of the monitoring points is improved, meanwhile, the node range capable of being monitored by each pressure monitoring device can be determined, the requirements for representativeness, comparability and feasibility of point distribution are met, and blindness of selection of the pressure monitoring points at present is reduced.

The invention discloses a building framework structure damage detection method. The method comprises the following steps of: firstly, testing a framework structure before being damaged to obtain a structural modal parameter (omega 0, phi 0); then, testing the damaged structure, and performing modal analysis to obtain a modal parameter (omega D, phi D); establishing a first-order modal parameter sensitivity equation S1D'=delta f and a second-order modal parameter sensitivity equation S1D'+S2D''=delta f; calculating first-order and second-order modal parameter sensitivities by adopting an improved modal truncation method; and solving a unit damage coefficient Di (i is 1, 2...n) by using a first-order and second-order sensitivity equation-based mixed iteration solving method so as to fulfill the purpose of simultaneously identifying the number, position and size of damages of the whole building structure. The method is suitable for damage detection of the building framework structure, saves the calculation workload, has high efficiency, and greatly improves the detection precision.

The invention relates to a method for generating testing vectors of an artificial circuit. The method for generating the testing vectors of the artificial circuit comprises the steps of carrying out testability analysis on the circuit to be tested, namely the optimum testing node set of the circuit to be tested is selected from valid testing nodes according to a testability measurement value T of the circuit to be tested, and when the testability measurement value T is smaller than the number of circuit elements in the circuit to be tested, regular ambiguity sets are determined and at most one element is selected from each set to serve as the element to be diagnosed; establishing the sensitivity equation of each testing point in the optimum testing node set according to the variance (y(t)-y'(t)) <2> and obtaining a needed testing vector set by calculating the frequency of the extreme point of a flexibility curve, wherein y(t) is the normal output of each testing node and the y'(t) is the fault output of each testing node; deleting part of the testing vectors in the testing vector set to optimize the number of the testing vectors. The method for generating the testing vectors of the artificial circuit has the advantages that the complexity of calculation and processing is reduced, and the fault diagnosing speed is improved. The method for generating the testing vectors of the artificial circuit is particularly suitable for being used for testing and diagnosis of large-scale analogue integrated circuits.

The invention discloses a structural damage identification method based on subspace projection and sparse regularization, comprising the following steps: (1) arranging an acceleration sensor structurally for recording structural response information; (2) arranging a force sensor at the excitation point, performing the experimental modal analysis on the structure under the lossless state and the structure under the damage state separately, and extracting structural modal information; (3) establishing a sensitivity equation; (4) constructing a measurement matrix that satisfies the D-RIP condition; (5) performing subspace projection on the sensitivity equation; (6) introducing l1 norm regularization to establish a structural damage identification equation; (7) solving the recognition equationby using the signal space compression sampling matching tracking algorithm; (8) introducing damage prior information to rationalize the recognition results. According to the structural damage identification method based on subspace projection and sparse regularization, the damage is effectively located and the damage degree is quantified, the computational cost of the solution process is reducedeffectively, and the needs of assessing the structural health status timely and effectively in actual project are satisfied.

The invention relates to a shape optimization method for an I-beam two-dimensional model, and the method comprises the steps: firstly, employing an NURBS spline to give a two-dimensional body parameterization model of an I-beam, and enabling parameters to comprise an NURBS coordinate point, a weight and the like; giving a shape optimization target equation and constraint conditions, deriving a sensitivity equation with control points and weights as design variables and achieving shape optimization design of the I-beam two-dimensional model by optimizing the two parameters. According to the method, the geometric model is constructed by adopting the NURBS spline, and the shape of the geometric model can be expressed more accurately. Seamless combination of the CAD system model and the CAE system model is realized by adopting an isogeometric analysis method. The advantages and characteristics of the spline model are integrated, the geometric analysis method is effectively applied to structural boundary shape optimization, the analysis process and the optimization process are integrated, the optimization accuracy and the calculation efficiency are improved, and a smooth model boundaryshape can be expressed more accurately.

