Parameter Identification Procedure Research Articles

Modeling of residual stiffness phenomenon in modified Iwan model of bolted joints and its application

Bolted joints have been widely used in various mechanical structures. Due to the presence of contact interfaces, the joints exhibit complex nonlinear behavior under dynamic loading. Effective prediction of the dynamic response of bolted structures requires the construction of appropriate dynamic models. This paper proposes a modified Iwan model which gives a more comprehensive description of joints than the previous Iwan models, especially for the phenomenon of residual stiffness in macro slip. The equations of the model’s backbone curve, hysteresis curve, and energy dissipation are derived. The parameter identification procedure is also provided. Subsequently, connection elements based on the modified Iwan model are integrated into a single bolted joint and a thin-walled cylinder containing multiple bolted joints, the responses under quasi-static unidirectional loading, quasi-static cyclic loading and constant-frequency excitation are investigated. The physical interpretation of the parameters in the model is discussed, thus explaining the relationship between the bolted joint’s physical parameters and some important variables. The results indicate that the model can effectively characterize the nonlinear mechanical behavior of the bolted joint for both micro and macro slip regime, with significant improvement in computational efficiency.

A novel scale-bridging method for MSMA linking continuum thermodynamics constitutive formulations to lumped system-level models

This work introduces a novel scale-bridging method between a continuum thermodynamics constitutive model and a lumped system-level model for magnetic shape memory alloys (MSMA). With this method, system models for real-time operations are generated based on virtual experiments using the constitutive model. The proposed method addresses the fact that, while constitutive models for MSMA typically only require small sets of parameters as input, their evaluation is still computationally expensive. System models for control engineering, however, require extensive experimental parameterization, while their evaluation is highly time-efficient. The proposed scale-bridging method has the potential to combine a small parameterization effort and a low computational cost of the real-time system model. Additionally, the constitutive model is utilized to investigate whether it can determine the individual behavior of MSMA samples. This is important since the inherent model parameters, while valid for ideal single crystals, deviate for non-ideal MSMA sample behavior. To this end, the MSMA constitutive model, based on a global variational principle originally proposed by Kiefer et al is supplemented by various extensions, including a more robust algorithmic treatment. A parameter identification procedure is introduced to optimize the constitutive model parameters based on an outer hysteresis curve for a particular load case. By conducting virtual experiments with the constitutive model, data sets are generated to parameterize Preisach hysteresis models as numerical approximations of the constitutive models. The resulting hysteresis models are compared with physical experiments using an MSMA test bench for different load cases. It is shown that the proposed scale-bridging method successfully generates hysteresis models derived from constitutive models. While maintaining accuracy comparable to strictly phenomenological models across various load cases (as validated through physical MSMA test bench experiments), these models require significantly less parameterization effort than classical system models. This translates to faster model creation and broader applicability.

Crow Search Algorithm for Modelling an Anaerobic Digestion Process: Algorithm Parameter Influence

Corn steep liquor is a waste product from the process of treating corn grain for starch extraction. It is used as a substrate in anaerobic digestion with simultaneous hydrogen and methane production in a cascade of two anaerobic bioreactors. For process research and optimisation, adequate mathematical models are required. So, the authors aim to present a high-quality model of the corn steep liquor process for the sequential production of H2 and CH4. This paper proposes a technique for identifying the best mathematical model of the process using the metaheuristics crow search algorithm (CSA). The CSA was applied for the first time to mathematical modelling of the considered two-stage anaerobic digestion process, using real experimental data. Based on the analysis of the numerical data from the model parameter identification procedures, the influence of the main CSA parameters—the flight length, fl, and the awareness probability, AP—was investigated. Applying classical statistical tests and an innovative approach, InterCriteria Analysis, recommendations about the optimal CSA parameter tuning were proposed. The best CSA algorithm performance was achieved for the AP = 0.05, fl = 3.0, followed by AP = 0.10, fl = 2.5, and AP = 0.15, fl = 3.0. The optimal tuning of the CSA parameters resulted in a 29% improvement in solution accuracy. As a result, a mathematical model of the considered two-stage anaerobic digestion process with a high degree of accuracy was developed.