The embodiment of the invention discloses a frequency domain finite element model correction method based on a reduced basis, and relates to the field of dynamic finite element model correction, and the method comprises the steps: carrying out vibration test of a bogie structure, obtaining a measurement frequency response function, and converting the measurement frequency response function to a reduced coordinate through a basis matrix; establishing an initial finite element model of the structure, and calculating a frequency response function analysis value under reduced coordinates; and calculating a residual error of an analysis value and a measurement value of the frequency response function under the reduced coordinates and a sensitivity matrix of the frequency response function relative to a to-be-corrected parameter, solving a corresponding sensitivity equation to obtain an updated parameter and a finite element model, and taking the updated parameter and the finite element model as an initial finite element model for repeated iteration until the residual error is minimum. The invention is suitable for the correction problem of the bogie finite element model with a large number of degrees of freedom, the calculation efficiency can be remarkably improved on the premise that the precision is guaranteed, and therefore the dynamic finite element model of the bogie structure is efficiently corrected through actual test data.

The invention discloses a method of analyzing structural reliability of an aeroengine turbine disc; a random variable mathematical model is established according to non-uniformity of turbine disc material, and a stress analysis model is established according to stress condition; PDS (probabilistic design system) in ANSYS environment is used to perform Monte Carlo sampling on random variables of a turbine disc three-dimensional model to obtain maximum stress MAXSTRESS distribution of the turbine disc under different conditions; Monte Carlo simulation tests of different levels are performed on the random variables on MATLAB (matrix laboratory) platform, and reliability of the turbine disc is calculated according to structural functions to obtain the structural reliability of the turbine disc under different conditions; sensitivity of the random variables influencing the structural reliability of the turbine disc is calculated according to sensitivity equation. The method has the advantages of high convergence speed, low cost and high precision, and theoretical basis is provided for the optimal design and reliability management for a turbine disc.

A design supporting apparatus includes a detecting unit that detects a path constituting a circuit from circuit information of the circuit; a sensitivity-equation producing unit that produces a calculating equation for a sensitivity indicating a change rate of a parameter regarding a delay of a circuit element constituting the path, for every path detected; and an element-sensitivity calculating unit that calculates a sensitivity of the circuit element by using the calculating equation produced.

The invention discloses a sensitivity-based method to recognize overall damage of a bridge; the method comprises the steps of 1, calculating a cross-correlation function of a node between healthy-state response and actual response; 2, giving a damage factor and simulating response of the node of a bridge structure; 3, calculating a cross-correlation function of the node between the simulated response and the healthy-state response and its sensitivity; 4, constructing a sensitivity formula to solve damage factor increment; 5, judging whether convergence occurs; if not, correcting the damage factor, and repeating the steps 2 to 4; 6, if yes, ending iteration to obtain a damage vector of the bridge structure. The method of the invention has the advantages that damage recognition is performedon the bridge structure, a complete sensitivity-based damage recognition process is established, monitoring data are analyzed directly, information loss during data processing is decreased, and the monitoring data is worthier of practical application.

The invention discloses a structure corrosion two-stage detection method and system based on rapid vibration testing, and the method comprises the steps: judging the strain flexibility of a structureaccording to the strain response and impact force time history of a long-scale-distance FBG sensor, positioning a corrosion part through employing the strain flexibility difference of the structure before and after corrosion, and achieving the corrosion positioning of a first stage; after the corrosion part is determined, reducing the rigidity of the unknown parameter to be identified of the structure from the rigidity of all units to the rigidity of the corrosion unit, establishing a sensitivity matrix for the structural section rigidity based on the long gauge length strain flexibility, solving the rigidity of the structural corrosion unit according to a sensitivity equation, and judging the corrosion amount according to the rigidity change; meanwhile, forming a two-stage strategy structure corrosion detection system based on rapid vibration by a rapid detection vehicle, a data acquisition system and a data analysis system which are matched with an impact device, wherein the two-stage strategy structure corrosion detection system is mainly used for current safety state evaluation and long-term performance evaluation of the structure, high in test precision and high in noise resistance, and can realize long-term monitoring of structure corrosion.

The invention discloses a differential interference phase-based along track interferometric SAR baseline calibration method. The method includes the following specific steps that: an along track interferometric SAR baseline calibration system including an SAR image interference module, an interference phase estimation module, a sensitivity equation module and a precision judgment module is constructed; a range direction corresponding to a certain orientation moment is selected according to a predetermined flight path, and N static corner reflectors are arranged evenly as much as possible in acalibration field, wherein N is larger than or equal to 3; the SAR image interference module acquires the differential interference phases of the calibration points; the interference phase estimationmodule estimates differential interference phases between adjacent calibration points; the sensitivity equation module calibrates baseline component error; and the accuracy judgment module judges whether accuracy meets a requirement. With the method of the invention adopted, the influence of interference phase offset error on baseline calibration accuracy is eliminated, and the calibration accuracy of the baseline component of the system can be improved.

The invention discloses a method for positioning an active load voltage sag source. The method comprises the following three steps of identifying upstream and downstream active parameters by using a Thevenin theorem-based multi-point method to obtain a voltage sensitivity equation of the upstream and downstream parameters at a monitoring point, and introducing a weight idea to perform quantitativeanalysis on upstream and downstream positioning of the voltage sag source. According to the method for positioning the active load voltage sag source based on the multi-point method and the sensitivity, the weight idea is introduced to carry out quantitative analysis on the upstream and the downstream of the voltage sag source, and the confidence coefficient of a positioning result is improved.

The invention discloses a method for calibrating an airborne interference synthesis aperture radar (SAR) under the squint condition. By the method, the problems of insufficient calibration accuracy and unstable and unreasonable calibration result in the calibration of the airborne interference SAR are solved. The method comprises the following steps of: calculating squint angles at which calibration points are positioned by geometrical relationship between the calibration points and a main antenna; establishing a system delayed calibration equation under the squint condition according to processing geometry which is adopted in a squint SAR imaging algorithm, and completing the calibration of system delay by utilizing the obtained squint angles; establishing a target elevation equation under the squint condition according to the squint geometrical relationship of the interference SAR, solving partial derivatives of interference parameters to obtain an elevation sensitivity equation, and establishing a squint interference calibration model; and substituting initial interference parameters, airborne interference SAR elevation measuring values and elevation information of the calibration points into the squint interference calibration model to obtain a calibration equation set, so that interference parameter errors are calculated.

The invention relates to a generator dynamic characteristic excitation degree evaluation method based on measurement data quality inspection. The method comprises the following steps: firstly, analyzing generator sub-transient parameter identifiability based on measurement data interval inspection, establishing correlation between a disturbance data sampling interval and excited dynamic characteristics of a generator, and proposing a requirement specification for the real-time performance of PMU device data; and secondly, analyzing the dynamic characteristic excitation degree of the generatorbased on measurement data disturbance depth inspection, and constructing an evaluation system of the dynamic characteristic excitation degree of the generator by establishing a sensitivity equation ofthe relationship between the measurement disturbance data and transient and sub-transient information, thereby realizing the selection of an identification disturbance data band. The effectiveness ofmeasurement data can be effectively identified, and the identification precision of the practical parameters of the generator is improved.

The invention discloses a structural damage identification method based on subspace projection and sparse regularization, comprising the following steps: (1) arranging an acceleration sensor structurally for recording structural response information; (2) arranging a force sensor at the excitation point, performing the experimental modal analysis on the structure under the lossless state and the structure under the damage state separately, and extracting structural modal information; (3) establishing a sensitivity equation; (4) constructing a measurement matrix that satisfies the D-RIP condition; (5) performing subspace projection on the sensitivity equation; (6) introducing l1 norm regularization to establish a structural damage identification equation; (7) solving the recognition equationby using the signal space compression sampling matching tracking algorithm; (8) introducing damage prior information to rationalize the recognition results. According to the structural damage identification method based on subspace projection and sparse regularization, the damage is effectively located and the damage degree is quantified, the computational cost of the solution process is reducedeffectively, and the needs of assessing the structural health status timely and effectively in actual project are satisfied.