Identification, uncertainty quantification and validation of orthotropic material properties for additively manufactured polymers

The mechanical behavior of polymeric parts manufactured by fused filament fabrication is often characterized as orthotropic because of the layer-wise extrusion of the material. To perform reliable simulations of the mechanical response of these parts subjected to certain loads, the material parameters have to be known. This leads to the task of material parameter identification from suitable experimental data. In this work, the identification of the material parameters for orthotropic material behavior is studied in detail with a focus on the specific characteristics of additively manufactured parts. This comprises working out the differences that arise compared to the parameter identification for classical orthotropic composite materials. Moreover, the material parameters are identified from tensile and shear test information together with full-field displacement data from digital image correlation measurements. Then, the obtained parameters are compared for analytical and numerical approaches, where a non-linear least-squares method with finite elements is drawn on. The parameters are not only identified, but also an uncertainty analysis is carried out and, subsequently, the different methods are validated. Further, a clear derivation of commonly applied analytical equations is provided with a special focus on the underlying assumptions. It turns out that the analytical parameter identification procedures cannot be easily transferred to numerical procedures, especially when using full-field data, because of correlations between the parameters. Moreover, the identified parameters are employed to prove the reasonability of orthotropic material behavior for specimens manufactured by fused filament fabrication. Finally, during validation it turns out that all parameter identification methods provide a good agreement with experimental data, showing only small differences between the results of the different calibration strategies.

Identification for nonlinear systems modelled by deep long short-term memory networks based Wiener model

This paper is concerned with modeling and identification methodology for practical nonlinear system via deep long short-term memory (DLSTM) networks-based Wiener model. To determine the unknown parameters and simplify parameters identification procedure for the Wiener model, a two-step identification scheme is implemented applying hybrid signals involving separable signal and random data. First, the separable signal to separate the two blocks in Wiener model is imported, then parameters of the linear block is estimated using correlation function-based least squares technique, which handles the issue that the intermediate variable information in Wiener model cannot be measured. Moreover, integrating the advantages of adaptive stochastic gradient descent algorithm and root mean square propagation, an adaptive momentum estimation technique is created to optimize the DLSTM networks parameters based on available random data, which improves the accuracy of identified Wiener model. Compared with the other existing schemes, the superiority of the proposed method in terms of predictive performance and control results are illustrated by permanent magnet synchronous motors.

Parameter identification procedure for hysteretic shear-resistant properties of beech wood dowels

To evaluate the shear-resistant behavior of wooden dowels used in Blockhaus shear walls under cyclic load, 19 specimens under ten groups of conditions were prepared and tested. The failure modes, hysteresis curves, mechanical properties, stiffness degradations, and energy dissipation capacities of the specimens were studied. The test results showed that with the increase in the number of dowels, the initial stiffness and peak load of the specimens increased greatly. The diameter of the dowels had little influence on the mechanical properties of the specimens. Furthermore, the test findings demonstrated that the pretension load between the walls greatly enhanced the initial stiffness and energy dissipation capacity of specimens. A simplified finite element model was established in Opensees. Considering the effect of material variability, the parameters of single dowel shear spring and friction spring were identified by Genetic Algorithm with modified objective function in Matlab. The identified parameters were applied to the finite element model of the multi-dowel specimens. The simulation results were in good agreement with the test results, and the validity of the numerical model and parameter identification method was verified.

Distributed robust data-enabled predictive control based voltage control for networked microgrid system

The networked microgrid system (NMG) has become an effective alternative for integrating various types of distributed energy resources (DERs). However, because of the increasing share of DERs and high R/X ratio in the system, the uncertainty and variability of DERs' power generation may cause significant voltage violations in the system. To address these issues, this paper introduces a novel distributed data-driven voltage control strategy based on data-enabled predictive control (DeePC) to address voltage violations problems in the NMG. The DeePC algorithm uses only historical system trajectories, eliminating the need for parameter identification procedures of power system. Based on the system data model, the proposed controller coordinates MGs in the NMG in a distributed manner by employing a consensus version of the fast alternating direction method of the multiplier algorithm (FADMM), which achieves a better privacy and scalability. Simulation studies in a modified two-MG NMG demonstrate the effectiveness and superiority of the proposed algorithm.