The invention discloses a compressible turbulent fluid topological optimization method based on automatic differentiation, and relates to topological optimization. The method comprises the steps: establishing a geometric model corresponding to flow channel topological optimization; acquiring the basic parameters of a topological optimization object, and constructing a CFD topological optimization model; constructing a target function according to the basic parameters, and forming a nonlinear programming problem; deriving a sensitivity equation based on an adjoint method; solving the fluid control equation to obtain a flow field result and a value of a target function, and outputting a new flow field result; building a Jacobian matrix and a gradient vector by using an automatic differential technology; establishing a matrix form adjoint equation to obtain an adjoint multiplier; substituting the new flow field result and the adjoint multiplier into a sensitivity equation to solve the sensitivity; establishing a mathematical model by using an MMA numerical optimization method in combination with a nonlinear programming problem; carrying out optimization solution on the flow channel, updating design variables to obtain an optimal solution, and outputting an optimal two-dimensional topological configuration. And the problems of insufficient flexibility, tedious process, error proneness and the like of manual derivation of a compressible fluid accompanying equation are avoided.

The invention discloses a method for determining heat source model parameters of single wire submerged arc welding numerical simulation. The method comprises the following steps: I, establishing a double ellipsoid heat source model to obtain a heat flux density distribution function; II, establishing a finite element model to simulate a temperature field, and taking a set of welding voltage, welding current, welding speed and welding angle which is matched with single wire submerged arc welding as a base parameter of simulation to obtain a set of appropriate double ellipsoid heat source model parameters based on experimental results; III, adjusting the double ellipsoid heat source model parameters obtained in step II by 10%, and implementing finite element numerical simulation on each parameter combination to obtain multiple sets of sample values of weld width and weld penetration so as to determine sensitivity equations of the double ellipsoid heat source model parameters and the welding speed to the weld width and weld penetration; IV, ignoring the parameters that affect the sensitivity equations slightly to obtain the simplified sensitivity equation; and V, promoting and verifying the equations. Compared with a traditional method for artificially searching the heat source model parameters, the method disclosed by the invention is high in efficiency and can be used for greatly reducing the calculating time.

The present invention discloses a corrected sensitivity structural damage recognition method based on a joint index and finite information. The method comprises: firstly, characterizing a damage and an error by setting an element stiffness coefficient and a modeling error coefficient; secondly, calculating a displacement-frequency joint index based on a static and dynamic result and correcting the joint index; afterwards, extracting finite information to construct a displacement-frequency sensitivity matrix and correcting the matrix; then, calculating a change amount of element stiffness by using the corrected sensitivity matrix and the joint index; and finally, changing a model error coefficient to calculate results of different errors. The corrected sensitivity structural damage recognition method based on the joint index and the finite information provided by the present invention is based on a static and dynamic joint index, considers the finite information and by correcting a sensitivity equation, ensures that each term of a sensitivity matrix can reflect joint information of a degree of freedom in static displacement sampling and a natural frequency sampling order. The method provides a reference for a recognition operation on a dynamic and static information joint damage of a large and complex structure, and explores a new solution for a damage recognition operation where a plurality of degrees of freedom only have finite sample information.

The invention discloses a structural response acquiring method based on substructures and a sensitivity acquiring method. The structural response acquiring method includes: dividing an overall structural finite element model into independent substructure models unrelated to one another; acquiring the main mode of each independent substructure model, building an overall structural dynamics vibration equation according to the main modality, equivalent residual quantity and load in a time domain range, and acquiring the structural response of the overall structure according to the overall structural dynamics vibration equation. The structural response acquiring method and the sensitivity acquiring method have the advantages that the dynamics vibration equation and response sensitivity equation of the overall structure are represented by a small number of low-order modes, and the contribution of high-order modes are compensated by one equivalent residual quantity; due to the fact that thedimension of the equations is equal to the number of the reserved low-order modes, and the dimension of the equations is reduced greatly; accordingly, the provided substructure method can efficientlyand precisely calculate structural response and the sensitivity thereof.