Data-Driven Accelerated Parameter Identification for Chaboche-Type Visco-Plastic Material Models to Describe the Relaxation Behavior of Copper Alloys

Abstract Background Calibrating material models to experimental measurements is crucial for realistic computational analysis of components. For complex material models, however, optimization-based identification procedures can become time-consuming, particularly if the optimization problem is ill-posed. Objective The objective of this paper is to assess the feasibility of using machine learning to identify the parameters of a Chaboche-type material model that describes copper alloys. Specifically, we apply and analyze this identification approach using short-term uniaxial relaxation tests on a C19010 copper alloy. Methods A genetic algorithm forms the basis for identifying the parameters of the Chaboche-type material model. The approach is accelerated by replacing the numerical simulation of the experimental setup by a neural network surrogate. The neural networks-based approach is compared against a classic approach using both, synthetic and experimental data. Results The results show that on the one hand, a sufficiently accurate identification of the material model parameters can be achieved by a classic but time-consuming genetic algorithm. On the other hand, it is shown that machine learning enables a much more time-efficient identification procedure, however, suffering from the ill-posedness of the identification problem. Conclusion Compared to classic parameter identification approaches, machine learning techniques can significantly accelerate the identification procedure for parameters of Chaboche-type material models with acceptable loss of accuracy.

Direct model parameter identification of twisted string actuators using Nelder-Mead simplex method

A twisted string actuator (TSA) is a simple rotary-to-linear motion converter with a large transmission ratio. This paper presents a simple procedure for direct model parameters identification of TSAs, which accepts the model in initial ODE-based form, while the previous techniques required a complex reformulation of the model. Also, the identification process estimates all unknown or impossible-to-measure parameters directly (not in an arithmetic combination) in the original form of the mathematical model of the TSA, which is a benefit in comparison with common and classic adaptive parameter estimators. The proposed nonlinear identification procedure employs the Nelder–Mead simplex method to minimize the cost function as the core. Moreover, the identification results are verified in different working frequencies. The presented model parameter optimization procedure reduced the deviation between the mathematical model and the real TSA behavior for a set of optimum parameters up to [Formula: see text] in terms of the defined cost function. As an application for the mathematical model of the TSA with the identified parameters, a feedback linearization controller is designed for the position control of the actuator. The simulation and implementation of the controller prove the proper performance of the controller.

Modelling and identification methods for simulation of cable-suspended dual-arm robotic systems

This paper proposes rigid-body modelling and identification procedures for long-reach dual-arm manipulators in a cable-suspended pendulum configuration. The proposed model relies on a virtually constrained open kinematic chain and lends itself to be simulated through the most commonly used robotic simulators without explicitly account for the cables constraints and flexibility. Moreover, a dynamic parameters identification procedure is devised to improve the simulation model fidelity and reduce the sim-to-real gap for controllers deployment. We show the capability of our model to handle different cable configurations and suspension mechanisms by customising it for two representative cable-suspended dual-arm manipulation systems: the LiCAS arms suspended by a drone and the CRANEbot system, featuring two Pilz arms suspended by a crane. The identified dynamic models are validated by comparing their evolution with data acquired from the real systems showing a high (between 91.3% to 99.4%) correlation of the response signals. In a comparison performed with baseline pendulum models, our model increases the simulation accuracy from 64.4% to 85.9%. The simulation environment and the related controllers are released as open-source code.

Physical Model-Based State of Health Understanding of Severely Aged Lithium-Ion Batteries Under Real-World Automotive Operational Life

Lithium ion-battery (LIB) technology, featuring upstanding energy and power density, satisfying lifetime, high round-trip efficiency and very fast dynamics in a reasonably economic package, rapidly became the undisputed ruler of portable power and it is now the main driver of the electrification of transportation sector. However, despite the fully commercial development, understanding and predicting degradation of such devices is still a great challenge for the scientific and technical community, especially when dealing with real-life-operation induced aging. The reusability of such devices in a circular economy perspective is a hot topic to the sector to improve sustainability, but requires understanding “how” batteries are faded rather than only “how much” they are, to enable a physically consistent and second-life-related estimation of residual lifetime.In the present activity, a detailed analysis of high-power LFP (lithium iron phosphate) cells samples operated on IVECO hybrid buses are performed to assess their possible reusability, in the frame of a joint research cooperation. A large batch of cells with different ages (from 9 years old to brand new) and different positions inside the modules are investigated.State-of-art electrochemical diagnostics are performed embedded in a multi-measurement optimized protocol (full discharge, pulse test, electrochemical impedance spectroscopy) developed after a sensitivity optimization for a model-based improved parameter identification [1], as visible in Figure 1. Residual performances are analyzed and compared with limited on-board data collected from vehicles BMS and analyzed by means of an appositely-improved physical modelling platform.Both capacity and power capabilities have sensibly decreased over the cells lifetime (see Figure 2 for the full discharges at 0.1C, 25°C) with a clear pattern attributable to cells position beneath the modules, prompting the importance of a homogeneous thermal management during operation. Power-based state of health of the samples is higher than a capacity-based SoH, foreseeing a possible reuse of the samples in a power-intensive second-life. Residual performance interestingly feature a high consistency with data recently published in [2], relative to similar system despite operated in a completely different geographic area; this strengthens the generalizability of the results.Aged cells diagnostics were interpreted with a previously developed Newman P2D physical model provided with heath exchange, to identify the degradation mechanisms through the EIS-based parameter identification procedure [1] involving both thermodynamic and kinetic aspects.Interpretation of thermodynamic aging modes has been conducted on all the tested cell samples, based on 0.1C thermodynamic analysis and the differential voltage. Incremental capacity curves of aged cells have been reproduced with a PSO-based (particle-swarm-optimization) identification of three ageing parameters: loss of lithium inventory (LLI), mainly corresponding to solid electrolyte interphase (SEI) growth, and loss of active materials at negative (LAMn) and positive (LAMp) electrode, indicating loss of actives sites for the electrochemical reactions. Despite the severely low residual capacity, the model reproduces satisfyingly the features of the aged cells.Interestingly, a linear trend could be identified as common beneath all the samples involved in the analysis, indicating common aging mechanism appearing with different magnitude. As visible in Figure 3, the trend points out a two-steps aging path: (I) a first pathway mainly leading to LLI close to 20%, followed by (II) a second pathway with both LLI and LAMn occurring at the same time. In the literature, similar observations have been already performed by some authors in previous works, with a lower extent of degradation [3,4]. They agree in this interpretation: the first stage is usually associated to the growth of the SEI layer, while the second stage is usually associated to the onset of lithium plating (due to a dense SEI which inhibits the lithium intercalation into graphite). Confirmation of such interpretation is obtained by means of model based interpretation on non-equilibrium measurements, permitting estimation of physical parameters value and enabling identification of aging mechanisms, together with ex-situ measurements based on electrochemical and morpho chemical analyses.Additionally, several consistencies between on-line measurements, such as EIS, and equilibrium capacity loss of cells have been identified, theoretically discussed and tested under further accelerated aging tests, enabling possible strategies of SoH implementation based on fast and informative electrochemical measurements.

Model Identification of E. coli Cultivation Process Applying Hybrid Crow Search Algorithm

Cultivation process (CP) modeling and optimization are ambitious tasks due to the nonlinear nature of the models and interdependent parameters. The identification procedures for such models are challenging. Metaheuristic algorithms exhibit promising performance for such complex problems since a near-optimal solution can be found in an acceptable time. The present research explores a new hybrid metaheuristic algorithm built upon the good exploration of the genetic algorithm (GA) and the exploitation of the crow search algorithm (CSA). The efficiency of the proposed GA-CSA hybrid is studied with the model parameter identification procedure of the E. coli BL21(DE3)pPhyt109 fed-batch cultivation process. The results are compared with those of the pure GA and pure CSA applied to the same problem. A comparison with two deterministic algorithms, i.e., sequential quadratic programming (SQP) and the Quasi-Newton (Q-N) method, is also provided. A more accurate model is obtained by the GA-CSA hybrid with fewer computational resources. Although SQP and Q-N find a solution for a smaller number of function evaluations, the resulting models are not as accurate as the models generated by the three metaheuristic algorithms. The InterCriteria analysis, a mathematical approach to revealing certain relations between given criteria, and a series of statistical tests are employed to prove that there is a statistically significant difference between the results of the three stochastic algorithms. The obtained mathematical models are then successfully verified with a different set of experimental data, in which, again, the closest one is the GA-CSA model. The GA-CSA hybrid proposed in this paper is proven to be successful in the collaborative hybridization of GA and CSA with outstanding performance.

Prediction of magnetic energy loss of Giant magnetostrictive materials under different prestresses, AC excitations and DC biases

Magnetic energy losses of giant magnetostrictive material (GMM) significantly depend on a number of factors including prestresses, AC excitations, and DC biases. The existing magnetic energy loss prediction models require further optimization to account for the sensitive magnetic hysteresis of GMM. A magnetic energy loss prediction model that can adapt to different operating conditions is very essential for GMM applications. Herein, the dependency of magnetic energy losses to the operation conditions is interpreted by the parametric variations of the Jiles-Atherton model. A novel four-step parameter identification procedure with great generalizability is proposed. In particular, the combined effects of three external conditions on model parameters are considered. The measurement and simulation data of major hysteresis loops, symmetric minor hysteresis loops, and biased minor hysteresis loops under different operating conditions are compared, which verified the effectiveness of the modified model. Finally, the magnetic energy losses of biased minor hysteresis loops of GMM at different frequencies are calculated using the modified model and compared with the measured data. The average relative error is 5.59 %, and the maximum relative error is 12.05 %.