The invention discloses a parameter measurement method and device for a hysteresis system containing a Jenkins unit and a medium. The measurement method comprises the following steps: determining a kinetic equation, a kinetic response sensitivity equation and a real acceleration response; and setting a parameter initial value, solving a response sensitivity equation according to the real acceleration response and the parameter initial value, obtaining a parameter increment, executing a plurality of iterative processes, updating system parameters, returning the obtained parameters when the iterative processes meet an end condition, and the like. When the system of the hysteresis system is measured, the conditions of various hysteresis components are analyzed on the whole level, so that theparameters of all the hysteresis components in the hysteresis system containing the Jenkins unit can be identified at one time. The invention is low in requirements for measurement time and measurement step length, and can adapt to the conditions that a hysteresis system contains a plurality of hysteresis components, and the hysteresis components may influence one another. The invention is widelyapplied to the technical field of computer assistance.

The invention discloses a reactive voltage control sensitivity analysis method aiming at scaled wind power. The method comprises the following steps that a system sensitive equation is calculated; a Jacobi matrix including the studied node power or the voltage sensitivity information is calculated; the sensitivity control is carried out by aiming at the response features of each wind power plant. On the premise of ensuring the safe and economic operation of an electric network, the goals of greatly improving the receiving and sending capability of the electricity network on new energy sources, reducing the wind curtailment and improving the new energy online electricity quantity are achieved.

The invention relates to a phase-shift interference information processing method based on error compensation, and belongs to the technical field of optical detection and digital information processing. The method detects the sensitivity equation of a random error source to phase-shift interference measurement based on phase-shift laser interference, obtains a constraint equation set through adding a to-be-determined weight to a least square method, and determines a weight through solving the constraint equation set, thereby determining the phase-shift interference information processing method which is not sensitive to the error source. The method is based on the thought of error compensation, can eliminate the impact on phase-shift interference detection from various types of error sources, remarkably improves the repeatability, reproducibility and precision of a phase-shift laser interferometer, and facilitates the application of the technology of the phase-shift laser interferometer in high-precision optical detection.

The invention provides a distributed power supply acceptance capability uncertainty analysis method and device, and a medium. The mapping relation between the multivariate uncertainty factors and the voltage sensitivity in the power distribution network of the distributed power supply is quantified by adopting interval mathematics and affine mathematics, so that the method has the advantages that upper and lower bounds of uncertain variables of an interval method are easy to obtain, the model is simple, the applicability is high, the solving speed is high and the like; the method also has the advantages of the affine method in the aspect of tracking the correlation and coupling of multivariate uncertain variables; the affine three-phase voltage sensitivity equation based on the Jacobian matrix is deduced, and the random scene simulation method based on Monte Carlo is combined, so that the accuracy and rapidity of the acceptance capability analysis of the distributed power supply of the power distribution network are considered; and meanwhile, the possibility is provided for assisting distribution network planners to carry out on-line rapid analysis and comprehensive and accurate decision-making on the acceptance capability of the distributed power supply. Compared with an existing distributed power supply acceptance capability analysis method, the method has better performance effects and remarkable theoretical value and practical significance.

The invention discloses a method for detecting sensitivity of a transient non-uniform temperature field in an object by using ultrasonic waves. According to the correlation between propagation time and temperature of the ultrasonic waves in a base metal to be tested at different temperature, and overall measuring time obtained by an ultrasonic pulse echo method and the ultrasonic wave propagation time at the corresponding time, solving heat conduction problem based on a sensitivity equation, optimizing obtained equivalent temperature boundary conditions to minimize the difference value between the measured ultrasonic wave propagation time and the propagation time obtained by numerical simulation, heat conduction through direct problem solving can get the temperature distribution inside the specimen state at different times. Fast and accurate access the advantages of metal or metal alloy surface temperature and internal non-uniform temperature field. The method is used for real-time measurement of the metal or alloy surface temperature and the temperature of the internal transient non-uniform temperature field.