Histology-informed multiscale modeling of human brain white matter

In this study, we propose a novel micromechanical model for the brain white matter, which is described as a heterogeneous material with a complex network of axon fibers embedded in a soft ground matrix. We developed this model in the framework of RVE-based multiscale theories in combination with the finite element method and the embedded element technique for embedding the fibers. Microstructural features such as axon diameter, orientation and tortuosity are incorporated into the model through distributions derived from histological data. The constitutive law of both the fibers and the matrix is described by isotropic one-term Ogden functions. The hyperelastic response of the tissue is derived by homogenizing the microscopic stress fields with multiscale boundary conditions to ensure kinematic compatibility. The macroscale homogenized stress is employed in an inverse parameter identification procedure to determine the hyperelastic constants of axons and ground matrix, based on experiments on human corpus callosum. Our results demonstrate the fundamental effect of axon tortuosity on the mechanical behavior of the brain’s white matter. By combining histological information with the multiscale theory, the proposed framework can substantially contribute to the understanding of mechanotransduction phenomena, shed light on the biomechanics of a healthy brain, and potentially provide insights into neurodegenerative processes.

A two-stage approach for material parameters identification in spark plasma sintering

A fully coupled electrical-thermo-mechanical model is essential to an in-depth understanding of the spark plasma sintering (SPS) process, where the mechanical modeling is heavily dependent on the constitutive equations and their material parameters. This paper proposes a two-stage approach that integrates direct experimental measurements with numerical simulations, providing a more comprehensive and reliable basis for identifying the material parameters in SPS. We develop a finite element-based fully coupled process model in COMSOL Multiphysics® and validate it experimentally. The parameter identification procedure achieves an average prediction error below 1.5% when applied to copper and nickel SPS at different heating rates from 25 to 100 K/min. This robust numerical–experimental approach establishes a transferable technique that can be used for other materials commonly used in SPS.

Prediction of carbon nanotubes reinforced interphase properties in fuzzy fibre reinforced polymer via inverse analysis and optimisation

This paper presents the parameter identification procedure of carbon nanotubes (CNTs) reinforced interphase in fuzzy fibre reinforced polymer (FFRP). The procedure was completed with ANSYS Workbench 19.2 software by combining Mechanical ADPL and Goal-Driven Optimisation. Firstly, a three-phase representative volume element (RVE) containing carbon fibre, CNTs reinforced interphase and epoxy resin was developed as a collection of Mechanical APDL commands. This RVE model was simulated to evaluate the elastic constants of FFRP lamina. CNTs reinforced interphase was characterised by transversely isotropic model. Interphase properties were parametrised and became input parameters in the Goal-Driven Optimisation. FFRP lamina elastic constants were set as the output parameters. Multi-objective Genetic Algorithm (MOGA) was used to identify the interphase properties, so that the output FFRP lamina elastic constants match the objective and constraints. The optimisation algorithm converged after 585 evaluations. Five potential candidate point, which met required objectives and constraints, were found. The identified interphase properties agreed well with the literature (an average percentage error of around 2%). This inverse procedure shows the potential to identify the interphase properties in nano-engineered composites, which are extremely difficult to measure experimentally.

A constitutive modeling approach to simulate time‐dependent phenomena in rubber‐like materials

AbstractIndustrial rubber materials and similar rubber‐like materials exhibit complex mechanical behavior including nonlinear stress‐strain behavior up to large strains, hysteresis, Mullins effect, permanent set, as well as time‐dependent effects, like relaxation and rate dependency. The modeling of all these phenomena is a challenging task. One constitutive model that is capable to capture many effects in the large strain regime is the so‐called model of rubber phenomenology (MORPH). However, it is not able to capture any of the mentioned time‐dependent phenomena. Thus, this contribution deals with the extension of this model to simulate relaxation and rate dependency of rubber‐like materials. Thereby, a basic modeling approach is proposed, where only a slight change in the original system of tensorial equations is necessary. This approach is further extended by applying not only a constant relaxation time, but also loading history‐depended relaxation properties. For numerical simulations, a time discretization has to be applied to the constitutive equations, which is briefly shown. Finally, the extended MORPH model is applied to two different materials: an industrial rubber material and a polyurethane based adhesive. In both cases, the extended MORPH model is adjusted to uniaxial tension test data by parameter identification procedures. It will be shown that basic time‐dependent phenomena of rubber‐like materials can be captured well with the proposed extensions.

Estimation of iron losses in Terfenol-D for variable DC-biased and AC excitation conditions

Giant magnetostrictive material (GMM) is well known for its hysteresis behaviors related to multiple influencing factors, such as bias magnetic field and excitation level. This feature greatly challenges the loss prediction of giant magnetostrictive transducers. The existing loss prediction models need further improvement to cover the sensitive magnetic properties of GMM. In this paper, the variations of the iron losses with the operation conditions are interpreted by the variations of the Jiles–Atherton model parameters, and a concise parameter identification procedure with great generalizability is proposed. The iron losses of Terfenol-D under variable excitation levels and the DC biases are further investigated. With the proposed procedure, the introduced eight additional modification parameters for the original Jiles–Atherton model are easy to obtain, and merely a few hysteresis loops of Terfenol-D are involved. An experimental setup is established for further demonstration. Comparisons between the measured and calculated results indicate the effectiveness of the proposed approach. Throughout the bias-excitation space within the frequency range under investigation, the iron losses can be precisely estimated with an acceptable error of less than 5%.

Empowered parameter identification procedure for anaerobic digestion lumped model, stability and reliability analysis

Mathematical modeling of Anaerobic Digestion is fundamental for the prediction of crucial quantities such as CH4 and CO2 content. Among many possibilities, the AMOCOHN model, an upgraded version of the AMOCO model, represents a simplified mathematical model and is qualified for control purposes, avoiding long calculation time while assuring precise enough results. Their differences rely on the parameter identification procedure. While AMOCO model calibration is linear-based, AMOCOHN is nonlinear-based. Because of its inherent sensitivity to fluctuations, this produces some deceptive results in terms of coefficients assessment when the regression is performed with a nonlinear algorithm. This work aims to simplify and improve the robustness and stability of the AMOCOHN identification procedure by integrating an adaptation of the same dual-step approach originally proposed in AMOCO. The results, illustrated by a comparison between literature and ADM1 simulation data, reveal a mean Radj2 of 0.98, demonstrating its effectiveness while preserving the model’s simplicity and flexibility.

APPLICATION OF SPLINE FUNCTIONS AND WALSH FUNCTIONS IN PROBLEMS OF PARAMETRIC IDENTIFICATION OF LINEAR NONSTATIONARY SYSTEMS

Context. In this article, a generalized parametric identification procedure for linear nonstationary systems is proposed, which uses spline functions and orthogonal expansion in a series according to the Walsh function system, which makes it possible to find estimates of the desired parameters by minimizing the integral quadratic criterion of discrepancy based on solving a system of linear algebraic equations for a wide class of linear dynamical systems. The accuracy of parameter estimation is ensured by constructing a spline with a given accuracy and choosing the number of terms of the Walsh series expansion when solving systems of linear algebraic equations by the A. N. Tikhonov regularization method. To improve the accuracy of the assessment, an algorithm for adaptive partitioning of the observation interval is proposed. The partitioning criterion is the weighted square of the discrepancy between the state variables of the control object and the state variables of the model. The choice of the number of terms of the expansion into the Walsh series is carried out on the basis of adaptive approximation of non-stationary parameters in the observation interval, based on the specified accuracy of their estimates. The quality of the management of objects with variable parameters is largely determined by the accuracy of the evaluation of their parameters. Hence, obtaining reliable information about the actual nature of parameter changes is undoubtedly an urgent task.
 Objective. Improving the accuracy of parameter estimation of a wide class of linear dynamical systems through the joint use of spline functions and Walsh functions.
 Method. A generalized parametric identification procedure for a wide class of linear dynamical systems is proposed. The choice of the number of terms of the expansion into the Walsh series is made on the basis of the proposed algorithm for adaptive partitioning of the observation interval.
 Results. The results of modeling of specific linear non-stationary systems confirm the effectiveness of using the proposed approaches to estimating non-stationary parameters.
 Conclusions. The joint use of spline functions and Walsh functions makes it possible, based on the proposed generalized parametric identification procedure, to obtain analytically estimated parameters, which is very convenient for subsequent use in the synthesis of optimal controls of real technical objects. This procedure is applicable to a wide class of linear dynamical systems with concentrated and distributed parameters.